Handbook of Environmental Economics [4, 1 ed.] 0444537724, 9780444537720

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Handbook of Environmental Economics, Volume 4 Edited by

Partha Dasgupta Subhrendu K. Pattanayak V. Kerry Smith

North-Holland is an imprint of Elsevier Radarweg 29, PO Box 211, 1000 AE Amsterdam, Netherlands The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, United Kingdom Copyright © 2018 Elsevier B.V. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Details on how to seek permission, further information about the Publisher’s permissions policies and our arrangements with organizations such as the Copyright Clearance Center and the Copyright Licensing Agency, can be found at our website: www.elsevier.com/permissions. This book and the individual contributions contained in it are protected under copyright by the Publisher (other than as may be noted herein). Notices Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary. Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein. In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility. To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the material herein. Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library ISBN: 978-0-444-53772-0 For information on all North-Holland publications visit our website at https://www.elsevier.com/books-and-journals

Publisher: Zoe Kruze Acquisition Editor: Jason Mitchell Editorial Project Manager: Shellie Bryant Production Project Manager: Vignesh Tamil Designer: Matthew Limbert Typeset by VTeX

Contributors Joshua K. Abbott Arizona State University, School of Sustainability, Tempe, AZ, United States of America Maximilian Auffhammer University of California, Berkeley, Berkeley, CA, United States of America NBER, Cambridge, MA, United States of America William A. Brock University of Wisconsin, Madison, WI, United States of America University of Missouri, Columbia, MO, United States of America Olivier Deschenes UC Santa Barbara, Santa Barbara, CA, United States of America IZA, Bonn, Germany NBER, Cambridge, MA, United States of America Eli P. Fenichel Yale University, School of Forestry & Environmental Studies, New Haven, CT, United States of America John Hassler Institute for International Economic Studies (IIES), Stockholm, Sweden CEPR, London, United Kingdom of Great Britain and Northern Ireland Geoffrey Heal Columbia University, New York, NY, United States of America Kelly Jones Department of Human Dimensions of Natural Resources, Colorado State University, Fort Collins, CO, United States of America Matthew E. Kahn Department of Economics, University of Southern California, Los Angeles, CA, United States of America University of California, Berkeley, Berkeley, CA, United States of America Ann Kinzig Arizona State University, Tempe, AZ, United States of America

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Contributors

Per Krusell Institute for International Economic Studies (IIES), Stockholm, Sweden CEPR, London, United Kingdom of Great Britain and Northern Ireland NBER, Cambridge, MA, United States of America Erin L. Litzow Vancouver School of Economics, University of British Columbia, Vancouver, BC, Canada Kyle C. Meng UC Santa Barbara, Santa Barbara, CA, United States of America NBER, Cambridge, MA, United States of America Antony Millner Grantham Research Institute, London School of Economics and Political Science, London, United Kingdom of Great Britain and Northern Ireland Emily L. Pakhtigian Sanford School of Public Policy, Duke University, Durham, NC, United States of America Subhrendu K. Pattanayak Sanford School of Public Policy, Duke University, Durham, NC, United States of America Charles Perrings Arizona State University, Tempe, AZ, United States of America Elizabeth J.Z. Robinson School of Agriculture, Policy, and Development, University of Reading, United Kingdom of Great Britain and Northern Ireland Erin O. Sills Department of Forestry and Environmental Resources, North Carolina State University, Raleigh, NC, United States of America Thomas Sterner Department of Economics, University of Gothenburg, Gothenburg, Sweden Anastasios Xepapadeas Athens University of Economics and Business, Athens, Greece University of Bologna, Bologna, Italy Seong Do Yun Mississippi State University, Mississippi State, MS, United States of America

Introduction to the Series The aim of the Handbooks in Economics series is to produce Handbooks for various branches of economics, each of which is a definitive source, reference, and teaching supplement for use by professional researchers and advanced graduate students. Each Handbook provides self-contained surveys of the current state of a branch of economics in the form of chapters prepared by leading specialists on various aspects of this branch of economics. These surveys summarize not only received results but also newer developments, from recent journal articles and discussion papers. Some original material is also included, but the main goal is to provide comprehensive and accessible surveys. The Handbooks are intended to provide not only useful reference volumes for professional collections but also possible supplementary readings for advanced courses for graduate students in economics. Kenneth J. Arrow† Michael D. Intriligator†

† Deceased.

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Preface Over the past 35 years Elsevier has published six Handbooks surveying many aspects of the field of resource and environmental economics. This series has had a key role in shaping our understanding of the progress in the field. The most recent three volume addition to it in 2002, by Karl Göran Mäler and Jeffrey Vincent was organized into three broad themes – Environmental Degradation and Institutional Responses, Valuing Environmental Changes, and Economy-Wide and International Environmental Issues – thirty chapters in all1 . When these volumes were prepared the editors had to justify their sustained attention to environmental problems. Indeed, their Preface begins by arguing it would be a serious mistake to accept the views of those naysayers who were claiming, at the time, that most environmental problems had been solved. The past decade and a half has proved Mäler and Vincent’s answers to the skeptics were correct! We were just beginning to understand the full dimensions of our environmental problems. The pace of transformation to our earth’s ecosystem seems to be accelerating. So it should not be surprising to find that today environmental economics is one of the most active research fields in economics. We cannot attempt to offer readers survey chapters that document all that has been accomplished over this time and fortunately we do not need to. There are a growing set of publications that provide literature reviews on a periodic basis. Instead, we propose a different goal. Rather than look backward over the nearly two decades since Mäler and Vincent’s masterful overview, our authors consider topics that highlight where as a field we need to go. In short, they take a selective sampling of current research and use it to highlight the frontier questions for the future. This volume has ten chapters after this short Preface. While each is focused on distinctive issues, there are multiple common themes that link them and we will highlight a few here. Climate change is a recurring theme throughout all the chapters. As most geologists have argued, it appears the earth’s ecosystem has entered the Anthropocene epoch, where humans are the dominate force shaping how future scientists will characterize the global changes taking place today. As a result, the issue of the scale of these impacts, of the associated policies, and of the people’s responses to them arises in many chapters. Perrings and Kinzig, for example, in providing their overview and assessment of the past 40 years of collaboration between ecologists and economists highlight the issue of the scale used in defining ecosystems and their resilience as key insights that have shaped subsequent research. Brock and Xepapadeas’ chapter recognizes scale in multiple ways – considering the spatial 1 Two of us had the great opportunity to be among the authors of chapters in those volumes and the other

(Pattanayak) had just started his career at RTI International. As a result it has been especially rewarding to have the opportunity to revisit the terrain.

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and temporal dimensions that arise in the modeling of how to couple economic systems with ecosystems. These couplings must capture the dynamic interactions and the feedbacks between these systems. Scale is central to such characterizations. As they suggest, climate change is the “Mother of all Collective Action Programs”. Consistent with this theme, Sterner and Robinson’s chapter reviewing policy instruments recognizes how free riding and global scale can create conflicting institutions that govern public and private actions on a global scale. This point is reinforced by the Sills and Jones’ arguments about the importance of recognizing the roles played by formal and informal institutions. While the former is more readily recognized, both can influence measures of the effectiveness of policy interventions. Knowledge of these types of local conditions, together with an appreciation of the potential heterogeneity in treatment, is essential for interpreting estimates of the effectiveness of policy instruments. The bottom line general implication of these arguments for efforts to address climate change is that policy design must foster local adaptation and global mitigation – again recognizing how scale matters in different ways for the two types of activities. Effective policy must also recognize the importance of the issues in decomposing the temporal and spatial dimensions of the physical and economic models that Brock and Xepapadeas (B&X) describe in their analysis of these couplings. The joint economic and natural system responses to global change can lead, as they demonstrate, to solutions involving bifurcations and/or tipping points. Another complementary relationship between chapters arises between B&X’s analysis and the Hassler–Krusell (H&K) chapter. H&K also use climate change as an organizing feature for their discussion of what might be termed environmental macro-economics. They highlight the importance of a general equilibrium perspective and of recognizing how market incentives interact with those created by policy. B&X adopt a social perspective that allows them to focus on how varying the modeling of the connections between economic and natural systems as constraints to the planner affect what can be expected from the “best” of policies. By contrast, Hassler and Krusell consider how relative prices in a dynamic setting signal the importance of policy induced constraints. A key insight from the two papers taken together is described by B&X as “scale matching” of the benefits and costs of different actions. It is possible with adaptation as a response to climate change but not with mitigation policies. The complexity of the climatic change implies uncertainty in what we know must be acknowledged and, as Heal and Millner note, must be treated differently. Analysts simply do not know enough to characterize the uncertainty. As a result, applications of conventional approaches to decision making under these conditions, such as expected utility analysis, must be reconsidered. They propose that the concept of ambiguity be introduced into the framework to reflect how “uncertainty about the nature of the uncertainty” can be integrated into the evaluation of policy design. Ambiguity describes the lack of resolution in how to characterize the uncertainty about what is known. If we are prepared to assume policy makers are “ambiguity averse”, then by using a framework that considers all the probability distributions consistent with a given information set, we can describe how policies should be selected. Within a

Preface

static setting, these choices would favor policies that offer greater resolution, or more consistency in the outcomes, so ambiguity is reduced. In some cases the choices would imply greater stringency in the incentives for pollution control over situations where decisions are made in the absence of this ambiguity. Extensions to a dynamic setting have begun and B&X describe some of them. The global nature of climate change also highlights the importance of taking account of the equity implications of what happens under business as usual as well as with alternative policies. This issue is a common theme of the Auffhammer and Kahn (A&K) and Pattanayak, Pakhtigian, and Litzow (PP&L) chapters. A&K emphasize the mechanisms for adaptation and whether they will exacerbate or reduce the impact of climate change on the low income households predominantly in developing economies. They cast their analysis in terms of the decision context for the “farmer” in the less developed economy – how each one can adapt given that their current situations yield only a subsistence level of consumption. Current empirical studies provide preliminary answers, but A&K emphasize the need for panel studies with longer time horizons. PP&L focus on all the environmental risks these households currently face; what we know about them; and how their current situations will affect their abilities to respond to a changing climate. Policy selection in this context must recognize how resources devoted to private and public adaptation can interact – are they complements or substitutes? Both chapters point to the limitations in our understanding when and why policies work and when they fail. Incentives are important but so also is the culture and the level of education of these low income households. Trust in the performance and reliability of institutions at different scales clearly matters to the potential performance of policies. Unfortunately, we simply don’t have the empirical information to fully describe what we can expect. Both chapters highlight priority research needs. Resolving these information needs would be easier if experiments were possible. They are not. Fortunately, recent advances in empirical modeling show promise and Deschenes and Meng’s chapter provides an ideal window on what we can and cannot expect from quasi-experiments. Their focus contrasts what has been learned when these methods were applied with private goods versus what is feasible when our attention is turned to local public goods. By distinguishing the individual and the group level effects of changes in a public good they identify the potential sources of bias in current quasi-experimental methods and offer a strategy for resolving these sources of bias. They close with a discussion of how new methods of analysis might come to grips with the empirical changes for climate change. They review two strategies. The first considers on small scale studies that focus on outcomes that are not likely to be impacted directly by general equilibrium price changes. In these cases quasi-experimental methods hold the promise of estimating unbiased reduced form effects. The second calls for a process of extracting empirical hypotheses from structural models of large scale impacts and testing the implied effects of climate change against the null hypothesis of no effect. This approach provides one means of offering support the model’s description. It is not necessarily a test of the prediction but rather

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a strategy for accumulating support for the model’s characterization of climate’s impact. Another potential area for extension recognizes the potential to use the methods for detecting casual structures reviewed in Sills and Jones chapter together with the strategies Deschenes and Meng describe in assessing the plausibility of estimates of climate impact at different scales. Finally, many of the issues confronting environmental economics at the local, national, and global scales arise because there are not market mechanisms that allow us to “keep score”. During the Great Depression the need for aggregate information on the economy was recognized and today we take for granted the extensive data that resulted. In the U.S., the Department of Commerce, working with the NBER, produced the first set of information on the national income accounts and capital stock measures in the mid 1930s. Unfortunately, there has not been a comparable effort for environmental resources. Fenichel, Abbott, and Yun’s chapter detail what will be needed by describing the theory and empirical dimensions of developing natural capital measures for ecosystem services. Their chapter integrates many of the concepts developed throughout this volume. By focusing on the factors influencing the shadow value of natural capital under different economic programs – they highlight how institutions influence what we can observe about the values of ecosystem services that are implied by our current rules of access and how policy might be designed to change them. Many people contributed to this effort. We want to especially thank our authors for preparing their chapters, for assisting us in the process of assuring all the chapters offered accessible descriptions of the research challenges facing environmental and resource economics, and for their patience with us over the long process during which this volume developed. We would also like to thank our colleagues who also contributed to assuring the authors were aware of research contributions relevant to their chapters including Joseph Aldy, Scott Barrett, Maureen Cropper, Gretchen Daily, Tatyana Deryugina, Stephanie Fried, David Kaczan, Faraz Usmani, and many other whose general council was especially helpful. Our home institutions and supporting personnel along with Jason Mitchell and the editorial team at Elsevier also assured our efforts and those of our authors would result in a volume consistent with the high standards this series’ past volumes has maintained. Partha Dasgupta Subhrendu K. Pattanayak V. Kerry Smith

CHAPTER

Modeling coupled climate, ecosystems, and economic systems

1

William A. Brock∗,†,# , Anastasios Xepapadeas‡,§,1,## ∗ University

of Wisconsin, Madison, WI, United States of Missouri, Columbia, MO, United States ‡ Athens University of Economics and Business, Athens, Greece § University of Bologna, Bologna, Italy 1 Corresponding author: e-mail address: [email protected] † University

CONTENTS 1 Introduction ...................................................................................... 2 Coupled Ecological/Economic Modeling for Robustness ................................. 2.1 Robust Control Methods in Coupled Ecological/Economic Systems ....... 3 Climate Economics with Emphasis on New Modeling: Carbon Budgeting and Robustness ....................................................................................... 3.1 Cumulative Carbon Budgeting to Implement Temperature Limits .......... 3.2 Climate Change Policy with Multiple Lifetime for Greenhouse Gases ..... 4 Implementation .................................................................................. 5 Energy Balance Climate Models and Spatial Transport Phenomena .................... 5.1 Spatial Pattern Scaling ........................................................... 5.2 Discounting for Climate Change ................................................. 6 Spatial Aspects in Economic/Ecological Modeling ........................................ 7 Future Directions ................................................................................ 7.1 Bottom Up Implementation Rather than Top Down Implementation ......

2 4 7 11 12 21 21 23 27 29 32 33 33

# Brock thanks the DMUU: Center for Robust Decision Making on Climate and Energy Policy of the University of Chicago (RDCEP) under the NSF for essential support both intellectual and financial. Brock thanks Evan Anderson, Ian Foster, Lars Hansen, Ken Judd, Liz Moyer, Alan Sanstad, Victor Zhorin, and the RDCEP community for many conversations on climate science and economic science. None of the above is responsible for errors or other problems with this article. ## Xepapadeas acknowledges that this research has been co-financed by the European Union (European Social Fund – ESF) and Greek national funds through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF) – Research Funding Program: “Thalis – Athens University of Economics and Business – Optimal Management of Dynamical Systems of the Economy and the Environment.” We would like to thank Partha Dasgupta and Geoffrey Heal for valuable comments and suggestions on an earlier draft of this paper. We would like to thank Joan Stefan for technical editing. Handbook of Environmental Economics, Volume 4, ISSN 1574-0099, https://doi.org/10.1016/bs.hesenv.2018.02.001 Copyright © 2018 Elsevier B.V. All rights reserved.

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7.2 Stochastic Modeling and Computational Approaches ........................ 7.3 Bifurcations and Tipping Points ................................................. Appendix A .......................................................................................... A.1 Robust Control Methods .......................................................... A.2 The Case of Additive Uncertainty ............................................... A.3 Time Consistency Issues of Solutions to Zero Sum Robust Control Games A.4 Climate Change Policy with Multiple Lifetime for Greenhouse Gases ..... Appendix B Spatially Extended Deterministic Robust Control Problems ................... B.1 An Example ......................................................................... References............................................................................................

34 35 36 36 38 43 45 48 51 54

1 INTRODUCTION Human economies and ecosystems form a coupled system coevolving in time and space, since human economies use ecosystems services2 and at the same time affect ecosystems through their production and consumption activities. The study of the interactions between human economies and ecosystems is fundamental for the efficient use of natural resources and the protection of the environment through the design of policy and management rules. This necessitates the development and use of models capable of tracing the main interactions, links, and feedbacks. Models are necessary in order to understand the issues involved and to derive efficient policies. It is clear that, in order to attain these objectives, these models should be coupled models of ecosystems and economics systems. The modeling of coupled ecological and economic systems can be traced back to models dealing with management of natural resources. The natural link between ecosystems and human economies has been manifested in the traditional development of resource management or bio-economic models (for example, Clark, 1990), in which the main focus has been on fishery or forestry management where the impact of humans on ecosystems is realized through harvesting and biomass depletion. Closer links have been developed, however, as both disciplines evolve. Thus the classical phenomenological-descriptive approach to species competition based on Lotka–Volterra systems has been complemented by mechanistic resourcebased models of species competition for limiting resources (Tilman, 1982, 1988). This approach has obvious links to competition among economic agents for limited resources. Furthermore, new insights into the fundamental issues of the valuation of ecosystems or the valuation of biodiversity have been derived (e.g., Weitzman, 1992, 1998a; Brock and Xepapadeas, 2003) by linking the functioning of natural ecosystems with the provision of useful services to humans; or by using concepts 2 Examples of useful services to humans include provisioning services, such as food, water, fuel, or genetic material; regulation services, such as climate regulation or disease regulation; and cultural services and supporting services, such as soil formation or nutrient cycling (see Millennium Ecosystem Assessment, 2005).

1 Introduction

such as ecosystems productivity or insurance from the genetic diversity of ecological systems against catastrophic events; or by developing new products using genetic resources existing in natural ecosystems (Heal, 2000). The size and the strength of the impact of human economies in ecosystems depend on the way in which certain actions, such as harvesting, extraction of resources, emissions of pollutants, or investment in harvesting or pollution abatement capacity, which can be chosen by humans and which influence the evolution of ecosystems, are actually chosen. These actions can be regarded as control variables, and the way in which they are chosen affects the evolution of quantities describing the state of the coevolving coupled ecosystem and economic system. The state of the coupled system depends on the evolution of ecological variables, such as species biomasses or stock of pollutants or greenhouse gases, which determine the flow of ecosystem services, along with traditional economic variables such as consumption, investment, and stock of produced or human capital. The typical approach in economics is to associate the choice of the control variables with forward-looking optimizing behavior. Thus, the control variables are chosen so that a criterion function is optimized, and the economic problem of ecosystem management – where management means choice of control variables – is defined as a formal optimal control problem. In this problem the objective is the optimization of the criterion function subject to the constraints imposed by the structure of the ecosystem and the structure of the economy. These constraints provide the transition equations as well as other possible exhaustibility constraints associated with the optimal control problem. For example, in models of resource harvesting with generalized resource competition, the ecosystem dynamics describe both biomass and limited resource evolution (e.g., Brock and Xepapadeas, 2002; Tilman et al., 2005) in biodiversity valuation problems. Brock and Xepapadeas (2003) show that genetic constraints associated with development of resistance should be part of the optimal control of the coupled system. The solution of coupled ecosystem-economic system models, provided it exists, will determine the paths of the state and the control variables and the steady state of the system. These paths will determine the long-run equilibrium values of the ecological and economic variables as well as the approach dynamics to the steady state.3 In principle, two types of solution can be characterized: (i) a socially optimal solution where all known constraints associated with the problem and externalities associated with action of individual agents are taken into account, and (ii) a privately optimal solution which corresponds to an unregulated market equilibrium where forward-looking agents maximize private profits and externalities are not internalized. The deviations between the private solution and the social optimum justify regulation. Thus, policy design in this context implies that instruments, such as taxes 3 Managed ecological systems which are predominantly nonlinear could exhibit dynamic behavior charac-

terized by multiple, locally stable and unstable steady states, limit cycles, or the emergence of hysteresis, bifurcations or irreversibilities.

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or quotas, are determined so that the social optimum is implemented in a competitive equilibrium. In developing this chapter, our objective was not to review the large body of literature on modeling of coupled ecosystem and economic systems, but rather to focus on a segment of rapidly developing literature on coupled ecological/economic models with an emphasis on climate change. The advantage of this approach is that it introduces the reader to a very important current research topic, but it also allows, by using climate as the reference ecosystem, the exploration of new modeling approaches which are relevant and useful for the modeling of other types of coupled ecological/economic systems. These include modeling of deep structural uncertainty by using robust control methods, exploring modeling through cumulative carbon budgeting, and studying spatial transport phenomena and spatial aspects in economic/ecological modeling.

2 COUPLED ECOLOGICAL/ECONOMIC MODELING FOR ROBUSTNESS Consider the following social optimization model of an economy dependent upon a biosphere stock x given by  ∞ max e−ρt u(c (t) , x (t) )dt c

t=0

s.t.

(1)

x˙ (t) = F (x (t) , c (t) ), x(0) = x0 . For example consider the Steele–Henderson (1984) model of a fishery below, F (x, c) = rx(1 − k/x) − c − aR(x) R(x) = x 2 /(b2 + x 2 ),

(2)

where x (t) is a valuable stock, e.g. biomass of fish and c(t) is stock consumption. Note that in the case of a fishery, the term x(t) typically would not appear in the utility function, unless concepts of existence value are introduced.4 The term R (x) introduces nonlinear feedbacks, which are physical processes that further impact on initial change of the system under study. Feedbacks could be positive if the impact is such that the initial perturbation is enhanced, or negative if the initial perturbation is reduced. In the context of renewable resources, feedbacks can be related to nonlinear predation terms. In the analysis of eutrophication of lakes, positive feedbacks are related to the release of phosphorus that has been slowly accumulated in sediments 4 To ease notation in many case we will omit the explicit dependence of a variable on time t and write x

instead of x (t) and so on.

2 Coupled Ecological/Economic Modeling for Robustness

and submerged vegetation, while in climate change issues they can be related, for example, to the permafrost carbon pool (Brock et al., 2014a). Nonlinear feedbacks in the resource dynamics introduce nonconvexities which are related to the existence of multiple steady states, hysteresis, or irreversibilities and cause the emergence of Skiba points (see the collection edited by Dasgupta and Mäler, 2004). In the case of an ecosystem that is stressed by consumptive activities (e.g., Dasgupta and Mäler, 2004), x˙ = F (x, c) = λc − δx + aR(x), x(0) = x0 R(x) = x 2 /(b2 + x 2 ),

(3)

where x is a stock of something “bad”, e.g. the stock of phosphorous sequestered in algae in a lake ecosystem (Carpenter et al., 1999; Mäler et al., 2003; Dasgupta and Mäler, 2004) and c is consumptive activities that yield utility but damage the services that enjoyers obtain, u(c, x), where the utility function u(c, x) increases in c but decreases in x, and the nonlinear feedback term R (x) introduces nonconvexities. An example in which optimal control c can be obtained in a closed form solution analytically is the case a = 0, u(c, x) = ln(cα e−Dx ), D > 0, 0 < α < 1.

(4)

Thus the current value Hamiltonian for problem (1)–(3) is H (x, c, p) = u(c (t) , x (t) ) + p [λc − δx + aR(x)]

(5)

and the first order necessary conditions (FONCs) resulting from the maximum principle, using (4), imply: 1 = −λp c   c˙ = (ρ + δ) c + 1 − aR  (x) λc2 x˙ = λc − δx + aR(x).

(6) (7) (8)

All cases may be analyzed using phase diagram techniques in co-state and state space since the FONCs of the optimal control problem result in two ordinary differential equations (ODEs) for the stock x (t) and its shadow value p (t) which are autonomous. We refer to the collection edited by Dasgupta and Mäler (2004) for analysis of selected cases and Crépin et al. (2012) and Levin et al. (2013) for many examples. Mäler et al. (2003) and Kossioris et al. (2008), by using a utility function which is logarithmic in benefits and quadratic in damages, u (c, x) = ln c − βx 2 , β > 0,

(9)

study a situation in which enjoyers interact strategically. The lake ecosystem problem is analyzed as a differential game with open loop and nonlinear feedback Nash equilibrium with the feedback Nash equilibrium strategies obtained numerically. For the

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same problem, Kossioris et al. (2011) study the structure of optimal state-dependent taxes that steer the combined economic-ecological system towards the trajectory of optimal management, and provide an algorithm for calculating such taxes. More examples, together with discussion of early warning signals of impending regime changes and tipping points, are given in the collection published in Theoretical Ecology, edited by Dakos and Hastings (2013). The discussion above focuses on positive feedbacks and nonlinearities associated with the dynamic constraints of the optimization problem. There is also a large body of research on modeling preferences that include natural capital, such as the introduction of the green golden rule by Chichilnisky et al. (1995), the valuation of the productive base of the economy which includes natural capital (Arrow et al., 2003, 2012a, 2012b). In the lake literature the stock (phosphorous sequestered in algae) appears in the utility function with a negative impact on utility (Maler et al., 2003). At the abstract theoretical level we exposit here, natural capital appears in both the utility and production functions. We will treat a special case in which the atmosphere is treated as “natural capital” in more detail when we develop a climate economics model. Before continuing with our analysis, we insert a word of caution. Brook et al. (2013) caution that one-dimensional models like the above that focus on nonlinear responses to anthropogenic forcing must be restricted to the appropriate time and spatial scales in order to be relevant. For example, they identify settings in which such models might be relevant: (i) there must be enough spatial homogeneity in drivers and responses; (ii) there must be enough interconnectivity at the spatial and temporal scales under scrutiny. At the global level they argue that the “usual suspects” – climate change, land use change, habitat fragmentation, and species richness – are not likely to satisfy the conditions needed for a strong enough nonlinearity at the global scale to induce a global scale tipping point. They do not dispute, however, that tipping points may occur at smaller regional scales. Regarding the characteristics of the solutions for the above problems, for cases in which x(t) is a desirable stock, there is at least one critical level of stock, typically called a “Skiba Point” after Skiba’s pioneering article (Skiba, 1978), such that if initial x(0) is below this point is optimal to decrease x(t) and if x(0) is above, it is optimal to increase x(t). If x(t) is a negatively valued stock, e.g. the stock of phosphorous in lake water in the eutrophic lake example, then if x(0) is above the Skiba point it is optimal to increase x(t), i.e. continue degrading the lake, while if x(0) is below the Skiba point it is optimal to decrease x(t) i.e. improve the lake. That is, initial conditions play a key role in the long-run optimal state of the system. For lakes there may be more than one “Skiba” point that determines which long-run optimal state it is optimal to “steer” the system towards. Brock and Starrett (2003) analyzed a lake model with several “Skiba” points, while Grass et al. (2017) identified Skiba paths in a lake model with two dynamic equations, the phosphorous dynamics and the mud dynamics which are responsible for the positive feedbacks. We turn now to introducing robustness into the analysis of management models of human-dominated ecosystems.

2 Coupled Ecological/Economic Modeling for Robustness

2.1 ROBUST CONTROL METHODS IN COUPLED ECOLOGICAL/ECONOMIC SYSTEMS 2.1.1 An Introduction to Robust Control Methods Robustness is related to the major and interrelated uncertainties associated with coupled ecological/economic systems. These uncertainties are primarily associated with two basic factors: (a) the high structural uncertainty over the physical processes of environmental phenomena, and (b) the high sensitivity of model outputs to modeling assumptions. As a result, separate models may arrive at dramatically different policy recommendations, generating significant uncertainty over the magnitude and timing of desirable policies. These uncertainties may impede adequate scientific understanding of the underlying ecosystem mechanisms and the impacts of policies applied to ecosystems. A central feature of the above structure of uncertainty is that it might be difficult or even impossible to associate probabilities with uncertain prospects affecting the ecosystem evolution. This is close to the concept of uncertainty as introduced by Knight (1921) to represent a situation in which probabilities cannot be assigned to events because there is ignorance or insufficient information. Knight argued that uncertainty in this sense of unmeasurable uncertainty is more common in economic decision making. Knightian uncertainty should be contrasted to risk (measurable or probabilistic uncertainty) where probabilities can be assigned to events and are summarized by a subjective probability measure or a single Bayesian prior. Inspired by the work of Knight, economist, and others have attempted to formally model preferences when probabilistic beliefs are not of sufficiently high quality to generate prior distributions (Gilboa et al., 2008). Gilboa and Schmeidler (1989) developed the axiomatic foundations of maxmin expected utility, an alternative to classical expected utility for economic environments featuring unknown risk. They argued that when the underlying uncertainty of an economic system is not well understood, it is sensible – and axiomatically compelling – to optimize over the worst-case outcome (i.e., the worst-case prior) that could conceivably come to pass. Motivated by concerns about model misspecification in macroeconomics, Hansen and Sargent (2001a, 2001b, 2008) and Hansen et al. (2006) extended Gilboa and Schmeidler’s insights to dynamic optimization problems, thus introducing the concept of robust control to economic environments. A decision maker characterized by robust preferences takes into account the possibility that the model used to design regulation, call it benchmark or approximating model P, may not be the correct one but only an approximation of the correct one. Other possible models, say Q1 , . . . , QJ , which surround P, should also be taken into account with the relative differences among these models measured by an entropy measure, or an entropy ball containing the approximate model P. Hansen and Sargent (2003) characterize robust control as a theory “. . . [that] instructs decision makers to investigate the fragility of decision rules by conducting worst-case analyses,” and suggest that this type of model uncertainty can be related to ambiguity or deep uncertainty so that robust control can be interpreted as a recursive version of maxmin expected utility theory. The models inside the entropy ball are close enough to the benchmark model that they are difficult

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CHAPTER 1 Coupled climate and economic systems

to distinguish with finite data sets. Then robust decisions rules are obtained by introducing a fictitious “evil or adversarial agent” which we will refer to as Nature. Nature promotes robust decision rules by forcing the regulator, who seeks to maximize (minimize) an objective, to explore the fragility of decision rules with regard to departures from the benchmark model. A robust decision rule means that lower bounds to the rule’s performance are determined by Nature – the adversarial agent – which acts as a minimizing (maximizing) agent when constructing these lower bounds. In terms of applications, climate change is an area where ambiguity and concerns about model misspecification are present and significant. As Weitzman (2009) points out, the high structural uncertainty over the physics of environmental phenomena makes the assignment of precise probabilistic model structure untenable, while there is high sensitivity of model outputs to alternative modeling assumptions such as the functional form of the chosen damage function and the value of the social discount rate (e.g., Stern, 2006; Weitzman, 2010). Thus robust control approaches fit very well with climate change problems, as well as with more general environmental and resource economics problems, given the deep uncertainties associated with these issues.5 For example a specific density function for climate sensitivity from the set of densities reported by Meinshausen et al. (2009) can be regarded as the benchmark model, but other possible densities should be taken into account when designing regulation. One of these densities that corresponds to the least favorable outcome regarding climate change impacts can be associated with the concept of the worst case. A typical formulation of a robust control problem takes the form of a penalty problem or multiplier robust control problem which is defined as:  max min E0 c(t) h(t)

∞

e t=0

−ρt

  1 2 u(c (t) , x (t) )+ θ h (t) dt. 2

(10)

In this problem the regulator chooses c(t) to maximize its objective, while h (t) represents the departure from the benchmark model which is chosen by Nature with the purpose of penalizing the regulator. The size of the penalty, which is 12 θ h2 (t), is also determined by the penalty parameter θ in (10) which is small when confidence in the baseline model is low and large when the regulator is highly confident about the benchmark model. Note that the evil agent minimizes and the primary agent maximizes. The joint operation “maxmin” is sometimes called “extremization”. The extremization in (10) is subject to a stochastic differential equation which describes

5 Issues of regulation under ambiguity have been studied using two main approaches: smooth ambiguity and robust control. Smooth ambiguity (Klibanoff et al., 2005) parameterizes uncertainty or ambiguity aversion in terms of preferences and nests the worst-case, corresponding to robust control, as a limit of absolute ambiguity aversion. The approach has been used in climate change issues (e.g., Millner et al., 2010), but questions regarding the calibration of the regulator’s ambiguity aversion remain open. Robust control methods have been applied to climate change by Athanassoglou and Xepapadeas (2012).

2 Coupled Ecological/Economic Modeling for Robustness

the evolution of x (t) dx(t)= [F (x (t) , c (t) ) + σ (x (t) h (t))] dt + σ (x (t)) dZ (t) , x(0) = x0 ,

(11)

where {Z (t) , t ≥ 0} is a Brownian motion in the underlying probability space ( , F, P) and h (t) is the departure from the benchmark model chosen by Nature. Note that h (t) distorts the expected rate of change (drift) of the evolution of the state variable. For example, if (11) describes the stochastic accumulation of a pollutant, h(t) is the Nature choice to increase the expected rate of accumulation and thus penalize the regulator through (10). The minimizing distortion and the associated penalty basically determines the lower bound of the performance of the regulatory rule. A more formal statement of the problem is presented in Appendix A.1. The multiplier robust control problem, which is the more analytically tractable of the two, is solved by using the Hamilton–Jacobi–Bellman–Isaacs (HJBI) condition (Fleming and Souganidis, 1989):  1 (12) ρV (x) = max min u(c (t) , x (t) )+ θ h2 (t) c(t) h(t) 2  1 + V  (x) [F (x (t) , c (t) ) + σ (x (t) h (t))] + σ 2 (x (t)) V  (x) , 2 where V (x) is the value function for the problem. As shown in Hansen et al. (2006, Appendix D), if σ (·) is independent of the control, then the HJBI condition is satisfied and the orders of maximization and minimization can be exchanged in (12). Thus ρV (x) = maxc(t) minh(t) {·} = minh(t) maxc(t) {·}. In the rest of the chapter we assume that this independence assumption is satisfied.6 Solution of problem (12) will determine the optimal robust paths (c∗θ (t) , x ∗θ (t)) for a given level of robustness θ which express the regulator’s concerns about model misspecification. Solution of the same problem for θ → ∞ will provide paths (c∗∞ (t) , x ∗∞ (t)) when the regulator is not concerned about model misspecification and regards the benchmark model as adequate.

2.1.2 A Deterministic Approximation to Robust Control Methods in Ecosystem Management Robust control theory is when the model written down as an optimal control problem is not completely trusted. In reality parameters of models must be estimated and these estimates possess standard errors. Many fields of science, including economics, use robust control theory. The main idea is to design a control that performs well over a set of alternative specifications of a baseline model (Hansen and Sargent, 2008, Chapter 1). We formalize this idea by setting up a game where the maximizing agent pretends that there is 6 For a complete treatment of the conditions under which max min = min max see Hansen et al. (2006, Appendix D).

9

10

CHAPTER 1 Coupled climate and economic systems

an “evil agent” who tries to choose an alternative model to hurt the maximizing agent the most within a constraint set that the evil agent faces. The maximizing agent maximizes its payoff over its control set while the evil agent minimizes the maximizing agent’s utility over its own control set. The fictitious evil agent does its minimization subject to its constraint set which is “tighter” i.e. “smaller” the more confidence the maximizing agent has in its original specification. Here is a simple linear quadratic example of a deterministic robust control problem that illustrates the basic principles of robust control analysis for those readers not familiar with robust control analysis. Consider the problem  ∞

 max min −Qx 2 − Ru2 ds u

v

s=t

subject to x˙ = F x + Gu + Cv , x (t) = xt  ∞ e−r(s−t) v 2 ≤ η2 . s=t

Apply the usual Lagrange multiplier method by letting θ be the Lagrange multiplier for the integral constraint on the minimizing agent, which yields the problem,  ∞ 

 W (xt ) = max min −Qx 2 − Ru2 + θ v 2 ds (13) u

v

s=t

subject to x˙ = F x + Gu + Cv, x (t) = xt . Problem (13) is the deterministic version of the multiplier problem presented in the previous section.7 For this extremization problem the current value Bellman type equation which is the deterministic analogue of the HJBI equation defined above, is written below,



 rW (x) = max min −Qx 2 − Ru2 + θ v 2 + Wx (F x + Gu + Cv) (14) u

v

dW (x) . Wx ≡ dx

(15)

Note that when θ = ∞, i.e. η = 0 we are back in the familiar world of standard control theory. If we extremize with respect to u, v and insert the trial solution, W (x) = −P x 2 , we obtain a quadratic equation in P much like one gets in the nonrobust control case. However, in this case, we may not have a real positive root and the roots can even be complex. We obtain, from (14),     1 1 rW (x) = −Qx 2 + (16) (Wx G)2 − (Wx C)2 + Wx Fx 4R 4R 7 See Hansen and Sargent (2008, Eq. (2.4.2)) for a linear quadratic example in discrete time.

3 Carbon Budgeting and Robustness

After inserting the trial solution, W (x) = −P x 2 , into (16), x 2 cancels out of both sides of (16) to obtain the algebraic equation, −rP = −Q +

(P G)2 (P C)2 − − 2P F. R θ

(17)

As before there will be two roots to Eq. (17) but, if C is large enough or is small enough, the roots may not be real or we might not have a positive root, P+ > 0. Note that when θ = ∞ or C = 0, we are back in the standard non-robust control case. Hence when θ is large enough, we will have a real positive root and robust control theorists say that we can “robustify” ourselves against the evil agent in this case. Less dramatically, we can just say that we can find a control that’s not “brittle” to a particular specification and that performs well over a set of alternative specifications. There will be a critical value of θ , call it θc > 0, which is sometimes called a “breakdown point” in the literature such that for θ < θc we cannot find a positive root for (17). In this case there is no control appropriate for the set of possible specifications. Stochastic robust control is treated by just adding Wiener “noise” to the constraint equation much as one does for the case of stochastic non-robust control. In this case the relevant HJBI equation is (12), which contains the added term for Wxx and σ 2 (x). If σ 2 (x) = σ0 x 2 , one obtains a quadratic equation which can be solved in closed form as in the deterministic case.

3 CLIMATE ECONOMICS WITH EMPHASIS ON NEW MODELING: CARBON BUDGETING AND ROBUSTNESS It is standard in a handbook chapter to review the relevant literature in each section of the chapter. However, in the case of integrated assessment modeling in climate economics, the literature is huge and there are already good sources that review this massive area of research. A few of the most recent sources that also give critiques are Nordhaus (2008, 2013), Pindyck (2013a, 2013c), and Stern (2013). Brock et al. (2014d) review recent literature on inter-temporal spatial dynamic environmental economic modeling. Rather than going over terrain that is competently covered elsewhere, this section discusses some very recent work that emphasizes spatial transport phenomena in climate-economics models and also reviews a cumulative carbon budgeting approach that abstracts from the difficult issues surrounding the parametric specification of a damage function. We also include some discussion of robustness and stochastic forcing where the robustness parameter is scaled relative to the standard deviation of the stochastic shocks in such a way as to yield an approximate deterministic problem (Anderson et al., 2014).8

8 While this type of scaling in small noise expansions in robustness analysis is a useful device for simplifying a complex stochastic problem into a simple deterministic problem for analytical work, it has to

11

12

CHAPTER 1 Coupled climate and economic systems

In addition we provide a brief discussion of policies needed to deal with greenhouse gases (GHGs) that have different lifetimes. Pierrehumbert (2014) argues that appropriate policies should focus on putting more emphasis on long-lived GHGs in contrast to basing policies on global warming potentials (GWPs) independent of lifetime of the GHGs. Even narrowing the focus to this much smaller slice of the area requires that we concentrate on a relatively narrow spectrum of the hierarchy of climate-economic models. Models of the climate component range from the complex general models, which are computer models with spatial resolution as fine as current computer technology can handle, to simple analytical energy balance models and “box” models. Models of the economic component also have a similar complexity hierarchy. We use the simplest possible models of both the climate component and the economic component here.

3.1 CUMULATIVE CARBON BUDGETING TO IMPLEMENT TEMPERATURE LIMITS We begin this section by discussing an approach which could mitigate some controversies in the literature IAMs. Pindyck has written a series of papers (see the references, especially Pindyck, 2013a, 2013c) that argue that too many assumptions, especially regarding damage functions, are made that do not have strong support in reality. That is, he argues that the exact specifications of “damage functions” seen in a lot of the literature on IAMs are weakly supported by hard evidence. Roe and Baker (2007) explain why it is difficult to make progress on reducing the uncertainty about a key parameter, the climate sensitivity. Roe and Bauman (2013) critique the use of the uncertainty distribution of climate sensitivity in the existing literature on IAMs because much of the uncertainty is only relevant in the very distant future. Finally, Roe (2013) criticizes IAMs by arguing that the whole IAM enterprise is just a “numbers game”. To put it another way, these objections to the usual approach in climate economics based upon cost benefit analysis (CBA) are similar to the list of problems with CBA discussed by Held (2013). However, we do not want to overstate criticism of CBA. For example, recent research on damages at the regional level (e.g., Barreca et al., 2015), suggests that regional damages could be aggregated appropriately to produce a global scale damage function with stronger foundations than simple “made up” specifications of global damage functions that commonly appear in aggregate IAMs. Furthermore, Burke et al. (2015) argue that nonlinearity in damages at the regional level survives aggregation to the world level and study global nonlinear effects on economic productivity due to climate change. In terms of estimating regional damages the Risky Business Project in the U.S. does detailed work on damages at the regional scale for the U.S.9

be handled with care because the scaling needed may be inconsistent with detection probabilities that are consistent with available data sets (Anderson et al., 2012). 9 See the Risky Business project report at https://riskybusiness.org/reports/.

3 Carbon Budgeting and Robustness

Meanwhile Matthews et al. (2009) and Matthews et al. (2012) have advanced a very interesting argument that the increase in mean global yearly temperature, which we refer to as just “temperature” from now on, is approximately proportional to cumulated carbon emissions in each of the respected big climate models that they simulate. They call this constant of proportionality the cumulated carbon response parameter (CCR). Matthews et al. (2012) argue that this finding of approximate constancy of the CCR parameter allows a cumulated carbon budget to be set that should not be exceeded for a given threshold temperature. Matthews et al. (2009) and Matthews et al. (2012) argue that there is evidence to support the proportionality relationship in reality and, hence, this relationship could be used for policy purposes. Here is the potentially radical idea that we develop in this section. Instead of struggling with the problem of specifying an exactly parameterized damage function, we will let the climate science community set a threshold temperature that they agree should not be exceeded in order to avoid catastrophic climate change. We then use the Matthews et al. (2009) CCR parameter to set a cumulated carbon budget which should not be exceeded. Of course this implies an “implicit” damage welfare cost function which is essentially plus infinity when the threshold is exceeded. To put it another way, output that is left over for consumption is full output until the threshold is reached, and then it becomes zero.10 Our effort could also be viewed as a very crude simplification of Weitzman’s (2012) much more sophisticated treatment in which he replaces the “standard” quadratic damage function with a damage function that increases much more sharply as temperature increases and replaces thin-tailed distributions of climate sensitivity with fat-tailed distributions like the Pareto distribution. It can be argued that this is taking too extreme a stand on a particular threshold temperature. In any event we explore the conclusions that taking this stand implies. This stand implies that our job as economists is to design a set of efficient institutions, i.e., policy instruments to implement the optimal path of emissions of the economy that do not exceed this cumulated carbon budget. In some sense we are taking the position that the climate science community has the expertise to set the limiting global average temperature increase that the climate system can tolerate, and that the economic science community’s job is to design the best set of policies to maximize the welfare of the world economy, subject to this cumulated carbon emissions budget constraint. This idea is not unique to us. It is similar to the cost effectiveness analysis (CEA) advocated by Held (2013). As far as we know, using the Matthews et al. (2009) and Matthews et al. (2012) climate module to implement Held’s CEA and the discussion of implementation of CEA by decentralized market-based institutions is new, although it is closely related to some of the analysis in Anderson et al. (2014). We realize that our approach has uncertainty problems that may be as great or greater than the traditional approach with detailed specification of objects like dam10 For a similar approach see Llavador et al. (2015). See also Anderson et al. (2014) for a sketch of this kind

of approach to carbon budgeting using the Matthews et al. (2009) CCR concept to simplify the climate side of the modeling.

13

14

CHAPTER 1 Coupled climate and economic systems

age functions and approaches that deal with the “fat-tailed” distribution of possible values of the usual climate sensitivity parameter (e.g., Weitzman, 2011; Roe and Baumann, 2013). For example, climate science has not settled on what the value of the critical threshold temperature is, and readers of Matthews et al. (2009) and Matthews et al. (2012) will notice right away that the CCR parameter varies across respected big climate models. In any event, for readers who feel that our approach is too radical, it is fairly straightforward to extend it to cases where the damage function increases sharply over a domain of temperatures for which the climate science community has a strong consensus that going beyond temperatures in this domain would be truly catastrophic. We discuss these problems later. It is easiest to explain our approach with formal modeling. We will do the simplest deterministic case first because that will be enough to explain the basic ideas before turning to more complicated and realistic cases. We assume that the global average temperature evolves much as in the Anderson et al. (2014) working paper, which used the temperature dynamics climate model from the Matthews et al. (2009) and Matthews et al. (2012) papers. To our knowledge the Anderson et al. paper is the first paper in the climate economics literature to use the Matthews et al. approach for coupled climate-economic models. Anderson et al. still use damage functions as in Golosov et al. (2014), Nordhaus (2008), and others. The approach we use here is new and is not in Anderson et al., although it is closely related to some of the analysis in section 2 of that paper.

3.1.1 Deterministic Case: The Simplest Possible Model We start with a specification in which a closed form solution is available. Suppose Tc is chosen by the climate science community as the temperature which should not be exceeded in order to avoid catastrophic climate change. Since it is standard to work with the increment to temperature since pre-industrial times, “temperature” here is always short for “incremental temperature”. For example, a standard choice for Tc is 2 °C, that is two degrees Centigrade. However, this choice has recently become controversial (e.g., Victor and Kennel, 2014). Nevertheless, it stands to reason that climate scientists and policy makers in general might want to try to keep the temperature from getting much bigger than, say, 3 °C even if they felt that 2 °C was too cautious. Indeed some climate scientists and economists (e.g., Hansen et al., 2013) argue that 2 °C is too high for the planet to tolerate without serious harm and that 1 °C should be the limit. Held (2013) argues for the 2 °C limit as a sensible limit to set, based upon current knowledge in climate science. Stern (2013) discusses many extremely unpleasant effects that might occur if the Earth’s temperature reaches 4 °C. While the approach based upon cumulative carbon budgeting that we use here is extremely stark, it does have the advantage of separating the model component specification tasks according to relative expertise. That is, specification of the global average temperature target not to be exceeded is left to the climate science community, and design of incentive structures to implement a cumulative carbon budget not to exceed that target is left to the economic science community. Since specification of a target temperature not to be exceeded is specifi-

3 Carbon Budgeting and Robustness

cation of an “extreme” damage function of zero until the target is reached, then minus infinity for temperatures larger than target, what our approach is basically saying is this: The climate science community has expertise in specifying a “penalty function” on temperature increases and the economics community has expertise in incentive mechanism design that should be exploited. This separation of specification tasks in the modeling exercise has elements of transparency and specification task separation across science communities according to relative expertise, which could be related to the ideas in Stern (2013) and Pindyck (2013b). Repetto (2014), in his review of Nordhaus (2013), takes issue with the cost benefit approach to climate economics. Our approach here could be viewed as a start in developing an alternative approach that avoids some of the problems with the CBA approach at the expense of introducing other problems. Our view is that it is useful to place our approach on the table for discussion. We will not take a stand on its value relative to traditional approaches such as Nordhaus (2013) and many others who use a CBA type of approach to climate economics. In any event, the Matthews et al. (2009) and Matthews et al. (2012) framework allows specification of a target cumulative carbon budget not to be exceeded once a target temperature not to be exceeded is specified. It is easiest to explain the approach proposed here by working out some simple examples. The proportionality of temperature to cumulated carbon emissions can be specified as 

t

T (t) − T (0) = λ

E (u) du,

(18)

0

where T (t) and T (0) denote current temperature and initial (e.g. preindustrial) temperature respectively, λ is the CCR parameter and E (u) is emissions of GHGs emitted at time u ∈ [0, t]. Thus the rate of change of temperature is proportional to current emissions or T˙ (t) = λE (t) , T (0) = T0 .

(19)

Probably the simplest “precautionary” approach to cumulative carbon budgeting that might appeal to some climate scientists and that might be illustrated with a toy model like this one is to take a value of the CCR parameter λ from the high end of the distribution of values across models displayed in, for example Matthews et al. (2009), call it λmax , and simply solve the problem, 

∞

max E(t)

e

−ρt

 α

u(yE )dt

(20)

t=0

subject to T˙ = λE, T (0) = T0 ,

(21)

15

16

CHAPTER 1 Coupled climate and economic systems

for the dynamics of global average temperature, where y is an exogenous productivity function, and S˙ = −T˙ = −λmax E, S(0) = Tc − T0 S(t) ≡ Tc − T (t).

(22)

This problem is just a standard exhaustible resource problem with the initial reserve set equal to Tc /λmax .

(23)

We will see this same theme appear in the simple robust control problem with multiplicative uncertainty that we discuss below.

3.1.2 Robust Emission Control with Multiplicative Uncertainty The simple example (20)–(21) centers attention on the Matthews et al. (2009) CCR parameter λ. However Matthews et al. (2009, Figs. 3 and 4) show that the value of λ is highly uncertain, i.e. it varies a lot across respected big climate models. How should a planner behave in the face of such uncertainty? One way of dealing with this level of “deep” uncertainty where attaching probabilities and conducting a Bayesian analysis is not appropriate (Hansen and Sargent, 2008, Chapter 1) is to use robust control to construct a policy that works uniformly well over a set of alternative models surrounding a “baseline” model. Intuitively the robust control method leads to the welfare planner maximizing against a “worst case” model. We will say more about what we learn from this exercise after we conduct the analysis below. We introduce uncertainty and concerns about model misspecification in the temperature dynamics of model (20)–(21). Assuming that the drift distortion – which is chosen by the adversarial (i.e. the minimizing) agent – enters temperature dynamics multiplicatively, the deterministic approximation of the stochastic robust control problem discussed above requires solving the robust control problem11   ∞ max min e−ρt (u(yE α ) + (1/2)θ v 2 )dt (24) E

v

t=0

subject to T˙ = (λ + v)E, T (0) = T0 .

(25)

The ODE (25) describes the dynamics of global mean temperature (GMT), denoted here by T (t) for each date t, with v denoting the distortion of the temperature dynamics due to model misspecification concerns which is chosen by the minimizing agent, and E denoting GHGs emissions which by a suitable choice of units can become

11 As we will see below, the multiplicative uncertainty problem is much easier to solve than the additive

uncertainty case.

3 Carbon Budgeting and Robustness

equivalent to fossil fuel usage. Furthermore, R˙ = −E, R(0) = R0 S˙ = −T˙ = −(λ + v)E, S(0) = Tc − T0 S(t) ≡ Tc − T (t)

(26)

describe the dynamics of fossil fuel usage and the dynamics of the “safety reserve” S(t) ≡ T (t) − Tc . The idea here is that the planner feels that he/she knows from Gillett et al. (2013), Matthews et al. (2009) and Matthews et al. (2012) that there is some true value of the CCR parameter12 and sets for example, λ = 1.5 °C/1000 PgC,

(27)

based on the mean value reported by Matthews et al. (2012, p. 4369), but wishes to, for example, robustify its choice against a possible choice of Nature in the 5–95% range of 1 to 2.1 °C reported by Matthews et al. (2012, p. 4369). Specifying the utility function as u(yE α ) = ln y + α ln E, and noting that since ln y is exogenous it does not affect optimization, the current value Hamiltonian is given by H = max min{α ln E + μS (−(λ + v)E) + θ v 2 /2}. v

E

(28)

The FONCs for a Nash equilibrium imply E = α/(μS (λ + v)) v = μS E/θ = α/(θ (λ + v)).

(29)

The solution of (29) for v is v ∗ = (−λ + D 1/2 )/2, D ≡ λ2 + 4α/θ.

(30)

We have chosen the positive root since a larger CCR is worse for the welfare of the maximizing agent. Since the path for the co-state variable is given by μS (t) = μS (0)eρt , using the constraint  ∞  (λ + v ∗ )E(t)dt = S0 = t=0

∞

t=0

(λ + v ∗ )(α/(μS (t)(λ + v ∗ )))dt =

(31)

(32)

⇒ μS (0) = α/(ρS0 ) 12 The CCR parameter λ is expressed in terms of degrees Celsius per 1000 PgC. 1 PgC (petagram of Carbon) = 1 GtC (gigatonne of carbon). 1 GtC = 109 tonnes C = 3.67 Gt carbon dioxide.

17

18

CHAPTER 1 Coupled climate and economic systems

allows us to solve for μS (0). The solutions for energy use and the dynamics of S(t) are given by E(t) = αe−ρt /(μS (0)(λ + v ∗ )) = (ρS0 e−ρt )/(λ + v ∗ )  S(t) = S0 − = S0 −

t

s=0  t

(33)

(λ + v ∗ )E(s)ds [(λ + v ∗ )(ρS0 e−ρs )/(λ + v ∗ )]ds = S0 e−ρt .

(34)

s=0

Note that in the non-robust case, i.e. when there are no concerns about model misspecification so that θ → ∞ and v → 0, energy use is independent of energy’s share in production, i.e. energy use is independent of α. But in the robust case, energy use decreases in every period when energy’s share increases. Another useful result is the time consistency of the equilibrium solution which is easy to show from (34). An extremely important property of the multiplicative uncertainty case is that S(t) ≥ 0 holds for all positive dates for solution (34). Thus our solution procedure has actually produced an equilibrium solution to the zero sum game. The value of the equilibrium of this zero sum dynamic game for the maximizing player is  ∞  ∞ −ρt e α ln(E(t))dt = e−ρt α ln(ρS0 e−ρt /(λ + v ∗ ))dt. (35) t=0

t=0

Although the case of logarithmic utility is popular, the equilibrium solution has many useful properties that are special to this case. We investigate the more general case, u(yE α ) = [(yE α )1−γ − 1]/(1 − γ ).

(36)

The Hamiltonian for this case is H = [(yE α )1−γ − 1]/(1 − γ ) + (1/2)θ v 2 − μS ((λ + v ∗ )E).

(37)

The FONCs give us the equations (suppressing the dependence upon t except when needed for clarity): μS (t) E (t) θ 1 ∗ E (t) = [μS (λ + v ∗ (t) )y γ −1 ]1/[α(1−γ )−1] α μS (t) = μS (0)eρt .

v ∗ (t) =

(38) (39) (40)

Eqs. (38)–(40) imply that the solution for v(t) must satisfy

(λ + v ∗ (t))y(t)(γ −1) v ∗ (t) = (1/θ)[ μS (t)(α(1−γ )) ]1/[α(1−γ )−1] . α

(41)

3 Carbon Budgeting and Robustness

We see right away from (38)–(40) that for the logarithmic case, γ = 1, the time dependent terms drop out of (41) and we obtain Eq. (29) for v(t) = v ∗ , which is constant in time and is independent of the shadow price μS (t) of the state variable, S(t). Since α(1 − γ ) − 1 < 0, we see that the RHS of (41) is decreasing in v and the LHS is increasing in v. It is easy to see that for each date t there is a unique v ∗ (t) that solves (41). Even if y(t) is constant, there will still be time dependence of v ∗ (t) unless γ = 1. The constancy of v ∗ (t) as a function of time is important for time consistency of the equilibrium solution of the game. For the nonlogarithmic case (γ = 1), the system (38)–(40) needs to be solved numerically. Assuming y (t) = y0 egt , where g > 0 denotes an exogenous growth rate and replacing the discount rate ρ with ω = ρ − g (1 − γ ), an algorithm for numerically solving the nonlinear system can be described as follows: 1. Take a discrete time horizon t = 0, . . . , T for sufficiently large T and calculate the discrete  approximation ωˆ of the continuous time discount rate ω, using ω = ln 1 + ωˆ ; 2. Choose an μs (0) and numerically solve (38), (39) for Et∗ and vt∗ , t = 0, . . . , T ;  3. Calculate the sum S0∗ = t (λ + vt∗ )E ∗t ; 4. Repeat steps 2 and  3 fordifferent values of μs (0). Select the value for μs (0) for which the paths Et∗ , vt∗ result in a sum S0∗ that approximates the true S0 .

3.1.3 Cumulative Carbon Budgeting and Climate Changes Damages The cumulative carbon budgeting framework can be combined with an explicit damage function associated with climate change to determine robust optimal emission policy. Writing the utility function as y (t) E (t)a e−DT (t) , with the term e−DT (t) reflecting climate change damages and assuming logarithmic utility, the robust control problem for the regulator can be written as: 

∞

max min E

v

e−ρt (α ln E − DT + (1/2)θ v 2 )dt

 (42)

t=0

subject to R˙ = −E, R (0) = R0 T˙ = (λ + v)E, T (0) = 0  ∞ Tc − (λ + v)Edt ≥ 0.

(43) (44) (45)

0

The current value Hamiltonian for this problem is H = α ln E − DT + (1/2)θ v 2 − μR E + μT (λ + v)E    ∞ ρt (λ + v)Edt , Tc − + φe 0

(46)

19

20

CHAPTER 1 Coupled climate and economic systems

with optimality conditions α μR − μT ) (λ + v (t))  1  ρt v (t) = φe − μT E (t) θ    ∞ (λ + v)Edt = 0, φ ≥ 0 φ Tc −

E (t) =

+ (φeρt

(47) (48) (49)

0

μ˙ R = ρμR μ˙ T = ρμT + D.

(50) (51)

∞ Note that taking the forward solution of (51), μT (t) = s=t e−ρ(s−t) (−D) ds = −D/ρ for all t , which is constant. We assume that the initial reserve R0 is infinite or the constraint (45) binds so that μR = 0 for all t ≥ 0. Using (47) to substitute E (t) into (48), we obtain α . θ (λ + v (t))

(52)

α . (φ + D/ρ) (λ + v ∗ )

(53)

v (t) = Thus v (t) = v ∗ constant and E∗ =

Substituting E ∗ into the isoperimetric constraint (44), a φ ∗ that satisfies the constraint can be determined. The procedure can easily be extended to the case where T (0) = T0 > 0, T0 < Tc . As far as we know, our analysis and that of Anderson et al. (2014) is the first analysis of a robust controlled simple climate policy model with the climate side modeled using the Matthews et al. (2009) CCR framework to simplify the climate dynamics side of the model. However, we wish to emphasize that there are a number of papers that use robust control theory in climate economics. Hennlock (2009) is a pioneering paper, Athanassoglou and Xepapadeas (2012) study the precautionary principle in the context of a robust control model of climate change, while Li et al. (2016) apply robust control to show that the use of coal is substantially decreased under robust control. Intuitively, since coal is the “dirtiest” of the fossil fuel energy sources, its use will be decreased the most under the “worst case” model. Temzelides (2016) gives an excellent argument for the need to do robust control in climate economics, while Xepapadeas and Yannacopoulos (2017) study spatially structured ambiguity using robust control methods. What did we learn from this exercise? First, as one might expect from intuition, the robust policy is more cautious about tampering with the climate than the nonrobust policy. Second, the worst case CCR parameter,     1 4α 1/2 ∗ 2 λ+v =λ+ −λ + λ + , 2 θ

4 Implementation

increases as confidence by the policy maker in the baseline value λ decreases (i.e., θ decreases). Third, the increase in the worst case CCR as α increases might not be obvious at first blush. Fourth, constraint (45) can be viewed as a crude way of modeling an abrupt increase in damages for T ≥ Tc .

3.2 CLIMATE CHANGE POLICY WITH MULTIPLE LIFETIME FOR GREENHOUSE GASES Pierrehumbert (2014) has raised the important point that policy needs to take into account not only the global warming potential (GWP) of a GHG but also the atmospheric lifetime of the gas. For example, methane has a much shorter lifetime but a higher GWP than CO2 . This part of our climate economics section explores policy on multiple lifetime gases in the context of a simple energy balance model with forcing determined by stocks of two GHGs, one with infinite life and another with short life but larger GWP, modeled as in Appendix A.4. Intuition suggests that under economically plausible sufficient conditions, the optimal tax will be higher per unit CO2 emitted compared to the optimal tax per unit of the shorter lived GHG even if the GWP of the shorter lived GHG is larger (but not too much larger) than the longer lived GHG. Readers interested in this more complex but rather technical analysis are referred to Appendix A.4. We include this analysis in this chapter because, as Pierrehumbert (2014) stresses, it may be optimal to focus more on CO2 because of its long life relative to, for example, methane, even though the GWP of methane is much larger. We turn now to a very short illustrative discussion of implementation of equilibrium solutions by decentralized market institutions.

4 IMPLEMENTATION The framework above assumes that the economist’s job is just to implement the best way to satisfy the cumulative carbon budget constraint recommended by climate scientists. A natural way (at least for economists) is to try to find an optimal energy tax that implements the optimal solution to problem (24) in competitive equilibrium. A representative consumer solves the problem   ∞ −ρt max e u(c)dt , (54) c

t=0

subject to c + b˙ = π + pE + rb + T r, b(0) = 0.

(55)

Here T r(t) is lump sum redistribution to consumers of the energy taxes imposed on the representative firm at each date t , and pE is the lump sum redistribution of revenues from the representative energy firm to consumers.

21

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CHAPTER 1 Coupled climate and economic systems

The representative firms solve the problem π = max {yE α − (τ + p)E}.

(56)

{x,E}

Let E ∗ (t) denote the equilibrium function of energy use in the robust control problem (24), which is a function of date t. Define p(t) + τ ∗ (t) = yαE ∗ (t)α−1 .

(57)

A representative energy firm solves  ∞    t e− s=0 r(s)ds p(t)E(t)dt + μR 0 R0 −  = max {E}

t=0



∞

E(t)dt

.

(58)

t=0

The FONCs for the representative energy firm are t

e− s=0 r(s)ds p(t) = μR0 ⇒ p(t) ˙ = r(t) , p(0) = μR0 . p(t)

(59)

This “Hotelling’s Rule” is just what we would expect since this is standard economics. An interesting wrinkle here occurs when the robust control problem recommends leaving some of R0 in the ground. In this case the energy price p(t) = 0 for all dates t , and the value of the representative energy firm is zero. Proposition 1. Assume that the solution to problem (54) leaves some of R0 in the ground. Suppose firms solving problem (56) face an energy tax function, τ ∗ (t) = y(t)αE ∗ (t)α−1 , then they will pick their profit-maximizing level of energy use to be E ∗ (t) at each date t . If the profits and taxes distributed lump sum to the consumer solving problem (54) subject to the constraint (55) are evaluated at the (∗ )-solution, then in equilibrium where borrowing and lending b(t) = 0 for all dates t , the consumption will be c(t) = c∗ (t) = y(t)E ∗ (t)α for all dates t . Proof. Facing τ ∗ (t) = y(t)αE ∗ (t)α−1 + p(t), the representative firm’s FONC is y(t)αE(t)α−1 = τ ∗ (t) + p(t) = y(t)αE ∗ (t)α−1 + p(t).

(60)

We will show that p(t) = 0 for all dates, t . Hence, in this case, by (60) it must be the case that E(t) = E ∗ (t) for all dates t . This shows that the firms pick the (∗ )-level of energy use at each date t . Suppose by way of contradiction that μR0 > 0. Then by the FONCs for the representative energy firm we will have p(t) > 0 for all dates t and the energy firm will exhaust all of R0 , because μR0 > 0. However if p(t) > 0 for all dates t in (58) (actually if it is positive for any date t ), then less energy will be used in the (∗ )-solution since the price is higher. Thus the total energy use must be less than the total energy used in the (∗ )-solution. This contradicts μR0 > 0. Hence μR0 = 0

5 Energy Balance Climate Models and Spatial Transport Phenomena

and thus p(t) = 0 for all dates t . This ends the proof for the case of the representative firm. Turning to the consumers, the budget constraint when there is no borrowing and lending (which must be the case in equilibrium) is c(t) = π(t) + T r(t) = π ∗ (t) + T r ∗ (t) = yE ∗ (t)α − τ ∗ (t)E ∗ (t) + τ ∗ (t)E ∗ (t) = yE ∗ (t)α .

(61)

Remark 2. Notice that the function of time E ∗ (t) can be an arbitrary function of time and the method above can still be used to find a tax function τ ∗ (t) that will implement it, provided that the sufficient condition, λR0 > Tc , for μR0 (0) = 0 holds. Note that the equilibrium return on assets is given by r ∗ (t) = ρ −

u (c∗ (t))(dc∗ (t)/dt) , u (c∗ (t))

(62)

which can be worked out in closed form for this particular example, if needed.

5 ENERGY BALANCE CLIMATE MODELS AND SPATIAL TRANSPORT PHENOMENA Energy Balance Climate Models (EBCMs) are a useful and tractable way to model spatial transport effects on local temperatures caused by outside forcing of the climate system (North et al., 1981), e.g. by emission of GHGs. The ideas behind ECBMs are quite intuitive. Short wave solar energy arrives at the Earth and long wave energy is emitted by the Earth. Temperature is the quantity that equilibrates incoming energy to outgoing energy. The Earth’s atmosphere leads to a warmer equilibrating planetary temperature compared to the case with no atmosphere. Energy is transported from the Equator to the further latitudes away from the Equator towards the Poles. It would be colder in the Temperate Zones if this type of transport did not exist. Eq. (63) below describes the dynamics when no humans impact the system. The first term on the right hand side (RHS) is solar energy which is larger at the Equator and tapers off towards the poles. The second term on the RHS is outgoing long wave energy leaving the Earth. The third term is the diffusive transport term which captures the transport of energy away from the Equator and towards the Poles. A very nice and understandable treatment of ECBMs is the book by North and Kim (2017). More will be said as we proceed towards analysis. Consider the following EBCM, C

∂T b (x, t) = QS(x)a(x) − (A + BTb (x, t)) dt   ∂ 2 ∂Tb (x, t) D(x)(1 − x ) , + ∂x ∂x

(63)

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CHAPTER 1 Coupled climate and economic systems

where the notation follows North et al. (1981). That is,   ∂ 2 ∂Tb (x, t) C, Q, x, S(x), A, B, Tb (x, t), D(x)(1 − x ) , ∂x ∂x denote respectively heat capacity per unit area (a constant), solar constant, sine of latitude x, solar energy received at latitude x, empirical constants A, B, “baseline” temperature of the climate system at latitude x with no outside human-induced forcing, and spatial energy transport operator. Now assume that for t ≥ 0 a human-induced forcing h(t) is “switched on” where we imagine that date zero is pre-industrial, e.g. date zero is 1750 and h(t) is produced by humans using fossil fuels. This produces an “anomaly”, i.e. a departure from the solution of (63), which we denote by T (x, t) which satisfies the equation, C

∂ ∂T (x, t) = −BT (x, t)+ [D(x)(1 − x 2 )∂T (x, t)/∂x] + h(t), ∂t ∂x T (x, 0) = 0.

(64)

In writing h(t) instead of h(x, t) for the human injections into the dynamical system, we are assuming that the effects of the emissions at each latitude are rapidly distributed across the globe’s atmosphere relative to the time scale of the dynamics (64). In order to show the relationship between the spatial climate dynamics (55) and the dynamics of global temperature, integrate both sides of (64) over latitudes, x = −1 (minus 90 degrees) to x = +1 (plus 90 degrees), to obtain ∂T (x, t) ≡ C ∂t



1

T˙ (x, t)dx

x=−1



= −B  +

(65) 

1

dxT (x, t) +

x=−1 1

1

dx x=−1

∂ [D(x)(1 − x 2 )∂T (x, t)/∂x] ∂x

dxh(t) x=−1

= −BT (t) + 2h(t), T (0) = 0. The usual formulation of h(t) is h(t) = ξ ln(M(t)/M0 ), ˙ M(t) = −mM(t) + bE(t), M(0) = M0 given,

(66)

where ξ, M(t), m, b denote respectively the climate sensitivity, the concentration of GHGs, e.g. CO2 in the atmosphere (in ppm), removal rate parameter, and unit effect parameter of each unit of fossil fuels used. Allen et al. (2009), Matthews et al. (2009, 2012), and Gillett et al. (2013) suggest that when the reaction of the carbon cycle

5 Energy Balance Climate Models and Spatial Transport Phenomena

(e.g. the response of the ocean and land to increased human-induced injections into the atmosphere) is taken into account, the dynamics (65) and (66), which we rewrite below as T˙ (t) = −(B/C)T (t) + (2/C)ξ ln(M(t)/M0 ), T (0) = 0, ˙ M(t) = −mM(t) + bE(t), M(0) = M0 given,

(67)

might be quite closely approximated by the dynamics (if an “ocean” is added as in Pierrehumbert, 2014, Eq. (4)), T˙ (t) = λE(t), T (0) = 0,

(68)

for an appropriate value of the climate carbon response parameter, λ, of Matthews et al. (2009) and Matthews et al. (2012). Pierrehumbert (2014, Eq. (4), Fig. 3) obtains the near linearity of the increase in global mean temperature as cumulated emissions increases with a simple two box model that includes an ocean as well as a shallow mixed layer like the above simple energy balance one box model (58). Cai et al.’s (2012b) DSICE model has a two layer temperature dynamics and a three layer carbon cycle. It is plausible that approximate linearity of the increase in global mean temperature with cumulated emissions might occur in their model too. The papers of Brock et al. (2014b) and Brock et al. (2013) use the spatial energy balance approach like Eq. (64), together with specification of damage functions at each spatial location, to discuss the impact of energy transport as well as to offer a framework for allocating the burden of mitigation across space. If we abandon the attempt to specify damage functions and allocate the job of specifying a safe limit for global average temperature to climate scientists, we can adapt the simple logarithmic utility example above to illustrate some approaches to allocating the burden of mitigation across locations. Consider the problem    ∞

max t=0

e−ρt (

1

w(x) ln(y(x, t)E(x, t)α )dx)dt

x=−1

subject to (68) and  1 E(x, t)dx = E(t).

(69)

x=−1

The statement of problem (69) leads us to the key issue raised by spatial concerns and that is how to specify the welfare weights, {w(x)}. In a series of works, Chichilnisky and Heal (1994, 2000) and Chichilnisky and Sheeran (2009) have long argued that poorer countries and countries that have not polluted as long as the developed countries should bear less of the burden of mitigation. While it is somewhat standard to give larger weights to countries or locations with larger populations, there are other considerations for assigning weights besides population weighting.

25

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CHAPTER 1 Coupled climate and economic systems

FIGURE 1 Fossil fuel CO2 cumulative emissions 1751–2012. Source: Hansen et al. (2013).

A recent paper by Saez and Stantcheva (2013) proposed an approach to choosing welfare weights in optimal tax theory that could be adapted here. Their approach is to use empirical evidence on attitudes towards redistribution and who should bear the biggest tax burden to discipline the choice of welfare weights. We believe that it would be useful to adapt their approach to specify welfare weights as a function of each country’s historical emissions, current yearly emissions, yearly emissions per capita, growth in yearly emissions per capita, etc. Of course it is beyond the scope of this chapter to do the empirical work that would be required to data-discipline the choice of welfare weights here. The simplest illustrative approach is just to base the weights on the “relative blame” for the problem. This could be done by specifying the welfare weight function as a decreasing function of the share of total emissions since 1750 as in Eq. (71). Fig. 1 shows these shares across countries. A possible allocation of welfare weights that captures the idea that locations that have emitted relatively heavily in the past should be allowed a smaller share of the world carbon budget in the future can be characterized as follows. Let 

0

−∞

(70)

E(s)ds

denote total world emissions up to the reference date zero. Define    0 1 E(t)dt) , exp(−βs(x) w(x) = Z −∞  1  0   Z≡ dx exp(−βs(x ) E(t)dt), x  =−1

−∞

(71)

5 Energy Balance Climate Models and Spatial Transport Phenomena

where β > 0 is an “intensity” tuning parameter for penalization of locations that have emitted heavily in the past, and s(x) denotes the share of location x in past total world emissions. While x denotes the sine of latitude in our illustrative example here, the approach in (71) could be extended to actual countries by replacing x by (x, y) where x is latitude and y is longitude and integrating over the set of (x, y) that characterizes a country. Even easier is to replace x and the integral with country index k and a sum over countries. Solving the subproblem  1  1 α w(x) ln(E(x) )dx, s.t. E(x)dt = E, (72) max x=−1

x=−1

we obtain E(x) = w(x)E,  1  α U (E) = w(x) ln(E(x) )dx = x=−1

1

w(x) ln(w(x)α )dx + ln(E α ).

(73)

x=−1

Hence, we see that for the case of logarithmic utility we can easily adapt the above treatment of robust control to get the solution of problem (69) for any limit temperature, Tc , and for any set of welfare weights. This brings us to implementation. One way to implement the solution is to allocate at base date zero, to each x, a number of “rights to emit” equal to  ∞ E ∗ (t)dt = w(x)((Tc − T0 )/λ), (74) w(x) t=0

where example values of Tc , T0 , λ are 2 °C, 0.85 °C (IPCC working group 1 contribution to AR5), and 1.5 °C per 1000 PgC emitted (Matthews et al., 2012). Then, as in Chichilnisky and Sheeran (2009), a world trading market for emission permits would set the world market price. Of course, in the real world, settling on the weights, i.e. the initial allocation of rights across countries, the number of rights to be allocated, etc., is a very difficult problem. Chichilnisky and Sheeran (2009) suggest possible ways of getting around such political problems, e.g. by bargaining over the distribution of marketable rights. Weitzman (2014) is a recent paper which suggests that negotiating over a uniform price for carbon can induce a large free riding emitter to support a higher price when it considers that everyone else being bound to pay that price would reduce negative externalities imposed by the rest upon that free riding emitter. The Chichilnisky– Sheeran type bargaining over the distribution of rights might be harnessing similar type incentives since the trading market will strike a uniform world-wide price.

5.1 SPATIAL PATTERN SCALING Another way to describe spatial climate dynamics, which is extensively used by climate scientists, is emulation of Atmospheric Ocean General Circulation Models

27

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CHAPTER 1 Coupled climate and economic systems

(AOGCMs) combined with pattern scaling for smaller scales, e.g. Castruccio et al. (2014). Emulation is a way to obtain good approximations of AOGCM output when one wants to do a number of runs, e.g. with different forcings of the AOGCM, but the AOGCM is so complex that it takes a very long time even with today’s computer technology to produce output from one run, much less many runs. For example, Castruccio et al. (2014) fit the equation Tt = β0 + β1

  k=t  1 CO2,t−1 CO2,t−k CO2,t + ln ρ k ln + εt ln + β2 (1 − ρ) 2 CO2,0 CO2,0 CO2,0 k=2

εt = φεt−1 + σ zt , {zt } I I DN (0, 1) T0 given, CO2,t concentration of CO2 at t, CO2,0 preindustrial concentration, to regional yearly temperature data generated by their AOGCM for one scenario to “train” their emulator. They then use their estimated equation for that scenario to mimic the output of their AOGCM for another scenario. They carry out this procedure for 47 regions (see Table S1 of Castruccio et al. (2014) supplementary material for estimates). Their performance measure suggests that the emulator does a fairly good job of mimicking the output of the much more complicated AOGCM. Castruccio et al. (2014, Fig. 6) displays the emulated temperatures with the top of the display corresponding to northern latitude regions and the southern latitude regions at the bottom. The pattern of higher temperatures in the northern latitude regions compared to the southern latitude regions is clear. Pattern scaling is advocated and explained by Castruccio et al. (2014) as a method to obtain output for smaller scales using the emulated output at the large scales. Emulation has advantages over the Matthews et al. (2009) and Leduc et al. (2016) approximate relationship between cumulative emissions and temperature change. Climate scientists argue that the Matthews et al. (2009, 2012), Leduc et al. (2016) approximations are more appropriate to longer time scales than yearly, whereas emulation can mimic the output of AOGCMs at shorter time scales like yearly. Yearly time scales are more appropriate for economic analysis. Brock and Xepapadeas (2017) exhibited a plot at time scales appropriate to economic modeling of climate change using MacDougall and Friedlingstein’s (2015) equations that lie behind the Matthews et al. (2009, 2012) approximation of temperature response to cumulative emissions. While their plot was approximately linear at the yearly time scale which supports using the Matthews et al. (2009, 2012) approximation at the yearly time scale, future research should use better approximations of temperature response to cumulative emissions at the yearly time scale. Furthermore emulation plus pattern scaling can mimic the output of respected AOGCMs at smaller time scales and smaller spatial scales much better than simple approximations like Matthews et al. (2009) and Leduc et al. (2015, 2016) as well as doing a much better job of mimicking the output of AOGCMs than the simple Energy Balance Models used in our own research. However these advantages are not free. Ideally in order to optimize an economic model we would need to have emulations for each

5 Energy Balance Climate Models and Spatial Transport Phenomena

of a large enough set of intertemporal forcings to approximate the optimal solution of an economic model. Future research should use the work on emulators to get a better model of climate dynamics in climate economics models, with more attention spent on modeling climate dynamics at smaller intertemporal and spatial scales. For example, Hsiang et al. (2017) have recently shown for the U.S. at the county level that damages show a clear pattern of more damages for southern counties compared to northern counties.

5.2 DISCOUNTING FOR CLIMATE CHANGE There is a substantial literature on the choice of the discount rate, or the consumption discount rate, which is appropriate for discounting future costs and benefits which are associated with environmental projects (e.g., Arrow et al., 1996; Weitzman, 1998b, 2001; Newell and Pizer, 2003). In this section we show how the approach of cumulative carbon budgeting can be used to adjust the consumption discount rate in order to take climate change into account. The consumption discount rate can be defined by the equilibrium condition in two equivalent ways: (i) following Arrow et al. (2012a, 2012b, 2014) and considering a social planner who would be indifferent between $1 received at time t and $ε received today when the marginal utility of $ε today equals the marginal utility of $1 at time t , or (ii) following Gollier (2007) and considering a marginal investment in a zero coupon bond which leaves the marginal utility of the representative agent unchanged. Assuming that the utility function of the representative agent depends on consumption and damages associated with the time path of global average temperature U = u (c (t) , T (t)) ,

(75)

the equilibrium condition associated with the Arrow et al. (2014) approach implies that εuc (c (0) , T (0)) = e−ρt uc (c (t) , T (t)) , or ε=

e−ρt uc (c (t) , T

(t)) = e−rt t , uc (c (0) , T (0))

(76) (77)

where rt denotes the annual consumption discount rate between periods 0 and t, and ρ is the utility discount rate. The equilibrium condition associated with the Gollier (2007) approach implies that uc (c (0) , T (0)) = e−ρt uc (c (t) , T (t)) ert t ,

(78)

where rt is interpreted as per period rate of return at date 0 for a zero coupon bond maturing at date t . Both approaches are equivalent for determining the consumption discount rate. Assume, as is common in this case, a constant relative risk aversion utility function 1−η 1  , 0 < η < ∞, (79) c (t) e−DT (t) u (c (t) , T (t)) = 1−η

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CHAPTER 1 Coupled climate and economic systems

where η is both the coefficient of relative risk aversion and (minus) the elasticity of marginal utility with respect to consumption. Then using equilibrium condition (78), the Matthews et al. (2009) and Matthews et al. (2012) framework where T˙ (t) = λE (t) implies that  d d  ln uc (c (t) , T (t)) = ρ − −ηc (t) − (1 − η) DT (t) dt dt rt = ρ + ηg (t) + (1 − η) DλE (t) ,

rt = ρ −

(80) (81)

where g (t) = c´ (t) /c (t) is the consumption rate of growth, ρ + ηg (t) is the standard Ramsey discount rate, and the term (1 − η) DλE (t) is the climate change adjustment to the Ramsey rule for discount rate. The sign of the adjustment depends on the value of η. Regarding this value, Mehra and Prescott (1985) suggest that a value above 10 is not justifiable, while Dasgupta (2008) suggests that values of η in the region of 1.5 to 3 would be reasonable.13 Thus values of η greater than 1 are plausible, and therefore in such cases climate damage effects cause market discount rates to be smaller than the Ramsey rule. Since the effect is larger the larger are D and λ and the emissions path E (t), the plausible assumption that the world will continue increasing emissions before they finally start to decrease (e.g., see Pierrehumbert, 2014, Fig. 1) implies that the effect of climate change on market discounting in (81) could be quite large for η greater than 1. Consider now the case where spatial considerations are explicitly introduced by allowing for spatially dependent welfare weights w(x) along the lines of welfare weights introduced in section 5, and spatial differentiation of damages, so that the utility function is defined as  U = u (c (x, t) , T (x, t)) = w (x)

c (x, t) e−D(x,T (t)) 1−η

1−η .

(82)

The term D (x, T (t)) can be regarded as shorthand for the impact of the global heating of the Earth on damages at location x, which includes heat transport effects as in the EBCMs discussed in Brock et al. (2013) and Brock et al. (2014b). The equilibrium condition associated with the Arrow et al. (2014) approach implies that  −ρt uc (c (x, t) , T (x, t)) dx Xe (83) = e−rt t . u 0) , T 0)) dx (c (x, (x, c X Using the specific utility function we obtain      −η −(1−η)D(x,T (t)) w c t) dx e (x) (x, 1  rt = ρ − ln  X , or −η−η −(1−η)D(x,T (0)) t dx e X w (x) c (x, 0)

(84)

13 Note that Cline (1992) uses ρ = 0, η = 1.5, Nordhaus (1994) ρ = 3%, and η = 1, Stern (2006)

ρ = 0.1%, η = 1. See Dasgupta (2008) for a detailed discussion of these assumptions.

5 Energy Balance Climate Models and Spatial Transport Phenomena

rt = ρ −

d ln dt

   w (x) c (x, t)−η e−(1−η)D(x,T (t)) dx .

(85)

X

This can be regarded as an average global consumption discount rate between periods 0 and t , that a social planner will use for cost benefit calculations over the entire spatial domain. The location specific discount rate can be determined by using the equilibrium condition (81) to obtain d ln uc (c (x, t) , T (x, t)) , or dt ∂D (x, T (t)) λE (t) . rt (x) = ρ + ηg (t, x) − (1 − η) ∂T rt (x) = ρ −

(86) (87)

In this case the consumption discount rate in a certain location depends on the location specific consumption rate of growth and the damages due to climate change associated with the location.14 It should be noted however that if there is a world capital market, arbitrage would force the local rates rt (x) equal to a global market rate rt . A thorough analysis of this would need to model borrowing and lending in each location in world capital markets. Of course, if for some reason each x is treated as a closed economy, then rt (x) would be the equilibrium rate inside that “country” x. This analysis could be an interesting area for future research. Another, perhaps more important, area for future research on the impact of climate change on discounting would be to reorganize discussion of discounting in climate and environmental economics around the central notion of the stochastic discount factor process and to try to understand the influence of climate change and environmental factors on the intertemporal structure of the stochastic discount factor process. Useful references are Dietz et al. (2016, 2018) and Lemoine (2017). In finance, John Cochrane (2011, p. 1091) says “Discount rates vary a lot more than we thought. Most of the puzzles and anomalies that we face amount to discountrate variation we do not understand. Our theoretical controversies are about how discount rates are formed. We need to recognize and incorporate discount-rate variation in applied procedures. We are really only beginning these tasks. The facts about discount-rate variation need at least a dramatic consolidation. Theories are in their infancy. . . . Throughout, I see hints that discount-rate variation may lead us to refocus analysis on prices and long-run payoff streams . . . ”. Elsewhere in his address, Cochrane (2011) discusses the search for factors to explain the time variation and cross sectional variation in discount rates for different kinds of assets. Brock and Hansen (2017) discuss the potential role climate change may play in long-term risks and, hence, long-term impacts on the stochastic discount factor process.

14 The utility discount rate ρ and elasticity of marginal utility η are assumed to be the same across locations. This assumption can easily be relaxed.

31

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CHAPTER 1 Coupled climate and economic systems

It is beyond the scope of this chapter to say more here except to urge future researchers to try to use more of the recent research progress in macro-finance in addressing discounting issues in environmental economics and climate economics.

6 SPATIAL ASPECTS IN ECONOMIC/ECOLOGICAL MODELING In section 5 we introduced EBCMs as a tractable way to model spatial effects in local temperatures. While spatial effects are a very important aspect of climate change economics, their importance is extended to a large number of areas related to environmental and resource economics (e.g. Wilen, 2007; Brock and Xepapadeas, 2010; Xepapadeas, 2010; Kyriakopoulou and Xepapadeas, 2013; Brock et al., 2014c, 2014d, 2014f) but also to other areas. Biology has been an area where spatial effects in the context of mechanisms generating form, or spatial patterns, have been extensively studied. The question of ‘how the leopard got its spots’ has been central to this type of analysis (e.g., Levin and Segel, 1985; Okubo and Levin, 2001; Murray, 2003). In economics, spatial patterns in a static framework have been extensively studied in the context of new economy geography (e.g., Krugman, 1996; Fujita et al., 1999; Baldwin et al., 2001; Fujita and Thisse, 2002). Recent research in this area explicitly studies spatial dynamics agglomeration formation in models of competitive industries and models of economic growth (Boucekkine et al., 2009, 2013; Brock et al., 2014c, 2014f). In environmental and resource economics, the spatial dimension has been introduced mainly in the context of fishery management with the use of metapopulation models to study harvesting rules or reserve creation (e.g., Sanchirico and Wilen, 1999, 2001, 2005; Smith and Wilen, 2003; Sanchirico, 2005; Wilen, 2007; Costello and Polasky, 2008). More recently Brock and Xepapadeas (2005, 2008, 2010) and Brock et al. (2014e), by using continuous spatial dynamic processes (see also Smith et al., 2009), generalized the concept of Turing diffusion-induced instability to dynamic optimization problems and studied pattern formation and agglomeration emergence in optimal control problems with applications to resource management. It is interesting to note that the spatial pattern of local temperatures in models of climate and the economy can be studied in the same general context with models studying interactions in natural, economic or unified systems of ecosystems and the economy, which evolve in time and space. Uncertainty or ambiguity related to concerns about model misspecification and robust control approaches discussed in the previous sections can be naturally extended to spatial settings. In this case, a situation emerges in which a decision maker or a regulator distrusts his/her model and wants good decisions over a cloud of models that surrounds the regulator’s approximating or benchmark model, but these concerns have a spatial structure and may differ across locations given the characteristics and structure of the problem. The problem of spatially structured uncertainty has been studied by Brock et al. (2014e) in which a central result is the development of spatial

7 Future Directions

robust control regulation, and the potential emergence of spatial hot spots, which are locations where the spatial structure of uncertainty causes regulation to break down. In Appendix B we use methods that allow us to obtain a deterministic robust control problem (Campi and James, 1996; Anderson et al., 2012, 2014) to study spatially extended models of ecosystems and economy. The purpose is to show how models with spatially structured ambiguity can be developed and explicitly solved in order to obtain spatially dependent robust control rules, and explore the potential emergence of hot spots. The technical analysis in the Appendix is useful for understanding how computational methods are developed to deal with infinite dimensional spatial models in infinite horizon optimization. For example linear operators like the diffusion operator in the ECBMs of North et al. (1981) and in the textbook on ECBMs by North and Kim (2017).

7 FUTURE DIRECTIONS The literature on climate economics models is huge; this chapter has reviewed only a relatively narrow slice of work on climate economics models in which space and distributional questions play a major role. We think that the tools and methods presented in this review, using climate economics as the main vehicle, provide useful insights about the way to model coupled ecosystems and economic systems. In this section we become even more speculative and discuss potential future directions that research might take.

7.1 BOTTOM UP IMPLEMENTATION RATHER THAN TOP DOWN IMPLEMENTATION Ostrom (2009) has stressed the problems inherent in any kind of top down central authority organizing effective adaptation and policy measures in a massive collective action problem like global climate change. Indeed the climate management problem could be labeled, “The Mother of all Collective Action Problems”. This is so because the spillover effects are world-wide. Given the difficulties of organizing any kind of collective action at such a large scale, Ostrom argues for a bottoms up approach in what she calls a polycentric approach, in which entities at multiple scales adapt and respond individually. For example, California, which is bigger than a lot of countries, has instituted strong responses to climate change on its own. Since California tends to be a world leader, its example may prompt others to take action. This is a good place to discuss adaptation as well as mitigation in dealing with climate change. Adaptation has the attractive feature that its benefits tend to be local so that any unit of government at any scale that bears costs of adaptation will also capture its benefits at the local scale. For example, a unit of government at the scale of a beach front that taxes beach front owners to pay for adaptation to storm surges serves a public that benefits directly from that adaptation when the next storm surge hits that beach front community. This “scale matching” of benefits and costs of adap-

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CHAPTER 1 Coupled climate and economic systems

tation is absent in the case of mitigation. In the case of mitigation, a nation or state that pays costs of mitigation ends up benefiting the whole planet and, hence, failing to capture the full benefits of its contribution. As units of government at different scales struggle to organize collective action on adaptation, this may lead to formation of effective institutions that might be leveraged to organize collective action on large scale issues such as mitigation. We see this kind of work, given the lead of Ostrom, as especially promising in the study of potentially effective policy actions to deal with global climate change. In particular the benefits from adaptation can be quite large relative to costs, e.g. it can be quite dramatic as documented by de Bruin et al. (2009) in the context of the DICE model modified for adaptation, which they dub AD-DICE. At smaller scales than DICE or even RICE’s regional scales, Deschênes and Greenstone (2007, 2011) document climate damages at smaller scales. The recent report, “Heat In The Heartland” (Gordon, 2015), projects climate damages at smaller scales for the U.S. Midwest. As coping and adaptation develops at smaller scales, it is feasible that units of government will form at scales of spillover externalities (e.g. river authorities to manage increased flooding from climate change and water management authorities to manage increased stress on aquifers). As these units of government form, it is plausible to imagine that they might cooperate to manage externalities that spill across their boundaries. Thus we believe that an especially fruitful area of future research is to draw on work such as Ostrom (2009) for endogenous institution formation at various scales, work like Deschênes and Greenstone (2007, 2011) for documentation of climate damages at various scales, and work on adaptation at various scales to try to understand what institutions are likely to form at what scales.

7.2 STOCHASTIC MODELING AND COMPUTATIONAL APPROACHES Climate models come in a hierarchy ranging from the simplest models of energy balance (North, 1975a, 1975b; North et al., 1981), energy and moisture balance (Fanning and Weaver, 1996), which can be solved analytically, to models that are larger but still small enough that their mechanisms can be comprehended with a combination of analytical and computational work. Examples of the latter are Nordhaus’s (2008, 2013) DICE and RICE models and the DSICE model of Cai et al. (2012a, 2012b, 2012c, 2013a, 2013b) and Cai et al. (2014), which contrast with the big General Circulation Models (Weaver et al., 2001). An important area for future research would be to extend work on the coupled heat balance EBCMs and economic models of Brock et al. (2013) and Brock et al. (2014a, 2014b) to coupled heat and moisture balance EBCMs like the Fanning and Weaver (1996) model. This approach adds to the PDE describing the dynamic evolution of temperature across latitudes, and a second one describing the evolution of surface specific humidity at latitude x. Human actions take the form of emissions of GHGs and geoengineering that blocks incoming short-wave radiation. The advantage of this approach would be to provide more insights into the spatial impacts of climate change and the associated policies in terms of temperature precipitation and evaporation. This research would fit well with the work recently developed by Brock et

7 Future Directions

al. (2014d, 2014e) on spatial hot spots, which are locations where regulation breaks down due to deep structural uncertainty. Hot spots indicate locations where damages might be excessive and extra attention is required by regulators. Hot spot research regarding changes in precipitation and evaporation at localized scales may be more important than hot spot research regarding temperature changes at smaller scales. Local damages can be modeled by damage functions of the form exp[−D(x, t)T (t)], which have been useful in characterizing spatial discounting.

7.3 BIFURCATIONS AND TIPPING POINTS Cai et al. (2012b) extend their DSICE model to include tipping points which may or may not be caused by bifurcations. However, they do not treat spatial transport or space itself in their model. We see a particularly promising line of research to be that of extending the work of Lontzek et al. (2012) to include spatial transport phenomena. This kind of framework would be very useful for economic analysis of the risk of bifurcations and how much it might be worth to society to avoid such risks. A major concern in spatial settings when compensatory transfers are not available is inequalities of burdens of future climate change across the globe. Recent papers have appeared on potential bifurcations of Arctic Sea ice (Eisenman and Wettlaufer, 2009; Abbot et al., 2011). One potential value of spatial transport modeling is that it might augment the case for different policies treating GHGs that have short lives in the atmosphere but much higher GWPs compared to GHGs like CO2 emitted from coal and oil usage that have very long lives in the atmosphere. To explain further if there is a relatively short-term immediate “damage reservoir” threat like a potential bifurcation of Arctic Sea ice, it might make sense to tax short-lived GHGs with very large GWPs like methane emissions at a temporary higher rate to slow down current global warming even though the extra consumption of fossil fuels with long-lived GHGs will result in more damaging warming in the long-term future. The framework used by Brock et al. (2014b) and Brock et al. (2013) which couples economic models with energy balance models with spatial energy transport, could be extended to GHGs with different lives in the atmosphere and different GWPs. Brock et al. (2013) includes the phenomenon of polar amplification, while Brock et al. (2014a) includes a damage reservoir that is present because of an endogenous ice line as in the papers by North (1975a, 1975b). North’s bifurcations are not the same as the bifurcations discussed in Eisenman and Wettlaufer (2009) and Abbot et al. (2011), but are related in mathematical structure. We believe that this kind of framework could shed light on the temporal spatial structure of optimal policy intervention on emissions of GHGs with different lives in the atmosphere and different GWPs. For example, while there are strong arguments for uniform taxes on a unit of emissions independent of location, especially if costless compensatory transfers are available for poorer areas, Pierrehumbert’s (2014) argument which we discussed earlier reminds us that short-lived GHGs with relatively large GWPs should be treated differently than long-lived GHGs like CO2 . Local bifurcations and local tipping points might be sources of extreme local events that are accentuated and magnified by climate change. Leeds et al. (2013)

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CHAPTER 1 Coupled climate and economic systems

have done work on simulating future climate under changing covariance structures. They discuss forcing by spatial stochastic processes with thicker tails than the spatial white noise processes used by, for example, Kim and North (1992) in their spherical energy balance model. Later versions of spherical spatial energy balance models used by Brock et al. (2013) have polar amplification effects. We believe that a useful direction for future research would be to include the bifurcation possibility of Abbot et al. (2011) and the resulting impact on damages across space and to compare the changing spatial covariance structure that results with the findings of Leeds et al. (2013). In the same context, designing an optimal “Tech Fix” path to a sustainable low carbon economy is an area of promising future research (David and van Zon, 2014).

APPENDIX A A.1 ROBUST CONTROL METHODS To provide a more formal presentation, let the set of states of the world be , and consider an individual observing some realization ωt ∈ . The basic idea underlying the multiple priors approach is that beliefs about the evolution of the process {ωt } cannot be represented by a probability measure. Instead, beliefs conditional on ωt are too vague to be represented by such a single probability measure and are represented by a set of probability measures (Epstein and Wang, 1994). Thus for each ω ∈ , we consider P (ω) as a set of probability measures about the next period’s state.15 The individual ranks uncertain prospects or acts α. Let u be a standard utility function. The utility of any act α in an atemporal model is defined as (Gilboa and Schmeidler, 1989; Chen and Epstein, 2002)  (88) U (c) = min u (α) dQ, Q∈P

while in a continuous time framework, recursive multiple prior utility is defined as:   T −ρ(s−t) e u (α) ds . (89) Vt = min EQ Q∈P

t

These definitions of utility in the context of multiple-priors correspond to an intuitive idea of the ‘worst case’. Utility is associated with the utility corresponding to the least favorable prior. With utility defined in this way, decision making by using the maxmin rule follows naturally, since maximizing utility in the multiple-priors case implies the maxmin criterion. Given the set of probability measures P, the decision maker considers the reference probability measure P and another measure Q ∈ M ( ). The discrepancy 15 Formally P is a correspondence P : → M ( ) assumed to be continuous, compact-valued and

convex-valued and M ( ) is the space of all Borel probability measures.

A

between the two measures is determined by the discounted relative entropy    +∞ 1 2 −δt R(Q//P) = e EQ ht dt, 2 0

(90)

where h is a measurable function associated with the distortion of the probability measure P to the probability measure Q. To allow for the notion that even when the model is misspecified the benchmark model remains a “good” approximation, the misspecification error is constrained. Thus we only consider distorted probability measures Q such that    +∞ 1 R(Q//P) = e−δt EQ h2t dt ≤ η < ∞. (91) 2 0 Using (91) as the entropy constraint, Hansen and Sargent (2008) define two robust control problems, a constraint robust control problem and a multiplier robust control problem. Using problem (1) as reference the constraint robust control problem is written as:  ∞ e−ρt u(c (t) , x (t) )dt (92) max min E0 c(t) h(t)

t=0

subject to d (x) = [F (x (t) , c (t) ) + σ (x (t) h (t))] dt + σ (x (t)) dZ (t) , x(0) = x0 and (91),

(93) (94) (95)

where {Z (t) , t ≥ 0} is a Brownian motion in the underlying probability space ( , F, P) and h (t) is a measurable drift distortion which reflects the fact that the probability measure P is replaced by another measure Q. The drift distortion incorporates omitted or misspecified dynamic effects on the dynamics of the state variable. The multiplier robust control problem is defined as:    ∞ 1 e−ρt u(c (t) , x (t) )+ θ h2 (t) dt (96) E0 2 t=0 (97) subject to (94) and x(0) = x0 . In both extremization problems, the distorting process h (t) is such that allowable measures Q have finite entropy. In the constraint problem (92), the parameter η is the maximum expected misspecification error that the decision maker is willing to consider. In the multiplier problem (96), the parameter θ , which is called the robustness parameter, can be interpreted as a Lagrangean multiplier associated with entropy constraint (91). Our choice of θ lies in an interval (θmin , +∞), where the lower bound θmin is a breakdown point beyond which it is fruitless to seek more robustness. This is because the minimizing agent is sufficiently unconstrained that he can push the criterion function to −∞ despite the best response of the maximizing agent. Thus when θ ≤ θmin , robust control rules cannot be attained. On the other hand, when θ → +∞,

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or equivalently η = 0, there are no concerns about model misspecification and the decision maker may safely consider just the benchmark model. As stated in the main text, the multiplier robust control problem, which is the more analytically tractable of the two, is solved by using the Hamilton–Jacobi–Bellman– Isaacs (HJBI) condition (Fleming and Souganidis, 1989)  1 (98) ρV (x) = max min u(c (t) , x (t) )+ θ h2 (t) c(t) h(t) 2  1 + V  (x) [F (x (t) , c (t) ) + σ (x (t) h (t))] + σ 2 (x (t)) V  (x) , 2 where V (x) is the value function for the problem, and ρV (x) = maxc(t) minh(t) {·} = minh(t) maxc(t) {·} under the conditions described in Hansen et al. (2006, Appendix D). Solution of problem (98) will determine the optimal robust paths (c∗θ (t) , x ∗θ (t)) for a given level of robustness θ . When θ → ∞ the regulator is not concerned about model misspecification and regards the benchmark model as adequate.

A.2 THE CASE OF ADDITIVE UNCERTAINTY While we believe that the case of multiplicative uncertainty that we treated in the main text does a better job of reflecting the model uncertainty, i.e. the variation in the CCR parameters across respected climate models discussed by Matthews et al. (2009) and Gillett et al. (2013), for completeness we treat an example of additive uncertainty in this Appendix. Consider the following deterministic robust control problem which is a drastic simplification of the model of Daniel et al. (2014) but with robustness added:   ∞ −ρt α 2 e (u(yE ) + (1/2)θ v )dt (99) max min E

v

t=0

subject to T˙ = λE + Cv, T (0) = T0

(100)

for the dynamics of GMT, denoted here by T (t) for each date t , and, R˙ = −E, R(0) = R0 S˙ = −T˙ = −(λE + Cv), S(0) = Tc − T0

(101)

S(t) ≡ Tc − T (t) for the dynamics of fossil fuel usage and the dynamics of the “safety reserve” S(t) ≡ T (t) − Tc . Although robustness is typically associated with stochastic models, deterministic models can be derived from stochastic robustness models by scaling the robustness parameter with the standard deviation of stochastic forcing shocks

A

and then taking the standard deviation to zero in a type of “small noise” approximating procedure (Anderson et al., 2014). This type of procedure leads to problem (99)–(101). We say more about this later but treat deterministic problems for now. Note that the requirement that S(t) ≥ 0 for all dates t translates into Eq. (102) for the central case, Tc = 2 °C. Here y = y(t) is an exogenously given function which is augmented by fossil fuel input E α , 0 < α ≤ 1 to give total consumption, y(t)E(t)α at each date t. The utility function u(c) is assumed to be strictly concave, strictly increasing, twice continuously differentiable and to satisfy the usual Inada conditions, u (0) = ∞, u (∞) = 0. At the risk of repeating, what we have done with (101) and the requirement S(t) ≥ 0 is this. Rather than attempting to specify a detailed parameterized damage function, we simply let the climate scientists specify Tc and impose the constraint  ∞ Tc ≥ (λE + Cv)dt. (102) t=0

As Hansen and Sargent (2008) explain in their book, the presence of the minimizing agent is simply a device to help the maximizing agent design a policy that works well for a set of deviations around a baseline and the role of the parameter θ is to index the width of the set of deviations the maximizing agent wishes to robustify against. The equilibrium value of v in the problem (99) is the drift distortion that is most consequential for the robust planner. We refer the reader to Hansen and Sargent (2008) for detailed exposition of robustness in economic modeling. The idea here is that if T (t) > Tc happens at any date t , then catastrophic climate change may occur and the level of risk is unacceptable at a GMT equal to, Tc , e.g. 2 °C as in Held (2013). Hence we impose the constraint S(t) ≥ 0 to keep T (t) ≤ Tc for all dates t. When we want to illustrate with a particular value of Tc , we use the focal 2 °C benchmark for catastrophic climate change because it is the one commonly used in the literature. Of course when we solve the problem above for a candidate equilibrium, we need to check that S(t) ≥ 0 actually holds for all dates t ≥ 0 before we can actually proclaim that it is an equilibrium. We can use a smaller or larger benchmark and the same analysis used here will apply. Some climate scientists might select a larger (smaller) threshold temperature if they were doing cumulative carbon budgeting. We interpret the literature as saying that many researchers have the same concerns about the levels of deep uncertainty in the layers upon layers of assumptions built into the IAMs that Pindyck (2013a, 2013b) has in economics and researchers like Curry and Webster (2011) have in climate science. The robust control specification (99) and (100) is an attempt to capture the model uncertainty emphasized by Matthews et al. (2009) and Matthews et al. (2012) in their discussion of the CCR parameter. An alternative specification of (100) is T˙ = (λ + Cv)E, T (0) = T0 ,

(103)

where the term (λ + Cv) is a more direct representation of the uncertainty of the CCR parameter discussed in Matthews et al. (2009) and Matthews et al. (2012). We will

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call (103) multiplicative uncertainty and (100) additive uncertainty. If specification (103) is used, Eq. (101) and the constraint (102) are replaced by S˙ = −(λ + Cv)E, S(0) = S0 = T0 − Tc  ∞ Tc ≥ (λ + Cv)Edt.

(104)

t=0

We solved the robust control problem with specification (104) in the main text. Note that Eq. (101) basically says that we have two reserves, a fossil fuel reserve and a safety reserve. Since both of these reserve dynamics in Eq. (101), R˙ = −E, R(0) = R0 , S˙ = −(λE + Cv), S(0) = S0 , imply the integral constraints  ∞  Edt ≤ R0 , t=0

∞

(λE + Cv)dt ≤ S0 ,

(105)

(106)

t=0

we could replace the dynamics (105) by the integral constraints (106) and treat our problem as a robust isoperimetric control problem. This approach may be easier in some applications. However, we use the reserve dynamics equations (105) here because for the non-robust case we see that our problem is just a standard exhaustible resource problem but with two reserves rather than just one. The FONCs for a dynamic Nash equilibrium of problem (99) are given from optimal control theory as H ≡ u(yE α ) + (1/2)θ v 2 + μR (−E) + μS (−λE − Cv) 0 = Hv = θ v − μS C 0 = HE = (uα )yαE α−1 − μR

(107)

μ˙ R = ρμR − HR = ρμR , μ˙ S = ρμS − HS = ρμS . Here is a simple result that follows directly from the FONCs (107). Result 1. If λR0 > Tc , then some of R0 is left in the ground. That is, some of the world’s fossil fuel reserves become worthless, i.e. the shadow price function μR (t) of fossil fuels must be zero. Proof. The proof is by way of contradiction. From (107), μR (t) = μR (0)eρt . Hence if μR (0) > 0, then all of the reserve R0 is exhausted as t → ∞, hence, if we use specification (102), recalling that we show below that the FONCs for v(t) imply v(t) ≥ 0 for all t, we have  ∞  ∞ (λE + Cv)dt = λR0 + C vdt > λR0 . (108) Tc ≥ t=0

t=0

A

But (108) is a contradiction to λR0 > Tc . If we use specification (104) and modify the FONCs (107), we have  ∞  ∞ (λ + Cv)Edt = λR0 + C Evdt > λR0 , (109) Tc ≥ t=0

t=0

which is a contradiction just as above. The requirement that limt→∞ T (t) ≤ Tc and the dynamics of global average temperature specified in (100), above as well as the FONCs requiring v(t) ≥ 0 for all dates t, are what really drive this result. Note that the result is independent of the presence of a minimizing agent, i.e., it holds even if C = 0 or θ = ∞. The presence of the minimizing agent just makes the bound on how much of the initial reserve can be used tighter. Recently some organizations have received a lot of publicity over the idea that known reserves of fossil fuels are already so large that some of the known reserves are at risk of becoming wasted assets (e.g. Carbon Tracker, http://www. carbontracker.org/). Hence, it is useful, as a thought experiment, to analyze the case where some of the known reserves will be left in the ground. Here we focus on the case where Assumption 1 below holds. Assumption 1. λR0 > Tc , i.e., Result 1 holds. If the utility function u(c) = ln(c), we may solve the FONCs for a closed form solution. The FONCs for this special case become, H ≡ ln(y) + α ln(E) + (1/2)θ v 2 + μR (−E) + μS (−λE − Cv) 0 = Hv = θ v − μS C 0 = HE = α/E − μR − λμS μ˙ R = ρμR − HR = ρμR , μ˙ S = ρμS − HS = ρμS .

(110)

We start the procedure of solving Eqs. (110) under Assumption 1 in order to uncover sufficient conditions that need to be imposed to reach a solution, recalling that Assumption 1 implies μR (0) = 0,  S0 =

∞

(λα/(μR + λμS ) + C 2 μS /θ )dt  ∞  ∞ 2 −ρt (α/μS + C μS /θ )dt = e (α/μS (0))dt + (eρt C 2 μS (0)/θ )dt = t=0 t=0 s=0  ∞ (eρt C 2 /θ )dt. = α/(ρμS (0)) + μS (0) t=0 ∞

s=0

(111)

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Hence, in order to obtain a solution, we need to impose conditions that imply,  ∞ (eρt C 2 /θ )dt < ∞. (112) s=0

One route is to assume θ is constant and to require that the function C(t) satisfy  ∞ eρt C 2 dt < ∞. (113) s=0

Motivated by (113) we assume the following. Assumption 2. C(t) = C0 e−φt , ρ − 2φ < 0. Under Assumptions 1 and 2 we arrive at the equation S0 = α/(ρμS (0)) + C02 μS (0)/(θ (2φ − ρ)),

(114)

which can be written in the equivalent form, C02 μS (0)2 /(θ (2φ − ρ)) − μS (0)S0 + α/(ρ) = 0

(115)

with roots μS (0) = [S0 ± D 1/2 ]/[2(C02 /θ(2φ − ρ))] D ≡ S02 − 4(α/ρ)(C02 /θ(2φ − ρ)).

(116)

We next make the following assumption. Assumption 3. The roots of (115) are real. Therefore D ≥ 0, i.e., S02 − 4(α/ρ)(C02 /(θ (2φ − ρ))) ≥ 0.

(117)

Note that given the values of the other parameters, (117) holds if θ > θc where θc solves the equation D = 0. In analogy with work on robust control in economics (e.g., Hansen and Sargent, 2008), we call θc the breakdown point. We select the negative root since it agrees with the non-robust solution μS (0) = α/(ρS0 ),

(118)

i.e. the solution when θ = ∞. This can be seen by applying L’Hôpital’s Rule to the limit by taking 1/θ → 0. The dynamics of the candidate solution for the safety reserve are given by ˙ = −T˙ (t) = −α/μS (t) − C 2 (t)μS (t)/θ, S(t) = −(α/μS (0))e−ρt − C 2 (0)μS (0)e(ρ−2φ)t /θ S(0) = Tc − T0 ≡ S0 S(t) ≡ Tc − T (t).

(119)

A

We call the solution (119) a candidate solution because one must check that the solution satisfies S(t) ≥ 0 for all positive dates. It can be shown that for θ large enough, solution (119) satisfies S(t) ≥ 0 for all positive dates. The proof uses (118) and the negative root goes to zero as θ → ∞. The distortion to the dynamics of temperature induced by the robust planner is C 2 (0)μS (0)e(ρ−2φ)t /θ,

(120)

i.e., the robust planner twists the temperature dynamics towards higher temperatures to induce the economy towards smaller use of fossil fuels compared to the non-robust case θ = ∞. Note that a solution to the simple non-robust case requiring that S(t) ≥ 0 for all dates t is analytically equivalent to an exhaustible resource problem where the reserve, R0 , is replaced by the adjusted reserve, Tc /λ. We must deal with one more issue before turning to a discussion of implementation and that is time consistency.

A.3 TIME CONSISTENCY ISSUES OF SOLUTIONS TO ZERO SUM ROBUST CONTROL GAMES Let, for any date t , S(t|S0 ) denote the solution to the dynamic zero sum game (99) starting with initial condition S0 . If t2 > t1 > 0 are any two dates, for time consistency we must check the property S(t2 |S(t1 |S0 )) = S(t2 |S0 ).

(121)

That is to say that the players will choose to play the same equilibrium value at date t2 starting from initial condition S(t1 |S0 ) at date t1 with t2 − t1 periods “to go” as the players will choose to play with the full t2 periods to go starting from date zero. We compute (121) to check if and when it holds.  S(t2 |S0 ) = S0 − (α/μS (0))

t2

dte−ρr − C 2 (0)μS (0)



r=0

t2

dte(ρ−2φ)r /θ

r=0

= S0 − (α/(ρμS (0)))[1 − e−ρt2 ] − (C 2 (0)μS (0)/(θ (2φ − ρ)))[1 − e(ρ−2φ)t2 ] S(t2 |S(t1 |S0 )) = S(t1 |S0 ) − (α/μS (t1 ))



t2

dte−ρr − C 2 (0)μS (t1 )

r=t1

(122)



t2

dte(ρ−2φ)r /θ

r=t1

= S(t1 |S0 ) − (α/(ρμS (t1 )))[1 − e−ρ(t2 −t1 ) ] − C 2 (0)μS (t1 )/(θ (2φ − ρ))[1 − e(ρ−2φ)(t2 −t1 ) ].

(123)

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If (122) and (123) behaved like solutions to an ODE, (121) would hold because it is a basic property of solutions of ODEs. However, here, the shadow price is μS (0) ≡ f (S0 ) = [S0 − D 1/2 ]/[2(C02 /(θ (2φ − ρ)))] ≡ [S0 − D 1/2 ]/(2a) a ≡ C02 /(θ (2φ − ρ)) D ≡ S02 − 4(α/ρ)(C02 /θ(2φ − ρ)) = S02 − 4ac

(124)

c ≡ α/ρ μS (t1 ) ≡ f (S(t1 |S0 )) = [S(t1 |S0 ) − D 1/2 ]/[2(C02 /θ(2φ − ρ))] D ≡ S(t1 |S0 )2 − 4(α/ρ)(C02 /θ(2φ − ρ)).

(125)

It seems pretty clear that unless C0 = 0 or 1/θ = 0, i.e. we are back in the pure non-robust, non-distorted dynamics case, the time consistency condition S(t2 |S(t1 |S0 )) = S(t2 |S0 ) will not hold. This problem is a common difficulty with the open loop concept of Nash equilibrium used here. Unless one is willing to take the view that this kind of equilibrium can be used as a rolling plan where the planner re-solves the system at each date t and does not worry about whether what it had planned to do at a later time based upon a plan made at an earlier time is actually desirable when a new plan is drawn up at an intermediate time, then the open loop concept of equilibrium here is not satisfactory. As shown in Kossioris et al. (2008), re-optimization might also be necessary in order to reach the best steady state, even if we consider nonlinear feedback Nash equilibrium strategies. Re-optimization takes place in the following sense. Given an initial state, the feedback Nash equilibrium strategy is calculated. This strategy will lead to a steady state which is not the best, after some time has elapsed the state of the system is estimated and the feedback strategy is recalculated using this state as an initial state. The process is continued until the calculated feedback strategies lead to the best steady state. We view our results here as a very rough preliminary insight into what conclusions from robust planning under carbon budgeting may look like. Future research should attempt to develop time consistent concepts of dynamic Nash equilibrium for use in robust planning. It is also useful to investigate the equilibrium value of the planner’s objective for the log utility example worked out above. We have:  ∞ e−ρt α ln(e−ρt α/(λμS (0)))dt = (α/ρ){ln(α/λ) − ln(μS (0))} V (S0 ) ≡ t=0  ∞ e−ρt αρte−ρt dt. (126) − t=0

Recall from (126) that μS (0) = f (S0 ). We explore the shape of the equilibrium value function by computing, V  (S0 ), V  (S0 ), V  (S0 ) = −(α/ρ)f  (S0 )/f (S0 ) V  (S0 ) = −(α/ρ){f  (S0 )/f (S0 ) − f  (S0 )2 /f (S0 )2 }.

(127)

A

It is easy to check that f  (S0 ) < 0. Hence, V  (S0 ) > 0, which is what would be expected from the economics. It appears that V  (S0 ) might have either sign. For the case θ = ∞ it is easy to check that μS (0) = α/(ρS0 )  ∞ e−ρt α ln(e−ρt α/(λμS (0)))dt = (α/ρ){ln(α/λ) − ln(μS (0))} V (S0 ) ≡ t=0  ∞ e−ρt αρte−ρt dt = k0 + (α/ρ) ln(S0 ), (128) − t=0

where k0 is a constant. Hence V (S0 ) is concave increasing which is what would be expected in this non-robust case, because it is essentially the same as a standard exhaustible resource problem.

A.4 CLIMATE CHANGE POLICY WITH MULTIPLE LIFETIME FOR GREENHOUSE GASES As mentioned in the main text, Pierrehumbert (2014) suggested that policy should take into account the lifetime of the GHGs, in addition to their GWP. For example, methane has a much shorter lifetime but a higher GWP than CO2 . This part of our climate economics section explores policy on multiple lifetime gases in the context of a simple energy balance model with forcing determined by stocks of two GHGs, #1 with infinite life and #2 with short life but larger GWP, modeled as in the Eqs. (130)–(131) below which abstract from the spatial considerations presented in section 6. We represent the problem and the different effects of the two gases introduced below in a very stark way and caution the reader thus. Notation is close to that in section 6. Furthermore, instead of a limit temperature Tc , we have introduced a damage function in (129). The positive value of β > 0 penalizes increases in global mean temperature by loss of consumable output. Consider the following problem:   ∞ e−ρt u(y(t)(E1 (t) + E2 (t))α e−β(T (t)−T0 ) )dt (129) max {E1 (t),E2 (t)}

t=0

subject to C T˙ (t) = −BT (t) + ξ ln[(M1 (t) + N M2 (t))/(M1 (0) + N M2 (0))], T (0) = 0 M˙ 1 (t) = b1 E1 (t) , M1 (0) = M10 > 0 given M˙ 2 (t) = −m2 M2 (t) + b2 E2 (t) , M2 (0) = M20 > 0, given R˙ 1 (t) = −E1 (t), R1 (0) = R10 , given R˙ 2 (t) = −E2 (t), R2 (0) = R20 , given.

(130)

(131)

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CHAPTER 1 Coupled climate and economic systems

For clarity of focus we study a polar case where GHG #1 stays in the atmosphere forever and GHG #2 decays according to m2 > 0, but the GWP of #2 is N > 1 times that of #1. Initially it might be thought that, in order to simplify the problem, we could also assume that the known reserves of the two sources of energy that produce emissions of the two GHGs are so large that the optimal costates will turn out to be zero. However, under the damage function above, this causes contradictions for any finite reserve, no matter how large, as we will show below. The Hamiltonian and FONCs for this problem for the log utility case are, putting M ≡ M1 + N M2 and dropping terms that are irrelevant for optimization, H = ln y + α ln(E1 + E2 ) − β(T − T0 ) + μM1 (b1 E1 )

(132)

+ μM2 (−m2 M2 + b2 E2 ) + μT [(−B/C)T + (ξ/C)] ln(M1 + N M2 ) − μR1 E1 − μR2 E2 . The FONCs of optimal control for (132) associated with the evolution of the costate variables which are interpreted as the shadow values of the corresponding stocks are: μ˙ T = (ρ + B/C)μT + β

(133)

μT (t) = −β/((ρ + B/C)) ≡ μ¯ T , for all t

(134)

μ˙ M1 = ρμM1 − ((ξ μ¯ T /C)(1/M))

(135)

μ˙ R1 = ρμR1  ∞ e−ρ(s−t) (ξ μ¯ T /C)(1/M(s))ds μM1 (t) =

(136)

μ˙ M2 = (ρ + m2 )μM2 − ((ξ μ¯ T /C)(N/M))  ∞ e−(ρ+m2 )(s−t) (ξ μ¯ T /C)(N/M(s))ds μM2 (t) = N

(138) (139)

μ˙ R2 = ρμR2 .

(140)

(137)

s=t

s=t

In (133)–(140) we write the differential equations and their forward solutions for the co-state variables for the two gases as well as for the temperature co-state variable. These are part of the solution for the optimal control problem. We always impose the usual transversality conditions which help pick out these solutions for the co-state variables. Note that the co-state variable solution for temperature turns out to be a constant in time. The Hamiltonian (132) can be written, after setting E := E1 + E2 , as H = ln y + α ln(E) + μM2 b2 E − μR2 E     + μM1 b1 − μR1 E1 − μM2 b2 − μR2 E1 − β(T − T0 ) − μM2 m2 M2 + μT [(−B/C)T + (ξ/C) ln(M1 + N M2 )].

(141)

A

Since the Hamiltonian is linear in E1 , we obtain the switching rule, E1 = 0, E2 = E, if b1 μM1 − μR1 < b2 μM2 − μR2 E1 = E, E2 = 0, if b1 μM1 − μR1 > b2 μM2 − μR2 .

(142)

One might think it is intuitive that the shadow prices of the reserves, μRi (0; ρ, R0i ), i = 1, 2 would go to zero as R0i → ∞, i = 1, 2, but it is not quite so simple. Eqs. (137) and (138) imply that the shadow prices grow at rate ρ from any positive initial value, no matter how small, so we must proceed with care. For example, at first glance, one might think that as ρ → 0, it would be obvious that the long-lived GHG, #1, would not be used, but the fact that the initial shadow prices of the reserves, μRi (0; ρ, R0i ), i = 1, 2, depend upon ρ and may even increase as ρ decreases, makes it difficult to actually prove precise results for this system. Nevertheless we may obtain some results and stay within the scope of this chapter. We do enough here to make a strong case that policy analysis for multiple lifetime GHGs is a very fruitful and important area for future research. Put ζ ≡ −ξ μ¯ T /C. Since μMi < 0, i = 1, 2, the switching rule (142) may be written in the more transparent “cost” form E1 (t) = 0, E2 (t) = E (t)   ∞ e−ρ(s−t) (ζ /M(s))ds + μR1 (0; ρ, m2 , R10 )eρt > if b1  s=t  ∞ e−(ρ+m2 )(s−t) (ζ /M(s))ds + μR2 (0; ρ, m2 , R20 )eρt b2 N

(143)

s=t

E1 (t) = E (t) , E2 (t) = 0   ∞ e−ρ(s−t) (ζ /M(s))ds + μR1 (0; ρ, m2 , R10 )eρt < if b1  s=t  ∞ e−(ρ+m2 )(s−t) (ζ N/M(s))ds + μR2 (0; ρ, m2 , R20 )eρt . b2 N s=t

The rule (143) says to use the GHG that is cheapest in terms of social marginal cost at each point in time. Pierrehumbert (2014) stresses that policy focus should be on mitigating emissions of the long-lived gas #1 which plays the role of CO2 in our model, in contrast to the short-lived gas #2, which plays the role of methane, even though the short-lived gas has a larger GWP. Even though the switching rule in (143) is somewhat complicated, we may still draw some conclusions without too much work. First, if some of R10 is not used, if the shadow price of #2 is positive, then it is not optimal to eventually specialize in using #2. To show this, by way of contradiction, note that the shadow price of #1 is zero, μR1 (t) = 0, if it is not all used, and if the shadow price of #2 is positive it must grow at the rate ρ. But since, M10 > 0, we must have 1/M(t) ≤ 1/M10 for all dates t . Thus the social marginal cost of #1 is bounded above by ζ /(ρM10 ) while the social marginal cost of #2 is eventually growing at least by rate ρ. Hence eventually it will be cheaper to switch to #1. This is a contradiction.

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Second, here is a corollary to the above argument: μR2 (0; ρ, m2 , R20 ) − μR1 (0; ρ, m2 , R10 ) ≤ 0. To prove this by way of contradiction, subtract μR1 (0; ρ, m2 , R10 )eρt from both sides of (143). Note that if our claim does not hold, repeat the same type of argument as above to get a contradiction. Third, since R˙ i = −Ei , i = 1, 2, the shadow price of one of the GHGs, can’t be zero if the other is positive. We prove this assertion by way of contradiction. If the shadow price of gas i were zero at some point in time, then it must be zero at date t = 0, since μ˙ Ri = ρμRi . But the shadow price of the other gas, call it j , being positive, grows at rate ρ. Eventually the social marginal cost of GHG j , i.e. −μMj (t)+μRj (t), because it grows at least at rate ρ, must exceed the social marginal cost of GHG i, by an argument similar to that above, which causes a switch to i and usage of i until the reserve is exhausted which then causes the shadow price to become positive. This is a contradiction. Fourth, at first we thought it would be simple to show that as ρ → 0 eventually it would be optimal to specialize in using GHG #2 since it decays in the atmosphere but GHG#1 does not decay. However, since the shadow prices depend upon the decay rate m2 as well as the discount rate ρ it is not so straightforward. While we have barely scratched the surface of the interesting interaction of economics and climate science stimulated by Pierrehumbert (2014), we think that we have done enough to indicate that this is a promising area for future research. Of course we have neglected adjustment costs of switching and other complexities of the real world. This analysis has been pushed far enough to suggest that it is important to develop this kind of analysis of management policies toward multi-lived GHGs emissions in more realistic models. There are many directions in which this analysis can be taken. Implementation by differential taxes on different GHGs, for more general specifications of utility functions, general production functions, etc., as well as extension to robustness to treat specification doubts on the part of the planner as in Anderson et al. (2014) are all promising research directions.

APPENDIX B SPATIALLY EXTENDED DETERMINISTIC ROBUST CONTROL PROBLEMS We develop a spatially extended linear–quadratic (LQ) robust control problem, which can be regarded as an LQ version of problem (6) with spatial transport related to the state variable. In particular we consider a bounded spatial domain. Then c (t, z), x (t, z), and h (t, z) denote control, state and distortion at time t and location z, respectively. Spatial transport can be introduced in the following way. Assume that the mass or substance associated with the state variable which is located at point z moves to nearby locations and that the direction of the movement is such that mass from locations where mass is abundant, i.e., locations of high mass concentration, moves toward locations of low mass concentration. This is the assumption of Fickian diffusion, or Fick’s first law, and is equivalent to stating that the flux of mass denoted by x (t, z) is proportional to the gradient of the mass concentration, i.e., the spatial

B Spatially Extended Deterministic Robust Control Problems

derivative of concentration, or J (t, z) = −D

∂x (t, z) , ∂z

(144)

where D is the diffusion coefficient or diffusivity measuring how fast mass moves from locations of high concentration to locations of low concentration. In terms of the spatial EBCM, the state variable can be interpreted as heat moving from the equator to the Poles. In terms of ecosystem modeling, the state variable can be interpreted as concentration of a resource or pollution at a specific location. Following Brock et al. (2014d, 2014f), the spatiotemporal evolution of a state variable under Fickian diffusion and concerns about model misspecification reflected in a Hansen–Sargent entropic constraint can be written as   ∂ 2 x (t, z) 1/2 + ε σ h (t, z) dt + ε 1/2 σ x (t, z) dW, dx = λc (t, z) − δx (t, z) + D ∂z2 (145) where W is a Hilbert space-valued Wiener process.16 Thus the LQ version of problem (6) is   ∞ β e−ρt αc (t, z) − c (t, z)2 (146) max min c(t,z) h(t,z) 0 2 Z  θ (ε) γ h (t, z)2 dzdt (147) − x (t, z)2 + 2 2 subject to (145) , x (0, z) = x (z) , and appropriate spatial boundary conditions. Let γ θ (ε) β c (t, z)2 − x (t, z)2 + h (t, z)2 2 2 2 ∂ 2 x (t, z) f (x, c, h, xzz ) = λc (t, z) − δx (t, z) + D + ε 1/2 σ h (t, z) . ∂z2 g (x, c, h) = αc (t, z) −

The HJBI equation for problem (146) can be written as   g (x, c, h) dz + V  (x) f (x, c, h, xzz ) ρV (x) = max min c h Z   + V (x) ε (σ h)2 dz , where V  (x), V  (x) are Frechet differentials of the value function. 16 For definitions, see for example da Prato and Zabczyk (2004).

(148) (149)

(150)

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Following Campi and James (1996), Anderson et al. (2012), and Anderson et al. (2014) let θ (ε) = θ ε and scale the θ with ε in such a way that as ε → 0 we obtain the HJBI equation which is associated with the deterministic robust control problem in the spatiotemporal domain, or      g (x, c, h) dz + V (x) f (x, c, h, xzz ) dz . (151) ρV (x) = max min c

h

Z

Eq. (151) can be associated with the spatial deterministic robust control problem    ∞ γ θ β e−ρt αc (t, z) − c (t, z)2 − x (t, z)2 + h (t, z)2 dzdt max min c(t,z) h(t,z) 0 2 2 2 Z (152) subject to ∂ 2 x (t, z) ∂x (z, t) . = λc (t, z) − δx (t, z) + σ h (t, z) + D ∂t ∂z2 Problem (152), which has been studied by Derzko et al. (1984), Brock and Xepapadeas (2008), and Brock et al. (2014d), has a Hamiltonian representation:  γ θ β (153) max min αc (t, z) − c (t, z)2 − x (t, z)2 + h (t, z)2 c(t,z) h(t,z) 2 2 2   ∂ 2 x (t, z) . (154) p (t, z) λc (t, z) − δx (t, z) + σ h (t, z) + D ∂z2 The maximum principle implies the following FONCs for the controls: α + λp (t, z) β σ h (t, z) = − p (t, z) . θ c (t, z) =

(155) (156)

Then the Hamiltonian system is a system of backward–forward PDEs: ∂ 2 p (t, z) ∂p (t, z) = (ρ + δ) p (t, z) + γ x (t, z) − D ∂t ∂z2  2  ∂x (t, z) λα λ σ2 ∂ 2 x (t, z) . = + − p (t, z) − δx (t, z) + D ∂t β β θ ∂z2

(157) (158)

As shown analytically in Brock et al. (2014d), by using solutions of the form nπ

 x (t, z) = xn (t) sin z L n (159) nπ

 p (t, z) = pn (t) sin z L n

B Spatially Extended Deterministic Robust Control Problems

where n is the number of Fourier modes, the system of backward-forward PDEs (157)–(158) can be transformed into a countable set of linear ODEs. This system can be written as: dpn (t) = (ρ + δ + φn ) pn (t) + γ xn (t) dt  2  dxn (t) λα λ σ2 = + − pn (t) − (δ + φn ) xn (t) dt β β θ xn (0) = ξn , lim e−ρt pn (t) xn (t) = 0 t→∞  nπ

nπ

 2 L ξn sin x (z) sin z , ξn = z dz x (z) = L L 0 L n φn =

(160)

Dπ 2 2 n . L2

Solving system (160) for a sufficient number of Fourier modes and substituting back the solutions into (155), (156), and (159) we can obtain the optimal robust spatiotemporal paths for the state, costate and control variables.

B.1 AN EXAMPLE To provide a worked out example of the approach we use the following parameterization of the linear quadratic pollution control problem.17 Parameter α β γ δ σ ρ λ D

Value 224.26 1.9212 0.0223 0.0083 0.2343 0.03 1 1

The spatial dimension is introduced by considering a spatial domain Z = [0, 2π ], allowing for spatial transport with diffusion parameter D = 1, and considering the following initial spatial distribution for the stock variable:  (161) x (0, z) = 100 exp − (z − π)2 , z ∈ [0, 2π ] .

17 This parametrization has been used by Karp and Zhang (2006) and Athanassoglou and Xepapadeas

(2012) for the study of linear quadratic climate change models. We use the same parametrization here, although we are not calibrating a spatial climate change model, to show how the spatially dependent solution for the states and the controls can be constructed

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FIGURE 2 The stock of the pollutant.

FIGURE 3 The spatiotemporal path of the pollution externality cost.

We solved the system (160) for the first six modes n = 1, . . . , 6 and for two different values of θ = {1, 10}. The steady state of the Hamiltonian system corresponding to each mode was a saddle point. Setting the constant associated with the positive eigenvalue equal to zero, the solutions for the state and the costates were of the general form pn (t) = pn∗ + υn1 Cn esn t

(162)

xn (t) = xn∗

(163)

+ υn2 Cn esn t ,

    where xn∗ , pn∗ is the steady state for mode n, sn is the negative eigenvalue, υn1 , υn2 is the eigenvector corresponding to the negative eigenvalue, and Cn is a constant determined by initial conditions on xn (0). The mode-solutions (162), (163) are substituted into (159) to obtain the spatiotemporal paths for the state, x (t, z), and costate,

B Spatially Extended Deterministic Robust Control Problems

FIGURE 4 The emissions path.

FIGURE 5 The distortion path.

p (t, z), functions, the control function c (t, z) and the spatiotemporal distortions to stock dynamics “chosen by Nature” h (t, z). Figs. 2–5 show these paths for θ = 10. It should be noted that if the control, c (t, z), is interpreted as emissions generating a quadratic benefit function, and the state as the stock of pollutant which generates quadratic damages and which diffuses in the spatial domain from high concentration to low concentration, then the example can be interpreted as a spatial pollution control problem under uncertainty. In the graphs below, the spatiotemporal evolution of the cost of the externality which is the costate function p (t, z) can be used as a basis for spatially structured emissions taxes. In this example the problem was solved for a penalty parameter θ = 10 which reflects the regulator’s ambiguity regarding pollution dynamics. Solving for different values of θ will provide spatiotemporal paths corresponding to different levels of confidence towards the benchmark model.

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As explained in the main text, large values of θ corresponds to high confidence in the benchmark model. Solutions of the model for different θ indicate that when θ increases the distortion h (t, z) is reduced. Note that high spatial distortions imply high externality cost and relatively lower emissions.

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CHAPTER

Ecology and economics in the science of anthropogenic biosphere change

2

Charles Perrings1 , Ann Kinzig Arizona State University, Tempe, AZ, United States of America author: e-mail address: [email protected]

1 Corresponding

CONTENTS 1 Introduction ...................................................................................... 2 The Dynamics of Coupled Hierarchical Systems ........................................... 3 Carrying Capacity and Assimilative Capacity ............................................... 4 Resilience and Stability ........................................................................ 5 Biodiversity and the Portfolio of Natural Assets............................................ 6 The Value of Ecosystem Functions ........................................................... 7 Concluding Remarks ............................................................................ References............................................................................................

61 63 65 67 70 73 76 77

1 INTRODUCTION In this paper, we examine the consequences of a forty-year experiment in interdisciplinary collaboration between ecologists and economists. It is an experiment that has brought researchers from both disciplines together to understand anthropogenic impacts on the biosphere. The effort has sometimes been stimulated by economists, and sometimes by ecologists. Along the way it has spawned an array of new journals and professional societies, as well as new teaching and research programs. As an experiment, it has provoked more than its fair share of controversy. While it has united some ecologists and economists in a common cause, it has also led to rifts in each of the constituent disciplines. In what follows we consider the impact of this experiment on the science of anthropogenic biodiversity change. This is not the only long-term effort to realize the potential gains from interdisciplinary collaboration. In announcing a new program of research designed to uncover the ‘rules of life’, the National Science Foundation recently noted that deep integration across disciplines has already put us “on the cusp of solving one of the greatest Handbook of Environmental Economics, Volume 4, ISSN 1574-0099, https://doi.org/10.1016/bs.hesenv.2018.03.002 Copyright © 2018 Elsevier B.V. All rights reserved.

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challenges in understanding the living world – namely, predicting how the set of observable characteristics (phenotype) arises from the genetic makeup of the individual in concert with environmental factors acting at diverse spatial and temporal scales” (National Science Foundation, 2017). Increasing collaboration across the biological sciences, computer and information sciences, engineering, geosciences, mathematical and physical sciences, and social, behavioral, and economic sciences has already deepened understanding of the emergent properties of living systems. Anthropogenic biosphere change expresses the emergent properties of living systems in a world in which environmental factors reflect the effects of economic growth and development, and in turn enable or constrain that growth. The experiment we report has yielded a number of striking benefits for both disciplines. It has strengthened our understanding of the impact of anthropogenic biodiversity change on the dynamics of hierarchical ecological systems. Appreciation of the biological factors determining the carrying and assimilative capacity of the environment has provided a different perspective on the substitutability of produced and natural capital. Research on the linkages between biodiversity and ecosystem function has offered a proper scientific basis for the valuation of non-marketed environmental goods and services. Perhaps most important, work on the resilience of ecological systems has deepened our understanding of the stability and sustainability of economic states and processes. In what follows we take the areas in which the experiment has affected the science of anthropogenic biodiversity change and ask how interdisciplinary collaboration has altered our approach to the problem. We consider the spatial and temporal scale at which the problem is addressed, the level of abstraction sought (the biophysical processes included or excluded from models of the coupled system), the data used to calibrate and validate those models, and the range of interventions considered. We do not offer an exhaustive review of the literature. It spans too many fields, and too wide an array of problems for this to be feasible. Instead we identify cases where the experiment has led to a change in approach that has given real traction on the problem. Einstein famously said that a model should be as simple as possible but no simpler. In some cases, traction has been gained by adding ecological detail – taking account of processes that have traditionally been neglected or treated parametrically in economic models. In other cases it has come by redefining the spatial and temporal scale of the problem. Anthropogenic environmental change involves stocks whose dynamics play out at very different temporal scales. It also involves processes that have effects at very different spatial scales. More importantly, progress has come by developing an understanding of the ways in which the emergent properties of the coupled system reflect interactions between the organisms involved and the environment, broadly interpreted, in which they exist.

2 The Dynamics of Coupled Hierarchical Systems

2 THE DYNAMICS OF COUPLED HIERARCHICAL SYSTEMS One of the earliest impacts of work at the intersection of ecology and economics was the realization that the economy and the natural world co-evolve (Norgaard, 1984). An obvious current example of this is anthropogenic climate change. The short-term climatic impacts of anthropogenic carbon emissions modify the climatic effects of the much longer-term Milankovitch cycles, in turn stimulating change in the economic system. But the same interdependence between economic and natural systems plays out at many different spatial and temporal scales. One of the key lessons from ecology is that the dynamics of natural systems involve a combination of slow large-scale and fast small-scale processes. A good example is Holling’s work on boreal forests (Holling, 1973, 1988), which showed how the dynamics of the system involve cycles ranging from the scale of the leaf over a period of days to the scale of the forest over a period of years. Hierarchical systems of this kind are nested at different spatial and temporal scales. Small fast-moving systems are embedded in and constrained by large slow-moving systems, although there also occur junctures at which smaller systems are able to disrupt larger systems. In ecology, this has prompted analyses that focus on interactions between biotic and abiotic processes at different scales (O’Neill et al., 1989; Levin, 1992; Allen and Starr, 2017). While economists have a concept of stocks that remain invariant over some period of time (the short-run), and have some notion of renewal processes in ‘business’ and ‘product’ cycles, they have not typically modeled economic processes in the same way. But if the economic and ecological components of a coupled system both consist of a structure of subsystems, each operating at distinct spatial and temporal scales, then the analysis of the coupled system needs to address the interactions between them. Gunderson and Holling referred to such a system as a ‘panarchy’, arguing that it should be understood through interactions between cycles at different scales (Gunderson and Holling, 2002). There are now many examples of studies of the dynamic interactions between the economic and ecological components of coupled systems (Brown and Roughgarden, 1995; Finnoff and Tschirhart, 2003; Batabyal, 2005; Eichner and Pethig, 2005; Tilman et al., 2005; Eichner and Tschirhart, 2007). From an economic perspective, what matters is that not all interactions are factored into peoples’ decisions. Consider the role of spatial structure. In ecological systems, a landscape typically contains a number of populations whose interactions determine the dynamics of the general system. Those interactions are constrained by topography, hydrology, vegetation and so on. In managed landscapes, interactions between populations of different species may be further constrained by a structure of barriers in the form of roads, railways, or fences, and by efforts to promote some species and to suppress others. Decisions that alter the dynamics of one species in one time and one place can have unintended consequences for other species at other times and other places. In the Greater Yellowstone Area (GYA) of the USA, for example, interactions among cattle, bison, and elk are dominated by elk migration, which is constrained by landscape structure, habitat connectivity, and land use. Contact between elk, bison, and cattle is a source of concern because it is associated with the transmission

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of brucellosis. The establishment of elk feedgrounds to reduce localized contact between cattle and elk in the short-run has had the perverse effect of increasing elk densities and intra-specific competition for resources, leading to greater dispersal of elk in search of forage, and so more widespread contact between elk and cattle, and the greater spread of brucellosis in the longer-run (National Academies of Sciences Engineering and Medicine, 2017). In economic analyses of renewable natural resource systems, it has become common to model spatial interactions (Sanchirico and Wilen, 1999, 2001; Fenichel et al., 2010; Horan et al., 2011) and spatial externalities (Anselin, 2003) explicitly. The temporal structure of coupled systems is also increasingly recognized to be important. Models of renewable natural resource extraction assume that the dynamics of the social system ‘contain’ the dynamics of the exploited population. In other words, the decision-maker operates on a time scale (over a horizon) that exceeds the renewal period of the exploited population. For infinite-horizon problems this is trivially true. For finite horizon problems, it is a matter of choice. If the renewal period of the resource is greater than the decision-maker’s time horizon the resource is defined to be exhaustible, and its dynamics of little consequence. The insight coming from the study of hierarchical ecological systems is that localized short-term decisions affecting the dynamics of small fast-moving systems may have consequences for the time-behavior of large slow-moving systems. For example, the fast dynamics of many pests and pathogens can have significant consequences for the slower dynamics of human populations. Epidemics that involve the explosive growth of infectious agents may affect the longer-term demographics of the host population. HIV in Africa is a well-known example (Johnson and Dorrington, 2006), but there are numerous other historical examples of human societies where demographics have been transformed by epidemics (Diamond, 1997). The development of the field of economic-epidemiology is stimulated by the insight that human behavioral responses to disease risk may change both the course of the disease and the demographic and socio-economic factors that affect future disease risk (Delfino and Simmons, 2000; Fenichel et al., 2011; Perrings et al., 2014). Within environmental and resource economics more generally, the longer-term consequences of present decisions are frequently modeled as intertemporal externalities. In addition to the long term impacts of current investment decisions on future stocks of natural and produced assets (Solow, 1974; Hartwick, 1977, 1978), environmental and resource economists recognize the need to model the intertemporal externalities of current production and consumption decisions (McKitrick, 2011). This may be driven by concerns over the sustainability of current decisions (Baumgärtner and Quaas, 2010; van den Bergh, 2010), but it also reflects the long-standing recognition that many environmental processes play out on timescales that exceed the time horizon of private decision-makers (John and Pecchenino, 1994; John et al., 1995). What we have learned from the ecology of large-scale systems like boreal forests is that processes involving interactions between cycles of differing periodicity mean that interventions that change one stock affecting one cycle can have future consequences that affect many stocks over many cycles (Ludwig et al., 1978).

3 Carrying Capacity and Assimilative Capacity

What this element of the experiment has done is to push resource economists to move beyond the single stock models that characterized the initial development of bioeconomics as a field. The basic principles involved, elaborated by Colin Clark in the 1970s, remain intact (Clark, 1973, 1976, 1979; Clark et al., 1979). Decision makers are assumed to optimize an objective function that includes the benefits of exploiting some natural resource, subject to the dynamics of that resource. The state variables of the problem are available stocks of assets (including environmental stocks), and the control variables are feasible management actions. It is recognized that feedbacks within the system alter the dynamics of natural stocks, and that this has implications for their management. What has been added to this is the recognition that there are always multiple stocks involved, that feedbacks may induce changes that play out on quite different time scales, and that it is not sufficient to bundle all these effects into single parameters – such as carrying capacity. There is now a substantial body of papers that capture at least some of the complexity of coupled resource systems (see Schlüter et al., 2012 for a review). Examples include Bulte and Damania (2003), Bulte and Horan (2003), Brock and Xepapadeas (2004), Perrings and Walker (2004), Polasky et al. (2004), Polasky et al. (2005), Quaas et al. (2007), Horan et al. (2011, 2017). Most use an extended bio-economic model, in which economic agents optimize an objective function using controls that affect the dynamics of one or more species in a supporting ecosystem. Interactions between the economy and its environment depend on the ‘connectedness’ and so the dynamic structure of the joint system. Components that are unconnected over one time horizon may be highly connected over another, and a level of connectedness that is insignificant at one scale of activity may be highly significant at another (Perrings, 1987).

3 CARRYING CAPACITY AND ASSIMILATIVE CAPACITY A second area where the experiment has changed the science of anthropogenic biosphere change relates to the environmental limits to growth. Since Thomas Malthus first suggested that human populations would always be constrained by productivity growth rates, there has been a succession of attempts by natural scientists to warn of the consequences of exceeding the carrying capacity of the natural environment (Ehrlich and Holdren, 1971; Meadows et al., 1972; Rockström et al., 2009; Ripple et al., 2017). This has also led to the identification of measures of carrying capacity at the largest scale (Rees, 1996; Wackernagel and Rees, 1998). Economists have always reacted instinctively and dismissively to the assumption that the world would stand still while supplies of natural resources run out. However, a better understanding of the ecologists’ concept of assimilative or carrying capacity, and the degree to which environmental constraints are reflected in the decisions of households and firms, has yielded a better understanding of the environmental limits to economic growth.

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In the canonical bioeconomic renewable resource model, the carrying capacity that defines the natural equilibrium in a logistic equation does constrain the growth potential of an economy dependent on that resource. However, it is now recognized that carrying capacity may vary both with the way resources are used (technology) and with environmental conditions. Whether or not carrying capacity is treated as endogenous to the economic problem depends on the time horizon over which decisions are made, and on market conditions and property rights. If the time horizon is long enough, if the environmental constraints within which production decisions are made are reflected in resource prices, and if those constraints are sensitive to technology, then the carrying capacity of the natural system may be a choice variable. The enhancement of carrying capacity has in fact become an objective in environmental problems such as tourism (Brown et al., 1997; Liu and Borthwick, 2011). On the other hand, if environmental constraints are not reflected in resource prices – as when resources are open access – carrying capacity will be treated as exogenous to the problem. Activity levels will then be selected subject to a given carrying capacity. In ecological communities, carrying capacity for particular species is a function of trophic structure. It varies with the conditions that affect the relative abundance of species at different trophic levels. Classically, a Lotka–Volterra system of equations for predator prey interactions implies the dynamic interdependence in carrying capacity for both predator and prey. While biologists have criticized the Lotka– Volterra model for oversimplifying predator–prey interactions, work in statistical physics has shown that when spatial degrees of freedom and stochastic fluctuations are included, the results differ substantially from the deterministic mean-field model. Instead of singularities associated with particular population cycles, they find stable nodes (involving localized clusters of predators and abundant prey) and foci (involving complex spatio-temporal predator–prey patterns that oscillate irregularly in time) (Mobilia et al., 2007). The carrying capacity and stability of exploited predator prey systems remains a very active area of research (Wang et al., 2015; Ganguli et al., 2017). Capture fisheries – which originally motivated Lotka’s work – are good examples of resource systems where much effort has gone into the identification of time-varying limits on harvest, and the design of mechanisms, such as ITQs (individual transferable quotas), to implement those limits (Beddington et al., 2007). Many resource models in which the carrying capacity of the resource would previously have been given as a biological datum now model it as a function both of environmental conditions and policy interventions. The best-known examples relate to the exploitation of shallow lakes that may exist in either a eutrophic or oligotrophic state depending on the level of nutrient loading (Scheffer, 1997; Carpenter et al., 1999; Mäler et al., 2003; Peterson et al., 2003; Janssen et al., 2014), but the approach has been applied to other systems (Stringham et al., 2003; Perrings and Walker, 2004; Quaas et al., 2007). It is easy to see how this is related to the sustainability of activities that exploit the natural environment. Activities that remain within the carrying or assimilative capac-

4 Resilience and Stability

ity of the environment are sustainable. It is also easy to see that the sustainability of activities is always going to depend on context. Activities that are sustainable in one set of environmental, institutional, or technological conditions may not be sustainable under another set of conditions. The sustainability of harvest of a wild species at some level requires that level to be on the sustained yield curve, but the sustained yield curve itself depends on the environmental, institutional, or technological conditions that determine the topological structure of the system. The observation that some ecosystems are characterized by multiple stable states has become an important determinant of both the science and management of such systems (Ives and Carpenter, 2007). While empirical evidence for regime shifts in purely natural ecosystems is limited (Capon et al., 2015), there is substantial evidence for anthropogenically induced regime shifts – involving trophic cascades often at large scales (Österblom et al., 2007; Moellmann et al., 2009).

4 RESILIENCE AND STABILITY The third area in which the experiment has changed both science and management is closely related to the question of carrying capacity. The carrying capacity of any natural resource system is a function of the stable equilibria of that system. Ecologists typically analyze the stability of equilibrium using three different concepts: resistance, persistence, and resilience (Walker and Meyers, 2004). Resistance is a measure of the capacity to resist change, and is therefore a measure of local stability. Persistence, by contrast, is a measure of the capacity of the system in some state to endure, and so is a measure of the global stability of the equilibrium corresponding to that state. The third category, resilience is interpreted in two different ways. The first is a measure of local stability – the speed of return to equilibrium following perturbation (Pimm, 1984). The second is a measure of the size of a disturbance needed to dislodge a system from its stability domain, or the size of the stability domain corresponding to some attractor (Holling, 1973). More generally, it is the conditional probability that a system will flip into another stability domain given (a) its current state and (b) the disturbance regime. For systems that can exist in multiple stable states, the response to perturbations from any equilibrium give a sense of strength of local stability of that equilibrium, but not the capacity of the system to remain in that state. That capacity is given by the size of the perturbation needed to move the system to a different stability domain. Holling resilience is a measure of the shock needed to move the system from one attractor to another. If the system is away from equilibrium, an equivalent measure is the size of disturbance in any direction that is sufficient to dislodge the system to a different stability domain. For a system close to an unstable equilibrium (an unstable manifold of the system) the perturbation needed to dislodge it might be very small. To take the simplest case, consider a critically depensatory growth curve of the kind given in Fig. 1. If the system is at the stable equilibrium such that the population is at carrying capacity, X = K, its resilience with respect to perturbation in X is

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FIGURE 1 System resilience with and without anthropogenic disturbance.

the distance between carrying capacity and the critical minimum population size, M, K − M. If the population is reduced by harvest to that corresponding to the maximum sustainable yield, MSY, its resilience is reduced to MSY − M. In this simplest of cases the stable equilibria of the system are at carrying capacity and the origin – i.e. the death of all individuals in the population. In many other cases the system may exist in multiple stable states, the movement between stable states being a function of environmental conditions. Shallow lakes subject to nutrient loading, for example, are typically observed in one of two states: oligotrophic and eutrophic. Both states are locally stable only, so convergence on a eutrophic state does not preclude reversion to an oligotrophic state. The dynamics involved in the movement between states may, however, be quite complex. Reversion from a eutrophic to an oligotrophic state may, for example, be subject to hysteresis. That is, it may require nutrient loadings far below the level that induced the flip in the first place (Carpenter et al., 1999). And if the system includes negative feedbacks (e.g. the growth of vegetation in the eutrophic state reduces phosphorous loading), the same general phenomenon can lead to fast-slow cycling between states (Fig. 2). There are by now a large number of case studies using this approach (Walker et al., 1999, Perrings and Stern, 2000; van de Koppel and Rietkerk, 2004; Walker et al., 2004; Adger et al., 2005; Hughes et al., 2007). The focus of most such studies is the resilience of the system in particular states – whether desirable or not. From an economic perspective this maps into traditional concerns about the existence and stability of system equilibria. However, by treating resilience as endogenous it adds an extra dimension: the challenge of managing the local and global stability of systems, and adaptively responding to loss of local stability. Since the resilience of systems can be enhanced or eroded, systems can be engineered to absorb larger shocks without changing in fundamental ways, or can be made vulnerable to increasingly minor perturbations. A system that is destined to exist in a number of states can be made resilient across states by ensuring that it retains the components needed for renewal

4 Resilience and Stability

FIGURE 2 Negative feedbacks can induce cycling. (A) If vegetation has no negative effect on the phosphorus content in the lake, the system has alternative equilibria. (B) If vegetation has a negative effect and if the nutrient nullcline intersects the unstable part of the catastrophe fold, and the nutrient equilibrium sets slowly, there can be slow–fast cycles. (C) The system has alternative equilibria over a range of phosphorus loadings (F1 and F2 are fold bifurcations). (D) The system has cycles over a range of phosphorus loadings (H1 and H2 are Hopf bifurcations). (E) The effects of increasing and decreasing P loading on a system with alternative states. (F) The effect of P loading on a cyclic system. Source: van Nes, E.H., Rip, W.J., Scheffer, M., 2007, A theory for cyclic shifts between alternative states in shallow lakes, Ecosystems 10, 17.

and reorganization (Gunderson and Holling, 2002). The work on shallow lakes, for example, has highlighted the importance of the interactive effects of processes that work at different spatial and temporal scales. It is now understood that system stability and sustainability depends most heavily on the slowly changing variables of the

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system: i.e. state variables with slow turnover rates or stochastic processes with long return times (Scheffer, 1997; Mäler et al., 2003). An important implication of this approach is that system stability depends on particular sets of stocks – the infrastructure of the system. From an ecological perspective, these stocks (the ‘slow variables’ of the system) would include, for example, reservoirs of soil nutrients or the variety of genotypes and species (Folke et al., 2004; Folke, 2006). Most aggregate economic models capture such stocks only indirectly in total factor productivity – the part of output not explained by the factors explicitly listed in the aggregate production function. Economists have known for some time that summarizing all of the effects of institutions, markets, and the biophysical and social environment in total factor productivity is an unsatisfactory way to deal with a wide range of things, each of which may affect system performance in different ways (Prescott, 1998). If total factor productivity is constant it is understood that the rate at which wellbeing changes is determined by the rate at which each of the capital stocks (evaluated at its shadow price) changes. It is also understood that an economic program is sustainable if and only if aggregate net investment is positive, and aggregate wealth is non-declining. Moreover, wellbeing can increase over time if and only if the Lindahl criterion is satisfied, i.e. if consumption is less than the difference between output and depreciation of assets (Dasgupta and Mäler, 2000; Dasgupta, 2001). We return to the implications of this for wealth accounting later. Here we note only that if total factor productivity is not constant, as would be expected in an evolving system, then the sustainability of an economic program, and the resilience of the system, both imply conditions on the stocks embedded in total factor productivity.

5 BIODIVERSITY AND THE PORTFOLIO OF NATURAL ASSETS A fourth area in which deep interdisciplinary integration has altered the science of anthropogenic biosphere change relates to the way that biodiversity is conceptualized. Ecologists typically use four main measures of biodiversity. The first, alpha diversity, is a measure of the taxonomic diversity (the species richness) within a particular community or ecosystem. The most common indices of alpha diversity are due to Shannon (1948) and Simpson (1949), both of which measure a combination of the number of species present, and the abundance of each species. Other measures of alpha diversity exist, but like these focus on some combination of richness and abundance (Magurran, 2004). The second, beta diversity, is a measure of the difference in species diversity between ecosystems or along environmental gradients. More particularly, it measures the number of taxa that are unique to each of the ecosystems being compared. For example, if there are two ecosystems, the index of beta diversity developed by Sørensen (1948) takes the form: β = 2c/ (s1 + s2 ), where si is species richness in the ith community and c is the number of species common to both communities. Like the Simpson’s index, it takes a value of 0 when there is no species overlap between the communities, and a value of 1 when exactly the same species

5 Biodiversity and the Portfolio of Natural Assets

are found in both communities. The third, gamma diversity, is a measure of taxonomic diversity across all systems being evaluated. For the case of two systems it is γ = s1 + s2 − c, i.e. a count of the number of distinct species across all systems (Whittaker, 1972). The fourth, omega or phylogenetic diversity, is a measure of the taxonomic difference between species. A number of indices have been proposed for phylogenetic diversity (Schweiger et al., 2008), most falling into one of two classes: one using a minimum spanning path approach, the other using a pairwise distance approach. The pairwise distance approach most  familiar to economists is due to Solow et al. (1993) and Weitzman (1992), DD = i di min where di min is the nearest neighbor distance of species i to all other species. All indices explicitly or implicitly weight species in some way. The measure of gamma diversity given above implicitly weights all species at unity. Every species counts as much as every other species. Measures of alpha diversity weight each species by relative abundance, while measures of omega diversity weight species by their phylogenetic distance from other species. Where collaboration across disciplines has the largest impact on both science and management is in understanding the weights attaching to distinct species. Consider the gamma diversity of a region comprising both managed (agricultural) and wild (protected) land. If all species are weighted at unity, the gamma diversity is simply the union of the set of taxonomically distinct species in each land type. But land managers in each area might be expected to have very different perspectives. In both cases, the desired gamma diversity of the region would be the sum of taxonomically distinct species weighted by the value attached to each. Agricultural land managers would positively weight crops and other species supporting crop production. They would negatively weight crop competitors, pests, and pathogens. In the same way protected area managers would positively weight protected wild species, and would negatively weight competitors, pests, and pathogens including introduced species. One of the most significant results of the experiment is the deepening of the understanding of weighting systems across both disciplines (Perrings, 2014). Within ecology, the most telling evidence for this is the findings of the Millennium Ecosystem Assessment (MA). The MA analyzed biodiversity change in terms of the effects it had on four types of ecosystem service: provisioning services, cultural services, regulating services and supporting services (Millennium Ecosystem Assessment, 2005). The provisioning services correspond to the ‘goods’ in ‘goods and services’ obtained from renewable natural resource systems. They comprise foods, fuels, fibers, freshwater, pharmaceutical products and the like. The cultural services correspond to the ‘services’ element. They comprise the non-consumptive benefits yielded by ecosystems, including recreation, tourism, as well as the amenity, aesthetic, religious, spiritual and totemic value of systems. The remaining services identify the ecological functions that underpin and regulate the production of goods and services. They include processes such as photosynthesis, nutrient cycling and soil formation, and the processes that regulate air and water quality, soil erosion, disease transmission or natural hazards. The notion that biodiversity change might be analyzed in terms of the impact it has on the production of goods and services marked a

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sea change in ecology. While it created tensions within the discipline, it also fundamentally altered the way ecologists think about biodiversity and the role it plays in ecosystems. Increasingly, biodiversity change was analyzed less in terms of species richness and the taxonomic distinctness of species, and more in terms of ecosystem process and function. The ecological literature on the relationship between biodiversity, traits, and ecological functioning has led to the evolution of more appropriate and applicable measures of biodiversity than traditionally employed, focusing on functional diversity (Loreau et al., 2002; Díaz and Cabido, 2001; Naeem, 2002; Petchey and Gaston, 2002; Petchey et al., 2009). The literature has also explored the mechanisms involved in the relationship between biodiversity and stability (Naeem et al., 2009). It has, for example, been shown that the taxonomic differences between species is less relevant to the functioning of ecosystems than their functional traits (Solan et al., 2004; Bunker et al., 2005; McIntyre et al., 2007; Bracken et al., 2008). The biodiversity needed to assure the supply of freshwater, for example, differs from the biodiversity needed to assure the supply of timber, but in both cases is determined by the traits associated with those two functions. The main implication of this is that how much diversity is needed within functional groups depends primarily on the range of environmental conditions expected to occur. The greater the expected variation in environmental conditions, the greater will be the required diversity in functional groups (Elmqvist et al., 2003). Within economics, this has direct parallels in the risk-spreading function of asset portfolios. Called the insurance effect in ecology (Loreau et al., 2003), it postulates that if environmental conditions vary, some species in a community may be expected to perform well when others are performing badly. It has been shown that the diversity of functional groups reduces variability in system functioning (Tilman et al., 2001, 2005; Griffin et al., 2009) through the niche differentiation effect (Tilman et al., 1996). In particular, niche differentiation should lead to the emergence of species specialized in terms of environmental as well as geophysical conditions. Portfolio effects depend on the correlation between responses to some environmental change. So in the case of the gamma diversity described above, if a functional group consisted of just two species, s1 and s2 , associated with yields y1 = y1 (s1 ) and y2 = y2 (s2 ), then the expected yield of the portfolio would be: E (y) = i ρi E (yi ), i = 1, 2 in which ρi is the share of total biomass accounted for by the ith species. The variance in yield would be: σp2 = ρ12 σ12 + ρ22 σ22 + 2ρ12 ρ22 σ1 σ2 r12 in which σi is the standard deviation of the yield associated with si , and rij is the correlation coefficient between yields from species si and sj . If the correlation coefficient is positive, both species respond to environmental perturbations in similar ways. If the correlation coefficient is negative, the species respond in opposite ways (see, for example, Doak et al., 1998; Tilman et al., 1998; Lhomme and Winkel, 2002). Negative correlation coefficients unambiguously enhance stability, but the portfolio effect can operate even if the responses to perturbations of different species are positively correlated. Yachi and Loreau, for example, showed that unless species’ responses to environmental perturbations were perfectly correlated (rij = 1) increasing the number of species in

6 The Value of Ecosystem Functions

a system would at once increase average productivity and reduce temporal variance in productivity (Yachi and Loreau, 1999). The portfolio effect in ecological systems is closely related to the notion of redundancy: that species may be functionally redundant (their deletion would have little effect on ecosystem functioning) in some conditions. It implies that the contribution of individual species to ecosystem functioning is dependent on both environmental conditions and the degree to which species are substitutes or complements in the performance of some function. If there is some functional overlap between species as a result of fluctuating environmental conditions, the redundancy of particular species in particular environmental conditions (Naeem, 1998; Walker et al., 1999; Wohl et al., 2004) is evidence of a classic portfolio effect. While the treatment of biodiversity as a portfolio choice problem is motivated by reference to ideas of functional redundancy and insurance in ecology, it applies wherever the value of species varies with environmental conditions. This may occur because different species perform more or less effectively in different conditions – i.e. where value derives from function. But it may also occur because different species are more or less vulnerable in different conditions – i.e. where value derives from survival probability. Regardless of the source of value at risk, a major benefit of the experiment is that the power of the theory of portfolio choice, developed in financial economics, can be brought to the task of managing biodiversity change (Perrings, 2014). The approach is now common in agroecosystems where crop mixes are selected to balance risks (Di Falco and Chavas, 2007), but is less common in wild lands. Many protected wild lands are organized around the conservation of charismatic species or landscapes, with relatively little consideration being given to the balance between species. The set of all protected areas does, however, look much more like a portfolio choice problem.

6 THE VALUE OF ECOSYSTEM FUNCTIONS The final area in which the long experiment has changed the nature of both science and management is closely related to the weighting problem. Deep interdisciplinary integration has had a profound effect on the valuation of ecosystem services, and hence the valuation of environmental changes that alter the flow of ecosystem services. Building on the efforts of market researchers to uncover willingness to pay for new products, environmental economists have developed increasingly refined methods to estimate willingness to pay for non-marketed environmental resources. A wide range of methods now exists to measure preferences over non-marketed biotic and abiotic resources. As long as respondents have full information about the benefits they obtain from the resource, these methods yield reasonable estimates of willingness to pay to acquire (or willingness to accept compensation for the loss of) the resource. The information requirement does, however, limit the range of resources to which these methods can be applied.

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What collaboration across the disciplines has done is to enable the same methods to be used to derive demand for components of the biosphere that are unknown by (and unknowable to) respondents. Scientific understanding of the ways in which the processes of the natural environment support the production of ecosystem services makes it possible to derive demand for those processes. Prior to the MA, a number of studies had drawn attention to the relation between the benefits people derive from nature and broader environmental changes in terrestrial (Daily, 1997; Daily et al., 1997), marine (Duarte, 2000) and agricultural ecosystems (Björklund et al., 1999). There were also attempts to generate broad-brush estimates of the value of such changes (Costanza et al., 1997; Bolund and Hunhammar, 1999; Norberg, 1999; Woodward and Wui, 2001). After the MA the focus of research on the value of ecosystem change has been on the relationship between the goods and services that people consume directly, and the ecological functions and processes that underpin those goods and services. In the case of both provisioning and cultural services the approach is relatively straightforward, involving the specification of ecological production functions that connect the biophysical environment to the production of goods and services. From an economic perspective the core methodology involved follows Mäler (1974), a contribution as fundamental, in its way, as Hotelling (1931) or Gordon (1954). Mäler established the axiomatic foundations for all revealed preference approaches to the valuation of ecosystem services, and demonstrated the conditions in which ecosystems derive value from their role in supporting a stream of services as well as the conditions in which ecosystem services would be zero-valued. Nice applications include Allen and Loomis (2006), which addresses the problem of species that support some totemic species valued for cultural reasons. The value of species at lower trophic levels is derived from the results of surveys of willingness to pay for the conservation of species at higher trophic levels. The prey species in this case are ‘intermediate inputs’ in the production of the valued predator species. In addition to understanding whether environmental assets are complements or substitutes, the approach has allowed identification of ‘critical points’ in the supply of individual services – frequently thresholds, or boundaries between different potential states of the system. This has provided a route to estimating the value of the buffering functions of nature, the regulating services. Within the MA, the regulating services were defined to include: air quality regulation; climate regulation at multiple scales (changes in land cover affect both temperature and precipitation at a local scale, while changes in carbon sequestration or greenhouse gas emissions have significant effects at a global scale); regulation of hydrological flows including runoff, flooding, and aquifer recharge through changes in land cover; erosion control; water purification and waste treatment services including the capacity to assimilate and detoxify soil and subsoil compounds; disease regulation; pest regulation; and natural hazard regulation (covering a wide range of buffering functions, particularly in coastal ecosystems where mangroves and coral reefs can reduce the damage caused by hurricanes and storm surges) (Millennium Ecosystem Assessment, 2005).

6 The Value of Ecosystem Functions

The common feature of the regulating services is that they affect the variability in the supply of provisioning or cultural services, either by changing the consequence of environmental variability (including extreme events), or by changing the level of environmental variability. That is, the regulating services affect the variance and higher moments of the distribution of provisioning and cultural services. The approach is well illustrated by Brock and Xepapadeas (2003), which relates the degree of functional diversity in an ecosystem to the capacity of that system to deliver services over a range of environmental conditions. For example, the loss of functional diversity among pest predators reduces the effectiveness of pest predation, and so reduces the value of the ecosystem. Other good illustrations of the approach include efforts to estimate the role of mangroves in buffering coastal storm damage (Barbier, 2007, 2008). Barbier estimates the willingness to pay for the effect of a change in wetland area on expected damages from coastal storm events. That is, the value of a change in ecosystem state that reduces risk (the probability and severity of damage) is measured by the reduction in that risk. There is a clear connection between the valuation of regulating services and the resilience and stability of coupled systems (Scheffer et al., 2000; Walker et al., 2004; Kinzig et al., 2006; Scheffer et al., 2009). Integration of ecological models of the linkages between biodiversity and the security of ecosystem services (Reich et al., 2004; Hooper et al., 2005; Cardinale et al., 2012) and economic models of the linkages between biodiversity and risk (Di Falco and Chavas, 2007; Baumgärtner and Strunz, 2014) has the potential to signal the importance of stocks that affect future capacity to negotiate environmental fluctuations. While most ecological work on climate change focuses on the threat it poses to biodiversity, there is increasing interest in the role of biodiversity in supporting adaptation to a more variable climate (Thompson et al., 2009; Mercer and Perales, 2010; Frison et al., 2011; Dempewolf et al., 2014; Khoury et al., 2014). There is also a clear connection between the value of the MA regulating services and the value of biodiversity as a portfolio of natural assets. As in any portfolio, the combination of species that is ‘best’ depends on how decision-makers balance certain against uncertain gains. The value of the biodiversity portfolio then depends on the covariances in the responses of different species to changes in environmental conditions. We have already noted that economists have established the conditions on asset values for wellbeing to be non-declining. These build on conditions established for the sustainable exploitation of exhaustible natural resources by Hotelling (1931), Solow (1974), and Hartwick (1977, 1978, 1990). Significant progress has been made in the development of wealth accounts that test for these conditions in real economies. The most effective measure to date is the net change in the value of a country’s capital stocks, where that includes produced, human and at least some stocks of natural capital measure of change in wealth (adjusted net savings) (Pearce and Atkinson, 1993; Pearce et al., 1996; Hamilton and Clemens, 1999; Ferreira et al., 2008). A necessary and sufficient condition for wealth to be increasing over time is that adjusted net savings be positive (Hamilton and Hartwick, 2005; World Bank, 2011; Arrow et al., 2012; UNU-IHDP and UNEP, 2014). Other measures are in development (Fenichel

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et al., 2016). All show that social well-being increases over an interval if and only if net investment in an appropriate measure of inclusive wealth is positive. As of now this does not include the value of the biodiversity portfolio, which remains buried in residuals such as total factor productivity or the World Bank’s ‘intangible capital’. What can be done, however, is to keep some track of the performance of the portfolio in terms of the covariances in responses to common environmental shocks.

7 CONCLUDING REMARKS The most profound effect of deep interdisciplinary integration between economics and ecology has been the widespread adoption of the ecological concept of resilience (sensu Holling) in both the science and management of biosphere change. By focusing on the capacity of coupled systems to continue to function over an evolving range of environmental conditions, it provides both a foundation for sustainability science and a way to test the environmental consequences of demographic, technological, institutional and economic changes in human societies. An understanding of the capacity of systems subject to perturbation to return to an original state within an economically meaningful time frame provides a test of sustainability and the irreversibility of change. A loss of resilience to a system in some state implies a change in the range of socio-economic or environmental conditions over which the system can maintain the flow of services. It is economically interesting if the value of the system varies across states. An economic program is not sustainable if it is not resilient. It is not resilient if it induces the economy to flip from a desirable to an undesirable state, and if that change is either irreversible or only slowly reversible – noting that many examples of irreversible changes cited in the literature are not irreversible in any strict sense, but denote variables that are slow relative to the time horizon of the decision-maker (Pindyck, 2000; Perrings, 2006; Perrings and Brock, 2009). The challenge this poses for management is that there may be few signals of impending changes in the state of coupled systems. The dynamics of the system may be revealed only through the response of the state variables to the controls. Moreover, the closer a system is to the boundaries of the stability domain, the greater the risk that shock will result in irreversible or only slowly reversible loss. This complicates the use of economic instruments to protect against changes of state, or to induce restoration of an initial state (Brock et al., 2002). There is certainly considerable interest in the identification of leading indicators of impending state changes. It is argued that the dynamics of systems approaching state changes have generic properties. Critical thresholds correspond to bifurcations, beyond which positive feedbacks push the system into contrasting state. There are number of potential precursors to such bifurcations in both model and real systems (Scheffer et al., 2009). The most reliable advance warning of regime shifts lies in the high-frequency signal in the spectral density of a time-series (Contamin and Ellison, 2009). Candidates include rising variance in state variables (Carpenter and Brock, 2006), slowing rates of return (Carpenter et al., 2011), a combination of spatial variance and spatial skewness (Gut-

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tal and Jayaprakash, 2009), and flickering – where the system enters a bistable region between two attractors before a bifurcation (Carpenter et al., 2008). There are, however, many systems in which there are no advance indicators of impending change (Hastings and Wysham, 2010). There are also systems in which advance indicators give insufficient time to avert impending change. A study of advance signals of impending change in lake systems, for example, found that when the monitored variable was directly and causally linked to the regime shift, detection was quick enough to avert the change. But when it was only indirectly linked to the regime shift, detection came too late to head off the change (Carpenter et al., 2014). For regime shifts that are driven by human behavior, this is a very interesting finding. If variation in the spectral density of a price series signals impending changes in behavior, price interventions may head off the change. If variation in the spectral density of a price series reflects changes in behavior driven by other factors the information it gives may be too late. We do not yet have good advance indicators of impending changes in the stability of many managed or impacted ecosystems. Deep interdisciplinary integration across the ecological and economic sciences has, however, provided an understanding both of the stability properties of such systems, and the potential drivers of change. It has therefore given us places to look for advance indicators of impending change – both in the natural environment and in the human behaviors that are implicated in anthropogenic environmental change. More importantly, it has given us criteria to evaluate both the predictive power of those indicators, and the scope they offer for informing timely action.

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Pearce, D., Atkinson, G., 1993. Capital theory and the measurement of sustainable development: an indicator of weak sustainability. Ecological Economics 8, 103–108. Pearce, D., Hamilton, K., Atkinson, G., 1996. Measuring sustainable development: progress on indicators. Environment and Development Economics 1, 85–101. Perrings, C., 1987. Economy and Environment: A Theoretical Essay on the Interdependence of Economic and Environmental Systems. Cambridge University Press, Cambridge. Perrings, C., 2006. Resilience and sustainable development. Environment and Development Economics 11, 417–427. Perrings, C., 2014. Our Uncommon Heritage: Biodiversity, Ecosystem Services and Human Wellbeing. Cambridge University Press, Cambridge. Perrings, C., Brock, W., 2009. Irreversibility in economics. Annual Review of Resource Economics 1, 219–238. Perrings, C., Castillo-Chavez, C., Chowell, G., Daszak, P., Fenichel, E., Finnoff, D., Horan, R., Kilpatrick, A.M., Kinzig, A., Kuminoff, N., Levin, S., Morin, B., Smith, K., Springborn, M., 2014. Merging economics and epidemiology to improve the prediction and management of infectious disease. EcoHealth 11, 464–475. Perrings, C., Stern, D.I., 2000. Modelling loss of resilience in agroecosystems: rangelands in Botswana. Environmental & Resource Economics 16, 185–210. Perrings, C., Walker, B.H., 2004. Conservation in the optimal use of rangelands. Ecological Economics 49, 119–128. Petchey, O.L., Gaston, K., 2002. Functional diversity (FD), species richness and community composition. Ecology Letters 5, 402–411. Petchey, O.L., O’Gorman, E.J., Flynn, D.F.B., 2009. A functional guide to functional diversity measures. In: Naeem, S., Bunker, D., Hector, A., Loreau, M., Perrings, C. (Eds.), Biodiversity, Ecosystem Functioning, and Human Wellbeing: An Ecological and Economic Perspective. Oxford University Press, Oxford, pp. 49–59. Peterson, G.D., Carpenter, S.R., Brock, W.A., 2003. Uncertainty and the management of multistate ecosystems: an apparently rational route to collapse. Ecology 84, 1403–1411. Pimm, S.L., 1984. The complexity and stability of ecosystems. Nature 307, 321–326. Pindyck, R.S., 2000. Irreversibilities and the timing of environmental policy. Resource and Energy Economics 22, 223–259. Polasky, S., Nelson, E., Lonsdorf, E., Fackler, P., Starfield, A., 2005. Conserving species in a working landscape: land use with biological and economic objectives. Ecological Applications 15, 1387–1401. Polasky, S., Costello, C., McAusland, C., 2004. On trade, land-use, and biodiversity. Journal of Environmental Economics and Management 48, 911–925. Prescott, E.C., 1998. Lawrence R. Klein Lecture 1997: Needed: a theory of total factor productivity. International Economic Review 39, 525–551. Quaas, M.F., Baumgärtner, S., Becker, C., Frank, K., Müller, B., 2007. Uncertainty and sustainability in the management of rangelands. Ecological Economics 62, 251–266. Rees, W.E., 1996. Revisiting carrying capacity: area-based indicators of sustainability. Population and Environment 17, 195–215. Reich, P.B., Tilman, D., Naeem, S., Ellsworth, D.S., Knops, J., Craine, J., Wedin, D., Trost, J., 2004. Species and functional group diversity independently influence biomass accumulation and its response to CO2 and N2 . Proceedings of the National Academy of Sciences 101, 10101–10106. Ripple, W.J., Wolf, C., Newsome, T.M., Galetti, M., Alamgir, M., Crist, E., Mahmoud, M.I., Laurance, W.F., 2017. World scientists’ warning to humanity: a second notice. Bioscience 67 (12), 1026–1028. Rockström, J., Steffen, W., Noone, K., Persson, Å., Chapin III, F.S., Lambin, E., Lenton, T., Scheffer, M., Folke, C., Schellnhuber, H.J., 2009. Planetary boundaries: exploring the safe operating space for humanity. Ecology and Society 14. Sanchirico, J.N., Wilen, J.E., 1999. Bioeconomics of spatial exploitation in a patchy environment. Journal of Environmental Economics and Management 37, 129–150. Sanchirico, J.N., Wilen, J.E., 2001. A bioeconomic model of marine reserve creation. Journal of Environmental Economics and Management 42, 257–276.

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Wang, X., Peng, M., Liu, X., 2015. Stability and Hopf bifurcation analysis of a ratio-dependent predator– prey model with two time delays and Holling type III functional response. Applied Mathematics and Computation 268, 496–508. Weitzman, M.L., 1992. On diversity. The Quarterly Journal of Economics 107, 363–405. Whittaker, R.H., 1972. Evolution and measurement of species diversity. Taxon 21, 213–251. Wohl, D.L., Arora, S., Gladstone, J.R., 2004. Functional redundancy supports biodiversity and ecosystem function in a closed and constant environment. Ecology 85, 1534–1540. Woodward, R.T., Wui, Y.-S., 2001. The economic value of wetland services: a meta-analysis. Ecological Economics 37, 257–270. World Bank, 2011. The Changing Wealth of Nations: Measuring Sustainable Development in the New Millennium. World Bank, Washington, D.C. Yachi, S., Loreau, M., 1999. Biodiversity and ecosystem productivity in a fluctuating environment: the insurance hypothesis. Proceedings of the National Academy of Sciences 96, 1463–1468.

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The nature of natural capital and ecosystem income✶ ∗ Yale

3

Eli P. Fenichel∗ , Joshua K. Abbott†,1 , Seong Do Yun‡ University, School of Forestry & Environmental Studies, New Haven, CT, United States † Arizona State University, School of Sustainability, Tempe, AZ, United States ‡ Mississippi State University, Mississippi State, MS, United States 1 Corresponding author: e-mail address: [email protected]

CONTENTS 1 Introduction ...................................................................................... 2 Theory of Measuring Natural Capital Shadow Prices in Real Ecological-Economic Systems ........................................................................................... 2.1 Conceptualizing Natural Capital ................................................. 2.2 Derivation of Natural Capital Pricing Equations .............................. 2.3 Intuition About Natural Capital Prices and the Importance of Multiple Stocks and Adjustment Costs .................................................... 2.4 Non-convexity and Non-differentiability........................................ 2.5 Non-autonomous and Stochastic Dynamics ................................... 2.6 Using Shadow Prices to Assess Sustainable Investment/Consumption .... 3 Approximators to Measure Natural Capital Shadow Prices .............................. 3.1 Three Ways to Approximate Shadow Prices .................................... 3.2 Tradeoffs Among Approximation Approaches .................................. 3.3 The Approximation Domain ...................................................... 3.4 Additional Numerical Considerations ........................................... 4 The Measurement of the Economic Program and Ecosystem Income and Its Connection to Natural Capital Asset Prices ................................................. 4.1 The Economic Program – x(s) ................................................... 4.2 Dividends from Natural Capital – W ............................................ 4.3 Ecosystem Income from Market Production ................................... 4.4 Ecosystem Income from Household Production............................... 4.5 Direct Ecosystem Income ........................................................ 4.6 Accounting for Ecosystem Income .............................................. 5 Examples and Applications to Date........................................................... 6 Discussion and Future Challenges............................................................ References............................................................................................

86 88 88 91 98 100 102 104 107 109 111 112 114 115 116 119 120 122 125 127 128 131 134

✶ This work was supported by the Knobloch Family Foundation (Fenichel) and the Lenfest Oceans Program (Abbott). Handbook of Environmental Economics, Volume 4, ISSN 1574-0099, https://doi.org/10.1016/bs.hesenv.2018.02.002 Copyright © 2018 Elsevier B.V. All rights reserved.

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1 INTRODUCTION Wealth, then, includes all those parts of the material universe which have been appropriated to the uses of mankind. . . . The appropriation need not be complete; it is often only partial and for a particular purpose, as in the case of the Newfoundland Banks, which are appropriated only in the sense that the fishermen of certain nations have the right to take fish in their vicinity. . . I. Fisher, 1906. The Nature of Capital and Income. P. 4.

The opening quotation reminds us that, despite the ballooning interest in ecosystem services and natural capital, these ideas have a long history in economics. Gaffney (2008) reviews classical cases where nature is treated as capital. Irving Fisher clearly identified the fish stocks of the Newfoundland Banks as stores of wealth, natural capital, as the first example of a capital asset in his 1906 book. He makes it abundantly clear throughout the text that he intends that natural and human capital should be included in wealth accounts. Scott (1973), in his seminal text (first published in 1955), points to the long history of natural resources being viewed as capital assets, and argues there is “no need for a new and grandiose theory of natural resources” – natural capital is simply a critical part of society’s capital and should be treated as such. In the century following Fisher’s seminal work, capital theory became a foundational part of the economics of natural resources (e.g., Hotelling, 1931; Scott, 1973; Dasgupta and Heal, 1979; Wilen, 1985; Barbier, 2011a; Fenichel et al., 2015). What has lagged is the measurement of the contributions of ecosystems to income flows and the value of the natural capital stocks generating market and non-market income flows – especially for assets outside of markets or with poorly defined property rights. The need for natural capital valuation is critical given the tight connection between maintenance or growth of the value of a society’s capital stocks and the sustainability of the welfare of its citizens. Natural capital accounting has the potential to provide prescriptive and retrospective assessment of sustainable development (UNU-IHDP and UNEP, 2014). “Sustainability” may well replace “growth” as the watchword of the 21st century, but in the words of Solow (1993), “talk [of sustainability] without measurement is cheap.” Just as many economists spent the first half of the 20th century defining and implementing measures for economic growth, we are now at a similar juncture for operationalizing a measure for sustainability. The prevailing economic definition of sustainability – compactly defined as non-declining intertemporal social welfare2 through time – relies upon tracking changes in inclusive, genuine, or comprehensive wealth (Arrow et al., 2004; World 2 The generally accepted definition of sustainability or sustainable development from the World Commis-

son on Environment and Development (1987) states, “Sustainable development is development that meets the needs of the present without compromising the ability of future generations to meet their own need.” Intertemporal welfare is the present discounted stream of present and future social welfare flows. There is an important distinction between intertemporal welfare and wealth. Intertemporal welfare and wealth are

1 Introduction

Bank, 2011; UNU-IHDP and UNEP, 2014; Dasgupta, 2014; Hanley et al., 2015; Hamilton and Hartwick, 2014; Polasky et al., 2015). Changes in welfare are closely connected to changes in wealth, where wealth is measured as the summed value of properly valued capital assets, including natural capital, less liabilities. Such wealthbased metrics of sustainability have had influence well beyond economics (Matson et al., 2016). Moreover, various international institutions (e.g., World Bank, UNEP) are moving ahead with attempts to measure sustainability using wealth metrics – moving closer to realizing Fisher’s vision. However, measurements of natural capital wealth have generally been missing or imprecise.3 As a result, natural capital has taken on a largely rhetorical role, and its measurement has seldom been linked to capital theory. Solow (1993) laments this state of affairs, stating that “a few numbers, even approximate numbers, would be much more effective in turning the discussion toward concrete proposals and away from pronunciamentos,” and “that the difficulty of doing better does not make zero a defensible approximation for the shadow price of environmental amenity.” The lack of good measures of capital value for natural assets is a major barrier for implementing inclusive, genuine, or comprehensive wealth (UNU-IHDP and UNEP, 2014; World Bank, 2011; Polasky et al., 2015). Smulders (2012) writes, “The Achilles’ heel of the method [Inclusive or Comprehensive Wealth or Genuine Savings] is the determination of the shadow prices,” where shadow prices refer to the appropriate natural capital asset prices. Polasky et al. (2015) emphasize that in current attempts to measure inclusive wealth, “all measures included in natural capital were values for market commodities,” but “evaluating sustainability via inclusive wealth . . . requires an assessment of the changes in value of all types of capital (emphasis added).” Hanley et al. (2015) review the theory of natural capital prices in wealth indices, and note the dearth of theory for measuring the prices. Yet, Hamilton and Hartwick (2014) emphasize that, “Underpinning these results [using wealth to measure sustainability] are shadow prices measuring the social value of the marginal unit of each asset.” Early efforts to measure the value of natural capital stocks in situ assumed a competitive market for the stock and efficient allocation of income flows (e.g., Halvorsen

only strictly the same if the intertemporal welfare function is linear in capital stocks leading to constant prices for the asset. However changes in these metrics can be made to be equivalent so in practice wealth is an affine transformation of intertemporal welfare. Other candidate metrics for sustainability have been proposed, including non-declining consumption or utility and non-declining stocks of resources. However, these are not satisfactory. Sustaining consumption ignores the importance of benefits that do not flow through the market while sustaining utility obscures the role of intertemporal allocation and measurement issues. Jones (2016) investigates how people may forgo consumption to invest in technology that extends their life, which highlights problems with non-declining consumption as a sustainability criterion. A nondeclining stock criterion rules out innovation and substitution. For further discussion of the theoretical justification for non-declining wealth as a sustainability criterion see Barbier (2011a), Dasgupta (2007). 3 The business and accounting community have used the phrase “natural capital” to describe a firm’s “storytelling” about environment-related impacts and risks to a firm’s business rather than rigorously measuring and valuing capital in a way comparable to the firm’s financial capital (Gleeson-White, 2014).

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and Smith, 1984). Similarly, integrated assessment models (e.g., Nordhaus, 2014) typically rely upon assumptions of optimizing economies (aside from the modeled environmental externalities) to recover the marginal social costs of natural liabilities such as atmospheric carbon stocks. Other efforts assume that the value of the asset is exactly zero, as in the case of complete institutional failure or open access (Maler et al., 2009).4 However, public policy and informal institutions lead to nonmarket allocation mechanisms that make these polar assumptions untenable for the overwhelming majority of important natural assets. Recently, economists have demonstrated in particular cases how to integrate knowledge of biophysical dynamics with economic modeling of the flow benefits from natural capital to measure shadow prices (Maler et al., 2008; Lange, 2004). Fenichel and Abbott (2014b) and Yun et al. (2017b) advance this pursuit by developing a general theory of valuing single and interrelated natural capital stocks subject to market imperfections and inefficient management, and show that this theory conforms to Jorgensonian (1963) capital theory. They also provide computational approaches for recovering shadow prices from real world data. In this chapter, we clarify the concept of natural capital, connect it to standard capital theory, and develop the theory of natural capital asset pricing under realworld imperfect institutions that, despite pervasive kakatopia (Dasgupta, 2007), are capable of maintaining some natural capital asset value.5 We discuss numerical techniques that enable us to approximate the capital gains and interactions across capital stocks that are important for natural capital stocks but rarely observable given their non-market nature. Then, we discuss cases utilizing the theoretical framework we’ve developed to explore how research in economics and other disciplines can help to facilitate the measurement of natural capital values. We conclude by providing examples of how positive and normative economic content have been integrated to supply shadow values for natural capital.

2 THEORY OF MEASURING NATURAL CAPITAL SHADOW PRICES IN REAL ECOLOGICAL-ECONOMIC SYSTEMS 2.1 CONCEPTUALIZING NATURAL CAPITAL Economists often first encounter the notion of capital, in physical form (e.g., machines) in introductory texts as it is combined with labor services to produce goods.

4 Indeed, in the real world the shadow price for something believed to be an asset could be negative. Imagine an open access institution with a production subsidy. This could drive the asset price of the natural capital to be less than zero. Importantly, there may be stocks where the sign of the shadow price depends on management institutions (Zivin et al., 2000; Horan and Bulte, 2004). 5 Dasgupta (2007) uses the term kakatopia to describe an, “at best, not-so-good society.” Specifically, he says analysis of kakatopia does not presume, “that the State can be trusted” or “that it optimizes on behalf of its citizens.”

2 Theory of Measuring Natural Capital Shadow Prices

The durability of physical capital is typically secondary or ignored altogether in this introductory story, and yet it is the ability of capital to serve as a durable, albeit depletable, store of future services (and hence value) that is its defining trait (Scott, 1973).6 For convenience capital is often broke into subcategories, e.g., reproducible (manmade or built) capital, human capital, and natural capital.7 The focus of this chapter is natural capital. It is important to keep in mind that the vast majority of benefits humans derive from natural capital flow from combinations of natural capital with the other capitals, including labor flows from human capital. For example, service flows from the environment are directly combined with labor to produce consumable goods and services, e.g., food and leisure, while natural capital can also contribute to maintenance or growth in human and machine capital in the form of a supportive environment and ores. Barbier (2011a) suggests that the arc of human history is largely a story of converting natural capital into human and physical capital. In the simplest case, a unit of capital is valued as the net present value of the flow of future services it confers (Varian, 1992). A perfectly functioning market for capital harmonizes this value in use with its value in exchange – its spot price. However, even when markets for an asset are imperfect or completely absent, the individual and collective decisions made by society in terms of investment or depletion nevertheless affect the present value accorded by the last increment of capital – revealing an implicit (shadow) price. Dasgupta (2007, p. 142) says, “economists observe that to say someone is accumulating capital is to suggest that they are sacrificing something now for future benefit.” Acts of investment and depletion are therefore a form of intertemporal exchange between present and future generations (where these may overlap), priced at the aforementioned shadow price. The plans individuals and societies use to govern these (dis)investment decisions are called the economic program (Dasgupta, 2007, 2014) or the resource allocation mechanism (Dasgupta and Maler, 2000; Hamilton, 2016; Hamilton and Ruta, 2009).8 By observing the economic program, it is possible to approach the valuation of natural capital within the revealed preference paradigm. The value of capital is intertwined with institutions, including systems of formal and informal property rights (North, 1990; Libecap, 1994) but also norms and customs, that form the incentives and constraints that mold the economic program and alter the transaction costs of exchange. Property rights for natural capital are often incompletely defined (a point made by Fisher in the quotation at the start of this chapter).9 Incomplete property rights (i.e. through externalities or public goods asso6 Nadiri and Rosen (1969) discuss the distinction between machine rental services and machine capital. 7 For the sake of focus, we do not discuss human capital and the interesting literature in this area further. At times human capital is split into knowledge capital and health capital. There is a continuing debate about the concept of social capital; see Matson et al. (2016) and Dasgupta (2007) for countervailing arguments. 8 Natural resource economics has largely focused on the optimal program, which is one of many potential economic programs. 9 Even with individual private property rights, current individuals choose their savings and borrowing rates by projecting their preferences into the future, often without regard for the possible preferences of those

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ciated with the flows of income from natural capital) and the lack of capital markets suggest that the prices for natural capital implied by the economic program fail to reflect the optimal marginal social worth of capital. Human investment and consumption behavior is constrained by institutional arrangements; hence, the revealed value of natural capital is dependent on, and inseparable from, these institutions (Fenichel et al., 2016b). Nevertheless, as we demonstrate in the subsequent section, this value is non-zero except in pure open access cases. Furthermore, biophysical realities operate as complicated appreciation and deprecation process in an “adjustment cost” model. Determining whose values count is another important aspect of any exercise in natural capital valuation. This determination must be explicit in the case of shadow prices, but it is also implicit in the decision to utilize market prices. For example, when market asset prices exist, but property rights are incomplete or informal rights exist (e.g., there are problems of externalities or public goods), market-derived asset prices fail to reflect the marginal social value of the asset. In such cases the realized asset prices do not reflect the full scope of benefits and costs resulting from the inefficient economic program. Rather, the prices only reflect the values of those whose preferences are ‘internalized’ by the formal market institutions in place. Others may be affected, contemporaneously and in the future, by the decision to invest or consume a unit of the resource besides those whose preferences are reflected in the market. For example, consider the conservation of forestland for non-timber services. As a durable impure public good (Cornes and Sandler, 1994) we might expect this activity to be underprovided, even if conservationists are able to actively participate in the land market because some conservationist may choose to free-ride. The price revealed in this asset market fails to capture the net present value of the incremental value that free riders (or those not allowed to contribute) derive from an additional unit of conservation. Yet the net benefit accruing to the free riders’ or those excluded from the market is part of the marginal social value of the asset, even if the asset is sub-optimally provided. The spatial context of natural capital influences the definition of who receives its service flows. Concerns about the spatial extent of services provided by environmental stocks and decisions about the appropriate scale of valuation are well known (Smith, 1993), and the spatial juxtaposition of natural stocks may determine what services they provide (Plummer, 2009). While reproducible capital (e.g., machines) may provide excludable services to users distributed across a landscape, the value of these services is tightly linked to the asset itself through a combination of private property rights and the existence of capital markets. Therefore arbitrage is expected to yield a ‘law of one price’ after accounting for transportation costs. However, the spatial specificity of the services provided by many forms

that may take possession of the capital at a later date. Connected to this concern is the potential for imperfect credit markets to distort consumption and savings decisions related to natural capital (Zilberman et al., 2008; Fenichel et al., 2018; Tahvonen et al., 2001).

2 Theory of Measuring Natural Capital Shadow Prices

of natural capital, their immobility (or mobility at prohibitive cost), and complex property rights often make the transaction costs of arbitrage prohibitive. As a result, proximate natural assets (e.g., groundwater basins) may have very different shadow prices (Addicott, 2017). Therefore, tracking sustainability as changes in wealth may be important at local or regional scales using the “national accounting” approach of inclusive wealth (Dovern et al., 2014; Pearson et al., 2013; Addicott, 2017; Yun et al., 2017b). Prior to proceeding with theory, it is worth clarifying what we should call the marginal social worth of a unit of natural capital. Arrow, Dasgupta, Maler and colleagues (Dasgupta, 2009; Arrow et al., 2003; Dasgupta and Maler, 2000; Arrow et al., 2004; Dasgupta, 2014, 2007; Hamilton and Ruta, 2009; Maler et al., 2008) use the term “accounting” price, arguing that these prices are the appropriate prices for a system of wealth accounts. They differentiate the accounting prices from “shadow” prices, which they imply come from an optimizing economy, rather than what is observed in the real world. Obst and Vardon (2014) and Obst et al. (2016), writing from the standpoint of national accountants, use the term “exchange values,” which they suggest is the value at which goods and services are “exchanged” regardless of market prices, including the intertemporal exchange of natural capital. The rest of the literature (e.g., Hamilton and Clemens, 1999; Heal, 2012; Greasley et al., 2014; Hanley et al., 2015; Smulders, 2012; Hamilton and Hartwick, 2014; Barbier, 2013; Solow, 1993; Heal, 1998; Arrow et al., 2012a) uses the term “shadow price.” However, most authors assume the economy optimally allocates capital or are ambiguous about this assumption. We have found many economists find the term “accounting price” confusing, and associate it with accounting versus economic profit. The term “exchange value” is too imprecise for our purposes. Therefore, we adopt the term “shadow price” to describe a marginal value, not observed in a market, of a unit of capital at a given stock level under the existing economic program. Alternatively, we employ the relatively precise and unambiguous term “natural capital asset price.” We use the phrase “optimal shadow price” when the shadow price is derived through optimizing assumptions. Thus, saying “shadow price” alone implies the realized shadow price stemming from an actual observation in an imperfect, and potentially kakatopic, economy.

2.2 DERIVATION OF NATURAL CAPITAL PRICING EQUATIONS To derive an expression for a natural capital shadow price in an economy that does not necessarily optimally allocate natural capital consider an S-length vector of natural capital stocks, s(t) at time t .10 The dynamics of the capital stocks can be classified as time autonomous or time non-autonomous and as deterministic or stochastic. A time

10 Time is suppressed when doing so does not cause confusion. While we focus on natural capital, the

theory we develop could also be applied to stocks of human or reproducible capital, and all relevant capital stocks could be included in the vector.

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autonomous system implies that time does  not  directly enter into the equations of motion for the capital stock, e.g., s˙ (t) = G s(t) implies that time enters  . Non-autonomy  the equation of motion directly s˙ (t) = G s(t), t . A full theory of pricing natural capital assets including non-autonomous and stochastic dynamics has yet to be formally developed. Other features of dynamics that may impact shadow prices are adjustment costs, non-convexities, and non-differentiability. Nevertheless, considerable progress can be made by focusing on deterministic and time autonomous multi-stock dynamics, which we explore in section 2.3. We explain how in many important cases the deterministic and time autonomous approach extends naturally to cases with adjustment costs (discussed in section 2.3) and non-convexities and non-differentiability (discussed in section 2.4). In section 2.5 we discuss paths forward for incorporating non-autonomous and stochastic dynamics. In section 2.6, we discuss how natural capital asset prices are used in wealth accounting for sustainability assessment. The development of a theory for natural capital asset prices closely follows and builds upon the pioneering work of Dasgupta and Maler (2000), who develop a price concept without an optimizing economy.11 Maler et al. (2008) and Hamilton and Ruta (2009) sketch the connection between wealth accounting and shadow prices for natural capital assets. Fenichel and Abbott (2014b) formalize the theory of measuring shadow prices, connect it to classical capital theory, and provide numerical tools for connecting theory with data. Yun et al. (2017b) extend Fenichel and Abbott’s approach to multiple interacting stocks. A first step is to define M(s, ) as a time autonomous economic program that accounts for a vector of state variables (i.e., capital stocks) s that comprise the “state of the world” and a vector of parameters that define institutional arrangements,  (Dasgupta, 2007; Fenichel and Abbott, 2014b). Formally, the economic program maps the state of the world and institutions into a vector valued function M : (s, ) → x(s; ), where the length of x need not equal the length of s. The economic program provides a feedback rule connecting state variables into flows of human actions that are “relevant” in the sense that they directly or indirectly affect the dynamics of s and/or influence income flows. We suppress the dependence on  to reduce the notational burden of the exposition.12 Upon measuring the economic program we can define a system of equations of motion   (1) s˙ i = Gi (s) − f i s, x(s) , i = 1, . . . , S, where i indexes the ith element of the vector s. Gi is the environmental growth function for each stock i, which is zero for nonrenewable resources, and f i is a human impact function for each stock i for extraction or degradation of natural capital stocks 11 Dasgupta and Maler’s ideas are further developed in Arrow et al. (2004, 2012a, 2003), Dasgupta (2007, 2014). 12 If institutions are believed to be an endogenous function of capital stocks then they are functions of s. If institutions are changing exogenously through time, then approaches for addressing time non-autonomous systems (discussed below) could be used.

2 Theory of Measuring Natural Capital Shadow Prices

(Fenichel et al., 2016a). In relatively simple extractive contexts (such as the harvest of fish), f i may be thought of as a factor demand that enters into the production of profit, while in more complex cases, such as incidental degradation of habitat from recreation, f i may be the result of unintended joint production. The combination of (1) and the economic program captures Shogren and Crocker’s (1999) notion that economic and ecological systems are “jointly determined.” In dynamic resource systems, people make institutionally constrained consumption and conservation decisions with respect to nature capital, which in turn alter the dynamics of natural capital stocks and feedback once again to human behavior. Implicit in this feedback cycle is that the human behaviors captured in the economic program are “fast” in their rate of adjustment relative to that of the capital stocks so that x(s) specifies a forecast of the “behavioral equilibrium” reached in response to any given state (Maler et al., 2008). Natural capital then responds to this change in behavior, resulting in a new shadow price consistent with the forecasted paths of capital stocks and human actions consistent with (1) and the economic program. In any given modeling context the analyst must make important decisions about which margins of behavior to treat as variable, and hence part of x(s), and which to regard as either fixed or varying sufficiently slowly that they are best modeled as a separate capital stock. For instance, in a fishery context, variable dimensions of fishing effort (e.g., hours fishing) may be viewed as a component of the economic program, while the physical capital of a fishing fleet may be best included within s (Moberg and Fenichel, 2017; Clark et al., 1979). While x(s) is presented as a reduced-form feedback rule, it results from the purposeful actions of individuals within a given institutional context and therefore can be derived from a structural economic (i.e. constrained optimization) model. For now, we assume that x(s) can be measured, and discuss the conceptual and practical challenges of doing so later in the chapter. Fisher (1906) viewed income as “interest-like” returns  on wealth  (Weitzman, 2016) or dividends from capital net of capital gains. Let W s(t), x(t) be a Fisherian income index, expressed in monetary units, of the net benefits accruing to society from capital stocks s(t) and actions x(t) at time t . Though we express Fisherian income in money units, Fisher (1906, p. 105) defined “real income” as “enjoyable commodities and services” and including “the supplementary elements which we found lacking under the head of money-income. . . for it [real income] recognizes that money is only an intermediary, and seeks to discover the real elements for which that money-income stands.” This notion of real income is also reflected by Krutilla (1967), who is particularly concerned about income stemming directly from s. He writes, “When the existence of a grand scenic wonder or a unique and fragile ecosystem is involved, its preservation and continued availability are a significant part of the real income of many individuals.” Today, we might simply call this income moneymetric utility.   The critical features of W s(t), x(t) are that it consistently aggregates the individual preferences of those whose preferences figure in the analysis into a cardinal index of social welfare, and that it be expressed in stable (real) monetary units that

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are comparable across time after exponential discounting at a constant rate (Dasgupta et al., 1999). The latter property is important so that natural capital asset prices are comparable to asset prices of transacted capital and other market prices. The particular context will define the appropriate index. When welfare effects are limited to firms, measures of profits or producer surplus may suffice, while measures such as summed compensating or equivalent surpluses (as in cost-benefit analysis) or equivalent income metrics (Hammond, 1994) grounded in the theory of money-metric utility (Samuelson and Swamy, 1974; Samuelson, 1974) will be needed more generally. Embedded within the W function are specific institutionally-conditioned assumptions about how the benefit flows from stocks of capital, directed by the economic program, are allocated across individuals. Furthermore, W embeds ethical considerations of whose dollar-denominated individual benefits count in a relative sense, if at all.13 With W defined as an income index, we define “ecosystem income” as the component of W that is the dividends yielded by natural capital.14 In practice, however, these dividends are likely not additively separable within the function W , so that ecosystem income is really only meaningful for ceteris paribus changes in natural capital relative to a baseline. Much of environmental economics focuses on measuring ecosystem income (i.e. valuing ecosystem services), particularly ecosystem income that does not “flow through the cash drawer” as Fisher refers to non-market values. At time t , the present value of net benefits or intertemporal social welfare function is  ∞     e−δ(τ −t) W s(τ ), x(s(τ )) dτ (2) V s(t) = t

where the evolution of s(τ ) through time follows Eq. (1). Substitution of the economic program into W , the assumption of an infinite time horizon, and assuming that the resource dynamics in Eq. (1) and economic program are time autonomous, enables V to be expressed solely as a function of s(t). Substituting through x(s) it is    possible to redefine W over the stock vector s so that W ∗ s(τ ) ≡ W s(τ ), x(s(τ )) ,

13 In keeping with the logic of traditional benefit-cost analysis the W in applications we discuss weigh an increment of income change to different populations at a point in time equally. This coincides with the same Negishi (1960) social welfare function as that “maximized” by an idealized market, where all goods are private, conditional on the existing allocation of income. However, the Negishi social welfare function is regularly extended to the non-market context (Fenichel and Abbott, 2014a). While there is nothing preventing natural capital valuation using the methods in this chapter with W derived under the less restrictive assumptions of ‘social benefit-cost analysis’ (Dasgupta et al., 1972), the resulting shadow prices are not directly comparable to asset prices for marketed capital stocks. 14 We prefer the term ecosystem income to ecosystem service in this context. The first maintains symmetry with the broader notion of an income index while the latter creates the potential for ambiguity between a quantity measure of benefits from nature and the valuation of that quantity. The distinction is important since, much like a quantity of goods, the same ecosystem service may generate different values of ecosystem income under different conditions.

2 Theory of Measuring Natural Capital Shadow Prices

where the asterisk indicates the elimination of x. Given the assumption that behaviors in the economic program are always in (short run) equilibrium, we slightly abuse notation and assume the partial derivative of W includes the feedback through the   dx ∂W economic program: Ws i s(τ ), x(s(τ )) ≡ Ws∗i = i + (∇x W ) i , where ∇x W is ∂s ds dx the gradient vector of W with respect to x, i is the Jacobian matrix of x(s) with ds respect to s i , and  indicates the transpose.15 The elimination of x is akin to an economic equilibrium process that allows “quantity demanded” to adjust to prevailing conditions, conditional on institutions, in ways similar to a location equilibrium in a sorting model (Smith et al., 2004). The shadow price of stock i at time t for a given economic program is     p i s(t) ≡ ∂V s(t) /∂s i (t).

(3)

Definition (3) states that the shadow price of stock i is the change in the net present value to society from holding more natural capital stock i in situ – from exchanging the stock with the future. Furthermore, definition (3) emphasizes that the shadow price of stock i is a function of all capital stocks. Therefore, a change in capital stock j = i can influence the shadow price of stock i. This is not surprising; it simply implies that some stocks of capital are substitutes or complements for other stocks of capital, leading to effects akin to general equilibria in asset markets among natural capital asset prices. The potential for such ‘cross-effects’ arises beyond the role of capital stocks in income flows themselves, W . Varying degrees of substitution can also arise through the dynamical system (1) and through behavioral feedbacks between stocks in the economic program x(s) – where the latter influences income flows and stock dynamics. It is these substitution and complementarity relationships that are at the root of the sustainability problem (Barbier, 2011a; Quaas et al., 2013; Drupp, 2018). There are no constraints on the sign of pi (s). Shadow prices may be positive, implying stocks are assets, or negative, implying stocks are liabilities. Since V (s) is a function of x(s), the sign and magnitude of shadow prices depends on the management of the stocks themselves, so that the value of natural capital is highly dependent on the market, political and social institutions that undergird management of stocks and flows, and the innate dynamics of the stock (Maler et al., 2008). Assume V is differentiable, following Dasgupta and Maler (2000) and Arrow et al. (2003), Fenichel and Abbott (2014b) and Fenichel et al. (2016a) differentiate

i   15 A similar substitution of the economic program into f i yields f i s, x(s) = f i ∗ (s) so that f i = ∂f + i si ∂s dx ∗ (∇x f i ) i = f ii . The first step is substituting in the economic program. So, while the second term looks s ds

like it comes from a total derivative, it is in fact just an application of the chain rule.

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  V s(t) using the definition on the RHS of Eq. (2), with respect to t to obtain   dV = δV − W s, x(s) . dt

(4)

Eq. (4) states that the change in the present value of the net benefits with respect to time is equal to the present value of the net benefits multiplied by the discount rate less the current dividend or income flow. The time derivative of Eq. (4) can also be expressed as   dV ds = (∇s V ) = p s(t) s˙ , dt dt

(5)

ds where ∇s V is a (S × 1) gradient vector, = s˙ is a (S × 1) Jacobian matrix, and dt   p s(t) is (S × 1) shadow price vector. Eq. (5) states that the time rate of change of the present value of benefits is equal solely to the sum effect of changes in the natural capital stocks. In the second equality in Eq. (5) we substitute in the definition of the natural capital price from (3). Since Eqs. (4) and (5) are equivalent, it follows that   δV = W s, x(s) + p(s) s˙ = H (s, x, p) = H ∗ (s, p) (6) H (s, x, p) is the current value Hamiltonian (CVH), which comprises the flow of  current benefits (dividends), W s, x(s) , and the value of increments to the stock (capital gains), p s˙ .16 The substitution of the economic program allows the CVH to be expressed as a function of s and p. By using the observed, and likely nonoptimized, economic program we are replacing the optimized control rule that would be found using Pontryagin’s maximum principle with what actually happens in the world.17 Eq. (6) demonstrates   that the  CVH is the  current return on the present value of net benefits: δV s(t) = H ∗ s(t), p(s(t)) . The Hamilton–Jacobi–Bellman (HJB) equation remains valid, even in the case of non-optimized, autonomous systems (Dasgupta, 2009; Fenichel and Abbott, 2014b; Dasgupta and Maler, 2000). Rearranging Eq. (6) yields       V (s) = δ −1 W s, x(s) + p s(t) s˙ (7) Upon moving the discount rate to the left-hand side, Eq. (7) takes the form of the fundamental asset equation (Shapiro and Stiglitz, 1984), or if W is strictly a consumption index then Eq. (7) has connections to net national product (Weitzman, 1976).18 16 Asheim (2000) suggests a generalization for non-autonomous systems. 17 For those who wish to assume that existing institutions optimally allocate resources, this is akin to

an empirical approach to the first order condition. For those doubtful that existing institutions optimally allocates resources, this approach enables us to understand the valuation of natural capital implicit in society’s actions via the economic program. 18 For further discussion of the welfare and sustainability implications of net national product see Dasgupta (2009).

2 Theory of Measuring Natural Capital Shadow Prices

Next, differentiate Eq. (7) with respect to s i  i j  ∂p j   ∂p i i ∂V i −1 i ∂ s˙ j j ∂ s˙ s, x(s) + = p (s) = δ s ˙ + p + s ˙ + p W (8) i s ∂s i ∂s i ∂s i ∂s i ∂s i j =i

∂p i i s˙ = p˙ i follows from assuming time∂s i autonomy. This simplification makes it possible to derive an equation of motion for the shadow price of the stock of natural capital, which is mathematically identical to the adjoint equation associated with the maximization of the CVH (see Fenichel and Abbott, 2014b, for details). However, in this case the adjoint equation holds along the system dynamics given by the arbitrary “feedback control rule” embedded in the economic program, (1) and the initial conditions. Furthermore, in the multi-stock case the evolution of the price dynamic is linked to other stocks of natural capital and shadow prices (Yun et al., 2017b). Eq. (8) can at long last be rearranged to isolate p i If there is only a single stock, then

p (s) = i

∂p j j  j =i ∂s i s˙ + j =i  i  i − Gs i (s) − fs i (s, x(s))

Ws i (s, x(s)) + δ

 ∂pi ∂s i

s˙ i +



p j ∂∂ss˙ i

j

.

(9)

Eq. (9) modifies the discount rate in the denominator by the rate of physical change in the quantity of the natural capital.19 The notion that one can recover theoretically grounded shadow values for natural capital stocks, regardless of whether “management” maximizes the present value of income (and hence the CVH at all instants), may be surprising, even startling, at first blush. Indeed, economists are accustomed to bundling the adjoint equation (Eq. (7)) along with the condition to maximize the CVH as twin necessary conditions for a dynamic optimum under the Pontryagin maximum principle. However, closer inspection of the derivation of the maximum principle reveals that the adjoint equation is not indicative of a dynamic optimum. Instead it is a description of how the co-state variable must appreciate or depreciate over time for any given control rule (i.e. economic program) so that the influence of current actions on future streams of welfare are completely captured by p s˙ in the CVH – so that the co-state is indeed the first partial of the value function (Leonard and Long, 1998, p. 153). It is a rule for how an asset price must behave under the forecasts embodied in the coupled capital dynamics and economic program. Additional intuition can be gained from the simple single-species fishery model (Clark, 2005). It is well known in this context that the social planner outcome can be implemented through a time path of harvest taxes that are equalized with the adjoint variables along the optimal path. In other words, charging a series of harvest 19 This modification also appears in Brock and Xepapadeas (2018) as a climate adjustment to the discount rate.

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taxes τ (s) = p ∗ (s), where the asterisk indicates optimality, will provide fishermen the appropriate price signals to implement the optimal economic program x ∗ (s). Conversely, open access management can be implemented by setting these taxes to zero in all time periods. Other choices of harvest tax rules will result in other behavioral choices by fishermen, and hence distinct economic programs. The harvest tax rule τ (s) that implements a particular kakatopic economic program, τ (s) → x(s), are therefore the shadow prices revealed by the economic program and mathematically captured in Eq. (9). This vector of shadow prices reflects the actual intertemporal exchange ratio employed by society. Therefore, it is this ratio that should be used to assess whether past decision lead to non-declining intertemporal welfare through time or whether future actions, guided by the same institutions, will lead to non-declining intertemporal welfare.

2.3 INTUITION ABOUT NATURAL CAPITAL PRICES AND THE IMPORTANCE OF MULTIPLE STOCKS AND ADJUSTMENT COSTS Considering a single stock, omitting superscripts to minimize notational burden, helps build intuition. In the case of a single stock of capital, Eq. (9) corresponds to Jorgenson’s (1963) equation (p. 249) for the value of invested capital.20 Jorgenson’s equation, expressed using the previously defined notation and setting his “rate    p˙  . Jorgenson assumes of direct taxation” to zero, is Ws s, x(s) = p −˙ss + δ − p that the marginal change in production with respect to capital can be multiplied by a constant marginal price per unit output to give the current marginal benefit, marginal dividends, from an expected increase in capital stock. The definition of   Ws s, x(s) is more general, encompassing the case of downward sloping market demand or non-market contexts where the ecosystem services provided by s have diminishing marginal value. Given that Jorgenson develops his model for private capital, he refers to the discount rate, δ, as “the rate of interest.” He defines the net marginal productivity of the stock, −˙ss , as the “rate of replacement”, which is the (constant) rate of capital depreciation in his model of physical, and hence non-renewable, capital. Jorgenson does not consider the multiple stock case. In the multi-stock case Jorgenson’s approach would lump cross-stock effects into the observable capital gains term, p, ˙ since the capital gains are observable for capital assets priced in the market. Finally, the shadow price of the stock, p, is the “price of capital goods” in Jorgensen’s framework. Aside from differences of nomenclature and our exclusion of taxation, Eq. (9) nests Jorgenson’s more specialized capital pricing equation. Eq. (9) says the shadow price of a natural capital asset equals the marginal   income flow from a change in natural capital stock, Ws s, x(s) , adjusted by an20 In practice all capital prices rely on some sort of forecast about the future. Therefore, capital asset prices

are always in terms of expectations. Jorgenson develops theory in a deterministic framework, as do we. Therefore, we do not emphasize the expected nature of the quantities in the expressions.

2 Theory of Measuring Natural Capital Shadow Prices

ticipated shadow price (scarcity) changes, which include capital gains or losses and cross substitution or complementarity impacts, divided by a discount rate adjusted for the effect of natural capital on its own growth. Since the economic program is substituted prior to taking derivatives, the stock changes include both natural (e.g. through density dependence) and human-induced changes through behavioral feedbacks. The adjustments to the discount rate in the denominator of Eq. (9) can be thought of as the net rate of natural capital productivity (NRNCP). This adjustment term creates a wedge between the rate of return to holding natural capital and δ. If ∂Gi (s) > 0, then the effective discount rate, the denominator, adjusts downward to ∂s i reflect the productivity of natural capital. On the other hand, if increases in natural ∂f i (s, x(s)) > 0, then the discount rate capital increase anthropogenic degradation, ∂s i adjusts upward in response to this endogenous depreciation. Jorgenson’s assumption of perfect capital markets is untenable for natural capital, and the capital asset pricing approach must be extended to the cases with the potential for meaningful cross-stock effects. Cross-stock effects emerge in the pricing of natural capital because stocks of real capital – especially natural capital, interact and affect each other. In practice, it will be important to account for interconnections among tightly coupled stocks to develop prices reflecting these effects as part of wealth accounting. Considering additional capital stocks results in the additional numerator terms provided in Eq. (9), relative to Jorgenson’s equation. These terms capture the influence of conserving an increment of natural capital i on the future productivity of the fund of capitals in delivering valued services (i.e. capital gains), given the biophysical dynamics and economic program. The  ∂p i i N ∂p j j  s˙ + j =i i s˙ reflects the effects of investment second numerator term ∂s i ∂s i in s on capital gains through its effects on the shadow prices of all assets (i.e. “price effects”). In the single-stock case this collapses to dp/dt = p˙ = (∂p/∂s)˙s .

j j i The third numerator term in Eq. (9) N j =i p (∂ s˙ /∂s ) captures an effect that is only present in multi-asset systems, the effects of an investment in s i on the physical growth of other natural capital stocks in the fund (i.e. “cross-stock effects”). Together, price effects and cross-stock effects enable shadow prices to capture nonlinear substitution possibilities and complementarities among stocks as their quantities change. Eq. (9) provides a basis for deriving shadow prices for capital conditional on economic programs, which may not arise from dynamic optimization and perfect arbitrage. By computing shadow prices in this fashion it is possible to compare them to market derived capital asset prices, and therefore, when multiplied by quantity changes, they may be used in wealth accounting (Fenichel et al., 2016a, 2016b; Yun et al., 2017b). Tobin (1967) criticizes the Jorgenson approach because, “there are no

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frictions or speed-of-adjustment costs.”21 However, this critique may be addressed by the inclusion of additional capital stocks (see section 2.5).

2.4 NON-CONVEXITY AND NON-DIFFERENTIABILITY Convexity of preferences and production is central to price theory (Spence and Starrett, 1975; Starrett, 1972; Skiba, 1978), but non-convexity is ubiquitous in biophysical production systems (Dasgupta and Maler, 2003; Fenichel and Horan, 2016; Maler et al., 2003; Tahvonen and Salo, 1996). Therefore, it is important to ask how non-convex ecological production or economic programs impact natural capital asset prices. The concern about non-convexity in resource economics pertains to the problems that non-convexities create for the use of the price mechanism – as in cap and trade markets – to implement a desired outcome; in general the decentralized mechanism of the price system cannot be relied upon in non-convex settings (Starrett, 1972). Our concern, mirroring that of Dasgupta and Maler (2003), is different – merely asking whether non-convexities affect our ability to use (10) and its associated shadow prices as valid intertemporal welfare measures. Discontinuities, a special case of nonconvexity leading to non-differentiability (and undefined marginal changes), in V or its first derivatives can arise from positive feedback loops and complex interactions in the underlying biophysical dynamics – so-called stock non-convexities (Dasgupta and Maler, 2003).22 Discontinuity and non-convexity can also emerge from underlying features of the flow of benefits W (s, x), including ‘transitional non-convexities’ such as start-up or shut-down costs (Davidson and Harris, 1981), and even the economic program x(s). Non-convexities seem as though they should lead to shadow price discontinuities.23 Indeed, if the economic program is optimized, a non-convexity can lead to a point of indifference where the optimal program in not uniquely defined (Skiba, 1978; Maler et al., 2003). However, in non-optimized systems, where the economic program is pre-determined, non-convexity merely appears to make the realized shadow price function p(s) nondifferentiable at a specific point (Arrow et al., 2003), but piece-wise continuous. Using the classic shallow lakes problem as an example, Arrow et al. (2003) show that non-convexity poses at most minimal challenges, conditional on a predetermined economic program, for assessing sustainability using wealth accounting metrics in systems with a non-convexity in the state dynamics. As another illustration, consider the case of a policy-induced moratorium driven by a non-marginal 21 Tobin also criticizes Jorgenson’s example as “barely dynamic” and criticizes his solution technique for

the optimal investment program. While valid critiques, they do not diminish the contribution of Jorgenson’s asset price equation. 22 Institutional features of a real-world resource management system can create a non-convexity in a setting where an optimal economic program would otherwise yield convexity, but non-convexity in biophysical production is not generally sufficient for non-convexity in the intertemporal welfare function (Fenichel and Horan, 2016). 23 If the intertemporal welfare function, V (s) is non-convex in s, this means that there exists at least one value for s where p(s) = Vs (s) is undefined.

2 Theory of Measuring Natural Capital Shadow Prices

shift in harvest activity when the stock crosses a policy threshold – a form of transitional non-convexity (Davidson and Harris, 1981). For simplicity of argument, we utilize a single stock, deterministic, time-autonomous system. First, consider a moratorium on stock withdrawal when s < s, with some well-defined economic program of harvest x(s) > 0 if s ≥ s and x(s) = 0 if s < s. Assume, without loss of generality, that there are no direct flow benefits from the stock itself, so that there are no benefits received during a moratorium. Also, assume the moratorium is expected to recover the stock such that it exceeds s in finite time. Finally, for simplicity of argument, assume that the dynamics induced by x(s) never lead to the stock falling below s along the transitional path for s ≥ s. This assumption allows us to directly recover p(s) for values of s ≥ s using (9). When 0 < s < s there is some transitional interval τ (s) with τ  (s) < 0, during which the stock recovers to the moratorium threshold, at which point V (s) = V (s). However, there are no flow benefits or dividends of any sort over the recovery period, only capital gains. Therefore, V (s | s < s) = e−δτ (s) V (s). The shadow price for s < s is therefore p(s | s < s) =

  ∂V (s | s < s) = e−δτ (s) Vs (s) − δτ  (s)V (s) ∂s

(10)

where p(s | s < s) > 0 (assuming V (s) > 0 and p(s) = Vs (s) > 0) because τ  (s) < 0. This does not induce a discontinuity in the shadow price at s so long as τ  (s) goes continuously to zero, which must be the case if the stock changes continuously in time. Rather, the price is piece-wise continuous. Intuitively, in a system where the economic program and biophysical dynamics yield a deterministic trajectory from a given initial condition, all thresholds and other non-convexities along that trajectory are fully internalized in the value function at each stage. Therefore, much as a major market event would not alter stock prices if it were fully anticipated, we should not observe the value of a marginal unit of natural capital changing discontinuously. This implies a piecewise continuous function for capital prices and suggests that – as argued by Dasgupta and Maler (2000, 2003) – shadow prices derived from models that incorporate the non-convexities in question fulfill all the informational demands of a price, even at the precipice of a threshold or tipping point into an alternative basin of attraction. Non-convexity plays a much greater role in identifying optimal economic programs and optimal shadow prices then it does in measuring realized shadow prices. Non-convex production or preferences creates challenges in identifying the optimal program because they can create multiple conditionally stable equilibria separated by indifference manifolds, Skiba manifolds, in state space which must evaluated numerically (Skiba, 1978; Caulkins et al., 2009; Fenichel and Horan, 2016; Horan et al., 2011; Fenichel et al., 2015; Brock and Starrett, 2003). This problem does not occur in the context of recovering realized shadow prices in a deterministic model because the economic program, and hence the relevant basin of attraction, is determined ex-ante.

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2.5 NON-AUTONOMOUS AND STOCHASTIC DYNAMICS The pricing of multiple stocks subject to real-world management and deterministic and time autonomous dynamics provides a substantial toolbox for policy. However, future work will need to consider how to expand this theory to incorporate nonautonomous and stochastic dynamics. In this section we discuss some ideas and conjectures about constructive paths forward, while highlighting the emerging nature of this literature. There are many cases where non-autonomous dynamics are likely a first-order concern for measuring the value of natural capital and assessing sustainability. Variables such as climate change, urbanization, and human population growth are sources of exogenous forcing for many resource systems and therefore are naturally viewed as functions of time itself (and hence non-autonomous). Such non-autonomous dynamics can enter the system in multiple ways – whether through stock dynamics (e.g., climatic impacts on recruitment), the economic program (e.g., exogenous technical progress), or the income index (e.g., exogenous changes in market prices). Prior contributions in the wealth accounting literature provide promising, albeit untested, approaches for addressing non-autonomy in natural capital pricing. Arrow et al. (2012a) state that the time autonomy assumption is not restrictive because “time can be regarded as an additional form of capital asset,” with the partial derivative of the intertemporal welfare function with respect to time as “the shadow price of time at a specific time.” In this treatment time effectively functions as a residual capital stock – much like a ‘Solow residual’ measure of total factor productivity (TFP) in growth accounting. While the mathematical analyses that lead Arrow et al. to this theoretical conclusion are compelling, at a minimum treating time as an explicit capital stock creates some technical challenges for implementing the approximation approaches for recovering shadow prices described in section 3. A key feature of these approaches is that the future dynamics of the state variables can be defined within a bounded set. The path of time is unbounded. Thus, the approaches to measurement discussed in section 3 may fail if time is included as a state variable. However, this problem can be approached in at least two ways. First, while time is always increasing and is unbounded, the approximation error associated with truncation of the upper bound of its state space will decline to an arbitrarily small extent as this bound increases due to the influence of discounting. Second, the unbounded domain for the time state variable can be mapped into a bounded domain through a change of variables (e.g., through the use of a logit function). An alternative approach to non-autonomy is to transform a seemingly nonautonomous problem into one that is autonomous. While Arrow et al. (2003) question the broad applicability of this approach, we conjecture that in some of the most important cases, e.g., climate change, it may be possible to map the non-autonomous system to a time autonomous system by delving deeper into the underlying mechanisms and structure of the non-autonomy. For example, Fenichel et al. (2018) make a time  au tonomous model of tree growth, s˙ (t) = F (t) into a model such that s˙ (t) = G s(t) . A similar approach seems possible for climate change forecasts, where a measure of temperature at time t is commonly projected as a function of current temperature and

2 Theory of Measuring Natural Capital Shadow Prices

a future date. However, if temperature change is taken as exogenous (or conditional on an exogenously chosen scenario), then it seems feasible to introduce temperature with autonomous dynamics as a separate “stock.” This should be sufficient to decontaminate the shadow prices of the stocks of interest from climate change effects. This approach is appealing because climate sensitivity is ultimately bounded (Roe and Baker, 2007) while time itself is not. Furthermore, if temperature is indeed the important factor, then this approach allows for a deeper understanding of the shadow value of temperature as an asset – as opposed to the less interpretable role of time as a “residual” capital asset. The case of stochastic stock dynamics also merits future investigation. For the case of geometric Brownian motion, Stokey (2008) and Dixit and Pindyck (1994) emdV ploy Ito’s Lemma to show that can be written as a function of Vs (i.e., p(s)) and dt Vss – creating a generalization of the HJB equation and suggesting that the derivation in section 2.2 can be extended to at least the multivariate geometric Brownian motion case, including covariances between assets. More generally, it is likely that techniques and numerical methods employed in the financial asset pricing literature may be adapted for natural capital – albeit with suitable modifications to the dynamic maximization assumptions that typically underlie these models. Brock and Xepapadeas (2018) explain an extension of the Hamilton–Jacobi–Bellman (HJB) equation known as the Hamilton–Jacobi–Bellman–Isaacs (HJBI) equation to motivate the robust control of systems under misspecification of climate and ecosystem dynamics. We postulate, without proof, that this approach may be fruitful for developing a form of natural asset pricing under Knightian uncertainty or ambiguity. Alternatively, Reed and Heras’s (1992) approach to transforming Poisson jump processes into deterministic optimization problems seems adaptable to our general theory, but, again, more research is needed in this area. We largely focus on the case when stochasticity is associated with the stock dynamics. However, there may be times when stochasticity is fundamentally a part of the economic program. To the extent that these represent small deviations from a deterministic rule that are smoothed through time (e.g., disproportionate number of fir trees cut in December), then this is probably not a substantial issue. Discrete shifts in the economic program that are anticipated may be handled along the lines of the moratorium example in the previous section. On the other hand, if these structural breaks are unanticipated (e.g., social or military revolutions), then their occurrence will yield discrete changes in shadow prices and the associated sustainability indices – even if the objective probability of the state change was properly capitalized ex ante. However, all sustainability assessments are inherently conditional on a particular forecast of the economic-ecological system dynamics, such that current sustainability does not guarantee future sustainability (Arrow et al., 2004). Of course, there is also the issue of uncertainty associated with the measurement of the economic program, which in many cases may be non-trivial. We address this concern in section 4.

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2.6 USING SHADOW PRICES TO ASSESS SUSTAINABLE INVESTMENT/CONSUMPTION The motivation and derivation of genuine savings and inclusive wealth as measures of sustainability are thoroughly developed elsewhere (Arrow et al., 2012a; Dasgupta, 2007; Hamilton and Clemens, 1999; Hamilton and Hartwick, 2014; Dasgupta and Maler, 2000; Hamilton and Ruta, 2009); therefore, we only provide a brief sketch here. A definition of sustainability rooted in the intertemporal maintenance of ‘productive capacity’ – the potential of all capital stocks and the institutions that coordinate their use to provide a discounted stream of welfare – requires a nondeclining intertemporal welfare, V , through time as expressed in Eq. (2) (Dasgupta, 2007). Therefore, if V remains undiminished over a given time interval, then we would say that the system has been managed sustainability over this interval (at least within the bounds of the system captured by V ).24 From Eq. (5), dV =

S  ∂V i=1

∂s

ds i = i

S 

p i (s)ds i = dW

(11)

i=1

This expression shows that for infinitesimally small changes in capital stocks the change in a system’s productive capacity can be reduced to a linear index of the changes in each of the capital stocks, weighted by their respective shadow prices at the initial stock levels. However, this definition holds exactly only in the case of infinitesimal changes in the underlying capital stocks. For real-world applications non-marginal changes in capital stocks this relationship becomes: V =

S with i (s)s i +  = W, so that V ≈ W.  represents higher-order approxip i=1 mation errors, which may be non-trivial. This is most easily seen in one dimension in Fig. 1 by comparing panels A and B. Consider a loss of stock from s1 to s2, with the associated change in shadow prices from p1 to p2 . Panel A shows the welfare loss V as the shaded area under the shadow price curve between the two stock levels. This must be case given the definition of price and the fundamental theorem of calculus. Panel B shows the standard accounting wealth lost by subtracting the area of the gray rectangle from the area of the hashed rectangle. By valuing capital at each point in time at current shadow prices – as opposed to evaluating at a constant price as in inclusive wealth – this calculation does not result in the same quantity as the shaded area in panel A.25 The ratios of the shadow prices reveal the sustainable marginal rate of substitution between capital stocks – the relative substitution potential between different types of

24 This notion of sustainability can be myopic, however, in the sense that the economic program may

embody a commitment to future reductions in W and V that are not captured in the current interval. Fleurbaey and Blanchet (2013) demonstrate how changes in inclusive wealth with proper shadow prices provide an ‘early warning’ of such declines – where the extent of anticipation decreases in the discount rate. 25 We demonstrate the calculation of inclusive wealth in panels C and D and discuss below.

2 Theory of Measuring Natural Capital Shadow Prices

FIGURE 1 Illustrating the connection between changes in welfare and changes in wealth using shadow prices. Panel A shows the change in welfare associated moving between stocks s1 and s2 . Panel B shows wealth measured at stocks s1 and s2 ; however, differencing these does not give the correct change in inclusive wealth. Panel C shows how change in wealth from stocks s1 to s2 is measured using a constant price. Panel D shows that a constant price can be chosen so that change in wealth equals change in welfare.

capital. Therefore sustainability can be assessed by whether this ‘genuine savings’ or ‘comprehensive investment’ is nonnegative. This measure can also be regarded as the change in the ‘inclusive wealth’ (W) in the system – measured at constant prices over the interval in question (Maler et al., 2008). While it is common to refer to (10) as a ‘wealth-based’ metric of sustainability, with W being reported in some important policy documents (UNU-IHDP and UNEP, 2014), it is ultimately only changes in W that matter for sustainability assessment. The fixed price, linear-in-quantities form of genuine savings and inclusive wealth has occasionally led to misconceptions that wealth metrics fail to capture the limitations of substitution by imposing an assumption that capital stocks are perfect substitutes for one another. This has caused some to circumscribe wealthbased indicators as criteria measures for weak sustainability (Greasley et al., 2014; Pearce and Atkinson, 1993; Hanley et al., 2015; Hamilton and Clemens, 1999; Heal, 2012).26 However, this judgment is mistaken in that it fails to realize that, 26 Hamilton and Hartwick (2014) provide some other conditions that could lead such indices to fail as measures of sustainability.

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when derived from a model of system dynamics, the shadow prices embedded in (10) are functions of the underlying capital stocks, and the quality of their management is reflected in the economic program (Dasgupta, 2007). Therefore, the potential for or limits to substitutability among capital stocks are incorporated in the shadow prices. These are reflected outward in the wealth metric through changes in the relative shadow prices of capital stocks (Yun et al., 2017b). Shadow prices of many forms of natural capital are likely highly “context dependent” (Hamilton and Hartwick, 2014; Maler et al., 2008), due to the frequent absence of capital markets, spatially heterogeneous valuation of ecosystem services, heterogeneous management (i.e. different economic programs), and biophysical and institutional barriers to arbitrage. The local nature of shadow prices may also be further enhanced by interactions among capital stocks and their varying degrees of substitutability. However, this context dependence has been abstracted away in most applications of real-world wealth accounting (see Addicott, 2017 for an exception) – with most forms of natural capital being grouped into a small number of aggregates evaluated at a common shadow price. Furthermore, shadow prices have typically been treated as quantities to be extracted directly from market data, perhaps after some adjustments for externalities or other market failures (Arrow et al., 2012a, 2012b; Hamilton and Hartwick, 2014; World Bank, 2011). While understandable, given the ambitious spatial and temporal scope of these studies, this approach has reinforced the notion that inclusive wealth is a linear index with essentially fixed, exogenous prices, and therefore poorly equipped to handle the realities of substitution between forms of capital. Utilizing a bottom-up approach to shadow pricing explained in this chapter for bounded subsystems at sub-national scales may help to counter this perception. The instability and endogeneity of shadow prices suggests that holding shadow prices constant over long intervals of time, or shorter intervals with large changes in the capital stocks, will likely yield misleading results about V , potentially even yielding qualitatively wrong inferences about whether the system is sustainable or not. Yun et al. (2017b) illustrate this in the context of changes in ecosystem wealth in the Baltic Sea. The time interval for which (10) can be relied upon shrinks as: 1) the curvature of the intertemporal welfare function (i.e. the first partials of the shadow prices) increase; and 2) the rate of change of capital stocks increases. When a system is far from its steady state, then the large flux in some or all capital stocks leads to heroic first-order extrapolations in state space – the effects of which are magnified if the underlying value function is itself highly non-linear (Fenichel et al., 2016b).27 Eq. (10) remains a valid measure of sustainability in such cases; however, the baseline

27 Holding shadow prices fixed over time intervals with substantial changes in capital stocks implicitly

assumes that the intertemporal welfare function is approximately linear in these capital stocks.

3 Approximators to Measure Natural Capital Shadow Prices

prices must be updated regularly, with price-constant changes in wealth only being valid over short time horizons.28 Under fairly reasonable assumptions, the mean value theorem establishes that Eq. (10) can be assumed to hold exactly for arbitrarily large changes in capital stocks. However, shadow prices must be evaluated at an intermediate point between the starting and ending capital stocks, where the placement of this point depends on the shape of the underlying intertemporal welfare function

and the size of the change (Fenichel et al., 2016b). This means that W[t1 , t2 ] = Si=1 p i s i perfectly matches the change in the intertemporal welfare function when pi is a specific convex combination of p i (t1 ) and p i (t2 ). For example, a quadratic intertemporal welfare function supports the use of the shadow prices at the midpoint of the beginning and ending stock levels. Establishing this point of evaluation requires a great deal of information about the properties of the intertemporal welfare function. We illustrate this point in Fig. 1 panels C and D. In panel C, p is the arithmetic mean of p1 and p2 . The change in wealth is the area of the black rectangle less the area of the rectangle defined by coordinates (0, 0) and (s1 , p). There are two errors in the resulting gray rectangle. The vertically hashed region is omitted from the calculation of W, contributing toward an under-estimate of V , while the horizontally hashed region is included, contributing towards an over-estimate of V . In panel C the latter error exceeds the former, yielding an over-estimate of V . However, if the shadow price curve were a straight line, as would be the case for a quadratic intertemporal welfare function, then the resulting errors would exactly offset. Panel D shows that an alternative convex combination of p1 and p2 can be chosen so that the approximation errors offset and changes in inclusive wealth exactly measure changes in intertemporal welfare. However, the appropriate combination will depend on the magnitude of the stock changes and the shape of the shadow price curve.

3 APPROXIMATORS TO MEASURE NATURAL CAPITAL SHADOW PRICES The absence of asset markets for many, if not most, forms of natural capital, and the reality of significant market failures for natural capital assets that are traded, makes the bottom-up approach to natural capital pricing presented in Eq. (9) attractive, if not necessary. At any given level of capital stocks it is possible – at least in principle –    ∂Gi (s) ∂f i (s, x(s))  through the combined efforts − to estimate Ws i s, x(s) and ∂s i ∂s i of economists and natural scientists. However, the effects of additional si on system  ∂p j j ∂p i j s˙ + p j ∂∂ss˙ i , are not observed. This omission wide capital gains, i s˙ i + j =i i ∂s ∂s 28 The problem of developing a consistent, comparable index when both prices and quantities are chang-

ing is known as the ‘index number problem’ in economics and has a long history with no easy solution (Samuelson and Swamy, 1974).

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can be addressed by realizing that specifying a complete bioeconomic model of the dynamics of capital stocks s˙ , human behavior with respect to capital stocks x(s), and their valuation W results in a forecast of the system’s trajectory – thereby providing all the information needed to value a change in any given capital stock from any initial condition. An intuitive approach to natural capital valuation directly exploits Eq. (2) to calculate shadow prices by simulation as follows: from an initial capital stock, perturb one capital stock by a small amount and use the system model to simulate the change in the present value of flows of W over the indefinite future. Repeating this perturbation process for every capital stock can supply numerical estimates of all shadow prices. While intuitive, this ‘brute force’ process can be tedious and computationally inefficient for forecasting or backcasting purposes – where shadow prices are needed over a large number of states. An alternative and practical approach is to develop a flexible approximator such that Eq. (9) holds with zero (or minimal) error at a series of approximation nodes in the space of s, thereby allowing reasonably accurate estimates of pi at stock levels between these nodes. In essence, the functional relationship of the approximating functions fill the gap left in (9) from the absence of information on capital gains. The shadow price function consistent with a given system model can be found either through use of the shadow price functional (9) or the HJB equation (6) and there are ˙ These approxithree potential functionals that can be approximated: V , or p, or p. mators leverage derivative relationships between intertemporal welfare and shadow prices and shadow prices and capital gains.29 Fenichel and Abbott (2014b) develop ˙ while Fenichel et al. (2016a) use the approximator for p. An an approximator for p, approximator for V is developed in Yun et al. (2017b). Fig. 2 illustrates that all three approaches can provide numerically identical shadow price functions when the nature of the model and available information is well suited to the three approximators. We base our approximation approach on value function approximation using collocation, which is commonly used to solve dynamic programming problems (Miranda and Fackler, 2002; Judd, 1998). We approximate the function at N nodes, where a node is a point in the S-dimensional space of natural capital stocks. For expositional purposes consider a single stock (see Yun et al., 2017b, for a full multi-stock development). This is not a restrictive assumption because it is possible to build up the S-dimensional approximator as the tensor product of 1-dimensional approximators (Judd, 1998). This assumption makes exposition and notation simpler without a loss of generality. Therefore, in this section we assume a single stock and treat s as a scalar. At each of N approximation nodes, s, let μ(s)β approximate an unknown function. Here, μ(s) is an N × k matrix of k distinct basis functions and β is a k × 1 vector of coefficients that weight the individual basis functions. We focus on using

29 Following Dixit and Pindyck (1994) similar approximators can likely be developed for stochastic dy-

namics.

3 Approximators to Measure Natural Capital Shadow Prices

FIGURE 2 The shadow price curve from reef fish reported in Fenichel and Abbott (2014b), reproduced using three different approximating techniques.

polynomial approximators of ascending order (Judd, 1998), specifically Chebyshev polynomials due to the closed-form nature of their derivatives and their desirable orthogonality properties that enable them to provide the lowest error approximations to unknown functions (Press et al., 2007; Vlassenbroeck and Van Dooren, 1988). These properties facilitate identification of the parameters in vector β. Each approximation approach requires finding the derivative of the approximation, which is given by μs (s)β. However, the polynomials associated with μs (s) do not maintain the orthogonality property. This might reduce the numerical appeal of the use of Chebyshev polynomials, although we have not found this limitation to be problematic in practice.

3.1 THREE WAYS TO APPROXIMATE SHADOW PRICES In this section we derive three shadow price approximators. The Capital Asset Pricing for Nature or capn package available in R,30 implements these three approximation approaches (Yun et al., 2017a). In the next section we explore the tradeoffs among the different approaches to approximating shadow prices for natural capital. First, consider approximating V (s) ≈ μ(s)β and Vs (s) = p(s) ≈ μs (s)β (V -approximation). In this case, we work directly with the fundamental asset equation (Shapiro and Stiglitz, 1984) δV (s) = W (s) + diag(˙s )Vs (s) ≈ δμ(s)β = W (s) + diag(˙s )μs (s)β,

30 Available at: https://cran.r-project.org/web/packages/capn/index.html.

(12)

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where diag(˙s ) is the diagonal matrix operator having the elements of s˙ on the diagonal and zeroes elsewhere. This implies   δμ(s) − diag(˙s )μs (s) β − W (s) = 0 (13) In the just determined case (when N = k), (13) can be satisfied at all approximation points, yielding  −1 β = δμ(s) − diag(˙s )μs (s) W (s). (14) In the over-determined case (when N > k), treating the LHS of (13) as the error and minimizing the sum of squared errors yields β=



  −1 δμ(s) − diag(˙s )μs (s) δμ(s) − diag(˙s )μs (s)    × δμ(s) − diag(˙s )μs (s) W (s) .

(14 )

The N × k matrix μs (s) is not of full rank. The first column is a column of zeros, as the derivative of the 0th order polynomial basis function (i.e. constant term) is zero. The value of income flows, W (s), and the rate of change of natural capital s˙ (each with the economic program substituted in) are the critical pieces of data for the reliable identification of the approximation coefficients. For any node where s˙ = 0 (to numerical precision) those nodes only contribute to the approximation through μ. The value μs β at a given s provides the approximate value of p(s). Second, consider approximating the shadow price p directly (p-approximation) with μ(s)β (noting that β will be different than in the V approximation case). ˙ Ws (s) + p(s) ≈ μ(s)β δ − s˙s   = diag(δ1N − s˙s )−1 Ws (s) + diag(˙s )μs (s)β

Vs (s) = p(s) =

(15)

In the just determined case  −1 β = diag(δ1N − s˙s )μ(s) − diag(˙s )μs (s) Ws (s)

(16)

where 1N is an N -length vector of ones. For the over-determined case (when N > k), then least-squares yields   β = diag(δ1N − s˙s )μ(s) − diag(˙s )μs (s)  −1 × diag(δ1N − s˙s )μ(s) − diag(˙s )μs (s)    × diag(δ1N − s˙s )μ(s) − diag(˙s )μs (s) Ws (s) (16 ) The third option is to approximate p. ˙ In the single stock case, begin as in Eq. (15). Then, take the time derivative to obtain p˙ =

((Wss s˙ + p)(δ ¨ − s˙s ) + (Ws + p)(˙ ˙ sss s˙ )) 2 (δ − s˙s )

(18)

3 Approximators to Measure Natural Capital Shadow Prices

Table 1 Shadow price approximators, information requirements and tradeoffs Approximator Information used to identify coefficients V W (s) and s˙ Vs (s) = p(s)

Ws (s) and s˙s

Vss s˙ = p(s) ˙

Ws (s), Wss (s), s˙s , s˙ss

Pros and Cons Easily handles multi-dimensional problems, approximations are non-targeted. Makes use of marginal effects, which are often what are estimated empirically. Approximations not targeted. Make use of more information than p approximator, but that means we must be more confident in that additional information. Requires twice differentiability especially in s˙ . If s˙ss ≈ 0, relies heavily on Wss (s) rather than Ws (s). Gives targeted approximation.

Making substitutions for the approximator  −1    μ(s)β = diag (δ1N − s˙s )2 diag(δ1N − s˙s ) Wss s˙ + diag(˙s )μs (s)β   + diag(˙sss s˙ ) Ws + μ(s)β (19) In the just determined case      −1 β = diag (δ1N − s˙s )2 μ(s) − diag s˙ (δ1N − s˙s ) μs (s) − diag(˙sss s˙ )μ(s)     (20) × diag s˙ (δ1N − s˙s ) Wss + diag(˙sss s˙ )Ws The p˙ approximator cannot be used if s˙s = 0.

3.2 TRADEOFFS AMONG APPROXIMATION APPROACHES Table 1 summarizes the information for each approximator and the tradeoffs associated with choosing one approach over another. The primary advantage of approximating V occurs in the case of multiple coupled capital stocks, as illustrated in Yun et al. (2017b). Approximating the intertemporal welfare function provides a straightforward means to obtain the full system of asset price equations (9) through a single approximator. The restrictions on capital gains across all the price equations are enforced through approximation of the HJB equation. This is because all shadow prices can be found through finding the first partials of V (s) ≈ μ(s)β. As shown in (14) (and (14 )), the ‘data’ for the intertemporal welfare function approximation approach, in addition to δ, which enters all approximators, are W (s), and the rate of change of natural capital s˙ (each with the economic program substituted in). This approach is conservative in its data requirements, especially in requiring only net growth of the capital stock at the approximation points. However, since the shadow prices are the partial derivatives of V , whereas the approximation is of V itself, this approach depends heavily on the quality of the functional approximation

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between approximation points – that is the curvature of the intertemporal welfare function (the rate of change of the shadow prices) is mild, or failing this, that the number of basis functions and the density of nodes in high-curvature regions of state space are sufficient to capture this curvature. Finally, a disadvantage of the approximating V is that it is the least ‘targeted’ of the three options. We will make this meaning more precise when we discuss p˙ approximation. In contrast with the value function approximator, directly approximating the shadow price (Eqs. (16) and (16 )) relies upon estimates of marginal ecosystem income flow Ws (s) and the marginal rate of appreciation (net of human impact) of the natural capital stock s˙S . The relative desirability of this approach depends on whether these derivatives are better estimated than W (s) and s˙ . In many non-market valuation contexts (e.g., hedonic price models) it is often the case that marginal benefit measures are better identified than their integrals (Palmquist, 2006). Fenichel et al. (2016a) found that derivatives were more reliably estimated than levels in their study of the Kansas section of the High Plains Aquifer. Inspection of the single stock asset price equation, Eq. (9), reveals that every aspect of the shadow price except for p˙ can be directly measured or estimated without the need for the approximation techniques in section 3.1. Therefore, the previous two approaches are less targeted approximations engaging to some extent in ‘approximation overkill’ – approximating either p or V when all that is really needed is p. ˙ By contrast, the p-dot approximation approach (Eqs. (18), (19), and (20)) is the most targeted, in that it only approximates the unknown capital gains portion, p˙ of the asset price equation, which can then be substituted directly into (9). Approximating p˙ allows for straightforward comparisons with valuation approaches that ignore aspects of the full asset price, such as ignoring the adjustments to the discount rate or assuming p˙ = 0. Fenichel and Abbott (2014b) use this approach for an empirical test of the broader theory laid out in this chapter. Nevertheless, the p˙ approximator makes heavy use of second derivatives Wss and s˙ss as fundamental ‘data’ for the approximation. If these are estimated with low confidence, which may be the case in many situations, then one of the other approximation approaches might be preferred. Finally, extending the p-dot approximator to multiple capital stocks appears especially challenging.

3.3 THE APPROXIMATION DOMAIN As with any approximation, careful consideration of the approximation domain is important to avoid extrapolation beyond this domain.31 However, there are two additional subtleties to consider when approximating shadow prices. First, any asset price – whether constructed using (9) or derived from an actual market is based on an implicit or explicit projection of the future (Maler et al., 2008). 31 In the case of Chebyshev polynomials, the approximation is defined over an explicit closed interval.

We discuss the approximation domain for the multi-dimensional case, and therefore denote the state as a vector.

3 Approximators to Measure Natural Capital Shadow Prices

FIGURE 3 Illustration of the domain of approximation (solid box) for a two stock problem. The dashed box represents the domain of stock values for which we are interested in approximating shadow prices.

It is this forecast that determines the rate of capital gains,

∂p i i  ∂p j j s˙ + j =i s˙ + ∂s i ∂s i

∂ s˙ j  . The bottom up approach to valuation described in this chapter requires the ∂s i projection to be explicitly embedded in the assumed economic program and capital dynamics. An important implication of this finding is that the approximation domain must be defined sufficiently broadly so that it fully captures the range of system dynamics originating from any s for which one wants to produce a shadow price (Fig. 3). Otherwise, the approximator will implicitly incorporate spurious predictions of future dynamics based upon “out of sample” predictions.32 In cases where the dynamics correspond to a global, non-spiraling, attractor in state space the range of the approximator can be constrained to exactly the range of state space for which shadow prices are desired. In this case – which often occurs in single state models – the system dynamics are fully contained within the approximation domain. However, in the multi-dimensional case, illustrated in Fig. 3, cyclical or spiral-like dynamics are likely, particularly for ecological systems. This implies that trajectories from certain nodes in the range of approximation can leave the approximation space, either temporarily or indefinitely. In such cases, the approximation domain must be enlarged so that all trajectories for the range of s for which one desires shadow prices are captured within this domain. In practice, defining this domain requires exploratory simulations of system dynamics prior to approximation. pj

32 This is also an issue in dynamic programming that usually only manifests in multi-dimensional problems

(Fenichel et al., 2018).

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A second concern is that the approximation should contain a steady state (or multiple steady states or other limiting behavior) reached from the desired approximation domain. This is essentially a corollary to the previous paragraph. However, there are also numerical reasons for inclusion of the steady states since when s˙ = 0 the terms involving μs (s) drop out of the approximation formulas when evaluated at this node. Therefore, including the equilibrium in the approximation domain may be desirable from a purely numerical perspective since nodes in the vicinity of the steady state are only minimally influenced by the lack of orthogonality in the derivative of the basis matrix.

3.4 ADDITIONAL NUMERICAL CONSIDERATIONS The order of the approximation, as defined by the number of basis functions k, is an important choice. Judd (1998) suggests that coefficients should decline monotonically (in absolute value) over multiple orders of magnitude for a good Chebyshev approximation for single dimensional systems. Therefore, the order of the approximation should be high enough to achieve this diagnostic. This provides guidance for a minimum order of approximation for the approximating function. However, in multi-dimensional systems there are two additional numerical concerns, the curse of dimensionality and the Gibbs (or Gibbs–Wilbraham) phenomenon. The curse of dimensionality states that the computational effort of functional evaluations grows exponentially with the dimension of the multiple function domains (Judd, 1998; Miranda and Fackler, 2002). This exponential growth causes the shortage of memory capability, numerical inaccuracies (akin to multicollinearity in econometrics), and computational inefficiency when designing and implementing numerical approximations (Miranda and Fackler, 2002). The Gibbs phenomenon is “overshoot” in the convergence of functional approximation (i.e., Gibbs oscillations) in the neighborhood of a discontinuity of the function being expanded, often mentioned in Fourier analysis (Hewitt and Hewitt, 1979; Jung and Shizgal, 2004). In general, moderate to high dimensional Chebyshev approximation can suffer from Gibbs oscillations when fitting a discrete sample of nodes (Mace, 2005; Gelb et al., 2008). The discrete sample of nodes generates numerical discontinuities even though the assumed function is smooth (i.e., differentiable). Both numerical issues, suggest that lower order polynomials may perform better than intermediate order polynomials, while higher order polynomials may be computationally infeasible (Yun et al., 2017b). A final question concerns the number and placement of the approximation nodes. These decisions are particularly important because – unlike in many econometric applications, where the data are given – the analyst in a “bottom up” natural capital pricing exercise will likely have a system dynamics model at hand with which to supply the approximator with the necessary ‘data’.33 In theory a just-determined system is sufficient to recover the coefficients of the approximating function. Indeed 33 It is possible to construct an asset price approximation based on purely empirical measurements of the

necessary data used for a given approximator. In this case the number of nodes and their placement in state

4 The Measurement of the Economic Program and Ecosystem Income

much work in computational economics, especially numerical dynamic programming, has adopted this approach – in which case the approximation process is known as ‘collocation’ (Miranda and Fackler, 2002; Judd, 1998). However, intuition from econometrics suggests that working with an over-determined system may provide ‘estimates’ of the β vector that provide global approximates that are more robust to potential fragilities of the estimates to the particular choice of the approximation nodes than in the just determined case. Furthermore, since the analyst is in control of the ‘data generation process,’ there may be gains in the quality of functional approximation from thoughtful placement of the nodes in the state space to minimize problems of multicollinearity and to increase the information content of each approximation node. These aspects may merit consideration given the non-orthogonality of the derivative basis matrix μs and may become critical with large-dimensional multivariate models, where concerns over multicollinearity and exponential expansion of the dimensionality of polynomial approximations using the tensor basis come to dominate. Much of the computational economics literature has selected approximation nodes in each dimension through the use of ‘Chebyshev nodes’ – the roots of a Chebyshev polynomial of an order at least as high as that of the underlying approximation problem. There is substantial theoretical support for this node placement in the univariate case (Press et al., 2007), although the case in the multivariate case is less clear. For the multi-dimensional case the Smolyak method, and its extensions, offer promising approaches to deal with the curse of dimensionality associated with tensor product bases (Judd et al., 2014). There may also be substantial reasons for the analyst to exercise a degree of control over the ‘shape’ of the approximation domain to utilize information about the regions actually visited by the systems model. The rectangular domain imposed by tensor product bases may be highly inefficient. All of these issues remain important areas of future research. Nevertheless, in practice, we have utilized Chebyshev nodes and their tensor products in over-determined systems and have typically found them to generate very small residual errors.

4 THE MEASUREMENT OF THE ECONOMIC PROGRAM AND ECOSYSTEM INCOME AND ITS CONNECTION TO NATURAL CAPITAL ASSET PRICES Accurate values for natural capital require a careful synthesis of positive and normative economic elements – of valuation of flows of benefits deriving from natural capital along with modeling of human behavior, in addition to considerable input

space (and hence the valid range of approximation) would be fixed to the analyst. However, we suspect this setup is unlikely in practice. Instead we expect that real-world data will first be used to estimate/calibrate a system dynamics model before using that model to supply the necessary ‘pseudo-data’ to the approximation process.

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from biophysical science. The benefits and behaviors must relate to the consumption of market and non-market services derived in part from natural capital, and the effects of this behavior on changes in capital stocks. While none of these elements are new to economic researchers, the degree of integration needed for natural capital valuation sets a high bar for coordination. Furthermore, the particular needs of natural capital valuation present unique methodological demands and challenges that may require new research programs, or perhaps the resurrection of older lines of research.

4.1 THE ECONOMIC PROGRAM – x(s) The feedback between the state of capital stocks and human behavior, the economic program, is a critical input to the forecast of the coupled bioeconomic system required for the valuation of natural capital.34 The marginal dividends from natural capital Ws and the adjustment of the discount rate for human impacts on depreciation fs must be measured in a way that accounts for the state-conditioned behavioral equilibrium embodied in this feedback rule. Behavioral feedbacks also affect the trajectory of natural capital, and hence the time path of capital gains. If a capital stock is at or very near a stable steady state, then ‘local’ information about x(s) (i.e. its derivative at current stock levels) is sufficient to provide the forecast of behavioral feedbacks needed to recover natural capital values. More generally, the need to estimate shadow values across a wide range of state space requires understanding the properties of x(s) as a function. If the current status of the resource is far from a stationary state then the characteristics of x(s) along the entire trajectory become salient, although the properties of x(s) for values of the s that are not traversed until the distant future are of less relevance because of discounting. The economic program is ultimately a vector of flows of human behavioral “inputs” that factor into the dividends received from capital stocks and that (potentially) influence the rate of human investment in or drawdown of these same capital stocks. When income is directly linked to depletion of natural capital the definition of the economic program can be fairly simple. For example, in a single-species fishery x(s) may be a single composite input knownas “effort”  (Squires, 1987) in a generalized Schaefer harvest production function f s, x(s) = qs α x(s)β (Fenichel and Abbott, 2014b; Zhang and Smith, 2011). In this case, f directly figures into profits so that ecosystem depreciation and dividends are integrally linked. However, in other cases the link may be less direct – as in the case of recreational trips to a fragile environment, where s, could be a set of measures of environmental quality (e.g., hectares of undisturbed habitat). In this case x(s) may be the number of trips per year, where x(s) enters into W in a manner consistent with single or multi-site travel cost models (Phaneuf and Smith,2005; Phaneuf and Requate, 2017). In this case human deprecia tion of the system f s, x(s) , e.g., erosion, may be purely incidental to the enjoyment

34 In the context of dynamic programming the vector of policy functions is the equivalent of the economic

program, but the economic program does not need to come from an optimizing system.

4 The Measurement of the Economic Program and Ecosystem Income

of the ecosystem services themselves – serving as “bad outputs” in a process of joint production (Nalle et al., 2004).35 The theory of natural capital valuation in kakatopia places few, if any, restrictions on the form of x(s). It is ultimately a forecast for how people respond to varying capital stocks under a particular institutional scenario. At first glance, the requirement that behavior be expressed solely as a function of capital stocks seems restrictive. How, for example, does this restriction accommodate the influence of changing input and output prices on behavior? What about the potential for technical and institutional changes to alter this feedback rule? Nonetheless, a great deal of flexibility can be achieved by expansion of the number of capital stocks. For example, trends in prices, exogenous technical change, or climate change can be accommodated by mapping these exogenous processes from the time domain to the state domain and treating them like additional states. This creates a version of x(s) that is robust to these structural changes. Additional flexibility in the specification of x(s) can be achieved by incorporating additional structure to endogenize economic processes within x(s). For example, if farmers drawing on a common aquifer face a downward sloping demand curve for their product while also facing stock-dependent marginal pumping costs, then a collective pumping rule incorporating both the output market and pumping cost effects can be derived as a function of the aquifer level – where the rule will vary depending on structural assumptions about behavior under the prevailing institutions (e.g., atomistic behavior vs. strategic pumping vs. sole ownership). Accommodating institutional change remains a profound challenge. Dasgupta (2007) describes how one could – if in possession of a process model of institutional change – allow institutions, and hence x(s) and even W , to evolve as a function of capital stocks (including time). For example, if a resource stock is expected to transition from open access to a form of management that enhances rents once the stock reaches a critical level of scarcity, then this could be accommodated in the functional specification of x(s) and W , and would be mathematically analogous to the case of the moratorium described previously. However, reliable quantitative models of institutional change remain aspirational for even the simplest systems. Furthermore, institutional systems are often categorical so that no well-defined marginal change exists. One path forward may be to model changes in the economic program as driven by an underlying stochastic process – relying upon an expansion of the asset pricing approach to the stochastic context to incorporate the risk of an institutional shift. However, accurately calibrating the parameters of a stochastic process

35 There may also be cases where certain elements of x(s) may be completely decoupled from human

impact to the capital stock in question. For example, boaters on a lake may derive significant ecosystem income from water quality. But, the amount of boating may have negligible impacts on water quality relative to other human activities (such as fertilizer use in the watershed), and these human activities in turn may not be tightly coupled with the capital stocks in question (as is likely the case for farmers’ fertilizer application decisions vis-à-vis lake water quality). In this case f may be made a function of exogenous human ‘forcing’ decisions that do not directly enter into W . However, this would leave out an important use of the capital stock, waste storage, leading to bias in the shadow price.

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to capture the ex ante risk of institutional change may be as challenging as developing a deterministic model. Given these formidable challenges, it is likely advisable to move forward under the maintained assumption that shadow prices are inherently contingent on the static institutions embodied in x(s). Sensitivity analysis can be conducted by comparisons of the shadow prices under alternative specifications of x(s) (and potentially W ) arising under different management institutions. Yun et al. (2017b) provide an example and contrast shadow prices and changes in natural capital wealth associated with two different institutional rules for managing harvests from a multispecies fishery. Given the relatively long time scales implied in the valuation of natural capital, it is important to consider which margins of behavior are fixed vs. variable as agents respond to changes in the underlying capital stocks.36 In many cases this will require working in the economic ‘long run’ where many margins, including many forms of physical capital, are malleable. Pfeiffer and Lin (2014a, 2014b), examine one such long-run adjustment by showing how the transition of farmers to efficient irrigation technology – spurred in part by government subsidies – lead to a strong rebound effect in water use. Fenichel et al. (2016a) incorporate these adjustments into their characterization of the economic program of water pumping, demonstrating how they ultimately reduced the shadow value of water in the aquifer. Developing economic programs that adequately capture the scope of relevant behavioral responses across a range of natural capital stocks presents a significant empirical challenge. Datasets that cover an adequate range of s are likely to be scarce due to the significant time scales involved, and those that do exist are likely to present challenges to identification of x(s) due to the non-stationary and idiosyncratic nature of institutional, technical and economic factors across the span of the data. In the absence of temporal variation in s, economists must utilize variation in the cross-section (e.g., space), with the well-known identification challenges this presents. Furthermore, the current emphasis in applied econometrics on the identification of causal effects using experimental and quasi-experimental methods (Imbens and Wooldridge, 2009) is arguably poorly suited to revealing the properties of x(s), focusing as it does on the immediate, low-hanging fruit of revealing short-run effects of changes in policies or, perhaps a marginal effect of x(s) at current stock levels. Most applied econometric work provides little direct insight into x(s) that is useful for the purposes of natural capital valuation. Indeed, the primary purpose of x(s) in natural capital valuation is not to establish a rigorous causal connection between capital stocks and human behavior; rather, it is to provide robust predictions of human behavior. This suggests that techniques from machine learning (Friedman et al., 2001; Varian, 2014) may prove useful for identifying x(s) in data-rich environments where the support of s in the data spans the relevant range for natural capital valuation. 



36 This consideration should also be extended to the technical parameters that influence f s, x(s) as well.

Fenichel and Abbott (2014b) derive shadow values for Gulf of Mexico reef fish under the assumption that the technical parameters of the generalized Schaefer harvest function are invariant. This assumption may not be supported in general.

4 The Measurement of the Economic Program and Ecosystem Income

The challenges associated with a purely empirical strategy for identifying x(s) suggest that a structural approach that leverages assumptions on preferences, technology and behavior (i.e. constrained optimization) to derive an economic program may be appropriate. A structural approach has two benefits for natural capital valuation. First, structural assumptions allow for behavioral predictions outside the range of observed states, which is frequently needed for natural capital valuation. Second, the maximized objective functions provide a direct link between behavior and welfare, ensuring consistency between x(s) and W . While predicated on the validity of the underlying behavioral assumptions, functional form, and model calibration, structural models are capable of providing useful predictions of x(s) in contexts where a purely empirical approach may fail (Wolpin, 2013). These models can be estimated econometrically or be calibrated. Yun et al. (2017b) provide an example that is applied to natural capital valuation. They utilize a non-linear programming model grounded on an econometrically estimated cost function by Hutniczak (2015) to simulate fishing behavior in a multispecies fishery across a wide range of stock combinations for three species. These ‘pseudo data’ were then used to fit a flexible functional approximation to derive the reduced form x(s).

4.2 DIVIDENDS FROM NATURAL CAPITAL – W The net benefit or dividends that society receives in connection to its stocks of cap ital at a point in time is represented by W s, x(s) in Eq. (2). However, this net income will typically be the joint product of environmental and non-environmental capital stocks. Due to nonlinearities in the production functions of ecosystem services (Barbier, 2007; Koch et al., 2009) and non-separability of preferences, it is not clear what portion of the net income in W should be considered ecosystem income (Boyd and Banzhaf, 2007). Fortunately, such parsing of total income is unnecessary for finding the shadow price of natural capital, as it is the marginal net income from the change in natural capital Ws that matters.37 Ws is the instantaneous inverse demand for the services generated by a unit of natural capital – the static marginal value from the services provided by an additional unit of natural capital.38 In practice, research in environmental valuation typically stops short of estimating Ws , focusing instead on providing estimates of the value of measurable final goods or services, productive inputs for market or household production, or complements to marketed goods or services. Extending these estimates of the demand for environmental goods and services to the marginal valuation of the underlying capital requires elucidating

37 This presents an additional practical reason why wealth as opposed to income accounts may be more

useful in measuring sustainability, since parsing of total income is required for income accounts. Maler et al. (2008) discuss reasons why wealth as opposed to income accounts are more useful for measuring sustainability. 38 By virtue of the substitution of the economic program into W , this valuation is measured after any behavioral adaptations captured in x(s). Therefore, W should incorporate the costs of these adaptations for internal consistency.

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the biophysical or technical links between natural capital, human behavior (i.e. the economic program), and these valued service flows (Barbier, 2007). There are three broad pathways for natural capital to impact income. The first is as a part of a production processes for marketed goods or services. Second, natural capital may contribute as an intermediate input to household or individual production of final goods or services or, alternatively, serve as a complement to individual/household consumption of market goods. Finally, there may be cases – motivated either by theory or convenience – such that natural capital enters directly into the net income index. In such cases there is a lack of a connection to observable behavior (e.g., nonuse value or quasi-option value, sensu Krutilla (1967)) but still the natural capital generates net income. The manner in which capital contributes to income matters a great deal for the internally consistent treatment of x(s) and f i s, x(s) , for the structure of W , and for how ecosystem income enters an income account.

4.3 ECOSYSTEM INCOME FROM MARKET PRODUCTION Perhaps the most straightforward setting occurs when natural capital is used as part of a production process for goods or services supplied into a market. In this context W is the sum of consumer and producer surplus in the final output market, and Ws is the change in these surplus measures after all supply and demand responses have occurred – where supply responses are embedded into x(s).39 Production function approaches (Barbier, 2011b, 2007) and factor demand approaches can be used analyze how a marginal change in the stock of natural capital affect behavioral response, the use of the resource, and ultimately income. This approach has been utilized to value ecosystem services from a variety of forms of natural capital including agricultural water provision from groundwater (Acharya and Barbier, 2000), the value of forested lands for recharge of coastal groundwater (Kaiser and Roumasset, 2002), effects on fishery rents from hypoxia (Huang et al., 2012; Smith, 2007), and the value of mangroves as nursery habitat for fisheries (Barbier and Strand, 1998; Barbier et al., 2002). Applications of natural capital pricing to date have almost exclusively focused on natural capital as an input to market production. Fenichel and Abbott (2014b) combined estimates of commercial fishermen’s economic program from Zhang (2011) and a Cobb–Douglas (modified Schafer) fishing production function from Zhang and Smith (2011) along with price and cost data for the US Gulf of Mexico to recover the shadow price of reef fish under prevailing institutions (Fenichel and Abbott, 2014b). Fenichel et al. (2016a) and Addicott (2017) follow a similar approach, building off an empirical model of groundwater pumping and crop choice (Pfeiffer and Lin, 2014b), to develop a net revenue function for valuing the shadow price of water stored in an

39 Most applications in this area have assumed perfectly elastic demand – which collapses income to pro-

ducer surplus alone. This is approximately satisfied if the production in question is a small portion of the market or faces many close substitutes.

4 The Measurement of the Economic Program and Ecosystem Income

aquifer. Bond (2017) builds on the methods of Fenichel and Abbott (2014b) to measure the value of wetlands in providing nursery habitat to commercially caught fish and avoiding storm loss damages, while Yun et al. (2017b) measure natural capital asset prices for the three species that dominate the Baltic Sea fishery based on multioutput fishery production models developed by Hutniczak (2015). Finally, Strong and Bond (2017) investigate the natural capital asset values of different rangeland grasses in a grazing production system. In the aforementioned cases, there is often a tight logical coupling between the economic program x(s), human impact f i , and the valuation of ecosystem income. Human impact in these cases is essentially the input demand for withdrawal from the stock of natural capital, where this input is transformed to output on a nearly one-to-one basis (i.e. fisheries) or through a relatively transparent production process (i.e. irrigated agriculture). However, there are cases when the natural capital stock of interest enables market production through sustaining other capital stocks but is not an input in a traditional sense. For example, substrate habitat in a fishery may affect the carrying capacity of harvested species, yet suffer damage in the process of fishing. Yun et al. (2017b) examine an analogous case by computing the shadow price of prey fish, whose value is partially derived from its value in sustaining harvested predator stocks (although the prey fish are also directly harvested). Strong and Bond (2017) consider the competition effects among grass in supporting grazing, when some grasses are preferred. In other cases, natural capital may generate benefits for industries that have little effect on its future stock – severing the link between W , x(s), and f i . For example, nutrient concentrations contribute to hypoxia-induced effects on fishery profits but are exogenous to the activities of fishers (Huang et al., 2012; Smith, 2007). The time scales of stock interactions are another important issue for the use of production function methods with multiple interacting capital stocks, along with the closely-related question of whether the effects of interactions among capital stocks are best dealt with through explicit modeling of cross-stock effects on capital gains or through modification of W . Consider the case of a fishery sustained by its underlying habitat. The most natural approach for valuing habitat as natural capital would be to directly use Eq. (9) using a full dynamic bioeconomic model of habitat and the fishery (Kahui et al., 2016). The shadow price of habitat would depend in part upon the capitalized future effects of additional habitat on the growth of the fish stock, so that these relationships are captured in the numerator cross-terms of (9). However, if fish stocks react relatively quickly to changes in their underlying habitat compared to the pace of habitat change itself (i.e. a short-lived species dependent on a slowly evolving substrate), then it may be sensible, given the harvests embodied in the economic program, to assume that fish stocks are in continual bioeconomic equilibrium relative to the timescale of habitat change. This would allow the cross-effects of habitat on fish stocks to be collapsed into an instant, with their effects now incorporated in W in a single-stock version of (9) focused on habitat alone. The use of Fenichel’s theorem (Fenichel, 1979) and singular perturbation approaches (Crepin, 2007; Grimsrud and Huffaker, 2006; Kokotovic, 1984) may provide a useful path forward – particularly

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for slowly-changing natural assets that derive much of their value from their effects on more rapidly evolving capital stocks. A similar issue pertains to the rate of adjustment embodied in the economic program. Some applications of the production function approach have assumed that human behavior adjusts instantaneously to equilibrium in response to changes in natural capital. For example, Barbier and Strand (1998) and Knowler et al. (2001) each assume that an open access equilibrium is instantaneously reached in their models with the result that changes in nutrients or habitat have no effect on fishers’ producer surplus. This assumption is relaxed by Smith (2007), who allows for a ‘sticky’ process of effort adjustment borrowed from Smith (1968). When the rate of adjustment of human behavior is slow relative to that of the biological system, transitory benefits from changes to nutrient inputs can be significant despite the lack of long-run fishery rents. This suggests that accounting for rigidities in behavior may be important for natural capital valuation as well. However, models of sticky adjustment create challenges for specification of the economic program x(s), since the level of behavior in any period is not solely a function of current capital stocks alone – history matters. One way around this challenge is to expand the domain of capital stocks. The rate of change of effort in the Smith (1968) model is a function of current effort and the current fish stock; therefore, effort can be treated directly as another capital stock in (9).40

4.4 ECOSYSTEM INCOME FROM HOUSEHOLD PRODUCTION Some of the most important, yet challenging, settings for natural capital valuation are those in which ecosystem income comes from cases where services from natural capital figure significantly in household production (Bockstael and McConnell, 2007). A tremendous volume of literature in non-market valuation has built on the household production approach, although often implicitly, to examine cases where households or individuals combine their time, transportation services and (spatially and temporally varying) environmental quality to produce ‘recreation services’ that enter agents’ utility. A similarly large literature has focused on the home purchase decision. In both cases, environmental variables typically enter as (weak) complements to the marketed goods. The numerous challenges of non-market valuation in these contexts are well documented (Parsons, 2003; Phaneuf and Smith, 2005; Freeman, 2003; Phaneuf and Requate, 2017) and remain an area of active research. We therefore limit our discussion to three methodological challenges of particular relevance to the valuation of natural capital. First, there is the challenge of establishing a link between measures of environmental amenities or ecosystem services and natural capital. Second, natural capital valuation demands a 40 Alternatively, effort can be viewed as a choice for fishermen (i.e. represented by the economic program)

subject to an upper-bound constraint on the amount of available physical capital, where the evolution of physical capital (perhaps subject to problems of imperfect malleability) is explicitly incorporated into (9) (e.g., Rust et al., 2016; Moberg and Fenichel, 2017).

4 The Measurement of the Economic Program and Ecosystem Income

great deal of valuation models: requiring valuation approaches with credibility across a wide range of natural capital conditions. Third, the pervasive importance of some natural capital stocks for market production and non-market benefits suggests that general equilibrium approaches to the measurement of W and the economic program may be important. Compared to cases where natural capital figures in the marketed production of firms, non-market valuation of individual or household decisions has typically fallen well short of establishing Ws . Instead, valuation typically focuses on measures of “amenities” or “environmental quality” (e.g., catch rates, water clarity, air quality) or proxies for the bundle of inherently multi-dimensional and multi-scalar services emanating from a single environmental amenity (e.g., Abbott and Klaiber, 2011). Linking these metrics to changes in the underlying natural capital stocks is rare. This follows from the challenge posed by a) linking salient measures of environmental quality (to the agents making decisions) to objective measures available to the analyst, and b) specifying the functional relationship between these objective measures and capital stocks.41 The challenge of establishing these links is increased by the fact that the spatial footprint and magnitude of the service flows from a single unit of natural capital of a particular type and management (e.g., an acre of publically accessible open space) may depend heavily on its placement in the larger landscape and the spatial availability of complements or substitutes (Abbott and Klaiber, 2010; Kopits et al., 2007) – thus making the establishment of a stationary ‘unit of account’ for such some forms of natural capital challenging. A second challenge for natural capital valuation in the household production context is that many existing modeling approaches often provide predictions of behavior and welfare effects that are ‘local’ in their applicability. The overwhelming majority of hedonic price models provide marginal values of environmental quality in a particular equilibrium, with relatively few studies imposing the assumptions or possessing the appropriate data to identify amenity demands (Palmquist, 2006). While it may be possible in these cases to link marginal amenity values to the underlying changes in natural capital, such point estimates of Ws are of limited usefulness outside of steady-state scenarios, since establishing a single marginal value for natural capital at current stocks depends on the ability to establish Ws and the economic program x(s) over the range of values that will be traversed in the future. This need to understand the marginal value of changes in amenities across a range of natural capital levels, while incorporating the adaptations of buyers and sellers in the housing market (and how those adaptations may feedback to influence capital stocks)

41 There are some exceptions. Massey et al. (2006) develop a bioeconomic recreation demand model in

which fish catch rates are linked to an underlying stock index and water quality measures. Acharya and Barbier (2000) use a household production function approach to model villagers’ utility maximizing decisions to purchase their domestic water vs. collect this water from wells. They then link reduced groundwater recharge to changes in consumer surplus. Abbott and Klaiber (2013) link the annualized capitalization of neighborhood lakes as club goods to nearby homes to the annual flows of recharge water required to maintain lake water levels.

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suggests a prominent, but hitherto unexplored, role for structural locational sorting models in natural capital valuation (Kuminoff et al., 2013). Furthermore, the fact that the home purchase decision is itself an investment decision for a longlived asset, suggests integrating our valuation approach with dynamic models of housing supply and demand (Bayer et al., 2016) is a fruitful area for future research. Many common recreation demand models are also somewhat limited in their usefulness for natural capital valuation – in large part due to a tendency of modelers to focus on a relatively narrow range of recreational decision-making. This tendency is often driven by data and budget constraints. For example, many models focus on whether and where to take a single trip but often do not model overall seasonal recreational demand; the latter is essential for natural capital valuation, for characterizing demand x(s) and human impact f i in addition to recovering Ws (Abbott and Fenichel, 2013). Furthermore, many recreation demand models draw on sample frames dominated by individuals that are current users (where intercept surveys are an extreme case). However, natural capital valuation, by virtue of the need to consider conditions along future trajectories of natural capital stocks, may require models that allow for endogenous changes in the population of resource users as resource stocks evolve. Accordingly, models that integrate extensive and intensive margins of decision-making across a broader array of current and potential users, including primal and dual generalized corner solution models (Phaneuf et al., 2000; von Haefen and Phaneuf, 2005), are likely better suited to natural capital valuation (Abbott and Fenichel, 2013). However, the ability to empiricize such models is often limited by the lack of variability in the revealed-preference data that are used to estimate them. Valuing natural capital may require understanding the valuation of service flows from natural capital under conditions that simply are not present in historic data, or, alternatively, when there are deep time series or data with wide spatial coverage spanning significant variation in the underlying capital stocks, one may worry that the preferences and institutional constraints that undergird Ws and x(s) are unstable over time or space. The use of contingent behavior approaches, and the use of the resulting data in combination with revealed preference data (e.g., Adamowicz et al., 1994; Englin and Cameron, 1996) could dramatically improve the usefulness of non-market valuation models for the valuation of natural capital. A third challenge lies in whether the specification of W , and hence x(s), should incorporate general equilibrium considerations, or if partial equilibrium approaches, which dominate applied research in non-market valuation, are sufficient. This concern is relevant across many contexts in public and environmental economics (Bergman, 2005), but there are reasons to think that general equilibrium approaches may be especially salient for natural capital valuation in some contexts. First, the horizon for asset pricing is the indefinite future; therefore, it is somewhat awkward to avoid feedbacks to prices within the economy when long-run feedbacks to capital stocks and behaviors are considered. Second, certain forms of natural capital that offer services with a low degree of rivalry and excludability to a wide array of economic

4 The Measurement of the Economic Program and Ecosystem Income

sectors (e.g., carbon sequestration) may be so pervasive as to stimulate non-trivial general equilibrium effects for even small changes in the underlying capital stock. Alternatively, certain species may have such high leverage on the productivity of an ecosystem that relatively modest changes in their populations may influence the productivity of other species in a highly correlated fashion – creating sufficiently large disruptions in a swathe of product markets to have significant product and input market effects. This could be the case for certain ‘keystone species’ (Mills et al., 1993) or plantivorous pelagic species such as sardines in a ‘wasp-waist’ ecosystem (Curry et al., 2000). Third, as demonstrated by Carbone and Smith (2013), the general equilibrium effects of even fairly minor perturbations to non-market services from natural capital can be substantial in cases where there are complementarities between these ecosystem services and market goods or services. Similarly, Walsh (2007) develops a structurally grounded economic program to demonstrate how policies to increase the natural capital in preserved open space, which is imperfectly substitutable with unprotected lands, can have large general-equilibrium feedbacks to land markets and overall provision of open space. Nevertheless, there are reasons to question the ubiquity of general equilibrium effects for natural capital. The goods or services provided by one capital stock may have close market substitutes provisioned by decoupled capital stocks in other bioeconomic systems. This is the case for many fish species that sell into an integrated ‘whitefish’ market (Asche et al., 2004). Arbitrage between natural assets is often heavily restricted due to natural, institutional, and economic factors. For example, the shadow values of water in neighboring aquifers may wildly differ due to transportation costs and institutional rules that prohibit transport of water between aquifers (Addicott, 2017), and the idiosyncratic recreational services provided by one wilderness area cannot typically be transferred to another. In other words, natural capital will often resist aggregation into broader asset classes valued at a common price, such that even substantial changes to individual natural capital stocks may have minimal effects on input and output markets that span wider geographies. Therefore – whether due to substitutability of natural capital’s services across a broad suite of assets, or because of the specificity of many natural capital assets – there are likely many occasions where a partial equilibrium approach is defensible.

4.5 DIRECT ECOSYSTEM INCOME In the previous two cases the good and service flows from natural capital enter into a commercial or household production function as an intermediate input to the production of a valued good or service. Such cases allow the analyst to rely upon methods of market valuation and revealed preference forms of non-market valuation. While these cases capture many of the policy relevant benefits from natural capital, there are cases where human welfare is tied to the state of natural capital stocks in such a way that the production process for the associated goods or services ‘leaves no trace’ in human behavior or consumption of market goods and yet individuals may nonetheless be willing to forego time or money to secure or avoid changes to these capital

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stocks. Given the latency of the underlying production processes it is best to think of natural capital as entering directly into income flows, W (s).42 Stated preference techniques are called for in such cases. Stated preference techniques offer the distinct advantage of allowing the analyst to carefully control many aspects of the value elicitation process, whereas revealed preference methods inherently constrain the analyst to the data and context in hand.43 Of course this control comes at a cost. One challenge is that the analyst directly controls whose preferences count through their choice of population and sample frame for the survey instrument and (to a lesser extent) by how stated preferences are weighted in the vertical summation after welfare estimation. Individuals with no preference for the ecosystem good/service in question are, of course, free to vote their indifference through their responses, but those excluded from the survey are implicitly assigned zero values. Therefore, while stated preference techniques are typically employed to value non-excludable goods, the choice of sample frame necessitates a strong a priori assignment of property rights – of exclusion. A second challenge of stated preference methods is that the very specificity of design required to generate results with strong internal validity typically results in welfare estimates that are of direct relevance for only a narrow range of scenarios. The conditions for valid benefits transfer of these results can be stringent (Boyle et al., 2010). Also, since most stated preference surveys are purpose-built to uncover the welfare effects of a narrowly defined range of policy or environmental quality changes, they typically only identify marginal and total values along a limited portion of the range of variation. This can be problematic, even if all that is desired is a marginal shadow price of natural capital under current conditions, since the shadow price includes the capital gains associated with changes to future changes in natural capital stocks.44 The results in section 2 imply that obtaining a valid marginal price for capital requires identification of W (or its derivatives depending on the approximation method) over the future trajectory of s. This suggests that the design of stated preference surveys may need to be altered to trace out a far greater extent of the demand curves for ecosystem services and the ecosystem income they generate (and hence the underlying range of variation in natural capital stocks) in order to be of more use for natural capital valuation.45 However, achieving this end faces signifi42 Another rationale for direct inclusion of natural capital into W may include natural capital whose ser-

vices are so ubiquitous or pervasive in household production (e.g., so-called supporting or regulatory services) that their role is not easily parsed. 43 Stated preferences techniques carry their own well-known challenges and potential biases (Kling et al., 2012). In addition to intellectual and methodological challenges for stated preference approaches, they are sometimes viewed with extreme skepticism in some communities, e.g., national accountants (Obst et al., 2016). Johnston et al. (2017) provide best practices and show that many traditional concerns of stated preference may be somewhat exaggerated, particularly relative to revealed preference approaches. 44 This concern goes away in the steady state. However, Fenichel and Abbott (2014b) demonstrate that ignoring capital gains away from the steady state can result in serious valuation errors. 45 See Armstrong et al. (2017) for a case where marginal valuations at three provision levels are used to calibrate a global valuation function for cold-water corals.

4 The Measurement of the Economic Program and Ecosystem Income

cant challenges in terms of tradeoffs in experimental design under binding attention constraints, cognitive limitations, as well as increased risks of hypothetical bias associated with expanding the range of variation in a natural capital stock or its service flows. A peculiarity of valuation of natural capital in the case that it generates direct ecosystem income is that it imposes no a priori links between the valuation of natural  capital and human behavior and its impacts on natural capital (i.e. x(s) and f i x(s), s ). The individuals holding such ‘non-use’ values may have little or no impact on the evolution of the natural asset itself. However, it is often the case that these values for pure conservation (Krutilla, 1967) are met by opposing direct or indirect demands for the consumptive use of the resource for market or household production. Such opposing demands may be institutionally constrained in ways that indeed reveal feedback rules from the state of the resource through behavior to the value of the natural capital in use. In this case, the approach of the previous sections should be utilized to augment the net income from non-use with these consumptive values while also providing a mechanism for incorporating endogenous human impacts to the natural capital stock.

4.6 ACCOUNTING FOR ECOSYSTEM INCOME There is considerable policy concern for developing ecosystem income and service accounts (National Research Council, 2005; WAVES, 2012; Hartwick, 2011; Obst and Vardon, 2014). Therefore, we comment briefly on green accounting issues for ecosystem income.46 Ecosystem income created in market production is not ‘new’ – it is fully revealed in the value of market goods and services (Barbier, 2013). Ecosystem services in this case are intermediate goods; therefore, their gross value is captured properly under the current boundaries of national accounts (Obst et al., 2016). This has been used as an argument against including some types of ecosystem income in income accounts (Boyd and Banzhaf, 2007; Barbier, 2013). However, while the gross income flows from natural capital may be captured in national accounts, the contribution of this income to wealth is excluded except in the most straightforward cases (UNU-IHDP and UNEP, 2014) and is seldom netted out of income, though chapter 10 of the 2008 System of National Accounts suggests it should be (United Nations Statistics Division, 2009). Importantly, the loss p i s˙ i , assuming s˙ i < 0, and p i (s) > 0, is a legitimate decline in wealth that does not net out and is rarely captured in market transactions. The spirit of the 46 National accounting and economics may share a common ancestor, but have diverged. One goal of the

WAVES program, managed by the World Bank, was to enhance communication between environmental economists and national accountants in order to overcome divergent ideas between practicing national accountants and economists interested in sustainability and wealth accounting. What most economists are taught about national accounts is not what is in the current system of national accounts or what national accountants actually do. National accountants also may not be up-to-date on the economics of the environment. We are grateful to Carl Obst for helping us see these barriers and begin to appreciate the challenges from a national accountant’s perspective.

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Hartwick rule (1990) suggests a need to reinvest p i s˙ i in new capital to achieve sustainability. The failure to account for losses of ecosystem wealth likely stems from two challenges. The first is likely due to lack of appropriate measurement. The second is that gross domestic product does not adjust for depreciation of produced (traditional) assets and net domestic product receives limited attention (Obst and Vardon, 2014). The income measured in the market enables measurement of the capital asset value, i.e., shadow price, of natural capital being used in production, which is important for wealth accounting, net income accounting, and measuring sustainability, particularly that of ecosystems (Yun et al., 2017b). Income generated through household production is not measurable through market transactions; therefore, it may lie outside the production boundary for national income accounts (Obst et al., 2016). This is not important in theory or practice for economists, but matters for some policy discussions and national accountants. But, not all income generated through household production processes that use environmental inputs should be attributed to the environment (Barbier, 2013; Boyd and Banzhaf, 2007); for example, while the ecosystem is essential for the production of services from recreational fishing, this service also requires other, non-ecosystem inputs (Boyd and Banzhaf, 2007). Therefore, it is important to value these ecosystem components using their value marginal products. This is why understanding the environmental and household production processes are important. For example, Berry et al. (2017) attempt to measure the loss of full income from an increase in the prevalence of Lyme Disease, which reduces the quantity, and perhaps value, of forest leisure services. While, they find a strong behavioral shift away from outdoor recreation (a substitution effect), they also find that people readily engage in non-forest based recreation, which may limit the actual income loss. All the concerns associated with ecosystem income from household production are magnified when considering direct ecosystem income.

5 EXAMPLES AND APPLICATIONS TO DATE We offer a few peer-reviewed examples to make the ideas in this chapter concrete using a few recent applications of the theory and techniques presented in this chapter. Fenichel and Abbott (2014b) demonstrate the theory and techniques presented in this chapter for the Gulf of Mexico reef fish complex under kakatopic management. Building off of empirical work by Zhang and Smith (2011) and Zhang (2011), the authors utilize p-dot approximation to recover shadow price functions for the Gulf of Mexico reef fish fishery under a complex set of regulations that included entry restrictions, catch per trip limits, and season and spatial closures. Fig. 2 shows their original price curve and shadow price functions using p-dot, p, and V approximation approaches. At the system’s steady state (pre-2005), Fenichel and Abbott compute a shadow price of $3.08/lb. This price is the marginal value of leaving a pound of fish in the water conditional on pre-2005 management policies and output/input prices. In 2007, an individual transferable quota (ITQ) policy was initiated for red snapper,

5 Examples and Applications to Date

a dominant and highly valued species in the ecosystem (Agar et al., 2014). Individual tradable quota (ITQ) systems create long-run, transferable harvest rights to a share of the allowable catch, thereby providing a market mechanism to reveal the shadow value of an additional unit of fish biomass, given the harvest cap and other institutions in place (Arnason, 1990). This ITQ policy led to consolidation of the fleet, lowered costs, and increased fishery profits (Agar et al., 2014). These changes in the fishery are expected to be reflected in a higher asset price in the ITQ market relative to the shadow price under prior management. Indeed, in 2007 red snapper traded at $8.73/lb, a substantial increase relative to Fenichel and Abbott’s $3/lb under the previous, less efficient management. Despite this increase, the Fenichel and Abbott shadow price is of the same order of magnitude as the revealed ITQ price, lending support to the validity of the approach. Outside of fisheries, Fenichel et al. (2016a) build on the empirical work of Pfeiffer and Lin (2012, 2014b) to value groundwater capital in Kansas. They find that the in situ shadow price of groundwater in the High Plains Aquifer is on the order of $7–22 per acre foot (2005$), with a large drop in shadow price between 1996 and 2005. The drop in shadow price, despite declines in stock, is partially explained by the subsidized adoption of high water efficiency drop nozzles that made water appear less scarce. The apparent decline in scarcity led to increased water withdrawal and a rebound effect in excess of 100% (Pfeiffer and Lin, 2014a). Such a rebound effect “backfire” (Chan and Gillingham, 2015) is fully consistent with a decline in shadow price. Fenichel et al. (2016a) find for the Kansas section of the High Plains Aquifer that the wealth stored as groundwater declined $110 million per year on average for years between 1996 and 2005. They point out that this average annual loss is approximately equal to the state’s 2005 budget surplus, illustrating that the changes in wealth are of a magnitude that policymakers may be concerned with and have ability to do something about. The authors argue it is important to consider whether Kansas made offsetting investments over this period to avoid non-declining aggregate wealth and thus remain “sustainable.” Bond (2017) creates a stylized model extending Fenichel and Abbott (2014b) to consider linked natural capital stocks with a recursive bioeconomic structure. He focuses on the role of coastal wetlands as fish habitat and as a source of coastal flood protection. Bond first recovers the shadow price of the fish stock. Next, he exploits the recursive structure of the fishery-habitat linkage (i.e. the habitat stock influences fish populations but fish populations do not influence habitat) by using the fish stock shadow price to recover the shadow price of coastal wetlands. Bond emphasizes the important role of capital gains and the potential for interactions among stocks. Yun et al. (2017b) extend the approach to natural capital shadow prices for a multiple stock system under generalized, non-recursive conditions and apply it to the Baltic Sea cod, sprat, and herring fishery. Like Bond, Yun et al. emphasize the importance of capital gains, but focus on cross-stock effects on price, which are especially important in the context of wealth metrics for measuring sustainability (Arrow et al., 2004; World Bank, 2011; UNU-IHDP and UNEP, 2014; Hamilton and Hartwick, 2014; Dasgupta, 2014). Building upon Hutniczak’s (2015) empirical work, Yun et al.

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FIGURE 4 Shadow prices of Baltic Sea fishery. The solid lines present the shadow prices of each species when the other two species are fixed at 2013 stock levels. The dashed lines shows the shadow prices of each species when the other two species are fixed at the steady state.

FIGURE 5 Complementarity or substitutability of species in the Baltic Sea fishery.

(2017b) use V -approximation to jointly recover shadow prices for all three fish species (Fig. 4). In the Baltic Sea fishery the three species are substitutes in production of revenue, but Yun et al. (2017b) show how shadow prices reflect ecological relationships, especially predator-prey relationships, that can lead to complementary relationships among natural capital assets (Fig. 5). Specifically, predators and prey can be capital complements. By explicitly modeling the ecological and economic interplay between capital stocks, Yun et al. demonstrate how the resulting shadow prices reflect capital stocks’ substitutability in the production of sustained benefits from the ecosystem. The implication is that when natural capital prices are accurately measured, focusing on wealth as a sustainability metric does not imply weak sustainability (Pearce and Atkinson, 1993). Rather, these natural asset prices explicitly account for limits to and opportunities for substitution. Echoing Dovern et al. (2014) and Pearson et al. (2013), Yun et al. (2017b) also argue for the importance of using natural capital asset prices to develop bioeconomically grounded wealth measures for the sustainable management of local systems below the national scale that

6 Discussion and Future Challenges

dominates the green accounting and economic sustainability literatures. Finally, because Yun et al. (2017b) recover V , they show that the inclusive wealth index tracks V well, when the quasi-constant shadow price is calculated using the arithmetic mean of the shadow prices at both bounds of the time difference for which a change of inclusive wealth is calculated.

6 DISCUSSION AND FUTURE CHALLENGES A system of accounts that tracks changes in long-run wealth is important for informing policy in a world concerned with sustainability. National income and product accounts have helped policymakers focus on short-run and employment concerns. However, without associated capital accounts, the income and product accounts paint an incomplete picture. Indeed, the development of capital accounts generally has been an important and difficult topic for national accountants (Obst et al., 2016), and the current state of capital accounts omits most natural capital, despite the 2008 System of National Accounts (Chapter 10) call to develop these accounts in a way that includes many forms of natural capital (United Nations Statistics Division, 2009). Certainly, accounting alone will not lead to policy that promotes sustainability (Obst and Vardon, 2014), but it is likely a necessary input for discussions to lead to such policies (Heal, 2012; Stiglitz et al., 2010; Solow, 1993). Therefore, it is imperative to develop tools to identify appropriate prices for measuring the changes in wealth associated with changes in natural capital. In this chapter, we have developed the necessary theory and an approach to measurement. Nevertheless, significant technical, operational, and cultural challenges remain for making full-scale implementation a reality. Beyond the aforementioned technical challenges of addressing time nonautonomy, stochasticity, and non-convexity in natural capital valuation, there are important, if perhaps more mundane, operational decisions (i.e. “judgment calls”) that will face most practitioners. One is the question of just how many and which capital stocks to include in a multi-stock depiction of the world. Ecosystems are comprised of a very large number of biotic and abiotic stocks. Furthermore, species may function differently and provide distinct services at different life stages or in different settings. This potentially leads to a very large number of capital stocks in a bioeconomic model, including some from the same stock but of different “vintages.” Given the limits of data and computational capacity – not to mention human capacity to make sense of the results – judicious aggregation of some stocks and pruning of others will inevitably be needed. Furthermore, while we have focused in this chapter on natural capital and interactions among forms of natural capital, it may be equally (or more) important to consider the joint determination of asset prices across natural capital and stocks of reproducible and human capital. Nadiri and Rosen (1969) show how the marginal value of reproducible and human capital may be interrelated in non-intuitive ways. The same is likely true for natural capital, and these interactions will ultimately be important for accurately capturing changes in wealth.

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The nature of the dynamics of many real-world systems present fundamental challenges to the interpretation of the wealth indices that natural capital shadow prices inform. Specifically, many stocks of natural capital may go through cycles. These may include exogenous cycles driven by environmental variables or predator-prey relationships, but may also include endogenous cycling created by policy itself. Yun et al. (2017b) show that the wealth stored in an ecosystem, valued using realized shadow prices, may oscillate. In a world where changes in wealth are inherently assessed over discrete snapshots, whether inclusive wealth is non-declining (and hence consistent with most wealth-based definitions of sustainability) may depend heavily on the accounting period. This feature of natural capital may make interpreting changes in wealth in practice more challenging than the theory suggests. There are also cultural challenges that must be met in order to develop a vital interdisciplinary research community in natural capital valuation and wealth-based sustainability assessment whose core focus is accurate measurement and not necessarily promoting a conservation agenda. Indeed, the greatest barrier to more widespread measurement of natural capital values is not technical; rather it reflects a coordination failure across disciplines and within the community of environmental and resource economists. The asset pricing equations developed here, and articulated as a framework for interdisciplinary research in Fenichel et al. (2016a), make it clear that natural capital pricing is an inherently interdisciplinary venture – one involving (at minimum) biophysical scientists and economists. However, to date it is difficult to find studies that estimate the necessary natural science and economic models for the same system on similar enough scales that the two may be comfortably resolved. Furthermore, the scope of interdisciplinary engagement for natural capital valuation is inherently greater in many cases than that required for the valuation of ecosystem services alone. Natural capital valuation requires linking ecosystem service values to changes in underlying capital while simultaneously accounting for natural capital dynamics and feedbacks to these dynamics through human adaptations to changes in capital stocks. Some reorientation of research priorities is needed, and collaborations with natural scientists may be challenging. Beyond the usual tensions of vocabulary and epistemology that often attend interdisciplinary work, natural capital valuation brings its own issues of resolving varying temporal and spatial scales between ecological and economic models and data, determining the definitions of stocks and service flows, and resolving which model simplifications are acceptable. There may also be a strong case in many settings for coordination with social scientists outside of economics that can help elucidate the links between institutions and human behavior captured in the economic program – coordination that presents its own set of unique challenges. Less obvious, although implicit in our presentation, is the need for additional coordination and engagement within the sub-communities of environmental and resource economists. As demonstrated in this chapter, there is a rigorous theoretical basis, grounded in a venerable tradition, for the explicit treatment of nature as capital. This provides the profession with rigorous and powerful tools that are needed by policymakers for assessing the sustainability of socio-ecological systems and

6 Discussion and Future Challenges

policies (Donovan et al., 2015). Despite this strength, the dearth of natural capital measurement by economists (as opposed to valuation of ecosystem services) has ceded much of the rhetorical ground on natural capital. To remedy this shortfall, resource economists must move beyond the comfortable “bookend” approaches of social planner and open access models to apply their capital-theoretic tools to the messy, kakatopic world of real-world resource management. This is not to discount evidence of progress; research in positive resource economics has grown substantially in the last couple of decades and has contributed greatly to our understanding of the governance of resource systems. However, this work has largely avoided any discussion of the valuation of capital in these cases. Conversely, environmental economists who have focused on valuation have utilized their methods to evaluate the value of changes in environmental amenities and policies, often with the intent of including these estimates in benefit-cost analyses. However, as we discussed above, there is a significant gap between valuation of a service flow from natural capital and the valuation of the underlying capital itself. We have discussed some changes in the practice of non-market valuation – some marginal, others less so – that would facilitate closing this gap. As a result of these respective tendencies, valuation of natural capital has fallen into an awkward middle ground. The measurement of natural capital values for sustainability assessment (as well as social benefit-cost analysis) presents opportunities for new, impactful collaborations among colleagues in an inherently unified field. These new collaborations, though building on past research and impact, can potentially develop large-scale environmental and resource accounts on the order of the current national income and product accounts – moving society towards a vision that has repeatedly emerged in the literature (Solow, 1993; Fisher, 1906). It is important for environmental and resource economists to leverage the excitement surrounding the rhetoric of natural capital and sustainability to develop a library of useful examples of natural capital valuation for a range of natural assets that are understandable to economists and non-economists alike, and to update them through time to demonstrate the usefulness of this valuation for tracking progress toward sustainability. Considering the role of ecosystem services provided by natural features in production is important (Guerry et al., 2015), but it is not truly measuring or accounting for natural capital. Furthermore, it is important that valuation be grounded in economic theory and not based on ad hoc empirical approaches (sensu Costanza et al., 1997) that fail to conform to economically-based notions of value (Bockstael et al., 2000). New efforts to measure the value of natural capital can be pursued at local and national levels. However, we see considerable value in extending shadow pricing and wealth-based sustainability assessment to smaller scale systems than nation states – where problems of over-aggregation of inherently distinct natural capital stocks and limited data and modeling capacity may impede progress. Ideally, each nation state would comprehensively track their wealth embodied in natural capital (not to mention other forms of wealth). However, this is likely unrealistic, even in the medium term, since natural capital needs to be measured at the local level because many natu-

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ral capital stocks are inherently distinct in terms of their services, in the management and the behavior of the individuals that appropriate their benefits, and because there is limited potential for arbitrage. It is possible – although difficult to foresee at this stage – that best practices for ‘benefit transfer’ of natural capital values can be developed for cases where the capacity for bottom-up estimation of shadow values is not feasible. Economists have long conceptualized natural resources as capital assets, and the idea of natural capital has attracted attention well beyond economists. However, empirical measurement is badly needed. This chapter laid a theoretical and empirical foundation for measuring natural capital asset prices – realized shadow prices in imperfect, but not necessarily open access, economies. We hope that the community of environmental and resource economists will respond to the broad interest in natural capital by building upon this research to develop a rigorous and complete theory of natural capital valuation while simultaneously building a wealth of case studies for policymakers. It has been more than 100 years since Irving Fisher firmly established natural capital on par with other forms of the wealth of humankind. It is time to measure and manage our natural capital in a way that reflects this understanding.

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CHAPTER

Through the looking glass: Environmental health economics in low and middle income countries✶

4

Subhrendu K. Pattanayak∗,1 , Emily L. Pakhtigian∗ , Erin L. Litzow† ∗ Sanford

† Vancouver

School of Public Policy, Duke University, Durham, NC, USA School of Economics, University of British Columbia, Vancouver, BC, Canada 1 Corresponding author: e-mail address: [email protected]

CONTENTS 1 The Economics of Environmental Health .................................................... 1.1 Environmental Health in LMICs ................................................. 1.2 Economics and Environmental Health.......................................... 2 Choice and Behavior ............................................................................ 2.1 Simple Analytics ................................................................... 2.2 Measuring Demand: Valuation (Willingness to Pay) .......................... 2.3 Shifting Demand: Adoption ...................................................... 2.4 Predicting Impact: Evaluation ................................................... 3 What We Know About Environmental Health in LMICs .................................... 3.1 Valuing Environmental Risk Reductions........................................ 3.2 Adopting Environmental Risk Reducing Technologies ....................... 3.3 Evaluating Environmental Health Impacts ..................................... 4 Path Forward ..................................................................................... 4.1 Multiple Risks ...................................................................... 4.2 Supply and Political Economy ................................................... 4.3 Environmental Hazards and Climate Change .................................. 4.4 Beyond Experiments and Average Treatment Effects......................... 4.5 Closing Thoughts .................................................................. References............................................................................................

144 145 148 151 153 155 158 160 161 163 167 171 175 175 177 180 181 183 184

✶ We would especially like to thank V. Kerry Smith for his thoughtful comments on an earlier draft of this work. We would also like to thank the many students who took the Environmental Health Economics course at Duke university from 2009–2018 and provided helpful feedback, which greatly improved the exposition of the arguments presented in this review. Handbook of Environmental Economics, Volume 4, ISSN 1574-0099, https://doi.org/10.1016/bs.hesenv.2018.08.004 Copyright © 2018 Elsevier B.V. All rights reserved.

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1 THE ECONOMICS OF ENVIRONMENTAL HEALTH Human interactions with nature can have important and lasting impacts on many outcomes – health being chief among them. This interplay between nature and human behaviors (or human ecology) dictates how the environment impacts health.1 Often the focus is on environmental determinants of morbidity and mortality, a reality made clear through decades of endemic-levels of environmentally-originated, infectious diseases that continue to claim countless lives and hurt human productive capacity in low and middle income countries (LMICs).2 The ecological basis for disease dates at least as far back as 400 B.C., to Hippocrates’s On Airs, Waters, and Place. Unsurprisingly then, global efforts by the World Health Organization, United Nations Environment Program, and others persist even today in putting environmental health concerns front and center in the United Nation’s Sustainable Development Goals. Most recently, a Lancet–Rockefeller commission on planetary health summarized how environmental degradation (climate change, soil erosion, freshwater depletion, air and water pollution) is threatening human health worldwide, especially through malnutrition, pneumonia, diarrhea, malaria, and other diseases of the poor (Whitmee et al., 2015). Accordingly, research has examined and continues to examine the links between the environment and health to both understand and contain the harms. This research suggests several key patterns (Prüss-Üstün and Corvalan, 2006; Prüss-Üstün et al., 2016; Smith et al., 1999). First, while the nature of environmental threats changes across time and space, the burden of disease attributable to environmental risk hovers stubbornly around one quarter of the total global disease burden. Second, environmental risks are particularly damaging to the health of children, but also of the elderly and the impoverished. Third, as the global health community makes strides in decreasing the prevalence of infectious diseases such as diarrhea and malaria, non-communicable diseases of environmental origin increase in prevalence. In this chapter, we examine human–environmental interactions and their implications for health, highlighting the ways in which economic tools provide analytical insight into this relationship as well as potential solutions to preventing (and treating) diseases. Specifically, we contend that the household production framework – which focuses on the beneficiary and households – provides a helpful conceptual tool to understand when and how households will expend resources to avert environmental risks. We review the empirical literature in environmental health economics, focusing particularly on studies that value environmental risk reduction, that examine household adoption of environmental health technologies, and that evaluate health impacts of these technologies. While economists have been mostly on the sidelines of the 1 An older human ecology tradition posits that we humans modify our natural environment, sometimes increasing disease risks, and ultimately adapt to the new disease risk environment (Wessen, 1972; MacCormack, 1984). 2 Throughout this chapter we will refer to low and middle income countries as LMICs. We define LMICs according to the World Bank’s income groups (World Bank, 2018).

1 The Economics of Environmental Health

FIGURE 1 Environmental disease burden, measured in disability adjusted life years per 1000 people (Institute for Health Metrics and Evaluation, 2018).

research on environmental health in LMICs, there is a growing empirical literature on values, drivers, and impacts. At the risk of simplification, this literature reveals considerable heterogeneity in estimates and some methodological blind spots, with sobering overall findings. While there are exceptions to the following observations, we find relatively low values for environmental risk reductions, which is mirrored by limited adoption of environmental health technologies and, accordingly, disappointing results regarding health impacts. Because much remains to be learned about valuation, evaluation, and adoption, we conclude by outlining a research agenda for LMICs that must focus on multiple risks, on the political economy of how interventions are supplied, and on environmental disasters, especially in the light of mounting climate change risks.

1.1 ENVIRONMENTAL HEALTH IN LMICs While environmental degradation generates health burdens around the world, the distribution of these burdens is far from equal, with LMICs facing disproportionally higher risks (Fig. 1). Recent analysis of the global burden of disease attributable to environmental factors reveals that in many LMICs in Africa and south Asia, the environmental disease burden is as high as one third, whereas in the developed world it may be as low as nine percent (Prüss-Üstün et al., 2016). Furthermore, the nature of the risk shifts with location, with more developed countries primarily facing non-communicable disease threats and infectious diseases continuing to plague LMICs. By definition (and our choice to focus on these health outcomes), many of the world’s greatest global health challenges, like diarrhea, respiratory diseases, and malaria are fundamentally environmental. It would be challenging and short sighted, therefore, to combat these diseases without seriously addressing environmental degradation.

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As countries proceed along the development pathway, a familiar pattern in environmental health appears – the prevalence of infectious disease decreases and that of non-communicable disease increases (Prüss-Üstün et al., 2016). This trend is fairly intuitive. As countries develop, more people have access to higher quality environmental amenities and environmental risk averting technologies, decreasing the prevalence of infectious diseases, like diarrhea, respiratory infections, and malaria, that are common in the absence of such improvements. When these more immediate environmental diseases decrease in prevalence, however, the threats of environmental health risks do not. Prolonged exposure to some environmental risks such as arsenic does not cause an immediate disease response, rather it increases the likelihood of cancer later in life (Pattanayak and Pfaff, 2009). This shift demonstrates that, as societies develop and life expectancies increase, the nature of the environmental risks most pressing from a public health perspective change as well, necessitating examination of both infectious and non-communicable diseases. Among infectious diseases, we focus on respiratory infections, diarrhea, and malaria, caused primarily by air pollution exposure, microbial contamination in drinking water, and poor vector control, respectively. We also briefly comment on non-infectious environmental hazards as they relate to chronic pulmonary disease, non-microbial groundwater contamination, and natural disasters. As quantitative methods and data quality improve in both epidemiology and economics, more precise, accurate figures of the disease burden are possible. While many of these methods have been applied frequently in rich countries, there is a small but growing literature on LIMCs – further contributing to our understanding of the environment–health link in these settings. Our contribution focuses on the economics of environmental health in LMICs primarily because of the disproportionate burden on LMICs, but secondarily because of this growing body of new empirical research. The notable differences in the health–environment link between developed countries and LMICs are mainly explained by the following socio-economic and political economy arguments. First, many households in LMICs suffering these exposures are poor; thus, they cannot afford prevention through piped water, private latrines, improved cookstoves, insecticide treated bed nets and or mitigation through health care and medicines. Furthermore, many of these households also lack access to quality healthcare services (Banerjee and Duflo, 2007). Second, geography and climate may play critical roles. Many LMICs lie within the tropics, regions with climate that favors the spread of infectious disease (Pattanayak and Pfaff, 2009). Third, LMICs also suffer from weak institutions relating to environment and health, especially surrounding property rights, administrative capacity, and regulation and enforcement. Overpopulated urban centers encourage infectious diseases; rural villages without access to healthcare services may become endemic regions for diseases like malaria. Without strong institutions to address these environmental health concerns, conditions deteriorate (Pattanayak and Pfaff, 2009). Furthermore, environmental quality may be sacrificed along the path to development; thus, rapid exploitation of natural

1 The Economics of Environmental Health

ecosystems may contribute to the diseases observed in many LMICs today (Bauch et al., 2015; Keesing et al., 2010). Among the infectious diseases plaguing LMICs, the most devastating remain respiratory infections, diarrhea, and malaria. The recent assessment of the global burden of disease attributable to the environment finds that over 900,000 lives are lost each year to respiratory infection; over 800,000 to diarrhea; and over 500,000 to malaria (Prüss-Üstün et al., 2016). These diseases clearly impose a large mortality risk, but non-fatal bouts of these diseases can also hurt the growth and development of young children. That is, even when the diseases are not fatal, they can lead to malnutrition and compromised cognitive capabilities, which impose substantial costs on productivity and quality of life (Currie and Vogl, 2013; Prüss-Üstün et al., 2016). Here we briefly review the causes, symptoms, and costs of these three infectious diseases.

ARI. Air pollution exposure threatens human health in both the short-term (acute respiratory infections) and in the long-term (chronic pulmonary and cardiovascular diseases). While it has been challenging to exactly identify the dose-response function for air pollution exposure, the literature clearly links exposure and increased rates of acute respiratory infections, eye and ear infections, tuberculosis, asthma, chronic obstructive pulmonary disorder, lung and other cancers, and low birth weight (Ezzati and Kammen, 2002). There are many potential contributors to air pollution levels, both indoor air pollution (typically from incomplete combustion of biomass fuels used for cooking) and outdoor or ambient air pollution (from numerous sources). The World Health Organization estimates that indoor air pollution accounts for at least a third of the disease burden of respiratory infections. This estimate increases to over half when considering young children (Prüss-Üstün et al., 2016). Similarly, outdoor air pollution contributes substantially to the prevalence of respiratory infections, pulmonary disease, cardiac disease, and stroke. Diarrhea. Stemming largely from insufficient water, poor sanitation, and unsafe hygiene, diarrhea continues to impose a mortality and productivity burden on global populations, claiming the lives of up to half a million children under the age of five each year (Prüss-Üstün et al., 2016). Diarrhea is mainly caused by contact with fecal pathogens such as rotavirus and E.coli; this contact may be a result of poor hygiene behaviors including the lack of handwashing with soap and or the spread of pathogens through insects and vermin in the context of inadequate sanitation. In addition to the mortality burden, billions of children contract diarrhea each year; the resulting nutritional losses impact future health outcomes, even if children recover from the disease episodes themselves. Many studies have linked nutritional deficiencies with cognitive and developmental delays as well as shorter heights, demonstrating the long-term physiological costs of childhood diarrhea (Currie and Vogl, 2013; Spears et al., 2013). Malaria. Parasitic and vector-borne diseases also pose major threats to human health and productivity, with malaria remaining one of the most common and deadly among

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such diseases. Caused by the Plasmodium parasite, malaria is transmitted to and from humans through the Anopheles mosquito. Environmental modifications to the local habitat and micro-climate of mosquito populations link ecological change to malaria; however, the literature finds significant variation in the environment–mosquito link, making it difficult to generalize how these modifications affect malaria risk (Yasuoka and Levins, 2007). Malaria is both deadly – killing over half a million people each year – and resistant – with drug resistance presenting a very real challenge in combating the disease (Pattanayak and Pfaff, 2009; Prüss-Üstün et al., 2016). Furthermore, while malaria has been completely eradicated throughout much of the world, it remains endemic in certain areas, particularly throughout sub-Saharan Africa and pockets of Asia and Latin America. In addition to the mortality risk, malaria imposes fever, anemia, and spleen disorders on its victims and also increases vulnerability to other infectious diseases and malnutrition. Environmental hazards also factor into the environmental burden of disease including natural contamination of drinking water (i.e., arsenic contamination) and natural disasters, among others; however, this chapter focuses on infectious diseases with environmental foundations for three main reasons. First, the presence of environmental hazards is less amenable to policy change; that is, while improved water and sanitation policies may reduce diarrhea risks, policies and behavioral changes cannot realistically prevent tsunamis and earthquakes, at least in the short run. Second, behaviors related to control of diarrhea, malaria, and ARI are more environmental, whereas behaviors related to chronic outcomes involve lifestyle changes (e.g., diets, activity). Third, practical space constraints force us to omit some important topics. We briefly visit these other environmental health risks in Section 4.3.

1.2 ECONOMICS AND ENVIRONMENTAL HEALTH While epidemiology and ecology clearly improve our understanding of environmental determinants of diseases and of public health engineering solutions to disease control, in this chapter we make the case for economics. We believe economics is critical to understanding not just the physiological determinants of health but key behavioral and institutional aspects as well. That is, whether environmental risks translate into harms to human health, as predicted by theory or laboratory experiments, depends in part on the nature and extent of averting and mitigating behaviors undertaken by families and societies. Below we summarize how economics can help both (i) make sense of the environmental health patterns as they are – a positive perspective, as well as (ii) argue for how much better these patterns could and should be – a normative perspective on environmental protections to safeguard human health and wellbeing. Consider two views through the positivist lens. First, we see regions or countries with low (high) environmental quality and poor (good) health because of institutional choices regarding consumption, environmental protection, and human health. In cases with binding resource constraints, there are clear tradeoffs between consumption, health, and environmental quality. As implied by the environmental Kuznets

1 The Economics of Environmental Health

FIGURE 2 Demand for and supply of environmental services.

curve logic (Gangadharan and Valenzuela, 2001): at low levels of consumption, society may experience high environmental quality; however, as a society develops and consumption increases, it usually comes at the expense of the environment. Once a society has reached a sufficiently high level of development, environmental quality may regain a position of social importance; however, the environmental health damages accrued during the development transition may have lasting implications. Further, if the signal from science on the environmental–health links is unclear, societies will over-consume and under-protect the environment. Of course, not all regions begin at low development and high environmental quality; Pattanayak and Pfaff (2009) argue that a common setting in LMICs is one of low development and low environmental quality. In this case, it is unclear which path society will take: will it invest equally in consumption and environmental quality and, by extension, health? It is challenging to resolve this more nebulous relationship, suggesting a closer look at more micro choices. We consider the following stylized model depicted by Fig. 2 to illustrate demand for environmental quality. In a high income country such as Norway, demand for environmental quality is high and provision is relatively inexpensive as a result of mature markets, high quality infrastructure, and a well-functioning public sector. In a low income country like Haiti, the opposite is true. Demand, or at least perceived demand, for environmental services is low and the cost of provision is high. Even without considering further market imperfections in this domain (e.g., externalities), the combined low demand and high cost results in a low level of environmental service provision. The state of development – high income, competent institutions – is partly responsible for high quality environmental service provision, but, of course, this is not a guaranteed outcome. Rather, provision is the result of a combination of factors, including functionality and efficiency of governments (politicians and bureaucrats), civic society, NGOs, the private sector, and other external actors (as we discuss in Section 4.2). Second, this positive lens can be applied to why households and individuals do or do not avert health risks from air and water pollution, vector- and parasite-borne diseases, and other natural hazards. While they do expend time and effort in avert-

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ing environmental risks, household utility functions include more than just health, and sometimes include consumption items that compromise their health while providing other benefits. Rates of adoption and use of risk reducing technologies remain stubbornly low throughout LMICs (Ashraf et al., 2010; Jeuland et al., 2016; Kremer and Miguel, 2007; Pattanayak and Pfaff, 2009; Somanathan, 2010). Accordingly, the literature on averting behaviors examines a series of questions, chief among them: how do households value reductions in environmental risk; what are the determinants of environmental health technology adoption; and are existing environmental health technologies effective in reducing environmental risk and improving health? In LMICs, these questions are most commonly asked for infectious disease – specifically risks related to air pollution, water contamination, and vector-borne disease. Turning now to the more normative lens, economics can also be used to determine if the state of environmental health is socially optimal, and, if not, what policy levers and program tools can help install environmental safeguards for human health. Here we briefly offer four perspectives. First, justifications of public policies for environmental health risk reductions usually take efficiency or equity perspectives. The clearest example of an efficiency argument is the near pervasiveness of infection and prevention externalities (Gersovitz and Hammer, 2003). For example, households do not internalize all benefits associated with their personal risk reductions. Further, even if they engage in risk reductions, because of the quasi-public good nature of these technologies, if sufficient numbers of their neighbors and fellow citizens reduce insufficiently, they will remain exposed – a classic case of the free riding that results in an underinvestment in environmental health technologies (Kremer and Miguel, 2007). Incomplete information and imperfect competition also prevail in these settings, providing other ‘efficiency’ justifications for public intervention. Second, the previous sub-section shows that the environmental health burdens are concentrated in some pockets of the world (e.g., sub-Saharan Africa, south Asia, central America), for some demographics (young children, pregnant mothers, elderly), and for socially marginal groups. Thus, equity and/or environmental justice provides another justification. Third, whether or not to intervene depends in part on a careful evaluation of the suite of costs and benefits because these likely vary by ecology, climate, market development, human capital, and socio-demographics. Additionally, many of the benefit and cost indicators are non-market – requiring the economic tools of stated preferences and revealed preferences (for related goods) for accurate measurements of social welfare. Fourth, the normative questions also apply to the choice of instruments to finance the policies – local taxes, public debt, international grants and loans, etc. This choice of revenue source influences and is, in turn, influenced by institutional governance – that is, the levels and types of institutions involved in delivery of environmental health technologies and services.

2 Choice and Behavior

Table 1 Behavioral response to environmental risk Respiratory infection Environmental condi- Air pollution tion (PM, CO) Averting or mitigating • Kitchen ventilation behaviors • Improved cookstoves • Shifting cooking outside • Facemasks • Decreased time outside External intervention

Diarrhea

Malaria

Water pollution (E.coli) • Drinking water treatment (filtration, boiling) • Safe drinking water sources • Improved latrines • Handwashing with soap

Mosquito habitat

• Insecticide treated bed nets • Indoor residual spraying • Integrated vector management • Other environmental management • Information, education, and communication provision (through interventions) • Targeted subsidies • Infrastructure (banking/credit, transportation) • Regulations, policies, and standards (along with monitoring and enforcement)

2 CHOICE AND BEHAVIOR The economics approach to environmental health starts with choices regarding environmental risk reducing behaviors. Choices are not limitless: choices are guided by preferences and limited by constraints. Thus, the economics approach to examining environmental risks to health is to endeavor to fully characterize the preferences and constraints and empirically verify the same with data on households’ choices and behaviors. Households can allocate their resources to consumption goods, including risk reduction behaviors and technologies, which we shall interchangeably call averting behaviors. Averting environmental risk typically requires, at minimum, time, money, and knowledge. Because households have limited budgets and information and face non-zero prices, households must make tradeoffs in choosing averting behaviors. Importantly, households must have and appreciate the information on the risks they face in order to choose optimal averting behaviors. In this section, first we catalog a range of potential behaviors that can reduce ARI, diarrhea, and malaria (Table 1 summarizes these behaviors). With these explicit examples in mind, we present a simple stylized characterization of choices and behaviors that produce human health by reducing environmental risks (Section 2.1). Next, we show how this modeling framework can be used to model and measure households’ valuation (demand/WTP) of risk reductions (Section 2.2), their adoption of risk reducing behaviors and technologies (Section 2.3), and how their choices impact human health, potentially (Section 2.4).

ARI and Air Pollution. One of the largest contributors to indoor air pollution is the use of biomass fuels in cooking, particularly because these fuels are often inefficiently

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used in unimproved cookstoves. While transitions to modern fuels are underway in many parts of the world, biomass fuels remain a common fuel source for forty percent of the world’s households (Smith et al., 2000). Accordingly, we must understand the demand, or lack thereof, for improved cookstoves. Households can also lower indoor air pollution by shifting cooking outside, keeping children away from cooking areas and opening windows to ventilate. Air pollution, however, is not a unidimensional threat. Despite the dominance of IAP, (Prüss-Üstün et al., 2016), outdoor air pollution presents a sizeable threat to human health. While households have less agency regarding the outdoor air pollution they confront, they have some choices, including (i) permanent migration, (ii) temporarily moving away, say in high pollution seasons, (iii) staying indoors on high pollution days, (iv) installing air conditioning and or air purifiers, or (v) wearing particulate filtering facemasks (Zhang and Mu, 2017).

Diarrhea and Water Pollution. There are a variety of averting technologies and behaviors that households can undertake to minimize diarrheal risks. Households can (i) build and use latrines, (ii) wash hands with soap, (iii) use clean water sources, and or (iv) treat water in-house by boiling or filtering (Ashraf et al., 2010; Guiteras et al., 2016; Pattanayak et al., 2009a). Nevertheless, in many cases traditional practices such as open defecation persist, perpetuating the incidence of diarrhea. While the burden of disease associated with water and sanitation risks remains high, it is important to note substantial improvements in access, particularly for improved water sources. About ninety percent of global population has access to improved water sources; nearly sixty-five percent to improved sanitation (PrüssÜstün et al., 2016). While the benefits of behavioral shifts towards improved water and sanitation practices appear sizable, traditional water and sanitation practices remain sticky. Malaria and Mosquito Habitats. Given malaria’s highly infectious transmission pathway as well as the rise in drug resistance, a focus on human ecology and prevention is essential (Pattanayak and Yasuoka, 2008). Here too households near habitats conducive to anopheline mosquito populations have options to prevent (and/or treat) malaria. Prevention is largely vector control – both indoor and outdoor residual insecticide spraying (Brown and Kramer, 2018) and the use of insecticide treated bed nets (Dupas, 2009, 2014). Further, environmental management and land transformation, including destroying habitats best suited for mosquito larvae and careful infrastructure design may limit interaction of humans and malaria carrying mosquitos. The applicability of strategies, however, differs by malaria ecology, making it challenging to design general environmental management strategies to limit malaria transmission (Prüss-Üstün et al., 2016). In addition, large scale land transformation such as deforestation appears to be positively correlated with malaria incidence, direct ecological change, as well as changing demographics. In-migration to previously forested regions exposes new populations, many of whom lack resistance, to malaria, expanding the scope of transmission (De Silva and Marshall, 2012; Laporta et al., 2013; Texier et al., 2013).

2 Choice and Behavior

Looking across the three environmental risks domains, there are factors that influence household decisions to allocate resources to averting behaviors, as conceptualized in Section 2.1 and described in Section 3. Note, conceptually, there is no clear dichotomy between prevention and treatment in the case of infectious diseases. Although households can take steps to prevent the transmission of infectious disease, prevention is imperfect, necessitating some discussion of treatment. While treatment of respiratory infections, diarrhea, and malaria provide real benefits to infected patients, treatment reduces transmission because it reduces the rate of contact between infected humans. Thus, it is also possible to combat these infectious diseases with access to high quality healthcare services, including trained medical professionals who have the tools to diagnose these illnesses, to prescribe appropriate treatment, and to monitor compliance with treatment.3

2.1 SIMPLE ANALYTICS To understand household decision-making, we draw on idea that reductions in environmental health risks are produced by households (Smith, 1991). This logic was adapted for the case of LMICs by Pattanayak and Pfaff (2009). Here we adjust their deterministic model to explicitly introduce risk and to frame the discussion in terms of expected utility. We do this primarily because of the risks inherent in both how averting behaviors reduce exposures and how exposure reductions impact health; household choices can realistically change the health risks of harmful environmental exposures, not health per se. Further, because households’ appetites for risks vary – i.e., few are risk loving, some are risk neutral, and many are risk averse – this risk preference will determine how households respond, as reflected in the shape and concavity of the expected utility function (Freeman et al., 2014). Households maximize expected utility (u) by allocating time and money across health and consumption. Thus the household faces the following maximization problem (summarized by the Lagrangian in Eq. (1)) subject to a set of income, time, and health production constraints: (1) L1 = max π [u [l, c, s (e[a, A, G], h) ; θ ]   + μ n − c − pm − rk + w (24 − s(e [a (t, m, k) , A, G]) − l − t)   − λ f (e, a [t, m, k] , A, G) • • • •

π is the probability of the particular state of the world; l is leisure; c is consumption; e is household environmental quality (e.g., air or water quality);

3 In the case of malaria, antimalarial medications are a viable treatment option; however, concerns about

drug resistance and over prescription threaten the sustainability of current treatment options (Cohen et al., 2015).

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• • • • • • • • • • • •

s is time spent sick (produced by the health production function); a is household risk-averting behavior (A is the community aggregate of a); h is baseline human capital G is government action to reduction pollution; θ reflects a set of household-specific preferences (e.g., risk aversion); n is non-wage exogenous income; p is unit price of materials; m is materials spent to avert risks; r is unit price of knowledge (search costs) k is knowledge needed to avert risks; w is wage rate; t is time spent to avert risks

Thus, s is decreasing in household averting behavior (a – described below), aggregate community averting behavior (A), government pollution reduction (G), household environmental quality (e), and baseline human capital (h). The household production function specifically reflects how households “produce” environmental quality, which is affected by averting technologies or behaviors (a) that are, themselves, produced by combining time (t), materials (m), and knowledge (k) inputs. In the model, f is the environmental quality function that captures this process. Accordingly averting behavior affects the environmental quality (e) to which households are exposed. Importantly, e is not determined exclusively by household averting behavior; aggregate averting (A) and government intervention (G) matter as well. Instead of a simple reduced-form health production function, here we argue that it is a composite function (of averting behavior, environmental quality, and health production) that links household inputs to the health output. Both the health and environmental quality production functions are assumed to be twicedifferentiable, continuous, and convex. Given the complexity of the relationships, none of these production processes are deterministic – there are probabilities associated with each link: from t, m, k to a, from a to e, from e to s, and, finally, from s to the experienced (dis)utility, u. Instead of assigning separate probabilities to each link, to keep the model tractable, we focus on the key intuition that households maximize expected utility (π · u) because of these cumulative risks. The household’s total income from exogenous income (y) and wages obtained through work hours compensated at a wage rate (w) is spent on consumption (c, with the price of consumption normalized), the purchase of averting materials at price (p), and the acquisition of knowledge about the efficacy of averting behavior at unit cost (r). Finally, the 24-hour time budget is allocated to leisure (l), time spent engaged in averting behavior (t), and to time spent sick (s); the residual household time is for wage labor. Note, we have assumed the time constraint binds and folded it into a full income constraint. Furthermore, given the probabilities assigned to utility (and by extension to health production), household risks also influence the income constraint. Households will allocate their time and monetary resources towards averting behaviors as long as the cost of one additional unit of averting is equal to its perceived

2 Choice and Behavior

health and psychological benefits, in expectation. Solving for the reduced form of the first order condition of Eq. (1), yields the optimal averting behavior as shown in Eq. (2) π · [us · se · ea (at + am + ak ) − μ · w · se (ea (at + am + ak ))]

(2)

= w · ea · at + p · ea · am + r · ea · ak where the left-hand side represents the marginal expected utility of averting (reduced pain and suffering from illness and decreased wage loss due to illness) and the righthand side represents the marginal costs of averting (time, material, and knowledge).4 In LMICs, households’ marginal expected utility of consumption (which is what is given up to pay for averting technologies) may be higher than marginal expected utility of environmental quality (for health), especially at low income levels. This key insight from economics sometimes surprises the public health and engineering communities, who are puzzled by why we see little or no investment in environmental protections in many LMIC contexts.

2.2 MEASURING DEMAND: VALUATION (WILLINGNESS TO PAY) The framework described so far can characterize household demand for reductions in environmental risk, which is a specific input in policy discussions: what are households willing to pay for reducing environmental risks? That is, if there is an exogenous change in e, how would households’ economic welfare change, as in, how much would they pay (or accept) to experience this change. We are interested in how changes in e (∂e) due to changes in government policy (∂G), for example, affect household utility. We can then derive an economic measure of the utility gains (i.e., WTP) related to averting behaviors. For that, we would start with a marginal WTP by taking partial derivatives of the first-order conditions of the Lagrangian in Eq. (1). Alternatively, we can express this measure more directly in cost terms by appealing to duality theory (Pattanayak et al., 2005; Freeman et al., 2014). In the dual characterization, let x ∗ be the minimum cost required to attain u∗ , the optimum expected utility that is consistent with household production and consumption choices summarized above (Freeman et al., 2014). Now consider a different kind of cost function () that represents the minimum nonlabor income, n, necessary to achieve expected utility level, u∗ , given the health production function, time endowment, preferences, prices, and probability distribution over potential states of the world, π ·  meets all the conditions of a regular expenditure function, referred to in

4 We acknowledge that in many LMIC contexts, social interactions forge a link between individual averting

behaviors, a, and aggregated averting behaviors, A, which would generate additional benefits or costs to the household. Our simplified model in Eq. (2) omits these connections.

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the environmental economics literature as the variation function (McConnell, 1990).  L2 = min π c + pm + rk + w (s + l + t − 24)   1 ∗ + (3) u − u [l, c, s (e[a, A, G], h) ; θ] μ By applying the envelope theorem, we can take the first derivative of this quasiexpenditure function with respect to e to derive a utility-constant WTP measure as the change in nonlabor income that will compensate for a change in e. Recognizing that the optimal amounts of c, l, t, m, k, and s ∗ all depend on the level of e, WTP can be described as follows:   1 e = π w · te + p · me + r · ke + w · se − · us · se (4) μ e is the change of nonlabor income, ∂n, that could be taken away from the household to compensate for the expected u arising out of e, holding the household at the initial expected welfare level, u∗ . The WTP measure is obtained by integrating e over the relevant change in environmental quality. Thus, WTP for environmental risk reduction comprises averting costs, cost of illness, opportunity costs of lost work days, and money value of pain and suffering (Harrington and Portney, 1987). This result illustrates the duality between household maximization of expected utility or household minimization of costs: households spending on t , m, and k to reach the same optimal environmental quality that is associated with u∗ .5 The empirical literature has measured this WTP using revealed and stated preference methods (Whitehead et al., 2008). In practice, however, applications using revealed preference approaches focus on and recover only pieces of the full suite of benefits included in Eq. (4). In principle, stated preference approaches can be structured to make respondents consider the full range of benefits, but this remains an open question. In any case, both approaches assume that the analyst knows all the ways in which e and or a directly or indirectly impact utility. If e or a enters utility directly or through other non-health services, it introduces other impacts on utility; Jeuland et al. (2015b) present the case for non-health effects of smoke-reducing cookstoves that are directly tied to tastes. More generally, as we adapt conceptual frameworks and data collection approaches developed outside of LMICs to LMICs, analysts must be prepared to incorporate how norms, culture, and local institutions influence households’ conceptions of the utility associated with s, e, and a, and the WTP for reductions in environmental risks. The θ parameter is a placeholder for why WTP measures (and utility functions) differ by households and settings, even if the usual parameters in constrained optimization (price, information, income) are the same. 5 In Eq. (4), changes in t , m, and k (t , m , and k ) attain the cost minimizing environmental quality. e e e Whereas in Eq. (2), ea .at , ea .am , and ea .ak represent the dual counterparts: changes in t , m, and k to

achieve utility maximizing levels of environmental quality.

2 Choice and Behavior

Revealed preference methods rely on observations of actual household choices to determine the value of changes to environmental quality or exposure. That is, household expenditures that effectively avert environmental risk or cope with its consequences. Consider several examples. First, households cope with environmental risks such as those associated with water shortages or water pollution by spending time and money to collect or pump water from safe sources, storing water, treating or boiling water before its use in drinking or cooking, and buying water (Pattanayak et al., 2005). Second, households in rural areas of LMICs will expend their most readily available resource – their time – to collect water (Whittington et al., 1990). Third, households may simply locate in areas with lower environmental risks – cleaner air, ready access to water, no concerns about mosquito-borne illness. Hedonic models rely on this location choice and the capitalization of environmental risks into housing value to measure environmental amenities such as clean air, water, and green space, among other local public goods. As these methods rely on rich data for both the housing or labor market and exposures to environmental risks, they are rarely applied in LMICs. Stated preference methods are based on eliciting household preferences for constructed scenarios in carefully implemented surveys. By far the most common approach is the contingent valuation method (CVM) in which respondents are presented with a hypothetical market (‘contingent’ scenario) or set of choices, where each choice is associated with implicit prices. For example, a respondent may be asked to choose between types or levels of indoor residual spraying (IRS) that would eliminate her family’s malaria risk at different prices (Brown et al., 2016). Household responses to this choice reveal their WTP for reducing the environmental risk, in this case of malaria. Contingent behavior methods or choice experiments present a generalization of CVM; these are more complicated scenarios that more closely reflect reality, but also impose greater cognitive burdens on respondents. For example, respondents can be asked which cookstove they would prefer from among a selection of cookstoves with different attributes. Revealed preference methods are useful precisely because they are based on actual choices that households make and the realized consequences of those choices. These methods rely on data from surveys or administrative sources regarding choices by people or firms, sometimes across time. These high data demands make it difficult to utilize them in data-scarce domains and locations. Additionally, in many settings, the variation that researcher seek to use – e.g., the variation in environmental risks or the prices of the market commodities that ‘capitalize’ this variation – also coincides with the variation in some other confounding variable. Finally, the assumptions underlying household choice, such as in hedonic property and wage models (free mobility, full information, functional complementary infrastructure such as banks that can lend money) are challenging to support in many LMIC settings. Stated preference methods represent a complement to revealed preference methods, as they provide a direct response to many of the limitations of revealed preference methodologies – i.e., they can be implemented ex ante and designed to only introduce the relevant variation (e.g., in e) to the survey respondent. They can also

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be used to elicit non-use valuations, something revealed preference methods are unequipped to address. Stated preference methodologies, however, have faced substantial methodological criticism, calling into question the accuracy of their findings. Concerns about hypothetical bias, yea-saying, strategic behavior, and framing plague implementation of stated preference surveys. Specifically, stated preference surveys must be crafted to be incentive compatible and consequential (Carson and Groves, 2007; Bishop et al., 2017).6 Some researchers use real (or hypothetical) auctions to improve the consequentiality and incentive compatibility of their value elicitations (Hoffman, 2009; Yishay et al., 2017).

2.3 SHIFTING DEMAND: ADOPTION The household production framework can help policy design by identifying what might shift household demand for averting behaviors. The marginal costs and marginal benefits that define the optimal choice by households (Eq. (2)) provide clues about how to reduce costs and/or increase benefits to household so that households will choose more environmental risk reductions. Here we discuss two clusters of factors: (i) a more obvious set of price and information drivers, and (ii) some subtle preference related factors. As a reminder, we are interested in deliberately incentivizing households to shift demand because their private choices are socially sub-optimal. That is, given the infectious nature of diseases discussed, prevention and infection externalities alone might be reason for policy interventions (Pattanayak and Pfaff, 2009). Starting with the obvious, the chief demand shifters are changes in the (i) input prices of averting behaviors, (ii) information and education regarding the health benefits of averting – as the science could be unclear, and/or (iii) campaigns that show how the behaviors and technologies (with the joint impact on health) influence other aspects of utility, e.g., aesthetics. Similarly, the model also suggests that demand would shift in response to exogenous shocks such as reductions in income and productivity, natural disasters that transform health production, or other health shocks. Whether demand increases or not, and health improves or not, also depends on a few possibilities. First, we consider the income and substitution effects related to price changes. Will the income increase from lower prices be ploughed into environmental or health improvements or into more consumption? (see Eq. (5))     ∂a ∂m ∂a ∂t ∂a ∂k ∂c ∂l da = + + · 1+ + (5) dp ∂m ∂p ∂t ∂p ∂k ∂p ∂a ∂a + − + − + − ? ? 6 Survey questions must be crafted with a clear idea of the respondent’s strategic incentives and how these

incentives influence their responses. Likewise, for the survey questions to be consequential, the respondent must believe that the survey results can potentially influence an agency’s actions and the outcomes of those actions are something about which the agent cares. In such a case, response to survey questions should be interpretable using mechanism design theory concerning incentive structures (Carson and Groves, 2007).

2 Choice and Behavior

Here, first three terms are somewhat intuitive to sign; averting behaviors will increase with m, t , and k by assumption that the averting inputs are complementary, yielding ∂t ∂k negative signs on ∂m ∂p , ∂p , and ∂p . If this represented the entire derivative, the intuitive story of increased averting behavior resulting from price subsidies would hold. The last two terms, however, are more ambiguous. From a theoretical perspective, it is not clear whether averting behaviors are substitutes or complements for all other consumption goods and leisure (see the next paragraph). The direction and magnitude of these relationships will influence how averting behaviors respond to price changes. Second, averting behaviors may negatively and directly affect utility. For example, while many improved cookstoves are fuel efficient and reduce indoor air pollution, if improved cookstoves or cooking fuels are incompatible with traditional cooking practices or negatively affect the taste of food, the health-based utility gains may not outweigh the disutility of these changes. While there may be compatible technologies, there is often a disconnect between product development and distribution, leading to technologies with effective prices that are too high for widespread adoption and use by households (Jeuland et al., 2015b). Third, consumption could directly harm local environmental outcomes and health such that consumption-related pollution will outweigh environmental gains from averting behavior. Examples of the second cluster of demand shifters are implicit in the preference parameter θ in Eq. (1), and include risk preferences, time preferences, and social preferences. We briefly discuss each, recognizing that these preferences are often not amenable to policy (i.e., it is difficult to change time preferences). Nevertheless, examination of these preferences could explain fast or slow responses to policy interventions or even low initial rates of technology adoption and diffusion. Starting with time preferences, households with higher discount rates are likely to invest less in averting technologies – e.g., sanitation – to reduce environmental risks for future health payoffs. Atmadja et al. (2017) provide some evidence of this, where baseline surveys used responses to money-time tradeoff questions to identify discount rates, which then helped predict rates of adoption of environmental health technologies. This is particularly relevant for environmental risks that cause disease in old age as individuals may not easily observe (e.g., air pollution and chronic pulmonary disease) or understand the tradeoff between current exposures and future ills (e.g., arsenic-contaminated drinking water and cancers). Similarly, risk averse individuals are less likely to shift behaviors (e.g., adopt environmental health technologies), even if on paper it seems like the new technology or new behavior reduces environmental risks. This is because there are many unknowns and risks regarding the technology–exposure–health link (Treich, 2010). This could happen, for example, when there is poor alignment between the technology developed and household preferences (Troncoso et al., 2011). The interaction of time and risk preferences further clouds the issues and warrants more careful research. Socially-embedded preferences, or the influence of the group on an individual, also play a potential role, especially for infectious diseases that depend in part on group level adoption. One form is competitive consumption – i.e., individuals lose social status if their consumption of a given good falls below a certain level, relative

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to others in their community (Veblen, 1924). Environmental risk related behaviors are likely to reflect such preferences, for example, the idea of individual and community cleanliness in the context of village sanitation (Pattanayak et al., 2009a). Other preference parameters that can shift demand include ambiguity aversion (Klibanoff et al., 2005) and socially-directed preferences or altruism (Dasgupta et al., 2016).

2.4 PREDICTING IMPACT: EVALUATION The household production model also provides a framework for impact evaluation. To see how, we extend the model developed in Section 2.1 to include complementarity and substitutability between averting behaviors. We return to the household’s expected utility maximization problem (Eq. (1)) and note that the optimal averting behavior (in Eq. (2)), a ∗ , is a function of averting prices, wages, and income (r, m, w, y) as well as aggregate levels of community averting, governmental intervention, and environmental exposure (A, G, e). Given our interest in evaluating the health impact of averting behavior, if we take the total derivate of the health production function (s (e [a, A, G] , h)) with respect to a, we find ds ∂s ∂e ∂G ∂s ∂e ∂A ∂s ∂e ∂s ∂h = + + + da ∂e ∂G ∂a ∂e ∂A ∂a ∂e ∂a ∂h ∂a − + ? − + ? − + − 0

(6)

The expected sign of each term is included below Eq. (6), demonstrating the ambiguity in the overall effect of the interventions on health because of the ambiguity induced by interactions with other inputs into health production. That is, while we assume that sickness is decreasing in baseline human capital and in environmental quality (and environmental quality is increasing in individual, aggregate, and government efforts), it is not clear how government and aggregate behaviors respond, for example. We turn to examine the possible cases of these ambiguous terms. Consider first the response of the government. The government can reallocate its resources away from these populations that are self-protecting and towards those households who are not averting (Ga < 0), demonstrating the case of substitution. Alternatively, the government could allocate more resources to these populations that have demonstrated commitments to averting behaviors (Ga > 0), demonstrating the case of complements. Next, consider the community response, where the ambiguity depends, in large part, on the generalized functional form relating household averting (a) to community averting (A). If, for example, A is a simple sum of each individual household’s a, then, holding all else equal, an increase in one household’s averting behavior would increase in aggregate averting, Aa > 0. These averting decisions, however, are likely non-linear as suggested by the literature on social learning and infections dynamics. Consider two possible responses by the community. First, given the infection externalities, households do not capture all the benefits or pay for all the costs of their averting efforts, leaving space for free riding. The presence of free riding

3 What We Know About Environmental Health in LMICs

demonstrates substitution, Aa < 0; of course, the distribution of free riders and nonfree riders within the community will modify the magnitude of this effect. Second, evidence of positive social learning in technology adoption points to complementarities between household and community averting, Aa > 0; that is, one household’s investment may actually generate additional interest in and demand for averting technologies within a community. Next consider another complication. The last term in Eq. (6) appears largely inconsequential because by definition the baseline human capital or health stock (h) prior to averting, will not be influenced by averting. However, what if instead of an additive functional form of the health production, the health production is Leontief, for example. At very low levels of baseline human capital or health stock (e.g., severe malnutrition as discussed in Section 4.1), averting behaviors cannot measurably improve health. Finally, we must remember connections between this discussion on impacts and the discussions of valuation and adoption. The increase in averting investments (∂a) discussed here will arise either as response to a demand shifter (e.g., price subsidy, information campaign) and/or because of high WTP for the expected health improvements. What if neither is true – response and/or WTP is low – for reasons discussed in Sections 2.2 and 2.3? This alone will imply little or no health impacts. We see here two important implications of expanding the model to evaluate health impacts of averting behaviors and technologies. First, the overall health impact realized from averting behaviors depends on a number of ambiguous parameters, many of which are context specific. Second, this ambiguity in the theory calls for careful empirical work but portends challenges to clean causal identification. Indeed, the empirical literature finds somewhat complicated and varied evidence on the health impacts of technologies to reduce environmental risks (see Section 3.3).

3 WHAT WE KNOW ABOUT ENVIRONMENTAL HEALTH IN LMICs The household production model provides key theoretical insight regarding how households facing time and other constraints adopt averting behaviors that reduce environmental risks. Theoretical predictions, however, are limited because the model is ill-suited to dictate all the behavioral interactions, which lead to ambiguities highlighted in Sections 2.2–2.4. Thus, empirical analyses are needed. While there is growing recognition that the interaction between human behavior and the natural environment is key in determining health outcomes in LMICs, mainstream economics has made less progress on estimating household valuation for reductions in environmental risk, on disentangling the determinants of environmental health technology adoption, and on identifying health impacts from averting behaviors. For example, using a LMICs lens, only nineteen studies have appeared in top economics journals on the tightly interconnected relationships between behaviors, the environment, and

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health in the entire last decade.7 Even within the environmental economics field journals, empirical evidence remains thin.8 This could be because of various challenges to studying these links, namely: (i) health effects may appear only after prolonged environmental risk exposure, limiting the power of short-term analysis; (ii) households may ‘stack’ by continuing to use traditional ‘dirty’ technologies along with adopting environmental health technologies; and (iii) households often face multiple environmental risks (see Section 4.1). There also could be data reasons; researchers rarely have access to high quality public data in LMICs, often requiring them to rely on primary data such that samples are small and panels take a long time to build. Nevertheless, there is now a body of high-quality, careful empirical studies seeking to identify how households value environmental risk reductions, why households adopt environmental health technologies, and if averting behaviors impact health and other human capital outcomes. This work employs important economic methods ranging from stated and revealed preference valuation to experimental and quasiexperimental methods and, in a few cases, careful studies using observational data. In the sections that follow, we describe illustrative cases and provide some takeaways from the environmental health economics literatures on valuation, adoption, and evaluation. In each section, we: (i) highlight the contributions of key studies in the field; (ii) organize this literature by describing study features in each of the three environmental risk domains of air pollution, water pollution, and vector populations; and (iii) offer main takeaways. Importantly, we do not claim to provide a comprehensive overview of the literature within Tables 2, 3, and 4; rather, we seek to identify a variety of studies that introduce the reader to these valuations, adoption, and evaluation literatures. Studies were selected based on three main criteria: coverage of three infectious diseases (respiratory disease, diarrhea, and malaria), geographical representation of LMICs, and peer reviewed economics publications.9 Furthermore, we acknowledge that studies may fall into multiple categories – i.e., report a willingness to pay valuation and drivers of adoption (Jeuland et al., 2015a; Hoffman, 2009), report drivers of adoption and health impacts (Tarozzi et al., 2014), or report a willingness to pay valuation and health impacts (Kremer et al., 2011). In these cases, while we have selected a key result, the papers contain more than what we could fit into each table, 7 Studies were identified based on topical relevance to the infectious diseases of malaria, respiratory infections, and diarrhea, key environmental health technologies such as bed nets, latrines, cookstoves, and water treatment, and important drivers such as air and water pollution. The websites of the American Economic Review, Econometrica, the Quarterly Journal of Economics, the Journal of Political Economy, and the Review of Economic Studies were used for this search. In addition, a total of four studies were found that examined demand for intestinal parasite treatment, gender-differentiated health inputs, and migratory responses to environmental risk. 8 A similar search of the Journal of Environmental Economics and Management and the Journal of the Association of Environmental and Resource Economics revealed 12 studies in the last decade. 9 We prioritize published work over working papers in Section 3, with the exception of Miller and Mobarak (2013), Rangel and Vogl (2016), Gertler et al. (2015) and Meyer et al. (2018). Unpublished work is discussed in Section 4, where we explore the path forward in this field.

3 What We Know About Environmental Health in LMICs

without repetition. In each section, we also point readers to systematic reviews of valuation, adoption, and evaluation in each environmental health domain. As these reviews cover a variety of fields, economics being just one among many, there exists substantial variation in the statistical and research methods included; however, they provide a systematic introduction to the literature.

3.1 VALUING ENVIRONMENTAL RISK REDUCTIONS From an economics perspective, the value placed on reductions of environmental risks to health is of key importance; that is, it is essential to understand and measure how much households are willing to invest in technologies and the opportunity costs of behaviors intended to diminish environmental risks. As discussed in Section 2, revealed and stated preference methods are the main tools for valuation. In Table 2, we present some key empirical applications of these methods to value reductions in air pollution, in water pollution, and in malaria risks. Van Houten et al. (2017), Shretta et al. (2016), and Trapero-Bertran et al. (2013) are some systematic reviews of this literature.10 First, we consider a catch-all category of averting expenditures and costs-ofillness calculations as the most common example of revealed preference applications. For example, if a household does not have access to adequate piped water, it must collect, pump, store, and treat water, and sometimes pay for bottled water. In the case of Kathmandu, Nepal, one of the first empirical applications of this averting expenditure methods shows that a typical household pays nearly US$3 per month to cope with unreliable water supply (Pattanayak et al., 2005).11 In such studies, since time is an important component of coping, researchers must deal with the common challenge in the valuation process of converting time costs into monetary figures.12 Another example is the purchase of face masks to avert ambient air pollution in China: a 100 point increase in the air quality index increases face mask consumption by over 50 percent (Zhang and Mu, 2017). Next, we discuss hedonic property valuation studies. Although this method is much more popular in the United States and the European Union, there is a growing body of LMIC applications. Most cases link housing value to air pollution exposure in large cities in LMICs (Gonzalez et al., 2013; Yusuf and Resosudarmo, 2009; Tan Soo, 2017). Hedonic methods have also been used to value access to piped water, best exemplified by an application to several cities in Central America (Nauges 10 To the best of our knowledge, there is not a systematic review of air quality valuation studies in LMICs. 11 Although not from the collection of health outcomes considered in this chapter, an example from ru-

ral Bangladesh shows that one way to estimate value water free of arsenic pollution is by examining households’ source switching behaviors, and estimate the time spent collecting water from a safe source (Madajewicz et al., 2007). This is a form of a travel cost model – in that values are revealed by how far households are willing to travel. 12 Following standard convention in the literature, Madajewicz et al. (2007) use a percentage of the rural wage rate to value time spent engaged in averting environmental risk. In this case, they value the time female household members spend collecting water at half the rural wage rate.

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Table 2 Valuation: selected studies on environmental risk reduction in LMICs Air pollution [Respiratory diseases]

Water and sanitation [Diarrhea]

Citation Gonzalez et al. (2013) Jeuland et al. (2015a) Donfouet et al. (2014) Zhang and Mu (2017) Yusuf and Resosudarmo (2009 ) Kremer et al. (2011) Whittington et al. (2002)b Madajewicz et al. (2007) Rosado et al. (2006) Yishay et al. (2017)

Environmental risk Particulate matter

Country Mexico India

Methods Hedonic pricing and instrumental variables Choice experiment

Sample size 4267 housing sales 2120 households

Results US$36.34–43.47/ unit US$10/stove

Biomass fuel emissions Ambient air pollution

Cameroon

Contingent valuation

Particulate matter

China

Averting expenditures

Lead, total hydro carbon, sulfur dioxide, carbon monoxide Microbial water contamination Unreliable water supply

Indonesia

Hedonic pricing

496 household heads 40584 demand days 470 households

US$0.42–0.67/ month US$38,356/ pollution daya US$28–85/unit

Kenya

Travel cost Contingent valuation Contingent valuation

184 springs, 1354 households 1500 households

US$2.95/year US$17.64/year US$12–14/month

Nepal

Arsenic contamination

Bangladesh Averting expenditures

1994 households

US$6.90/month

Microbial water contamination Inadequate sanitation

Brazil

789 households

US$11.00/month US$6.56/month US$20–50/latrine

Cambodia

Averting expenditures Contingent valuation BDM auction

1500 households

(continued on next page)

Table 2 (continued ) Vector population [Malaria]

a

Citation Cropper et al. (2004) Whittington et al. (2003) Haque et al. (2014) Hoffmann (2009)

Environmental risk Malaria-carrying vector population Malaria-carrying vector population Malaria-carrying vector population Malaria-carrying vector population

Country Ethiopia

Methods Cost of illness Contingent valuation Mozambique Cost of illness Contingent valuation Bangladesh Cost of illness Uganda

BDM auction with money and bed nets provided

Sample size 848 households 282 individuals 285731 malaria cases 131 households

Results US$7–24/episode >US$3/vaccine US$2.47–3.85/year US$14/vaccine US$0.51/treated case Average bids between US$6.02–7.22/net

This result is obtained by measuring the change in mask purchases associated with a 100 point increase in the Air Quality Index (AQI), from 105 to 205. The authors calculate the total cost of this increase to be US$80,247, of which they attribute US$38,356 to mask sales. b Pattanayak et al. (2005) examine the same data and estimate coping costs of unreliable water supply in Kathmandu to be about US$3 per month per household.

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and Strand, 2007). Endogeneity and other econometric concerns plague this literature. For example, Gonzalez et al. (2013) exploit seasonality and rainfall variation to account for omitted variables in their hedonic model of housing demand in several Mexican cities. Tan Soo (2017) represents a more contemporary application to value improvements in air pollution, using a structural sorting model for Indonesia. Turning to stated preference methodologies, these studies have been useful when governments are planning a new service (e.g., expansion of piped water grid) or good (e.g., a novel solar cooker) and have no historical data on a comparable service or good. An example of this comes from a large CV survey in Kathmandu in the context of a World Bank loan to the government of Nepal (Whittington et al., 2002). The authors find that the average household is willing to pay US$12–14 per month for a reliable, private, piped connection, which is substantially higher than the water bills paid by current respondents and suggests latent demand for improved services. Unfortunately, the CV scenario may not be particularly relevant for capturing the many aspects of the improved water services in tandem – convenience, reliability, and perceived quality, among others. Choice experiments address these shortcomings of the contingent valuation approach (van der Kroon et al., 2014). Consider the case of household cooking with biomass fuels that generate indoor air pollution. How would households value a new improved cookstove that would reduce smoke emissions? Because improved cookstoves change more than just emissions, a choice experiment is better situated to examine stated tradeoffs between smoke emissions, cooking capacity, firewood needs for cooking, and the stove price. Jeuland et al. (2015a) provide an application from the Indian Himalayas in which they show that, while households value cookstoves that would reduce health harming smoke emissions, there is a strong status quo bias – many households prefer their traditional cookstoves. Furthermore, because of the design and sample size, the paper is able to examine and identify substantial heterogeneity among this seemingly homogeneous rural Himalayan population; that is, the standard deviations of coefficients specific to cookstove attributes are also highly statistically significant. Empirically, there are differences in estimates of WTP for environmental risk reductions from the revealed and stated preference methods, partly because of differences in household perceptions (Orgill-Meyer et al., 2018). Thus, there is a small literature that compare and or combine stated and revealed preference methods. A few examples include comparisons of contingent valuation and coping costs for improved water reliability in Kathmandu, Nepal (Pattanayak et al., 2005) and contingent valuation and cost of illness calculations for malaria vaccines in Ethiopia (Cropper et al., 2004) and Mozambique (Whittington et al., 2003). While in most cases the revealed preference measures are lower bound of the economic values estimated from stated preference methods, this is not always true (e.g., Cropper et al., 2004; Orgill-Meyer et al., 2018). There are four main takeaways from the valuation literature. First, while there are noteworthy exceptions – hedonic models of air pollution, averting expenditure calculations – valuation studies of new technologies rely on stated preference methods.

3 What We Know About Environmental Health in LMICs

Second, across a broad swath of this literature, valuations for environmental risk reduction are low, which may seem surprising given the mortality and morbidity threats from environmental risk. This could be because households do not understand the true environmental risks to their health or that scientists overestimate such exposures or cannot appreciate all the tradeoffs households confront. It could also simply reflect low ability to pay and/or missing markets (e.g., for credit and insurance such that households cannot borrow or buy insurance). Third, it is more common than before to directly compare stated and revealed preference values within the same sample. Overall, these comparisons help us more fully and carefully characterize the different ways in which households think about environmental risk reductions. Fourth, there is considerable heterogeneity in the estimated values. Systematic reviews and meta-analysis can help identify study features that explain the variation – location, study time frame, socio-demographics, wealth, technology, etc. For example, a recent meta-analysis of stated preference for piped water finds that willingness to pay varies from US$3–US$30 per month, which is explained partly by differences in the scope of water infrastructure, household income, and the baseline water access (Van Houtven et al., 2017). In short, context matters.

3.2 ADOPTING ENVIRONMENTAL RISK REDUCING TECHNOLOGIES As the household production model indicates (Section 2.1), a number of factors influence the decision to adopt environmental health technologies: time and money, prices, information, and preferences, among others. Thus, the empirical literature has sought to identify which mechanisms are most effective in motivating and sustaining behavioral change and whether these mechanisms are consistent across environmental health domains and geographical regions. Table 3 provides a selective synthesis of the empirical adoption literature. These studies use either experimental, quasiexperimental or observational methods to estimate determinants of adoption. There are some examples of systematic reviews of the adoption literature on water and sanitation (Evans et al., 2014; Garn et al., 2017), improved cookstoves (Lewis and Pattanayak, 2012), and bed nets among pregnant women (Singh et al., 2013). In the remainder of this subsection we discuss the influence of: (i) price/income, (ii) information, (iii) social pressures, and (iv) gender. Economists have strong priors about income and prices: households that are richer and/or face lower prices are more likely to demand and therefore invest in environmental health technologies (Pattanayak and Pfaff, 2009). This has a basis in the empirical literature (Spears, 2014; Yishay et al., 2017). For example, an analysis of fuel use patterns in India shows that income and, relatedly, price influence households’ decisions to invest in and use cleaner fuel sources (Farsi et al., 2007). In general, many studies that show that adoption increases when prices are lowered through subsidies (Pattanayak et al., 2016), but relatively fewer test how exogenous changes in income induce adoption of environmental health technologies. Income alone, however, does not provide a comprehensive understanding of the role of financial constraints in LMICs because of incomplete capital markets. For example,

167

Table 3 Adoption: selected studies on household investment in environmental health technologies in LMICs Air pollution [Respiratory diseases]

Water and sanitation [Diarrhea]

Citation Miller and Mobarak (2015) Farsi et al. (2007)

EHT Improved cookstoves

Jagger and Jumbe (2016) Bensch et al. (2015) Edwards and Langpop (2005) Ashraf et al. (2010)

Improved cookstoves Improved cookstoves Fuel type and stove ownership Home water purification

Zambia

Brown et al. (2017)

Drinking water treatment

Cambodia

Pattanayak et al. (2009a)

Latrines

India

Jalan and Somanathan (2008) Shakya et al. (2015)

Drinking water treatment

India

Latrines

India

Fuel type

Country Bangladesh

Methods Randomized marketing intervention India Observational [Ordered probit] Malawi Discrete choice experiment Burkina Faso Propensity score matching Guatemala Observational [FIML]

Sample size 2280 households

Results Social network effects decrease cookstoves demand by 21 percenta

46918 households

10% income increase associated with 5% increase in LPG use

383 households 1473 households 7276 households

80% of households still using improved cookstoves six months after provision Extremely low (10%) cookstove adoption Access to credit and stove subsidies increase adoption

Randomized marketing intervention Randomized information intervention

1260 households

Randomized latrine promotion intervention Randomized information intervention Observational [network analysis]

1086 households

100 Kw price increase decreases demand by 7 percentage points but increases use by 4 percentage points Informed households were 11 percentage points more likely to treat water, but only in less developed areasb Latrine ownership increased from 6% to 32% in treatment villages

1006 households

11% increase in treatment of drinking water

16579 individuals/6911 households

Individuals whose social contacts have latrines are more likely to own latrines

912 households

(continued on next page)

Table 3 (continued ) Vector population [Malaria]

a

Citation Dupas (2014)

EHT Insecticidetreated bed nets

Country Kenya

Tarozzi et al. (2014)

Insecticidetreated bed nets

India

Atmadja et al. (2017)

Bed nets

India

Brown et al. (2016)c

Indoor residual spraying

Uganda

Methods Randomized bed net subsidy with follow-up analysis Randomized microfinance intervention

Sample size 1120 households

Results 98% initial demand for free bed nets and 30% demand for bed nets priced at US$1.50

1844 households

Observational [multivariate regression] Discrete choice experiment

9750 households

96% “purchase” rate for households receiving free bed nets and 52% purchase rate for households with access to MF loans Ownership correlated with discount rates, wealth, education, proximity

612 households

80% of households stated willingness to participate in IRS

Additional social networks impact analysis, also demonstrating negative learning, appears in the study. Heterogeneity analysis is key for interpreting the results of this analysis; see study for complete details. c See Brown and Kramer (2018) for a structural model of indoor residual spraying participation heterogeneity in Uganda, parameterized using this discrete choice experiment. b

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Tarozzi et al. (2014) find that households randomly assigned to receive a financing offer (e.g., easy credit) to purchase a bed net were much more likely to purchase compared to control households that could not finance the bed nets. Second, a branch of the empirical literature focuses on knowledge and, especially, on information. Households with limited information may misallocate their resources because they do not know the full extent of the risk they face (Ashraf et al., 2013; Kremer et al., 2008). A series of water and sanitation studies find that giving households information on the microbial contamination of their drinking water elicits a strong response (Brown et al., 2017; Hamoudi et al., 2012; Jalan and Somanathan, 2008; Luoto et al., 2014; Lucas et al., 2011). There is more to the story than the average treatment effect. For example, Brown et al. (2017) find that households with lower baseline knowledge about their water quality and lower socioeconomic status were more swayed by the information intervention. Third, there are particular ways in which information may be more salient; learning, peer pressure, or some other form of social interaction matters (Adrianzén, 2009; Gertler et al., 2015). Consider the case of sanitation: household sanitation decisions are largely observable by the surrounding community because household decisions to defecate in the open or to build an exterior latrine is observable. Accordingly, it is reasonable to expect social factors such as learning, imitation, or peer pressure to play a larger role in household sanitation behavior. This logic underlies the Community Led Total Sanitation (CLTS) interventions, which rely on social influence to promote community-wide commitment to ending the practice of open defecation (Gertler et al., 2015; Guiteras et al., 2016; Luby et al., 2006; Pattanayak et al., 2009a). Even though empirical identification of the social effect is plagued by econometric challenges such as the reflection problem, early evidence suggests that latrine adoption is socially motivated (Dickinson and Pattanayak, 2009; Miller and Mobarak, 2015). Fourth, some economists have begun to open the black box of gender and environmental risk reductions, given the disproportionate impact of environmental exposures on women and on the children in their immediate care. Intrahousehold bargaining lies at the core of this conundrum because men typically control the finances whereas women (and children) stand to benefit most from both reductions in environmental exposures (air pollution, water contamination) and in coping costs of inadequate water and energy – traveling long distances daily to haul water and firewood. An experimental evaluation in Bangladesh considers the role of gender in a household’s decision to buy an improved cookstove (Miller and Mobarak, 2013). They confirm what we suspect; female household members exhibit higher demand for improved cookstove technology but lack the financial autonomy to act on this preference. There are three takeaways from the adoption literature. First, unsurprisingly, household characteristics impact adoption: income, price, and education are often cited as important determinants of adoption. The education mechanism likely operates through lowering the cost of knowledge acquisition but could also reflect the effect of higher incomes. Second, on the technology side, many studies show that households care about product characteristics: the smell and taste of clean water,

3 What We Know About Environmental Health in LMICs

the emissions and firewood requirements of improved stoves, the inconvenience of bed nets. Suppliers can respond to these product characteristics, but discussions of adoption overlook supply-side drivers like social marketing, strengthening access and maintenance options, and improving institutional capacity (Lewis and Pattanayak, 2012). Third, the current mix of studies tell us too little about what motivates and sustains adoption. Some of the most influential and impactful findings come from heterogeneity analysis based on age, gender, and socioeconomic status, among other baseline characteristics. We will return to this point in our discussion in Section 4.1.

3.3 EVALUATING ENVIRONMENTAL HEALTH IMPACTS Will adoption of technologies that allegedly reduce environmental risks deliver health impacts? The evidence is mixed. In this sub-section, we examine the literature that evaluates health impacts of environmental health technologies (e.g., bed nets, cookstoves, toilets) and related behaviors (e.g., use of these technologies, handwashing), paying close attention to the strength of econometric identification given the complicated relationship between technological adoption and health impact. Table 4 provides a flavor of this literature. Keiser et al. (2005), Wolf et al. (2014), and Thomas et al. (2015) provide examples of systematic reviews of the evaluation literature on environmental risks and malaria, diarrhea, and indoor air pollution. As the previous section on adoption suggests, the causal link between health and household technology adoption could be confounded by household self-selection into ‘treatment status’ (Heckman and Smith, 1995; Pattanayak and Pfaff, 2009). For example, households without ventilation and poor health may be more inclined to invest in improved cookstoves – generating impact estimates that are biased downward (Bruce et al., 2000; Dasgupta et al., 2006). Randomized control trials (RCTs) are increasingly used to deal with the issue of selection bias. Some examples include the impacts of improved cookstoves on respiratory illnesses in Senegal (Bensch and Peters, 2015), of household latrines on diarrhea in India (Dickinson et al., 2015), and of insecticide treated bed nets on malaria (Tarrozi et al., 2014). While RCTs offer some insights into short-term environmental health impacts, there is mixed evidence on impacts over time (Meyer et al., 2018). For example, a study on the sustainability of improved cookstove interventions finds little evidence that households continue using the new technology even a few years after it is provided (Hanna et al., 2016). The authors argue that preferences for food cooked on traditional stoves, lack of maintenance, and limited supply side fuel availability and maintenance knowledge contribute to the lack of anticipated health impacts. A similar story unfolds 11 years after an experimental campaign to promote latrines in Orissa, India (Meyer et al., 2018). Most research on the health impacts of environmental risk reductions does not use experimental methods because of political, ethical, and practical reasons. Further, because RCTs may be limited for studying long-term impacts given the many other factors that could change, some studies have used historical data to examine the long-term economic and health impacts of malaria eradication programs, for example. While the outcomes measured by these studies are not always explicitly health,

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Table 4 Evaluation: selected impact evaluation studies of environmental health technologies in LMICs

Air pollution [Respiratory diseases]

Water and sanitation [Diarrhea]

Citation

Exposure

Health outcome Health history and expenditure Respiratory symptoms and eye infections Infant mortality

Country

Methods

India

RCT of improved cookstoves RCT of improved cookstoves DID analysis of kerosene conversion policy DID analysis of privatization

Hanna et al. (2016)

Biomass fuels

Bensch and Peters (2015)

Biomass fuels

Imelda (2018)

Kerosene to LPG fuels

Galiani et al. (2005)

Water contamination

Child mortality

Argentina

Dickinson et al. (2015)

Inadequate sanitation

Diarrhea and nutritional status

India

Jalan and Ravallion (2003) GamperRabindran et al. (2010)

Water contamination

Diarrhea among children

India

Water contamination

Infant mortality

Brazil

Quantile treatment effects

3568 county years

Newman et al. (2002)

Water contamination

Under 5 mortality

Bolivia

DID of matched sample

2369 households

Senegal

Indonesia

Randomized latrine promotion intervention Propensity score matching

Sample size 7310 cooks, 14188 children 1977 individuals

Results

38,225 individuals

1 percentage point reduction in infant mortality rate

4732 municipality years 1086 households

5 percent decrease in child mortality after privatization of water systemb Children in treatment villages exhibit higher nutritional status; no effect on diarrhea

33216 households

Diarrhea rates 21% lower with private, pumped water; illness duration 29% shorter Reduced infant mortality by 1.25 deaths per 1000 live births at the 90th percentile; 0.55 deaths at the 10th percentile Significant reduction in death

No health impacta

7 percentage point reduction in respiratory and eye disease

(continued on next page)

Table 4 (continued )

Vector population [Malaria]

Citation

Exposure

Kleinschmidt et al. (2006)

Vector populations

Tarozzi et al. (2014) Lucas (2010)

West et al. (2014) a

Health outcome Malaria

Country

Methods

Equatorial Guinea

Vector populations Vector populations

Malaria incidence Educational attainmentc

India

Pre-post intervention analysis RCT of bed nets DID analysis of malaria eradication

Vector population

Plasmodium falciparum prevalence rate in children

Sri Lanka/ Paraguay

Tanzania

RCT of bed nets and indoor residual spraying

Sample size 4881 children

Results

1844 households 5822 individuals/2931 individuals

No significant health benefits found 10 percentage point reduction in malaria increases educational attainment by 0.1 years PFR lower when households use bed nets and indoor residual spraying

1834 households

Infection prevalence decreased from 46% to 31%

Analyses were run for different health outcomes and expenditures separately for primary cooks and children. No consistent, statistically significant health effects were measured across any specification. b Heterogeneity analysis using matching estimators reveal interesting patterns. Please see paper for complete results. c While educational attainment is not a direction health outcome, many malaria-reducing studies consider long-term economic productivity consequences. Thus, we consider this study relevant to the discussion of evaluation of environmental health technologies. See Bleakley (2010) and Cutler et al. (2010) for analysis of similar outcomes.

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they are closely tied to long-term productivity and human capital, and the mechanism is usually health related. Such studies have found that interventions can increase educational attainment (Cutler et al., 2010; Lucas, 2010) and raise incomes (Bleakley, 2010; Cutler et al., 2010). More specifically, efforts to eradicate malaria in multiple countries (Paraguay, Sri Lanka) shows that a ten percentage point decrease in malaria incidence corresponds to an increase of 0.1 years of educational attainment as well as a two percentage point increase in the probability of being literate (Lucas, 2010). These retrospective studies have typically combined quasi-experimental methods (e.g., the roll-out of malaria eradication programs) and/or panel data (e.g., differencein-difference strategies). More generally, economists rely on natural experiments, weather patterns, and policy decisions, employing difference-in-difference, instrumental variables, and, recently, sorting models to identify causal effects, exemplified by studies of the health impacts of ambient air pollution (Frankenberg et al., 2005; Jayachandran, 2009; Rangel and Vogl, 2016; Tan Soo, 2017). A popular approach here is to find the variation in outdoor air pollution related to patterns in implementation of regulations and policies (Davis, 2008; Gallego et al., 2013; Greenstone and Hanna, 2014; Rich et al., 2015). Attempts to evaluate the health impacts of environmental risk reductions (through careful identification, experimental or otherwise) have largely been sobering: the impacts are small and or insignificant. What explains this lack of impact? First, these analyses remain unable to provide a comprehensive understanding of the link between environmental risks and health, particularly because many behavioral components of adoption are not well controlled by experimental designs or in the quasiexperiments that mimic them. For example, while households may be inclined to try new technologies such as improved cookstoves, particularly if free or highly subsidized, there is little evidence that technology is used exclusively: that is, households stack, but do not switch.13 Second, households often face a variety of environmental risks in tandem; thus, addressing one type of exposure with one environmental health technology may not result in the anticipated health outcomes (Jeuland et al., 2015b; Kremer et al., 2011). Finally, measurement challenges abound: if economists do not genuinely collaborate with epidemiologists or learn about health biomarkers, they rely on self-reported health outcomes. Such outcomes are riddled with recall bias and various forms of measurement errors. Some responses have been to use nutritional outcomes such as age adjusted z-scores for height, weight, mid-upper-arm circumference (Dickinson et al., 2015) and infant mortality (Gamper-Rabindran et al., 2010).14 Other cases have deployed better methods such as rapid diagnosis tests to measure malaria (Tarozzi et al., 2014). 13 For example, households do not necessarily desist from using traditional stoves; rather, they practice

stove stacking – using the improved stove in addition to existing cooking technology, detracting from the potential exposure reductions and health improvements offered by improved technology. 14 While objective indicators could be more reliable than self-reports, some measured outcomes, like infant mortality, may not align as closely with expected health outcomes of environmental exposure as do some self-reported health outcomes, such as diarrhea episodes among children.

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There are three main takeaways from the literature on evaluation of environmental health outcomes. First, we see causal identification is prioritized, with a heavy reliance on randomized experiments. While randomization strengthens internal validity, questions remain regarding the generalizability of these studies (Peters et al., 2018). Quasi-experimental methods mimic RCTs too closely, in the sense that they say little about who is using the technology and why (e.g., the first stage of the instrumental variables regression), which provides little insight into the mechanisms by which these interventions induce change that could be sustained (or not). Second, while some environmental health technologies have produced measurable health impacts, most studies report insignificant or no health effects. There are several potential explanations for these results previewed in the paragraph above – behavioral and epidemiological externalities, thresholds in environmental exposure, incomplete and/or unsustained switching. Practical constraints such as research budgets make it difficult to implement long-term experiments that allow for evaluation of impact sustainability. Third, economists have studied a range of direct and indirect health outcomes: (i) self-reports, (ii) objective health incomes, (iii) economic productivity, and (iv) education. While health and other aspects of human capital are clearly connected, the pathway from environmental risks to education could be confounded by many factors. This broader view of environmental exposure is salient for policy design and implementation because it would be risky to sell these technologies on the promise of immediate health effects. Instead, if we view the broader social benefits of environmental health technologies such as time savings, safety, and prestige – we would have a stronger case for their social value.

4 PATH FORWARD This chapter has sought to provide an overview of environmental health in LMICs from an economic perspective. Accordingly, we have discussed the infectious and non-communicable diseases most burdensome from an environmental perspective, outlined a household production model of environmental health technology adoption, and highlighted key insights from the valuation, adoption, and evaluation literatures to characterize what is known about behavioral response to environmental risk. Still, much remains to be sorted topically and methodologically: our review leads us to argue that four areas warrant more careful and concerted attention from economists. Three relate to research topics and domains – multiple risks, political economy, and climate change-related environmental hazards, and one relates to practical methods.

4.1 MULTIPLE RISKS For reasons that are beyond the scope of this chapter, almost all the research summarized in Section 3 focuses on a single environmental health risk; in reality, the exposures are multiple and interacting (Smith and Ezzatti, 2005; Myers et al., 2013). For example, many families exposed to indoor air pollution often are also exposed

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to waterborne microbial risks and to water-related anopheline risks (e.g., standing water and mosquito larvae). Even when scholars have considered multiple outcomes like diarrhea, malaria, and ARI as dependent variables in their analysis (e.g., Bauch et al., 2015), the research rarely looks at disease interactions and joint risk exposures. Perhaps the best case of multiple risks are the nutrition–infection dynamics, which reflect a certain perverse circularity and presage the challenges to easy policy fixes (Currie and Vogl, 2013; Scrimshaw, 2003). On one hand, infections worsen nutritional status and children’s growth because of appetite loss, intestinal absorption, metabolic changes, and excretion of specific nutrients, which leads to poor synthesis and tissue growth and is directly proportional to infection severity. On the other hand, malnutrition makes infections in children worse and more frequent, with risk of death from infections increasing exponentially with decreasing nutritional status. The baseline human capital parameter (h) in the health production model (Section 2) reflects these interactions of multiple risks in general, and the baseline nutrition and infection link in particular. Tests of this logic, however, are rare. One exception is a study that relies on a rich Philippine panel data set to show that while diarrheal and ARI infections clearly impact a nutritional outcome like weight gain, there is no evidence that malnutrition impacts infection probabilities (CEBU Team, 1992). An especially poignant, but in some ways narrower, case of multiple risks are the joint impacts of indoor and outdoor pollution in LMICs. While there is a growing literature on the health impacts of ambient/outdoor air pollution (e.g., Greenstone and Hanna, 2014), none of this literature examines how indoor air pollution modifies this relationship. This can be a serious oversight if household responses to the twin exposures (rather than single exposures) are meaningful because, a priori, it is impossible to know if households will substitute averting behaviors such as switching to cleaner stoves (to reduce IAP exposures) for more substantive evasive actions such as moving residence to reduce their exposure to ambient pollution. Alternatively, households may view these exposures as complementary. Why bother averting one risk if the exposure from the other source is high? Relating back to the model in Section 2, while there are now two non-independent risk probabilities, we do not know if these two risks are additive or multiplicative (Smith et al., 2006). Pakhtigian et al. (2018) use a household panel data set from Indonesia on child respiratory outcomes spanning two decades and find some evidence of complementarity between ambient and indoor air pollution. A further extension of this logic considers substitution and complementarities across disparate environmental risks – for example, air and water pollution – and the related averting behaviors. Shannon et al. (2018) implement a unique contingent valuation design to consider whether households are willing to invest in cookstoves and water purification in the presence of multiple health risks. Results indicate that conditional on having already mitigated some of the health risks related to air pollution (water contamination), households are more (less) willing to make additional

4 Path Forward

health investments that mitigate risks related to water contamination (air pollution) in sample of rural Indian households from Rajasthan.15

4.2 SUPPLY AND POLITICAL ECONOMY Naturally, the bulk of research to-date focuses on the ultimate beneficiary – households and their demand for reductions in environmental health risks. As we describe next, household preferences and, more importantly, the constraints they face, are set by a myriad combination of higher level agents or suppliers such as nongovernmental organizations (NGOs), community councils, markets, donors, and governments (politicians and bureaucrats). The actions of these suppliers primarily influence the marginal cost of risk reduction to the household, and, therefore, the nature and amount of averting activity. Returning to Fig. 2, households in Haiti face a completely different choice set compared to households in Norway. The household production framework from Section 2 can be modified to consider the supply side of reductions in environmental health risks. Let γ (a) represent household net benefits, still conditional on its choice of averting (a), but now also dependent on the actions taken by suppliers (ζ ). These actions affect the marginal costs (MC). If we assume that suppliers’ actions – say subsidies from donors or better matching of technologies to preferences of consumers – decrease the price of materials, p, knowledge, r, and/or time, t , then we can sign the “supplier effect” as positive (Usmani et al., 2018): ∂2γ

− da ∂a∂ζ =− 2 =− ∂ γ dζ ∂a 2

∂MC(a,ζ ) ∂ζ ∂2π ∂a 2

>0

(7)

This suggests that households will increase averting behaviors because of actions taken by suppliers. While cost changes undoubtedly factor into the equilibrium, in some cases suppliers can and do influence elements of the marginal benefits, too. Below we discuss their motivations, drawing from three strands of literature – new public management (Besley and Ghatak, 2007), new political economy (Besley, 2007), and new institutional economics (Ostrom, 2005). The literature to date, limited and patchy as it is, has not linked the demand and the supply side. That is, there is no theoretical or empirical modeling of the equilibrium conditions reflecting the response of any suppliers to community or household demand. Non-governmental Organizations (NGOs) can improve supply through a number of channels. First, they can effectively reduce costs by avoiding political and bureaucratic frictions. Further, if NGOs are better able to hold local leaders accountable, they can reduce supply costs by reducing corruption. Second, because of their familiarity with local conditions, grassroots NGOs in particular can better match services 15 In an evaluation of latrine adoption on diarrhea episodes, Duflo et al. (2015) find small decreases in

malaria incidence in communities receiving water and sanitation interventions, suggesting that safe water and sanitation practices may have far-reaching health benefits.

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and products to local preferences, increasing households’ marginal benefits of averting behaviors or technologies. In addition, households may have more faith in the efficacy of services offered by a trustworthy provider. Not all NGOs are alike, and some may impose costs if they are rent-seeking or focused solely on organizational existence, as opposed to being mission-driven (Towsend et al., 2004). Additionally, as non-democratic organizations, they may suffer from elite capture or mission misalignment. NGOs whose organizational longevity factors into their objective function can also become trapped by external donor demands, increasing costs and undermining their ability to match services to community preferences (Troncoso et al., 2011). One of the first empirical tests of these questions is from Uttarakhand, India, where Usmani et al. (2018) find that an NGOs modifies a cookstove intervention, increasing the purchase of improved stoves by as much as 30 percent in communities in which it has historically operated. This “NGO-effect” is especially important for risk averse households. Local community councils can improve supply and influence household choices in ways similar to grassroots NGOs. That is, following the literature on fiscal federalism and devolution, community leaders are more likely to match services and products to local needs and thereby shift demand (Mansuri and Rao, 2004). Second, decentralized delivery can also lower the costs of acquiring technologies and services for households. This is especially true if communities are small, relatively homogeneous, and have a history of functional governance. In contrast, if there are substantive scale economies in supply, a community or small clusters of communities may face prohibitively high costs of provision. Their costs would also be high if the intervention is highly complex and the community lacks technical capacity. There is some empirical evidence of the community-demand-driven development model (Khwaja, 2004; deWilde et al., 2008). Consider the case of such a model for water and sanitation. Using a three year panel data set of 10,000 households from 250 villages in Maharashtra, India and an estimator that combines matching and differences-indifferences, Pattanayak et al. (2010) show that coping costs of water and sanitation are lower in these community managed villages, compared to control villages. Firms (producers, distributors, retailers) are the main suppliers and, therefore, likely the chief sources of constraints on household choice. In principle, firms respond to competition, which forces them to improve the quality and/or lower the costs of environmental health technologies and services.16 One mechanism by which firms improve quality is by offering higher salaries (compared to public servants) to recruit more competent staff. Higher salaries, however, may not attract more intrinsically motivated individuals with social service delivery skills (Ashraf et al., 2014). Further, firms will reliably improve quality while lowering costs only if households are able to judge quality because they have full information. There are two main 16 Empirically, privatization has been shown to improve service delivery in phone, mail, electricity, and

municipal service sectors (Besley and Ghatak, 2007). In the environmental health domain, the only examples are in the context of water, sanitation, and electricity, where private sector participation led to mixed success (Gassner et al., 2008).

4 Path Forward

arguments against exclusively depending on the private sector to reduce environmental risks. First, firms can ignore the poorest rural households as willingness to pay is often low and provision costs are often high. Especially in LMICs, private firms face high costs of doing business due to regulatory hold-ups, missing credit markets, corruption, and weak laws. Second, because infection and prevention externalities play a big role in environmental health risk reductions and many private goods are quasi-public in nature (e.g., a private stove reduces socially harmful emissions), firms cannot account for key externalities and will not appropriately price their products and services. Bureaucrats are key cogs in the effectiveness of how NGOs, communities, and firms deliver environmental health services because they can ease or add to the barriers described above. Creating more performance-based bureaucracies – competitive salaries, internal promotion, clear procedures for hiring and firing, and meritocratic recruitment through competitive exams – can attract qualified bureaucrats (Rauch and Evans, 2000). Critically, if professional bureaucrats are recruited and promoted on the basis of merit and not tied to elections and political cycles, their tenure and autonomy can allow them to invest in infrastructure with long-term payoffs (e.g., water, sewage, electricity, roads), as shown during the Progressive Era in the United States (Rauch, 1995). Absent this, bureaucratic incompetency and corruption can drive up costs to households of acquiring environmental technologies – e.g., giving bribes, jumping bureaucratic hurdles. The early empirical tests of these propositions are mixed (Nagin et al., 2002). More recently, field experiments show that recruiting career-oriented public health providers, as opposed to those more socially motivated, resulted in more home visits and improved health outcomes (Ashraf et al., 2018). Donors are some of the highest level, yet least studied, actors who often work directly with NGOs, local communities, private firms, and even bureaucrats. If donors behave according to the role of benevolent social planners, they effectively offer direct subsidies (monetary resources) or indirect subsidies (technical expertise – e.g., qualified consultants) in the delivery of environmental health technologies. Unfortunately, donors can also increase costs if transfers are too small and introduce numerous frictions (Birdsall, 2004). For example, donors sometimes require certain technologies or programs to be implemented, which may not match household preferences. In some cases, donors’ utility enters directly into the objective functions of local NGOs or community leaders, who then attempt to maximize their visibility (Troncoso et al., 2011). In such settings, donor support may reduce incentives for local capacity building and thereby increase long-term costs. In general, donors, especially foundations and multilateral development banks, often fail to invest in the regional and global goods that they are most well-positioned to provide (Birdsall, 2004). Politicians are perhaps the most studied agents in the relatively small literature on the supply side of environmental health technologies. In many LMICs, nationalor state-level governments are the main providers of environmental and health services. In an idealized world, politicians would maximize social welfare and there is no principal–agent problem; that is, they would be intrinsically motivated and

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be influenced by the utility of the constituents (principals). If so, politicians would seek to loosen income, time, and knowledge constraints. Politicians who share the preferences of or must answer to their constituents may be able to match service provision to preferences, mimicking communities and NGOs. Even if politicians are intrinsically motivated, however, provision costs could still be high in LMIC contexts because of low institutional capacity of the bureaucrats and poor infrastructure. However, many other factors may enter a politician’s objective function. If a politician acts to maximize her own personal utility, i.e., through graft or corruption, this may increase households’ marginal costs of acquiring environmental technologies. Or, if the politician favors one group, she could undermine socially optimal service provision; placing a higher utility weight on marginalized groups could improve their access to environmental health technologies, but elite capture would have the opposite effect. If politicians only care about re-election, the provision of environmental technologies depends on the representativeness of the electoral system, free media, and an informed electorate. There is some evidence that democracy (Wendland et al., 2014), an informed electorate (Acharya et al., 2008), and a more representative system via reservations for marginalized groups (Chattopadhyay and Duflo, 2004) can improve environmental service provision. All of this points to the central role of representation and accountability for all suppliers, be it at the ballot box, the marketplace or through other mechanisms (Besley and Ghatak, 2007).

4.3 ENVIRONMENTAL HAZARDS AND CLIMATE CHANGE Our final suggestion concerns non-communicable disease and injury risks that result from environmental exposure, including those induced by our changing climate. These events, along with the rise in non-communicable and often terminal diseases that result from long-term environmental exposure, threaten health and productivity in both the short- and long-terms. Natural disasters, for example, pose immediate morbidity, mortality, and productivity threats as well as lasting impacts on physical and mental health, human capital, and economic development. In the absence of well-functioning alerts and warnings, households may have little time to prepare for an impending disaster, increasing the mental and physical costs of these events (Bohra-Misra et al., 2014). Further, some human activities actually intensify the damage of natural disasters: land conversion for agriculture may contribute to loss of storm-protective barriers (Das and Vincent, 2009), and climate change is increasing the frequency and intensity of natural disasters (Kousky, 2014). There are two important considerations for economics of valuation, adoption and impact related to coping with disaster risks: (i) non-linearities in the severity-outcome relationship and (ii) methods ill-suited to examine questions of valuation, adoption, and evaluation in this domain. Turning first to non-linearities, Pattanayak and Pfaff (2009) argue that the wide range in severity of environmental threats makes it unreasonable to expect a uniform effect of decreasing or increasing exposure severity across this range. Rather, impacts of shifting from high to extreme exposures are likely quite different than those occurring from a shift from low to medium exposure

4 Path Forward

– i.e., there is a non-convexity in the system (Dasgupta and Mäler, 2004). Accordingly, we must examine a variety of these regime shifts in exposure-response. While these non-linearities have been observed in the literature of infectious diseases discussed so far, Pattanayak and Pfaff (2009) argue that natural disasters create a special case because of (i) the increasing frequency of extreme events and/or (ii) permanent and significant behavioral changes (i.e., migratory responses). Turning next to the relevance, or lack thereof, of current methods, we argue that these disaster-related environmental risks are not well suited to common causal identification strategies. While quasi-experimental methods provide some evaluation tools, these circumstances are not conducive to randomized experiments or fieldbased data collection. Furthermore, due to the damages imposed by natural disasters not only to human health but also to infrastructure and general development, these settings create general equilibrium effects (Pattanayak et al., 2009b). Therefore, the effects measured by quasi-experimental methods do not necessarily represent marginal willingness to pay for environmental risk reduction (Kuminoff and Pope, 2014; Muehlenbachs et al., 2015). Without offering any judgments on the size or relevance of such effects, we simply note that general equilibrium effects are outside the scope of this chapter on a partial equilibrium framework for the valuation, adoption, and evaluation of environmental risk reductions.

4.4 BEYOND EXPERIMENTS AND AVERAGE TREATMENT EFFECTS Analytical precision in theoretical models and methodological rigor (e.g., clean identification of key parameters) have been the forte of economics. In LMICs, however, the constraints and objectives may or may not match what are stated in textbook models of constrained optimization or the empirical methods used to characterize the resulting behaviors. Thus, economists could, for example, conduct iterative field research as suggested by Udry (2003), to update their theories (of objectives and constraints) and then carefully test hypotheses with empirical methods that balance accuracy (that comes from rigor) with feasibility and policy value. For example, we should be more circumspect about proposing simple theories about the influence of information or subsidies on demand and testing these hypotheses with RCTs.17 More generally, to realize the full potential of economics of environmental health in LMICS, economists must carefully choose which theories to test and how to field test them. Based on our review of the research and extensive fieldwork and policy engagement in LMICs, we offer five considerations for applied environmental health economics. 17 One example of how to implement Udry’s (2003) recommendation is the experimental study of household air pollution and demand for improved cookstoves in the Indian Himalayas. Early stages of the study identified household preferences for improved cookstove attributes (Jeuland et al., 2015a) and NGO capability to service household energy needs (Usmani et al., 2018). Subsequent stages then used a randomized control trial to promote the improved cookstoves for which households had expressed demand, which was subsequently delivered through NGOs they trusted (Pattanayak et al., 2016).

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First, because the causal chain of environment and health is neither short nor simple, external validity of impact estimates is key to assessing the sustainability and scalability of interventions (Pattanayak and Pfaff, 2009). Reflecting a larger trend in public health towards translation research (focus on dissemination, diffusion, translation), such translation depends on scholars identifying practical impediments to widespread adoption and institutionalization of an intervention. Experiments or RCTs, which are currently in vogue, usually stop short of such questions, at least as currently implemented. Second, because the environmental or the socio-economic context underlying environmental health risks is rarely uniform, heterogeneity underlies all of the nonmarket valuations, adoption and impact evaluations studies (Pattanayak et al., 2017). Average impacts or values are rarely a useful stopping point. Instead, because there are winners and losers, we must track impacts for sub-populations, to help understand the political economy. While winning and losing is typically correlated with socio-economic status, it can also be associated with other factors, including gender and age. For example, women and children who generally bear the greater burdens of environmental health risks, also have the least political agency. We can also track impacts by ecology and space; that is, downstream (or downwind) areas can bear water and air pollution costs of economic development in upstream (or upwind) areas. Third, economists will need to increase interdisciplinary scholarship that seeks to work through the long chains from public/private interventions, to environmental risk reductions, and then to human health and wellbeing. Too often, studies focus only on a segment of the chain and thus the evidence is unusable for implementation. For example, studies that carefully appraise opportunity costs and net economic benefits of alternative policies only rarely carefully quantify health impacts. On the other hand, the few studies that have quantified the impact of policies on health through the mechanism of reducing environmental health risks have not considered the full costs and benefits of those policies. This suggests a return to practical methods for computing costs and benefits such as “benefits transfer” (Smith and Pattanayak, 2002). More generally, it calls for a closer integration of the two sub-fields of ‘program impact evaluations’ and ‘non-market valuation’, which have evolved independently without any cross-fertilization (Ferraro et al., 2011). Fourth, this re-orientation of scholarship (e.g., towards external validity and comprehensive cost benefit analysis) might be more feasible if the economics research is mainstreamed into decision making by national governments, international corporations, municipal governments, donors, NGOs, and others. For there to be genuine collaboration between economists, on one hand, and policymakers and practitioners on the other in the co-creation of knowledge, environmental health economists would be well served by applying more of a ‘practice-based-evidence’ lens in research design. That is, scholars could conduct more studies of practices on the ground, instead of conducting highly controlled studies and insisting that practices should now be ‘evidence based’. Research collaborations with the community-of-practice could go a long way to theoretically and empirically link household demand to agency supply, which are two strands of scholarship that are currently progressing in an inexplicably

4 Path Forward

disjointed fashion. For example, it could allow formal political economy modeling of how choices by politicians and firms (or donors and NGOs for that matter) to reduce environmental risks depend on households’ strategic decisions to try to influence the policy choice through the ballot box or through the marketplace. Such modeling would need to consider how these household decisions in turn depend on the policy effectiveness for reducing diseases and households valuation of such disease reduction, all implying that the equilibrium is co-determined. Finally, it is worth reconsidering how this research is produced and who produces it. Given the preponderance of environmental health burdens in LMICs and the heightened awareness of these burdens among local in-country researchers, we must expend greater efforts at building and enhancing the capacity of environmental economics in the global South (Mukhopadhyay et al., 2014; Sterner et al., 2014).18 This aspiration, along with others discussed above, will have profound implications for the practice of environmental health economics.

4.5 CLOSING THOUGHTS The burden of disease imposed by environmental conditions constitutes a crisis of planetary health proportions (Whitmee et al., 2015), especially for children, pregnant mothers, and other physiologically vulnerable populations. The health burden is not equitably distributed across geographies; rather, low and middle income countries face higher mortality and morbidity costs of this crisis. While there is some careful research by climate scientists, epidemiologists, engineers, and others on these issues, economists remain relatively underrepresented and, therefore, do not play a large role in policy design. We have shown that economics can be very useful for policy planning and program implementation, especially in three ways: (i) to justify (how large are the externalities and inequities?), (ii) to evaluate (how large are the impacts of policies? do the benefits exceed the costs?), and (iii) to finance (who can and who should pay for righting the wrongs?). Specifically, we contend that the household production framework – which puts the beneficiary and households front and center – provides a helpful conceptual tool to understand when and how households will expend resources to avert environmental health risks (Smith, 1991). Without repeating the details summarized in Section 3, economists have made progress in three aspects related to environmental health risks: (i) the valuation of such risk reductions, (ii) the adoption of risk reducing behaviors and technologies, and (iii) the evaluation of the health impacts of these reductions. Economists have made less progress in linking the literatures on valuation, adoption and impacts with each other – a fruitful future pathway for research. In addition, we must tie the demand side research on household WTP and health impacts

18 We could achieve this by creation of a center-of-excellence or networks-of-scholars that support (i)

knowledge co-creation with users, (ii) trans-disciplinary research and training of practitioners and users, and (iii) science-based communications, including with local communities.

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of environmental risks reductions to the decision calculus of the suppliers – NGOs, politicians, donors, firms, and others. Time and again, engineering and epidemiological interventions have failed to reduce environmental health risks because their recommended strategies either underestimate or simply overlook human behavioral responses. Unlike lab specimens, humans respond to their changing environmental health risks, sometimes in ways that appear at cross purposes with what the intervention seeks. This is true not just for families, but also for higher level agents such as NGOs, firms, bureaucrats, and politicians. The non-economists working in this space would do well to incorporate conceptual insights from economists regarding the roles of choice, of incentives, and of institutional design as well as the statistical rigor economists use in their examination of supply of and demand for environmental risk reductions. Economists, however, must also make themselves more relevant by clearly and constructively communicating insights regarding household valuation and program impacts of environmental health technologies to the practitioners and policy makers who are dealing with poverty, health, and the environment from within their sectors. Economists could also work harder to adapt their toolkit by listening to what other academics (e.g., epidemiologists, sociologists) and practitioners (e.g., those implementing public health and engineering approaches) have learnt about combating global environmental health burdens.

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The farmer’s climate change adaptation challenge in least developed countries✶ ∗ University

5

Maximilian Auffhammer∗,†,1 , Matthew E. Kahn‡,∗

of California, Berkeley, Berkeley, CA, United States of America † NBER, Cambridge, MA, United States of America ‡ Department of Economics, University of Southern California, Los Angeles, CA, United States of America 1 Corresponding author: e-mail address: [email protected]

CONTENTS 1 Introduction ...................................................................................... 2 Historical and Anticipated Climate Change ................................................. 3 Estimating the Impacts of Climate Change on LDC Agriculture .......................... 3.1 The Impact of Climate Change on a Farmer’s Investment Decisions ...... 3.2 Aggregation and General Equilibrium Effects ................................. 4 The Farmer Climate Adaptation Challenge .................................................. 4.1 Income Inequality and Climate Change ........................................ 4.2 LDC Farmer Climate Change Adaptation Opportunities...................... 4.3 Rural Data Collection Needs to Accelerate Adaptation Research Progress 4.4 Rural to Urban Migration as an Adaptation Strategy ......................... 4.5 The Dimensionality of the LDC Migrant’s Urban Choice Set ................ 5 General Equilibrium Effects Induced by Rapid Urbanization ............................. 5.1 Urban Political Economy Issues Related to Climate Change Adaptation .. 5.2 The Adaptation Benefits of LDC Urbanization................................. 5.3 The Productivity of LDC Urban Firms in a Hotter World ..................... 5.4 Will LDC Urban Growth Significantly Exacerbate the Global GHG Externality Challenge? ............................................................ 5.5 Research Needs.................................................................... 6 Conclusion........................................................................................ References............................................................................................

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✶ We thank the editors and several reviewers for useful comments. We thank Brian Casey and Nolan Jones for valuable research assistance. All errors are ours. Handbook of Environmental Economics, Volume 4, ISSN 1574-0099, https://doi.org/10.1016/bs.hesenv.2018.04.001 Copyright © 2018 Elsevier B.V. All rights reserved.

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1 INTRODUCTION The economics literature investigating climate change can be divided into two main themes. First, there is research on the mitigation challenge. This branch of the literature examines the costs of reducing greenhouse gas emissions from power generation, transportation and other key sectors. It also examines the economic incidence of reducing greenhouse gas emissions and studies the role of both the private and public sector in achieving this goal (Stern, 2008). Rising global greenhouse gas concentrations portend that most nations will face increasing risks caused by climate change. Climate adaptation research investigates the economic consequences that are likely to unfold as human and natural systems respond to changing environmental conditions due to the evolving aggregate stock of greenhouse gas emissions. Vulnerability to climate change varies by geography and by the economic circumstances of the exposed population. Coastal areas will face the challenge of sea level rise, and most parts of the earth will face more extreme heat as well as increased temperature and rainfall variation. The further down in the within and across country income distributions households are located, the lower is the ability to adapt to these challenges as adaptive capacity is closely linked to income. In the poorest nations, most people continue to work in agriculture. Given that these individuals work in maybe the most climate sensitive sector and have access to fewer costly adaptation strategies, it is essential to survey what we know and do not know about this vulnerable group’s capacity to cope with this new climate reality. In this survey, we present a micro economic approach for explaining adaptation choices and predicting challenges for poor farmers in the developing world. Building on the climate science that delivers predictions of shifts in the spatial distribution of temperature and rainfall patterns as well as natural disaster risks, we examine how farmers are expected to cope with the marginal increase in anticipated and in some cases unanticipated risks. Farmers have always faced climate variability. However, uncertain climate change adds to the volatility and persistence of this risk. Given the known unknowns about climate change, these risks are ambiguous in the sense that it is difficult to form precise expectations of future states of the world. The poor have the least financial resources to cope with changing circumstances. The poor have been shown to have lower levels of literacy and less accumulated human capital. Such individuals would face constraints and challenges even in the absence of climate change. Climate change represents an additional challenge that manifests itself through changing poor peoples’ production possibilities and the prices of goods they buy in markets as well as their access to natural resources such as water and animal feed that they need to achieve their daily goals. We begin our survey in the countryside of the past, where farmers enjoyed a stable climate. We outline the basic decision problem a farmer faces and then introduce a shift in local and global climate. Given that a significant share of people in poor nations are farmers, we study how the well-being of farmers is affected by a set of climate change induced risks. An expansive literature in development economics has

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characterized the source of the climate risk and variability that farmers face in earning a living – the income variability due to weather shocks (Rosenzweig and Binswanger, 1993; Townsend, 1994). A more recent literature focuses on extreme events (Hsiang, 2010). Climate change accentuates these risks in ambiguous ways. There is some uncertainty about how the spatial and temporal distribution of climate outcomes will evolve over the 21st century. The literature suggests that climate change will affect agricultural yields, health, energy production and consumption, water use, the spread of vector borne disease, labor productivity and incomes to name but a few. In this chapter, we study the causal chain, which begins with understanding the climate change induced risks to agriculture, with a special focus on the changing risks to subsistence farmers and their responses to this warm new world. This survey delves into the econometric research designs that researchers have used to study “climate economics” (Carleton and Hsiang, 2016). Since researchers are unable to run field experiments in this setting, we pay close attention to the role of natural experiments and other instrumental variables strategies for recovering causal effects. We relate the statistical estimates to the economic objects of interest that are required for judging the economic incidence of climate change. Urbanization represents one adaptation strategy. When young people move to the city, they often find employment in the service or manufacturing sector and this offers their rural family a source of diversified income. If enough rural residents move to the cities, this induces general equilibrium effects such that real per capita incomes increase in the countryside as rural wages rise and remittances received from the city increase. This sectoral integration between the rural and urban areas opens up potential topics for future research. Urbanization and rising educational attainment are strong complements. Given that urbanization raises household income, urbanites have better access to electricity, housing, higher quality medical care, and market goods to protect themselves from climate change related challenges. While urbanization offers private benefits to recent migrants, as they would not have urbanized otherwise, such mass urbanization imposes both pecuniary externalities and social costs as the influx of migrants raises rents, lowers wages, and increases local public bads such as local air and water pollution. In the developing world, local governments may have limited fiscal capacity and incentives to manage these costs of city size. Our survey explores these issues. To organize this survey, we will start with farmers in the country side who are exposed to a range of shifting shocks posed by climate change.

2 HISTORICAL AND ANTICIPATED CLIMATE CHANGE There is overwhelming evidence that the observed climate has already shifted over the past 50 years and that this change is largely due to anthropogenic activities (IPCC, 2013). The Intergovernmental Panel on Climate Change (IPCC) has produced five assessment reports, which synthesize the state of the published climate science (the

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sixth report is currently getting started). The IPCC both studies observed changes in climate, by analyzing the historical record of temperatures across the globe as far back as data exist. For the very long past this done by looking at paleoclimate reconstructions using proxies, such as tree rings. For the more recent record, measured temperatures are analyzed. The IPCC concludes that over the period 1880–2012, the average land sea temperature has increased by 0.85 [0.65–1.06] degrees Celsius (IPCC, 2013). The observed changes are not uniform across space and season (IPCC, 2013, figure SPM1). Brazil, parts of the US and large swaths of Central Asia have experienced measurably larger increases in surface temperatures. While detection of historical changes is challenging due to data availability and phenomena like the urban heat island effect, attempting to describe what will happen going forward over the next century or two is much more difficult. In order to simulate future climate, one employs so called General Circulation Models (GCMs), which are frequently referred to as “climate models” (for a survey of their use in economics, see Auffhammer et al., 2013). These models simulate the impact of different future emission paths greenhouse gases (e.g. CO2 , methane) and aerosols (e.g. dust and air pollution) on the climate system. Most economists have focused on the role of changes in temperature, but these detailed models produce predictions of precipitation, humidity, sea surface temperatures, and sea levels to name but a few variables. Output from these models is publicly available from the IPCC, yet in formats that are difficult to process. Also, the “official” climate model output available through the IPCC is not downscaled to a level of geography useful to economists. There are several efforts underway to make this information available in a usable format (e.g. https://www.impactlab.org; https://climexp.knmi.nl/). These products allow researchers to produce projections of changes in economically relevant variables (e.g. daily min/max temperatures, precipitation and relative humidity), which can then be used with estimated damage functions to project economic impacts of climate change. It is impossible to summarize the state of climate science, but the summary for policy makers of the 5th Assessment report of the IPCC is a great start (IPCC, 2013). The degree of climate change depends crucially on the future trajectory of greenhouse gas emissions. The two extremes considered by the IPCC characterize two possible worlds – RCP 2.6 and RCP 8.5. RCP stands for representative concentration pathway, leading to an increase in radiative forcing (2.6 or 8.5 Watts per m2 ). In language that economists can understand, these are two scenarios with very different underlying emissions pathways. The first (2.6) is consistent with radical reductions in emissions with negative annual emissions around mid-century. The second, RCP 8.5 is a somewhat aggressive business as usual emissions scenario consistent with continued rapid growth of emissions. The difference in impacts is drastic. The RCP 8.5 scenario results in a significantly hotter world, where major crop growing regions are expected to see increases in surface temperatures in the range of 4–6 degrees Celsius. If you consider wheat growing areas for example, Russia, North America, and Australia are all expected to see significant warming, which is projected to result in depressed wheat yields. If ma-

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jor producers are negatively affected, an inward shift of the supply curve will result in higher prices, which translates into welfare changes across the world. The elasticity of demand for wheat will play a key role in determining equilibrium price changes. This elasticity is a function of the availability of wheat substitutes. Higher prices are good if you are producer, but bad if you are a consumer. As food markets are closely linked across the globe, changes in one region might have significant ramifications for the welfare of market participants elsewhere. Predictions for rainfall patterns are more difficult. Overall there is more model agreement since the last IPCC assessment report, yet the predictions do not fully agree across models. In general the current best available science suggests that higher latitudes are in general expected to be wetter and hotter. In this review, we will focus on the challenges climate change poses to the Least Developed Countries. While the IPCC assessments provide global and regional assessments, they do not break up the world along the same dimensions an economist would. It is an empirical regularity, that countries with warmer climates have lower per capita GDP in the cross section (Dell et al., 2012, 2013). This cross-sectional relationship cannot be interpreted as causal, as there are many other determinants of per capita GDP leading to this observation. One question one may ask is whether climate change will “level this playing field” by warming rich countries more than poor countries. The first question we investigate is whether this cross sectional observation holds. Using an ensemble of climate models from the IPCC’s fourth assessment report, the World Bank provides projections of temperature and precipitation for a large suite of climate models by country out to the end of the century.1 We match these country level projections with per capita GDP in 2010 US$ and the share of value added from agriculture. Fig. 1 plots this cross-sectional relationship between the log of current per capita real GDP and future temperature. Specifically, we plot the median temperature prediction across climate models for a business as usual emissions scenario (IPCC A2) for the period 2080–2100 against 2010 per capita income in 2010 US$. The widely observed negative correlation between per capita income and future temperature holds. A regression between the two variables indicates that for each US$ 10,000 higher current day GDP the expected temperature is 1.41 degrees Celsius lower. This figure does not display the impacts of higher future temperatures on per capita GDP. This is the subject of a lively recent literature (see Burke et al., 2015; Dell et al., 2012, 2013). One obvious question is whether poor countries are more likely to experience greater increases in temperatures than rich countries? Using World Bank Data, the source for Fig. 1, we plot the median climate change prediction across climate models for the high emissions scenario A2 for the period 2080–2100 against 2010 per capita income in 2010 US$.

1 More recent country level projections based on CMIP5 for temperature and precipitation are not readily available at this point.

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FIGURE 1 Projected 2080–2100 temperature against per capita GDP.

What Fig. 2 shows is a cloud of data with a slight negative correlation between both precipitation (left) and temperature (right) changes. The correlation between temperature change and log income is not statistically significant. The correlation between precipitation change and income is statistically significant. This suggests that lower income countries are predicted to experience slightly more warming and higher precipitation than higher income countries. What is more important to note is that while some countries are predicted to be drier and some are predicted to be wetter, the predictions for the temperature are positive across the board. All countries will be hotter. The question is by how much. The IPCC observes that model agreement for the temperature predictions is significantly greater than model agreement for the precipitation predictions. But this simply means that we cannot say with much certainty which places will get wetter and which place will get drier, but there will be both. For temperature, the prediction is clear – it will get hotter for everyone – on average and in the extremes. This is an issue as least developed countries are thought to have a lower adaptive capacity and worsen observed disparities (Burke et al., 2015). This is further significant, as future population growth is expected to be greatest in sub-Saharan Africa, which includes most of the LDCs (see Tilman et al., 2011). This could amplify many of the projected economic effects of climate change.

2 Historical and Anticipated Climate Change

FIGURE 2 Projected changes in precipitation and temperature against per capita GDP.

We repeat the same exercise for share of value added from agriculture in Fig. 3. The pattern that emerges is not surprising as share of value added from agriculture and per capita GDP are highly negatively correlated (−0.84). The image displays a positive, and in the case of precipitation, statistically significant positive correlation between share of agriculture in GDP and the two climate outcomes. Every country will be warmer, with the average warming under the business as usual A2 scenario here predicted to be 4 degrees Celsius (7 degrees Fahrenheit). In the case of precipitation, the average change is very close to zero, with massive variation in terms of sign and magnitude. Overall, what this suggests is that while every nation is getting warmer, lower income countries on average will experience incrementally more warming – off an already warmer baseline. It is hence of key importance to empirically document the relationship between climate and agricultural outcomes flexibly across the temperature spectrum and by region/country. In the next section we will describe the different ways of estimating the relationships between different agricultural outcomes and climate.

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FIGURE 3 Projected changes in precipitation and temperature against agriculture share in GDP.

3 ESTIMATING THE IMPACTS OF CLIMATE CHANGE ON LDC AGRICULTURE Farmers facing more frequent and intense climate shocks will be more likely to suffer from bad harvests (Seo and Mendelsohn, 2007). Those who raise rural livestock will face increased risk of animal death and malnutrition (Seo and Mendelsohn, 2008). The combination of frequent drought and extreme heat in many LDCs raises the chance of large income losses and, in many places, consumption dropping below subsistence levels. A recent empirical literature seeks to quantify how farmers are affected by anticipated and unanticipated climate shocks. A challenge for the econometrician, but a potential benefit for the farmer, is that there are a number adaptation strategies to self-insure against climate risk. In order to estimate the effect of climate on farm outcomes, the researcher would ideally like to observe a large sample of otherwise identical farmers growing the same crop in randomly assigned climates over time to identify a crop specific “dose response” of climate outcomes on a given crop’s yields and net profits. In reality, farmers do not necessarily stay put or continue farming the same crop in a world with a changing climate – they adapt. The farmer might switch crops, opt out of farming altogether and move to another geographic rural or urban area. Measuring this adaptation response is of key importance when one is interested in

3 Estimating the Impacts of Climate Change on LDC Agriculture

quantifying the damages from climate change going forward. The magnitude of this adaptive response, especially for the rural poor, depends crucially on the formation of expectations, available information, and access to human, physical and financial capital. For any given hazard, spatial and temporal variation in the outcome and its drivers offers the opportunity for studying the consequences of changes in environmental conditions. An emerging literature has focused on estimating the impact of climate and weather on a variety of agricultural outcomes. Consider the following setting in a pre-climate change world. w t is a vector of weather realizations a farmer faces in a given season. This vector could be a measure of temperature, precipitation, humidity and wind speed over a short period of time, like a single season or year. In most empirical settings this measure of weather is recorded as the average value of each indicator over the entire season or more highly resolved measures such as the counts of days the e.g. daily average temperature falls in certain quantiles of the temperature distribution. The key is that the measure is defined over a relatively short period of time. In a pre-climate change world, these weather realizations are drawn from a distribution. Moments of this distribution generating weather are commonly referred to as “climate”. The most common use of the word “climate” in the literature is using 30-year averages of the weather observations. Hence a vector of climate variables co represents the long run average of a vector of weather indicators w t . Note that this weather indicator itself does not have to be an average annual temperature, but could be a seasonal temperature, growing degree day measures or any set of more complex indicators of weather. Assume that the farmer has an area of land at . She makes a decision each period as to crop choice, inputs and technology based on her expectations of the discounted stream of net profits from her activities. This is a difficult problem, which has received massive amounts of attention in the agricultural economics literature. In a world without climate change, this problem has been comprehensively studied (Mundlak, 1963, 2001). It is instructive to discuss the basic problem here as this farmer will face a changing climate and hence has a more complicated decision to make as climate is no longer a stationary variable. At the beginning of each season, she has to choose which use to put her land to. She could choose between planting one or multiple crops (farming), using the land for raising livestock, or not farm it and put it to an alternate use. She also has to choose which technology to use to grow the crop she chooses. Many crops like rice, require special investments in the fields themselves so they can be flooded. A farmer at the beginning of the season does not start from scratch. The fields were used to grow something in the previous season(s) and fields and technology were chosen over a long period of time to best match the chosen crop. Making changes to fields or investing in new technologies requires often significant fixed costs initially as well as variable costs to use them during the season (e.g. electricity to operate pumps). Hence changing from one use to another is costly and those costs can be non-trivial. So at time t , the farmer has to form expectations of future profits. Let’s at first simply think about this for a single season. The farmer has to form expec-

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tations about the price each crop will get at the end of the season. We can think of a simple process whereby the farmer forms price expectations based on the prices crops received in the prior year and possibly taking into account any announced government support prices. Expected revenues hence depend on expected input and output prices as well as expected output for each crop planted. Output is a function of the physical inputs used for production, such as land (at ), capital (kt ), and labor (lt ) as well as other inputs (it ) such as fertilizer, pesticides and irrigation water. Of course, in agriculture as in many other sectors, a major input which is beyond the farmer’s control is the weather (wt ) during the growing period. A production function can then be expressed as qt = f (at , kt , lt , it , wt ; θ o ). There are many types of production functions used in practice, such as Cobb– Douglas, CES, and Translog. It is of course important that the functional form used reflect properties of actual crop production, but we want to focus on the parametrization of the production function here instead of the choice of functional form. For a given stationary climate, farmers optimize their production technology accordingly, which here we denote as θ o . This technology, of course can have crop specific features (e.g. growing rice requires irrigation infrastructure in many settings). The expected end of season profits depend on end of season realized input costs (e.g. labor, capital, fertilizer, pesticides, irrigation) rt and if the farmer chooses to switch crops, possible adjustment costs for installing the new necessary capital or any other transaction costs it . A single period static profit function could be written down as: E(πt ) = E[p t · q t − rt − it ] In a stationary climate, there are year to year fluctuations in weather, which will affect physical output (e.g. a hot year may retard plant growth), input prices and use (e.g. increased demand for inputs may drive up their prices), and output prices (e.g. a hot year with low output combined with low aggregate storage levels may drive up output price). Weather shocks hence affect output directly through physical impacts on agricultural output and livestock productivity and survival rates and indirectly through input and output prices. Variation in weather hence leads to well documented variability in farm profits across seasons. Also, in much of the developing world not all output is sold by each farm. In many settings part or all of the crop the farmer grows is consumed by the farm household or traded for other goods and services within the local community. In this stationary climate setting there will be year to year fluctuations, which farmers will respond to by taking actions to maximize expected profits throughout season (e.g. apply additional irrigation water, fertilizer, pesticides, labor). Using well documented econometric techniques from the literature in agricultural economics, one can parameterize the profit or a production function, provided one has data with a sufficiently large degree of variation. The estimated coefficients from these regressions capture the short run responses in the outcomes of interest to fluctuations in input, output prices, and weather (Mundlak, 1963, 2001).

3 Estimating the Impacts of Climate Change on LDC Agriculture

3.1 THE IMPACT OF CLIMATE CHANGE ON A FARMER’S INVESTMENT DECISIONS The increase in anthropogenic emissions of greenhouse gases causes gradual changes in climate, such that the vector of climate co changes to c1 .2 This changing climate regime will permanently shift the weather distribution. This could be a mean shift only or a change in higher order moments of the weather distribution. If the farmer does not learn about the change in climate, but assumes that she still faces the old climate regime, she will use the old technology θ o to produce her output and produce a suboptimal level of output as the technology is not optimized for the new climate regime. If no one learns, each farmer will continue to produce using the wrong technology, which will lead to suboptimal output of the crop in the long run. This is sometimes called the “dumb farmer” assumption. This is not a tenable assumption in the long run. If the farmer learns that climate has shifted, (s)he will re-optimize and shift her production technology to θ 1 , if the benefits from doing so outweigh the costs of doing so. If they do not, the other explanation for observing farmers producing output with the “wrong” technology is the possibility that the costs of switching technology are greater than the benefits (e.g. higher yields) from doing so, so it may be perfectly rational for the farmer to produce with θ o – even in a new climate regime (Quiggin and Horowitz, 1999). If the benefits of the technology outweigh the costs, the farmer adopts the now optimal technology for the new climate regime. This could entail the installation of irrigation equipment, a switch in the type of crop planted etc. to maximize expected profits for the farmer. This change in technology from θ o to θ 1 is often referred to as adaptation to climate change. It is important to note that this change in technology can change both the output-climate relationship as well as the input-climate relationship (e.g. installation of irrigation infrastructure leads to increased use of irrigation water). This behavior is distinctly different from the within season response to weather shocks. For example, if a farmer experiences a relatively hot and dry year, she may apply less fertilizer that year as high concentrations of fertilizer can “burn” plants. However, if the farmer learns that the climate has changed and that the frequency of hot dry years will go up significantly in her area, she may respond by installing irrigation infrastructure. This has often been described as the difference between the weather sensitivity and the climate sensitivity of a sector. Any credible study that estimates the impact of climate change has to deal with the issue that long run (climate) and short run (weather) responses of sectors are different and it is the long run sensitivity that should be used in climate impacts estimation. One other important dimension of looking at farmers has to do with the fact the decision the farmer has to make in year t is not a static decision, but a dynamic one. In reality, the farmer has to form her expectations over the random variables (prices, 2 In practice climate change is gradual and will lead to slowly changing weather patterns over time. For simplicity, we stick to a discrete change in climate for this paper.

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availability of inputs, costs and effectiveness of new technologies and climate) and discount the stream of expected future profits to determine the optimal investment and crop choice decision at time t . This is a much more complex optimization problem, that has been modeled extensively in the agricultural economics and development economics literatures (Mundlak, 2001; Moschini and Hennessy, 2001; Nerlove and Bessler, 2001). A further, and maybe most challenging, complication is the fact that farmers are not necessarily risk neutral in the way they make decisions as we have implicitly assumed in our basic framework. In reality, most farmers are risk averse. Early work on these issues are Sandmo (1971) and Batra and Ullah (1974). The relevant literature in agricultural economics has been nicely synthesized in Moschini and Hennessy (2001). A final important aspect is how and when the farmer learns about the fact that the climate has changed. The easiest way to think about this is to imagine that there is a mean shift in climate. Pre climate change the farmer has adopted a technology that allows for some flexibility in production as firms might want to produce a range of output depending on input prices (Stigler, 1939). Once climate changes, farmers need to learn that this happens and then adopt a technology that allows for their new preferred range of possible output. There is a big literature on adoption of technology in agriculture in an uncertain world, which is summarized nicely in Sunding and Zilberman (2001). Some recent work has looked at the issue of learning in the context of monsoon onset in Indian agriculture (Kala, 2015), which provides a nice entry point into the learning literature. The simple model presented above is the assumed simplified data generating process underlying the data observed by the econometrician attempting to quantify the responsiveness of a farmer to changes in climate/weather. Over the past four decades a number of statistical approaches have emerged, each with their strengths and weaknesses. We summarize the main approaches here. Other detailed methodological reviews have been provided by Carleton and Hsiang (2016) and Dell et al. (2013). The literature on climate change impacts on agriculture was started by using agronomic process based models of crops. This literature builds and uses complex computer models of individual plants’ physiological processes. Modelers then use these “all knowing” models to simulate responses of different crops to climate stresses and simulate yield impacts (e.g. Rosenzweig and Parry, 1994; Rosenzweig et al., 2014). This literature, as it just focuses on plant behavior, largely ignores actions the farmer can take to offset adverse changes in the climate. Hence a social science literature has developed to incorporate the farmer and hence adaptation. In the empirical econometrics literature, there are four categories of estimation approaches used in climate impacts estimation. The overarching goal is to estimate the impact of long run climate change on different economic sectors. Here we focus on agriculture literature only, since this sector is acutely climate sensitive. While it only accounts for 2% of global GDP, it produces the majority of the calories humans and their pets consume. We are not interested in how farmers respond to year to year

3 Estimating the Impacts of Climate Change on LDC Agriculture

FIGURE 4 Crop choice and profits in the long and short run. Modified version of Fig. 1 in Mendelsohn et al. (1994).

weather fluctuations, as this does (in many settings) not account for adaptation. Below we describe the state of the literature for this application and point out explicitly which methods account for adaptation and which ones do not (also see Plantinga, 2017). The estimation methods found in the literature vary by whether they actually estimate the impact of climate or weather on the agricultural outcome. Second, they vary by the type of variation used to identify climate/weather effects. Some use cross sectional variation only, others use panel data relying on within location time series variation to identify effects, which has consequences for the degree of causal inference in the studies. The first class of models, which are by far the most widely applied in the literature in both the developed and developing country context, are referred to as Ricardian Models. Mendelsohn et al. (1994) exploit the fact that climate (the 30 year average of weather in a given location) varies across space – even in a stationary climate. Farmers in each location have hence optimized their local production technology/choice of crop according to the local climate. Fig. 4 illustrates their conceptual model’s key ideas. The insight here is that as climate shifts the temperature distribution towards higher temperatures, if you assume that technology stays constant (e.g. by estimating a single crop production function), one would drastically overestimate the impacts of climate change on the value of farming. For example, if a farmer who is growing crop 1 and currently producing at point B, faces a warmer climate and continues to farm crop 1, she will get D in profits. If she adapted to growing crop 2 she would get C in profits. This means that holding technology constant would overestimate the damages from climate change by C–D. The empirical model they derive from this insight is that if one observes a cross section of net profits and climate, one could regress

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net profits on climate and recover the climate elasticity of the agricultural sector. The key assumption here is that in the long run farmers have optimized to their local climate regime. This approach hence recovers the climate response by looking at the climate response across the cross section of individually climate optimized farmers. The advantage of this method is that it recovers an actual climate sensitivity, yet at a cost. As with all cross-sectional approaches, these regressions suffer from omitted variables bias (OVB). If, for example, soil quality is correlated with climate and one fails to control for soil quality in the regression, one would falsely attribute the effect of better soils to climate and bias the elasticity. Several papers point out the fragility of such estimates to OVB, the most well-known of which point out the importance of accounting for irrigation (Schlenker et al., 2005). Other “Ricardian” studies set in developing countries quantify the sensitivity of the agricultural sector to variation in climate conditions (Kurukulasuriya et al., 2006; Mendelsohn and Dinar, 1999; Kurukulasuriya and Mendelsohn, 2008; Seo and Mendelsohn, 2008). One challenge facing these studies is the matching of the crop calendar to the climate outcomes. There is a vast crop and location specific agronomic literature that studies the importance of different environmental factors throughout the life cycles of different crops (Yoshida and Parao, 1976). It is hence important to use climate variables in regressions which match the crop calendar and possibly within growing season life cycle of crops. The vast majority of Ricardian studies simply uses quarterly averages, which is a naïve approach to specifying how climate affects yields, as different crops have different life cycles throughout the year. This introduces measurement error, which if classical, attenuates the effects of climate on yields. Recent work by Welch et al. (2010) has shown the importance of improving this temporal match. Further, most Ricardian studies use simple seasonal quadratics in the climate variables, which forces a symmetric response around an “optimal” temperature. A more recent branch of the literature has tried to overcome the omitted variables bias critique of the Ricardian models. Ricardian models attempt to address the issue by explicitly controlling for any possible confounders correlated with climate and the outcome (e.g. yield, net profits). The argument against this has been that one cannot possibly control for all relevant confounders, as some are unobservable. Auffhammer et al. (2006) and Deschenes and Greenstone (2007) estimate panel data models by regressing measures of agricultural output (e.g. output, yields, net profits) on annual or within season weather outcomes across space and time. The regressions carefully control for spatial unit and time fixed effects to flexibly control for time varying confounders affecting all states/counties and unobservable differences across counties. Auffhammer et al. (2006) conduct this exercise for rain fed rice agriculture in India at the state level and abstain from a projection exercise in favor of a historical detection and attribution exercise. Deschenes and Greenstone (2007) use the estimated weather response coefficients to project impacts of climate change on the US agricultural sector out to the end of the century. Guiteras (2009) conducts a similar exercise for India’s agricultural sector at the district level. Chen et al. (2016) provide a study for China. What many of these studies have in common is that they all

3 Estimating the Impacts of Climate Change on LDC Agriculture

use flexible functional forms for the temperature response, by binning the number of days a given area encounters in discrete temperature bins. This nonlinear functional form was pioneered in the United States by Schlenker and Roberts (2006, 2009). This overcomes the issue introduced in the Ricardian approach, where simple polynomials have been used historically forcing a symmetric response. For the four major crops (soy, wheat, cotton, and maize) it has been suggested that days with temperatures above 31 degrees Celsius result in significant yield losses. There is no evidence of such a threshold for rice. This approach has been applied widely not just to the agricultural sector but to farmer suicides (through a possible reduced yield channel) (Carleton, 2017), migration, mortality and macroeconomic activity more generally (Hsiang et al., 2017). The significant drawback of this approach is that it uses the response of an entity to weather – not climate. A farmer’s response to a single additional hot day in a season is very different than the same farmer’s response if she expects there to be one more hot day per year in perpetuity. A short run response may be the temporary application of more inputs at the margin. The long run response maybe the investment in durable capital (e.g. irrigation infrastructure), change in crops, change in planting schedules, migration of the farm or the abandoning of farming activities altogether. Hence, studies using high frequency weather data will likely drastically overestimate the damages from climate change, since these studies ignore much of the long run adaptation. A recent literature using quadratics in temperature combined with high frequency weather data as control variables finds that the use of polynomials allows for some degree of adaptation. The argument is two fold. First, if one uses fixed effects and a second order polynomial, the fixed effects demean the level and the square term, which makes the estimator use both within spatial unit as well as across spatial unit variation to identify the impact of e.g. temperature on the outcome of interest (McIntosh and Schlenker, 2006). Hsiang (2016) and Deryiugina and Hsiang (2017) in an application of the envelope theorem argue that using short run variation in weather is valid as long as all cross sectional units optimize their production according to their local climate. A third, more recent innovation marrying the best of the Ricardian approach with the best of the panel data approaches was proposed by Burke and Emerick (2016) and is referred to as the long differences approach. For the US agricultural sector, they exploit the fact that we have long time series across counties of both outcomes and weather. They then regress the change in five year moving averages at the beginning of the sample to the end of the sample of the outcome of interest on the same long difference in weather. This removes county unobservable differences. This approach is made possible by exploiting variation in observed warming trends across counties. It requires long panels of outcomes and temperatures. The advantage of this method is that it sweeps aside the main OVB concerns and estimates a climate – not a weather – sensitivity. It is the best of both worlds and could be applied to developing country settings, where data are available. It is interesting that for North America, they find little difference in short run (weather) and long run (climate) impacts on the main

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food crops, which they suggest is consistent with a very small or limited degree of adaptation. Shrader (2017) points out the importance of how agents form expectations about future climate and questions whether one can use historical data to study the adaptation response to expected climate change. In order to do this correctly, one would want to study the adaptation response to expected climate change of agents. More broadly, however, what the literature has failed to do so far is to detect specific evidence of adaptation at the field level (e.g. change in cropping patterns, planting calendars, crop mixes) and analyze the effectiveness of these adaptation mechanisms. If there really is, like Burke and Emerick suggest, no adaptation taking place, we need to better understand why that is the case. Specific areas ripe for research should focus on the role of information, credit constraints, and government subsidies. A fourth approach, which is more recent and has high data requirements builds on the panel data approach proposed by Auffhammer et al. (2006). If one can estimate temperature response equations for different areas (e.g. ZIP codes, counties) one can change the shape of the dose response function empirically. The first evidence of this was proposed by Auffhammer and Aroonruengsawat (2012) for electricity consumption and Butler and Huybers (2013) for agriculture. These papers estimate the dose response functions for different areas (e.g. ZIP codes, counties) or time periods (1960s, 1990s) and look for differences in the dose response as a function of differences in climate during the time period or across spatial units. Auffhammer and Aroonruengsawat (2012) use detailed micro datasets on household electricity consumption to estimate the causal short run response to temperature at the ZIP code level. They then explain cross sectional variation in electricity temperature response across ZIP codes as a function of climate. They then link these equations to state of the art downscaled climate models and calculate projections of impacts of short and long run response. Butler and Huybers (2013) adopt a similar approach by letting the dose response function change over time, as there is warming in the later part of his sample. To the best of our knowledge this has not been applied in the developing country context. This has much to do with data availability. As more high resolution global daily weather data come online (e.g. Berkeley Earth Project), it should be possible to conduct more of this type of research in the developing country context. Next, the literature focuses on the main food crops (soy, rice, wheat, maize) and cotton. We know little about the climate sensitivity of food crops important in large parts of the world (e.g. millet, taro, cassava). It is paramount that we better understand the climate response of these important crops. Finally, none of these approaches measure the cost of adaptation (it ) (Plantinga, 2017). If the goal of the economist’s exercise is to derive the monetized effect of climate change on agriculture, then adaptation costs should be included. There is a current effort underway to develop methods to do this for mortality out of Chicago’s climate impact lab, but no public papers were available at the time of the writing of this chapter.

3 Estimating the Impacts of Climate Change on LDC Agriculture

3.2 AGGREGATION AND GENERAL EQUILIBRIUM EFFECTS Many econometric studies examining global climate change impacts struggle with incorporating general equilibrium effects. If climate warms and yields drop everywhere or in a majority of crop producing regions, prices will change, which will invalidate the partial equilibrium simulation results of all of the studies cited above. Roberts and Schlenker (2013) and Lobell et al. (2011) provide one avenue to identify global general equilibrium effects, but more work needs to be done on this topic. If we view climate shocks as “supply shifters”, then the elasticity of demand for a given agricultural good plays a central role in determining general equilibrium effects. Given that agricultural produce is heavy to ship and can be stored for a finite amount of time, both spatial arbitrage considerations and intertemporal storage (i.e. Hotelling’s law) will have implications for how a shock at a point in time and space ripples through the economic system. One path forward is recent work that involves an effort to merge findings from econometric yield impacts models and the GTAP model (Moore et al., 2017). The general equilibrium effects of local weather will also depend on government international trade choices over tariffs and quotas. Imagine a small LDC nation whose leaders choose to have no trade barriers for agricultural goods. In this case, the nation’s farmers compete with world exporters and urban consumers are insulated from local climate shocks (Glaeser, 2014). If climate change lowers the nation’s farm output, the farmers do not receive higher prices for their produce. Instead, they grow less and receive less income. Many developing nations enact agricultural trade barriers. These barriers provide some monopoly power for domestic farmers and this means that urban consumers face more volatile price dynamics as a function of local climate conditions. Going forward, as scientists devise new resilience strategies and technologies, how quickly will they diffuse across poor farmers? What are the impediments slowing down such a transition? Field experiment research designs are the ideal research tool here. Conley and Udry (2010) present findings on the diffusion of information within social networks. In growing pineapples, farmers imitate their neighbor’s successful strategies. Work done by Kyle Emerick and coauthors pushes the envelope in important dimension of the literature, which is how to deliver a new climate resilient technology to the farmer. He looks at the yield benefits of submergence resistant rice varieties in South Asia (Dar et al., 2013). They show significant yield benefits of these new varieties when rice is submerged for up to 10 days with no yield penalty when there is no submergence – a win-win. In a second study he studies how to get new seed varieties to farmers. He randomizes how this successful new technology gets dispersed among villages – via salesperson or through farmer social networks and shows evidence of significant under adoption in the farmer networks (Emerick, 2018).

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4 THE FARMER CLIMATE ADAPTATION CHALLENGE Fig. 4 implicitly assumes a frictionless transition as land is redeployed from one use to another as the climate changes. In reality, both time and resources must be spent to bring about this transition such as reallocating land from wheat to corn. These transition costs are likely to vary across space and across farmers. While the land will eventually be allocated to its new highest and best use, there will be distributional consequences involved in this transition. What happens to the original user of the land parcel? Does she sell the parcel to another user who has a comparative advantage in coping with the new climate conditions? Does the original farmer find a way to redeploy her capital and skills that she used to grow the original crops or are these sunk costs that must be included in the cost of adaptation? If the new best use of the land features a fixed cost to implement, will small farmers be able to finance these? These questions highlight that climate change will have important distributional consequences across farmers. Each of these questions merit future research. We start by discussing property rights. If the property rights for farmland are well defined and costlessly enforced, then the land market will allocate this scarce resource to its highest use. Those with a comparative advantage at coping with new climate conditions will acquire access to these lands (assuming they can borrow on capital markets) and the land will make the efficient transition. In reality, much LDC land is not formally titled and the rule of law is weak. In such a setting, classic “Tragedy of the Commons” issues arise. Farmers and those with livestock may seek to move onto other more productive lands. Such a threat of encroachment will lead incumbents to take costly self-protection actions to secure their property (Fields, 2005). This investment of time and resources in repelling the threat of encroachment is another adaptation cost that should be factored in determining the cost of adaptation. If rural people face subsistence level constraints such that they starve if their caloric intake falls below some minimum level, then violence may emerge as an equilibrium in the countryside as desperate people hunt for increasingly scarce resources (Glaeser, 2014). Repeated social interactions between long term neighbors builds up trust and social capital and this helps to attenuate the Tragedy of the Commons problem (Ostrom, 2010). Whether such “neighborly good will” holds up under the pressure of increased climate variability is an important future research question. Recent research has examined the link between climate change and rural violence. Cross-national research based on panel data from 1980 to 2005 in Sub-Saharan Africa has documented that the probability of civil war is higher in nations experiencing hotter summers (Burke et al., 2009; Hsiang et al., 2013; Hsiang and Meng, 2015). For violence to erupt suggests that rural people have few coping strategies and are desperate to find food and shelter. More recent research has studied the impact of higher commodity prices on conflict. McGuirk and Burke (2017) document using commodity pricing for the entire African continent that rising world commodity prices reduce violence among producers due to an opportunity cost effect while violence among consumers increases.

4 The Farmer Climate Adaptation Challenge

4.1 INCOME INEQUALITY AND CLIMATE CHANGE An important open research question is whether climate change will increase overall income inequality. Sala-i-Martin (2006) has argued that global inequality is falling because of the reduction in poverty in the developing world – especially in highly populated nations such as China and India. If, however, the poor in LDCs have little ability to cope with climate change, then such shifts will increase a poor nation’s income inequality. Subsistence farmers may suffer large income losses due to climate change. Consider a case in which given a new climate, corn is now the right crop to grow on a specific parcel. Small farmers may not have the physical, financial or human capital to make this transition. In this case, larger farms are likely to have market power in negotiations and purchase the land at a lower price from the small farmer. This example highlights how the industrial organization of LDC farms may change due to climate change. In this case, the land will be efficiently repositioned but the incumbent farmers will be displaced and receive a low rate of return on their land assets. Sugar represents a prime example. This is a crop that is more efficiently grown on larger plantations. Historical research by Sokoloff and Engerman (2000) shows that in Brazil the agricultural sector featured large land holdings because of scale economies. This structure of property ownership led to an inequality of income and this inequality persists over time. Acemoglu et al. (2001) argue that nations with more income inequality feature an elite who use their political power to create extractive institutions that transfer more resources to the elites. A human capital theory would posit that those farmers with higher incomes will invest more in their childrens’ human capital and this boost in skill formation will form the basis for a persistent intergenerational correlation of income. Both the “extraction” theory and the human capital theory imply that climate change will exacerbate an agricultural nation’s income inequality in the long run. To test these claims, researchers would need to study how parcels of land are being aggregated and who owns them over time as climate conditions change. Are farms becoming bigger (Jayne et al., 2003)? Do small farmers sell their land for low prices and then transition to low paying jobs? So far, this discussion has focused on how individual farmers cope with a changing climate. A recent US climate literature has focused on how rural places cope with change. Research in the United States has projected how climate change will increase cross-county inequality in per-capita income (Hsiang et al., 2017), albeit not taking into account full adaptation. Other research has examined how the Dust Bowl was affected by the natural disasters it faced in the 1930s (Hornbeck, 2012). Similar work studying the long run consequences of natural disasters for places in the developing world would be quite valuable. For example, the impact of the 2004 Asian Tsunami has been studied in several papers (Gray et al., 2014; Gillespie et al., 2014).

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4.2 LDC FARMER CLIMATE CHANGE ADAPTATION OPPORTUNITIES Investment in human capital facilitates adaptation through several different channels. The skilled are more productive in both the rural and the urban sector. The educated are more likely to be literate. Those with more cognitive capacity will be more likely to anticipate emerging challenges and to react sooner and more creatively to emerging challenges (Becker and Mulligan, 1997). The behavioral economics literature also predicts that those with more human capital will be more likely to detect that the climate is changing (Benjamin et al., 2013). The rise of rural education efforts reduces rural poverty (Jensen and Miller, 2017). If low levels of education cause impatience and an inability to solve problems and anticipate emerging trends, then rising education can help the poor farmers be more nimble in the face of a changing climate (Benjamin et al., 2013). Recent research has used natural disasters as natural experiments to test how rural households reallocate childrens’ time when the returns to farming are low. Shah and Steinberg (2017) document in rural India that childrens’ educational attainment rises when disasters occur. This work highlights that parents are aware of the benefits of education and are responsive to opportunity cost. The Big Data revolution raises new adaptation possibilities for LDC farmers. As remote sensing technology improves, geographers have an increased ability to create spatially refined data that can be used to provide customized information to farmers. Given that information can be a public good, development economists could educate farmers by providing land “report cards” to farmers to nudge them to consider shifting their lands to higher value uses. More spatially refined data on the quantity of rainfall will play a key role in the creation of weather insurance markets. A buyer of a weather insurance contract would receive a payoff if there is extreme temperature or rainfall or drought at a specific monitoring station. Such a contingent contract would provide income to the farmer in “bad states of the world”. One challenge with specific farmers using such markets as a risk hedging approach is that these weather monitoring stations are sometimes far from the actual plots of land. This means that the insurance payoff is less highly correlated with the actual climate conditions experienced by a specific farmer’s plot of land (Mobarak and Rosenzweig, 2013). The value of such weather insurance increases as the volatility of shocks increases. A third adaptation strategy is the rise of the adoption of GMO technologies (Qaim and Zilberman, 2003; Barrows et al., 2014). While there are many unsettled scientific issues here, GMO varieties such as heat resistant wheat offer to the farmer the possibility of facing less crop loss when extreme weather events occur. If these technologies deliver as promised, an open question is whether such technologies will be affordable for both small and large farms. It is possible that only large farms will adopt these technologies. In this case, the smaller farmers’ land will be consolidated into larger farms and the physical place will adapt but the original small farmers will have to transition to a new way of life. The economic and personal costs of such a transition must be counted as part of the cost of climate adaptation and have implications for the extent that the poor bear the greatest costs from climate change.

4 The Farmer Climate Adaptation Challenge

This point must be caveated by recognizing the income effect when a poor farmer sells his land to a large “GMO farm”. The ability of the small farmer to recover from the original weather change hinges on the terms of the deal. If the large farm buys the small farmers out with very low payments because of asymmetries in bargaining power then the local land will be redeployed, but the original farmers face even greater poverty risk. This example highlights that land markets break the link between how places and people are affected by persistent weather shocks. Dating back to work on California’s Owens Valley, there has been the concern that small farmers lose out in land negotiations (Libecap, 2007). Whether such a dynamic will play out in different developing nations will be an important research question with clear equity implications.

4.3 RURAL DATA COLLECTION NEEDS TO ACCELERATE ADAPTATION RESEARCH PROGRESS The building blocks for studying rural dynamics in the face of climate change will be a matched panel sample of farmland and farmers. Starting in a base year, a researcher would need to observe for each parcel of land, what it is being used for, who owns it, who manages it, and what is the land’s current productivity. Such data would allow the researcher to test for interesting heterogeneous treatment effects. Different farmers might respond to the same climate shock by moving along different margins. Some might adjust by switching crops while others might sell their land to a larger farm. These data would permit an accurate portrayal of the land use dynamics and what happens to the farmer. Such a data set could be assembled by combining remote sensing data by land parcel with surveys of the farms to collect data on outputs and inputs and other farm geographic variables. The greater data challenge would be to track people over time such as those that leave a specific farm to move elsewhere or to a city. In this cell phone age, an individual’s co-ordinates could be tracked and this would create a way to study the life path for individuals who leave a specific parcel of land. Such a matched data set would be the analogue of the data creation strategy used by labor economists in the US and Europe (Abowd and Kramarz, 1999; Abowd et al., 2006). In the US, matched firm/worker data sets allow one to study how the firm’s average worker changes over time due to hires and separations. In the labor economics literature, economists exploit natural experiments such as a factory closing to examine what are the subsequent labor earnings dynamics for workers who lost their jobs. Such income dynamics speak directly to capturing how nimble on net different individuals are. For workers who leave a firm after the firm closes, researchers study how the earnings of displaced workers are affected (Jacobson et al. 1993; Davis and von Wachter, 2011). The distributional effects of sectoral change can be explored by studying the quantiles of the change in earnings say two years after the displacement shock. This natural experiment research design is highly relevant for studying farm land and farmer income dynamics. Researchers could study how natural disasters or shift-

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ing climate conditions impact a farm’s overall profitability, output, and labor force changes. Using this research design, one can study the gross flows of workers both joining the farm and the subsequent outcomes for those workers who leave the farm. If such a panel data set could be created, then researchers could implement randomized field experiment designs to randomly assign treatments such as free transportation or the first year urban rent to be paid to test how such treatments work to attenuate the negative effects of natural disasters and extreme climate events (Bryan et al., 2014a). This work would be analogous to the famous Move to Opportunity experiments in the United States (Chetty et al., 2016). By encouraging LDC farmers to move, do outcomes for them and their children improve? Such experimental evidence would be directly relevant for judging the importance of overcoming frictions that inhibit migration. Gray and Mueller (2012) study the impact of natural disasters on population mobility in Bangladesh. Past research has argued that social capital anchors farmers in the countryside (Banerjee and Newman, 1998). How large must urban/rural income differentials be to stimulate migration remains an open question (Young, 2013).

4.4 RURAL TO URBAN MIGRATION AS AN ADAPTATION STRATEGY A researcher who has longitudinal data for a large set of farmers will observe some of them move to cities. If a data set could incorporate information on where the new urbanite lives, what industry and occupation the person works in, then this data collection effort yields a detailed picture of how the former farmer’s quality of life has been affected by the rural to urban transition. Migration from the countryside to a city represents a risky investment. In the classic Harris and Todaro (1970) and Sjaastad (1962) models, the migrant incurs a fixed cost for leaving one’s origin. This fixed cost may reflect both financial costs of leaving and also the psychic cost of leaving one’s rural social network (Banerjee and Newman, 1998). In a LDC context, climate shocks may set off large migration flows as many people seek to exit the rural sector. Key issues arise concerning the ability of urban areas to cope with a sudden influx of migrants. The ability to migrate will be determined by liquidity constraints, perceived opportunities in cities and the human capital and imagination to consider making such a key life choice (i.e. moving to a distant city). A key issue arises concerning the timing of such migration, if some farmers figure out early on that the climate is changing then they will be more likely to move early and the process of rural to urban migration will be more orderly. Conversely, if farmers only migrate after the realization of a climate shock, then the transition dynamics will be much more costly for the destination areas. This discussion points to several promising research areas. Recent work in Bangladesh has used a field experiment design to demonstrate that transportation costs limit migration. When free bus passes were provided, farmers send young adults to the city to work and this urban income was remitted back to the countryside. This income portfolio helped the rural family to smooth consumption during a time of low farming productivity (Bryan et al., 2014a). These results have important implications for climate adaptation if climate change increases the volatility of weather conditions.

4 The Farmer Climate Adaptation Challenge

It is easy to state that the risk neutral rural farmer will urbanize if the expected present discounted value of moving to the highest paying city net of rents is greater than the opportunity cost of continuing to farm plus the migration cost. Yet the difficulty here is how to operationalize this concept. Both the individual farmer and the econometrician, who seeks to study the farmer’s adaptation efforts, face the challenges of: 1. Estimating future income of remaining in the countryside, 2. Estimating the probability of finding a job and the wage in each potential destination city, 3. Estimating one’s earnings profile over time and rents paid in each potential destination city, 4. Measuring the non-market quality of life in each of these cities. Only by constructing the farmer’s actual budget set, can the econometrician recover the tradeoff that the farmer faced at the point when he chose to move. To appreciate this point, consider the study of Avery et al. (2012) in investigating college choice. Since they were able to observe the actual scholarship tuition deals offered to each student, they were able to reconstruct the actual choice set that students faced. A researcher who simply observes a student’s college choice and the “sticker tuition price” of each school would not recover the student’s actual willingness to tradeoff university attributes such as school quality versus actual tuition. Recognizing this point, researchers have estimated reduced form regressions studying how migration patterns to LDC cities are affected by origin climate conditions (Barrios et al., 2006).

4.5 THE DIMENSIONALITY OF THE LDC MIGRANT’S URBAN CHOICE SET In LDC nations featuring more cities, migrants will have a larger choice set. Such a larger menu of possible destinations offers more adaptation possibilities. These cities will differ with respect to their industrial composition, congestion, and housing conditions as well as their proximity to the migrant’s origin location. For young, less educated rural people, they will be more likely to find gainful employment in cities if the cities are industrializing. Manufacturing is a sector whose output is less likely to be positively correlated with agricultural production. Recent research by Henderson et al. (2017) studies African urbanization and finds that 75% of the cities in these nations specialize in agricultural “middle man” services. This means that there is a positive correlation in income between Africa’s rural and urban areas. Thus, when the rural country side is suffering from low harvests and the farmers increasingly seek to migrate, the majority of the cities are suffering from a recession as well. The spatial diversification gains from urbanizing are larger if the city’s economy specializes in industries whose output is not correlated with agricultural production. While Deichman et al.’s research takes the industrial structure of African cities as exogenous, this raises the question of whether more African cities will make a transition to being manufacturing centers because climate change poses a risk to core incomes? In recent years, there has been a backlash against international migration. Some nations in Europe such as Germany have received a huge influx of migrants. Some nations have responded by erecting limits to such international migration. These barriers to international migration raise adaptation costs for rural people in the de-

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veloping world as they lose possible adaptation pathways. A structural researcher could estimate this cost by estimating the expected utility of a migrant as the number of possible destinations shrinks (due to immigration constraints). An open question concerns the incentives of destination nations such as European nations to be more open minded in receiving refugees. Ongoing research in mechanism design is needed to design incentive compatible rules that encourage migration to areas more willing to accept new migrants (Delacrétaz et al., 2016). The current backlash against international migration inhibits the ability of LDC rural people from moving to cities in Europe and other richer areas. In smaller nations with fewer cities, rural people will have fewer destination choices (Alesina and Spolaore, 1997). Environmental scholars have argued that the dislocation caused to destination nations by such flows portends future trends as “environmental refugees” will also seek safe havens. While the refugee challenge is clear, it is important to note that such migrants have strong incentives to seek out local labor markets where their skills are in demand. For example, if there is a city seeking low skill workers and wages for such workers are high, this is a clear price signal that this city seeks more of such workers to move there. In this sense, market price signals will direct the “refugees” to destinations where their effort is most highly valued. The allocative mechanism of capitalism thus plays a key role in reducing the costs of sector adjustment induced by climate change. During a time of declining support for international migration, the possibility of creating more potential destination cities within nations would appear to be of increased importance. Fuller and Kahn (2013) discuss the climate adaptation opportunities created by the opening of new cities. While there would be fixed costs to create such cities, they can be operated under new rules because there are no status quo interest groups blocking such rule adoption. For nations whose topography is such that there are some geographic areas that face less extreme heat and flooding risk, these might be the most promising places to build new cities. If the fixed costs of creating the first stage of urban infrastructure can be reduced, then these experiments will not be that costly to run. If the cities take root, then the second generation of infrastructure can be built to a higher quality.

5 GENERAL EQUILIBRIUM EFFECTS INDUCED BY RAPID URBANIZATION Severe climate shocks to the LDC countryside may create large urban migration flows that shift out the aggregate supply of labor in cities and increase aggregate housing demand. If large enough, these shocks have general equilibrium effects and thus affect the well being of incumbents in these cities. Consider a LDC city that specializes in low skill manufacturing. If the manufacturing wages in this city are quite high, then incumbent firms will be delighted as new migrants move to the city. Such an influx of migrants will lower local wages and incumbent workers will experience an income loss. Rents will rise in areas expe-

5 General Equilibrium Effects Induced by Rapid Urbanization

riencing an in-migration. These general equilibrium effects hinge on the underlying elasticities and these are crucial for the political economy discussion of urban migration that we present below. The effects of migrants on local labor and real estate markets is a hotly debated US issue but it has not been explored in enough depth in the LDC context. The Mariel Boatlift represents a famous case study of how a city is affected by rapid migration (Card, 1990). In the standard Econ 101 short run perfectly competitive model, a rapid increase in the supply of low skill workers lowers equilibrium wages for low skill workers and raises rents (Saiz, 2003). Borjas et al. (1997) extend this to a two sector general equilibrium model. As Miami’s wages went down and rents rose (due to the Cuban immigration), some Miami incumbents started to move out and moved to places such as Atlanta. In the resulting long run spatial equilibrium, wages and rents adjust so that the footloose are indifferent between living in the treated city “Miami” or the non-treated city (Atlanta). Whether the Mariel Boatlift offers a preview for likely general equilibrium effects in the developing world hinges on several factors. Ades and Glaeser (1995) document that in the developing world a large percentage of urbanites live in the capital city. This effect is even larger if the nation is authoritarian and is closed to international trade. For LDCs that fall into this category, it is likely that rural migrants will also seek to move to the capital city. A growing development economics literature has studied urban slums. In these areas, people squat for years on land often owned but not policed or serviced by the state (Fields, 2005). In such areas, rising population density can contribute to infectious disease risk and fears of violence. Brueckner (2013) has studied the housing conditions in Indonesia’s slums. Residents in these areas live in low quality housing such that natural disasters are more likely to cause more death risk, destruction and infectious disease. An emerging literature has been examining urban slum housing (see Brueckner and Selod, 2009; Brueckner, 2013). Empirical research tends to survey such properties to collect data on whether the home has a secure roof, toilet pipes and access to electricity. Such descriptive research could be augmented to study whether such housing, both due to its physical location and its quality, is less resilient in the face of natural disasters and extreme weather conditions than housing in the formal sector. Such research would be highly relevant for studying whether climate change will exacerbate quality of life inequality between the poor and the urban rich. This could occur if the urban rich live in higher quality structures that are more resilient to extreme heat and natural disasters (because of better roofs and better sanitation investments). As rural people move away from their villages to the cities, land resources percapita in the countryside increase (Young, 2005). This means that rural incomes will rise and thus the LDC urbanization trend could help the remaining rural people to better adapt to the emerging climate conditions. Research from Brazil has documented that the preservation of countryside natural capital contributes to lowering disease risk (Bauch et al., 2015). The electrification of the countryside and the increased

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access to Internet Technology raises the possibility that rural quality of life improvements could help to slow rapid climate change induced urbanization (Wolfram et al., 2012). If improvements in information technology could allow countryside people to earn income while not working in farming, then this will provide some risk diversification for countryside residents.

5.1 URBAN POLITICAL ECONOMY ISSUES RELATED TO CLIMATE CHANGE ADAPTATION As LDC cities grow in population size, local leaders will face key decisions. Do they provide key infrastructure such as electricity, housing and sanitation for the rural entrants or do they try to discourage migration to their city by making living conditions miserable? The urban poor tend to live in the riskiest parts of the city, in high density areas. While high population density living is considered “green” in rich nations as it yields a low carbon footprint (think of high rise Hong Kong and Manhattan), in developing countries high density is associated with infectious disease risk from water pollution and air pollution exposure. Poor people have the least ability to use market products such as air conditioning to self protect. An open question is whether local officials recognize this point, step up and provide public goods for this group. In US cities, cooling centers have been opened to shelter the urban poor on the hottest days. As developing countries grow richer, will they devote more of their expenditure to “pro-poor” public goods that helps to shield the poor from increased risks? Research from Brazil highlights that local urban officials often do not engage in “pro-poor” policies. Feler and Henderson (2011) provide a cautionary tale from Brazil. Using a cross-section of data across cities, they find that cities are intentionally under-providing water connections to urban migrants. One explanation for this fact is to act as a barrier to entry. A city that is accommodating to new migrants will likely receive even more migrants. By denying such water connections, these leaders are trying to discourage rural to urban migration. Whether this Brazilian case is typical across LDC nations is an important question for future research. Work by Besley and Burgess (2001) finds that in India government officials are more responsive in providing public goods in geographic areas featuring a more literate public. They argue that the media plays a key role here in publicizing elected officials’ actions. If a local mayor seeks to upgrade local public goods, this raises the question of how to finance these investments. If international capital markets were integrated, cities with a good reputation for paying back past debts could borrow on such markets by issuing municipal bonds. In many developing countries, the federal government does not allow them to issue such debts both because the center wants to keep control over the localities and because the center recognizes that it will held responsible if a city borrows and then due to corruption defaults on such a debt. Cutler and Miller (2006) document an optimistic US historical case study. They show that in the 1930s US cities were able to sharply reduce their water borne disease death risk by issuing bonds to build such treatment facilities. In the absence of such financing mechanisms,

5 General Equilibrium Effects Induced by Rapid Urbanization

there are likely to be many climate adaptation friendly infrastructure projects that are not implemented because of financing constraints. Examples include water treatment facilities, flood water disposal, and coastal flood protection. Standard Ricardian logic predicts that any public investment such as reducing water disease risk will be capitalized into local land values. This suggests that land owners in cities are an interest group with strong incentives to encourage leaders to engage in efficient public goods provision. If LDC cities can introduce a property tax then this would provide a strong incentive for mayors to invest in such climate adaptation friendly public goods, because the mayor would have a larger revenue from the tax base. A second pathway to incentivize urban leaders in democracies in LDCs is to provide report cards on their respective performance (Ferraz and Finan, 2008). For those LDC nations featuring multiple cities, a type of beneficial Tiebout competition allows urbanites to “vote with their feet” such that they move away from cities whose taxes are high relative to the public services they provide. Such potential for population loss provides an incentive for local officials to deliver services. We recognize that this accountability movement will be less successful in dictatorships in the developing world. The political economy of the incentives of local officials in dictatorships to protect the urban poor remains an open question.

5.2 THE ADAPTATION BENEFITS OF LDC URBANIZATION Urban economists posit that urbanization raises individual income through encouraging human capital accumulation, learning and specialization (Glaeser, 1998). The human capital externality literature has emphasized the key role that knowledge spillovers play in economic growth and in raising individual’s income (Rauch, 1993). Education and urbanization are strong complements. In cities, women have greater labor market opportunities and this encourages them to have fewer children and to invest more in each of their children (Becker and Lewis, 1973). This Becker quality/quantity tradeoff has implications for climate adaptation as more educated young people will be more nimble in adapting to new emerging risks. If urbanization has a causal effect on raising one’s income, then a household has greater capacity to protect itself from climate risks. A richer household has the income to purchase an air conditioner (Davis and Gertler, 2015; Barreca et al., 2016), cell phone (Aker, 2010; Jensen, 2007), high quality housing, better food, proper transportation and access to better medical care. Together these market inputs act to protect urbanites from a variety of challenges. Access to electricity plays a key role in all of these activities. In LDCs, the urban sector has better access to cheaper reliable electricity. This higher quality of consumption of housing and access to basic durables reduces the population’s fatality risk in the face of increased quantity and severity of natural disasters (see Kahn, 2005). Kellenberg and Mobarak (2008, 2011) argue that in the poorest nations that urbanization and slow urban economic development combine to expose the population to higher death count risk relative to if the population were uniformly distributed.

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Over time, the purchasing power of urban incomes increases as world quality adjusted prices for durables decline. What is the minimum income a household needs in each nation to have access to a cell phone, air conditioning, medical care, safe housing and refrigeration? Such an expenditure function approach would allow researchers to quantify the ability of a given nation’s diverse population to adapt to new risks using private self protection. As LDC cities grow richer, it is likely to be the case that the urban populace demands greater safety and environmental regulation. The Environmental Kuznets Curve argument is predicated on a rising demand for regulation as economic development takes place (Dasgupta et al., 2002). The so called “j-Curve” for regulation optimistically posits that as the urban middle class grows, this group becomes an active interest group seeking improved local public goods (Selden and Song, 1995). In the case of adapting to climate change, the urban middle class in LDCs will increasingly support policies that provide public goods (i.e. sea walls) that protect the local populace from emerging threats. The hypothesis that the growing LDC middle class supports increased investment in defensive public goods is a promising future research topic.

5.3 THE PRODUCTIVITY OF LDC URBAN FIRMS IN A HOTTER WORLD The previous section argued that LDC urbanization will accelerate per-capita income growth and human capital attainment. How will climate change affect this gradient? The answer hinges on whether climate related events sharply lower urban firm productivity. A recent literature has studied how indicators such as firm level output and total factor productivity over the course of a year vary with local climate conditions (Heal and Park, 2016). A fruitful area for future research could merge micro data on LDC urban firm productivity with local measurements of temperature and rainfall. Such data could be used to estimate firm level production functions augmented by climate variables. These regressions yield an estimate of the marginal productivity costs of extreme climate. A central difference between agriculture and urban production is the possibility of adopting air conditioning. In an economy featuring heterogeneous firms, the most productive firms will be the most likely to adopt this costly technology. Zivin and Kahn (2016) present a model of the adoption of air conditioning by urban firms. The adoption of air conditioning is a costly investment. Zivin and Kahn (2016) present a model of heterogeneous firms within an industry. In their model, firms all produce the same output but differ with respect to their productivity. This source of productivity is taken as exogenous. Extreme heat lowers the productivity of workers. Each firm calculates its profit from having air conditioning (and bearing the fixed cost and operating cost of the air conditioner) versus its profit from not having air conditioning. In their model, there is a cutoff firm in the productivity distribution such that all firms, who are more productive than that firm, adopt the air conditioning. This

5 General Equilibrium Effects Induced by Rapid Urbanization

result immediately suggests that the most productive firms will be more likely to be insulated from climate change. As outdoor conditions grow hotter or if the price of air conditioning declines, the less productive firms will become more likely to adopt air conditioning. Zivin and Kahn solve for the macro aggregate industrial output that is insulated from the heat due to air conditioning. Their model predicts that the most productive firms will grow as extreme heat takes place and they will hire more workers who will be air conditioned. Extreme heat in cities could exacerbate income inequality as the less productive workers work for the less productive firms who choose not to provide air conditioning. This hypothesis could be tested if matched worker/firm level data in LDC nations could be collected. Such a data set would include worker attributes such as age, education, gender and standardized test scores and firm attributes such as the firm’s industrial sector, price of output, inputs used in production, the firm’s physical location and its energy used and ideally indicators of air conditioning. Such a data set could be used to test whether high skilled workers are working at air conditioned firms and whether in hot years these firms perform better based on output per worker compared to firms in the same industry that do not have air conditioning.

5.4 WILL LDC URBAN GROWTH SIGNIFICANTLY EXACERBATE THE GLOBAL GHG EXTERNALITY CHALLENGE? Adaptation is easier if global GHG emissions are lower. In the near term, the developing world will contribute a growing share of the world’s greenhouse gas emissions (Auffhammer and Carson, 2008). A simple decomposition exercise represents total GHG emissions as equal to population ∗ GNP ∗ Emissions per dollar of GNP. Given this formula, how much will LDC urbanization and economic growth contribute to the overall GHG production externality? Urban growth should slow down overall population growth. A standard Beckerian model of the optimal number of children to have incorporates the full costs and benefits of children. In cities, the value of alternative uses of their time over work in the household sector is higher. Urbanization and education go hand in hand and more educated (men and) women can earn higher urban wages (Becker and Lewis, 1973). This higher value of household time creates an incentive for women to substitute from quantity of children to quality of children as urban women have fewer children and invest more time in each one. In recent years, nations such as Vietnam have had a dramatic decrease in fertility rates. While urbanization slows down LDC population growth, it accelerates per-capita income growth. Richer people consume more private goods that run on electricity and fossil fuels. The prime examples are private vehicles, and household durables such as air conditioning and refrigerators. If power is generated by coal then this consumption will be socially costly. If the developing world adopts natural gas, nuclear and renewables, then the resulting GHG externality associated with the rise of the “American Dream” in the developing world will be lower. Glaeser and Kahn (2010) present an empirical approach for measuring the household carbon footprint by city. This approach has

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been used to rank Chinese cities with respect to their carbon footprint (Zheng et al., 2010). Endogenous technological change can reduce emissions per dollar of GNP. New innovations such as electric vehicles charged by solar panels raises the possibility that developing nations can have access to personal services without the resulting carbon externality. Of course there are many sources of uncertainty in the engineering prospects for these nascent technologies. The interesting economic question here is whether the growth of LDCs as urban centers of consumption (think of the product demands of China’s large upper middle class) acts as a “Big Push” encouraging further R&D in green technology. Put simply, if China’s growing middle class demands electric vehicles then this creates a huge market for firms that can produce this variety (Acemoglu and Linn, 2004). In a growing world economy, the rising stock of human capital raises the possibility of significant progress in the development of green technology such as electric vehicles and renewable power generation equipment (Freeman and Huang, 2015). A countervailing trend has been the rise of technological progress in the fossil fuel sector such as the fracking revolution. This race between progress in green versus brown technology will play a crucial role in determining whether the LDC rural to urban (and the resulting growth in per-capita income) transition accelerates global GHG emissions production.

5.5 RESEARCH NEEDS Throughout this survey we have emphasized the importance of using micro longitudinal data at the individual, land parcel and firm level to trace out the effects of climate change on diverse economic agents. Such data will allow researchers to test for heterogeneous treatment effects of climate impacts. By simultaneously tracing out how the dynamics of the land parcel and the pathway followed by workers at that land parcel, research teams can study how people and places are affected by climate shocks. For example, an optimist would posit that after a permanent climate shock that the land will quickly transition to its highest value use and the people who were employed there will easily transition to their next best alternative. A research team with longitudinal data on parcels and people can directly test this hypothesis and thus will be able to measure who bears the economic incidence of climate change. Empirical research progress in climate adaptation research will mainly come from exploiting natural experiments. As natural disasters and heat waves inevitably occur, this exogenous variation will allow the researcher to trace out the short run and medium term effects. Field experiment research designs can be introduced to see if certain low cost interventions attenuate the negative effects of a given shock. For example, if climate change increases the severity of coastal hurricanes, then a field experiment that randomly assigns a subsidy for more sturdy roofs on homes will yield a test of whether housing structure insulates a poor household from such shocks. Much of the new climate economic research estimates reduced form models using a single equation to link “cause and effect”. This research plays a crucial role

6 Conclusion

in teaching us new facts. A prime example is Barreca et al. (2016). This US study documents the reduced mortality effects of extreme heat over time perhaps due to the diffusion of air conditioning. A gap we see in the literature is a paucity of structural modeling. Optimizing households and firms choose where to locate and how to produce. This raises classic self selection issues of sectoral choice based on evolving comparative advantage. Costinot et al. (2016) provide such an analysis for the agricultural sector. This approach would explicitly allow researchers to study who “is the marginal economic agent” induced to change sectors because of a given shock.

6 CONCLUSION Around the world, the share of people whose income is below the poverty line is declining over time. But per-capita income is not a sufficient statistic for quality of life. Climate change could lower the standard of living in LDC nations even if per-capita GDP is rising. The poor who live in poor nations are the most likely to bear the greatest costs caused by climate change. This chapter has investigated many facets of the anticipated challenges posed by weather shocks and natural disasters. By adopting a microeconomic perspective, this paper has focused on the distributional impacts likely to be caused by emerging climate change. Rural people may face subsistence consumption risk, dislocation and higher levels of violence. Poor urbanites living in informal areas could face an influx of desperate rural migrants who through market competition will raise rents and lower wages for incumbent urbanites. We have emphasized the importance of testing for heterogeneous responses and measuring the economic incidence of coping with new ambiguous risks. The value of this research agenda is that it complements an emerging macro literature that makes cross-country comparison in the standard of living (Jones and Klenow, 2016; Stiglitz et al., 2009). This “well being” literature has not incorporated the long run looming threat of climate change. We have explicitly examined how self interested decision makers are likely to cope with the new challenges they face. This chapter’s proposed research agenda will lead to a better understanding of how the standard of living of the poor will evolve in LDCs dealing with climate change.

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Selection and design of environmental policy instruments✶ ∗ Department

6

Thomas Sterner∗,1 , Elizabeth J.Z. Robinson†

of Economics, University of Gothenburg, Gothenburg, Sweden of Agriculture, Policy, and Development, University of Reading, UK 1 Corresponding author: e-mail address: [email protected]

† School

CONTENTS 1 The Need for Policy ............................................................................. 2 Policy Failures ................................................................................... 3 The Menu of Instruments ....................................................................... 3.1 Price-Type Instruments ........................................................... 3.2 Rights-Based Policies ............................................................. 3.3 Regulation .......................................................................... 3.4 Information or Legal-Based Policies ............................................ 3.5 The Process of Policy Making at National or Other Levels .................. 4 The Selection of Instruments .................................................................. 4.1 Efficiency ........................................................................... 4.2 Information Asymmetries and Uncertainty..................................... 4.3 Intertemporal Efficiency .......................................................... 4.4 Spatial Efficiency .................................................................. 4.5 Practical and Political Aspects .................................................. 4.6 Normative Principles, Distributional Aspects, and Environmental Justice 5 Selected Examples .............................................................................. 5.1 Taxing Carbon ...................................................................... 5.1.1 Effects of CO2 Taxation ......................................................... 5.2 Taxing (and Subsidizing) Transport Fuel ....................................... 5.3 Cap and Trade Schemes .......................................................... 5.4 Refunding Emission Payments .................................................. 5.5 Regulation Versus Taxation: The Example of a Hazardous Chemical....... 5.6 Policies to Modify Behavioral Norms ...........................................

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✶ We would like to thank the editors and two very knowledgeable and generous referees for good comments. We would also like to thank Kristin Seyboth for exceptional editorial assistance. Financial support from Mistra Carbon Exit and the University of Gothenburg (UGOT) Centre for Collective Action Research (CeCAR) is gratefully acknowledged. Handbook of Environmental Economics, Volume 4, ISSN 1574-0099, https://doi.org/10.1016/bs.hesenv.2018.08.002 Copyright © 2018 Elsevier B.V. All rights reserved.

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6 Designing Policies for the Anthropocene.................................................... 6.1 An Expansion of Geographic and Political Scope ............................. 6.2 Significant Extension in Time-Scale ............................................ 6.3 Significant Extension of the Number of Pollutants and Scientific Complexity .......................................................................... 6.4 Equity, Ethics, Risk, Uncertainty, and Governance ........................... References............................................................................................

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1 THE NEED FOR POLICY In economics, we often assume each consumer or firm chooses actions that are optimal for that actor. If all non-market interactions are assumed away, the first welfare theorem states that the outcome is an efficient allocation of resources. Government policy cannot improve upon this ‘perfect’ market system, (only on distribution of assets) and may in fact be damaging. In such a ’perfect’ world, there would be no environmental problems – suggesting a potential libertarian bias. Reality, however, is not well described by a perfect market populated by rational “homines economici.” Rather, non-convexities are pervasive. These include externalities, public goods, poorly defined property rights, noncompetitive markets, increasing returns to scale, and asymmetric information, all of which are compounded by uncertainty. These market failures are conditions under which the free market fails to reach an optimal outcome. We need to understand the nature and extent of such imperfections in order to suggest remedies in the form of policy instruments. Externalities are side effects of production or consumption. The unregulated market oversupplies negative externalities, such as smoke or polluted water that can have significant yet avoidable health and welfare consequences, and undersupplies positive externalities. Cropper and Oates’ (1992, p. 678) early review of environmental economics suggests that “the source of the basic economic principles of environmental policy is to be found in the theory of externalities”. Public goods are products or services, including “ecosystem services”, enjoyed in common, such as a healthy atmosphere or the pollination services of bees, which are undersupplied by the market. Similarly, world knowledge is a global public good, thus investment in cleaner energy R&D may be undersupplied due to international knowledge spillovers (Bosetti et al., 2008). Common pool resources are those with high subtractibility, for which it is costly to exclude people, and where individual and group interests may differ (Buck, 2017). In these cases, ownership and management may be best undertaken collectively, such as by a group of people in a village or local community, as eloquently described by Ostrom (1990). Poorly defined property rights also create imperfect conditions. If rights are not well-defined for all possible goods and services, externalities result – as with neighbors who create disturbances, blocking a view or access to water, or producing unpleasant odors or noise. If all these aspects were governed by well-defined property rights (and there were low or zero transaction costs), then in principle external effects

1 The Need for Policy

would be avoided (Coase, 1960). Yet it would be impractically costly and probably impossible to define and enforce sufficiently detailed property rights to cover every aspect that might give rise to external effects. Noncompetitive markets are those in which individual actors such as international companies are large enough to have market power and therefore undue influence on prices and rules in the marketplace. If there are increasing returns to scale or indivisibilities, implying production sets are not smooth or convex, then markets without government intervention are likely to fail to maximize social welfare. Extreme cases are monopolies, whether resulting from scale economies or protection. Asymmetric information, the lack of equal access to information, and incomplete information can each stop the market from operating perfectly (see Ulph, 1998, 2000, for examples of asymmetric information and federal systems). An example of asymmetric information is in the design of contracts for payments for ecosystem services, where land owners typically know more about the costs of contractual compliance than do the buyers of the conservation service (Ferraro, 2008). An example of where incomplete information leads to market failure is with respect to investment in innovations linked to climate change, where uncertainty is particularly acute (Jaffe et al., 2005). According to the theory of second-best, easy inferences can be drawn if there is just one (small) market failure. In reality, however, market failures can be plentiful and large, in which case it is very complex to know whether correcting one market failure at a time will move us progressively in the right direction. Market failures are one key motivation for environmental policy, but there are others that are also relevant. For example, behavioral biases and anomalies. Behavioral economics helps to explain why individuals do not always simply maximize utility and why individual behavior may be more complex than can be described by economists’ simple models, ultimately making it harder to evaluate welfare implications. When people act in groups, they may feel envy, altruism, anger, revenge, and many other feelings that can influence behavior. These insights help us understand why, for instance, some communities are able to overcome incentives to free-ride on the efforts of others and instead collaborate to manage a local resource, when standard economic theory of utility maximization would suggest the opposite (see for example, Cárdenas, 2000, 2016). This also encourages economists to consider aspects such as non-standard incentives, collective action, network externalities, and social norm externalities. Many market failures can be described as a so-called ‘prisoner’s dilemma’. The natural outcome of selfish rational decision making is that both individuals are worse off than if they trusted each other to behave in the way that makes the group better off as a whole. The theory of repeated games demonstrates that, with a sufficiently small discount rate, it may be individually rational to “cooperate”, such that all are better off, rather than “cheat”, which yields short-term individual gains but long-term losses to all. Yet game theory teaches us little about how to reach the cooperative equilibrium. Experimental economics and societal observations can give us some understanding of how society can reach a “better” equilibrium through changing in-

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dividual and group norms (Nyborg et al., 2016). This builds on the recognition that individual wellbeing depends on individual behavior relative to societal norms, and that societal norms can encourage individuals to make choices that either benefit or harm society and the environment as a whole. These critiques of neoclassical economics (with its emphasis on individually “rational” behavior, convex preferences, and a world in which absolutes rather than relatives matter) are deep and damning. There is increasing awareness that neoclassical assumptions – such as the concept of the “perfect market” and the efficiency of the “invisible hand” – are the exceptions rather than the norm. As a result, economists are increasingly recognizing and incorporating concepts of happiness, relative consumption, and utility functions that include the wellbeing of others (examples linked to environmental considerations include Welsch, 2006; and Ferrer-i-Carbonell and Gowdy, 2007). If, for example, social comparison and adaptation based on past experiences matter, then optimal environmental quality is greater than standard neoclassical economics would predict, implying that stricter environmental regulation is needed where relative consumption matters for environmental policy (Welsch, 2009). Some claim that the market fails to manage ecosystem resources because of vagaries of human “nature” such as ignorance, greed, and procrastination (see e.g. Naess, 1989). These are powerful forces indeed, but the main reasons why we have environmental disasters and overuse our resources are market (and policy) failures (see Section 2), as in collective action dilemmas where the incentives for individual action fail to align with societal interests (Ostrom, 1998). The picture of the perfect market as a safe norm and market failures as small exceptions needs to be abandoned. The perfect market is in fact, the strange abstraction (see Nyborg, 2016, for an entertaining illustration). Coordination mechanisms such as social norms may spontaneously evolve and do sometimes partially address the problems (Ostrom, 2000). Public policy can strengthen or create new norms and these can be seen as policy tools that help tip us toward a good equilibrium, for instance by internalizing potential positive network externalities or helping overcome problems of coordination and monitoring in common pool resource use (see further, Nyborg, 2016, 2017). The abstract case for policy instruments to correct for market failures is clear, but often their scale and complexity is hard to grasp and not easy to analyze with the tools of economics alone. There is a need to bring together the natural and physical sciences with economics to enable policy appraisals to take explicit account of the spatial variability and dynamics of the natural environment, and thus the feasibility and cost of implementing environmental policy.

2 POLICY FAILURES Where markets fail, policies should be able to rectify or at least dampen the extent of the failure. Yet many times these market failures are instead exacerbated by bad pol-

2 Policy Failures

icy. Policy failure is not unique to environmental policy and there is a broad literature in political science concerning policy failure in general; see, for instance, McConnell (2015) or Derwort (2016). Fisheries provide many such examples. The absence of property rights leads to a tragedy of open access, and the situation is often compounded by policy failure. When there is overfishing and fishers are impoverished because of small catches, public policy should reduce fishing effort. Instead, politicians typically hand out subsidies intended to “help” fishers. These handouts may benefit fishers in the short run, but typically exacerbate the depletion of fish stocks, resulting in even higher costs and lower earnings. Bad policies thereby exacerbate the market failure, because those subsidies are typically spent on bigger boats and longer nets that speed up stock depletion. For examples, see, for instance Sanchirico and Wilen (2007), Khalilian et al. (2010), and Costello et al. (2016). Conversely, policy failures may also be a consequence of poor governance systems. The State, or the Government, is normally the ultimate designer and enforcer of institutional arrangements, including environmental policies. Both “input” and “output” characteristics of a state-centered political system potentially drive predatory policies and policy failures (Sjöstedt and Jagers, 2014). Input characteristics are defined as the procedures preceding a policy decision, such as the type and level of democracy and citizens’ access to public authorities. Output characteristics refer to the way in which that authority is exercised. On the one hand, lack of highstandard input components increases the risk of both weak policies and eventually poor compliance. On the other hand, low levels of impartiality in the exercise of public authority can generate policy failure, because factors such as corruption and poor government effectiveness negatively affect the public’s compliance with laws and regulations, and ultimately discourage successful collective action outcomes (Diamond, 2007; Rothstein, 2011). To what degree it is primarily input or output characteristics that generate policy failures and undesired outcomes remains an open empirical question. More and more countries are finding it hard to form governments capable of surviving in fragmented parliaments, and at the same time governing effectively (Rodrik, 2017). That market failure should be compounded by policy failure might appear as an evil but unlikely coincidence. Unfortunately, this is not so, because many market failures are related to the power and influence of some market agents. These agents will have power and influence not only in the market place but in the policy arena too. The dominance of perverse policies often reflects lobbying forces, characterized by large and powerful agents, and a political economy that systematically promotes them, particularly in the climate area (Berkes, 2006; Hepburn, 2010; Oreskes and Conway, 2010). The increased concentration of wealth and power of individual persons and companies may threaten the very fabric and functioning of democracy. The descriptions of market and policy failure above should not be taken to imply that the environment is constantly deteriorating everywhere and in all aspects. Many aspects of the environment are deteriorating while others have improved over time. We used to have smog in London that killed thousands and the air is today much

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better. There are famous incidences of dramatic pollution in the past that led to the creation of the EPA and the Clean Air Act and Clean Water Act in the USA and it is often asserted that many of these problems are solved over time. Interestingly though, Smith and Wolloh (2012) find that water quality across water bodies in the USA has actually not improved in the 40 years since the act. Even in those cases where local environmental quality has improved it may sometimes be at the expense of moving pollution elsewhere (symbolized by policies of building higher chimneys). See for instance Henry and Tubiana (2017) for one assessment.

3 THE MENU OF INSTRUMENTS Having identified some causes of ecosystem mismanagement, we turn to the menu of policy instruments available. Traditionally, policy making has occurred at the national level simply because this is where the power to implement and enforce exists. Increasingly, however, the powers and responsibilities for managing environmental resources such as forests and fisheries are being devolved to sub-national levels, in parallel with a recognition and acceptance of supranational policies required for managing global commons. One simplified way of organizing our menu of traditional policy instruments (adapted from Sterner and Coria, 2012) is in the overarching categories of 1) Pricetype; 2) Rights; 3) Quantity type regulation; and 4) Informational/Legal. The list below is by no means perfect or definitive. Many instruments can be classified in several ways. For example, tradeable permits could be considered either property rights or quantity type regulation. 1) Price-type • • • • •

Taxes Subsidy and subsidy-reduction Charges, fees or tariffs Deposit-refund Refunded charge

2) Rights • • • •

Property rights Tradable permits and quotas (Green) Certificates Common property resource management

3) Quantity type regulation • Technological standard • Performance standard • Ban

3 The Menu of Instruments

• Permit • Zoning 4) Information/Legal • • • • •

Public participation Information disclosure Voluntary agreement Liability and financial rules International treaties

3.1 PRICE-TYPE INSTRUMENTS Our first category, price-type instruments, comprises those instruments that are designed to act directly on prices, such as taxes, fees, and subsidies. Whilst many instruments will ultimately affect market prices, what is unique about the instruments in the first group is that they directly add to or subtract from prices. That is, the instruments create incentives to change behavior directly through price, and thus “the market”, in such a manner and degree that will theoretically result in the cost effective allocation of the overall control burden (Hahn and Stavins, 1991). Sometimes the terms “market-based” or “economic” instruments are used to describe these policy instruments that we refer to as “price type”. We prefer to avoid this nomenclature, as the terms “economic” and “market based” can be both too broad (perhaps covering any rule recommended by economic theory) and too fuzzy (for example, covering cap and trade, which is primarily driven by assignment of property rights). The most famous of these price-type instruments is the environmental tax, often referred to as Pigouvian after the economist Pigou. A typical tax is levied by the state, with its proceeds going to the general budget. The purpose of a Pigouvian tax is to “internalize” the external effects. Such a tax has several effects: it makes the good or input which bears the tax more expensive, leading firms and households to economize on its use, whether through the use of substitutes, through changed technology, or changed consumption. The tax makes inputs to production, such as lead, sulfur or carbon emissions, more expensive. This reduces emissions directly, and also makes the final consumption good (comfort, miles traveled, lighting, etc.) more expensive, which affects consumption patterns (and thus again emissions – but this time indirectly). A Pigouvian tax is set equal to marginal damages, such that consumption is changed sufficiently to align private choices with socially optimal choices. The third effect of the tax is that it also gives the public sector revenues that can be used to reduce other taxes or increase public spending. The tax can be shown (under simple and ideal conditions) to be the optimal instrument, allowing other instruments to be benchmarked against it. The advantage that the same instrument serves several purposes (correcting for externalities as well as generating state revenues) has given rise to a whole literature on the so-called “double dividend”. A weak description of double dividend roughly states that an environmental tax has additional benefits. A strong (in fact,

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extreme) description states that environmental taxes have so many advantages that they are beneficial even without a primary environmental problem. It is an advantage if any environmental policy instrument also “happens” to provide tax revenue (of which many states are in chronic need). In general, taxes are hard to raise without distorting the economy away from optimal choices, whilst environmental taxes raise revenues and reduce distortions. The double dividend idea first appeared in the literature well before the 1990s, but it first received growing interest with early writings by Bovenberg (Bovenberg and Mooij, 1994a, 1994b; Bovenberg and de Mooij, 1997; Bovenberg and Goulder, 1996). It is also summarized well in Goulder (1995). Since these early writings on the double dividend, there has been much debate about its validity. The results depend very clearly on the exact question posed and exact baseline examined; see e.g. Jaeger (2011, 2012). A general conclusion across the literature examining the double dividend is that revenue recycling – or the use of environmental tax revenues to finance reductions in preexisting distortionary revenue – is real; see e.g. Goulder et al. (1997); Fullerton (1997). Returning revenues from market-based instruments as lower distortionary taxes rather than as lump sums raises aggregate welfare. The introduction of an environmental tax may cause the tax base to change due to the indirect effects on individual preferences. For example, West and Williams (2007) find that gasoline and leisure are complements. Raising the price of gasoline might therefore increase labor supply (and consumption), causing a fiscal welfare gain in addition to an environmental welfare gain. However, market-based instruments that raise little or no revenue are often favored for reasons of political acceptability to interest groups (Pezzey and Park, 1998). Double dividend enthusiasts sometimes argue that GDP would grow faster, unemployment would go down, and so forth, if only more environmental taxes were levied. In general, while the stronger versions are “too good to be true”, the more careful weak version – that Pigouvian taxes can have some other advantages such as revenue recycling – is quite reasonable. The counterpart of a tax is a subsidy, typically paid for by a nation state, which can be thought of as a negative tax. From an environmental perspective, conceptually, subsidies are used to encourage more of an activity that supports the environment and is under-provided relative to the social optimum. One common example is the provision of subsidies for abatement equipment in industry. Another is payments for ecosystem services (PES) when, for instance, farmers are paid to keep some attributes of nature in a certain state that might variously be beneficial for water fowl or endangered species (Wunder, 2005; Engel et al., 2008). In practice, subsidies tend to encourage the formation of lobbies by beneficiaries that serve to protect and prolong the subsidies (Baylis et al., 2008). In some cases subsidies have existed for so long that their original objective is gone or forgotten and they continue just because the lobbies defend them. This is so common that “subsidy removal” – the removal of perverse subsidies for inputs that are polluting (such as coal) – has come to be considered a policy instrument in its own right (Myers, 1998; Sterner and Köhlin, 2015).

3 The Menu of Instruments

Subsidies have also been used by governments to encourage the development and/or adoption of particular existing or new technologies. The UK government has long subsidized nuclear power, whilst it recently canceled subsidies to support the development of carbon capture and storage. The US subsidies for carbon capture and storage technology have been praised by some, but criticized by others for promoting the continued use of fossil fuels (Conniff, 2018). Governments may also directly invest in, or subsidize, investments into adaptation and building resilience. Taxes and subsidies can also be levied by a municipality or agency, in which case a tax is often referred to as a charge or a fee. It is also possible, and increasingly popular, to design policy instruments that are combinations of fee and subsidy. These can be designed to be (approximately) revenue neutral. An example of this is refunded emission fees, where the proceeds of the pollution charge are not paid into the treasury or general budget but are earmarked for environmental purposes or repaid in some way to the general public, to the polluters, or to the victims of pollution. Section 5.4 gives more details of refunded emission payments in various countries. Other examples include deposit refund systems, tax, and dividend (for example, in the USA) and the Bonus Malus system (for example, for vehicles in France, where buyers of cleaner-than-average cars get a subsidy financed by an extra charge on the more emissions-intensive cars). Such combinations of fees and subsidies can use one instrument to influence behavior, and the second to compensate on aggregate for the cost of the first (see e.g. Section 5.4).

3.2 RIGHTS-BASED POLICIES The second category addresses rights-based policies. Property rights are the most fundamental of all rights-oriented “instruments” or institutions. Much of what is referred to as environmental policies can really be seen as a clarification of property rights – be they private, state, or communal. In the theory of rights-based management, researchers go into considerable depth concerning the formation and characteristics of rights (see for example, Leach et al., 1999, who give examples from India, South Africa, and Ghana). Property rights are often said to be a bundle of different rights, including notably the right to enjoy the use of a resource, but also in many cases the right to sell, lease, inherit or even destroy the property (Schlager and Ostrom, 1992). Thus, questions to be answered might include, for example, whether a land owner also holds rights to subsoil minerals and water, and whether she owns the rights to wildlife, radio frequencies, air, water, ecosystems, and space immediately adjacent to her land. When no one owns a resource (or when no one enforces their rights over a resource), market failures are likely to occur (Hanemann, 2014). Instruments that can proxy for property rights include tradable permits for emissions (for which new markets are typically created), and quotas for fishing or other resource use (which require the creation of markets only when the quotas are transferable). Tradable permits have even been proposed for regulating road transport externalities (Verhoef et al., 1997). Rights may be shared or held in common. There is a broad literature on the management of common pool resources, building on the

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work of Elinor Ostrom and many others, which shows that there are categories of resources which are particularly apt to being managed jointly, under common property regimes, CPR; see Ostrom (1990, 2000, 2005); Cole (2002); and Agrawal (2007). CPR may be a particularly appropriate instrument when, for instance, the economic benefits are sufficiently low and sufficiently variable as to make the costs of enforcing private property (e.g. division and fencing) unwarranted. Payments for Ecosystem Services (PES), as mentioned above, are often voluntary agreements in which those who benefit from ecosystem services pay those who provide the specific services. A water utility company might pay landowners to manage their farmland in the watershed so as to provide clean water downstream (Wunder and Wertz-Kanounnikoff, 2009). The rights-based analogue of this instrument is to create quasi property rights such as offsets or credits for some biodiversity, wildlife, water quality or forest cover attribute. Oil companies or developers can be required to buy a quantity of such credits that corresponds to what their business destroys. This creates a market and thus an opportunity for local communities to sell such credits.

3.3 REGULATION The third category, regulation, forms the core of environmental policy in most countries. Regulations directly control quantities of production or pollution, instead of the indirect approach taken with the price-based instruments. Activities may be banned totally or regulated so that they must be performed in a certain way, at a certain time, or within a certain area (for example, zoning forms the basis for much of city planning). This group of instruments is a lot less monolithic than one might think, and one should be wary of the simplified view that “economic” instruments are more flexible than regulation – often referred to as “Command and Control” (which does somewhat conjure up a Stalinist bureaucracy). Compare, for instance, a technology standard (which prescribes exactly what the firm must do) with a performance standard (which only specifies the environmental result – leaving the choice of technology to producers). The performance standard might be a certain maximum vector of emission coefficients in relation to output. It gives more freedom to entrepreneurs, which is valuable because producers often have information on technology options that a regulator might lack. It also somewhat helps to give the producers incentives to look for improvements themselves, i.e. incentives for research and development above and beyond what may be offered by alternative policies such as permits (see, for example Montero, 2002). However, as long as there is heterogeneity in pollution abatement costs, the standard will fall short of maximizing social welfare (which would require either pollution pricing by taxation or permit trading), see for example, Jung et al. (1996), Goulder et al. (1999). A technology standard, on the other hand, might tell the producer to use a particular kind of equipment or process. Technology standards are easier to inspect and monitor – it is easier to verify whether a firm has installed a piece of equipment than to measure its emissions. This is presumably the reason why technology standards (such as the height of chimneys, the existence of certain

3 The Menu of Instruments

filters, or catalytic converters) are still quite common in legislation in many countries, in the reality of a second-best world. Even so, numerous scandals such as the Volkswagen emissions scandal in 2015, show how sophisticated firms can be in trying to circumvent monitoring and control efforts.

3.4 INFORMATION OR LEGAL-BASED POLICIES The fourth category contains other instruments that act by providing information, adjusting legal liability, or setting rules in other sectors such as the financial sector. Obvious examples include information disclosure rules. We take the approach here that it can be useful to cast the net a little wider and see that there are many rules in, say, banking and insurance that have considerable bearing on the environment or, for instance, the transition to a low-carbon economy. To take but one example, regulation of banking, insurance or even criminal liability clearly has effects on other productive sectors. In some cases, these effects may systematically affect technology choices. In the energy sector, for example, renewable energy can be produced at a much smaller scale than nuclear or other conventional technologies. Households may be a viable producer group but this requires a total overhaul of the requirements for information, the rules concerning liability, the writing of contracts and the way assets are calculated in energy companies, the responsibility for back-up power, the way electricity tariffs are structured or the manner in which creditworthiness is calculated by banks or other credit institutions, and so forth. Banking rules can thereby become instruments for sustainable management. Basel III, for example, is a package of reform measures, developed by the Basel Committee on Banking Supervision, to strengthen the resilience of the banking sector with respect to risk management. The package aims to improve the sector’s ability to adjust to shocks arising from financial and economic stress and to improve governance and risk management.1 Basel III was developed largely in reaction to the magnitude of risks in this sector. However, closer inspection shows it can also have important environmental effects. Because solar energy is more capital intensive (i.e., has a higher share of fixed rather than variable costs) as compared to fossil energy plants, different requirements on bank liquidity that change capital costs relative to labor or raw material costs may reduce the incentives to substitute solar power for fossil-based power production (Lowder, 2012; Gursoy, 2016). The profitability of different types of energy also hinges decisively on rules concerning the social cost of carbon and the discount rates that are applied to projects with public funding. Thus the rules or guidelines for discounting can turn out to be important policy instruments. The development and performance of the insurance sector can be very important for the assessment of damages from climate change and

1 See https://www.bis.org/bcbs/basel3.htm for more information.

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thus indirectly for adaptation and mitigation strategies. Insurance rules can also affect the cost of different energy sources or technologies (Mills, 2005).

3.5 THE PROCESS OF POLICY MAKING AT NATIONAL OR OTHER LEVELS The traditional approach to policy making focuses almost exclusively on instruments at the disposal of national governments, ignoring other agents and levels. Yet nation states are not the only agents to have a policy agenda. Municipalities, subnational regions, firms, NGOs, multi-national entities such as the EU or free-trade areas, and regional groups such as ASEAN or even the United Nations have their own priorities and agendas. The policy instruments they need or can use will often be somewhat different from those at the national decision makers’ disposal. NGOs or consumers’ groups might use labeling, education or information disclosure (Caswell and Mojduszka, 1996). Multinational alliances and the global community will typically have recourse to international treaties. This implies multi-tiered policy making, from the international to national to regional arenas. An added complexity is that some instruments at, say, the local level might be more suitable to combinations with certain instruments at the international level. As an example, a global cap and trade system is hard to combine with other local instruments such as taxes or technology subsidies. On the other hand sometimes companion policies exist and need to be dealt with carefully; see for instance Coria (2009) and Burtraw et al. (2018). The rise of corporate environmentalism (see, for example, Hoffman, 2001) – and its counterpart, the growth and globalization of environmental NGOs – has resulted in a diverse group of non-government actors searching for policy instruments. Large multinational corporations have agendas that may be very relevant for the environment, yet their background may be quite complex. For example, fossil firms may be expected to be less favorable to addressing climate change than firms in renewable energy. However, over time the former may see themselves more as “energy” companies, and with technical progress they can transform their business models (Pulver, 2007). Private sector organizations may be more science-based and more farsighted than many political organizations driven by the electoral cycle. Firms that are high users of fossil fuels, or high polluters, most likely understand that they will be regulated and are mainly interested in affecting the timing, the methods and the international coordination of regulation that is inevitable, and thus they will be strategic. Environmental NGOs, such as WWF, Greenpeace, EDF or the Nature Conservancy, have millions of members and large professional staffs and are quite influential, particularly in the US. The process of policy making, with its risks of policy capture, distributional and equity effects of instruments or the opportunity created for political corruption has been discussed in the literature for some time (see Olson, 1965; Stigler, 1971; Posner, 1974; Peltzman, 1976; and Becker, 1983). Policy capture reflects the tendency of powerful groups to steer policy away from the social optimum. A distributional question in environmental policy is whether the poorest nations or people will

4 The Selection of Instruments

be losers or gainers. Corruption includes misdirection of resources that were intended for the public good. Just as behavioral economics looks at individual behavior, political economy studies how political institutions adopt, implement, and enforce policies, including environmental policies. Keohane et al. (1998), for example, presents an explanation of why the environmental policy instruments selected in the United States for decades have diverged strikingly from the recommendations of normative economic theory. Often when policies are badly needed to counteract the dominance of strong economic players, we see there is a risk that these same players will be able to corrupt the policy process in their favor. Sometimes this implies that policy failure is added on top of market failure. Many of the growing environmental problems are complex, trans-boundary global issues, which are likely to require new approaches that do not fit in the traditional policy instrument columns above. New environmental policies are likely to be needed to initiate cultural transformations, new lifestyles or consumption habits, technological revolutions and overarching sustainability policies. Such policies will most likely need to reach across traditional boundaries, regarding the creation of new institutions or population policy to achieve an optimal or sustainable scale of the economy. Some observers call for stopping growth or engaging in “de-growth”. Though literally degrowth is the opposite of growth, a decrease in production, the term is often intended not as an economic concept, but signifies more of a social movement that calls for the downscaling of production and consumption in higher-income countries (Demaria et al., 2013). From an economist’s perspective, if growth is sensibly defined to mean an increase in that which is desirable, which includes taking into account ecological restrictions, then growth should be consistent with aspirations to improve human wellbeing, such as through improving health or education services, or access to clean water, without threatening ecological systems. The relevant problem then becomes defining what sustainable growth is and to find the policy instruments that promote that kind of growth while minimizing growth of sectors or technologies that have negative repercussions.

4 THE SELECTION OF INSTRUMENTS Having looked at market failures and at the menu of policies, we turn now to policy selection. To derive theoretical results in economics, we are generally obliged to simplify and abstract from numerous real-world circumstances in order to focus on one particular aspect of the market failure. The optimal choice of policy instrument is likely to be affected by market structures, existing market failures, transactions costs (see the review article by Krutilla and Krause, 2011), asymmetric information, considerations of equity, and preferred trajectories over time. Some of these aspects have been the object of considerable analytic effort and we are thus able to repeat some clear-cut results that are central to the profession (see Stavins, 1995, 2003; and Sterner and Coria, 2012, for a fuller treatment).

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4.1 EFFICIENCY At the heart of economic theory on policy selection is a consideration of economic efficiency. We draw here upon some of the most basic lessons from the functioning of the overall economy. Competition between different producers in a market tends to produce an outcome that is “economic” in the direct sense of the word: it saves resources. The intuition behind this is that competition will spur effort and innovation (both technological and organizational). This will reward the best producers, which will tend to be favored by competition. Adam Smith praised the competitive market precisely because it is the profit motive and not altruism that makes sure we get the best bread from the collective of bakers (Smith, 1776). In a similar vein, environmental economists like to point out that we could get a cleaner environment at a much lower cost if we used general instruments that build on market principles rather than clumsy regulation. The subject of economic efficiency in environmental instrument choice deserves careful consideration. Regulations are often less flexible than would be optimal. For example, if a total reduction in pollution is required, regulators might require equal reductions from each source of pollution, rather than taking into account that abatement costs often are heterogeneous. That is, different producers will have different marginal costs of achieving the same reduction in pollution in which case, the usual market analogy applies. Cleanup costs could be reduced by allowing the best performers in the market to do more of the “heavy lifting”. The greater the heterogeneity in costs, the greater the saving from exploiting this difference. For example, if abatement in one firm is half as costly as in the other, a society can save around 10% of total costs of cleanup by allowing the firms to distribute the abatement cost efficiently than if they were constrained to do the same amount each. If one firm can undertake abatement at one-tenth of the cost of the other (i.e. 90% cheaper), then savings of around two-thirds of the overall costs can be achieved through market allocation (for details see Sterner and Coria, 2012, Table 9.1, p. 146). Next, we need to consider what types of instrument will lead to this efficient market allocation. A key requirement is the existence of a price on the pollutant. This could be achieved by using a subsidy, a tax or a physical regulation such as a certain abatement requirement, so long as this requirement is tradable. A tax will incentivize those firms with lower abatement costs to do a larger amount of abatement. A regulation provides a similar incentive – if trading of permits is allowed – because then the company where abatement is cheaper will offer to do the abatement, selling its “right” to pollute to the plants where such abatement is more expensive, and resulting in the same total abatement but at lower cost. Cost heterogeneity is not the only factor. The degree of competition is also important. In the extreme case of a single monopolist, the cost of abatement will be the same for any given level of abatement irrespective of instrument used. However, the performance of taxes (or other price type instruments in first group, above) in the face of monopoly or restricted competition is often quite complex. One reason for this is that monopolists already tend to under-produce (not pollution but products). A tax will tend to aggravate this problem. If we have a polluting monopolist, we are in fact

4 The Selection of Instruments

faced with two market failures: the monopoly and the externality. This will typically require two instruments: one to increase competition and one to reduce pollution. The case of a monopoly is relatively simple, but that of duopolies or other market structures can be analytically very complex to deal with (Simpson, 1995). Studying an interconnected web of countries with trade complicates things further. Whether standards or taxes dominate has been shown theoretically to depend on, inter alia, whether trade is modeled as a Stackelberg or Cournot equilibrium (Ulph, 1992). More generally, when there is imperfect competition in global markets, pollution taxes can lead to “pollution shifting” and “rent capture” (Kennedy, 1994), and governments may relax or strengthen environmental standards, depending on specific market structures (Barrett, 1994). Environmental regulations in large countries will affect world prices of traded commodities, suggesting the need for second best environmental taxes (Krutilla, 1991). Subsidies and taxes may look similar in the simplest of models. Both raise the relative cost of pollution and lower that of abatement. If production is clean, the firm either avoids paying a tax or it receives a subsidy. At the margin, the last unit of pollution will cost the firm $x either way – either as a tax or a subsidy lost. In a more complete analysis, however, the tax and subsidy are clearly not identical. A company that is on the very verge of bankruptcy might be pushed over the edge by an environmental tax scheme but it might be saved by a cleanup subsidy scheme. We can (again under certain simplifying assumptions) show that the correct and optimal instrument is the tax, and not the subsidy. The final product price should include the shadow rent on scarce environmental resources and companies that do not bear their total costs should go bankrupt. But of course these arguments are hard to make in the face of angry lobbyists or politicians who are worried about job loss. We will come back to political feasibility and similar arguments later.

4.2 INFORMATION ASYMMETRIES AND UNCERTAINTY Another area that restricts instrument choice is the character and availability of information flows and the structure of incentives. Typically high levels of uncertainly exist about the environmental damages themselves. For example, even when a pollutant is known to cause adverse health or environmental damage, the exact extent of that damage may be unknown. Though climate change is known to be a significant global challenge, substantial uncertainty surrounds its potential economic damages. Toman and Shogren (2010) provide a broad assessment of uncertainty surrounding costs and benefits with respect to climate change and the relevance for policy. See Maler and Fisher (2005) and Aldy and Viscusi (2014) for a discussion of risk and uncertainty in the environmental realm. Here, we focus on uncertainties specific to policy-making: 1) asymmetries between local agents and central authorities; 2) uncertainties/information asymmetries regarding abatement costs; and 3) uncertainties that arise when pollution cannot be readily measured or monitored. Typically, in an economy, the agents most directly involved have better information than the central authorities when it comes to local costs of technology and

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resources. The dilemma is that those best informed may have an incentive that is not aligned with social preferences. It is important that an instrument mobilizes these agents, and indeed the advantage of decentralization lies in empowering local agents to use their knowledge and giving them incentives to search for better means of production.2 There is a huge literature that analyzes the often complex instruments that policymakers need to design to entice polluters to reveal information to them through their choices of pollution management contracts (or water, service provision, etc. contracts). See, for instance, Laffont and Tirole (1993), Hoel (1998). Uncertainty about abatement costs is the epitome of a well-studied special condition in environmental economics. Weitzman (1974) shows that, for a special type of uncertainty concerning abatement costs, both quantity-type regulations and taxes may lead to certain errors, because the abatement achieved will typically not be optimal from the viewpoint of the ex post knowledge about costs. However, the expected cost implied by the deviation will be different for standards versus taxes. If we know the slopes of the costs and damage functions, then it can be shown that price-type policies are preferred on social welfare grounds if the abatement costs are steeper, and quantity-type regulation is preferred if the damage costs are steeper. This is a result that has sparked a good deal of further research that looks at more complicated or realistic cases (e.g. Pizer, 2002), for example, if there is a correlation between benefits and costs (Stavins, 1996). A particular kind of uncertainty occurs when pollution cannot be readily measured or monitored, for instance, Non-Point Source Pollution (NPSP). Examples are found in run-off of nutrients such as phosphorous and nitrogen in agriculture (see Carpenter et al., 1998, for one such example in the literature). Government authorities may observe aggregate pollution in, for instance, a body of water, but may not have the capability of measuring and assigning individual responsibilities to individual farmers. This again has spurred a large literature looking at different situations. For example Xepapadeas (1992) addresses policy instruments for dealing with NPSP when there is pollutant accumulation, thus requiring a dynamic framework. Cabe and Herriges (1992) use a Bayesian approach, addressing asymmetric information and transport costs. One line of thinking builds on the assumption that, though the central authorities are incapable of monitoring, it may be possible for the decentralized agents themselves (the farmers) to monitor each other. Sometimes it may be possible to create a system where the local agents have both the incentive and the capability to jointly manage a common pool resource (Ostrom, 1990; Cason and Gangadharan, 2013).

2 These arguments do generally speak in favor of using a price mechanism but it is important to recognize that, for most environmental management, the bread and butter of environmental protection agencies is often regulation. It is worth considering why this is so, but the fact remains that regulations are frequently used and some regulations are much better than others from the viewpoint of allowing agents a greater freedom of choice, as was discussed in Section 2 concerning the difference between technology and performance standards.

4 The Selection of Instruments

4.3 INTERTEMPORAL EFFICIENCY Dynamic efficiency – that is, efficiency of resource use over time – is a particular area of study often related to resource scarcity (Nordhaus, 1974). A given resource may be fixed or it may only grow at a certain rate under certain conditions. The body of work known as natural resource management deals with how to allocate use over time. At first glance, it may seem impossible to allocate a finite resource over infinite time. Conceptually, however, it is quite easy. If we use only a fraction of the remaining resource each year, it can “last” for centuries on the condition that we use less (in absolute terms) each year. This might occur in parallel with gradually improving technology or successive improvements in substitute goods or inputs. If so, one can also show that such a resource allocation will typically be associated with exponentially rising scarcity rent, so that the price of the resource rises, encouraging successively more frugal consumption each year or the use of more effective production technologies. Hotelling (1931) showed that such a regime with consecutively rising scarcity rents is to be expected (under certain ideal assumptions) if there are secure property rights to the resource in question. (Variations may be due to all kinds of different assumptions with respect to market structure, technology and so forth.) There are various ways to prove or illustrate the Hotelling principle. The relevant conditions emanate from mathematical optimization but the most intuitive economic explanation comes from the so-called arbitrage condition.3 The modern field of intertemporal resource and environmental economics was pioneered by a series of articles by Geoffrey Heal and Partha Dasgupta that is nicely summarized in their seminal book, Dasgupta and Heal (1979). In policy-making, Hotelling insights apply to the intertemporal performance of regulations as well as cap-and-trade programs with banking (see e.g. Rubin, 1996; Wigley et al., 1996; Kling and Rubin, 1997). A crucial issue for policy making is how to deal with those resources that lack secure, or indeed any, ownership rights – such as the atmosphere. In an analogy with Hotelling, we might expect that there should be a policy instrument such as a scarcity rent on carbon and other greenhouse gases in the atmosphere and that this scarcity rent should rise analogously with a Hotelling rent. Interestingly, there is a large literature analyzing what happens in other cases. The Green Paradox literature (Jensen et al., 2015; Sinn, 2015) shows that perverse incentives can be created. If, for instance, the policymaker announces that in the year 2030 there will be a high and rapidly rising carbon tax, she may inadvertently be creating an incentive to produce and burn as much coal as possible today (before this policy depresses the rents to be earned).

3 Simply stated, an investor who invests X $ in a business, some stock, foreign exchange etc., would

normally expect these assets to have a total value (including dividends, and correcting for uncertainty) in the future equal to X(1 + r)t . If one asset is not expected to rise in value so that its future value is equal to its current value times (1 + r)t then it must fall in value immediately otherwise no one would buy it. Thus the spot price (or actually scarcity rent) of that asset falls immediately and when it has found its correct value then it will again be expected to rise exponentially.

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When resources are biological and their growth dependent on temporal, spatial and ecological constraints, we refer to the area as natural resource economics (see textbooks by Fisher, 1981; Conrad and Clark, 1987; Hanley et al., 1997; or Conrad, 1999; and Brown, 2000, on the characteristics and management of renewable natural resources). When multiple ecosystem services related to the natural resources are taken into account, this area of research becomes particularly rich and interesting, with variations or interdependencies between growth rates of various species, possibly featuring nonlinearities, thresholds and complex tradeoffs between different sustainability goals4 (Dasgupta, 1983; Brock and Xepapadeas, 2010).

4.4 SPATIAL EFFICIENCY Just as the benefits of environmental goods and the costs of negative externalities are not spread evenly across time, they are typically not spread evenly across space. This spatial heterogeneity may be driven not just by a particular environmental good or a particular externality, but also by the location of people who use an environmental good or amenity. In either case, policies that are applied uniformly across space may be suboptimal, and spatial targeting may provide better outcomes (Sanchirico and Wilen, 2005; Albers et al., 2017). Just as we need to optimize resource use over time, we also need to optimize the spatial allocation of resource use. As an example, at the most basic level, if a remote area of forest is far enough from human populations that it is protected by distance alone, it would be inefficient to allocate scarce enforcement budget to that area. Conversely, areas of forest very close to human populations may be very expensive to protect and thus it might again be inefficient to enforce there, but for very different reasons (Albers, 2010). Thus, one might not be surprised to see zoning of protected areas and forests, particularly in lower-income countries where people are highly dependent on the resource base, in which more distant areas do not need to be protected; very close areas are too expensive to protect; and so protection is concentrated at intermediate distances from villages or towns, with a possible buffer zone adjacent to the community (Robinson et al., 2013). As another example, payments for ecosystem services can often times be more effective when spatial aspects (the locations of costs, benefits, and those affected) are taken into account. This includes environmental service provision, risk of environmental service loss (e.g. through deforestation), and the cost of participation for the landowners (Wünscher et al., 2008). Similar arguments apply to the management of fisheries and marine protected areas, with the additional spatial element that most fish species move across institutional boundaries. Similarly, “Marine Spatial Planning” requires “appropriate planning activity at different spatial scales” (Gilliland and Laffoley, 2008, p. 787). In the US and Canada, policies that have been proposed to encourage soil carbon sequestration have been demonstrated to 4 As an example, with respect to forests, optimal rotations tend to be different than the Faustmann rotation age when carbon sequestration and other ecological, non-market ecosystem services are taken into account.

4 The Selection of Instruments

be inefficient because they do not take into account spatial heterogeneity with respect to bio-physical and economic conditions (Antle et al., 2003). Yet measuring site specific differences introduces additional costs (Wu and Boggess, 1999; Antle et al., 2003). GIS-based spatial analysis is enabling improved spatial targeting for policy interventions such as agri-environmental schemes (van der Horst, 2007), and may make spatially targeted policies more cost effective. Biodiversity offsets are an explicitly spatial rights-based instrument (see Section 3 above), which allow developers to build at locations where biodiversity or habitat more generally will be negatively affected, so long as the ecological damage can be offset elsewhere, resulting in “no net loss” or a “net gain” (McKenney and Kiesecker, 2010). Biodiversity offset schemes have the potential to encourage developers to build in a different location, or in a different way, rather than undertake the offset. Thus, offsets can complement other regulatory arrangements such as standards or pricing approaches (taxes and subsidies), and can be considered closely related to tradable permit instruments. However, offsets can only be employed where the habitat or biodiversity being considered is spatially substitutable. As such, “critical capital” ecosystems that cannot be substituted could not be included. Examples of biodiversity offsets include the Wetland Mitigation Banking scheme, in the US, and many in South Africa that fall under the Western Cape Provincial Guidelines on Biodiversity offsets. Legislation is required to set out roles and responsibilities of developers, regulators, and groups representing third parties (Groom et al., 2014). Biodiversity offsets can be controversial due to the idea that biodiversity and habitats and locations in one area can be substituted elsewhere, and thus such ecosystem services are fungible. Habitats may be reduced to overly simplistic metrics to enable spatial substitutability, and the local benefits that are provided by these habitats for nearby communities may not be fully recognized (Bateman et al., 2013).

4.5 PRACTICAL AND POLITICAL ASPECTS In many practical applications, instruments such as individual pollution limits or pollution taxes are hard to use due to lack of adequate information, and other instruments must be designed. Often we have a multiplicity of these conditions at the same time and the complexity may be such as to defy rigorous analysis, turning instrument selection and design into something of an art. Considerations of lobbying and power inevitably lead one to think of political economy and of political process. The terminology of instrument choice may then be perceived as a social engineering approach. A complementary approach is to think of designing a process in which parties (be they polluters and victims of pollution or be they countries) negotiate a policy and the appropriate instruments of implementation and enforcement. Climate policies, for example, can either be discussed in terms of designing tax or cap-and-trade systems on the one hand, or, on the other hand, the design of international climate negotiations. In either case distributional problems are paramount, either within a country or among countries. Partly, the appropriate instruments and processes depend on the characteristics of the problem at hand.

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The process of political decision making in the real world tends to include difficult and sometimes not very transparent trade-offs between various interest groups. Environmental interests often argue for the “polluter pays” principle, which holds that polluters should not be able to pass through the cost of abatement to others. Conversely, existing polluters lobby to be “grandfathered in” and allowed to continue as before (Markussen and Svendsen, 2005; Lockie, 2013). Woerdman et al. (2008) address efficiency and equity aspects of each approach. Another complication is that the design of policy instruments should also take into account ecological realities very far away and on very different systems than those they originate from, due to complex natural transport and transformation processes. This is likely to make it more difficult to apply good regulation when polluters and polluted never physically meet. In such circumstances, negotiations between the different parties could be more difficult as well. In addition, some ecosystem processes tend to unfold slowly and delayed effects of actions taken in the past may suddenly change the nature of the problem. Using an approach that from the start integrates biosphere and social characteristics should improve the chance of success of a policy response simply by being able to account for more contingencies than when only taking a social perspective (Levin et al., 2013). In light of the catastrophic harm that is likely if planetary boundaries are transgressed, the “precautionary principle”5 argues that great efforts are necessary to minimize that risk. When processes are complex informationally, spatially, and socially because they involve many stakeholders, there is a risk that analysts are invited in only after the main policy choices have been selected. Then economic analysis is only used to compare a small number of given scenarios, for example, options for a new road, instead of being asked to compare a whole menu of solutions to an urban traffic problem including congestion pricing rather than roadbuilding. This is of course quite unfortunate. The discussion above on policy instruments is focused on instruments needed to reach an ideal state, to maximize welfare under market failures. It presupposes strong powers for the decision makers. In reality there are limits to political influence. Resistance to government is rife – and increasing in many parts of the world. There is furthermore often a lack of institutions – an absence of governance at the appropriate (local) or global levels. Finally, it is naïve to assume that governments simply seek to maximize welfare. They have their own interests, especially the incentive to be re-elected (or survive revolutionary attempts). 5 The precautionary principle, which started off as an environmental concept to deal with “increasingly

unpredictable, uncertain, and unquantifiable but possibly catastrophic risks”, through pre-damage rather than post-damage control, has morphed into a concept that incorporates an ethical stance (Comest, 2005: p. 7). It has been defined as follows: “When human activities may lead to morally unacceptable harm that is scientifically plausible but uncertain, actions shall be taken to avoid or diminish that harm” (www.precautionaryprinciple.eu/). See Gollier et al. (2000, p. 245) for an economic interpretation of the Precautionary Principle, which concludes “that more scientific uncertainty as to the distribution of a future risk – that is, a larger variability of beliefs – should induce Society to take stronger prevention measures today.”

4 The Selection of Instruments

Instead of assuming that governments strive to maximize social welfare and need advice on how best to do so, we might take an alternative worldview, seeing governments either as representatives for various economic interests or as autonomous agents maximizing their own utility. This may involve promoting the interests of powerful lobbies or it may be conceived of as selling “services” to such interests in return for support or simply money to be used to win elections. Either way, such models open up a much more active role for lobbyists and much larger risks of the capture of political processes by special interests.

4.6 NORMATIVE PRINCIPLES, DISTRIBUTIONAL ASPECTS, AND ENVIRONMENTAL JUSTICE Both environmental damage and associated abatement costs may differentially affect the rich and the poor or other significant groups in society, with equity implications across space and time. Whether they do so is often a very sensitive and hotly debated issue. Attention is often focused on the important cases in which the poor suffer the most from pollution. This is sometimes even used as an argument for more environmental policies. However, we can find empirical examples with different incidences of the distribution of the burden. Many policy instruments are hard to use because they have distributional effects that may have adverse effects on various segments of the population that command political influence (Barbier, 2011; Ward and Cao, 2012). Indeed, the same resource problem might be solved with different instruments, such as taxes, cap and trade, subsidies or regulations, with each typically having a different distributional effect. For example, different companies, social groups or countries will bear different proportions of the costs and benefits. Moreover, many of the agents of an economy are acutely aware of such distributional effects and thus real policy making is not a neutral technocratic choice of “optimal” instruments, but often better portrayed as a struggle between different economic forces, each of which is lobbying for some instrument or process they believe will be advantageous. Thus, issues of fairness and political process are crucial (Carlsson et al., 2013). This is particularly so when it comes to sharing risks and uncertainties, where the poor typically are more risk averse. That the poor will bear an unfair share of the costs of abatement has also been used as an argument against clean-up or abatement efforts. The Clean Air Act in the US, for example, was found to be regressive, because lower-income households allocate a larger share of total spending to energy, such as electricity and gasoline, that depends on fossil fuels (Gianessi et al., 1979; Fullerton, 2008). However, often there is equally a problem when a proposed instrument threatens the rich and powerful, who are effective at lobbying the political process. Some instruments are specifically designed to appease special interests by allocating favorable exceptions or emission permits to them. The truth is of course much more nuanced and hard to pin down, and it is useful to step back and consider who holds the relevant rights. It is further vital to consider how

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the presence of inequality at different scales (regions, countries, rural/urban, within urban areas, etc.) affects the way that policy instruments should be structured. Factors to be considered might include non-uniform/discriminatory pricing (taxes/subsidies); and different mechanisms of allocation of property rights, regulations, etc. Rights to nature may – much like land or water rights – be allocated to society, to the victims of pollution, or to current polluters (“grandfathering”). Property rights are essential for the definition of all other policy instruments (see Section 3). They appear to have developed in quite different ways in different countries. There are countries (such as the USA) where private property rights are very strong. With land rights may come the rights to minerals below the ground, hunting and fishing rights, rights to adjacent water bodies, and rights to build on the land with few or no restrictions. For a historical perspective on below the ground rights in the USA, see Libecap (1978). For a broader discussion of “3D” property rights, see Kitsakis and Dimopoulou (2014). There are other countries, including many in Europe and many lower-income countries, where the state keeps unto itself many of these rights (Heltberg, 2002). Historically, it seems that property rights developed first for immediate belongings and then for land. Water rights have a separate history but are sometimes related to land rights. The rights to minerals, to emit gases into the atmosphere, or to broadcast radio waves at different frequencies are examples of rights that have evolved over time as society has perceived a scarcity or a congestion that required such definitions. This process can be likened to the historic process by which land was privatized. In feudal societies like England or France, there was a process by which common lands were privatized that is often referred to as enclosure, because in England private land was often “enclosed” by fences or hedges (Wordie, 1983, provides a detailed discussion of enclosures in England). Different concepts of pollution rights can be seen as a counterpart corresponding to the distinction between different instruments such as taxes, subsidies and revenue neutral tax-subsidy or refunded tax schemes. If a polluting business is seen to have the rights to nature, it can be allocated property rights to land, to water or to pollute the air. The price-type instrument counterpart would be a subsidy: if a business owns the rights, then society can still require a cleaner environment – it just has to pay for it. On the other hand, if the rights reside with the state or the population of a country, then business must buy such rights. The corresponding price-type instrument is a tax,6 which means that firms can pollute – but they must pay for every unit of pollution. The quantity-type analogue is a tradeable permit scheme with auctioned permits, and, again, the cost is incurred by the firm. Table 1 provides a different view of how policy instruments can be categorized by their assumed property rights. In Column 1, polluters have absolute rights to the environment, while in Column 4 society (interpreted perhaps as a representative of the victims of pollution) has these rights. Columns 2–3 are intermediate. The table’s 6 Coase (1960) makes an important point when he says that the rights may be allocated either way – optimal

allocation can still be feasible. However, if the rights are unclear, and transactions costs sufficiently high, then it will be hard to reach an optimal allocation.

5 Selected Examples

Table 1 Policy instruments and property rights Instrument

Ownership rights to the environment Polluter Mixed Victim or society (partial) (polluter pays principle) (1) (2) (3) (4) Public cleanup CAC, VA, TEP TEP, partly TEP, auctioned (free) auctioned Subsidies REP, Partly REP BM, Tax, DRS taxsubsidy TD Polluter (absolute)

Quantity-type Price-type

Notes: CAC = control-and-command policy; VA = voluntary agreement; TEPs = tradable emissions permits; REPs = refundable emissions permits; DRS = deposit–refund scheme; BM = bonus malus; TD = tax and dividend.

first row is for price-type instruments while the second is quantity-type. This helps us disentangle a confusion that is quite commonly made between “cap and trade”, which is a quantity-type instrument and often thought of as more “business-friendly”; and tax, which is a price-type instrument that generates revenues for the state and implicitly gives the state rights over the environment. However, it should be clear that the choice of a price vs quantity instrument can be made irrespective of the desired distributional effect. A price instrument need not be a tax. If society considers the polluters to have the rights to the environment, or if for political or pragmatic reasons a distributional effect that benefits business is desired, then subsidies can be used. If rights are intermediate, revenue neutral instruments such as Bonus Malus, refunded emission payments, or tax and dividend can be used (see Section 5.4). Similarly, with quantity type instruments, the rights can be auctioned or allocated for free depending on the balance of rights or of power and income distribution effect desired. Some instruments like the voluntary agreement seek to achieve a reasonable allocation without open coercion or payments although there is often an implicit threat of other instruments, see Carraro and Lévêque (2013).

5 SELECTED EXAMPLES Any particular collection of examples will always be in some sense arbitrary. We choose to start with a tax because it is often thought of as the prime example of an environmental policy instrument. Because climate change is at the same time such a dominant environmental problem, we start with carbon taxes (Pearce, 1991). We turn then to fuel taxes, which can be seen as a sectoral carbon tax. In Section 5.3, we look at cap and trade schemes as an alternative mechanism for pricing carbon and in Section 5.4 we look at the refunding of environmental fees. Section 5.5 looks at regulation versus pricing, taking industrial solvents as an example. In Section 5.6, we turn to the influence of culture on behavior, and in particular tobacco use and meat consumption.

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5.1 TAXING CARBON Despite being the poster child of environmental economics theory and despite some attractive properties, carbon taxes are not nearly as common a policy instrument as might be expected. To date, significant carbon taxes have been instituted mainly in a few Northern European countries and in the Canadian province of British Columbia.7 Recently, France – which has a long history of trying to implement carbon taxes unsuccessfully – has emerged as a very interesting example with a strong focus on carbon taxation. In 2018, the French tax reached €45/ton CO2 and by 2022 it is scheduled to reach €86, which will bring it quite close to the tax-level in Sweden. The reasons why it has been so hard to get significant carbon taxation in other countries are not clear, though it is possible that lobbying plays an important role, particularly in countries that have fossil industries of their own. What is clear, however, is that a carbon tax, unlike a narrower sectoral regulation, attracts more hostile lobbying from fossil fuel interests, which have a lot to lose (Bjertnæs and Fæhn, 2008; Blackman et al., 2010; Sterner and Coria, 2012). It is likely that access to good examples of successfully implemented carbon taxes is important – perhaps the recent example in France, a major European country, will help break some of the resistance. To try to cast more light on how a carbon tax can function, this section describes some of the experiences of the CO2 tax introduced in Sweden in 1991. The Swedish experience is of interest because it is by far the highest level of taxation (more than twice as high as the neighboring countries Norway and Finland that have also had high carbon taxes for a number of years) and has been applied broadly and seemingly painlessly in a modern economy; see Hammar et al. (2013). In 2017, Sweden’s general CO2 tax corresponded to €117 per ton CO2 ,8 which can be compared with current tradable permit prices within the EU emissions trading scheme (ETS) around €10 per ton. The development of CO2 taxation and the use of revenues are determined in accordance with general Swedish national budgetary rules. A central element is not to earmark tax revenues for particular purposes; instead, the spending of tax revenues is decided in the normal budget process. Throughout the existence of the CO2 tax, policymakers have aimed at ensuring a balanced tax design. The tax was introduced in a step-by-step manner starting in 1991 and undesired distributional consequences on low-income households have been addressed by adjustment of the come tax rules. Sweden has applied quite high taxation to energy carriers for a long time. Up until the 1970s, the primary reason for taxation was to raise public revenues; taxation consisted of a single energy tax. In 1991, there was a major tax reform and Sweden complemented the energy tax with specific CO2 and sulfur taxes, because environmental policy was becoming increasingly important in the political agenda. The CO2 7 We highlight significant cases of high carbon taxes here. In addition there are many interesting examples of carbon taxes (generally at lower levels) in other countries around the globe as well. For a recent update of all existing carbon taxes worldwide, see the World Bank’s annual ‘State and Trends of Carbon Pricing’ reports. 8 1130 SEK per ton.

5 Selected Examples

tax was introduced on all major fossil fuels at rates equivalent to €27 per ton CO2 , in addition to a separate energy tax. As a result, although the energy tax was reduced, the combined energy and CO2 tax rose, which meant that fuel prices increased, and all fuels were taxed at very high levels compared to other countries. The introduction of this carbon tax was part of a major tax reform that included dramatically lower marginal income taxes on capital and labor, the elimination of various tax shelters, base broadening of the value-added tax, and major reform to property, wealth, inheritance, and corporate taxes. The political opportunity to introduce this rather unique tax consisted of the confluence of two separate political processes. On the one hand, there was demand for a drastic reduction in marginal income tax rates, which had reached very high levels (in some cases around 90%). The highest marginal tax rate was reduced to 50% (later it rose somewhat again but only moderately compared to the historic levels). At the same time, there was an increasing interest in environmental issues, politically and throughout Swedish society. The CO2 tax was thus introduced at a moment when there was a need to fill a gap created by reduced taxes on other factors of production. The tax yield from changes in energy-related taxation amounted to roughly one percent of GDP in 1991, of which introduction of value-added tax on energy consumption accounted for the major part. Importantly, the introduction of this new tax was not associated with an overall increase in the burden of taxation. On the contrary, the overall tax level in society, as measured by the tax share of GDP, although still high, fell substantially (by about ten percentage points) during the period when the carbon tax was introduced and raised. In other words, the effect of reducing other taxes was more important and the carbon tax thus helped finance other tax cuts – though only partially. The CO2 tax rates have been significantly increased over the years, with the purpose of achieving cost effective emissions reductions. The tax changes have, however, been implemented stepwise so that households and companies have had time to adapt. Typically, tax increases for companies and households in the energy and environmental areas in Sweden have been combined with general tax relief in other areas in order to avoid increases in the overall level of taxation, address undesirable distributional consequences, and stimulate job growth. Such a combination of measures has been the result of a desire to design the tax scheme in a way that ensures a sufficient balance between different policy considerations. Over the years, there has been a general consensus among the different political parties in Sweden to focus on the CO2 tax as the primary instrument to achieve greenhouse gas emission reductions. Sweden has had governments that were relatively left-wing and right-wing, but this has not led to any major deviations from the chosen road forward in this regard. Also, all major Government proposals are based on in-depth analysis and review by independent committees, experts and stakeholders. The advantage of a CO2 tax is that it is a market-based instrument, which enables households and firms to choose measures to reduce fossil fuel consumption – and thus greenhouse gas emissions – that are best suited for their specific situation. However, the effect of the CO2 tax was also complemented by aid schemes for limited

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time periods, to ensure that real options are available for households and firms. In Sweden, such schemes have included support for investments in energy savings in buildings, fossil-free electricity production, infrastructure projects for public transport, and urban district heating systems. Sweden is a fairly typical modern market economy so we think its experience of carbon taxation should generalize to other countries. It is worth reflecting however on whether there are any special features that helped make it possible to introduce such taxes. One striking factor is a long history of consensus politics and total absence of any fossil fuel industry – but on the other hand good access to hydropower and bioenergy resources. One factor does however need to be highlighted that applies to all “small open economies”: trade is a very high share of GDP (around 45%) and the economy is dominated by a small number of very large firms. There is therefore a well-founded fear of loss of jobs and of carbon leakage (when national policies targeting externalities locally lead to an increase in demand or movement of production elsewhere). For example, global net emissions could stay the same or increase if production moves from a country that is taxing carbon at a high rate to a country that is taxing carbon at a lower rate or not at all. To avoid these risks and make the policy more palatable to industry, Sweden only applies the full tax rate of the carbon tax to those sectors that are somewhat immobile or protected from full international competition. The idea is that when trading partners face the same tax levels, then Sweden will impose the full tax on sectors exposed to competition. Large industrial use of energy has therefore, ever since the introduction of the CO2 tax, faced a lower tax level (which has varied from 20 to 50% of the base level). Furthermore, most of industry is subject to the Europe-wide carbon emissions trading scheme. Initially, firms were subject to both carbon tax and the obligation to participate in the EU ETS. However, in 2011, the CO2 tax for industrial installations within the EU ETS was abolished, because companies complained of double taxation and because national policies for emissions subject to a cap at the EU level only result in emissions being moved within the ETS without affecting total emissions.

5.1.1 Effects of CO2 Taxation It is not easy from relatively limited experience to draw firm conclusions about effects – such a task really requires solid research. Typically, the research that does exist has been carried out for homogeneous industries9 rather than for the much more messy and diverse experience of a whole nation. Where research has been undertaken on the macro level of the economy, it is generally shown that carbon taxes do lead to reduced emissions (see Lin and Li, 2011; or Somanathan et al., 2014). As a simple illustration, Fig. 1 shows how the Swedish economy decarbonized much faster than the US, OECD or World averages in the period 1970–2014 in spite of starting at an unusually low level. Other countries with carbon taxes (although not as high as the Swedish taxes, such as the UK, Norway, and Denmark) also tend to have lower emission levels. 9 In Section 5.2 we review research from the transport fuel sector where there is more experience.

5 Selected Examples

FIGURE 1 CO2 emissions per GDP (Kg CO2 emissions per 2010 US dollars of GDP). Source: Own calculations based on emissions and GDP data from the World Development Indicators.

There is no strong theoretical reason to expect that carbon taxes or similar instruments would have effects on unemployment, deficits, growth or other macro variables. Nor would such effects be easy to identify and separate from other concurrent events in the economy. However, simplistic notions that carbon taxes are very damaging are quite common but they have little support since the economies like Sweden with high carbon taxes are in fact not performing worse, but if anything better, than other European countries. Turning to the microeconomic level of household-level and firm-level decisions, the fall in carbon intensity is particularly noticeable in the sectors where the full tax is applied. This is the case for example in the residential and commercial sectors, where Sweden, in spite of (or perhaps partly because of) a harsh climate and high energy taxation, uses no more energy for heating than countries farther south in Europe. The development is particularly noticeable in the district heating sector. District heating is itself an efficient way to heat houses because it allows for centralized heat production and further this technology can make use of waste heat, co-generation, heat pumps and other efficient technology. Sweden has a long tradition of district heating, which has expanded very significantly (roughly fourfold since 1970). Currently over 90% of all Swedish apartments are heated this way. The corresponding figure for space heating in the service sector is over 80%. At the same time as the system has expanded, it has also substituted its primary fuels, switching from fossil fuels to biofuels (e.g., wood residues and pellets) and household waste. Biofuels also have a large market share for heating in those houses that are not connected to district heating grids. The transition from fossil fuels to district heating and biofuels has been facilitated by targeted grants. However, the foremost factor responsible for the transition has been increased cost of fossil fuels due to CO2 taxes (Naturvårdsverket (Swedish EPA), 2004).

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In industry and other sectors, the use of biofuels and residues also has increased significantly, while the overall use of coal in the Swedish economy has been cut by more than 50% since its peak in the 1980s. Another sector where important long-run effects are noticeable is the transport sector, but here the effects are common to the whole of Europe; see Section 5.2.

5.2 TAXING (AND SUBSIDIZING) TRANSPORT FUEL This section discusses the effects of the taxation of transport fuels. Although general carbon taxes are unusual, a number of policies such as gasoline and diesel taxes have very similar effects. These taxes are applied to a subset of carbon fuels, yet they do cover a significant proportion of emissions in many countries. Fuel taxes are important for climate change mitigation because the transport sector represents a large and increasing share of carbon emissions (over 25% of global energy-related CO2 emissions in 2010; see Somanathan et al., 2014). In some countries, the fuel tax is clearly motivated by climate or other environmental factors. In others, it is not; the stated objective may instead be, for example, to finance road building. How do we decide when a tax is an environmental tax? To be frank, there is no bullet-proof definition. We will, however, take the approach here that fuel taxes can be considered environmental taxes, even though this may not have been their original stated purpose. The reason for this is that the effect of a tax will be largely independent of the motivation. A gas tax of US$1 will have the same effect on the climate whether motivated by climate, fiscal or roadbuilding reasons. We need to understand how a carbon tax would work if it could be enacted, and historical and geographic variation in fuel taxes actually does provide a perfect laboratory. For various reasons, different governments have at different times taxed gasoline and diesel at very different rates and researchers can use this variation to estimate the effects of a carbon tax. While the US federal, state, and local taxes average around US$0.50/gallon, many European countries have over seven times higher tax or around US$3.50/gallon (Parry and Small, 2005; Sterner, 2007). This amounts to an environmental tax of roughly US$400/ton of CO2 , implying that a large share of environmental revenues come from transport fuel taxes, which are common in Europe and Japan, as well as in lower-income, oil-importing countries. Fuel taxes thus seem easier to implement for the policymaker in some countries than other policies, partly because transport is not subject to much international competition and hence leakage rates are low. We can compare this situation with air travel, where planes can fuel in other countries and where politicians find that fuel taxation is much more difficult. Irrespective of their official motivation, the effect of taxes on fuel is clearly to raise prices to consumers and this is bound to reduce demand and thus act as if it were a climate-related carbon tax. Coincidental variation in policies in different countries, and occasional dramatic fluctuations in fuel prices, have provided a laboratory allowing us to gauge the effects of fuel prices (and hence taxes) on demand. Estimating

5 Selected Examples

fuel demand elasticities is quite a large industry and there are literally thousands of studies. There is of course a range of results depending on various factors. Fuel demand depends on income, urban architecture, population density, and the availability of alternative modes of transport. In the long run, these factors tend to influence each other, as higher fuel prices will tend to encourage people to live in denser cities and move closer to their jobs. They may also make public transport more profitable. There is also a good deal of inertia in demand patterns and hence elasticities vary significantly depending on the time horizon. Short-run elasticities may typically be as low as −0.1 to −0.2; a 10% increase in fuel price, for example, would decrease fuel consumption by only 1 or 2%, because people do not adjust their transportation patterns quickly. However, long-run elasticities tend to be in the range of −0.7. Thus, the high fuel taxes in Europe have probably been by far the most effective policy when it comes to actually reducing carbon emissions during the last three or four decades. Sterner (2007) estimates that if Europe had not followed a policy of high fuel taxation but had equally low taxes as the USA, then fuel demand would have been twice as large. Recently, new approaches in behavioral economics have focused on possible discrepancies between the impacts of taxes and the variation in fuel prices, due simply to variations in the oil market (Li et al., 2014). A recent study of the British Columbia carbon tax on transport CO2 emissions shows much bigger sensitivity (i.e. price elasticity) when the price of fuel is raised due to taxes (Rivers and Schaufele, 2015). Global variation in fuel prices is generated at least as much by subsidies as by taxes. Fossil fuel subsidies are still quite common in many countries, particularly in oil and coal producing areas. The IEA estimates the value of global fossil fuel consumption subsidies in 2016 around US$260 billion, with vast differences by country (IEA, 2016). Estimates vary widely by organization, depending on the methodology and whether externalities are included. (Note that some estimates of fossil fuel subsidies include tax exemptions, which is not always appropriate.) For example, the IMF estimated that energy subsidies globally totaled US$325 billion in 2015. A much broader and more general measure that includes unpaid externalities or damages was estimated at US$5.3 trillion, or 6.5% of global GDP (IMF, 2016). Ellis (2010) notes that subsidy removal would be akin to increasing global GDP by around 0.7% per year to 2050. The removal of these subsidies would also lead to a 15% reduction in global (energy related) CO2 emissions. One often mentioned problem of fuel taxation is its political economy. There is often considerable political resistance to fuel taxation and very often truckers and other special interests have been very active in lobbying against such taxes, making them difficult to implement. In this connection, it is often asserted that fuel taxes would be regressive. This is a good argument to mobilize opinion but not necessarily true, particularly not in the majority of countries that are low- or middle-income, where private transport is generally a luxury good, implying that it is higher-income people who spend more of their income on this good (Sterner, 2007). Very often, the poorest would be better off if the state raised revenue through taxing transport fuels than, for instance, value-added or some other broad-based tax. However, for the

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political feasibility of a tax, it is not really the welfare of the poor that matters most but the opinions of the most vociferous and influential groups, such as lobbies and the upper- and middle-income urban elites.

5.3 CAP AND TRADE SCHEMES In the last decade, more and more countries have instigated Emissions Trading Schemes (ETS) as important instruments to reduce emissions for climate-related issues and in some cases for other environmental or resource problems. The European Union touts its ETS as a mainstay of climate policy. In 2017, the World Bank estimated that there were 36 national level ETS programs implemented or scheduled for implementation (including those in the EU, Switzerland, Kazakhstan, and New Zealand) and 25 sub-national ETS programs (including in California, the US Regional Greenhouse Gas Initiative (RGGI) and Quebec) (World Bank and Ecofys, 2017). There is much debate among both economists and policymakers about the relative merits of taxes and ETS as instruments of climate policy. Clearly each has some advantages and some drawbacks. To start with the most pragmatic message: Any reasonably ambitious program will imply real resource costs and, if there is heterogeneity in abatements costs (which is the norm), then considerable savings can be achieved if an efficient market allocation is used – which implies that there must be a price on the pollutant, meaning carbon and other gases in the case of climate change. The choice of instrument, in this perspective, is secondary. The important thing is that we quickly attain a sufficiently high emissions price to fully internalize the externality and make real progress in dealing with climate change. Then, the choice becomes a pragmatic one: which instrument is politically most feasible. Experience to date shows that, if the programs are well designed, ETS can be effective, workable, and transparent tools for abatement in ways that mobilize the business sector, attract investment, and encourage international cooperation. At the same time, it is clear that both taxes and trading schemes face severe challenges in practice. Taxes are unpopular in general and resisted not only by the general public but more specifically by lobbies, as discussed in previous sections. In addition to this, it is hard to introduce taxes at the supranational level. Before creating the EU ETS, the European Union tried for several years to create a European-wide carbon tax. However, this was legally and politically very difficult. One might argue that this was a quarter century ago and that the gravity of the climate issue had not fully dawned upon all the member countries. But still today, the nation states are concerned because they zealously protect their taxation prerogative. Also, cap and trade faces a range of challenges, as we discuss below. This has induced at least some participants to think that it may actually on balance be easier to negotiate a global climate treaty that is focused on a joint (minimum) national carbon tax level than to negotiate one on quantities (Weitzman, 2017). In the textbook ETS, permits apply to all pollutants and all jurisdictions and for an unlimited period of time. Under such circumstances, one can demonstrate a lot

5 Selected Examples

of efficiency properties. However, in reality ETS tend to apply to some pollutants or some polluting activities but not others; they are typically decided for a limited “commitment period” and apply in a certain jurisdiction. Extending an ETS to cover more polluters or more pollutants is complex. Dealing with the changeover in commitment periods is also complex. The issue of banking (or even more so of borrowing) of credits is equally challenging, particularly between periods, though there have been cases of successful banking in other jurisdictions, e.g. the SO2 cap and trade program in the United States (Schmalensee and Stavins, 2013). Linking ETS schemes in different jurisdictions is similarly very complex because it opens up the Pandora’s box of the allocation of permits among countries – and thus indirectly of burden sharing between countries. Naturally, to maximize effectiveness, an ETS needs to be suitably designed in relation to its goals and context. Judging the success of an ETS program by the size of the price signal seems natural to many – to support this principle we can think of a tax of the same magnitude as the “dual” solution. In a simple programming sense, a tax of T should produce abatement roughly equivalent to a cap and trade scheme that has an equilibrium price of T. If the value T is judged unsatisfactory, then one could conclude that the ETS is not working well. Indeed, many observers in Europe are deeply disappointed by the very low EU ETS price signal of around US$5–10/ton CO2 . Recently reforms to the EU ETS, which imply retiring a large number of rights, have actually managed to raise the observed price. However, it did require a very considerable political fight. It is worth comparing with the highest carbon taxes mentioned earlier or the Obama administration estimate of the social cost of carbon, which was quite a bit higher at US$40 – but that has never been considered a feasible tax in the US and has not been reached in any mayor ETS either. If the tax was not feasible and the ETS is feasible, then clearly the ETS is better even if the price is low. The ETS also has a very different relationship to uncertainty. It gives certainty to a given emissions reduction but the agents of the economy have to live with uncertainty about the price signal. This has implications. When the price is too low, the environmentalists will complain. On the other hand it could be much worse if the prices rise too high – because then heavyweight economic interests may move in and disband the program altogether. The fear of this happening, together with the corruption and lobbying in the allocation process, tends to lead to an overallocation of permits with resulting low permit prices. This may be reinforced by pessimism concerning abatement possibilities. When the ETS is in place, firms often “discover” abatement options that were cheap and efficient which they did not know about. This is in fact one of the great advantages of a market mechanism. When these mechanisms combine with chance occurrences of sluggish growth, they may lead to a large excess supply of permits and a fall in the market. Other vicious circles can reinforce those mentioned. Decision makers become skeptical of the power of cap and trade to solve the problem and they start legislating or enacting additional programs of support for abatement, support for new technology, green certificates, mandates for energy efficiency and renewables, and so forth.

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All the additional programs, of course, may tend to lead to abatement – but within a cap and trade program, abatement in one firm or one sector just means that the price of permits is depressed and more emissions happen in another sector or country covered. All of this means that an ETS cannot, in fact, be judged simply by its permit price. The complications are compounded if, as mentioned, we have several gases, long time periods, banking between periods, and linking of permit schemes to each other. One can make a case that permit trading will work better if it applies to a larger geographic (and/or sectoral) coverage, but this is a simplification. Size can give stability but it can also easily propagate design errors. Lately there has been a number of interesting suggestions for improving the design of emission trading schemes. By giving the price of permits a floor and a ceiling, many of the disadvantages of uncertainty and variability can be combated. Theoretically, one can speak of a zone of hybrid instruments between a price-type and a quantity-type instrument. For example, there could be permit trading with quantity goals but price floors and ceilings which can be likened to elements of taxation and subsidization. Similarly, trading schemes can be linked to varying degrees (Burtraw et al., 2013; Green et al., 2014).

5.4 REFUNDING EMISSION PAYMENTS In theory, a uniform tax on all emissions is cost-effective if emissions are uniformly mixed. However Pigouvian taxes are not well understood nor liked: It may be that people resist the idea that their own behavior can be affected. They believe they only eat, drive, and consume what is necessary. For instance, they may say: “Look, my house is here, the daycare over there and my job on the other side of town. There is no public transport and so a fuel tax will not affect my miles driven but just be a transfer to the budget”. Econometric evidence shows that people do actually adjust behavior, but it seems that the argument is not popular (Klenert et al., 2017). For transboundary pollutants, we have problems of carbon leakage and often additional problems such as those created by cut-offs – the policymaker may want to impose a charge on some but not all firms. They may want to exempt small firms, or old firms, or firms in some regions or industries, etc. This creates additional problems of exit and entry of firms and control of pollution. The policymakers may also desire the “flexibility” afforded by giving out permits in a permit scheme to “pay off” political opposition. In all these cases, it is often overlooked that there are exactly analogous policies for price type instruments. For example, emission taxes can be made politically more feasible by exempting some firms from some proportion of the fees or taxes they have to pay and/or by earmarking the tax revenues and using them in some way that the polluting industries appreciate. Carbon pricing is becoming more popular, perhaps under the influence of the Paris Agenda. There are currently about 70 national or subnational schemes, with revenues of about US$26 billion in 2015 (World Bank et al., 2016; World Bank and Ecofys, 2017). However, concerns about competitiveness and carbon leakage stand in the way of wider adoption and higher carbon price levels (Aldy and Stavins, 2012;

5 Selected Examples

Aldy and Pizer, 2015; Ward et al., 2015). Many countries that do have carbon taxes have felt pressured to grant energy-intensive sectors exemptions or give them free permit allocations (Martin et al., 2014). Refunding the tax revenue can significantly ease the burden on the polluting firms and thereby reduce political resistance to the tax. Refunding emissions implies turning a tax into a fee, and then rebating it to polluters in some way. Tax revenues typically go into the national budget. Revenues from a fee can be refunded or be seen as payment for a service performed by a government agency or municipality. They can also be refunded directly to taxpayers. Kallbekken et al. (2011) show that citizens often fail to understand the Pigouvian aspect of carbon prices and only their revenueraising effect. When carbon revenues go into the general budget, some studies find public acceptance lower (Baranzini and Carattini, 2017). Sweden, with its generally accepted and very high carbon tax, may in this respect be an outlier that shows the importance of the process of fiscal reform by which the carbon tax is implemented (see Section 5.1). The clearest example of refunding is output-based refunding (OB, refunding in proportion to output) analogous to output-based allocation of permits (as was the case with the lead phase-out program in the USA, Tietenberg, 2003). Sweden has pioneered the use of OB for nitrogen oxides (NOx ). NOx is a byproduct of any combustion, whether oil, gas, coal or even biofuel, and in turn the NOx leads to acid rain, eutrophication, and other environmental problems. Just like sulfur oxides, this leads to health effects, and most industrialized countries have tried to reduce emissions. In Europe, this is regulated by the Gothenburg Protocol. Among the reasons for the use of refunded emission payments (REP) rather than a tax was the difficulty in dealing with a strong industrial lobby which would have opposed the tax virulently, arguing that companies would move abroad. It was thus impossible to set a sufficiently high tax on emissions to motivate abatement (Sterner and Isaksson, 2006). There is quite a large literature on the economics of output allocation; see, e.g., Fischer (2001), Fischer and Fox (2007), Gersbach and Requate (2004). Indeed, output-based refunding corresponds to output allocation or “benchmarking” in a tradable permit system (Fischer, 2001). OB allocation or refunding is often criticized because it generates an output subsidy and thus gives incentives for excess production. This effect is harmful in a competitive environment, but it can increase welfare under imperfect competition, where output is already suboptimally low due to restricted competition (Gersbach and Requate, 2004). Benchmarking in unilateral CO2 emissions policies is motivated by its potential to reduce carbon leakage and loss of competitiveness (Fischer and Fox, 2007). Refunding emission payments is often the only way of making a high emission fee politically feasible: It changes the political economy of policy making; the lobbies that form in opposition to a tax are very much weakened when faced by a REP because roughly half the firms in an industry actually make money from the scheme and thus tend not to oppose it (Fredriksson and Sterner, 2005). This is, in fact, the mechanism that allows the regulator to legislate a fee that is sufficiently high to have a real environmental effect.

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There are some alternative ways of buying support or reducing resistance that do not imply actual refunding of all the fees in proportion to output. In the French taxe parafiscale, the fees for NOx , SO2 , HCl, and VOCs were used generally to subsidize research and abatement (see Millock et al., 2004) in a more general sense. In the Norwegian system, a private NOx fund was created; it is allowed to collect the fees and use them to subsidize actual abatement costs at the firm level. This could be called a tax-subsidy combination or expenditure-based (EB) refunding. It can be shown that, if the OB system makes a high fee politically possible, the EB refunding makes it possible to reach the same environmental goal with a low fee. The efficiency of the low fee is heavily enhanced by the fact that the collected funds are used to subsidize abatement. Thus, this is a combination of a small fee and a subsidy for abatement equipment; see Hagem et al. (2012). Turning back to the bigger climate issues, revenue refunding straight to the polluters in proportion to output would probably not be practical because there are very many large and small polluters and it would be hard to define “output”. In this context, general revenue recycling is more reasonable. This is of course exactly what happens if the tax is put in the general budget and/or replaces other general taxes. Behavioral research has shown that the earmarking or refunding has to be salient and clear. It is important to label the tax a “fee” or a “climate contribution” and, to enhance acceptability, it is important to make the revenue recycling highly visible. The most obvious way may be through frequent and equal per capita transfers – perhaps in the form of checks; see further Klenert et al. (2017), Kallbekken et al. (2011), and Nature Editorial (2017).

5.5 REGULATION VERSUS TAXATION: THE EXAMPLE OF A HAZARDOUS CHEMICAL While environmental economists tend to think of cap and trade versus Pigouvian tax, the bulk of actual environmental regulation is focused on zoning, banning, phasing out, setting safe minimum standards, and other regulatory principles. Sometimes different countries choose different approaches and this gives us some opportunity to learn about the relative effectiveness of regulation versus price-based policies. One such case is the solvent trichloroethylene (TCE). Solvents are important industrial chemicals but can cause severe environmental and health problems because they are hazardous or toxic. One example is the effect of CFCs on the ozone layer. Other chemicals are persistent and bio-accumulating chemicals such as DDT (dichlorodiphenyltrichloroethane) or PCBs (polychlorinated biphenyls). Policymaking is difficult because there is genuine uncertainty about properties, costs, and alternatives. This section compares policy responses in some European countries to TCE and similar solvents which were banned in Sweden, taxed in Norway and Denmark, and strictly regulated in Germany. There are many possible policy instruments for policymakers to choose from: from taxes, charges, and deposit refunds, to tradable permit schemes, information provision, eco-labeling, liability legislation, refunded emissions payments, subsidies,

5 Selected Examples

and voluntary agreements (see Section 3). If there is a risk of serious and irreversible damages, the precautionary principle might seem to point in the direction of radical instruments like a prohibition. But if prohibition is not effective and leads to lobbying or “cheating” rather than research into new technologies, then market-based instruments that encourage such research may be more dynamically efficient. The Swedish parliament passed a law in 1991 banning the use of TCE in consumer products, starting in 1993, and prohibiting the professional use of TCE and methylene chloride, effective January 1, 1996. The Swedish case seems to illustrate the problems with such a strong instrument, which Sweden was alone in instituting: the ban is so absolute that it creates strong opposition among some users, who either find it particularly difficult to replace TCE or simply disapprove of the timing or policy method. The Swedish experience has shown that some firms spent a great deal of effort appealing and lobbying against the ban in the media and the courts. An alternative instrument would be that adopted by Germany: a very strict standard for technical and workplace ambient air that encouraged and in principle required completely closed systems for operation and even storage and transport. Detailed statistics show that the use of TCE in Sweden had already fallen from about 9000 tons per year to 3000 tons by the time of the ban. This rapid reduction appears to have been due to an arsenal of strong policies pursued by the Swedish authorities, and shows the power of day to day regulation by local authorities – at least when the latter are very motivated. Yet, when the ban was implemented, TCE was not completely phased out. Rather, use fell quite slowly after 1992. Interviews showed that companies did not believe the authorities would succeed with a ban and so decided to fight it. A group of industries even published an open letter to the Prime Minister in a leading Swedish newspaper, asking for a repeal of the ban and threatening to move abroad if the ban were enforced. In the end, many companies were given waivers, often after appealing to EU courts, and this explains why use did not fall rapidly. Detailed studies showed that most companies could easily and cheaply find alternatives to TCE. Fig. 2 shows reported marginal costs of abatement for a sample of companies and it is clear that most companies would have had an incentive to voluntarily stop using TCE if there were a tax or fee of SEK 50 per kilogram. Interestingly Norway did, later, introduce a tax per kilo on both TCE and PER of 50 Norwegian Krone, roughly the same as SEK 50. Denmark also has an environmental tax, though it is very low, and Germany has its tough regulation. Fig. 3 plots the rates of phase-out in the four countries compared with the rest of Europe. Although correlation is not proof of causation, all of the countries with stricter policies appear to have been quite effective compared to the majority of other European countries, whose policies were less stringent and where emissions have declined only very gradually. The conclusion appears to be that if the policymaker wants to avoid this health hazard then some policy instrument is needed, and that a ban is not necessarily more effective than economic instruments in quickly reducing emissions, because

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FIGURE 2 Marginal abatement cost and effects of tax compared with ban. Assumptions: 15-year equipment life, 4% real interest. Source: Slunge and Sterner (2001).

FIGURE 3 Rates of reduction of TCE. Source: Slunge and Sterner (2001).

it is tricky in practice to implement a ban effectively. A tax is easiest to administer, whilst the tough German regulations appear to have led to considerable technical development and even export opportunities for firms in Germany that manufacture particularly high-tech clean equipment. Ultimately, countries are likely to be influenced in their choice of policy according to their own legal and industrial traditions; see Sterner and Coria (2012, Ch. 20).

5 Selected Examples

5.6 POLICIES TO MODIFY BEHAVIORAL NORMS Consumer behavior is often driven by norms, habits, and culture. Where such behavior is detrimental to the environment (locally or globally), there is a role for public policy in changing cultural and behavioral norms. However, choosing the right policy mechanism is likely to be country-specific. Meat and tobacco are examples of commodities which are harmful to individual health when consumed/used in excess, and which are associated with negative environmental externalities. They are also products where use is strongly linked to culture and societal norms. Lessons can be learned from how the UK government changed cultural norms over smoking. In many countries, including the UK, smoking used to be prevalent in private and public spaces, including offices, pubs, and restaurants. In the 1970s, over half the adult male population and 40% of the adult female population in the UK smoked. This number fell to around one-third of the adult population in 1981 (Cairney, 2007) and to 16% in 2016 (UK Office for National Statistics). The UK government has relied on a number of policy instruments to reduce tobacco consumption; these span the four categories of pricing, rights, regulation, and information. Links between tobacco smoking and lung cancer were first rigorously demonstrated in the 1950s (Doll and Hill, 1956). The UK government started regulating tobacco in the early 20th century with a ban on the sale of tobacco to children under 16, and later a ban on TV advertising in 1965 (Cairney, 2007). Some regulations from the 1970s such as “non-smoking areas” in airplanes seem quite laughable today. Effective bans have followed more recently, such as a smoking ban in public places, including pubs, fully implemented in the UK in 2007. Note that this was motivated to a large extent as an environmental issue: to protect people from secondhand smoke. This ban was opposed by some. But the reality is that in 2007 there was already considerable support for the ban, as reported in the UK newspapers. The UK’s Office of National Statistics found that 77% of people agreed with the new legislation, and only 15% disagreed. Whereas 8% of those surveyed said that they would visit pubs less often, 15% said that they would visit more. These data suggest that the new legislation was easier to implement because public opinion already supported the proposed changes, and indeed many smokers wanted to quit and so welcomed legislation that would make continuing to smoke more difficult and less socially accepted. Governments have also long taxed tobacco. A tax on an addictive substance arguably acts less as a Pigouvian tax and more as a source of government revenue. Tax currently accounts for around 89% of the cost of a packet of cigarettes but price elasticities are low and effects small. Some have argued this might make governments less interested in really reducing the habits, though there is little evidence for this. The UK government increasingly is also using a number of nudges, which can “help to promote a culture that is accepting of legislation to promote health” (Marteau et al., 2011). For example, advertising campaigns have cast non-smoking and wanting to give up smoking as the norm; cigarettes are kept out of sight in retail outlets; cigarette packages now contain health warnings, often paired with pictures of diseased lungs; and standardized packaging was introduced in 2016.

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As norms have changed over time, and the location of consumption has changed as well, the relative importance of each policy instrument has changed, reflecting the shift of tobacco use away from the public sphere and an overall drop in consumption, with some conversion to e-cigarettes. Taxation has been progressively increased over time; the number of locations where smoking is permitted has fallen; and smoking has become less socially acceptable. Thus, public policy with regard to smoking has shifted from a focus on controls and increased prices, to a broader approach that also incorporates behavioral nudges. Similarly, social policies that change the social acceptability of smoking have been shown to be as important as taxation in reducing smoking rates in the US (Alamar and Glantz, 2006). Taxation has particular implications for equity when the price elasticity of demand is low; when the good being taxed is addictive, as is the case for tobacco; and when use is more concentrated among lower-income individuals. Ultimately, whether such taxes are progressive or regressive is an empirical question, and depends on the budget shares and relative price sensitivity of higher and lower income groups (Colman and Remler, 2008). It also depends on the incidence of benefits. Meat and dairy are food products that have particularly high greenhouse gas footprints, in addition to contributing to water scarcity and erosion. Reducing meat consumption would have both climate and health benefits (Watts et al., 2018). China is aiming to reduce meat consumption by 50% by 2030, so as to reduce greenhouse gas emissions and the increasing incidence of obesity and diabetes in the country (Milman and Leavenworth, 2016). Yet meat consumption is linked to socio-economic status and may have strong cultural links. For example, consumption is typically found to increase in countries as incomes increase and populations become more urbanized (Fiala, 2008). The lessons from the UK’s efforts to reduce tobacco consumption suggest a combination of taxation and societal nudges may be required. There is some evidence that, though reducing meat consumption is an important climate change mitigation strategy, governments in higher-income countries have not yet acted, and efforts led by NGOs are linked to health benefits rather than climate (Laestadius et al., 2014). Given the increasing evidence concerning the relative health and social impacts of various stimuli (alcohol, tobacco, narcotic drugs), the different policy responses to each in many higher-income countries often reflect historical biases and tones of morality rather than rational policy making. Whichever policies are chosen by government should, at a minimum, recognize explicitly the costs, benefits, harms, and unintended consequences of those policies. Domestic energy use choices similarly have important implications for the environment, yet consumers have been found to be “slow to habituate” to adopting more environmentally friendly choices (Allcott and Rogers, 2014, p. 3003). In such a circumstance, one role of government policy is directly to help individuals to change their habits, or to encourage utility companies to do the same. Presenting individuals with social comparisons is one approach has been demonstrated to change behavior across a wide variety of situations, including with respect to reducing energy use (Ayres et al., 2013).

6 Designing Policies for the Anthropocene

6 DESIGNING POLICIES FOR THE ANTHROPOCENE Research in Earth systems science shows that we face numerous large-scale environmental problems. Today humankind constitutes the largest driver of change at the planetary scale and the implications for global ecosystem stability and for society are profound. Social impacts often hit far away from the source of the problem and we risk crossing tipping points, with potentially catastrophic costs. A number of Geoscientists and Earth system scientists speak of the Anthropocene – the era when human activities and the global economy are the dominant forces of change that threaten the stability and resilience of the entire Earth system. Steffen et al. (2015) enumerate nine planetary boundaries that interact to regulate the overall stability of the planet. One of these boundaries, the composition of the atmosphere leading to climate change, is already proving to be a very hard problem for the nations of the world to deal with. Progress over the past 25 years has been insufficient. Similarly, biodiversity loss, ocean acidification, atmospheric aerosol loading, and stratospheric ozone depletion, are all pushing the Earth system up against planetary boundaries. There is controversy and debate concerning this work but no doubt that global ecosystems are under stress. The Millennium Ecosystem Assessment (2005) states: “Over the past 50 years, humans have changed ecosystems more rapidly and extensively than in any comparable period of time in human history. This has resulted in a substantial and largely irreversible loss in the diversity of life on Earth. The degradation of ecosystem services could grow significantly worse during the first half of this century and is a barrier to achieving the Millennium Development Goals. . . . The challenge of reversing the degradation of ecosystems while meeting increasing demands for their services can be partially met under some scenarios that the MA has considered, but these involve significant changes in policies, institutions, and practices that are not currently under way.” (Emphasis added by authors.)

The biosphere’s capacity for adaptation is being stretched to its limits, creating potential risks of sudden collapse. To stay within planetary boundaries, we must understand why we have a tendency to transgress boundaries. The fact that the human economy has pushed us up against, and in some cases perhaps past, some of the boundaries that define a safe operating space means that very skillful maneuvering will be required (Rockström et al., 2009). Economists, social, behavioral, and policy scientists must expand our analysis significantly to face the drastic changes needed in how we manage the ecosystem resources of this planet. Environmental policy design and related fields typically deal with one manageable problem within one single (national or maybe federal) jurisdiction. When dealing with planetary problems, it is seldom possible to implement traditional policy instruments, regulations or taxes, although there are large potential gains of taxing “societal ills” to generate revenues to meet environmental challenges. Serious concern about planetary-scale problems is rather recent in natural science and virtually non-existent in economic models, most of which disregard boundaries, ecological

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tipping points, and other complexities or uncertainties. Broadening the analysis of environmental policy making to deal systematically with policies to keep the Earth system within planetary boundaries is challenging because we need to deal simultaneously with several difficult aspects, which implies going far beyond the state of the art. We are speaking of an extreme degree of multi-pollutant, multi-governance, and multi-policy setting that will necessitate new, high-risk extensions in several different dimensions that are the major challenges we need to address: A. B. C. D.

Expansion of geographic and political scope Significant extension in time scale Significant extension in number of pollutants and scientific complexity Proper inclusion of equity, ethics, risk, uncertainty, and governance concerns

6.1 AN EXPANSION OF GEOGRAPHIC AND POLITICAL SCOPE Dealing with planetary boundaries requires a global response. This is not a simple matter of “scaling up” national instruments or applying the lessons from the federalism literature. Many of the most pressing environmental challenges imply an urgent need for collective action among multiple actors. For problems that are truly global, such as the climate issue, the stratospheric ozone issue and – by their very nature – most of the planetary boundary issues, most effective policies have to be formulated at a global level. Yet because there is very little power at global or international levels due to state sovereignty, most international policy making is obliged to take the form of international agreements, negotiations, and treaties among countries, concerning at least goals, and possibly also the application of policy instruments at the national level. Important elements in finding solutions for such critical transboundary problems that have been identified include dialogue that includes scientists and officials; “complex, redundant, and layered institutions”; and flexibility with regard to mixing institutional types, learning, experimentation, and change (Dietz et al., 2003). There are already several examples of long-standing international treaties created to manage global commons, natural resources shared by the globe as a whole, comprising the high seas, the atmosphere, Antarctica, and outer space (Ostrom et al., 1999; Buck, 2017). Two noteworthy examples cover the Antarctic (The Antarctic Treaty, see also Vogler, 2012) and Outer Space (The Outer Space Treaty of 1967; see also Chaddha, 2010), yet these have only required the cooperation of a small number of countries. More recently the Montreal Protocol on stratospheric ozone, signed in 1987, has proven a successful international governance regime (Dietz et al., 2003). For other global commons such as the climate, biodiversity, forests, and the oceans, global participation in any regulation is typically required, because most if not all countries benefit from and/or degrade the resources. Biodiversity has been addressed on many scales and by a variety of policy instruments (see evaluations done by e.g. Wätzold and Schwerdtner, 2005; Miteva et al., 2012). The Convention on Biodiversity, adopted by most countries in 1992, follows the model of employing international conventions for global transboundary issues.

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Global climate change has attracted significant analysis (see IPCC, 2014), though there is insufficient action in the political sphere. The United Nations Framework Convention on Climate Change (UNFCCC) Kyoto Protocol codifies the international climate change policy regime, sets targets for Annex 1 (industrialized) countries to reduce their GHG emissions, and allows for trading carbon credits in international markets. Lower-income countries can participate in these markets through the supply of carbon credits (certified emission reductions) through CDM (the Clean Development Mechanism) and more recently, through REDD (Reduced Emissions from Deforestation and forest Degradation). Each of these initiatives rewards lowerincome countries for reducing GHG emissions, through the transfer of funds from higher-income countries. In reality, the markets created by these policy mechanisms have not quite lived up to the original optimistic expectations. Theory generally has quite a pessimistic view of the possibility of reaching successful and sufficiently radical international environmental agreements due to national sovereignty: nations are always free to leave a treaty. Therefore, treaties have to be designed so that nations find it in their interest to remain and comply, which naturally puts limits on how far a treaty can be constructed to constrain behavior or emissions that are damaging to ecosystems. There is a considerable literature concerning how to get around this point by clever design of the treaty or by linking to other issues such as trade (see Barrett, 2003). Barrett (2013) has specifically analyzed the importance of discontinuous benefits, as would be given by the existence of an ecological threshold. He finds that if the threshold is known with certainty and the damage sufficiently large, then countries will coordinate to avoid catastrophe. Under these circumstances, climate treaties can sustain the efficient outcome. If, however, there is uncertainty – even moderate uncertainty – then the results can break down (Barrett and Dannenberg, 2014). In the implementation of international treaties, it is vital that all (or practically all) countries participate – not only for fairness, but because we face the problem of leakage. A small country with, say, 10% of world production, acting alone, can never hope to have more than a 10% effect on a global problem. Moreover, with the textbook example of leakage (e.g. carbon leakage), the effect may be much smaller than that because the production, jobs, and pollution will just increase in another country (see e.g. Hoel, 1991). More generally, spatial and temporal aspects, such as equity considerations across higher- and lower-income countries, and across current and future generations, are all very hard to deal with. For example, rapidly industrializing countries such as China and India, which currently have relatively low per-capita emissions, though high CO2 emissions in absolute terms, did not have obligations for emissions reductions in the 1997 Kyoto Protocol (Pittel and Rübbelke, 2008). However, the 2015 Paris agreement required commitments from all the 195 signatories, which include both higher and lower-income countries. Issues of measurement, accountability, regulation, and liability similarly come to the fore. For global commons, the reality of individual incentives differing from group incentives tends to be considerably amplified.

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Successfully mitigating the adverse effects of free-riding on a large scale is another difficulty in international policy-making. Nordhaus (2015) suggests a solution which he refers to as ‘Climate Clubs’. The basic principle for a club is based on the notion that, without enforcement and the possibility to sanction defectors, international agreements such as the Kyoto Protocol will break down. Within a club, countries would have ambitious emission reductions targets (high carbon prices). Countries that would not join the club would, in contrast, have low abatement costs (low or zero carbon prices) but would then face penalties by the countries that are members of the club, for example through trade tariffs. The probability of sustaining a solution based on a ‘club regime’ hinges upon a modest carbon price (too high a price would make countries prefer the penalties); on the other hand, Nordhaus (2015) shows that only small trade penalties are necessary for significant abatement levels. As the excruciatingly slow progress of climate policy clearly shows, the making of an international treaty is no simple task, largely because there is no world government, no global policy making arena. There is no clear set of universal rights (for instance, rights to emit climate gases into the atmosphere – or rights to clean air or rights to a stable climate regime). A direct consequence is that the primary set of instruments is radically different from that used in national policy making. We need to develop our understanding of treaty negotiations, remembering that these treaties, in turn, may require the use of national instruments. They must certainly coexist with the national instruments that countries choose as vehicles to implement the treaties and therefore we need to consider the linkage compatibility of instruments with various types of treaties (Stavins, 2016). Other instruments that focus on cultural and existential drivers, on the scale of the economy, on behavior, information, finance, culture, population demographics, and technology, may be important to truly transform rather than just modify societies (Barbier, 2015). Innovation – technical, organizational, and cultural – is similarly important. It may seem contradictory, but actions to stay within planetary boundaries will not only require action at the global scale, but also locally. Take as an example the disturbances to bio-geophysical flows of phosphorous or nitrogen, or land management decisions in farming or forestry with effects on emissions of climate forcing gases such as methane or nitrous oxides. Most of these emissions stem from non-point sources – emissions that cannot be easily measured or verified by national authorities. Even though the latter have formal jurisdiction over the emissions, the most realistic approach may be local Common Property Resource management (Ostrom, 1990). It is not uncommon that the same activity (say, forestry) can have effects on both local and global pollution and would thus possibly be subject to regulation at several levels simultaneously, which can lead to a fatal lack of clarity in rulemaking. Also, ecosystem health can depend on changes at a number of different geographical (and time) scales. The health of a coral reef depends not only on global climate and acidification but on local processes of erosion, pollution or overfishing. This is an area where we may be able to build on Ostrom’s theories on polycentric decision-making (Ostrom, 2009).

6 Designing Policies for the Anthropocene

By definition, policy instruments for managing global commons will almost certainly involve in some way lower-income countries. However, these countries will also need to design and implement environmental policy instruments to deal with national and sub-national environmental issues. It is crucial to consider the lowerincome country (“developing world”) perspective, because lower-income countries generally are characterized not only by inequality and poverty, but also by weak institutions, poor performance of markets, lack of data – in particular environmental data, and typically, lack of experience on design and implementation of environmental policies (Sterner and Somanathan, 2006). In the 1990s, Afsah et al. (1996) suggested that in many lower-income countries the pre-conditions for applying many policy instruments, including market-based instruments, did not yet exist. Regulators often did not have sufficient information, public mandate, nor capacity for priority setting. In many countries, this reality still exists. Further, whether public policy focuses on taxes, quantity restrictions, or regulation, governments must be able to enforce their policies, and this is particularly tricky in lower-income countries, where government departments tend to be underfunded, property rights tend to be poorly defined, and corruption and non-compliance may be a societal norm.

6.2 SIGNIFICANT EXTENSION IN TIME-SCALE Dealing with the environmental problems that threaten planetary boundaries implies significantly extending the time-frame of our analysis. A very long-run view is unusual in economics but imperative for this set of problems. The reason for this is the inertia of many planetary processes, such as the warming of the oceans. Longer time scales introduce numerous problems in policy making, including that of time consistency and commitment, in some ways analogous to including multiple jurisdictions. Just as there is no world government to force nations to comply, there is practically no mechanism by which current decision makers can commit future politicians to any particular course of action. Thus, a global treaty can stipulate carbon taxes that rise over time but nothing actually stops future governments from changing – or even leaving – the program. Creating property rights can, in some contexts, be a mechanism for creating long-run policy commitment and hence rights-based management might be seen as a shortcut to stability, but this feature makes them difficult to design – particularly in countries without a strong tradition of well-defined and enforced property rights. Longer time horizons not only raise the issues of time consistency and the “sovereignty” of each generation of politicians, they also raise issues of optimal resource use over time, as well as ethically contentious and risky issues, such as that of regulating economic growth and discussing population numbers. If the climate debate has succeeded in anything this far, one could point to a lengthening of our time perspective. It is now standard to consider developments up to the year 2100 – which is a lot longer than economic analyses have typically dealt with in the past. Still, hardly anybody is willing to seriously consider several centuries, which is clearly necessary when considering, for instance, climate-induced sea level

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rise. Conventional linear discounting at a rate of 3–5% diminishes all future values to virtual insignificance and thus is not appropriate in an economy that will be constrained from growing and where we must even face the risk that people may be impoverished. Ultimately, we need a vision of the future to set relevant prices, including social discount rates, that can vary over time and vary between sectors and instruments to guide society onto a sustainable path (Hoel and Sterner, 2007; Arrow et al., 2013).

6.3 SIGNIFICANT EXTENSION OF THE NUMBER OF POLLUTANTS AND SCIENTIFIC COMPLEXITY One needs also to consider that there is interaction between the drivers that are leading to transgression of the various planetary boundaries and local management of local ecosystems. For instance, the effect of, say, climate change on ecosystems such as coral reefs may depend on local actions, such as reductions in pollution runoff and fishing. This creates links between policy at the global and local levels and between different areas of concern or different pollutants/drivers. Thus we have multi-pollutant/multinational and multiple agents. One can in some cases see promise of good news: the incentives for countries to intervene in specific ways are stronger than the incentives to address the root cause of the problem. An example is perhaps given by those who argue that incentives to act on climate change by reducing coal use should be strengthened by the “ancillary benefits” of combating local healthissues and pollution related to coal (Watts et al., 2015, 2018). On the other hand, the level of complexity rises and the already considerable complexity of the planetary boundaries approach is further complicated. Policy making in the Anthropocene will mean working with multiple planetary boundaries as well as with the unintended side effects of other policies, for instance, to promote industry or agriculture. Many environmental issues will require close collaboration between natural and social scientists. There is some incipient work on the challenge of dealing with multiple pollutants (see Ambec and Coria, 2013). Generalizing this and extending it to cover the multiple challenges mentioned is a big step. There is clearly a risk involved in trying to take steps that are too big. The progress of science is typically by studying small extensions from given theory in order to stand on firm ground and to be able to prove analytically new results. On the other hand, it is sometimes possible to take a quantum leap and find completely novel ways of dealing with multiple problems.

6.4 EQUITY, ETHICS, RISK, UNCERTAINTY, AND GOVERNANCE Policy making for major environmental issues must deal with considerable uncertainty and risk. More risk, not only concerning the economy but more fundamentally ecological thresholds, will raise countless ethical and distributional issues, just as a longer time horizon does. Moreover, the poor are typically more vulnerable to uncer-

6 Designing Policies for the Anthropocene

tainties because they have fewer reserves and thus risks are tied to ethical and equity issues. At a global scale, the poor do appear to bear disproportionately the burden of many environmental problems – whether climate change, biodiversity or freshwater availability. Dealing with major global issues rather than standard domestic environmental issues will tend to exacerbate a whole series of problems related to the distribution of income and wealth. Indeed, policies to respect planetary boundaries will almost certainly have distributional implications within and among contemporary societies. When poor and very unequal societies are affected, issues of welfare and distribution will be more prominent, and perceived equity and justice issues dominant (Johansson-Stenman and Konow, 2010). The cultural settings of different nations are very varied and have profound implications for the acceptability of different policies (Barbier, 2011). Traditional policy instrument design tends to focus on issues of efficiency, but dealing with policy making for the Anthropocene forces us to focus on issues of distribution and fairness, which are decisive for political feasibility and for welfare consequences. Policy designed to deal with global environmental issues should allow scope for economic development of lower-income economies and must be compatible with poverty alleviation if it is to be globally acceptable. A common but misleading assumption in much of the policy literature is that we can calculate the effect of policy instruments by conventional neoclassical methods. In its most narrow sense, neoclassical economics assumes that human rationale is egoistic, individualistic and material. Hence, we can calculate profit or utility functions for firms or individuals and design instruments from the assumption that individuals are maximizing individual utility. However, we know this to be wrong: fairness and social norms are very important (Johansson-Stenman and Brekke, 2008). This brings us full circle to the start of this paper where we discussed the fundamental reasons for market failure and the ways in which economics describes human behavior. There are many areas where a more realistic description of human action than simple utility maximization should be used. Crucial issues include long-run choices over time under uncertainty and risk. These are typical for climate change and many other large environmental issues with which we are concerned and they are cases where behavioral economics has shown that conventional theory tends to do a poor job of analyzing human behavior. We are at a crossroads when the formulation of wise policy to deal with these global, complex, long-run planetary problems has become very challenging. The consequences for welfare can be very sizeable and very significant, making issues of distribution and fairness stark issues of survival. At this time, we need robust politics and strong systems of governance. Unfortunately there seem to be signs of the opposite. As the stakes get higher, petty conflicts over distribution escalate and politics runs the risk of degenerating into populism and strife.

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CHAPTER

Quasi-experimental methods in environmental economics: Opportunities and challenges✶ ∗ UC

7

Olivier Deschenes∗,†,‡ , Kyle C. Meng∗,‡,1

Santa Barbara, Santa Barbara, CA, United States of America † IZA, Bonn, Germany ‡ NBER, Cambridge, MA, United States of America 1 Corresponding author: e-mail address: [email protected]

CONTENTS 1 Introduction ...................................................................................... 2 The Lindahl–Samuelson Condition ........................................................... 2.1 A Model of Optimal Public Good Provision .................................... 2.2 Estimating the Lindahl–Samuelson Condition: Measurement Challenges. 2.3 Estimating the Lindahl–Samuelson Condition: Identification Challenges . 3 The Standard Quasi-Experimental Approach ................................................ 3.1 Background ......................................................................... 3.2 Potential Outcomes Framework.................................................. 3.3 Three Quasi-Experimental Methods ............................................. 4 The Quasi-Experimental Approach for Public Goods ...................................... 4.1 Distinguishing Public Good Source and Exposure ............................ 4.2 A Potential Outcomes Framework for Public Goods .......................... 4.3 Two Quasi-Experimental Estimators in the Literature ........................ 4.4 An Unbiased Estimator for Local Public Goods ............................... 4.5 Illustrative Simulations ........................................................... 5 Literature Review ................................................................................ 5.1 Publication Trends................................................................. 5.2 A Selected Review of Average Source Effect Estimates ..................... 5.3 A Selected Review of Average Exposure Effect Estimates ................... 5.4 A Selected Review of Marginal Cost Estimates ...............................

286 289 289 291 292 293 293 294 296 297 298 299 300 304 305 306 306 311 315 320

✶ Replication code for simulations can be found at www.kylemeng.com. We thank Clément de Chaise-

martin, Larry Goulder, Guido Imbens, Andrew Plantinga, Joe Shapiro, Kerry Smith, and Reed Walker for helpful discussions and feedback. All errors are our own. Handbook of Environmental Economics, Volume 4, ISSN 1574-0099, https://doi.org/10.1016/bs.hesenv.2018.08.001 Copyright © 2018 Elsevier B.V. All rights reserved.

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6 Moving Forward.................................................................................. 6.1 What To Do with Local Public Goods ........................................... 6.2 What To Do with Global Public Goods .......................................... 7 Conclusion........................................................................................ References............................................................................................

323 324 325 327 328

1 INTRODUCTION The optimal provision of environmental goods is a long-standing question in environmental economics. Environmental policy relies on estimates of the marginal social benefit and marginal private cost of providing environmental goods. In recent years, concerns over the potential endogeneity of environmental exposure have prompted the environmental economics literature to increasingly focus on causality. Knowledge of causal relationships is crucial for policy design: without it one cannot credibly claim that any environmental policy leads to specific outcomes. To that end, the literature has primarily turned to quasi-experimental methods. The central feature of quasi-experimental research is the care taken to understanding the nature of treatment assignment, and in defining treatment and control groups. These methods have fundamentally transformed the field of environmental economics. According to our review, quasi-experimental papers, which did not appear in the literature until 2000, now make up more than 30% of published environmental economics papers in prominent economics journals. This paper examines the quasi-experimental literature in environmental economics over the last two decades. In particular, it is organized around the following question: what are the implications of applying standard quasi-experimental methods to questions involving environmental goods? Our overall perspective is based on two observations. First, the standard set of quasi-experimental methods, which were largely developed for applications in labor economics, typically assume unit-level treatment assignment that is “as good” as random and do not spill over across units.1 Second, environmental economics, with its strong connection to public economics, is fundamentally interested in the study of environmental public goods. Public goods exhibit externalities.2 This implies that a public good treatment received by one unit often affects other units. We formally explore what happens when standard quasi-experimental methods are applied to public or environmental goods settings. In particular, the presence of 1 In environmental economics, units are typically households, firms, or locations. 2 According to Baumol and Oates (1988, p. 17), “an externality is present whenever some individual’s ...

utility or production relationships include real ... variables, whose values are chosen by others ... without particular attention to the effects on [that individual’s] welfare.” From this definition, a public good is a good which exhibits an externality that is non-rival, whereby consumption of the public good by one agent does not deplete public good consumption by another agent. There is a further distinction in the literature. An externality is typically the unintended consequence of a private action, whereas a public good can result from either government or private action.

1 Introduction

externalities complicates estimation of the marginal social benefit of a public good. To understand what happens to standard quasi-experimental estimates of this parameter, we first extend the potential outcomes framework to explicitly model the distinction between the unit-level source of a public good and the resulting grouplevel exposure to that public good. For example, consider an air quality regulation imposed on a randomly chosen power plant that reduces emissions. This treatment will lead to cleaner air over all downwind locations even if those locations were not directly regulated. Using this framework, we examine the two most commonly used quasi-experimental estimators for the marginal social benefit of a public good, both of which assume unit-level quasi-random assignment of public good sources with no treatment spillovers. We show that when there are externality spillovers, these assumptions alone are no longer sufficient for recovering unbiased estimates of the average treatment effect. The first estimator, which we call the average source effect estimator (ASEE), compares average outcomes across units that are and are not the source of the public good. A typical application of this estimator appears in studies of the U.S. Clean Air Act that compares average outcomes across more regulated (i.e., nonattainment) and less regulated (i.e., attainment) counties (see, for example, Chay and Greenstone, 2005). We show that for a local public good, the presence of externality spillovers violates the Stable Unit Treatment Value Assumption (SUTVA) making the ASEE biased downwards. For a global public good, where every control unit experiences public good spillovers, the ASEE produces an estimate of zero. The second estimator, which we call the average exposure effect estimator (AEEE), compares average outcomes across units that are and are not exposed to a public good following quasi-random assignment of a public good source. For example, this estimator is used in studies where outcomes from a given location are regressed on pollution exposure that is sourced from elsewhere (see, for example, Schlenker and Walker, 2016). Unlike the ASEE, the AEEE for a local public good need not be biased. A form of selection bias arises, however, if potential outcomes are correlated with the likelihood of spillover. To illustrate this bias, consider a setting along a river. Even if water pollution abatement were randomly assigned across locations next to the river, downstream locations are more likely to experience cleaner water. If downstream locations also have different baseline characteristics, perhaps due to residential sorting, the AEEE will produce a biased estimate. In general, this bias is of unknown sign. Furthermore, for a global public good, we show that the AEEE is undefined. Out of this formal analysis emerges several paths forward for future research. For local public goods, we suggest that researchers obtain unit-level likelihoods of externality spillovers. We propose an unbiased version of the ASEE for local public goods which uses spillover likelihoods as regression weights. The ASEE, however, may not be applicable for all empirical settings. For example, suppose the population of interest is households residing in locations without polluting firms. Here, only the AEEE can be estimated. To indirectly test for selection bias in the AEEE, we suggest that researchers examine whether spillover likelihoods are correlated with

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pre-determined characteristics. Of course, such tests would not be informative if the bias in the AEEE arises only from selection on unobservables. Unfortunately, when studying global public goods, such as climate change mitigation, adjustments or tests for either estimator do not address the fundamental problem of not having control units available. We offer some thoughts on how to work around this challenge while maintaining the advantage of causal inference provided by the quasi-experimental approach. Our observation that treatment spillovers may undermine experimental or quasiexperimental methods is not new. This critique has been made convincingly in other contexts (e.g., Miguel and Kremer, 2004 and Manski, 2013). For example, labor market interventions may lead workers to move from treated to control locations. Information treatments may inadvertently be available to individuals in the control group. Vaccine treatments may result in herd immunity for nearby control individuals. In all these contexts, identification requires the researcher to observe spillover probabilities. This is often very difficult. For example, researchers may not know where one labor market ends and another begins. Similarly, the spread of information is typically hard to observe. These factor market and informational spillovers are also present in environmental economics. However, we argue that environmental economists have an advantage when it comes to spillover of environmental goods. The availability of physical spatial models of pollution dispersal together with pollution measures at high-spatial resolutions allow researchers to observe where pollution is generated and where it goes. Finally, we note what this review does not cover. First, while our focus is on the use of quasi-experimental methods in environmental economics, this paper does not provide a thorough review of the methodological issues associated with quasi-experimental techniques. Nor do we contrast quasi-experimental and structural approaches.3 We also do not review papers in environmental economics that use randomized experiments, which have also become increasingly prominent.4 Our objective is more focused: we study the implications of applying standard quasiexperimental methods to environmental good problems. Second, while we will discuss at length how to obtain causal estimates of the marginal social benefit of an environmental good, we do not address how to select outcome variables that captures the marginal willingness to pay for that good. The correct use and welfare interpretation of various outcome variables is the subject of a long and important literature on revealed preferences, which is beyond our scope.5 Here, we simply assume that a proxy for marginal willingness to pay is available.

3 Interested readers can turn to excellent reviews in environmental economics by Timmins and Schlenker (2009) and Greenstone and Gayer (2009) and to more general reviews by Rosenzweig and Wolpin (2000), DiNardo (2008), Imbens and Wooldridge (2009), Heckman (2010), Angrist and Pischke (2010), Keane (2010), and Nevo and Whinston (2010), among others. 4 See for example Duflo et al. (2013), Allcott and Rogers (2014), and Fowlie et al. (2018). 5 We encourage interested readers to turn to Bockstael and McConnell (2007) and Freeman et al. (2014) for extensive reviews on revealed preference methods.

2 The Lindahl–Samuelson Condition

The rest of the paper is structured as follows: Section 2 reviews a central objective for empirical environmental economics: estimating components of the Lindahl– Samuelson condition for optimal public good provision. We review the Lindahl– Samuelson condition and discuss estimation challenges. Section 3 reviews the standard quasi-experimental approach. We define the standard quasi-experimental approach both broadly and formally using the canonical potential outcomes framework. Section 4 extends the standard potential outcomes framework to explicitly distinguish between public good source and exposure. We then evaluate two commonly used estimators in environmental economics both formally and through numerical simulations. Section 5 summarizes recent publication trends for quasi-experimental papers in environmental economics across methods, topics, and journals. We then review select papers in this literature through the lens of our extended potential outcomes framework. Section 6 offers suggestions for future quasi-experimental research in environmental economics for both local and global public goods. Section 7 concludes.

2 THE LINDAHL–SAMUELSON CONDITION A central concern in environmental economics is determining the socially optimal provision of an environmental good such as pollution abatement. This section reviews the optimality condition for public good provision and discusses its estimation. We begin by presenting a standard model that produces the well-known Lindahl– Samuelson condition, which states that optimality is achieved when the marginal social benefits of a public good equals the marginal private cost of its provision. We then discuss challenges to estimating these parameters both in terms of measuring welfare-relevant outcomes and identification of causal effects.

2.1 A MODEL OF OPTIMAL PUBLIC GOOD PROVISION There are i = 1, . . . , N agents in an economy, denoted by set N . The subset of households, H ⊂ N , is indexed by h = 1, . . . , H . The subset of producers, L ⊂ N , is indexed by  = 1, . . . , L. The public  good consumed by agent i is the sum of that generated by all producers, Qi = ∈L q . Households consume a private good xh and possibly a public good Qh , with utility function Uh (xh , Qh ), where ∂Uh /∂xh ≥ 0 and ∂Uh /∂Qh ≥ 0. Producers take r as an input to produce private good y and q . Production can be affected by the presence of public good Q , which we model as an input. This implies the following transformation function for producers: F (r , Q , y , q ), with ∂F /∂r ≥ 0, ∂F /∂Q ≥ 0, ∂F /∂y ≤ 0, and ∂F /∂q ≤ 0. To simplify the setting, we consider Qi to be a local, quasi-fixed, pure public good. It is “local” in the sense that the set of households and producers exposed to the public good is not the entire population. The subset of exposed households and producers, M ⊂ N , is indexed by m = 1, . . . , M. Qi is “quasi-fixed” in that an af-

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fected agent has no direct control over its production.6 Qi is “pure” or non-exclusive implying that, absent costly defensive behavior, the public good enters positively into either the utility function or production transformation function of an affected agent. Finally, Qi is “public” or non-rival with exposure being the same for all affected agents. The last two assumptions imply that Uh (xh , Qh = Q > 0) ∀h ∈ M and F (r , Q = Q > 0, y , q ) ∀ ∈ M. The planner’s objective is to determine the socially optimal level of Q with resource constraint R. Without loss of generality, suppose agent i = 1 is a household affected by the public good. The Pareto problem is max

x1 ,...,xH ,r1 ,...,rL ,y1 ,...yL ,q1 ,...,qL

U1 (x1 , Q)

s.t. Uh (xh , Q) ≤ u¯ h ∀h = {2, . . . , H } F (r , Q, y , q ) ≤ 0 ∀ = {1, . . . , L}    xh + r − y ≤ R h∈H

∈L

∈L

The socially optimal Q∗ must satisfy  ∂Uh /∂Q∗  ∂F /∂Q∗ − = ∂Uh /∂xh∗ ∂F /∂y∗ h∈M ∈M      

amenity benefits

productivity benefits





∂F /∂q∗ ∂F /∂y ∗   

∀ = {1, . . . , L}

(1)

marginal private cost

marginal social benefit

Eq. (1) is the Lindahl–Samuelson condition (Lindahl, 1919; Samuelson, 1954). It states that at the social optimum, the marginal social benefit of the public good must equal the marginal private cost of providing the public good across all producers. Marginal social benefit, the left hand side of Eq. (1) has two components. The first term captures the sum of the marginal rates of substitution between the public good and the private good for all affected households. This is typically referred to as amenity benefits. The second term captures the sum of the marginal rates of transformation between the public good and the private good for all producers. Because we treat the public good Q as an input to production, this captures the marginal productivity of Q in terms of output and is often referred to as productivity benefits. The marginal private cost of public good provision, shown on the right hand side of Eq. (1) is simply the marginal cost of increasing production of q in terms of output, y . To determine the optimal level of public good provision, all three components of Eq. (1) must be empirically estimated. Estimation of these components using observational data entails several challenges. Section 2.2 discusses the challenges as-

6 In the current setup, this is reasonable if the number of producers are sufficiently large such that q 0}

(5)

where W is a deterministic N-by-N adjacency matrix. The bilateral weight wki characterizes the transport of a public good that is sourced from unit k and exposes “downwind” unit i. W is sometimes referred to as the source-receptor matrix in environmental economics. We place two restrictions on W. First, we assume unit diagonal elements, wki = 1 ∀k = i. This implies P r(Qi = 1|Di = 1, Yi ) = 1, which is consistent with the nonexclusive nature of public goods: conditional on being a public good source, that unit is also exposed to the public good. Second, we allow for weakly positive off-diagonal elements, wki ≥ 0 ∀k = i. We place no additional structure on these off-diagonal elements such that conditional on not being a public good source, the probability of public good exposure varies across units. Denote this likelihood of externality spillover as P r(Qi = 1|Di = 0, Yi ) = Si . This probability of externality spillover captures the degree of SUTVA violation. It implies that the probability of being exposed to the public good Qi is no longer individualistic, even if assignment of Di is. The probability of spillover Si plays a crucial role in identification of the population average treatment effect, which we discuss in detail below. These two restrictions on W create four categories of units, with associated conditional probabilities of exposure displayed in Table 1. Having established this notation, we now discuss whether two commonly used quasi-experimental estimators in environmental economics identify the population average treatment effect, τ , from Eq. (2).

4.3 TWO QUASI-EXPERIMENTAL ESTIMATORS IN THE LITERATURE 4.3.1 Average Source Effect Estimator The average source effect estimator (ASEE) compares average outcomes across units that are and are not assigned to be a public good source. A classic example of the ASEE in environmental economics are comparisons of average outcomes across

4 The Quasi-Experimental Approach for Public Goods

FIGURE 2 Illustrating the average source effect estimator. N OTES: The left panel shows the direction of public good spillovers. The middle and right panels show comparisons for the ASEE corresponding to the public good source assignments shown in the middle and right panels of Fig. 1. Red (dark-shaded) cells represent locations that are public good sources with Di = 1. Blue (light-shaded) cells represent locations that are not public good sources with Di = 0. Cells with hatched lines show locations that are exposed to the public good both directly and via spillovers.

counties designated as nonattainment and attainment under the US Clean Air Act. Fig. 2 illustrates the comparison across units that underlies the ASEE for the spatial configuration of public good assignments shown in the middle and right panels of Fig. 1. Red (dark-shaded) cells are locations that are the source of the public good with Di = 1. Blue (light-shaded) cells are locations that are not the source of the public good with Di = 0. The ASEE is essentially a comparison of average outcomes across red (dark-shaded) and blue (light-shaded) cells in Fig. 2. Formally, the ASEE is τˆ S =

 1  1 Yi − Yi L (N − L) i:Di =1

1 = N

N  i=1

i:Di =0

Di (Qi Y1i + (1 − Qi )Y0i ) (1 − Di )(Qi Y1i + (1 − Qi )Y0i ) − L/N (N − L)/N

(6)

where the second line applies Eq. (3). The expected value of τˆ S over all D realizations is N 1  Y1i ED [Di Qi |Yi ] Y0i ED [Di (1 − Qi )|Yi ] S ED [τˆ |Yi ] = + N L/N L/N i=1

Y1i ED [(1 − Di )Qi |Yi ] Y0i ED [(1 − Di )(1 − Qi )|Yi ] − − (N − L)/N (N − L)/N N 1  = (1 − Si )(Y1i − Y0i ) N

(7)

i=1

where the first line expands the expression for the estimator. The second line applies (N−L) L ED [Di Qi |Yi ] = ED [Di |Yi ] = N and ED [Qi |Yi ] = L+Si N .

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The externality associated with public good source Di leads to spillovers in exposure, Qi , as characterized by Eq. (5). A comparison of average outcomes between units that are and are not the source of the public good yields a biased estimate of the population average treatment effect τ because some units in the control group also experience changes in public good exposure due to externality spillovers. These units are shown in gray hatched lines in Fig. 2. This non-individualistic assignment of public good exposure constitutes a violation of SUTVA. The degree of SUTVA violation is captured by Si , the probability that unit i is exposed to the public good conditional on not being a public good source. Since Si is bounded between 0 and 1, the sign of the bias in τˆ S is known. It is helpful to consider three cases. In the first case, Qi is a private good and all off-diagonal terms in the matrix W are zero so that there are no externality spillovers. In that case, we return to the standard unit-level randomization setting with Si = 0 ∀i and the ASEE is unbiased, ED [τˆ S |Yi ] = τ . The second case is the other extreme where Qi is a global public good and all off-diagonal terms in W are positive. Because the entire population is now exposed to the public good with Si = 1 ∀i, we have ED [τˆ S |Yi ] = 0. Finally, there is the intermediate case with a local public good where some off-diagonal elements in W are zero and others are positive such that Si ∈ [0, 1] ∀i. In that case, 0 < ED [τˆ S |Yi ] < τ . In summary, externalities from local public goods generate spillovers that biases estimates from the ASEE towards zero.

4.3.2 Average Exposure Effect Estimator Another common quasi-experimental estimator compares average outcomes across units that are and are not exposed to the public good arising from quasi-random assignment of public good source D. We call this the average exposure effect estimator (AEEE). A typical AEEE study regresses outcomes on pollution that originates from elsewhere. Fig. 3 illustrates how the AEEE compares units for the spatial configuration of public good assignments shown in the middle and right panels of Fig. 1. Brown (dark-shaded) cells are locations that are exposed to the public good with Qi = 1. Gray (light-shaded) cells are locations that are not exposed to the public good with Qi = 0. The AEEE takes the difference in average outcomes across brown (dark-shaded) and gray (light-shaded) cells. For simplicity, suppose the number of units receiving the public good, M, is fixed, and L ≤ M ≤ N . Formally, the AEEE is τˆ E =

 1  1 Yi − Yi M (N − M) i:Qi =1

1 = N

N  i=1

i:Qi =0

(1 − Qi )Y0i Qi Y1i − M/N (N − M)/N

(8)

4 The Quasi-Experimental Approach for Public Goods

FIGURE 3 Illustrating the average exposure effect estimator. N OTES: The left panel shows the direction of public good spillovers. The middle and right panels show comparisons for the AEEE corresponding to the public good source assignments shown in the middle and right panels of Fig. 1. Brown (dark-shaded) cells represent locations that are exposed to the public good with Qi = 1. Gray (light-shaded) cells represent locations that are not exposed to the public good with Qi = 0. Cells with hatched lines show locations exposed to the public good both directly and via spillovers.

where the second line applies Eq. (3). The expected value of τˆ E over all D realizations is ED [τˆ E |Yi ] =

N ED [Qi |Yi ] Y0i ED [(1 − Qi )|Yi ] 1  − Y1i N M/N (N − M)/N i=1

=



N L + Si (N − L) (N − L)(1 − Si ) 1  − Y0i Y1i N M N −M

(9)

i=1

where the second line applies the probabilities in Table 1 and ED [Qi |Yi ] = L+Si (N−L) . Eq. (9) shows that the AEEE heterogeneously weights potential outN comes for each unit. The weight on Y1i is the combined likelihood of experiencing L public good exposure from being the source, M , and from receiving spillovers, Si (N−L) . The weight on Y0i is the likelihood of jointly not being the public good M i) source and not receiving spillovers, (N−L)(1−S . N−M Again, it is useful to consider three cases. First, in the private good setting with no spillovers, the number of units receiving exposure equals the number of source units, M = L, and Si = 0 ∀i. In that case, the AEEE is unbiased, with ED [τˆ E |Yi ] = τ . Second, in the case of a global public good, all units become exposed such that M = N and Si = 1 ∀i. As a consequence, ED [τˆ E |Yi ] becomes undefined. For the intermediate of a local public good with L < M < N and Si ∈ [0, 1], Eq. (9) shows that the AEEE places greater relative weight on Y1i than on Y0i as Si , the likelihood of exposure from spillovers, increases. As a consequence, the AEEE is biased if potential outcomes and the likelihood ofexperiencing a public good spillover are correlated, or formally whenever N1 N i=1 Y1i Si = 1 N 1 N 1 N 1 N 1 N ( N i=1 Y1i )( N i=1 Si ) and N i=1 Y0i Si = ( N i=1 Y0i )( N i=1 Si ). This is a form of selection bias. In our air pollution example, poorer households may tend to

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live downwind from polluting plants (Heblich et al., 2016). Thus, even if pollution abatement policy were quasi-randomly assigned, sorting implies a greater likelihood that poorer households are exposed to a change in air pollution. Unlike the ASEE, unless the exact nature of sorting is known, the sign of the bias in the AEEE is generally ambiguous. When is the AEEE unbiased? It is unbiased when potential outcomes are uncorrelated with the likelihood of experiencing a spillover. To see this, observe that with fixed number of public good source and exposed units, we have N i=1 ED [(1 − L and ED [Qi |Yi ] = Di )Qi ] = M − L. Applying ED [Di Qi |Yi ] = ED [Di |Yi ] = N L+Si (N−L) , we have N N M −L 1  Si = N N −L

(10)

i=1

This implies that Eq. (9) can be further reduced to



N 1  L + Si (N − L) (N − L)(1 − Si ) ED [τˆ |Yi ] = − Y0i Y1i N M N −M i=1    N N N L 1  N −L 1  1  Y1i + Y1i Si = M N M N N i=1 i=1 i=1    N N N N −L 1  1  N −L 1  Y0i + Y0i Si − N −M N N −M N N E

i=1

i=1

i=1

N 1  (Y1i − Y0i ) = τ = N i=1

where the second equality applies the assumption that potential outcomes are uncor 1 N 1 N related with spillover likelihood, or N1 N Y S = ( Y )( i=1 1i i i=1 1i N i=1 Si ) and N 1 N 1 N 1 N i=1 Y0i Si = ( N i=1 Y0i )( N i=1 Si ). The third equality applies Eq. (10). In N summary, even if public good sources were quasi-randomly assigned, the AEEE is biased for local public goods when potential outcomes are correlated with the likelihood of externality spillovers. This bias may be due to selection on observables or on unobservables. In the case of selection on observables, we discuss how one can test for bias in the AEEE in Section 6.1. Of course, there are no direct remedies for selection on unobservables.

4.4 AN UNBIASED ESTIMATOR FOR LOCAL PUBLIC GOODS Eq. (7) suggests that a simple re-weighting of observations will allow the ASEE to produce an unbiased estimate of τ . Specifically, one can divide observations by 1 − Si , the probability of not receiving the externality spillover conditional on not being the public good source. This weighting scheme will down weight control units

4 The Quasi-Experimental Approach for Public Goods

that are likely to experience spillovers while up weight those that are less likely to experience spillovers. Specifically, the weighted average source effect estimator (WASEE) is τˆ W =

 Yi Yi 1  1 − L (1 − Si ) (N − L) (1 − Si ) i:Di =1

=

1 N

N  i=1

i:Di =0

Di (Qi Y1i + Di (1 − Qi )Y0i ) (1 − Di )(Qi Y1i + (1 − Qi )Y0i ) − (1 − Si )L/N (1 − Si )(N − L)/N



(11) The same derivation leading to Eq. (7) shows that ED [τˆ W |Yi ] = τ for local public goods. Unfortunately, as with the AEEE, the WASEE is undefined in the presence of a global public good. Eq. (11) seems to suggest that if unit-level spillover likelihoods were available, a researcher should always implement the WASEE, especially since the possibility of selection on unobservables will generate bias in the AEEE. Unfortunately, the ASEE and by extension, the WASEE may not be possible to implement in all empirical settings. Consider again the case of air pollution regulation. Suppose the subpopulation of interest are households residing in locations exposed to air pollution. However, these locations do not contain polluting firms and thus would never be pollution sources. In such a setting, only the AEEE can be implemented for the subpopulation of interest and the only remedy available to a researcher is to test for selection on observables, as will be discussed in Section 6.1.

4.5 ILLUSTRATIVE SIMULATIONS We now turn to simulations to illustrate the potential biases in our three estimators: ASEE (τˆ S ), AEEE (τˆ E ), and WASEE (τˆ W ). To avoid unnecessary complications, we consider the simple geography displayed in Fig. 1, with N = 9 units located on a 3 × 3 grid. For each policy realization, one randomly chosen unit receives the public good, Di = 1. Under the spatial pattern of externality spillover shown in the left panel of Fig. 1, the bottom right corner unit experiences the highest likelihood of spillovers, Si . To examine what happens when spillover likelihood and potential outcomes are correlated, we consider two configurations of baseline potential outcomes Y0i ∈ {1, . . . , 9}. In the first configuration, the bottom right unit has Y0i = 1 while elements in the set {2, . . . , 9} are randomly assigned to Y0i of other units. This generates a negative correlation between Y0i and Si . The second configuration exhibits positive correlation between Y0i and Si by assigning the bottom right unit Y0i = 9 with elements in the set {1, . . . , 8} randomly assigned to Y0i of other units. The simulation draws 10,000 realizations of D with the population average treatment effect set at τ = 5 and assumed to be constant across units. Table 2 shows the expected value for the ASEE, AEEE, and WASEE when Y0i is negatively correlated

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Table 2 Sample means of ASEE and AEEE estimates based on simulated data Private good Local public good

ED [τˆ−S |Yi ] 4.99

ED [τˆ+S |Yi ] 4.99

ED [τˆ−E |Yi ] ED [τˆ+E |Yi ] ED [τˆ−W |Yi ] ED [τˆ+W |Yi ] 4.99 4.99 4.99 4.99

4.64

4.65

3.9

5.4

4.99

4.99

N OTES : Table 2 shows estimates for the ASEE (τˆ S ), AEEE (τˆ E ), and WASEE (τˆ W ) averaged over 10,000 simulations when baseline potential outcomes, Y0i , are negatively (−) or positively (+) correlated with likelihood of spillovers, Si . The private good simulations assume the off-diagonal terms in the weighting matrix W are zero. The local public good simulations use W based on the spatial pattern of externality spillovers shown in the left panel of Fig. 1.

(−) and positively correlated (+) with spillover likelihood, Si . When treatment involves a private good, that is when off-diagonal terms in the weighting matrix W are zero and Si = 0 ∀i, all three estimators are unbiased and the spatial arrangement of baseline characteristics does not matter. When the treatment involves a local public good, the ASEE and AEEE are both biased. The ASEE is biased towards 0 due to a SUTVA violation. This bias does not depend on whether baseline characteristics, Y0i are correlated to spillover probabilities. The AEEE is also biased and the direction of this bias is negative when the likelihood of spillover effects is negatively correlated with baseline potential outcomes and positive when spillover likelihood is positively correlated with baseline potential outcomes. Table 2 also shows that estimates from the WASEE are always unbiased. The empirical distribution of the ASEE and AEEE estimates under the two correlation structures are shown in Fig. 4.

5 LITERATURE REVIEW This section reviews published environmental economics papers that apply quasiexperimental methods. We begin by summarizing recent publication trends. We then review select papers that employ the average source effect estimator and average exposure effect estimator to obtain the marginal social benefits of environmental goods. Finally, we also review quasi-experimental papers that estimate the marginal cost of environmental good provision.

5.1 PUBLICATION TRENDS We searched for environmental economics papers using quasi-experimental methods published between 2000–2017 in the Journal of Environmental Economics and Management, the Journal of Public Economics, and 10 general interest economics

5 Literature Review

FIGURE 4 Distribution of estimates of ASEE and AEEE for different configuration of baseline characteristics. N OTES: Fig. 4 shows the empirical distribution of the estimates for ASEE (τˆ S ) and AEEE (τˆ E ) for 10,000 simulations when baseline potential outcomes, Y0i , are negatively (−) or positively (+) correlated with likelihood of spillovers, Si .

journals.13 To perform this query, we searched for articles in the Econlit database using an extensive list of keywords.14 This initial search produced a total of 557 papers. We then manually examined each article to determine if they employed quasi-experimental methods, and then classified them according to the method used: difference-in-difference, panel fixed effect, instrumental variables, and regression discontinuity.15 We acknowledge from the onset that our search criteria and classification method may have omitted environmental economics papers in these journals that used quasi-experimental methods. Furthermore, articles published in other economics journals or journals outside of economics were excluded from this review.

13 The general interest journals are: American Economic Review (excluding papers published in the May

Papers & Proceedings), the American Economic Journals, Econometrica, the Journal of Political Economy, the Quarterly Journal of Economics, the Review of Economics and Statistics, and The Review of Economic Studies. We omit the Journal of the Association of Environmental and Resource Economists, an important field journal that only began publication in 2014. 14 The full list of title words is: environment, environmental, resource, natural, air, water, climate, temperature, pollution, agriculture, land, forest, deforestation, and energy. The search was conducted in February 2018. 15 We classify papers as using the difference-in-difference method when the treatment and control groups in the analysis are defined on the basis of a discrete environmental policy or regulation. We classify papers as panel fixed effects in cases where the causal effect of interest is identified from within unit comparisons of changes in treatment status over time, where the changes in the treatment status are more arbitrary (i.e., not tied to a policy or regulation).

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FIGURE 5 Trend in the share of published environmental economics papers using quasi-experimental methods. N OTES: Share of published environmental economics papers using quasi-experimental methods year of publication. Journals include American Economic Journals, American Economic Review, Econometrica, Journal of Environmental Economics and Management, Econometrica, the Journal of Political Economy, the Journal of Public Economics, the Quarterly Journal of Economics, the Review of Economics and Statistics, and the Review of Economic Studies.

We begin by looking at the relative role of quasi-experimental methods in environmental economics. Fig. 5 plots the annual share of papers using quasi-experimental methods among the set of environmental economics papers identified through our search criteria. Amongst the journals we consider, quasi-experimental methods have become increasingly prominent over the last two decades. The first quasiexperimental environmental economics paper identified in our literature review is “Effects of Air Quality Regulations on Polluting Industries” by Vernon Henderson and Randy Becker, published in the Journal of Political Economy in 2000. In 2017, 32% of published papers used quasi-experimental methods. Fig. 6 shows just the numerator from Fig. 5, i.e., the annual number of published papers in environmental economics using quasi-experimental methods. Following a relatively slow start in the 2000s, publications pick up around 2010 (one year after the introduction of the American Economic Journals), reaching a peak of 18 papers in 2017. Over this period, a cumulative total of 90 quasi-experimental papers have been published. Fig. 6 also breaks down annual published papers by quasi-experimental method. Table 3 shows the number of environmental economics papers and the subset of papers using quasi-experimental methods by journal and method during the 2000–2017 period. The Journal of Environmental Economics and Management has the most with 387 papers returned by our search criteria, of which 38 employed quasi-experimental methods. The next highest are the American Economic Jour-

5 Literature Review

FIGURE 6 Trends in the number of published quasi-experimental environmental economics papers by method. N OTES: The number of published papers using quasi-experimental methods in environmental economics by year of publication and method. Journals include American Economic Journals, American Economic Review, Econometrica, Journal of Environmental Economics and Management, Econometrica, the Journal of Political Economy, the Journal of Public Economics, the Quarterly Journal of Economics, the Review of Economics and Statistics, and the Review of Economic Studies.

nals, which have published 24 environmental economics papers, of which 13 were quasi-experimental. No quasi-experimental papers in environmental economics were published in Econometrica and only 2 were published in The Review of Economics Studies. Across the four quasi-experimental methods, difference-in-difference (including triple-difference and synthetic control methods) is the most popular, accounting for 50% of all quasi-experimental papers. Panel fixed effects, instrumental variables, and regression discontinuity account for 29%, 13%, and 8% of all environmental economics papers in these journals, respectively. Fig. 7 organizes our subset of published quasi-experimental papers in environmental economics (total = 90) into 4 groups based on the estimator, parameter of interest, environmental good, and outcome under study. These 4 categories account for 45, 14, 12, and 19 papers, respectively. The largest category, Box A, contains papers that use the ASEE to estimate the marginal social benefit of environmental policies. Outcomes examined in this part of the literature are (i) air pollution (11 papers); (ii) labor market outcomes and productivity (7 papers), health outcomes (4 papers), housing values (3 papers), and other.16

16 These other outcomes include environmental expenditures, patents, electricity consumption, and foreign

direct investment (20 papers).

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CHAPTER 7 Quasi-experimental methods in environmental economics

Table 3 Number of published papers in environmental economics by journal and method All EE papers

Quasi-experimental EE papers All QE methods DID Panel FE

IV

RD

American Economic Journals

24

13

6

6

0

1

American Economic Review

31

10

5

4

0

1

Econometrica

1

0

0

0

0

0

Journal of Env. Econ. and Mgmt

387

38

23

9

4

2

Journal of Political Economy

12

6

2

1

2

1

Journal of Public Economics

53

6

3

1

1

1

Quarterly Journal of Economics

7

5

1

2

1

1

Review of Economics and Statistics

37

10

5

2

3

0

Review of Economic Studies

5

2

0

1

1

0

557

90

45

26

12

7

TOTAL

NOTES: Published papers in environmental economics by journal and method during 2000–2017.

The papers in Box B estimate the marginal social benefit of air pollution, using the AEEE. These papers rely on sources of quasi-experimental variation in the source of air pollution originating from other locations. For example, some papers use the opening and/or closing of polluting plants nearby to generate exogenous local variation in pollution exposure. Other papers use traffic patterns, network congestion, and public transport strikes elsewhere as instrumental variables for local air pollution exposure. The main outcome variables in this group are health outcomes (6 papers), housing values (3 papers), labor market outcomes and productivity (3 papers), and school outcomes (2 papers). Box C summarizes an emerging literature on the economic effects of temperature fluctuations. These papers use the AEEE with the goal of informing the marginal social benefit of greenhouse gas abatement by estimating the damage associated with higher temperatures. The 12 published studies generally focus on identifying the effect of temporal variation in temperature for a given location across periods (e.g., days, months, years). The primary outcomes studied are agricultural outcomes (4 papers), health outcomes (4 papers), and other outcomes such as GDP growth rate (4 papers). The last category, represented by Box D, is composed of papers that concern other important parameters in environmental economics as well as other environ-

5 Literature Review

FIGURE 7 Breakdown of the quasi-experimental literature in environmental economics by parameter, estimator, treatment, and outcome.

mental goods. In addition to estimating the marginal social benefit of environmental goods, these quasi-experimental papers also examine the marginal cost of environmental policy as well as various related political economy questions. These papers also study other environmental goods such as toxic chemicals and water pollution. One striking observation from Fig. 7 is just how few quasi-experimental studies there are of environmental attributes besides air pollution and temperature. Of the 90 identified quasi-experimental papers published between 2000–2017, only a handful of papers examine other environmental goods. The general lack of quasi-experimental evidence for other environmental goods suggests potential opportunities for future research.

5.2 A SELECTED REVIEW OF AVERAGE SOURCE EFFECT ESTIMATES The average source effect estimator (ASEE) compares units that are and are not the source of an environmental good that is quasi-randomly assigned. The canonical application of this estimator exploits the introduction of a spatially-differentiated environmental policy, such as national environmental policies with sufficiently intricate local implementation to estimate the policy’s marginal social benefit. In such settings, the assignment of local regulation is argued to be exogenous to local economic circumstances. Here, we review several prominent papers in this literature.

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The Clean Air Act (CAA) is the primary national policy in the United States that regulates sulfur dioxide, particulates, nitrogen dioxide, carbon monoxide, ozone, and lead air pollution. Beginning with the seminal papers by Henderson (1996) and Becker and Henderson (2000), researchers have since examined over five decades of the CAA, and its amendments in 1970, 1977 and 1990. Most empirical analyses of the CAA employ the ASEE by comparing average outcomes between counties that are more regulated under “non-attainment” status with those that are less regulated under “attainment” status. The predominant identification strategy, pioneered by Chay and Greenstone (2005), uses a difference-in-difference research design, sometimes combined with an instrumental variables approach. These papers typically begin with a first-stage analysis estimating the change in ambient pollution before and after the introduction of a particular CAA amendment and between counties that are designated non-attainment and attainment. For example, Chay and Greenstone (2005) find the implementation of the first amendments to the Clean Air Act in the early 1970s led to a large relative change in T SP concentrations in non-attainment counties. In fact they attribute virtually all the national-level decline in T SP concentrations to the CAA regulation. Auffhammer et al. (2009) study the 1990 CAA and find substantial heterogeneity in the effect of this regulation on PM10 concentrations.17 In particular, they find no effect of the regulation on concentrations measured at the typical non-attainment county. However, there is an 11–14% reduction in PM10 concentrations for monitors located in high-pollution non-attainment counties.18 The second-stage analysis then proceeds by estimating how changes in local air pollution induced by regulations such as the CAA affects an economic outcome that help to recover the marginal social benefit of improving air quality. To do this, an instrumental variables approach is usually implemented on a first-differenced regression equation relating changes in the economic outcome in a location over time to corresponding changes in measured air pollution that is instrumented by early period non-attainment status in that location. Thus the identifying assumption is that early period non-attainment status only affects an outcome through its effect on the regulated air pollutant. A violation of this assumption would occur if early period non-attainment status led to changes in the outcome of interest through a channel other than air pollution, or if early period non-attainment status affects more than one pollutant. Since non-attainment status is a function of lagged air pollution levels, the assumption requires that unobserved shocks in the process under study are unrelated to past air pollution levels that determine non-attainment status. For example, nonattainment status may affect air pollution and local labor demand, thereby making the identification strategy invalid for estimating the effect of pollution on housing values, since the housing market may respond to local labor market conditions. 17 Under the CAA, particulate matter was denoted as total suspended particulates (TSP) until 1987 when

EPA began explicitly regulating PM2.5 and PM10. 18 Another part of this literature on the effect of environmental regulations on air quality examines trans-

portation policies (e.g., Auffhammer and Kellogg, 2011; Davis, 2008).

5 Literature Review

Motivated by hedonic theory suggesting that willingness to pay for non-market amenities can be inferred from housing values, the primary outcomes studied in this part of the quasi-experimental literature are housing values or rents.19 Chay and Greenstone (2005) present the first such study using quasi-experimental methods. Focusing on changes in average housing values for U.S. counties between 1970 and 1980 and using T SP non-attainment status in 1975 to instrument for pollution changes, they report estimates indicating that one µg/m3 reduction in T SP caused a 0.2 to 0.4% increase in housing values. This corresponds to elasticities ranging from −0.20 to −0.35. Chay and Greenstone (2005) also note that their IV estimates are remarkably larger than previous non-experimental estimates and attribute this difference to omitted variables bias. Grainger (2012) and Bento et al. (2015) extend the Chay and Greenstone (2005) approach to study the 1990 CAA amendments and exploit spatial heterogeneity in the impact of the amendments on air pollution. An innovation in Grainger (2012) is to estimate separate models for rents and owner-occupied housing values. He finds that a one µg/m3 reduction in PM10 leads to a 1% to 2% decrease in owner-occupied housing values. As expected, the corresponding estimates for rents are significantly smaller. Bento et al. (2015) further extend this idea by using track-level data and by estimating separate models for housing units located “closer” to and “farther” from PM10 monitoring stations. They find that most of the benefits of PM10 reductions concentrations accrue to housing units located within 5 miles of monitoring stations. This approach for measuring the benefits of air quality improvements has also been extended to studies of the contemporaneous effect of air pollution on health (Chay et al., 2003; Chay and Greenstone, 2003; Sanders and Stoecker, 2015), and to studies of the long-run effect of air pollution on labor market outcomes such as earnings and employment (Isen et al., 2017). Specifically, Isen et al. (2017) relate earnings (measured around age 30) to average T SP levels in the county and year of birth for a large sample of U.S. workers, and instrument for birth-year TSP levels with the early 1970s non-attainment status of each county. They those exposed to lower concentrations of T SP in early life as a result of the 1970 CAA amendments earn about 1% more on average 30 years later. The pollutant of interest in much of the quasi-experimental CAA literature is particulate matter (or T SP ). In the context of the identification framework in Section 4, environmental externality spillovers likely result in estimates of CAA affects that are biased towards zero. However, a focus on particulate matter over other regulated ambient pollutants has a distinct advantage: particulates tends to disperse locally. For example, a power plant in a non-attainment county may emit particulate matter that

19 Quasi-experimental estimates of housing values allow welfare interpretations only under certain assump-

tions, as summarized by Kuminoff et al. (2013). The literature offers various tests of these assumptions within quasi-experimental settings (Klaiber and Smith, 2013; Gamper-Rabindran and Timmins, 2013; Kuminoff and Pope, 2014).

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travels to an adjacent county, especially if that plant is located near the county border. However, it is unlikely for particulates to continue onto counties that are further away. This implies that the downward bias in the ASEE for particulate matter from a SUTVA violation will be smaller than for pollutants traveling greater distances. Deschenes et al. (2017) estimates a ASEE on the direct health impacts and defensive expenditures related to nitrogen oxides (NOx ) and ozone pollution. Specifically, they estimate the health impact of EPA’s NOx Budget Program (NBP), a cap-andtrade market affecting over 2,500 electricity generating units and industrial boilers located in the Eastern and Midwestern United States operating between 2003 and 2008.20 An important feature of this market is that it was only operational during the “ozone summer season,” defined as May 1st to September 30th of each year. Deschenes et al. (2017) first reports triple-difference estimates of the impact of the cap-and-trade market on NOx emissions, ambient ozone concentrations, and health outcomes. Using county-by-season-by-year level data for 2,500 U.S. counties, they find that NBP led to a 40% decline in NOx emissions during the ozone summer season as well as large reductions in high ozone days and sizable health benefits as captured by reductions in medication expenditures and premature mortality. While such reduced-form analysis can be interpreted under reasonably weak assumptions (e.g., the absence of county-by-season-by-year level unobserved shocks), Deschenes et al. (2017) also implement an instrumental variable strategy that follows in the spirit of prior CAA studies. Using the implementation of the NBP market as an instrument for NOx and ozone requires that the NBP market does not affect other determinants of health outcomes. Unlike previous instrumental variables studies of air pollution, Deschenes et al. (2017) report first stage estimates associated with the implementation of NBP for all air pollutants regulated under the CAA. They find that the reduction in NOx emissions caused by the regulation drives virtually all of the changes in ambient ozone concentrations. They also find less robust evidence that the NBP market led to changes PM2.5 and therefore caution readers about interpreting the resulting instrumental variable estimates in light of this potential violation of the exogeneity assumption. The fact that environmental policies may simultaneously affect more than one pollutant, thereby invalidating the exclusion restriction, should be taken on more directly in future research. In contrast to particulate pollution, NOx can travel large distances and create a SUTVA violation if downwind locations are assigned as control units.21 Deschenes et al. (2017) indirectly address this concern by estimating a coarse version of the weighted ASEE, introduced in Eq. (11). Specifically, they drop states from the sample that are immediately adjacent to states regulated under NBP to minimize concerns about pollution spillover.

20 The NBP market later became part of the Clean Air Interstate Rule, which was replaced by the Cross-

State Air Pollution Rule in 2011. 21 For example, according to Husar and Renard (1997), on the 96 percent of days in the NBP region where

wind speeds are below 6 meters per second, ozone and its precursors can travel up to 300 miles.

5 Literature Review

The ASEE has also been applied in various developing country settings. Greenstone and Hanna (2014) study the effect of major air and water quality policies in India using city-level data over 1986–2007. Using a difference-in-difference estimator to compare outcomes within Indian cities pre- and post-regulation adoption, they find that air quality regulations (in particular the mandate for new vehicles to adopt catalytic converters) led to large improvements in air quality (PM100 and SO2 ). However, water pollution regulations had no detectable effect on water quality (e.g., biochemical oxygen demand and dissolved oxygen). Overall the reductions in air pollution caused by regulations in India did not lead to significant reductions in infant mortality rates. Air quality regulations are sometimes introduced as temporary measures. An interesting example is the series of air pollution regulations implemented by the Chinese government in Beijing and surrounding cities starting around the time of the 2008 Beijing Olympics. Such regulations required the temporary shutdown of polluting industries, the installation of pollution control equipment at coal-fired power plants, and the implementation of traffic control policies. Because of air pollution spillovers, neighboring cities and provinces were also required to implement pollution control programs. He et al. (2016) document the effects of these regulations on air quality and mortality rates. Using city-month data for 34 large cities in China and the 2008 regulation as an instrument for PM10 , they find that PM10 concentrations fell by 25 µg/m3 , or roughly 25%, as a result of these policies. They also find a positive and statistically significant effect of PM10 concentration on mortality from cardiovascular disease.

5.3 A SELECTED REVIEW OF AVERAGE EXPOSURE EFFECT ESTIMATES The average exposure effect estimator (AEEE) compares units that are and are not exposed to the public good. Quasi-experimental AEEE implicitly assume that the origin source of this environmental good is sufficiently “far-away” such that whatever caused it has otherwise no direct effect on local outcomes. Here, we briefly discuss two broad sets of AEEE applications looking at the effects of ambient air pollution and local temperature on various outcomes. Graff Zivin and Neidell (2012) study the effect of daily ambient ozone pollution on the labor productivity of agricultural workers in California’s Central Valley. Their setting has three main empirical advantages. First, outdoor agricultural field workers, in this case blueberry pickers, are directly exposed to ambient pollution. Second, their productivity is quantifiable in terms of fruit harvested per hour and observable through payroll systems. Third, the authors argue that local ozone fluctuations over California’s Central Valley are plausibly exogenous to unobserved local determinants. This is because ozone is not directly emitted, but rather produced through nonlinear interactions between local environmental factors such as temperature and sunlight and the presence of nitrogen oxides (NOx ) and volatile organic chemicals (VOCs). In particular, it is assumed that conditional on controls, the factors caus-

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ing NOx and VOCs emissions from distant coastal locations and transported to the Central Valley are unrelated to local outcomes in the Central Valley. Graff Zivin and Neidell (2012) combine daily data from the 2009 and 2010 growing seasons on 1,600 workers with daily ozone concentrations measured from nearby agricultural sites. Using a panel fixed effects regression with worker fixed effects, they find that a 10 ppb decrease in daily ozone concentration leads to a 5.5% increase in worker productivity, although some point estimates are not statistically significant. This approach for documenting productivity benefits of environmental regulation has since been extended to other countries, other air pollutants, indoor office settings, and manufacturing settings (e.g., Chang et al., 2016 and He et al., 2016). Neidell (2017) presents an overview of this literature. Another prominent application of the AEEE is Schlenker and Walker (2016) who study the effects of carbon monoxide (CO), nitrogen dioxide (NO2 ), and ozone air pollution generated by major airports in California on hospital visit rates for households living near airports. Schlenker and Walker (2016) devise an identification strategy that exploits local air pollution shocks generated by conditions elsewhere. Specifically, they observe that plane taxi times in large California airports is driven, in part, by congestion occurring at large Eastern U.S. airports. These delays serve as instruments for cumulative taxi times in California airports and are unlikely to directly affect local health outcomes near California airports.22 Schlenker and Walker (2016) first document that taxi times in remote Eastern U.S. airports drive local air pollution in large California airports. They find that a 1000 minute increase in daily taxi time increases ambient CO concentrations close to airports by 45 ppb, an 8% increase relative to the mean daily concentration. They then report IV estimates of the effect of CO on hospital visits related to respiratory and heart diseases and find that a one standard deviation increase in CO concentrations leads to a 21% increase in daily hospital admissions for asthma, and to an 18% increase in daily hospital admissions for heart disease. A third air pollution example AEEE is the Currie et al. (2015) study which examines the effects of toxic hazardous airborne pollutants (HAPs) such as benzene, cumene, and nickel. Currie et al. (2015) estimate the economic costs associated with HAPs by comparing housing values and infant health across households exposed to different HAPs levels.23 Specifically they combine data on toxic releases by individual industrial plants from the Toxic Release Inventory database, housing transactions, and infant health at a high degree of spatial granularity from Texas, New Jersey, Pennsylvania, Michigan, and Florida. Their difference-in-difference strategy exploits the

22 The use of congestion from other parts of a transportation network to derive instruments for local air

pollution has appeared elsewhere in the literature (e.g., Moretti and Neidell, 2011, using boat traffic in ports, and Knittel et al., 2016, using road traffic). 23 Currie et al. (2015) is part of a rich literature in environmental economics that studies the economic, social, and health outcomes associated with the pollutants generated by industrial activity in the United States and elsewhere. See for example, Bui and Mayer (2003), Davis (2011), and Greenstone and Gallagher (2008).

5 Literature Review

timing of “toxic” plant openings and closing and compares outcomes for locations that are within 0.5 miles (treatment) vs 1–2 miles (control) away from the opening and/or of a closing toxic plant. This spatial distinction between treatment and control groups emerges from first empirically examining the spatial decay of hazardous pollution as a function of radial distance from a toxic plant. In this context, the identifying assumption is that unobserved circumstances leading to a toxic plant opening or closing has a uniform effect on housing market and infant health trends across treatment and control groups. Currie et al. (2015) finds empirical support for this assumption by failing to detect differential pre-trends in outcomes across treatment and control groups. Using this approach, Currie et al. (2015) find that toxic emissions have sizable negative effects on housing values. Specifically, they estimate that the opening of a toxic plant lowers housing prices by 11% while plant closings have little effect on housing values. They interpret this as suggesting that the presence of a toxic plant continues to create disamenities even after operation ceases, perhaps because of concerns about long-term environmental contamination. Finally, Currie et al. (2015) also find that the opening and closing of toxic plants reduces the probability of low birth weight for infants whose mother lives within 1 mile of a toxic plant. In all these studies, there is an acknowledged understanding that estimates pertain to particular subpopulations and may not generalize to a broader population. Graff Zivin and Neidell (2012) note that “While the impacts of ozone on agricultural productivity are large, the generalizability of these findings to other pollutants and industries is unclear.” Similarly Schlenker and Walker (2016) observe that zip codes closer to a major airport in California are more urban, more populated, wealthier, and have higher housing prices than zip codes from the rest of California, writing “Therefore, we would caution against interpreting the estimated dose–response relationship as representative for the entire population at large.” Finally, the subpopulation of interest in the Currie et al. (2015) study is U.S. residents living near industrial plants that emit toxic pollutants. Indeed, they report that locations that are further away from an industrial plant have higher housing values and different maternal characteristics. Our concerns about potential selection bias in the AEEE still hold for estimands defined over subpopulations. For example, in the case of air pollution from industrial plants, rather than define the set of locations that emit air pollution as the population of interest, one can instead consider a subpopulation of locations that contain industrial plants. The estimand of interest will then be the average treatment effect for this subpopulation. Identification of this subpopulation estimand using the AEEE requires that the likelihood of spillovers, Si , be uncorrelated with potential outcomes, Y1i and Y0i . We conclude this section with papers that apply the AEEE to examine the effects of atmospheric variables, such as temperature and precipitation, on various economic and social outcomes. These papers are primarily motivated by an interest in informing the marginal social benefit of climate change policy. Before describing these papers, it is first important to distinguish between climate and weather. In atmospheric physics,

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climate typically describes the distribution of an atmospheric variable while weather denotes a particular realization of that distribution. The distribution of interest may be defined either across space or time. For example, for a given time period, the climate can be summarized by the average temperature across locations and weather is the temperature in a particular location. Similarly, for a given location, the climate can be described by the average temperature over time while weather is temperature at a single period. Anthropogenic climate change (ACC) alters the distribution of atmospheric conditions in both spatial and temporal dimensions. ACC poses a particular challenge for quasi-experimental methods along the spatial dimension. It is the result of greenhouse gas emissions, a global pollutant by virtue of its atmospheric mixing and long decay properties. When a unit of greenhouse gas is emitted into the atmosphere anywhere on the planet, it changes local atmospheric conditions everywhere. There is no control group as every location on the planet is exposed. As we showed in Section 4.3.2, for a global public good the ASEE produces an estimate of and both the AEEE and WASEE are undefined. Thus, the key question along the spatial dimension is how to interpret estimates based on local weather as proxies for global ACC impacts. That is, how relevant are comparisons across locations that experience different weather conditions when the ultimate policy question of interest involves a global pollutant that simultaneously changes the global climate. We defer this important issue for now and return to it in Section 6.2. Much of the existing AEEE literature estimating the effects of atmospheric variables focuses on the distinction between climate and weather along the temporal dimension. In particular, these papers have explored whether quasi-experimental estimates include adaptation behavior in anticipation of expected changes in average temperature over any location. These studies have been labeled by Dell et al. (2014) as the “New Climate-Economy Literature.” The quasi-experimental literature using local weather variability begins with the Deschenes and Greenstone (2007) study of how weather shocks affect U.S. agricultural profits. The paper was motivated by the seminal cross-sectional Ricardian approach of Mendelsohn et al. (1994). Deschenes and Greenstone (2007) argue that such cross-sectional estimates of the effect of temperature on agricultural land values were not identified by quasi-experimental variation and so possibly biased. This bias would arise in the land value application when cross-sectional average temperatures are correlated with unobserved time-invariant determinants of land values such as unmeasured soil quality or the potential for conversion to non-agricultural land use. Deschenes and Greenstone (2007) propose using year-to-year variation in temperature and rainfall to estimate effects on agricultural profits. Under the assumption that temporal changes in weather in a given location are as good as randomly assigned, identification of the temperature effect on profits (or any other economic outcome) is straightforward via an application of the panel fixed effects method. Deschenes and Greenstone (2007) implement this approach using a county-year panel for the United States over 1987–2002 and report a statistically insignificant re-

5 Literature Review

lationship between weather shocks and U.S. agricultural profits. Based on that, they argue that climate change would have a relatively small economic impact on the U.S. agricultural sector, especially since damages measured from short-run variation are likely to overstate long-term damages. This paper has spawned a large subsequent literature on various outcomes beside agricultural outcomes including 12 of the published papers tabulated in Section 5.1 and numerous other papers not reviewed here.24 The findings in Deschenes and Greenstone (2007) attracted interest and also criticism. In particular, Fisher et al. (2012) identifies errors in the data used by Deschenes and Greenstone (2007) and argues as a result that the negative impact of climate change on agriculture was larger than the estimate reported in the original study. In their response to Fisher et al. (2012), Deschenes and Greenstone (2012) correct their estimates to account for such errors and use a more recent set of projections from the CCSM model (unavailable when the initial paper was published in 2007). Based on that, Deschenes and Greenstone (2012) conclude that the present discounted value of lost agricultural profits due to climate change over the next 90 years was $164 billion (in 2002 dollars), or about 5 times annual U.S. agricultural profit. Burke and Emerick (2016) proposed an extension of the original analysis by using long-differences (i.e., defined over 20 years) instead of the 5-year differences used in Deschenes and Greenstone (2007). The motivation for using longer differences is that it leverages quasi-experimental variation in temperature trends over longer time periods. In principle, this longer time horizon allows for a wider range of possible adaptation behavior to offset temperature effects provided that realized trends were indeed anticipated by agents ex-ante. In their application for the U.S. farming sector, Burke and Emerick (2016) find similar effects of high temperatures on corn and soybeans yields using the long and short difference approaches. They interpret this finding as evidence of limited longer term adaptation by farmers to mitigate the negative effects of high temperature on crop yields in the shorter term.25 Deschenes and Greenstone (2011) provides the first comprehensive study of the health cost of climate change accounting for both the direct cost in terms of reduced health, and the economic cost of adaptation, as approximated by electricity consumption. The paper uses a county-by-year panel for the U.S. over 1968–2002 to estimate the relationship between mortality rates (including age- and cause-specific mortality rates) and the daily distribution of temperature realizations, captured by the number of days per year that fall in various daily temperature categories. The benchmark regression model includes county and state-by-year fixed effects, so the identification comes from temperature deviations relative to county and state-by-year 24 For example, see the highly cited study by Schlenker and Roberts (2009) on the nonlinear relationship

between temperature and yields of corn and soybeans in the U.S. 25 An interesting question is whether the higher frequency variation is more suitable for estimating causal

effects than lower frequency variation. Hsiang (2016) discusses this “frequency-identification trade-off” and argues that lower frequency variation has lower internal validity for measuring causal effects than higher frequency variation.

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averages. This variation is assumed to be uncorrelated with unobserved determinants of health.26 Using this variation, Deschenes and Greenstone (2011) find evidence of heat- and cold-related mortality: each day with temperature above 90◦ F and below 40◦ F is associated with statistically significant increases in the annual mortality rate. Using the same type of panel fixed effect regression as the one described above, they detect a similar “flat U” relationship between energy expenditures and temperature extremes. Interestingly, the adaptation response to temperature variability (in proportional terms) is four times larger than the mortality response to the same temperature variability, suggesting that household defensive investments are important. The Deschenes and Greenstone (2011) analysis was expanded in subsequent studies to further consider the role of humidity in shaping the temperature-mortality relationship (Barreca, 2012), to examining cross-sectional differences in the temperaturemortality relationship across climates (Barreca et al., 2015; Heutel et al., 2017), and across long time periods (Barreca et al., 2016). An important finding in the Barreca et al. (2016) study is the remarkable reduction in the effect of high temperatures on mortality over time. Using a panel of state-byyear-by-month data, they find that high temperature effect on U.S. mortality rates declined by 75% after the 1960s. A second key finding is the protective effect of residential air conditioning on health. Barreca et al. (2016) document large negative interaction terms between air conditioning and high temperature (80–89◦ F and especially >90◦ F), while at the same finding no interaction effect for colder temperatures ( rr: a higher production cost in the future requires a compensating higher price increase to make the producer indifferent 15 See, for example, IEA, World Energy Outlook (2015).

2 The Neoclassical Growth Model: Why and How?

between production today and in the future.16 It should be noted that our analysis here aims at long-run assessments. If one looks at short time horizons, oil production is very costly to vary (less so for unconventional supplies) so a much richer set of dynamics must be specified in order to understand equilibrium in the oil market (see Bornstein et al., 2018). Notice, here, that we have discussed oil supply from the perspective of pricetaking. Given the existence of OPEC, this assumption may not be innocuous. However, many analysts actually argue that price-taking is a good approximation, and certainly a better one than monopoly, given that OPEC controls less than 50% of the market, and we will therefore not consider monopoly power here.17 Turning to coal, the total estimated amount of coal is much larger. The amount of recoverable coal resources is in the order of 15,000 GtC according to IEA, though only a part of this quantity is profitable to extract at current prices. Moreover, the marginal cost of coal is very close to its price (which is consistent with its available reserves being “nearly infinite”). Hence, we will, when modeling coal, approximate this production with that of a resource that is not in finite supply. Typically, we also will assume that its marginal cost is constant though possibly decreasing over time due to technical change. When we also look at green energy, we will treat its production like we treat coal: with a constant marginal cost and its own rate of technical change.

2.3.3 Equilibrium As announced, we focus on the special cases with coal only and oil only here.

Coal only. Looking first at the simple case where only coal is used, suppose that its marginal cost is constant in terms of labor units. Thus labor is allocated across finalgoods production and coal production to maximize F (k, A(h − he ), Ae Ac he ) with respect to he —the part of overall labor h used for coal production. Here we have used 1/Ac to denote the marginal cost of coal in terms of labor. This outcome presumes either a planning solution where the use of coal does not involve externalities (such as that involving climate change) or a market allocation where coal production is not taxed—if it is taxed, a tax will enter the labor allocation first-order condition. This formulation, which abstracts from the use of capital and energy in the production of coal, is very convenient because it allows us to easily solve for he in terms of h and k. In the Cobb–Douglas case—where the energy share is constant—matters are even simpler: he will be a constant share of h that depends only on technology parameters. Thus, in this case, we are formally back in the optimal growth model above—after maximizing over coal energy we have merely added a constant in the production function. 16 We obtain p t+1 /pt = 1 + r + mc(gmc − rr)/pt . 17 Monopoly power is also challenging to study since a monopolist in the oil market would view all macroe-

conomic variables in the world, today and in the future, as endogenous to its decisions; moreover, its profit-maximizing behavior under commitment would not generally be time-consistent.

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Oil only. The full model with costless-to-produce  oil only amounts to adding a resource constraint to the growth model above— ∞ t=0 Et = R0 —aside from including E in the production function. We then obtain the canonical model of oil/finite resources in Dasgupta and Heal (1974), except for the presence of technology growth here. Let us briefly look at that model in its planning version and let us use a quantitative version without hours choice, as it will constitute a core of sorts in the climate model below.18 Thus we have: max∞

 kt+1 ,Et

t=0

∞ 

β t log (F (kt , At , Aet Et ) + (1 − δ)kt − kt+1 )

s.t.

t=0

∞ 

E t ≤ R0 .

t=0

The nature of growth paths for this economy depends critically on F .19 Recall that in a calibrated version of the model we take F to be a low-substitutability CES function of the capital–labor composite and energy, if annual data are to be addressed, or a Cobb–Douglas in all inputs if the model is specified for long-run growth purposes. Starting with the long-run model, when F (k, A, E) = k α A1−α−ν (Ae E)ν it is straightforward to show that the present model delivers exact balanced growth (under the right initial condition for k0 , and monotone convergence otherwise) where E grows at rate β, i.e., it goes to zero asymptotically, with output, consumption, and ν capital growing at the gross rate (1 + g)((1 + ge )β) 1−α−ν , where ge is the growth rate of Ae .20 We show in Hassler et al. (2018a) that the present model can deliver exact balanced growth also when formulated at the higher-frequency horizon when the CES has an elasticity of substitution less than one between capital–labor and energy, but only in a knife-edge case: when β(1 + ge )(1 + g)−1/(1−α) = 1. When this expression is above (below) one, growth is not balanced in the usual sense; for example, energy share’s cost share goes to zero (one). However, we also show that when the technology growth rates g and ge are endogenous, then at least under certain assumptions the result is that energy’s share again is robustly balanced in the long run: the economy looks like a Cobb–Douglas world, though with a share parameter that is a nontrivial function of other primitives. An interesting feature of the long-run, Cobb–Douglas model here—where oil is a finite resource—is that oil use falls from time zero. That is, we do not obtain a rising path initially. Historically, oil use has been rising for a long time, and very steadily. Thus, one quantitative concern is whether the model ought not be altered, somehow, so as to match this rather basic fact. Interestingly, however, in the high-frequency version where oil and capital–labor have very low substitutability, this result obtains 18 With hours falling at some (small) exogenous rate we can simply reinterpret the growth of A as “net of

hours falling”. So abstracting from hours, in this sense, is without loss of generality. 19 It is straightforward to consider the utility function to be the more general power function, but since

log c is a focal point in applied work we use this formulation in most of our text. 20 Along this path, of course, the marginal product of oil (its price in equilibrium) rises at the net rate of

return on capital: its marginal product minus depreciation (the real interest rate).

3 The Natural-Science Add-Ons

straightforwardly given certain initial conditions on k0 , A0 , and Ae0 : if energy technology is, in some sense, at a high level relative to the capital–labor technology, adjusted for the initial size of the capital stock, then capital, not energy, is initially scarce and as capital is accumulated, energy follows along. Eventually, of course, as oil is finite, what factor is scarce in relative terms reverses, and oil use goes to zero at rate β.

3 THE NATURAL-SCIENCE ADD-ONS In this section we cover the main natural-science modules needed in our IAM. Versions of these modules have been developed in Nordhaus’s work; they summarize very complex natural-science mechanisms in a compact enough form that they can be feasibly used in a broad class of models, while still being quantitatively adequate. We keep this and the next section brief, however—much more extensive discussion can be found in Hassler et al. (2016). The overall logic of, and connection between, the modules should be clear: carbon dioxide is emitted by burning fossil fuel and atmospheric carbon dioxide—by virtue of being a greenhouse gas—causes warming. Carbon dioxide emissions quickly become global, i.e., their spatial spread is immediate from the perspective of modeling, but how long they remain in the atmosphere is a topic in itself. The “carbon cycle” describes this process and is described first. How atmospheric carbon then causes warming is dealt with in the climate module. We abstract from other aspects of climate than temperature.

3.1 THE CARBON-CYCLE MODULE A representation of the carbon circulation in IAMs is necessary in order to map emissions of carbon dioxide (CO2 ) to a path of atmospheric CO2 concentrations. In reality, carbon flows continuously between a number of carbon reservoirs (sinks) of which the atmosphere is one. The most important other reservoirs are the oceans and the biosphere. The interaction between these reservoirs is non-linear and implies that emitted CO2 does not leave the atmosphere following a geometric path with a constant decay rate. This is in contrast to other greenhouse gases, like methane, for which a constant decay rate is a more reasonable approximation. Carbon circulation can be modeled structurally, by defining the different sinks and the flows between them. A prototype example of this is the carbon-cycle model in the RICE/DICE model which contains three reservoirs, representing the atmosphere (S), the biosphere and upper layers of the ocean (S U P ), and the deep oceans (S LO ). The reason for separating the upper layers of the ocean from the deep ocean is that the gas exchange between the ocean surface and the atmosphere is much faster than that within the ocean as a whole. In the simplest structural model, the flows are modeled as proportional to the size of the respective source reservoir. In discrete time, this

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leads to a system of linear difference equations of the form UP St − St−1 = −φ12 St−1 + φ21 St−1 + Et−1 ,

StU P StLO

UP − St−1 LO − St−1

UP = φ12 St−1 − (φ21 + φ23 ) St−1 UP LO = φ23 St−1 − φ33 St−1 .

(3)

LO + φ33 St−1 ,

Here, Et is emissions into the atmosphere, adding to St in the first equation. The flow of carbon from the atmosphere to the biosphere and upper layers of the ocean is given by φ12 St−1 . This term reduces St and increases StU P , thus coming in with a negative sign in the first equation and a positive one in the second. The other terms have analogous interpretations. An immediate implication of modeling the carbon-cycle as a linear system is that the ratios of the sizes of the different reservoirs will be restored in the long-run whenever emissions stop. If the model is calibrated so that the three reservoirs have realistic sizes, this will imply that all but a few percent of emissions will end up in the deep oceans within a few hundred years. This is not a realistic prediction. One remedy is to make the size of deep oceans smaller. Another is to use a non-structural approach and approximate atmospheric carbon depreciation after s years linearly with the per-unit coefficient ds , using a sum of several geometric processes with different rates. The IPCC (2007) suggests 1 − ds = a 0 +

3   −s ai e τ i ,

(4)

i=1

with a0 = 0.217, a1 = 0.259, a2 = 0.338, a3 = 0.186, τ1 = 172.9, τ2 = 18.51, and τ3 = 1.186, where s and the τi s are measured in years.21 With this parametrization, 50% of an emitted unit of carbon has left the atmosphere after 30 years, 75% after 356 years and 21.7% stays for ever. A similar approach is used in Golosov et al. (2014). It is important to note that the validity of the structural and the non-structural models with constant parameters depend on the emission scenario. In particular, if emissions are very large, a larger share than 21.7% will remain in the atmosphere for a very long time. The carbon cycle is likely to be affected by other drivers than emissions. In particular, climate change will affect the ability of different reservoirs to hold carbon. Such mechanisms could be built into the structural model in (3) by letting the parameters be functions of, e.g., the global mean temperature. Both smooth feedbacks and drastic ones, causing thresholds and tipping points, can be included.

3.2 THE CLIMATE MODULE The most important driver of climate change is emissions of CO2 into the atmosphere—it is the factor that currently contributes the most to climate change, and its 21 See IPCC (2007), table 2.14.

3 The Natural-Science Add-Ons

effects are long-lasting. The fundamental reason why atmospheric CO2 affects the climate is that it changes the earth’s energy budget. This budget is defined as the difference between the inflow of energy to, and outflow of energy from, earth, where both flows are averaged over time and space. Carbon dioxide has the property that it allows sunlight to pass through more easily than infrared radiation. Since most of the outflow of energy is in the form of infrared radiation, more CO2 therefore implies a surplus in the energy budget and, thus, heat accumulates. This increases the temperature on earth, which in turn increases the outflow of energy until balance is restored at a new higher temperature. This basic mechanism was quantified already by Arrhenius (1896). The simplest representation of this mechanism modeled in discrete time is   η St Ft = log (5) log 2 S¯ Tt − Tt−1 = σ (Ft−1 − κTt−1 ) . In the first equation, Ft is the perturbation in the energy budget relative to the preemission (pre-industrial) steady state, often called forcing, St is the amount of carbon in the atmosphere, and S¯ is the pre-emission amount of atmospheric carbon. The parameter η determines the strength of the greenhouse effect. Specifically, a doubling of the CO2 concentration, i.e., SS¯t = 2, yields a forcing of η (W/m2 ). In the second equation, Tt is the global mean temperature deviation from the preemission steady state. The left-hand side is the change in the global mean temperature per unit of time. The two terms in parenthesis on the right-hand side come from the energy budget, consisting of forcing and the term κTt . The latter is a linear approximation of the so-called Planck feedback: the fact that hotter objects emit more heat radiation. The parameter σ determines the speed at which the temperature increases for a given surplus in the energy budget. Given a constant forcing F , the temperature has to reach Fκ for a new steady state to arise. It is also immediate to see that a doubling of the atmospheric carbon concentration leads to a new steady state with a global mean temperature of T = κη . This value is often referred to as the (equilibrium) climate sensitivity. According to the IPCC, the climate sensitivity is “likely in the range 1.5 to 4.5 °C”, “extremely unlikely less than 1 °C”, and “very unlikely greater than 6 °C”.22 The simplest model can be extended to include several energy budgets. The DICE/RICE model due to Nordhaus, for example, also includes a budget representing the flows of energy between the atmosphere and the oceans. Since the oceans have a much larger heat capacity than the atmosphere (more energy is required for a given increase in temperature), they will experience a slower increase in temperature for a given forcing. Additional forcing variables, like methane and particle emissions, can 22 The statement is taken from IPCC (2013a, p. 81) and IPCC (2013b, Box 12.1). The report states that

“likely” should be taken to mean a probability of 66–100%, “extremely unlikely” 0–5% and “very unlikely” 0–10%.

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be added to the first equation and potentially be made contingent on, e.g., the temperature. It is also straightforward to allow non-constant parameters. For example, the feedback parameter κ could be made dependent on current and/or past temperature, capturing threshold and tipping-point effects. An example of a threshold effect would be to add the equation  κ if Tt < Tth κ= 0 κ1 else to (5), where Tth is the threshold temperature and κ1 < κ0 . If instead the switch to κ1 is permanent and occurs the first time period such that Tt ≥ Tth , then we have an irreversible tipping point. Clearly, there is a lot of uncertainty around all the parameters in this and similar models. Specifically, uncertainty about the parameter κ is important. First, uncertainty about κ implies uncertainty about the climate sensitivity. Second, since κ enters in the denominator of the expression for the climate sensitivity, a symmetric distribution for κ around a mean would imply that the distribution of the climate sensitivity is skewed to the right (Weitzman, 2011). Energy-budget models usually do not have a geographic dimension. However, there is a systematic relation between regional climate change and the change in the global mean temperature. Statistical methods can be used to infer this from historical data or from advanced climate models. Such statistical downscaling can be used to predict regional climate change from the global mean temperature.

3.3 CONSTANT CARBON–CLIMATE RESPONSE A highly tractable way of representing both carbon circulation and climate change jointly has been proposed by Matthews et al. (2009). They show that several of the dynamic and non-linear mechanisms described above tend to approximately cancel in a very convenient way. In concrete terms, a reasonable approximation to the dynamic relation between the global mean temperature and CO2 emissions is that the temperature increase over any time period is proportional to the accumulated emissions over the same period. Furthermore, according to the approximation, the proportionality factor (denoted CCR) is independent of the length of the time period and of previous emissions. Tt+m − Tt = CCR

t+m−1 

Es .

s=t

To obtain some understanding for this surprising result, first note that when oceans are included in the energy-budget model, there is a substantial delay in the temperature response of a given forcing. Second, if carbon is released into the atmosphere, a large share of it is removed quite slowly from the atmosphere. It happens to be the case that these dynamics approximately cancel each other out, at least if the time scale is from a decade up to a millennium. Thus, in the shorter run, the CO2 concentration,

4 Damages

and thus forcing, is higher, but this effect is balanced out by the cooling effect of the oceans. Second, note that the Arrhenius law discussed in the previous chapter implies a logarithmic relation between CO2 concentration and forcing. Thus, at higher CO2 concentrations, an increase in the CO2 concentration has a smaller effect on the temperature. On the other hand, existing carbon-cycle models tends to have the property that the storage capacity of the sinks diminish as more CO2 is released into the atmosphere. These effects also approximately balance: at higher levels of CO2 concentration, an additional unit of emissions increases the CO2 concentration more but the effect of CO2 concentration on temperature is lower by about the same proportion. Matthews et al. (2009) argue that both model simulations and historical data suggest a best estimate of CCR of 1.5 degrees Celsius warming per 1000 Gt of carbon emissions. They also derive a 95% confidence interval for the CCR being between 1 and 2.1 °C/1000 GtC.

4 DAMAGES We now describe how the economy is affected by climate change. This description thus closes the loop from the economy, which generates emissions that enter the carbon cycle and drive climate change, back to itself. Nordhaus (1994) pioneered the “bottom-up” approach to aggregating damages. His idea was to compile a large number of microeconomic studies on various consequences of climate change, e.g., negative effects on agriculture, coastal damages, lowered amenity values, worsened health, and low-probability catastrophic damages to the overall economy. In these studies, the common problem in environmental economics of valuing effects that have no, or very imperfectly measured, market prices is particularly salient. Nordhaus (1994) constructed estimates of damages in 13 different regions of the world, allowing region- and mechanism-specific functional forms. Different ways of estimating these damages have been used; of particular interest is perhaps the “Ricardian” approach used in Mendelsohn et al. (1994) which estimates the relation between temperature and market prices of farm land across 3000 U.S. counties with the idea that institutions are very similar across these locations but temperatures are not. All the different types of damages were then aggregated into region-specific (RICE) and a global (DICE) damage functions mapping the increase in global mean temperature over the pre-industrial level (Tt ) into damages expressed as a share of current GDP. Given these estimates, a function  (Tt )—representing the share of GDP that remains after climate damages—can be derived. Using a second-order approximation, this function is expressed as  (Tt ) ≡

1 , 1 + θ1 Tt + θ2 Tt2

(6)

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with parameters θ1 and θ2 chosen so as to make the damage function approximate the sum of the underlying damage estimates. Obviously, higher-order terms can easily be included to increase the convexity of damages. Equally obviously, great care has to be taken when interpreting results that rely on extrapolations of the damage functions outside of the range over which it is estimated. An alternative and complementary way of estimating the aggregate effects of climate on economic activity is to use reduced-form relations in data on economic outcomes and temperature. Here, both time variation and regional variation have been used to draw inferences about the effects of climate change. Regarding the former, Dell et al. (2014) summarizes the literature which uses natural variation in temperature and climate characteristics to identify effects on aggregate economic variables. They conclude that in poor countries, losses on the order of 1–2% per degree Celsius are typically found for output, labor productivity, and economic growth. These effects are identified using temporary changes in temperature and are arguably well identified short-run effects also of climate change. However, the authors caution against also inferring that the effects are permanent. This warning seems particularly relevant when it applies to growth rates of output and other economic variables. There is also a systematic relation between geographic variation in temperature and economic output. Nordhaus (2006) uses data on output for 25 thousand 1 by 1 degree terrestrial grid cells and shows that there is a clear hump-shaped pattern between temperature and output per km2 . The peak of the hump, with the highest average output per km2 , was found at approximately 12 degrees Celsius.23 Under the assumption that the relation between temperature and output is invariant it can be used to infer the effects of climate change on global GDP. The estimates in Nordhaus (2006) indicate losses on the order of a few percent of GDP if the global mean temperature increases by three degrees. In contrast to the estimates using time variation, these effects do not suffer from the problem of being identified from short-run variation. More recent studies find hump-shaped patterns across regions for growth rates, indicating extremely strong long-run effects of climate on economic activity; see, e.g., Burke et al. (2015). However, these studies are far from uncontroversial.24 Let us finally describe a representation of the combined mapping from atmospheric CO2 concentration via climate change to damages. Golosov et al. (2014) show that an exponential damage function where the argument is the excess amount ¯ rather than temperature, is a reasonably good of carbon in the atmosphere (St − S), approximation to simple climate models and damage functions as in (5) and (6). In their formulation, damages as a share of GDP before damages are given by s (S) = 1 − e−γ



St −S¯

,

23 Interestingly, the relation between output per person and temperature is monotone and negative. 24 These estimates, in particular, are not consistent with a fairly stable distribution of GDP across regions

and are hence hard to square with historical data.

5 A Complete, Quantitative IAM

where γ is a constant. This implies that the share of GDP lost per unit of carbon in the atmosphere is constant at γ .25 This formulation is convenient for a number of applications. For example, under some additional assumptions, one can derive a very simple formula for the optimal tax rate on carbon; see Section 5.5.1 below.

5 A COMPLETE, QUANTITATIVE IAM We are now ready to formulate the first full macroeconomic model of climate change. It has one region only and a minimum of heterogeneity in other dimensions too. It is however, a framework that can be straightforwardly built on further, along the lines of the many branches of the macroeconomic literature—including consumer heterogeneity, multiple regions, and so on—and we will briefly look at examples of such cases below—without losing its quantitative anchoring in historical data: summary climate and growth facts. We will use a benchmark model with logarithmic utility, and hence there is risk aversion (to the extent there is uncertainty) but its level is moderate. Again, it is straightforward to incorporate higher curvature/Epstein–Zin preferences into this framework (see, e.g., Jensen and Traeger, 2014). We first formulate a planning problem and then look at a competitive equilibrium. We also state a formula for the social cost of carbon based on Pigou (1920). At the end of this section, we discuss how to solve the model computationally.

5.1 THE PLANNING PROBLEM We focus on the case of exogenous technical change and consider a long enough time horizon that a Cobb–Douglas production function is appropriate. Energy, in the present formulation, is a composite of several sources. max

 ∞ ct ,kt+1 ,Et ,Eot ,Ect ,Egt ,hct ,hgt ,St t=0

E0

∞ 

β t log ct

t=0

s.t. ct + kt+1 = e−γt St ktα (At (h − hct − het ))1−α−ν Etν + (1 − δ)kt ρ ρ ρ 1/ρ Et = κo Eot + κc Ect + κg Egt ∞ 

Eot ≤ R0 ,

t=0

25 ∂(s (S)Yt )/∂St = γ . (1−s (S))Yr

Ect = Act hct

∀t,

∀t,

Egt = Agt hgt

∀t

∀t,

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and St =

∞  (1 − dj )(Eo,t−j + Ec,t−j )

∀t.

j =0

Some comments are in order. First, in this formulation we opt for damages to be a function directly of the carbon concentration, hence bypassing temperature as a driver of this mechanism. An alternative we discussed above, and which will deliver similar quantitative conclusions, is to instead bypass carbon concentration and express damages as a function of temperature and temperature as the CCR function of total past emissions (undepreciated). Moreover, we let the damages be random through the dependence of γ on t . Second, the SEC energy composite contains the share parameters κ, which should be calibrated to reflect the relative efficiency with which the different energy sources are used in production. In particular, coal is “dirtier” than oil in that it gives rise to higher carbon emissions per unit of energy services. We let Eot and Ect have units measured in carbon, hence implying that κo > κc would be satisfied in a calibration of these parameters. Third, notice that there is technical change in production of final output as well as in the production of coal and green energy. The energy-saving technology variable Ae is not needed here, since the production function is Cobb–Douglas (Ae can be viewed as a part of A). We discuss how to solve this planning problem below. Note here that a solution entails whether or not to use up all the oil; oil is freely available but now—in contrast to above, where there was no negative effect of emissions on TFP—oil use has societal costs.

5.2 MARKET EQUILIBRIUM The definition of a sequential equilibrium closely follows that in Section 2.2.2. Here, a key point to notice, of course, is that no individual decision maker—consumer or firm—internalizes the effects of their decisions on aggregates. In particular, no consumer or firm internalizes their negative effect of the use of fossil fuel—a consumer selling Eo or a coal producer selling Ec —on TFP, via an increase in atmospheric carbon concentration (and hence warming). sequences  An equilibrium is thus mathematically formulated as a set ofstochastic ∞ ct , kt+1 , Et , Eot , Ect , Egt , hct , hgt , St , wt , rt , pt , pot , pct , pgt t=0 such that 1. {ct , kt+1 , Eot }∞ t=0 solves ∞ 

β max ∞ E0  ct ,kt+1 ,Eot t=0 t=0

t

log ct

s.t. ct + kt+1 = (1 − δ + rt )kt + wt h + pot (1 − τt )Et + Tt

∀t

5 A Complete, Quantitative IAM

and ∞ 

Eot ≤ R0 ;

t=0

2. rt = αyt /kt , wt = (1 − α − ν)yt /(h − hct − hgt ), and νpt = yt /Et , where yt =  e−γt St ktα (At (h − hct − het ))1−α−ν Etν and St = ∞ j =0 (1 − dj )(Eo,t−j + Ec,t−j ) ∀t ; 3. (pt , pot , pct , pgt ) satisfies 1−ρ  −ρ −ρ −ρ − ρ pt = κoρ−1 pot1−ρ + κcρ−1 pct1−ρ + κgρ−1 pgt1−ρ

∀t;

4. pct (1 − τt )Act = wt and pgt Agt = wt ∀t ; 5. Tt = τt (po tEot + pct Ect ) ∀t ; and ρ ρ ρ 1/ρ , Ect = Act hct and Egt = Agt hgt ∀t . 6. Et = κo Eot + κc Ect + κg Egt This definition does not include a Hotelling price equation; instead, it is implied by consumer choice (as the consumer owns and manages the sale of oil over time). In particular, two different forms of saving must give the same expected, marginal/pot p −δ utility weighted return: Et 1+rct+1 = Et o,t+1 . Hence a relative risk premium is ct+1 t+1 involved here across the two kinds of risky assets capital and oil. Instead of stating the profit-maximizing conditions for the different firms, we state the first-order conditions—as these are standard, and as in the definition in Section 2.2.2. The energy price index is also a result of profit maximization: it is derived from minimizing the costs po Eo + pc Ec + pg Eg of producing one unit of E. We see from the formulation of the problems that the consumer does not take into account how Eot affects TFP (hence current and future prices); similarly, the first-order conditions from the coal firm’s problem do not contain such effects either. However, the definition now includes taxes on fossil fuel, levied on the consumer for selling oil and on the coal producer for selling coal. Revenues are rebated back to the consumer as a lump sum. In a laissez-faire (zero-tax) competitive equilibrium, all the oil will be used up because the consumer has no interest in selling less than the total amount, as pot (the marginal product of oil in producing output) will be positive at all times. The only way in which some oil will be left in the ground is by setting taxes so that τt = pot at all times. Then the consumer is indifferent as to how much to sell at each point in time (and one of the possible choices is consistent with the given pot at that time—in consistency with an equilibrium).

5.3 MODEL SOLUTION The models just described are stochastic and non-linear and cannot, in general, be solved analytically. In economics there are different traditions in this regard: should one insist on models that can be solved analytically or is it acceptable to be aided

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by a computer? We first discuss this issue and then turn to some concrete comments regarding the “how-to” in our particular application.

5.3.1 Analytical vs. Numerical Model Solution The present section begins with a discussion of methods, chiefly with the purpose of providing arguments for the use of “complex” models solved with numerical methods. Then these methods are discussed briefly. A very common view among economists is to insist that theoretical models be formulated in such a way that they have closed-form solutions, or in any case so that their properties can be ascertained analytically in theorem-proof style. The argument in favor of this approach is usually that the logic of the model is the central piece of the modeling: the “understanding” of the theory is key and cannot, according to this argument, be attained sufficiently precisely based on numerical solution. Economic models are abstractions and should not move beyond this stage. In the approach to climate and economics pursued in this chapter, the goal is to formulate a model that can generate key features of the data. This cannot always be accomplished—rather, it is rare that it can—in models that allow analytical characterization. The idea is that if the most salient features of the data are captured correctly, the model can be used to interpret history, for prediction, or for policy analysis. The parameter selection in this procedure is often informal—and called calibration—but, conceptually, it is econometrics. An argument for the informality of the econometric procedure is that the model is not believed to be truth—many aspects of the realworld economy are abstracted from in the theory—and so the formal estimation loses an important part of its meaning (in particular the testing of hypotheses). Which method is better suited for practical applications? Often, economic commentators and policymakers (perhaps especially those in the area of macroeconomics) express the idea that complex formal models are not useful, because they are still too simple and cannot be thought of as truth. The implication is that the preferred method for informing policy is to have a number of ideas at hand (perhaps in the form of separate, analytically tractable models) and then informally weigh the relative importance of these and, thus, arrive at a conclusion. We take issue with this view. Applied macroeconomic models, such as those discussed here, are indeed often complex enough that closed-form solutions are not available, while still being drastic simplifications of reality. We nevertheless insist that it is better to use explicit models, thereby transparently applying quantitative weights to the different theory components. The complex model should be viewed as incorporating the different theories. Calibration, or formal estimation when feasible, is the way in which the weighting scheme is formally implemented. The model’s implications can still not be fully (or even half) believed, because important pieces of the theory can be missing, the parameter selection is fraught with errors, and so on. But at least this procedure is more transparent and, in particular, alternative viewpoints can be invited, in the form of introducing alternative mechanisms into the model, or even radically different models, so long as they are explicit and quantified. At the end, of course, a significant amount of subjective judgment has to be applied before actual decisions are made,

5 A Complete, Quantitative IAM

or final views are formed. We believe, however, that the decision process is fundamentally more robust and less likely to deliver undesired outcomes if a quantitative model is used as in input, not least because it is then easier to carry out an evaluation ex post. In the climate-economy area, an interdisciplinary field that in particular includes several natural-science areas, it would be particularly difficult to insist on having a set of small models and ideas and then informally weigh them together. When an engineer builds a bridge, a model is used: a quantitative model that abstracts from many aspects of reality but also captures what is key for the purpose at hand. We would not want to cross a bridge with a heavy truck if we knew that the bridge was constructed based on the informal weighing together of abstract arguments relating to the desired features of a bridge. The same goes for rocket launching and, closer to the subject here, meteorology. In all those areas, calculations are made based on explicit models, numerically solved. So, if nothing else to ease communication with climate scientists, the method here is what it has to be in order to have the credibility of a quantitatively grounded theory. It should be stressed, of course, that complexity is not a goal in itself. In fact, the core model we analyze below is far simpler than the typical business-cycle model used in macroeconomics, because it turns out that a large degree of analytical tractability can be allowed while still accounting for the main historical facts. Some (highly relevant) extensions of this setting do necessitate advanced numerical methods, however, leaving us no alternative but to use these in such cases. The quantitative-theory route has also been Nordhaus’s approach in formulating the DICE and RICE models: these models are non-linear and the non-linearities are believed to be important. In building these models, Nordhaus made an effort to summarize the appropriate natural-science modules so that the resulting IAM would be as compact as possible and so that it at least could be feasibly analyzed with numerical methods. The challenge was, in particular, that the number of state variables in typical climate and carbon-cycle models is very large and that dynamic economic models are forward-looking, thus requiring entirely different solution methods—fixed-point methods—than those used in the natural sciences.

5.3.2 How-to There are three challenges to consider: (i) transition dynamics, (ii) non-linearities, and (iii) uncertainty. Transition dynamics, i.e., the need to study the economy’s path toward a long-run steady state, or balanced growth path, is necessary in the climateeconomy context because the use of fossil fuels must end and the task at hand is to analyze the path toward that long-run outcome. Non-linearities are inherent in the model formulation, although it is not clear in any given case how significant the departure from linearity (or log-linearity) will be. Uncertainty is relevant to the extent one models the global climate, or damages, this way—a reasonable approach given that there is significant uncertainty in several dimensions, as discussed above. The numerical package that is most commonly used in macroeconomics is DYNARE. The main purposes of this use is monetary and fiscal policy analysis

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in the context of business-cycle fluctuations. DYNARE is potentially valuable in climate-economy applications too, because it has a module for solving for non-linear transition paths when there is no uncertainty. The procedure relies on convergence to steady state and backward solution: first a steady state is solved for and then the program simply finds a solution to a number of nonlinear equations: all the equilibrium conditions, including starting values for the state variables (in the case of the model above, K0 and S0 ). DYNARE is very convenient because it is highly automated: the researcher simply types in the equations and the parameter values, including initial conditions; the program does the rest (solves for steady state and then for dynamics). Recurring uncertainty is more challenging to study because the number of variables explodes with the time horizon. If there is one random variables with n possible outcomes each period and the model is solved 100 periods forward, the number of variables to solve for in a one-dimensional economy like the one-sector neoclassical growth model (assuming the first random realization is one period from now) is 1 + n + n2 + · · · + n100 —a prohibitively large number even for a coin-flip process. If the economy is (well approximated by) a linear system, however, then uncertainty can be handled with well-known methods from linear algebra: the analysis of stochastic differential (in continuous time) or difference (as here, in discrete time) equations, based on eigenvalue analysis, is straightforward and this method is also the core module on which DYNARE is built. The computation of equilibria for such economies is very fast and based on matrix manipulation. If the economy is not well approximated by a linear system, then DYNARE still offers solutions, namely higher-order approximations. The idea here is again to find a steady state in the absence of shocks and then to Taylor-expand—now to a higher order—the set of equilibrium conditions around that state. How well the resulting stochastic dynamic system behaves far from steady state is not known in any generality at all and it is therefore necessary in some applications—arguably the climate-economy case is one—to instead use “global methods”, i.e., methods that do not rely on approximating the economy’s behavior locally around a steady state. Appropriate global methods under uncertainty rely, as indicated above in Section 2.2.3, on recursive methods. Again taking the stochastic neoclassical growth model as an example, the unknowns are now functions such as the value function, which are infinite-dimensional objects, but there are computationally efficient methods for solving functional equations. In a non-trivial equilibrium setting (in particular where the equilibrium is not Pareto optimal, such as under externalities in the climate context), there are few theorems to rely on but there are a number of computational algorithms that have proven robust and fast in a large range of applications. The recursive equilibrium setting described in Section 2.2.3 involves a number of functions of several variables and to solve for all of these is challenging. However, the key functions are those determining the values of the endogenous variables, G1 and G2 , and these can be solved for directly without solving for the remaining functions. To see this, consider, for simplicity, the case where hours are given exogenously by a value h. Then the only equation to derive is G(A, K): that determining saving.

5 A Complete, Quantitative IAM

Then after deriving the consumer’s first-order conditions (together with an envelope condition) and the remaining equilibrium conditions, one arrives at u ((1 + R(K, A) − δ)K + W (K, A)h − G(A, K))

= βE (1 + R(G(A, K), A ) − δ) · u (1 + R(G(A, K), A ) − δ)G(A, K)

 + W (G(A, K), A )h − G(A , G(A, K)) for all (A, K), where R and W are known functions. Here we have one functional equation in one unknown function: G. The typical approach is then to select a grid in (A, K) space and apply an algorithm involving a starting guess on the function’s value at the grid points and then an updating scheme. There are a host of such procedures, and others as well, and for most problems studied in macroeconomics they work well. The challenges arise particularly when the number of endogenous functions increases and when the state space increases—especially the endogenous state space. In the climate application above—the deterministic benchmark model—the endogenous state variables are capital, the stock of undepleted oil, and the atmospheric carbon concentration and the nontrivial decision functions involve saving and the energy use of the three different kinds and it is straightforward to derive the corresponding functional equations. We will demonstrate, in Section 5.5, that a way to calibrate the present model based on long time periods actually leads to a number of closed-form solutions and few functional equations to solve. Thus, at least in important benchmark cases, it is possible to solve the model very easily without giving up on the model’s ability to replicate history quantitatively.

5.4 THE SOCIAL COST OF CARBON Before moving to a concrete application and concrete results—the next section— we want to highlight that one important result can be derived in a rather general formulation: the optimal-tax formula. This formula applies if a carbon tax can be implemented unrestrictedly and globally and the only model distortion is the externality occurring through carbon emissions. It also applies if there are other externalities, but these are taken care of optimally by separate taxes/transfers (e.g., a research spillover that is corrected by means of appropriate subsidies to research). The tax prescription can also be used to evaluate carbon capture and storage (CCS): if the cost of such a technology, per unit of carbon, is below the optimal tax, it should be adopted— otherwise not. The tax formula does not apply in the presence of other distortionary taxes, and indeed an important aspect is second-best taxation; we do not look into it here (see, e.g., Barrage, 2014, and Schmitt, 2014, who look at models very similar to that described here). The optimal-tax formula says that the tax on carbon, per unit of carbon, should equal the externality damage. The externality damage has many components but can

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be expressed with a transparent formula: τt = E t

  ∂Yt+j u (ct+j ) βj  · − · u (ct ) ∂St+j j =0      

∞ 

discounting

damage/C in atm

∂St+j ∂Ei,t   

.

(7)

C left in atm per emitted unit

It is straightforward, but tedious, to use insert this formula into the equilibrium conditions and verify that the implied system replicates the first-order conditions of the planner. The externality damage of a unit of emissions of fossil fuel of type i (coal or oil) is an expected discounted sum of current and future damages. The discounting involves the marginal rate of substitution of consumption units over time: β and the marginal utilities u , which vary over time with consumption. The formula contains the derivative of damages with respect to carbon concentration as well as the atmospheric carbon depreciation patterns: the further into the future, the less is left of a unit of carbon emitted now. The formula can of course be generalized in a variety of ways; one is to include damages elsewhere than to TFP—then the formula is also a sum across the different places in which damages appear. It is important to note that the optimal-tax formula, whose value in general depends on the allocation, is to be evaluated at the optimal allocation. One can label the expression on the right-hand side of Eq. (7) the social cost of carbon and evaluate it at any (equilibrium) allocation. It would then express the net social cost of a marginal change in emissions today. It would not equal the optimal tax unless the allocation is already optimal—which it would not be, for example, in a laissez-faire allocation.

5.5 A MICKEY-MOUSE MODEL? QUANTITATIVE ANALYTICAL IAMS As argued above, the climate-economy modeling, by virtue of trying to construct quantitatively accurate long-run models, cannot be restricted to settings with analytical solutions. However, it turns out, as shown in Golosov et al. (2014), that a “Mickey-Mouse model” of the climate-economy interactions, despite its simplicity, provides a close quantitative fit to the historical data and to models that are significantly more complex. Thus, the Mickey Mouse model can be taken as more than an abstraction: it can be thought of as a quantitative model—a quantitative analytical IAM. To be more concrete, consider the model in Section 5 above, with logarithmic utility (again, this remains the modal curvature choice for utility in the macroeconomic literature), Cobb–Douglas production, and full depreciation of capital from period t to period t + 1. The full-depreciation rate is altogether inappropriate for the businesscycle context where a period is usually a quarter or a year. Not only is the depreciation rate much closer to zero than to one at such horizons, but its level also matters importantly for equilibrium outcomes. Here, however, if a time period is 10 years or longer a realistic depreciation rate is much closer to zero and there is no sense in which the model behaves very differently for almost full depreciation compared to literally full depreciation. The upshot of setting δ = 1 is that the saving rate becomes constant:

5 A Complete, Quantitative IAM

regardless of the path for TFP, whether stochastic or deterministic, a fraction αβ of output is saved—this is easily verified both for the planner’s problem and the market economy. Moreover, the remaining energy choice can be handled rather straightforwardly. First, if the model has coal (and green energy) only, as we saw above, there is a closed-form solution in competitive equilibrium. The planner’s solution in this case is not as simple, as it involves a dynamic first-order condition, but it can be solved, in the absence of uncertainty, using a the “guess” that the Pigou formula works—see Golosov et al. (2014). Second, if the model has oil (in addition to, or along with, coal and a green input), then a simple shooting algorithm can be used. These models are thus possible to solve even in Excel. We will provide some of the outputs from such a model below. First, however, let us briefly revisit the optimal tax formula.

5.5.1 The Pigou Tax in the Quantitative Analytical IAM We now apply the optimal-tax formula in Eq. (7) to the analytical IAM. It is straightforward to show that ⎡ ⎤ ∞ τt ⎣  j = Et β γt+j (1 − dj )⎦ . yt j =0

Here, again, γt+j is the damage coefficient in period t + j and 1 − dj the fraction of atmospheric carbon remaining in j periods. The remarkable aspect of this formula is that the tax relative to output is a function only of exogenous parameters. That is, neither the level of output nor any energy variables, or the level of carbon concentration in the atmosphere, appears. Let us discuss the reason behind this result and its implications. First, a unit of carbon emissions today will give a damage that is a constant percentage of output at each future date (though different constant percentage amounts depending on the time horizon). This is, first, because of linear atmospheric depreciation rates, i.e., the share of a unit of emissions that remains in the atmosphere j periods after it was emitted only depends on j ; this assumption was found above to be a good approximation, unless one considers very different emission scenarios. Second, each unit of additional carbon in the atmosphere causes a constant damage in percent of output, an assumption we also found to be a good approximation. Stronger non-linearities in the carbon cycle and/or the climate parts of the model will break these results and the given level of carbon concentration will matter. Tipping points will give such effects but so long as no global tipping point can be discerned, which we argued above, our assumptions are at least a reasonable baseline. It will also be violated if we depart from an exponential damage function, such as under the assumption of a constant CCR and a standard damage function of temperature. However, the departure in this case will be minor in quantitative terms. Furthermore, a constant percentage output loss in the future will correspond to a constant percentage loss in terms of current output. To understand this, note that a

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FIGURE 21 Optimal carbon tax as a function of the discount rate.

higher level of output in the future of a current emitted unit means that the loss is higher, since it operates on a higher base. But on the other hand marginal utility is lower by the same proportion, given logarithmic utility. Moreover, when discounted to today, since constant saving rates mean that consumption–output ratios remain constant, we obtain the stated result. The result will be violated if u(c) is a different power function, but so long as the power/curvature is not very different from that of the logarithmic function (where the power is zero), the stated formula will be a close approximation if β is replaced by β times the gross output growth rate to the corresponding power. Thus, we note that output does not appear in the formula and, hence, size effects are absent—such as those that would appear under population growth. Population growth, and size effects more generally, would call for higher energy use, but the margin-based calculation here makes the larger size will be weighed down by a correspondingly lower effect on marginal utility.26 For the same reason, any issues relating to green vs. fossil energy are (approximately) irrelevant in computing the optimal tax on carbon. Let us display results according to this simple formula. The optimal carbon tax is thus contained in Fig. 21 for three scenarios: a high damage parameter, a modest one, and a probability-weighted mean (in solid).27 The CO2 depreciation parameters ds are set using three parameters only, so that a fraction 0.2 of any unit emission stays in the atmosphere forever, another fraction 0.393 exits the atmosphere immediately, and the remaining fraction decays at a rate of 0.0228 per decade. We see from the figure that the optimal tax on carbon depends strongly on the discount rate: a rate of 0.1% (like that adopted by Stern in his 2006 review) gives a high carbon tax for the average damage scenario: about $496/ton of carbon. This level is similar to (but not quite as high as) carbon tax rates in Sweden. Nordhaus 26 Population growth may affect discounting directly, depending on the utility function assumed, i.e., by

raising the effective β. 27 The different γ ’s are 1.06, 2.38, and 20.5, all in percentage points per 1000 GtC and calculated using

estimates from Nordhaus (2008).

5 A Complete, Quantitative IAM

FIGURE 22 Fossil-fuel use, laissez faire vs. optimal allocation.

has tended to focus on market rates, e.g., 1.5%, in which case the optimal tax is a magnitude higher: a little below $60/ton. The “catastrophe scenario” in terms of damages (where we envision a GDP flow loss of 30%—a very unlikely scenario) would roughly multiply all the taxes by a factor 10.

5.5.2 Quantitative Results from the Positive Model We now look at results from the calibrated economy. We will compare the optimal allocation to that obtained under laissez-faire. This comparison goes far beyond the computation of the optimal tax in the previous subsection, because it tells us the “total costs” of suboptimal policy, both in welfare terms and, for example, in terms of global temperature differences. We will also discuss the sensitivity to parameters. Rather than using an explicit stochastic structure here, we will follow Hassler et al. (2018a) where it is argued that the stochasticity itself is probably not key but rather the extreme outcomes. This point is also made in Weitzman (2011), but not by means of a quantitatively constructed example, which we will supply here. The model is the analytical IAM with three carbon depreciation parameters: the parameter vector uses an interest-rate based β and an average damage coefficient estimate. α is set to 0.3 here and ν to 0.04, whereas the growth rates of both coal- and green-production technologies are set at 2% per year. The stock of conventional oil is calibrated to data and the κs and ρ to match estimates of the elasticity of substitution between different energy sources and current relative prices.28 Fig. 22, first, shows that laissez-faire entails much higher fossil-fuel use than under the optimal allocation, even under Nordhaus’s market-based discount rate. Fig. 23 shows how the path of (conventional) oil use ought to be altered from the perspective of our quantitative model: barely at all. Oil use should be postponed somewhat but it should be used up. The reason for this is simply that the net societal benefits to oil, given how cheap it is to produce and how efficient it is as an

28 The specific numbers are κ = 0.543, κ = 0.102, κ = 0.357, and ρ = −0.058. o c g

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FIGURE 23 Oil use, laissez faire vs. optimal allocation.

FIGURE 24 Coal use, laissez faire vs. optimal allocation.

energy source; the postponement occurs because the timing of the damages, taking into account discounting, imply an optimal delay. Fig. 24, in contrast, shows how coal (including non-conventional oil) ought to be altered: very significantly. An optimal tax, even at the level implied by strong discounting, will make much of the coal stock unprofitable. The climate damages from an optimal vs. a laissez-faire policy are depicted in Fig. 25. Here, three lines are displayed for each of the optimal and laissez-faire outcomes, much like in the optimal-tax graph of the previous section: these cover “very high”, “average”, and “very low” damages. In Hassler et al. (2018a) an argument is put forth that it is not risk aversion (over modest fluctuations) per se that we need to worry about but rather the extreme (but low-probability) outcomes, and for this purpose it is useful to graph these outcomes, along with the knowledge of associated probabilities. The IPCC states that the climate sensitivity likely is in the range 1.5 to 4.5 degrees Celsius. The endpoints of this range are used as extremes, although neither higher nor lower values can be ruled out. Hassler et al. (2018a) use a metastudy by Nordhaus and Moffat (2017) to compute a similar range of economic sensitivities to climate change. The former also show that the upper endpoints (high climate and economic sensitivity) can be expressed as a damage elasticity of γ = 10.4. The lower

5 A Complete, Quantitative IAM

FIGURE 25 Climate damage, laissez faire vs. optimal allocation.

endpoints, on the other hand, correspond to a damage elasticity of γ = 0.27. The moderate level is the same as the moderate one used in the benchmark above.29 We see that under the mean damage scenario the optimal damages stay below a couple of percentage points of GDP in flow terms, whereas “business as usual” will imply rapidly rising costs up to levels that are over 10 percent of GDP (so a magnitude higher than today) by the end of the 23rd century. If we contemplate the very high damage scenario then the flow effects are very large: by the end of the period considered, comparable to (and even higher than) a perpetual Great Depression. The implications for temperature, finally, can be found in Fig. 26, similarly for the three different damage scenarios. The temperature paths are obtained by using the model-implied carbon concentration rates and then applying Arrhenius’s logarithm formula. The highest damage scenario is produced from a very high climate sensitivity; the economic damages per unit of carbon underlying this scenario also very high, actually tempering the temperature rise since lower output means less carbon use. The theory’s predictive features, despite being produced by our very simple model, are broadly in line with those from other models. The present treatment of temperature outcomes is particularly simple, since it rests on immediate equilibrium: there is no slow build-up, as in DICE or more elaborate climate models, e.g., because the ocean heat changes slowly. In this sense, the model overpredicts temperature increases early on. The model also does not feature tipping points, chiefly because global tipping points have not been pinned down quantitatively; the present analy-

29 See Hassler et al. (2018a) for details.

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FIGURE 26 Increase in global temperature, laissez faire vs. optimal allocation.

sis should perhaps be viewed as probability averaging over all the possible values of tipping points.30

6 EXTENSIONS The literature on economics and climate change has covered many more aspects than those discussed above. Arguably the two most important ones are endogenous technical change and multiregion analysis. We now briefly discuss these, without introducing much formal detail and instead emphasizing the key focus of each of these extensions and how they could be incorporated into our model setting.

6.1 ENDOGENOUS TECHNICAL CHANGE For the optimal tax on carbon, it is not obvious—following the arguments above— that taking the energy market into account is critical, at least not if there are instruments to ensure that R&D in the energy sector is handled efficiently. Indeed the optimal-policy view is that one can separate the analysis in two: ensuring that there is a tax to internalize the climate damage from emissions and ensuring that there are subsidies to ensure that any spillovers in the research sector are internalized. This way of thinking even suggests that if the energy technology spillovers are stronger for fossil technologies than for non-fossil technologies, there should be a higher subsidy to fossil technology development! However, as soon as one contemplates the possibility that an optimal carbon tax cannot be implemented globally, let alone in 30 For studies formally modeling tipping points, see, e.g., Lemoine and Traeger (2014) and Cai et al.

(2015).

6 Extensions

most of our large economic regions, R&D policy in the energy sector can become very important and, indeed, take center stage. In this short discussion, we will not have the ambition to arrive at a quantitative model; hence, we will also not be able to provide useful quantitative guidance in this important policy arena. We will instead (i) indicate how the model above can be, and has been, usefully extended to incorporate technology choice and (ii) make some comments about challenges and open questions in this area. Before addressing these issues, however, let us make reference to Hassler et al. (2018b), which looks at climate, damage, and welfare outcomes for different scenarios for technical change occurring in an exogenous fashion: the outcomes for technology are quantitatively very important for the future of the climate. One point is perhaps obvious: with a green alternative that is powerful enough in relative terms, fossil fuels can be abandoned soon at low cost, and may even be abandoned without any policy intervention. However obvious the point is, it comes out clearly and quantitatively in a model essentially of the kind considered above when different relative growth rates of the coaland green-energy production technologies are entertained. What are the technology potentials of green vs. fossil energy production? That is a key question and the literature so far has not had much to say on it. Fundamentally, of course, predicting the future course of technical change is very hard. There have been some attempts to formalize these questions in macroeconomic settings. The most well-known piece is Acemoglu et al. (2012), which uses endogenous directed technical change à la Acemoglu (1998), a paper that in turn applied the market-based endogenous-growth analyses from the seminal contributions by Romer (1990) and Aghion and Howitt (1992). Acemoglu et al. (2012) is stylized: it is not a quantitative paper. It looks at “clean” vs. dirty goods and has endogenous technologies for each of these. The negative effects of dirty goods are modeled in a reduced-form way in such a way as to generate a “true disaster” outcome if the atmospheric carbon concentration rises high enough. Hence, the focus of the technology policy analysis is to discuss how such a disaster outcome can be avoided. The paper offers a nice and potentially important analytical insight, which is that a temporary subsidy to green technology can be sufficient for the purpose of avoiding the disaster. The reason is that the accumulation equations for technology (i) have the usual unit roots and (ii) are not interdependent. Hence, if a temporary policy can push the green technology ahead of the fossil one, it is possible—under conditions of sufficient substitutability between clean and dirty goods—that dirty goods lose importance over time and vanish from the economy. Quantitative-theory analysis of endogenous directed technical change is most easily carried out by (i) first identifying the possible ways in which technology matters from the perspective of a model that maps to the available data and (ii) then estimating the necessary functional forms specifying the extent to which, and how, technology is subject to choice. The first of these is more straightforward than the second. Thus, rather than relying on abstract notions like dirty and clean goods—a classification that does not line up in an obvious way with the national accounts—one could simply identify energy-saving technology, on the demand side, and energy-producing

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technology, on the supply side. These are already expressed in the model above: alongside the standard capital/labor-saving technology A, Ae corresponds to general energy saving (and of course allows several notions of energy saving, both by simply reducing wasted energy and switching toward goods that are less energy-intensive), and Ac and Ag are the technologies for producing coal and green energy, respectively. It is, under some additional functional-form assumptions possible to back these technology variables out from the relevant aggregate data, in a manner similar to growth accounting. In particular, Hassler et al. (2017) use a nested CES and arrive at estimates for A and Ae . These can then, in turn, be related to each other and one can obtain some information about possible past tradeoffs, at least. It turns out that there is a significant and negative medium-run correlation between A and Ae , suggesting a tradeoff like that considered in the literature on directed technical change. Whether these variables develop under a unit root-like structure or are subject to decreasing returns is another important question and one that is far from settled so far. It would be interesting to consider similar aggregate-style estimates of Ac vs. Ag . A number of microeconomic studies are available too, e.g., Aghion et al. (2016) recently and earlier those discussed in Popp (2002), though it is a challenge so far to translate scattered results from very specific studies into parametric assumptions for our aggregate IAM. The specific modeling of directed can take different forms. One is that in Acemoglu et al. (2012), which likes most of the endogenous R&D literature rests on modeling competitive patent races (in the quality and/or variety dimensions). There, the dynamic returns to innovation are usually modeled as spillovers—standing on the shoulders of giants for free. Another one is that in Hassler et al. (2018b), which explores more of a reduced-form setting with spillovers: at each point in time any firm, entirely under perfect competition, can choose any technology pair (At , Aet ) from a technology frontier given by the past decisions of others (so under full dynamic spillovers here as well). I.e., the constraint reads G(At /At−1 , Aet /Ae,t−1 ) = 0, where G thus describes the frontier. Under appropriate assumptions on G and F (Ak α , Ae E), a competitive equilibrium exists here, having all firms choose the same technology at each point in time. Here, the arguments of G are growth rates; they could more generally be formulated in levels, or at least without long-run growth effects. Interestingly, when F is CES and G is log-linear, the reduced-form production function—after maximizing over technology—is Cobb–Douglas in the basic inputs k α and E. This general formulation can thus capture a low short-run substitution elasticity (once technology is fixed) and higher (in the special parametric case, unitary) long-run substitution. In terms of policy prescriptions, although research spillovers generally call for interventions, the direction of these interventions is not clear. If the overall research efforts are given and society can only choose their direction, then it may well be that no policy should be undertaken: subsidizing A, in the above example, is good from the perspective of internalizing the externality to A accumulation, but it is by the same token harming the spillover in the Ae direction. Indeed, in the benchmark case of Hassler et al. (2017), no subsidy at all is optimal. Of course, if a climate externality

6 Extensions

is present (it is not in that model) and is not appropriately handled by a carbon tax, then subsidies to Ae innovation would be called for.

6.2 MULTI-REGION MODELING When climate damages are concerned, as briefly mentioned in Section 4 above, what stands out is the heterogeneity in damages rather than a high global average. For many regions, damages are negative, i.e., a warmer climate is expected to improve human welfare, and the differences in outcomes between regions vulnerable to climate change and those benefiting from it are enormous by most measures. Thus, in some sense, what is really needed is an IAM that allows us to study regional impacts. Another reason for using a framework with many regions is that policy analysis in practice is far more difficult as policy is not coordinated (or at least not well, as evidenced by repeated summits without much concrete progress). Thus, positive analysis of policy combinations like “EU and China uses a carbon tax and the rest of the world does not” really demand a global IAM with explicit regions with different policies. Early on, Nordhaus developed RICE for this reason, and other researcher developed other multi-region settings. Here let us discuss how the present core model can be, and has been, extended to allow multi-regional analysis. First, Krusell and Smith (2016) constructed what is essentially a many-region version of the above setup, with “many” as in around 20,000, i.e., regions defined by 1-by-1 degree squares on the global map. Each region then runs its own production function and has its own energy supply—say, coal—and the only global market is the market for saving: there is a global general equilibrium determining the world real interest rate. Versions of the model also allow idiosyncratic (region-specific) climate/weather shocks that the region may want to insure against. The model is solved based on techniques from the macroeconomic literature on consumer heterogeneity and saving under idiosyncratic risks; here one region takes the place of one consumer in that literature (see Aiyagari, 1994, and Krusell and Smith, 1998). Thus, it builds on dynamic programming, as described above, where K, the aggregate state variable, is now replaced by some representation of the distribution of world capital across regions. Migration is not allowed in the baseline version, but it is straightforward to allow frictionless migration across neighboring regions (as in regions within a country or collection of countries such as the EU). In the multiregion model, countries differ in three dimensions: TFP (permanent differences are assumed and the calibration of these differences is based on matching initial output-per-capita differences across countries), differences in initial capital stocks (calibrated so that the marginal product of capital is the same initially across countries), and differential sensitivities to global temperature (for example, further away from the equator the responses to a given degree of global warming are stronger, i.e., there is more than one degree of warming; calibration of these sensitivities is based on “statistical downscaling”, i.e., regressions based on simulations of large climate models). Finally, in this work, damages are assumed to occur in the form of a TFP drag, as above, that simply uses a common,

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U-shaped function of local temperature. I.e., warming makes matter better (worse) for regions with local temperatures to the left (right) of the U’s minimum, since there the drag is declining (rising) with local warming. Clearly, for a region that starts far to the right of the U’s minimum, further warming can be very damaging. Indeed, when the world economy based on this IAM is solved and simulated forward, the effects of global climate change, while moderate on average, are disastrously bad for some regions and positive for many other regions, with only slight majority losing. The regions that stand much to lose are typically developing economies that are already at a very low standard of living in relative terms. This kind of IAM thus highlights the distributional impacts and the needs for policies that take this heterogeneity into account. Further work along these lines appears urgent, in particular when it comes to better understanding the vulnerabilities of the developing world and the potentials for adaptation policy there. A closely related approach is that in Hassler and Krusell (2012) and, in a more recent rendition, Hassler et al. (2018b). The idea here is again that an analytical setting offers a near-equivalent setting to the more elaborate one just discussed. The key simplification here is financial autarky: there is no world market for loans. In the Krusell and Smith (2016) approach just discussed, a world market for loans does make a difference compared to autarky, but the difference is rather minor. Hence, this is a case for autarky as a good approximation. Financial autarky, along with logarithmic utility, Cobb–Douglas production, and full depreciation again delivers constant saving rates. Hassler and Krusell (2012) also considers a world market for oil (Krusell and Smith, 2016, do not) using the simplifying assumption that there is a separate region of oil countries and that these countries cannot invest abroad. It is easy to show that if the oil economies only have income from oil and have logarithmic utility of consumption, they will simply run down the oil supply at a constant rate (equal to their discount rate). Hence, oil quantities in the world are entirely supply-driven (the income and substitution effects from oil-price changes cancel for the producer). The prices are demand-driven: the price of oil has to equal the marginal product of oil in each country (taking taxes into account, if such taxes are levied). Given that the global oil quantity is determined from supply, the equilibrium price is easily solved for period by period. The model is a very convenient vehicle for studying a range of issues, such as policy differences across countries (in Hassler and Krusell, 2012) and endogenous technical change and international R&D spillovers. Given its tractability, versions with many regions can be considered as well, allowing special focus on developing countries and their special features.31 A first-order issue in the climate area not yet studied much in the literature is migration. Allowing for migration, on the one hand, can limit the damages from climate change: given enough time—and climate change is expected to be slow—moving toward cooler areas is one way to adapt. Hence models building on an absence of

31 In ongoing work we explore a global model of this sort, paying special attention to agriculture and

adaptation in countries particularly vulnerable to climate change.

6 Extensions

migration can overstate the negative impacts of climate change. On the other hand, pressures for migration can lead to high costs in the form of social and, perhaps, armed conflict, as populations move across regions and borders. Solving models that allow for migration at a cost is a challenge; very promising approaches forward include Desmet and Rossi-Hansberg (2015) and Brock et al. (2014).

6.2.1 Leakage One of the important policy issues in this area concerns the possible “leakage” of economic activity that would occur if a uniform global policy is not adopted and instead only a subset of countries/regions impose significant restrictions or taxes on carbon use. Let us now briefly discuss this point and only from a conceptual perspective. From a quantitative perspective, it seems to us too early to be able to draw firm conclusions. There are some specific microeconomic studies on the topic, but the body of empirical evidence is quite scarce; and as indicated above, though holding much promise in general and for this topic in particular, the quantitative-theory literature looking at country/region heterogeneity is still in its infancy.32 Leakages can take on different forms. One is that, for a high carbon-tax area, production moves abroad. Or, put differently, costs matter in an industry competing across borders, and so even if no firms literally move across borders, sales or output levels are expected to react as cost structures change. This point is well known and the quantitative effects depend on transportation costs, the energy share, the existence of substitute goods or services, the returns to scale, and so on. Thus, a range of specific factors that differ by industry will matter and we are far from an overall, macroeconomic assessment of these effects. Another form of leakage that is perhaps less discussed is that occurring on the supply side of the energy market. This effect is present also if the use of energy is not subject to trade across borders, so long as the energy itself can move. Take transportation services as an example. As a given country raises its tax on diesel and gasoline, at some point the transportation structure will shift away from fossil-based transportation. In many countries, in fact, such a policy is high on the public-policy agenda; in Sweden, broad “political commitments” have already been made to reduce and eliminate fossil-based transportation going forward, according to a specific time schedule. What are the likely effects of these commitments, beyond the possible effect on transportation costs to the industries in the countries where the policy is undertaken? Given that gasoline and diesel are traded in world markets and imported, typically from far away at relatively low costs, the effects are—if a set of other countries do not impose similar taxes—that a share of the fossil fuels will be used elsewhere. Reduced demand in a set of countries will in general lead to a reduction in the world market equilibrium price and a lower equilibrium production of fuel. If the global supply elasticity is low, the world market price has to fall so as to (largely) compensate the decrease in demand in the taxing countries by increased consumption elsewhere and at a later

32 For the microempirical approach, see, e.g., Fowlie et al. (2016) and the discussion therein.

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time. Under the assumption—the one entertained in our simple model above—that there is an amount of oil in finite supply and that its production costs are negligible, the long-run supply elasticity of oil is zero and leakage of climate policy is complete. In the case of coal, the situation is quite different: here, the marginal cost coal is close to its price and moving coal across space is costly. This implies a large supply elasticity. Hence, leakage is much less of a concern in the case of coal. In sum, fossil-fuel leakage of this sort can be very important to take into account also for understanding the impact on the climate and not just for understanding the effects on local industry. The key features to look for in terms of a quantitative assessment is the transportation costs of the fuel and the marginal cost of its production relative to its price, since these factors are important for the supply elasticity. Another potentially important consideration is that the long-run supply elasticity may increase due to endogenous technical change. Suppose that a set of countries manages to reduce the world market price of oil price by introducing climate policies. This would reduce the incentive to develop technologies for extracting marginal fossil-fuel reserves, hence reducing the leakage from climate policy.

7 CONCLUDING REMARKS This chapter has focused rather singularly on the construction of a global integrated assessment model on the basis of what can be labeled quantitative theory. The text therefore started with a long, motivating section displaying the facts and pointing to the need for a framework that can account for these facts. The next section introduced the neoclassical growth model developed by Solow and extended, with optimal-saving and optimal-work decisions by households and profit-maximizing input demands by firms in a market context, so as to also address price facts, such as those on cost shares. This involved a fair amount of theory and methods discussion, after which the natural-science elements were briefly introduced and then the final integrated assessment model presented and analyzed. Section 6 discussed two important extensions—one to endogenous technical change in the energy sector and another to multi-region models—but many other topics were left without discussion. For example, an important policy issue is whether quotas (along with trade in permits) can have advantages over taxes. In models where quotas and taxes can be changed over time and in response to various shocks, the model would treat the two instruments as identical; in a richer, real-world context, they are of course not.33 Relatedly, there is a very important political-economy element in this area: how are policies chosen endogenously, and what are good institutions from the perspective of the challenges of global warming? These issues are also not discussed here, in particular because quantitative-theory models of endogenous policy are rare even in the context of standard macroeconomic policy (such as tax choice). Thus, the focus on 33 Hassler et al. (2016) discusses practical policy a bit more.

7 Concluding Remarks

a quantitative-theory approach has been a guiding principle throughout the chapter, and this approach was briefly defended in the introduction as well as in Section 5.3 of the paper. From this perspective, the reader may wonder about the tension between the approach advocated here and the view given in Pindyck’s critique of integrated assessment modeling (Pindyck, 2013). It would require a long discussion to address all the relevant points of contact here. In sum, our view is that the IAMs have much to offer, both in terms of accomplishments and future promise. In fact they are, to us, the only game in town. They are flexible tools that allow arguments to play out quantitatively. If one doesn’t like the conclusions, the natural next step is to suggest model amendments, adopt the associated quantitative discipline, and examine the implied results. IAMs do not close the door to obtaining either a call for very urgent and significant action to combat climate change or to the conclusion that no significant action is needed. The quantification is what allows us to obtain an answer. Moreover, the answer is by no means trivial. For the optimal social cost of carbon, we argue, subject to some qualifications, that the key parameters are three (governing utility discounting, damages, and carbon depreciation)—and their respective impacts are nonlinear. For the quantitative effects of no action, or partial action, many more aspects of the IAM become crucial, such as the future of technology, the substitutability between different energy sources, population growth, and so on. Constructing an explicit IAM will, more than anything else, force transparency in this area and this is our main argument behind why we advocate their construction and practical use. Finally, IAMs can be used to answer questions like “what is the most efficient way of making sure that a given temperature target is not exceeded?”, which represents a more modest view on what we can say about what is optimal in a broader sense. Finally, let us connect back to the introduction where we argued that climate change should be regarded as a first-order issue for macroeconomists and ask whether there might be other environmental challenges that of equal, or even greater, importance from a global perspective. At this point in time, it is hard to argue that another, equally important challenge can be identified, not because we know that such challenges do not exist but rather because the evidence and scientific studies of this evidence (in natural as well as social sciences) are very incomplete compared to what we know about the climate. One concern is the broad issue of sustainability of the world’s resources, defined to include natural non-renewable resources in finite supply as well as water supply and other strains on our planet. We find this area potentially very important, at the same time as it seems difficult to refer to direct, quantitative evidence of scarcity that is as “binding” as is that on our climate (for an early discussion that concluded that we were far from binding constraints at least in some dimensions, see Nordhaus, 1974). Moreover, it is much less clear what the market failures are in these contexts than in the climate area. Having said this, and as a final personal note, this topic is high on our own research agenda.

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Nordhaus, William, 2006. Geography and macroeconomics: new data and new findings. Proceedings of the National Academy of Sciences 103 (10), 3510–3517. Nordhaus, William, 2008. A Question of Balance: Weighing the Options on Global Warming Policies. Yale University Press, New Haven, CT. Nordhaus, William D., Boyer, Joseph, 2000. Warming the World: Economic Modeling of Global Warming. MIT Press, Cambridge, MA. Nordhaus, William, Moffat, Andrew, 2017. A Survey of Global Impacts of Climate Change: Replication, Survey Methods, and a Statistical Analysis. Cowles Foundation Discussion Paper No. 2096. Pigou, Arthur, 1920. The Economics of Welfare. MacMillan, London. Piketty, Thomas, 2013. Capital in the 21st Century. Du Seuil, Paris. Piketty, Thomas, Saez, Emmanuel, 2006. The evolution of top incomes: a historical and international perspective. The American Economic Review 96 (2), 200–205. Pindyck, Robert, 2013. Climate change policy: what do the models tell us? Journal of Economic Literature 51 (3), 860–872. Popp, David, 2002. Induced innovation and energy prices. The American Economic Review 92, 160–180. Rachel, Lukasz, Smith, Thomas, 2015. Secular Drivers of the Global Real Interest Rate. Bank of England Working Paper No. 571. Romer, Paul M., 1990. Endogenous technological change. Journal of Political Economy 98 (5), S71–S102. Schmitt, Alex, 2014. Beyond Pigou: Climate Change Mitigation, Policy Making and Distortions. Ph.D. Thesis, IIES Monograph series No. 85. Stockholm University. Solow, Robert, 1956. A contribution to the theory of economic growth. The Quarterly Journal of Economics 70 (1), 65–94. Solow, Robert, 1957. Technical change and the aggregate production function. Review of Economics and Statistics 39 (3), 312–320. Stern, David I., 2012. Interfuel substitution: a meta-analysis. Journal of Economic Surveys 26, 307–331. Stern, Nicholas, 2006. The Economics of Climate Change: The Stern Review. Cambridge University Press, Cambridge and New York. Uzawa, Hirofumi, 1961. Neutral inventions and the stability of growth equilibrium. Review of Economic Studies 28 (2), 117–124. Weitzman, Martin L., 2011. Fat-tailed uncertainty in the economics of catastrophic climate change. Review of Environmental Economics and Policy 5 (2), 275–292. Williamson, Jeffrey, 1995. The evolution of global labor markets since 1830 background evidence and hypotheses. Explorations in Economic History 32 (2), 141–196.

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Causal inference in environmental conservation: The role of institutions✶ ∗ Department

Erin O. Sills∗,1 , Kelly Jones†

of Forestry and Environmental Resources, North Carolina State University, Raleigh, NC, United States of America † Department of Human Dimensions of Natural Resources, Colorado State University, Fort Collins, CO, United States of America 1 Corresponding author: e-mail address: [email protected]

CONTENTS 1 Introduction ...................................................................................... 2 Average Treatment Effects of Institutions.................................................... 2.1 Instruments......................................................................... 2.2 Methods ............................................................................. 2.3 Findings ............................................................................. 3 Institutional Insights for Causal Models ..................................................... 3.1 Causal Diagrams ................................................................... 3.2 Institutions as Determinants of Assignment ................................... 3.3 Heterogeneous Institutional Treatments........................................ 3.4 Institutions as Moderators........................................................ 3.5 Institutions as Mechanisms ...................................................... 4 Summary and Future Directions ............................................................... References............................................................................................

395 399 399 400 403 406 406 410 412 416 422 426 427

1 INTRODUCTION Careful attention to institutions is essential for navigating the convergence of two currents that have swept environmental conservation and economics over the past 25 years. First, especially in the tropical biomes that harbor most of the world’s biodiversity, local people are increasingly recognized as central to conservation (Baland ✶ Paul Ferraro and Pam Jagger helped frame this chapter through extensive discussions and detailed input. We thank Yu Wu for her assistance with the equations and figures. Handbook of Environmental Economics, Volume 4, ISSN 1574-0099, https://doi.org/10.1016/bs.hesenv.2018.09.001 Copyright © 2018 Elsevier B.V. All rights reserved.

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and Platteau, 1996; Shahi and Kant, 2007; Agrawal et al., 2008; Brooks et al., 2013; Shyamsundar and Ghate, 2014; Vega and Keenan, 2016; Blythe et al., 2017; Garnett et al., 2018). This has manifested in greater attention to the consequences of conservation for local people; increased investment in decentralized and communitybased approaches to conservation; and modified design of instruments based on command-and-control (e.g., co-management of protected areas) and economic incentives (e.g., collective contracts for payments for ecosystem services). Second, economists increasingly use the Neyman–Rubin model of causal inference and experimental logic to identify causal effects in what has been called a ‘credibility revolution’ (Angrist and Pischke, 2010). This ‘causal empiricist’ approach has both changed the practice of applied economics and expanded the domain of economists to include questions about the effectiveness of interventions in fields such as environmental conservation (Greenstone and Gayer, 2009; Samii, 2016; Panhans and Singleton, 2017). Estimating causal effects in the context of a peopleoriented approach to conservation requires careful attention to institutions, or the rules that constrain and enable human behavior, because those rules are likely to both shape and be shaped by conservation instruments (Ostrom, 1990, 2005). Institutions include any durable system of established and embedded social rules (Hodgson, 2006), whether formal (i.e., explicit, written into law, and requiring external enforcement) or informal (i.e., tacit, not codified by law, and self-enforcing in that they are based on coordination games).1 New institutional economics suggests that institutions emerge in response to information asymmetries, transaction costs, and risks (Lambini and Nguyen, 2014), but they are also shaped by social preferences such as reciprocity, reputation, and trust (Ostrom, 1997). Compared to biophysical and macroeconomic factors, institutions can appear at more points in a causal chain, precisely because they are more malleable. This also means that they offer multiple possible leverage points for promoting conservation, e.g. not only as the instrument itself but also as a determinant of where the instrument is applied and a moderator of the effect of that instrument. In particular, many conservation interventions focused on local people are moderated by and expected to facilitate the emergence of local institutions, which include the rules and norms governing interactions among people who live in the same community and thus have a common history and use a common resource base (Vega and Keenan, 2016). In this chapter, we first review the methods and findings of economists who have taken a causal empiricist approach to evaluating instruments for environmental conservation, focusing on three that have or could fundamentally change institutions across large areas of the low-income tropics: protected areas, decentralization and devolution of management to communities, and payments for ecosystem services. 1 While the term “institution” sometimes refers to organizations that are agents in and of themselves, we

only use the term for organizations as systems of rules that structure social interaction among their members. Petursson and Vedeld (2017) clarify that “while institutions are cognitive and normative structures which stabilize perceptions, interpretations and justifications, organizations are seen as actors. Organisations are explicitly established, directed and maintained with goals, values, and norms.”

1 Introduction

Second, we elucidate the multiple roles of institutions in causal models, using the language and logic of causal diagrams or “directed acyclic graphs” (DAGs) (Pearl, 2009; Ferraro and Hanauer, 2015). When they incorporate these institutional insights into their empirical models, economists obtain results that are both more credible and more relevant to policy and practitioner decisions. This is true especially in the lowincome tropics, where the theory of common property governance and empirical evidence suggest that informal, local institutions are key in shaping environmental conservation. Both the importance and the challenges faced by these institutions are magnified by the limited formal governance capacity and the high transaction costs and information asymmetry that characterize the remote and globally valuable stocks of renewable natural resources in the tropics (Barrett et al., 2005; Vega and Keenan, 2014, 2016; Hodgson, 2006). However, we note that institutions are relevant to all governance and collective action problems and thus to causal inference in the environmental and conservation arenas more broadly. Causal identification based on the potential outcomes or counterfactual framework (Imbens and Rubin, 2006) was not taken up as quickly in environmental conservation as in other policy domains (Ferraro and Pattanayak, 2006), but the body of evidence based on experimental and quasi-experimental (observational) impact evaluations has grown over the past decade, largely through methods developed by economists (Imbens and Wooldridge, 2009). This evidence is largely comprised of estimates of the average effects of different conservation instruments, as they are used in projects, programs, and policies. When these instruments can be manipulated directly by governments or other external actors like international environmental organizations, they can be evaluated as “treatments.” As in the environmental domain more generally, the treatments include both command and control (e.g. limitations on equipment and harvest levels) and incentive-based measures that rely on price signals such as taxes, subsidies, or tradeable permit systems (Sterner and Coria, 2012). Both of these approaches change the parameters of the decision problem faced by local people and other users of natural resources, e.g. by changing the expected value of the fine for illegal resource extraction or the cost of inputs for sustainable resource management. In contrast, the three instruments that we consider in this chapter are intended to change the whole structure of the decision problem, by re-assigning property rights or by assigning value to previously unpriced services generated by natural resource stocks. There has been rapid uptake of these instruments across the tropics, and concomitant interest in understanding their effects among economists (e.g. Miteva et al., 2012) and proponents of evidence-based policy (e.g. the Collaboration for Environmental Evidence, 2018). In Section 2, we review the economic literature on the average effects of conservation instruments, considering three types of treatments (protected areas, decentralization and devolution of management responsibility to communities, and payments for ecosystem services) and two types of outcomes (environmental and local welfare). We provide a brief introduction to these treatments and to matching, which is the method of causal inference that has been most often used to estimate these effects. Finally, we synthesize findings from systematic reviews and other meta-studies

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FIGURE 1 Diagram of a generic causal model of the effects of treatments T on outcomes Y.

that have screened the economics and conservation literatures for credible estimates of the average effects of these three treatments, based on methods that convincingly distinguish the effect of the treatment from the influence of the people and places selected for treatment. To preview findings, most meta-studies have found at least some credible evidence that these treatments have positive causal effects on environmental outcomes. This is noteworthy in the context of skepticism about their efficacy, with long-standing criticisms including that they are “paper parks,” not actually implemented on the ground (Brandon et al., 1998); that they are subject to elite capture, and thus fail to incentivize conservation by most local people (Agrawal and Gibson, 1999); and that adverse selection means that there is little to show for the money invested in direct payments (Pattanayak et al., 2010). However, another common conclusion is that there are very few estimates of causal effects that can be considered credible, especially for local welfare (cf. Robinson et al., 2014 for property rights and Van Vliet et al., 2016 for land use change). In Section 3, we develop the argument that casual diagrams (and specifically DAGs) can help economists move from estimating average effects (which has been called “conservation evaluation 1.0”) to an “understanding of whether, under what conditions, and how conservation instruments work,” or “conservation evaluation 2.0” (Miteva et al., 2012). As illustrated by the generic DAG in Fig. 1, the causal pathway from assignment to treatment to final outcomes (Y) runs through possibly heterogeneous treatments (T) and mechanisms for those treatments. By recognizing the potential influence of institutions along this causal path, economists can both enhance the internal validity of effect estimates and relate causal inference to an underlying theoretical model. Institutions may also appear off the causal pathway in a DAG, as moderators or effect modifiers, which are key to establishing external validity. Based on this framework, we organize the rest of the chapter around four roles of institutions in identifying causal effects: (1) determinants of assignment into treatment including confounders, (2) sources of heterogeneity in treatments, (3) moderators, and (4) mechanisms. In all cases, incorporating institutions into the empirical analysis can lead to effect estimates that are more credible and more relevant to decisions about how to promote environmental conservation.

2 Average Treatment Effects of Institutions

2 AVERAGE TREATMENT EFFECTS OF INSTITUTIONS The ubiquity of budget constraints and trade-offs across social objectives has generated demand for “evidence” about the effects of alternative policy instruments on both their target outcomes and other outcomes of public interest (Davies and Nutley, 2000). Economists have contributed to the evidence base through program evaluation, or careful ex post estimation of the causal effects of policy instruments, relative to counterfactuals, on defined populations. Most commonly, the population of interest is the “treated,” or the people and places where the instrument has been applied, and the estimand is the average effect of the treatment on the treated (ATT). In this section, we first introduce three instruments that have been the focus of program evaluation in environmental conservation, then explain the framework and methods for causal inference that have been applied to them, and finally we synthesize the resulting evidence about their ATT for both conservation and local welfare outcomes.

2.1 INSTRUMENTS Policy instruments either operate within existing institutions or operate through changes in those institutions, i.e. establishing new rules of the game for natural resource use. In this chapter, we focus on three types of conservation instruments that are of interest because they clearly are intended to change institutions – specifically, property rights institutions. While these instruments have many other dimensions and many possible variants (Larson and Soto, 2008; Muradian et al., 2010), they are fundamentally about creating new institutions. First, protected areas assign property rights to states or other public actors for the explicit purpose of environmental conservation. Second, decentralization or devolution to communities assign property rights to lower levels of government or user groups. Third, payments for ecosystem services (PES) create and assign property rights for the public environmental benefits of natural resources to their owners or managers. These three instruments are also of particular interest because of their rapid expansion over the past 50 years, which in turn reflects international calls for new protected areas to preserve biodiversity (Naughton-Treves et al., 2005; Watson et al., 2014), but at the same time, recognition that central state control over natural resource stocks is often inefficient and inequitable (Somanathan and Sterner, 2006). PES was advocated by economists as a cost-effective way to meet conservation goals, potentially superior both to command and control (in a parallel to the argument for price-based instruments for pollution control (Sims and Alix-Garcia, 2017)) and to indirect approaches that promote conservation through changes in other prices, information, or technology (Ferraro and Kiss, 2002). The details of PES as implemented around the world vary substantially,2 but the core concept is to recognize and offer positive 2 Salzman et al. (2018) catalog over 500 PES schemes, most of them small scale and short-term. However,

many program evaluations have considered the three large, national programs of PES in low and middle income countries: Pagos por Servicios Ambientales (PSA) program in Costa Rica, the Sloping Lands

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incentives for provision of valuable public goods that can be secured through sustainable management of natural resource stocks. While we focus on these three instruments for environmental conservation, they are by no means the only instruments relevant to conservation, nor the only instruments that have been evaluated by economists. For example, forest policy instruments also include regulation of private forest management, education and research, protection (e.g. from fire, invasive species, or illegal harvest), subsidies and tax concessions, conservation easements, and private-sector driven incentives for sustainable management (Cubbage et al., 2007; Kamal et al., 2015). Economists have evaluated many of these instruments, e.g. regulation of private forest management in the Brazilian Amazon (Börner et al., 2015; Azevedo et al., 2017; Santiago et al., 2018) and forest certification in Indonesia (Miteva et al., 2015a; Rana and Sills, 2018). Program evaluations of these other instruments have used the same methods as described in Section 2.2 and could benefit from the more careful attention to the institutional dimensions of causal models advocated in Section 3.

2.2 METHODS The econometrics of program evaluation and methods for causal inference are the subject of numerous reviews (e.g. Abadie and Cattaneo, 2018) and books (e.g. Imbens and Rubin, 2015). Thus, here we just introduce key concepts, as relevant to environmental conservation. The impact of a treatment is defined relative to a counterfactual, or what would have happened without treatment, all else equal. That is, a treatment is defined as a change from one specific situation to another. For example, to estimate the effect of forest or marine protected areas, the analyst must specify how those resources would have been governed absent those treatments. This gives rise to two potential outcomes for each unit i (of area or people): y1i – outcome for unit i when treated y0i – outcome for unit i when not treated i = y1i − y0i – the causal effect, or impact, of the treatment on unit i

(1)

For any given unit, only one of these outcomes is observable, as defined by the treatment indicator Ti (= 1 if treated; = 0 if not treated). Assume that nonetheless, we can obtain estimates of i . The average treatment effect (AT) would be the average i for the population of interest (with N units). AT =

N 1  i N

(2)

i=1

Conservation Program (SLCP) in China; and the Pago de Servicios Ambientales Hidrológicos (PSAH) program in Mexico.

2 Average Treatment Effects of Institutions

If  is homogeneous, the AT for the entire population, the sub-population that is treated, and the sub-population that is not treated are all the same, and equivalent to the estimated coefficient on the treatment (T ) in an OLS regression of the observed y on an intercept and T (Sloczynski, 2018). However,  often has different distributions among individuals who are treated (T = 1) as compared to individuals who are not treated (T = 0), because of self-selection or administrative assignment based on confounders or the expected . In that case, the OLS regression coefficient is no longer equivalent to the AT for these populations. Differences in the multivariate distribution of both the causal effect and the covariates across the treated and control units motivate the use of program evaluation methods to estimate the AT for the population of interest. For retrospective evaluations of the impact of some treatment, the population of interest is the treated. ATT = E[y1i − y0i |Ti = 1]

(3)

In this case, the key challenge for evaluation is that E[y0i |Ti = 1] is not observable. Thus, a control group is used to obtain an estimate (τ ) of the ATT: τ = E[y1i |Ti = 1] − E[y0i |Ti = 0] This can be re-written as the sum of the ATT and the selection bias:   τ = E[y1i − y0i |Ti = 1] + E[y0i |Ti = 1] − E[y0i |Ti = 0]

(4)

(5)

Thus, ATT = τ when E[y0i |Ti = 1] = E[y0i |Ti = 0].

(6)

Program evaluation uses various methods to address this bias (Miteva et al., 2012; Vincent, 2016; Jagger et al., 2010). One possibility is random assignment or roll-out (i.e., randomized controlled trials) (Jayachandran et al., 2017). Another is to find a natural experiment that assigns treatment based on an instrumental variable (Angrist et al., 1996) or cut-off point in an assignment variable (Lee and Lemieux, 2010) in a way independent of other factors. In the environmental conservation domain, the most common approach is to incorporate measures of assignment or selection into the analysis as covariates in regression models, matching, or both for doubly robust or bias corrected estimators (Ho et al., 2007; Imbens and Rubin, 2015; Negi and Wooldridge, 2018). The goal of matching is to maximize the covariate balance between treated and control groups, as if they had been randomly assigned. Preferably, the analyst starts with a sample likely to include similar treated and control units, e.g. households in pre-matched villages (Sills et al., 2017), applicants to an oversubscribed program (Alix-Garcia et al., 2012), or current and future participants in a program (Hayes et al., 2017). Within that sample, the analyst can search for the best balance using only information on the covariates and treatment, without repeated estimation of the outcome. By balancing

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covariates, matching allows Eq. (6) to be replaced with the conditional independence assumption (CIA): E[y0i |x, Ti = 1] = E[y0i |x, Ti = 0] = E[y0i |x]

(7)

where x represents a set of observable characteristics that are assumed to fully account for any confounding. The sensitivity of the results to potential unobserved confounders is often tested using the approach proposed by Rosenbaum (2002). Within a matched sample, the treatment effect typically is estimated as the difference in means. This estimator can be generally written as:

ATT x =

N1   1  y1i − E(yˆ0i |Ti = 1) N1

(8)

i=1

where N1 is the number of treated observations. Many variants on matching methods are discussed in the literature and available in standard software packages (Stuart, 2010; Diamond and Sekhon, 2013). Perhaps the most common approach is to match to the nearest neighbor or more generally, the M nearest neighbors: E(yˆ0i |Ti = 1) =

M 1  yj (i) M

(9)

j =1

where the subscript j (i) indicates that j is a unit from the control group, matched to i. The matches yj (i) may be chosen to minimize the distance between the propensity scores Pi = Pr(Ti = 1|xi ) and Pj = Pr(Tj = 1|xj ) (Rosenbaum and Rubin, 1983), or  to minimize the total distance between the covariates M j =1 dij , which is commonly  defined based on the Mahalanobis metric dij = (xi − xj ) −1 x (xi − xj ) (Rubin, −1 1980), where x is the inverse of the covariance matrix of x. Summing up, the average treatment effect on the treated computed with matching to M nearest neighbors based on the covariate vector x is:  N1 M 1  1  yj (i) y1i − ATT x = N1 M i=1

(10)

j =1

Because matching improves but does not achieve perfect balance, a better estimate of the ATT can be obtained by estimating a regression model of the outcome in the matched control sample (Eq. (11)) and using the resulting coefficient estimates for

2 Average Treatment Effects of Institutions

“full regression adjustment” of the ATT (Eq. (12)) (Imbens and Rubin, 2015).3 yˆj (i) = αj (i) + β0 xj (i) + εj (i) adj yj (i)

= yj (i) + β0 (xi

− xj (i) )   1 adj adj  ATT x = y1i − yj (i) N1

(11) (12)

Matching may also be combined with differences-in-differences (DID) to sweep out time-invariant factors that influence selection (Jones and Lewis, 2015). Matching on lagged outcomes can help identify sub-samples for which the parallel trends assumption of DID is valid. Data from before the treatment are essential for this approach, but also needed for matching and regression adjustment, unless those are limited to time-invariant factors (Sills et al., 2017). To evaluate impacts on unit areas (e.g. the impact of placing forest into protected areas), this is typically accomplished with remote sensing or census data collected prior to the treatment. To evaluate impacts on agents such as households, data are typically obtained through surveys, preferably conducted both before and after the intervention, since baseline conditions are difficult to reconstruct ex post (Mullan et al., 2013; Ravallion, 2014).

2.3 FINDINGS We draw on systematic reviews to summarize the evidence generated through “conservation evaluation 1.0” on the average effects of protected areas, decentralization, and PES, with a focus on the biodiverse forest ecosystems of low and middle income countries. Most systematic reviews both report on a broad evidence base and identify a small sub-set of studies that estimate impacts relative to a counterfactual, control for confounding variables, and consider possible sources of bias and rival explanations. We supplement these reviews with findings from more recent literature, which often reports both an overall ATT and estimation results from the more nuanced analyses discussed in Section 3. The effectiveness of protected areas (PAs) at protecting ecosystems has been the subject of numerous impact evaluations. Many early studies of PA effectiveness (reviewed by Nagendra, 2008) compared trends inside and near protected areas. Economists pointed out that this naïve comparison overlooks both selection bias in the exact boundaries and the potential for spillover or leakage across those boundaries (Joppa and Pfaff, 2009). Following the recommendations of economists, matching has been widely adopted for evaluating protected areas; specifically, units inside a

3 The correct standard errors can be obtained through the TEFFECTS package in STATA. According to Wooldridge (2018), ATTadj is a consistent estimator when constructed from linear models estimated with

OLS, logistic models estimated with a Bernoulli quasi-log likelihood, and exponential models estimated with a Poisson quasi-log likelihood.

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PA are matched with units that are far enough away to plausibly claim that they are not subject to spillovers. The units are often pixels or grid cells that can be characterized in terms of forest cover and matching covariates such as market access and biophysical characteristics (e.g., slope, soil quality, precipitation). Systematic reviews (Miteva et al., 2012; Geldmann et al., 2013) of studies using this approach have found that protected areas are effective at reducing deforestation, even after controlling for the fact that they tend to be established in areas under lower threat of deforestation. The authors of these studies almost all report that the causal effects of protected areas are much smaller than would appear from naïve comparisons of deforestation rates. More recent studies continue to focus on deforestation as the key outcome (Vincent, 2016), reflecting the increasing availability of remote sensing data (Blackman, 2013). Those studies have confirmed that PAs in countries such as Brazil (Pfaff et al., 2014), Chile (Arriagada et al., 2016), Ecuador (Cuenca et al., 2016), and Peru (Miranda et al., 2016) (but only in some time periods in Mexico according to Blackman et al., 2015 and Pfaff et al., 2017) reduce deforestation on average, while also emphasizing variation across different types of PAs (see Section 3.2). For the case of Costa Rica, Robalino et al. (2017) also find heterogeneity across the landscape in spillovers from protected areas, suggesting an important area for future research. The literature on the local welfare effects of protected areas considers a range of outcomes, including measures of income, employment, livelihoods, and poverty. In recent systematic reviews of this literature, Oldekop et al. (2016) and Pullin et al. (2013) find that most studies of the social impacts of terrestrial protected areas have employed qualitative methods. Comparing the findings of qualitative and quantitative studies, Pullin et al. (2013) notes that “views expressed on impacts of PAs on economic capital are generally negative, with the exception of some views on the benefits of ecotourism. In contrast the quantitative evidence of impact from three studies on livelihood strategies was neutral to positive in terms of poverty reduction.” Specifically, the quantitative studies that passed their quality screen found that protected areas increased access to forest benefits and decreased poverty. The authors of these studies compiled and analyzed data for either jurisdictional or census units, considering them treated if they substantially overlapped with PAs. More recent studies examine households (Clements et al., 2014; Beauchamp et al., 2018) or individuals (Robalino and Villalobos-Fiatt, 2015), allowing consideration of how impacts vary across livelihoods, locations, and origin (locals vs. recent arrivals). In studies in Cambodia, the authors find mixed effects on welfare, with Clements et al. (2014) reporting small positive effects on a socio-economic index in one period, while Beauchamp et al. (2018) report small negative effects on the same index in the same study site but using panel data. One possible explanation is that PAs supported livelihoods by maintaining the supply of a non-timber forest product that declined in importance over time. Robalino and Villalobos-Fiatt (2015) find that protected areas in Costa Rica have positive effects on wages, especially for women, recent arrivals, and people who live close to the park entrances, where tourism development is most likely. As with evaluations of impacts on deforestation, the authors of these studies often report that their estimates suggest substantially different effects than naïve

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comparisons of treated groups to unmatched control groups. However, in the case of welfare outcomes, careful attribution sometimes results in larger and sometimes smaller effects, and sometimes flips the sign of the effect. Two systematic reviews by Samii et al. (2014) and Bowler et al. (2010, 2012) summarize evidence on decentralization of forest management. Samii et al. (2014) found eight impact evaluations of decentralized forest management that all reported positive point estimates (not always statistically different from zero) of effects on forest cover and three of which also estimate a positive effect on participants’ household income (from forests or in total). Using slightly different definitions and criteria, Bowler et al. (2010, 2012) found 10 evaluations of the impacts of community forest management that acknowledged and attempted to control for potential confounders. Eight of those studies found that community forest management results in higher forest quality, as measured by basal area and tree stem density. However, Bowler et al. found no consistent patterns in estimated impacts on other conservation or livelihood outcomes. Both Samii et al. (2014) and Bowler et al. (2010, 2012) call for more rigorous impact evaluations of a more representative and informative sample of interventions. In a regional review, Shyamsundar and Ghate (2014) identify three credible evaluations of decentralization of forest management in South Asia, using three different sources of data on outcomes: household surveys (Edmonds, 2002), remote sensing (Somanathan et al., 2009), and ecological surveys (Baland et al., 2010). The studies find less fuelwood extraction (as reported in household survey) and less evidence of lopping in the forest (as detected in ecological survey) in forests managed by local groups. Somanathan et al. (2009) find that community forest management does no worse than government management, at significantly lower cost. Recent reviews of the causal impacts of PES (Miteva et al., 2012; Börner et al., 2017; Samii et al., 2014; Alix-Garcia and Wolff, 2014) conclude that the limited available evidence shows that PES systems protect forest under PES contracts. Samii et al. (2014) screened for experimental or quasi-experimental studies with clearly delineated treated and control areas and some method for removing biases due to non-random assignment of the intervention, and found only 9 impact evaluations that met those quality criteria, with 6 of those evaluating Costa Rica’s PES system. They concluded that evaluations are more likely to find statistically significant positive impacts on total forest cover (including regrowth) than on gross deforestation. Alix-Garcia and Wolff (2014) confirm that most evidence on the impacts of PES is based on studies of the national systems in Costa Rica and Mexico, where deforestation rates are low. Thus, impacts appear larger when reported as percentage changes relative to the counterfactual rather than hectares of forest cover preserved or deforestation avoided. Miteva et al. (2012) reached similar conclusions about the state of the literature. All of these reviews point out that evaluations rarely consider the possibility of spillovers or leakage, i.e. impacts on lands and landowners not participating in the PES system (for an exception, see Alix-Garcia et al., 2012). Börner et al. (2017) suggest that evidence is also needed on the permanence of the impacts, noting that the only empirical study of permanence (Pagiola et al., 2016) examined a PES

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program that provided a suite of incentives, including technical assistance, to adopt silvopastoral practices, which would likely have different long-term effects than the cash payments provided by most large-scale PES systems. In addition to the program evaluations summarized in these reviews, there has been at least one randomized controlled trial (RCT) of PES for avoided deforestation. Jayachandran et al. (2017) demonstrate that a carefully implemented and well monitored PES program implemented in the context of high deforestation and low opportunity costs can have substantial and statistically significant impacts on deforestation. Like most RCTs (Peters et al., 2016), the intervention was implemented by an NGO that collaborated with the research team, “which might lead to more positive results than what can be expected if the intervention is implemented by a governmental agency.” While this may help explain why the estimated effect is larger than obtained in quasi-experimental studies in other locations, this RCT does demonstrate that carefully implemented PES in the right context can deliver conservation results. Pattanayak et al. (2010), Samii et al. (2014), and Alix-Garcia and Wolff (2014) also searched for evidence on how PES affect local welfare, or poverty. The very limited evidence base on this includes two studies on the Sloping Lands Conversion Program in China, showing that it shifted household labor allocation from on-farm to off-farm (Uchida et al., 2009) and increased household income by 14% on average (Liu et al., 2010). Samii et al. (2014) consider one study on PES in Mozambique to meet their quality criteria: Hegde and Bull (2011) found that participation raised income by 4% on average. Since these reviews were completed, other studies have been published, again on Costa Rica (Arriagada et al., 2015) and Mexico (Alix-Garcia et al., 2013). Arriagada et al. (2015) find no evidence that the participation in PES affects the well-being of landowners, suggesting that rather than income, pro-environmental preferences or the need to secure property rights may have motivated participation. Alix-Garcia et al. (2013) find that PES reduces poverty the most where the risk of deforestation is low, as further discussed in Section 3.3.

3 INSTITUTIONAL INSIGHTS FOR CAUSAL MODELS In addition to being the treatments of interest, institutions can influence causal models in several other ways, which should be taken into account in the estimation of treatment effects. In this section, we use the logic and language of directed acyclic graphs (DAGs) to categorize these influences. For each category, we discuss hypotheses (drawing on theory, framed field experiments, and social-ecological analysis as recommended by Mascia et al., 2017) and describe empirical findings to date.

3.1 CAUSAL DIAGRAMS DAGs and their associated terminology offer a way to clearly describe the role of institutions in a causal system. As explained by Shrier and Platt (2008), “all causal inferences based on statistical models are implicitly based on a causal structure –

3 Institutional Insights for Causal Models

the DAG approach simply makes the assumptions explicit. Causal DAGs represent theory.” From an economic perspective, DAGs are graphical representations of the underlying structural model of optimizing behavior, which may include both constrained maximization within the rules of the game and investments in maintaining or changing those rules. Thus, the rules of the game, or institutions, can appear at more points in the causal model than less malleable biophysical and macroeconomic conditions. DAGs represent economic theory by tracing out the potential pathway from a treatment (i.e. the intervention) to the outcomes of concern, through nodes that are either connected by unidirectional arrows, showing possible causal effects, or exclude arrows, showing no possible causal effects (i.e., exclusion restrictions). (See Fig. 1.) The same general structure of nodes and arrows is used across many fields to describe the underlying logic or theory of an intervention (Qiu et al., 2018). However, DAGs are constructed using specific terminology and rules that make explicit the assumptions about the role and therefore the appropriate empirical treatment of each factor in the causal model (Elwert and Winship, 2014). Specifically, DAGs include three types of statistical association between variables: (1) causal, as represented by arrows from one variable to the second, possibly through intermediate “mechanisms,” (2) common causes, as represented by arrows from a “confounder” to both variables, and (3) common effects, as represented by arrows leading from two variables to a “collider” (Hernán et al., 2004). The first and second of these are familiar concepts to economists. We expand on the concept of colliders, which are considered critical in other fields that use DAGs, but are rarely discussed by economists. Colliders are problematic for causal inference when they are caused by two variables that either are the treatment and the outcome or are causally related to the treatment and the outcome (Elwert and Winship, 2014). Fig. 2 illustrates two possibilities, where the collider is caused by the outcome or caused by another factor (U) that also causes the outcome. As an example, the population density of a village (U) may influence both the resource status (Y) and the frequency of social events. This frequency becomes a collider if it is also influenced by the treatment (T), such as NGO support for community forest management. Controlling for the frequency of social events could create spurious correlation between T and Y. More generally, the concept of colliders encapsulates economists’ concerns about several types of bias, including endogenous selection based on expected outcomes and matching or adjusting for covariates that were not determined prior to treatment. In the DAG framework, estimation of the ATT (as described in Section 2) is equivalent to isolating the causal source of statistical association, by controlling for

FIGURE 2 Colliders.

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common causes and excluding common effects. In many cases, economic theory suggests that the causal effect varies with moderators, or exogenous effect modifiers, and operates though mechanisms, or intermediate outcomes. In the environmental conservation domain, moderators and mechanisms are often institutions, and they are key to the external and internal validity of the estimated effect. Ferraro and Hanauer (2015) provide an elaborated DAG for this context. Candidate institutional moderators and mechanisms are often included in lists of factors related to successful management of common pool resource identified through the social-ecological framework (Agrawal, 2001; Pagdee et al., 2006; Ostrom, 2009; Gutiérrez et al., 2011; Persha et al., 2011; Cinner et al., 2012; Stevenson and Tissot, 2014). Following Ferraro and Hanauer (2015) and the generic DAG in Fig. 1, we categorize the structural roles of institutions as (1) determinants of assignment or selection into treatment, (2) treatments, (3) moderators, and (4) mechanisms.4 First, causal inference may be facilitated by institutions that affect only whether or when the unit is assigned to treatment and not the outcome for that unit (potential instrumental or assignment variables) or complicated by institutions that affect both whether a unit is treated and the outcome for that unit (confounders). Second, as reviewed in the previous section, there is a small but rapidly expanding evidence base on the average effects of institutional treatments. Many authors have suggested that these averages mask substantial variation in treatment effects, which is at least partly due to variation in the institutional details of treatments. Thus, we consider heterogeneous treatments as the second potential role of institutions. In this case, the analyst estimates more than one treatment effect (Eq. (13)), e.g. the ATT for protected areas designated for strict protection (T = 1) and the ATT for protected areas designated for sustainable use (T = 2). ATT 1 = E[y1i − y0i |x, Ti = 1]

(13)

ATT 2 = E[y2i − y0i |x, Ti = 2] Third, institutional moderators are key to understanding the external validity of effect estimates, because by definition, a treatment has different effects at different values of the moderator (Eq. (14)). Moderators are not on the causal path, i.e. they do not affect and are not affected by the treatment. Rather, they represent the context and hence influence both the treatment and its counterfactual. That is, unlike institutional variation in treatments, institutional moderators affect both potential outcomes (when T = 1 and T = 0). The goal of empirical analysis of moderators is to test for different effect sizes, rather than conditioning on the institution, e.g. the ATT when there is 4 In the literature, treatments are sometimes called “mechanisms,” while the term “mediator” is used for both moderators and mechanisms. One benefit of DAGs is that they clearly represent these different roles in terms of nodes and arrows, rather than terminology that varies across disciplines. The list of roles that institutions could play is not exhaustive. For example, they could also affect estimation by linking together the DAGs of different agents such that treatment of one agent could influence another agent, violating the stable unit treatment value assumption and creating interference (see Deschenes and Meng, this volume).

3 Institutional Insights for Causal Models

strong law enforcement (xm = 1) and the ATT when there is weak law enforcement (xm = 2). ATT|(xm = 1) = E[y1i − y0i |x, xm = 1, Ti = 1] ATT|(xm = 2) = E[y1i − y0i |x, xm = 2, Ti = 1]

(14)

Fourth, an institution may be the mechanism by which the treatment affects the outcome, i.e. an intermediate or proximate outcome (Eq. (15)). For example, collective action through informal community institutions is an expected mechanism for treatments such as decentralization policies that allocate rights and responsibilities to communities (Tacconi, 2007), collective contracts that offer rewards to communities (Chervier and Costedoat, 2017), or various co- or joint-management agreements for public lands (Jagger et al., 2018). These institutional mechanisms may change the entire structure of decision-making (e.g. by introducing learning, norms, or trust), rather than just particular parameters in the decision-making model (e.g. the farmgate price, or the production technology). Empirical models for estimating causal effects on the final outcomes should not control for mechanisms, as that would bias the effect estimate (called “over-control” bias) or create spurious correlation (if the mechanism is affected by an external factor that is also related to the outcome). However, hypothesizing and testing for mechanisms (Eq. (16)) can enhance the internal validity of effect estimates. Further, estimating effects on mechanisms can serve as a short-run test of the causal model.  m  m − y0i |x, mi = 1 (15) ATT m = E[m1i − m0i |x, Ti = 1] • E y1i Mechanism exists if E[m1i − m0i |x, Ti = 1] = 0 and

(16)

  m m − y0i |x, mi = 1 = 0 E y1i

where the superscript m indicates outcomes with and without treatment by the mechanism m (rather than T ). Institutions are typically not considered as the final outcome in an impact evaluation, because the “rules of the game” are not the goal in and of themselves. As Brooks et al. (2012) argue, the success of community-based conservation lies not in the strength or character of the community institutions, but rather in improved outcomes for nature and people. However, institutions may be a “marker” or an observable measure of final outcomes that are of interest. Vega and Keenan (2016) point out that community forest enterprises have been widely promoted, for reasons that go “beyond simple transaction cost reductions and economic justifications. Additional unquantifiable benefits, such as self-determination, control over resources that communities have historically used, political representation, and application of acquired skills to name a few, are also secured through community ownership.” Thus, even if

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collective action is not the ultimate outcome of interest, its existence may indicate success in other dimensions, especially in the case of community-based natural resource management. This means that institutional mechanisms may be of particular interest, as both a means to some end goals and as an indicator of other end goals. Specifying the role of an institution in the causal model can inform not only how it enters the causal analysis but also how and when it should be measured. Again, consider collective action through informal community institutions. To evaluate this as a mechanism, the analyst needs measures of community institutions after the treatment. On the other hand, institutional measures from before treatment are needed to account for the potential confounding role of community institutions (Baland et al., 2010). Pre-existing community institutions may also be moderators that influence the outcome under the counterfactual and/or the policy scenario, resulting in a different net effect on the outcome. Finally, the probability of some types of collective action may be affected by the condition of the resource, e.g. communities may be more likely to agree on and enforce rules when resources are noticeably scarce (Gibson et al., 2000). Thus, that dimension of community organization may be influenced by both the treatment and by the intended outcome (and hence be a collider). The recommendation here is clearly to measure the relevant dimension of an institution at the relevant point in time, as indicated by where it appears in the causal diagram. Following this recommendation can be challenging in practice because of path-dependence in institutional development (Petursson and Vedeld, 2017) and the frequent lack of baseline data.

3.2 INSTITUTIONS AS DETERMINANTS OF ASSIGNMENT Treatment may be assigned by the implementer (e.g. a national government agency or NGO) and/or selected by the participants (e.g. landowners or communities). Assuming that implementers and potential participants are rational decision-makers, they are likely to choose whether to participate based on expected benefits and costs, or predictors of those benefits and costs (potentially including pro-social or proenvironmental preferences). If the benefits and costs are outcomes of interest, or related to outcomes of interest, for the program evaluation (under either treated or counterfactual conditions), then assignment (or selection) creates an association between treatment and outcome that is off the causal pathway and may bias the causal effect estimate.5 In addition to creating this potential bias, assignment defines the population that is subject to treatment, and is thus an important factor in determining the total impact of the treatment. This is both because the size of the treated population matters for calculating total impacts and because the counterfactual outcome of the selected population directly influences effect estimates. For example, protected

5 As used in economics, the term “selection bias” maps to two distinct concepts represented in DAGs:

(i) confounding due to omitted causes of treatment and outcome, and (ii) conditioning on colliders, or common effects, also sometimes called “confounding by indication.”

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areas or PES placed where there is very little on-going deforestation threat can only reduce deforestation a very little. In program evaluation of environmental conservation, analysts control for assignment factors that are confounders, i.e. that affect both assignment to treatment and outcomes. Perhaps the best recognized example of confounding in conservation is that protected areas have historically been located “high and far.” Joppa and Pfaff (2009) find “that the significant majority of national PA networks are biased to higher elevations, steeper slopes and greater distances to roads and cities.” This in turn implies that those areas are relatively less profitable for extraction of natural resources or agriculture, and are therefore less threatened with conversion, than other parts of the landscape. This pattern is confirmed by a recent global analysis of the distribution of protected areas, which finds that they are consistently located in areas distant from market and with low population density (Baldi et al., 2017). Devillers et al. (2015) find the same pattern for marine protected areas (MPAs), noting that just ten MPAs in remote areas not currently under fishing pressure account for more than half the total area of ocean protected. More generally, in evaluations of treatments applied to spatial units of land or sea, analysts tend to focus on biophysical and other spatial factors, both as confounders and as outcomes (Vincent, 2016). In these evaluations, selection is often modeled across the entire policy-relevant space (e.g. location of protected areas across the entire territory or maritime zone of a country). Accounting for institutional variation across this space could substantially improve on these impact evaluations. For example, Abman (2018) shows that the effectiveness of protected areas varies with corruption/ rule of law and polity, and he calls for more research to determine whether this is because governments with those characteristics select different locations for protected areas, or because of moderating effects of those characteristics on the impact of protected areas. Program evaluations of treatments applied to resource users, such as PES, generally account for a wider range of selection factors including socioeconomic and demographic characteristics of the people and biophysical characteristics of their resources, but this selection process is only modeled within specific sites that were selected for treatment and for study. Allcott (2015) argues that the sites selected for study should be “as good as randomly selected from the population of target sites,” which he labels “external unconfoundedness.” This is not likely to be true, because implementers can maximize cost-effectiveness by selecting the sites and populations most responsive to treatment, because implementers with treatments that they know are effective are more likely to cooperate with external impact evaluations, and because in the case of RCTs, researchers prefer to work with highly capable implementing partners. For example, NGOs are likely to choose implementation sites where they have previous experience and connections with local leadership (Usmani et al., 2018; Lin, 2012). Caplow et al. (2011) note that rigorous impact evaluations of REDD+ initiatives are “facilitated by early establishment of research partnerships between implementers and universities,” which may in and of itself affect outcomes by increasing effectiveness and/or costs. Accounting for selection at the site level (e.g.

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the region or municipality selected for treatment and study) is a major outstanding challenge for this type of impact evaluation. At the micro level of household or landowner selection into PES, selection is often modeled as a function of both factors that vary across properties (e.g. land tenure) and landowner characteristics related to informal institutions (e.g. social ties). Bremer et al. (2014) review factors that have been found to influence participation by individual landowners, categorizing them according to whether they are related to program eligibility requirements (e.g. land title), ability to access the program (e.g. social capital), or intangibles like pro-social or pro-environmental motivations. In their study of PES in Ecuador, Bremer et al. (2014) highlight land tenure as a key factor. Grillos (2017) organizes selection factors into slightly different categories: barriers to entry, expected value of participation, and non-material motivations. In her study of PES in Bolivia, she concludes that “social embeddedness, in addition to material factors, helps motivate participation in the program.” Arriagada et al. (2009) combine semistructured interviews with analysis of survey data to identify factors that influence landowner participation in the Costa Rican PES program. Factors included biophysical characteristics of the land (with steep slope and poor soil quality decreasing the opportunity cost of participating), stage in life cycle (with payments to conserve becoming more appealing as the household ages), and the transactions costs of participating. Most analysts have found property size to be an important factor, perhaps because it proxies for social, human, and financial capital as well as the ratio of fixed transactions costs per contract to the sum of payments per hectare (James, 2018). Finally, we note that institutional factors also affect the assignment of conservation instruments across countries. Holmes et al. (2012) examine whether the distribution of aid for conservation across countries matches conservation priorities and conclude that it is “perhaps more driven by historical patterns, political considerations such as instability and legacy of colonial heritage, and donor interests.” The same has been claimed of specific types of environmental aid, like debt-for-nature swaps (Deacon and Murphy, 1997) and private initiatives such as certification (Van Kooten et al., 2005). Brandt et al. (2017) suggest that factors such as national culture and colonial legacies affect the choice of different forest management regimes by South Asian countries. Based on a cross-national analysis of protected areas, Kashwan (2017) concludes that “in relatively democratic countries inequality is associated with less land in protected areas, whereas in relatively undemocratic countries the reverse is true.” Because program evaluations typically consider only one or a few countries, they cannot account for these cross-national selection effects. Nonetheless, they are important for assessing the generalizability or external validity of results across countries.

3.3 HETEROGENEOUS INSTITUTIONAL TREATMENTS Within the three general categories of formal institutions for environmental conservation discussed in Section 2, there is substantial institutional variation. Here, we consider institutional variation that defines a specific treatment, i.e. a change from a

3 Institutional Insights for Causal Models

specific counterfactual to a specific treated state. This gives rise to “heterogeneous treatments.” In environmental conservation, the treatment that has most often been disaggregated is protected areas (Table 1). One of the key questions addressed by this literature is whether strict protected areas (IUCN categories I–III), with rules that prohibit or limit extractive uses, are more effective than protected areas that allow a greater range of uses (IUCN categories V–VI), with the categorization of IUCN category IV varying by study. By the letter of the law, strict protected areas should offer greater protection to environmental resources within their borders. However, the literature on governance of common pool resources suggests that permitting local use and involving local user groups could be more effective at protecting resources (Oldekop et al., 2016). Conversely, protected areas that allow more extractive use are designed to benefit local resource users, but strict protected areas may attract more tourists, and any type of protected area that effectively protects ecosystems could generate more locally valuable ecosystem services. Another comparison that has been drawn in recent analyses is between protected areas and indigenous reserves or territories. In a systematic map of the literature on forest protected areas, Macura et al. (2015) found increasing attention to the effects of different institutions or forms of governance for protected areas from 2002 to 2014. As with evaluations of protected areas in general, most of the studies they identified do not use counterfactual designs to establish attribution. For example, in two recent studies based on impressive global datasets on conservation outcomes, including species richness (Gray et al., 2016) and human pressure (Jones et al., 2018), the authors do not account for selection effects or attempt to construct counterfactual outcomes across different types of protected areas. Jones et al. (2018) suggest that lower increases in human pressure in large, strictly protected areas show “that they are potentially effective, at least in some nations,” without explicitly acknowledging that this finding may also reflect site selection. Against this backdrop of descriptive studies, there are an increasing number of studies that estimate and compare causal effects on deforestation or proxy measures across different types of protected areas, mostly in Latin America (Soares-Filho et al., 2010; Andam et al., 2013; Nolte et al., 2013; Pfaff et al., 2014, 2015; Blackman et al., 2015; Blackman, 2015; Miranda et al., 2016; Kere et al., 2017) with many fewer studies in Africa and Asia (Bowker et al., 2017; Miteva et al., 2015b; Shah and Baylis, 2015; Sims, 2010) or pan-tropical (Nelson and Chomitz, 2011). Many of the study authors conclude that either multiple use or indigenous territories are most effective at reducing deforestation (Table 1). As Vincent (2016) points out, the implications of these findings are difficult to assess without information on the economic benefits of avoided deforestation and the costs of the different types of protected areas. The economic benefits most often calculated are the value of avoided carbon emissions (e.g. Ferraro et al., 2015 for PAs in Brazil, Costa Rica, Indonesia, and Thailand). Sims and Alix-Garcia (2017) provide an example of estimating the costs of implementing protected areas with different effects on deforestation. They evaluate the impacts of protected areas in Mexico, both on average and disaggregated into strictly protected areas, mixed use protected areas,

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Table 1 Findings on effects of strict vs. sustainable (multiple) use protected areas, based on matching on covariates including accessibility and biophysical characteristics (precipitation, elevation/slope, soil quality). Studies vary in terms of additional matching covariates, use of propensity score vs. covariate matching, number of matches, whether match with replacement, and requirements for quality of match (use of a caliper) Countries where impacts of PAs on deforestation have been found: Larger in strict than Larger in sustainable use Not statistically different sustainable use than strict between strict and sustainable use Brazilian Amazon (Pfaff Brazilian state of Acre (Pfaff Brazilian Amazon (Kere et al., 2015; Nolte et al., et al., 2014); et al., 2017); 2013); Brazilian cerrado (Carranza Peruvian Amazon (Miranda Bolivia (Ferraro et al., 2013); et al., 2014; Paiva et al., et al., 2016); 2015 for state of Goiás); Indonesian mangroves Mexico (Blackman et al., Guatemala’s Maya (Miteva et al., 2015b); 2015); Biosphere Reserve (Blackman, 2015); Costa Rica, Indonesia, and Thailand (Ferraro et al., 2013).

Pan-tropical, considering fires (Nelson and Chomitz, 2011).

Costa Rica, considering regrowth (Andam et al., 2013).

The table omits studies that have estimated and compared the effects of different types of PAs either by simple comparisons inside and outside the PAs (Gray et al., 2016; Jones et al., 2018; Blankespoor et al., 2017; Nepstad et al., 2006; Pfeifer et al., 2012) or by using quasi-experimental methods other than matching (Soares-Filho et al., 2010; Sims, 2010; Sims and Alix-Garcia, 2017), as well as studies that have used matching methods to estimate the effect of one particular type of PA (Shah and Baylis, 2015; Weisse and Naughton-Treves, 2016; Carmenta et al., 2016).

and biosphere reserves. Their unit of analysis is the locality and their treatment is the share of the locality in a particular type of protected area. They find that biosphere reserves and mixed-use protected areas are generally located further from urban centers but are also under greater deforestation pressure than strict protected areas. Biosphere reserves are more effective at reducing deforestation, which the authors conclude is only partly due to the location of those reserves in areas under greater deforestation pressure. In addition, biosphere reserves are more effective at alleviating poverty. They also calculate administrative costs for the three types of protected areas and conclude that avoiding deforestation through strict protected areas is relatively more expensive than through either mixed-use or biosphere reserves. Ferraro et al. (2013) seek to facilitate cross-country comparisons by using a standard methodology (matching with bias correction) to evaluate similarly defined categories of protected areas (based on IUCN categories) on deforestation in four countries: Bolivia, Costa Rica, Indonesia (Sumatra), and Thailand. They find that stricter protection does protect more forest (i.e., reduce deforestation) in Indonesia and Thailand. In Costa Rica, they find that strict protected areas have been sited

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in places where they can more effectively protect against deforestation. In Bolivia, they find that strict protected areas were less deforested than they would have been with less strict protection, but otherwise the estimated effects of strict and less strict protection (e.g. compared to no protection) are not statistically significant. Thus, in contrast to many country-specific analyses, they find that strict protected areas do offer more protection. This is consistent with a recent systematic review of evaluations of marine protected areas (MPAs): Sciberras et al. (2015) “conclude that MPAs with partial protection confer advantages, such as enhanced density and biomass of fish, compared to areas with no restrictions, although the strongest responses occurred for areas with total exclusion.” One theme in this literature is that the heterogeneous effects of different types of protected areas are a function of systematic differences in both their implementation and their location. Strict protected areas are often placed in more remote areas, under less deforestation pressure (with exceptions such as Mexico). Depending on the jurisdiction, indigenous reserves and/or multiple-use protected areas are more likely to be placed in areas under higher deforestation pressures. As a result, strict protected areas generally have the lowest deforestation rates but also the smallest impacts. Gaveau et al. (2012) in Indonesia, Arriagada et al. (2016) in Chile, and Schleicher et al. (2017) in Peru control for this placement effect by comparing one type of protected area treatment to different counterfactuals. Gaveau et al. (2012) conclude that a treatment that creates a protected area in a forest slated for conversion is much more effective at reducing deforestation than a treatment that creates a protected area in a forest slated for logging. Arriagada et al. (2016) find that PAs avoid deforestation in comparison to private, but not public, lands. Schleicher et al. (2017) conclude that in Peru, indigenous territories and conservation concessions (managed by civil society organizations) avoid the most deforestation relative to comparable parcels in the broader forest landscape. The effects are not as precisely estimated relative to a counterfactual of logging concessions, and the matches are lower quality for comparison to a counterfactual of mining concessions. There is also institutional variation within decentralization and PES instruments. The literature on governance of common pool resources suggests design features for decentralization and community management that could increase the effectiveness of those instruments (Cox et al., 2010; Agrawal and Angelsen, 2009). Meta-studies of experiences with decentralization of governance or devolution of management rights, such as recorded in the International Forestry Resources and Institutions (IFRI) database, have also identified institutional dimensions associated with different outcomes (Poteete, 2009; Macura et al., 2015), e.g. monitoring and sanctioning by user groups (Coleman, 2009). Rasolofoson et al. (2015) apply matching methods to evaluate community management that allows commercial use of forest and community management that only allows non-commercial forest management in Madagascar. Only CFM restricted to non-commercial forest management reduces deforestation. Meta-studies of experience with PES have identified institutional dimensions associated with conservation or poverty alleviation outcomes. For example, based on a review of experiences with payments for watershed services, Brouwer et al. (2011)

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conclude that programs that establish collective contracts (with communities rather than individual landowners) are more likely to achieve their conservation goals.

3.4 INSTITUTIONS AS MODERATORS In addition to variation in effect sizes related to heterogeneous interventions and the particular places or populations selected for treatment, effects may vary with other exogenous or contextual factors, called moderators.6 By definition, the effect of a treatment varies across strata defined by a moderator (VanderWeele, 2012). Moderators are exogenous and not jointly determined with or affected by the treatment. Thus, they affect the potential outcomes both under treatment and under the counterfactual. This contrasts with treatment heterogeneity that is due to institutional variation in the treatment (e.g. Rasolofoson et al., 2015) or that only affects the counterfactual (Gaveau et al., 2012). Because moderators are unrelated to the treatment, omitting them does not undermine the internal validity of the estimated average effect. However, for both external validity and economic analysis, it is important to assess how effect size varies with moderators (Vincent, 2016). Many of the enabling factors that have been identified in research on socialecological systems are potential moderators. In particular, existing institutions, such as property rights regimes and community organization (Vatn, 2010; Engel, 2016; Robinson et al., 2018), are expected to moderate the effect of new conservation instruments. Testing for heterogeneous effects across institutional moderators can advance theory building and increase confidence in causal effects when they vary with effect modifiers as predicted by theory. When moderators are malleable, e.g. institutions rather than biophysical factors, the proponents of interventions, whether international donors, civil society, or governments, may seek to influence those moderators as part of their intervention packages, e.g. by investing in “readiness” for REDD+ (Minang and Van Noordwijk, 2014). Thus, institutional moderators may become bundled with treatments, as in some of the heterogeneous treatments discussed in previous sections. For example, recent evaluations of protected areas have considered how management effectiveness, as indicated by management performance, capacity, and budget, moderates conservation outcomes (Blackman et al., 2015; Carranza et al., 2014; Nolte and Agrawal, 2013). A potential funder of protected areas may be interested in their impact, given the existing capacity and budget for management, or may be interested in their impact if implemented with optimal management capacity and budget. Alternatively, we could conceive of the moderators as the level of government resources or funding available, as has been suggested as an explanation of heterogeneous effects of protected areas in Mexico by Sims and Alix-Garcia (2017) and Blackman et al. (2015) and community forest management in Madagascar by Rasolofoson et al. (2015).

6 Moderators, as described here, are also called “effect modifiers” or “effect heterogeneity” in the literature.

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At the local level, the pre-treatment level of community organization or selfgovernance (Ostrom, 1990; Dougill et al., 2012; Costedoat et al., 2015) or community experience with NGOs (Usmani et al., 2018) could moderate the effect of conservation interventions such as PES. Kerr et al. (2012) provide experimental evidence from Mexico, where they test how offers of no payment, individual payments, and collective payments to a village affected participation in a communal activity (litter collection). They find that the offer of collective payments only increased participation relative to no payment in a village that “appears to have better leadership, more trust among citizens, and more familiarity with how the PES program benefits are distributed” relative to other villages where corruption and distrust of leaders were the norm. Further, when no payment was offered, participation was higher in villages that had an existing norm or institution of frequent communal workdays. Likewise, if a conservation intervention were implemented across multiple communities that have different levels of organization, one might hypothesize that the treatment effect would vary by this exogenous condition. In a framed field experiment about communal forest management, Andersson et al. (2018) proxy for local institutions with a measure of trust among community members, as elicited by questions about beliefs regarding the likelihood that others will cooperate in management of communal forest lands (in a survey of more than 1000 households in five countries). The hypothesis is that high-trusting individuals will interpret the cooperation induced by the PES treatment as confirmation of their beliefs that others are also cooperative in collective action situations. To estimate the effect of the PES treatment on forest outcomes the authors estimate a linear mixedeffects regression. To test the moderating effect of trust on the persistence of behavior changes, they include an interaction term between trust and PES. The authors find that trust greatly amplifies the lasting conservation effect of PES interventions: individuals with higher trust scores reduce their post-treatment harvesting rates more so than individuals with low trust. Finally, as discussed in the next section, there is substantial experimental evidence suggesting that PES interacts with social norms and intrinsic motivations for conservation (Rode et al., 2015). Crowding out or crowding in can only occur where there are local institutions to be crowded, suggesting another way that they moderate the effect of PES (Van Hecken and Bastiaensen, 2010; Travers et al., 2011; Bluffstone, 2013). Potential institutional moderators at the national level include political conditions and environmental governance (Lockwood et al., 2010; Lemos and Agrawal, 2006; Baynham-Herd et al., 2018; Abman, 2018). Bare et al. (2015) find that international aid for conservation is more highly correlated with reduced deforestation in countries with better environmental governance indicators. Miller et al. (2015) attribute differences in the effects of increased enforcement on two sides of a transnational park to differences in governance quality and the extent of democratic decentralization in the two countries. Specifically, they find that increased enforcement increased mammal species abundance without affecting household incomes in Benin, but reduced income levels without affecting mammal species abundance in Niger. Abman (2018) finds that the effects of protected areas are correlated with rule of law/ corruption and

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polity, thus suggesting that those may be moderating the effect. National level institutions such as strong rule of law and an engaged civil society also have been described as key moderators for conservation interventions driven by the private sector, such as certification and supply chain initiatives (Lambin et al., 2014). The moderating effects of national institutions are frequently discussed in the literature on decentralization and community-based conservation. Nelson and Agrawal (2008) state that “CBNRM is fundamentally premised on institutional reforms that decentralize authority over – and benefits from – land and natural resources to local actors. In the absence of such reforms, the incentives for local groups of people to collectively invest in natural resource management are unlikely to exist or emerge.” Thus, the effect of community-based management may be moderated by decentralization of natural resource management. Taking this one step further, Coleman and Fleischman (2012) find that the variable effects of decentralization are explained only partially by theoretically important attributes of the decentralization policy (local user group empowerment and accountability mechanisms). They speculate that the remaining variation is due to institutional moderators including the existence and enforcement of rules for resource use and experience with decentralized governance outside of the natural resources sector. They argue that recognizing the effect of these moderating variables is key to understanding whether and where the lessons of decentralization in one country (like Mexico) are transferable to other countries (like Uganda). However, they have limited statistical power to estimate the effects of moderating variables, since their sample includes only a few countries. Given sufficient sample sizes, the role of moderators in creating heterogeneous treatment effects can be directly estimated. To identify average treatment effects, economists typically try to balance or sweep out any potential moderators, through matching or difference-in-differences approaches. These methods effectively isolate the effect of the treatment, but obscure heterogeneity in that effect across units. By including moderators in the empirical analysis, the analyst obtains valuable information on whether and how the results generalize to other settings including other institutional contexts. There are several approaches to relaxing the assumption of homogeneous effects (cf., Schochet et al., 2014 for a guide to methods used in the education sector). The simplest is to split the data into subsamples based on the theory of institutional moderators. Partitioning into subsamples allows estimation of treatment effects for different levels of the moderator, while also relaxing the assumption that all covariates and the structural form are the same across subsamples. Abman (2018) illustrates this approach by estimating the effect of protected areas in 71 countries, and then relating those effect estimates to governance indicators. Ferraro and Hanauer (2011) discuss analytical issues with subgroup analysis and demonstrate the use of regression adjustment to calculate treatment effects in matched sub-group samples. Another option is to include interaction terms between the treatment variable and the moderating variable. This allows the treatment effect to vary by subgroup, but imposes the same structural form and empirical specification for each subgroup. Ferraro et al. (2011) illustrate the use of partial linear models in a matched sample to estimate

3 Institutional Insights for Causal Models

these interaction effects. A third option is to use multilevel modeling, also referred to as hierarchical modeling or random coefficients modeling. A multilevel model is particularly useful when there are multiple strata or sub-groups that moderate the effect of an intervention (Kere et al., 2017). Multilevel models allow variation at the sub-group level and thus can provide more insight on the effect of moderators than linear models, while still including the same covariates for every unit in the sample. In the conservation domain, impact evaluations most commonly allow for heterogeneous effects across different biophysical or socioeconomic settings. These factors shape the counterfactual level of threat to natural resources and hence the possible effectiveness of an intervention at mitigating those threats. While these have been widely recognized as potential sources of confounding, studies have also tested their moderating effects on the impacts of various interventions. These studies could provide useful templates for analyses of institutional moderators. Pfaff et al. (2009) and Pfaff et al. (2014) find that where there is less human pressure in Costa Rica and Brazil, protected areas have smaller effects on deforestation. Also in Costa Rica, Ferraro and Hanauer (2011) find differences in the effect of protected areas on deforestation by land use capacity, slope, distance to major city, and percent of workforce in agriculture but not initial poverty, and similar heterogeneity in effects on poverty. In Costa Rica and Thailand, Ferraro et al. (2011) show that effects on both deforestation and poverty have non-linear associations with moderators such as slope and distance to major cities. As with the previous studies, they find that protected areas cause less avoided deforestation but more poverty alleviation in areas with the steepest slopes. Alix-Garcia et al. (2012, 2015) explore heterogeneity in the effect of PES on forest cover and wealth, finding that PES has a greater effect on deforestation in areas of Mexico that are subject to greater deforestation pressure and wealthier. In addition, they report larger positive impacts on household wealth in poorer areas facing less deforestation threat. Similarly, Hanauer and Canavire-Bacarreza (2015) find that protected areas in Bolivia are more likely to avoid deforestation and to exacerbate poverty in flat, accessible areas. In Cambodia, Chervier and Costedoat (2017) find that PES leads to the most avoided deforestation in villages with intermediate market access and low slopes. Blackman et al. (2017) find a more pronounced negative association between titling and forest cover change in communities closer to population centers in Peru (Blackman et al., 2017). Bocci et al. (2018) find that communitymanaged forest concessions have less effect, and possibly even a negative effect, on income in areas recently settled by migrants. A handful of counterfactual impact evaluation studies have explicitly assessed the moderating effect of institutions on decentralized natural resource management. They consider institutional moderators at scales from local government to household and thus have sufficient sample size for statistical analysis. Alix-Garcia et al. (2015) found that property rights institutions moderated the effect of PES in Mexico, with larger effects on common properties, compared to private properties. The other studies considered informal institutions, ranging from quality of local governance to local enforcement of rules. In some cases, the measures are indirect,

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based on different types of communities, whereas in other cases, they are directly measured, e.g. the frequency of meetings between government officials and community forest management organizations. Two of the studies (Hayes et al., 2017; Andersson and Gibson, 2007) discuss moderator effects but actually estimate the effect of the moderator conditional on treatment (by including a covariate or using a sub-sample). The other studies identify the effects of moderators on treatmentoutcome combinations either by sub-sample analysis (Coleman and Liebertz, 2014; Fortmann et al., 2017) or by including the moderator in a linear regression estimated in a matched sample (Wright et al., 2016; Alix-Garcia et al., 2015). Hayes et al. (2017) study collective action institutions and PES in Ecuador. They select a sample of six communities that have been included and five that are in the pipeline for collective PES contracts that limit grazing in the paramo ecosystem. They use a household questionnaire to elicit information on grazing and institutional factors such as community organization, history of local rules, and monitoring and enforcement on communal lands. The authors first test the impact of PES contracts on grazing by estimating difference-in-differences in matched samples of communities with and without PES contracts. They conclude that PES contracts reduce grazing on communal areas. Second, the authors test the role of community governance characteristics, controlling for the presence of a PES contract. They find that community governance characteristics directly influence the decision to stop grazing. While they do not empirically test whether community governance moderates the effect of the PES contract, they conclude that “more organized communities were more likely to transmit the PES conditions to their households, and households living in PES communities with a history of land-use rules were more likely to stop grazing in the paramo.” This conclusion is based on focus group discussions and survey data showing that households in more organized communities better understood the PES contract. Andersson and Gibson (2007) measure local institutional context through a municipal governance index developed from interviews with key informants in 30 municipalities in the Bolivian lowlands that had undergone a decentralization reform. Deforestation is measured using remote sensing data. The authors test the direct and indirect effects of local governance on deforestation in the context of the decentralization reform. They find a statistically significant and negative effect of local governance capacity on unauthorized deforestation, meaning that stronger governance decreased unauthorized deforestation following the decentralization reform. Governance also had an indirect effect, tested through the interaction between governance and deforestation prior to decentralization, by dampening the positive effect of prior deforestation on unauthorized deforestation following decentralization reform. Thus, they find that governance is an important determinant of deforestation, but they do not directly test whether it moderates the effect of decentralization. Wright et al.’s (2016) study of decentralization of forest governance in Bolivia builds on Andersson and Gibson (2007). Using longitudinal data from Bolivia and Peru, which has more centralized forestry policy, the authors estimate the average treatment effect of the decentralization reform on deforestation by estimating a gen-

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eralized estimating equation regression in a matched sample of municipalities. To obtain the matched sample, they pre-process the data to obtain balance on covariates describing biophysical conditions, the lagged outcome, and the local government’s budget. Deforestation is measured using remote sensing data. In addition to the average treatment effect, the authors also estimate the effect heterogeneity caused by local institutions. Specifically, they test whether the frequency of community engagement with local officials influences deforestation outcomes. To measure level of engagement, they ask key informants from the government and community organizations to rate on a scale of “1” to “5” how often community-based organizations expressed opinions regarding forestry to municipal government officials. The authors find that decentralization reform has a small but positive association with forest cover stability – Bolivian municipalities maintain more forest cover than their matched Peruvian municipalities. This effect varies with the level of community engagement with local government officials: decentralization has a more positive effect on forest cover where there is more local engagement. They confirm that municipalities with high engagement and subject to the decentralization reform had characteristics expected to lead to better outcomes for natural resource management according to the design principles postulated by Ostrom (1990). They also consider and reject rival explanations related to other differences between Bolivia and Peru. Coleman and Liebertz (2014) consider the impact of decentralization of property rights to forest user groups in Bolivia, Kenya, Mexico, and Uganda on common pool resource (CPR) benefits, including the moderating effect of an individual’s power to influence rule enforcement. Survey data from over 1500 households in 23 villages include information on the property rights of each household as related to government, community, and private forests, and CPR benefits as measured by a composite index of self-reported ecological, social, and economic outcomes. Power to influence rule enforcement is proxied by whether or not the household owned land apart from the CPR and whether or not the household is part of the majority ethnic group. A twostage least squares regression model is used to test the impact of property rights on CPR benefits. To test the moderating effect of power, they use sub-sample analysis for ethnic majorities versus minorities and private landholders versus non-landholders. The authors find that more extensive property rights are correlated positively with CPR benefits but that power critically moderates the effect of property rights. Those users with more power to influence rule enforcement enjoy more benefits than users without such power. Another study assessing the impact of community forest management (CFM) on deforestation tests how group heterogeneity moderates the effectiveness of CFM in Guatemala (Fortmann et al., 2017). A policy change around the Maya Biosphere Reserve led to the creation of 12 new CFM concessions. These concessions were made to communities that varied considerably in their length of residency and familiarity with forest management. The authors split concessions into three types – long-term residents, recent settlers, and nonresidents – and test the effect of each of these three types of CFM concessions on deforestation outcomes. Deforestation is measured using remote sensing data. The authors employ a matched difference-in-differences

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approach to test the effect of each sub-sample of concession types compared to nonCFM areas that were within the Reserve but unmanaged. All types of concessions reduced deforestation with slightly larger effect sizes in recently settled areas; however, these same areas also experienced more leakage than other concession types. The authors attribute these differences in part to variation in institutions across the three types of concessions, noting internal and external factors that resulted in more corruption and illegal activities in the recently settled concessions.

3.5 INSTITUTIONS AS MECHANISMS Causal mechanisms7 lie on the pathways between treatments and outcomes, that is, they are both caused by treatments and causes of outcomes. Informal institutions are often the mechanism (intended or not) for conservation instruments, i.e. new formal institutions may induce new informal institutions that establish “working rules” of natural resource use (Ostrom and Ahn, 2009) or they may displace pre-existing informal institutions that had established and enforced such rules (Rodrik, 2008). Thus, the mechanism effect depends on what informal institutions already exist, the role of intrinsic conservation motives and other-regarding preferences (Vatn, 2009) in those institutions, and therefore the potential for introducing new pro-environmental norms, improving communication and information-sharing among resource users, and building trust. In the context of protected areas, Ferraro and Hanauer (2015) argue that more attention to mechanisms would bolster the credibility of impact estimates, ensure that those estimates are not biased down by inappropriately controlling for mechanisms, and help design interventions that achieve the desired outcomes through mechanisms that are also beneficial (cf., Reimer and Haynie, 2018 for marine reserves). However, rather than new institutions, they suggest protected areas operate through mechanisms that affect “the benefit–cost calculation of potential users and consumers of the protected resources and related ecosystems.” PES were originally proposed as a more direct way to activate this same mechanism. But PES programs that offer collective payments to a community, or that condition payments on collective outcomes at the community level, are intended to change the local “rules of the game” about resource use. Allocation of property rights or co-management responsibility to local communities has the same goal. Both theory and meta-studies of experiences with community management of natural resources suggest that local institutions can achieve sustainable management of resources (Ostrom, 1990; Vega and Keenan, 2014; Pagdee et al., 2006; Cinner et al., 2012; Oldekop et al., 2016). For these institutions to serve as mechanisms, they must also be responsive to treatments (Hayes et al., 2015). Perhaps the most sought after mechanism for conservation is “community participation” (Lele et al., 2010), but in practice, participation is difficult to achieve and does not necessarily lead to desired outcomes (Pagdee et al., 2006; Cinner et al., 2012; 7 In some fields, mechanisms are referred to as mediation, i.e. they are the mediating or intermediary process by which the treatment produces the outcome.

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Nelson and Agrawal, 2008). Collective action is more likely when “the individuals who are interacting know one another, can communicate, trust one another to cooperate, and have accurate information about the situation they are in,” as summarized from experimental evidence by Poteete et al. (2010). While these factors are difficult to influence, Ostrom (2002: 1329) argues that “external authorities can do a lot to enhance the likelihood and performance of self-governing institutions.” Andersson (2013) demonstrate that the type of external authority and its commitment to natural resource management matter. Different conservation interventions are expected to operate through different mechanisms. Protected areas are typically not expected to operate through local institutions, except where there are integrated conservation and development projects (ICDPs) or collaborative management agreements (e.g. Jagger et al., 2018). Two institutional mechanism that have been suggested are that protected areas could induce more community cohesion (Canavire-Bacarreza and Hanauer, 2013) or facilitate external support for community organizations (Baird, 2014). In contrast, decentralization of forest management is generally expected to affect outcomes through institutional moderators (Coleman and Fleischman, 2012). When reduced collection pressure or improved forest quality are attributed to policies that transfer management responsibility to local communities, the mechanism is often assumed to be some form of collective action at the community level. For example, Edmonds (2002) notes that “the evidence from Nepal in this paper is encouraging for the potential of governments to initiate community resource management,” and Baland et al. (2010) state that better conditions in areas that had been under community control for longer are “consistent with the view that they reflect management differences.” PES programs that either offer payments or impose conditionality at the community level are designed to induce new community institutions (Vatn, 2010), effectively shifting the transactions costs of organizing payments to communities (Kerr et al., 2014). Researchers have described varied outcomes across cases. In an exploratory study of a PES program for reducing grazing pressure on natural grasslands in Ecuador, Hayes et al. (2015) find that a larger fraction of communities participating in the program had an organized system for monitoring grazing, and that most households in those communities believed that the PES program had helped clarify rules about grazing. However, the authors find no evidence that the PES program improved enforcement or compliance with the rules. In a case study of PES in protected areas in Cambodia, Clements et al. (2010) find that administering the program through local community institutions initially had higher transaction costs and lower impacts than a PES program that contracted directly with local households, but appeared likely to have a more sustained long-term impact. On the other hand, in a survey of households living in a biosphere reserve in Mexico, García-Amado et al. (2013) find that an ICDP was perceived to have been more effective than collective PES at encouraging collaboration and building social capital within the community. Much of the evidence relating environmental outcomes to local institutions has been generated through framed field experiments (as defined by Harrison and List, 2004) implemented in rural communities in the developing tropics. One line of in-

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quiry is about how the process of creating institutions determines their effectiveness (Ostrom, 2000; Cardenas et al., 2000; Cardenas, 2004; Chhatre and Agrawal, 2009; Velez et al., 2012; Abatayo and Lynham, 2016; Kaczan et al., 2017). That process could be part of the treatment, e.g. a policy that requires local resource users to vote on rules, or the first in a chain of mechanisms that connect a policy to an outcome. Some of the earliest work by Cardenas et al. (2000) and Cardenas (2004) reports variable effects, likely related to variation in the local institutions already in place. Velez et al. (2012) survey the experimental literature and conclude that having resource users vote on regulations can lead to better acceptance and compliance with those regulations, but that resource users often do not vote for efficient enforcement of the regulations (Velez et al., 2012). More recently, Abatayo and Lynham (2016) find that when they result in the same rules, exogenously imposed and endogenously adopted rules have the same effect. They conclude that communication is a more important mechanism for achieving conservation outcomes. A second line of inquiry has focused on the interaction of new institutions with existing social norms and specifically the possibility of motivational crowding (Rode et al., 2015). As demonstrated in the child care setting by Gneezy and Rustichini (2000), introducing a payment for desired behavior can crowd out intrinsic motivation to engage in that behavior, even after the payment is rescinded. Many experiments likewise find that PES “crowds out” pro-social or pro-environmental motivations, but there are also some findings of “crowding in” (Rode et al., 2015), depending on the design of the PES program and the social context. Crowding out can occur both with externally funded PES and with enforced local funding for PES (Jack, 2009). Both lines of inquiry point to the importance of interactions between other-regarding preferences (e.g. altruism, reciprocity, and inequity aversion) and institutions, so it is worth noting Levitt and List’s (2007) caution that participants in framed experiments may exhibit more prosocial behavior because they are being observed (Velez et al., 2009). Thus, it would be useful to embed empirical tests of the hypotheses generated by these experiments into program evaluations. For an observable mechanism, the most straightforward empirical test is to check whether it is both caused by the treatment and causes the outcome, using any of the methods of causal inference discussed in Section 2, e.g. matching, as long as CIA holds for the mechanism (Eq. (17)): E[m0i |x, Ti = 1] = E[m0i |x, Ti = 0]

(17)

However, data may not be available on the mechanisms of interest. A case in point is the recent literature on mechanisms for protected area impacts on local wellbeing (Sims, 2010; Ferraro and Hanauer, 2014; Robalino and Villalobos-Fiatt, 2015; den Braber et al., 2018). Most of these studies actually estimate heterogeneous effects across treatments or moderators, and then show that those are consistent with tourism being a key mechanism. For example, Sims (2010) shows that protected areas intended for tourism have a larger impact, and den Braber et al. (2018) show that protected areas that receive more tourists have a larger impact. Sims (2010), Robalino

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and Villalobos-Fiatt (2015), and den Braber et al. (2018) all show that location moderates impacts in ways consistent with tourism being the mechanism (i.e. impacts are higher closer to the entrances or paths used by tourists). Ferraro and Hanauer (2014) also use presence of the protected area entrance in a census tract as an indicator of the tourism mechanism, and then use a two-stage matching approach (Flores and Flores-Lagunes, 2009) to identify the effect of the protected area on poverty that is specific to the tourism mechanism (i.e. the reduction that would not have occurred but for the entrance to the protected area). This approach avoids the potential bias of comparing effect estimates obtained with and without a control for the mechanism (Richiardi et al., 2013). Their study thus demonstrates an approach to calculating the mechanism effect, rather than inferring it from evidence on heterogeneous impacts. While institutional mechanisms are often cited in the literature, they have rarely been empirically analyzed, and we are not aware of any evidence on both steps in Eq. (16). Coleman and Fleischman (2012) estimate the effect of decentralization policies on mechanisms, which they call policy outputs or intermediate objectives and measure as investment decisions and rulemaking in forest user groups. Using nearly exact matching of forest user groups, they find that decentralization increased rulemaking in Uganda, and increased forest investments in Uganda and Mexico while decreasing them in Kenya. They argue that local collective action to ensure monitoring and sanctioning of forest rules leads to better forest conditions, but they do not estimate the effect of either rulemaking or investments on their final outcomes, which are perceived forest condition and perceived income inequality. Likewise, Sharma et al. (2017) examine the effect of REDD+ on the functioning of forest user groups in Nepal that were selected for the sample based on matching. They estimate significant positive impacts of REDD+ on institutional functioning, including number of executive committee meetings, participation of women in the executive committee, and surveillance of forest fires, as well as self-reported satisfaction with institutional development. Chervier and Costedoat (2017) estimate the impact of PES contracts that Conservation International entered into with communities in Cambodia, offering a package of in-kind benefits for the community and cash payments to individuals who participated in forest patrols, in exchange for foregoing forest clearing for agriculture and commercial logging and helping to monitor compliance with conservation rules. They emphasize that the program was designed to induce new community institutions, e.g. the communities were required to establish committees to organize the patrols and distribution of benefits. Consistent with other evaluations of PES, they find that the contracts reduced deforestation, but by only a small fraction of the total area under contract. In their analysis of moderators, they find the largest effect in communities of moderate size (50 households). They suggest that “payments per head were too weak to motivate the collective enforcement of conservation rules in populated villages” and that “understanding how monetary incentives contribute to recraft community institutions could eventually be theorized relying on frameworks derived from the literature on common property institutions and socio-ecological systems.”

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4 SUMMARY AND FUTURE DIRECTIONS For economists taking a ‘causal empiricist’ approach based on the Neyman–Rubin model of causal inference, treatments and outcomes are generally the constructs of central interest. In environmental conservation, the treatments are typically policies or programs (i.e. sets of formal rules), and the outcomes are typically measures of ecosystems (like forest cover) or well-being (like income). Credible estimates of the effects of different policies on ecosystems and people in the highly biodiverse and low income tropics are a key part of the evidence needed in order to better direct scarce resources for conservation (Game et al., 2018). Our review of program evaluation of key instruments for environmental conservation shows that an evidence base is emerging, with economists consistently demonstrating that careful attention to identification generates different results (and often smaller effect estimates) than naïve comparisons. To ensure that their results are credible and relevant to policy-makers and practitioners, economists need to pay close attention to both informal and formal institutions. We have made the case that causal diagrams, such as DAGs, are a useful tool for incorporating institutions into impact evaluation, because they make transparent the assumed causal model, including the causal path, other possible sources of statistical association, and exclusion restrictions. For impact evaluations of conservation instruments, institutions matter because they define the treatment and key dimensions of heterogeneity in treatment, and they affect assignment to treatment as instruments and confounders. We suggest that evaluators should pay more attention to institutions as moderators, in order to understand variation in causal effects and judge the external validity of estimates, and to institutions as mechanisms, in order to understand the reasons for causal effects and relate those to economic theory. Specifically, one area for future work is incorporating polycentric systems, with their multiple layers of interacting institutions, into program evaluation of conservation instruments (Ostrom, 2010). Another area is assessing whether any of the biophysical factors that can be readily measured and tested as moderators may actually be proxies for institutional factors like enforcement of property rights. This matters, because institutional factors are more likely policy levers, if they can be de-coupled from biophysical conditions. While this chapter has focused on natural resources in the low-income tropics, the details of institutions matter for empirical economics research on non-market resources in general. Building on the suggestions for further work offered by Ferraro et al. (2013), general recommendations include applying consistent program evaluation methods across countries and treatments in order to generate comparable results, evaluating both environmental and social outcomes against the same counterfactual in order to assess trade-offs, considering moderators such as stringency of de facto enforcement of regulations in order to assess external validity and identify additional policy levers, and hypothesizing and testing mechanisms including changes in the informal institutions that set the working rules for management and use of natural resources.

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Uncertainty and ambiguity in environmental economics: conceptual issues ∗ Columbia

† Grantham

10 Geoffrey Heal∗,1 , Antony Millner†,#

University, New York, NY, United States of America Research Institute, London School of Economics and Political Science, London, United Kingdom of Great Britain and Northern Ireland 1 Corresponding author: e-mail address: [email protected]

CONTENTS 1 Introduction ...................................................................................... 1.1 Uncertainty and Climate Policy.................................................. 1.2 Uncertainty and Biodiversity ..................................................... 2 Alternatives to Expected Utility ............................................................... 2.1 Probabilities and Confidence .................................................... 2.2 Formal Development .............................................................. 2.3 Is Ambiguity Aversion Rational? ................................................. 3 Application to Environmental Policy Choices............................................... 3.1 A Simple Analytical Model ....................................................... 3.2 Applications in the Literature .................................................... 4 Conclusions ...................................................................................... References............................................................................................

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1 INTRODUCTION Uncertainty is ubiquitous in environmental economics. This is inevitable: we study the interactions between socio-economic systems and biogeochemical systems, and in general neither of these is fully understood. As a consequence, our grasp of their

# Millner acknowledges funding from the Centre for Climate Change Economics and Policy. Handbook of Environmental Economics, Volume 4, ISSN 1574-0099, https://doi.org/10.1016/bs.hesenv.2018.03.001 Copyright © 2018 Elsevier B.V. All rights reserved.

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interactions is necessarily rather limited. Climate change is a good case study: the scientific community understands some aspects of the behavior of the climate system well, but others poorly. We are certainly no better off, and often worse off, when it comes to our understanding of economic systems. And we are, as we will argue below, particularly weak on the interactions between the two. Biodiversity loss is another important problem for which our lack of knowledge is striking. We are in the midst of a mass extinction comparable to those of pre-history, an event which will transform the world around us, and one that scientists suspect will be greatly detrimental to human well-being. Yet we have little formal understanding of why biodiversity matters to us or of how to model the economic consequences of its loss. The prevalence of uncertainty in our field has long been recognized, and has led to some seminal papers. The work of Arrow and Fisher (1974) and Henry (1974) on the option value associated with uncertainty, learning, and irreversibility are well-known examples. Because of this, there are already several surveys of uncertainty in environmental economics. Mäler and Fisher (2005), Heal and Kriström (2002), Pindyck (2007), and Aldy and Viscusi (2014) survey the literature up to early this century. Rather than repeating what has gone before, in this chapter we review new ideas that were only beginning to gain currency in environment economics when these surveys were written. These ideas touch on deep conceptual questions about how uncertainty can be modeled, and which decision criteria should be applied when objective probabilistic information about the consequences of policy choices is not available.1 The early literature on decision under uncertainty is based on the expected utility model of von Neumann and Morgenstern (1944). They axiomatized preferences over ‘lotteries’, in which the probabilities of alternative outcomes are objectively known (e.g. the toss of a coin or the roll of a die). Their theory was powerfully extended by Savage (1954), who developed a sophisticated theory of choice under ‘subjective’ uncertainty. He showed that if agents obey certain primitive axioms, which do not presuppose the existence of probabilities, they should act as if they are maximizing a subjective expected utility functional. Subjective probabilities in the Savage framework capture ‘degrees of belief’ even when no objective information exists, as in answering the question “what is the probability of life elsewhere in the universe?” This development provided a basis for applying the expected utility model in a wide variety of contexts, both as a positive model of behavior (later largely refuted, Kahneman et al., 2000), and as a benchmark normative theory of rational decision-making. Since then however important developments in decision theory have challenged the applicability of expected utility theory in situations characterized by ‘deep’ uncertainty, or ambiguity. New models of rational decision-making designed for informationally poor environments have been developed, and are beginning to filter into applied economics, particularly finance and macroeconomics. Their recent applications in environmental economics are our subject matter here. 1 A previous review paper of ours (Heal and Millner, 2014a) covers some of the same ground, but in considerably less detail.

1 Introduction

Our treatment of uncertainty in environmental applications will be motivated by two leading examples: climate change and biodiversity loss. We argue that in these cases uncertainty is sufficiently far reaching that standard decision-making tools such as expected utility theory may no longer capture important aspects of our uncertainty preferences. Richer models of decision-making, which allow us to express lack of confidence in our information, may be desirable in these cases.

1.1 UNCERTAINTY AND CLIMATE POLICY Climate policy choices must be made in the face of several sources of uncertainty. At the highest level we can classify them into uncertainty about climate science and uncertainties about the socio-economic consequences of climate change. These categories can be further subdivided: scientific uncertainty is often resolved into internal variability, model uncertainty and emissions uncertainty, and socio-economic uncertainty into positive uncertainties about the magnitude of climate damages, opportunity costs of mitigation, and future mitigation costs, and normative disagreements2 about the welfare framework that should be used to evaluate policy options. We review the origins of scientific uncertainty first. Internal variability arises because climate models are highly non-linear, and exhibit sensitive dependence on initial conditions [“chaotic behavior”]. Small errors in the specification of initial conditions in model runs can lead to significant differences in predicted outcomes. Since the current state of the climate system is known imperfectly (our observation network is sparse, and measurement instruments introduce errors of their own), global climate models need to be run many times with a variety of initial conditions in order to build up an ensemble of projections that reflect the possible future states of the climate within a given model. Model uncertainty just reflects the fact that there is a lot that is still unknown about the physics of several important processes in the climate system. An important example is the so-called cloud radiative feedback, which is a major source of uncertainty in the response of the climate system to changes in GHG concentration (Stephens, 2005; Zickfeld et al., 2010). Changes in temperature affect cloud formation, and since cloud cover affects the emission and absorption of solar radiation, this has a feedback effect on temperature itself. The magnitude of this feedback is not well understood (although it is likely to be positive, Dessler, 2010), and different modeling groups represent cloud physics, and other poorly understood physical phenomena, in different ways.3 Finally, emissions uncertainty simply refers to the fact that we do not know the quantity of greenhouse gases that will be emitted over the coming decades. Climate 2 Normative disagreements are usually seen as conceptually distinct from empirical uncertainties. However, recent work by philosophers has somewhat blurred this distinction (MacAskill, 2016). 3 Technically, cloud formation is a sub grid process, i.e. it occurs on a spatial scale smaller than the spatial resolution of climate models. So cloud feedbacks are often put into the models through ‘reduced form’ parameterizations.

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models are thus usually forced with a variety of emissions scenarios, leading to a further expansion in the range of predicted outcomes. All of these types of scientific uncertainty are dependent on scale: uncertainties are largest on small spatial scales, and reduce significantly at continental and global scales. Uncertainty about the response of economic and social systems to climate change is probably greater than scientific uncertainty – though both are large in some absolute sense. Scientific uncertainty can be reduced by refining climate models and testing their ability to reproduce historical data, in many cases stretching back hundreds of thousands of years. Clearly there is no comparable data set that will allow us to understand the response of future social and economic systems to climatic change. Our current forms of economic and social activity are at most a few hundred years old, and during that period the global climate has been remarkably stable by historical standards. Socio-economic uncertainties can be roughly broken into two categories: model uncertainty again – including uncertainty about parameter values in a given model, and uncertainty about the structural relationships that govern the evolution of the climate-economy system – and disagreements about values. The importance of model uncertainty is highlighted by the substantial variations in the predictions of different integrated assessment models (IAMs). IAMs combine simplified scientific models of climate change with macroeconomic growth models, estimates of the dynamic costs of mitigation, and damage functions that quantify the impact of climate change on economic activity. Different models represent these components, and many other factors, in different ways, leading to a very large distribution of policy recommendations. These models are playing an increasingly important role in climate policy analysis. For example, an interagency committee of the US government used three IAMs to inform its choice of the social cost of carbon for regulatory cost-benefit analysis (Greenstone et al., 2013). Yet it is unclear what empirical basis we have for believing that any given IAM captures the evolution of the climate-economy system over the coming centuries. The reliance of IAMs on untested structural assumptions, and the strong dependence of their outputs on arbitrary modeling choices, has caused some to suggest that they “have crucial flaws that make them close to useless as tools for policy analysis” (Pindyck, 2013). To illustrate some of the empirical difficulties IAMs face, consider the problem of specifying a damage function – a function that translates climatic changes into changes in aggregate economic output. The climate impacts literature (IPCC 5AR WG3 2014) generally breaks the socio-economic impacts of climate change into several components. These include, for example, the impact of rising sea levels on coastal properties and infrastructure (Yohe et al., 1996), the impact of heat on food crop yields (Lobell et al., 2011), the effects of higher temperatures on labor productivity (Heal and Park, 2013), the effect on crime and conflict (Hsiang et al., 2013) and the effect of climate change on health through temperature stress and the spread of disease vectors. Reviews of the recent micro-econometric literature on climate damage estimates can be found in Dell et al. (2014), Houser et al. (2015), Carleton and Hsiang (2016). But there is as yet no systematic attempt to aggregate and monetize

1 Introduction

these damages for the world as a whole, so we are in the dark about the global economic costs of climate change. In practice, IAMs use reduced form damage functions to quantify climate impacts, but as Pindyck (2013) trenchantly notes, their “descriptions of the impact of climate change are completely ad hoc, with no theoretical or empirical foundation.” For example, it has become conventional, following Nordhaus (1994), to assume an inverse quadratic relationship between damages and temperature. Yet this assumption has no empirical or theoretical justification, and has great consequences for IAM outputs, especially when it comes to estimating the costs of extreme climatic changes. Other IAM components – e.g. their representation of longrun technological change – are subject to similar concerns (Millner and McDermott, 2016). A second type of socio-economic uncertainty is not really uncertainty at all, but rather disagreement about values. The values that are chosen for the parameters of intertemporal social welfare functions are key inputs to IAMs, and are the subject of debate and, on occasion, controversy. The most prominent examples are the pure rate of time preference, which discounts the wellbeing of future generations, and the elasticity of the marginal utility of consumption, which captures aversion to intergenerational consumption inequalities. Both of these parameters express distributional value judgments that have been hotly debated. These disagreements are fundamental, and can have a huge impact on the policy recommendations IAMs produce. Quoting Pindyck (2013) again, Nordhaus (2008) finds that optimal abatement should initially be very limited, consistent with an SCC (social cost of carbon) around $20 or less, while Stern (2007) concludes that an immediate and drastic cut in emissions is called for, consistent with an SCC above $200. Why the huge difference? Because the inputs that go into the models are so different. Had Stern used the Nordhaus assumptions regarding discount rates...he would have also found the SCC to be low. Likewise, if Nordhaus had used the Stern assumptions, he would have obtained a much higher SCC.

Disagreements on the ethical principles that should govern the measurement of intergenerational social welfare are unlikely to be resolved any time soon. As with many primitive ethical questions, reasonable people can reasonably disagree on this issue. This suggests that methods for aggregating diverse views on social preferences into some compromise judgment could be useful tools for achieving a measure of consensus, allowing us to move beyond an ethical impasse (Heal and Millner, 2014b; Millner, 2016; Millner and Heal, 2017). Nevertheless, we acknowledge that the aggregation of opinions on social preferences raises new normative questions – there is no free lunch. In the remainder of this section we set ethical disagreements aside, and focus on the empirical uncertainties that climate policy choices must contend with. Because of the substantial gaps in our knowledge about the magnitude and consequences of climate change, scientific and socio-economic uncertainties are not readily quantifiable by objective probability density functions (PDFs) that all reasonable people will agree on. It is common to find several PDFs for relevant variables in the

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FIGURE 1 Scientific estimates of equilibrium climate sensitivity.

scientific literature, or several expert opinions that need not be in the form of PDFs at all (Kriegler et al., 2009). By way of example, consider scientific estimates of the equilibrium climate sensitivity (ECS), perhaps the central summary statistic in climate change science. The ECS is the equilibrium increase in global mean temperatures that would occur if the concentration of atmospheric CO2 were doubled. It is thus a coarse measure of the sensitivity of the global climate to changes in CO2 concentrations. Fig. 1 shows twenty PDFs for the ECS from the scientific literature. The differences between the studies are largely due to differences in the climate models that are used by different modeling groups, but are also in part due to the use of different data sets and statistical methodologies. Although there are significant differences between these estimates, all are generated by intellectually respectable modeling groups. Given the substantial variation in scientific estimates of even highly aggregated summary statistics like the ECS, how should the analyst proceed? Should she seek to aggregate different PDFs into a single composite distribution and use decision techniques that rely on the existence of such a distribution, or should she work with the ambiguity inherent in the information available to her? Naively combining multiple PDFs is generally not advisable as different models are not independent estimates of a “true” underlying distribution. For example, although the climate models produced by different modeling groups have important differences, they are generally calibrated at least in part on the same data and based on the same physical principles and sets of equations. In order to objectively combine PDFs from multiple models of

1 Introduction

the same phenomenon into a single probability estimate it is necessary to account for the dependencies between models, and have some measure of their relative predictive performance. When meaningful verification data are available this can be a very productive strategy. For example, Nate Silver’s FiveThirtyEight blog used precisely such a methodology to aggregate many electoral polls into a single summary probability forecast which was more accurate than any individual poll. A lot of the skill in this exercise involves using the historical performance of each poll to design a weighting scheme for aggregating polls.4 Can we do the same thing for integrated assessment models of climate change? In principle there is nothing preventing us from evaluating the performance of these models on historical data sets (Millner and McDermott, 2016), however for some important model components – e.g. the damage function – this exercise is unlikely to reveal much information about which of the models is a better match to reality. One reason for this is that there has been only a small amount of warming in the roughly 150 years since the industrial revolution began, so finding a climate change signal in overall growth outcomes is very difficult.5 A second reason is that many of the crucial assumptions in IAMs are exogenously specified scenarios, rather than structural relationships that are subject to empirical verification. In the DICE model (Nordhaus and Sztorc, 2013) this applies to the trajectories of key time series such as population change and abatement costs. In the PAGE (Hope, 2006) and FUND (Tol, 1997) models the entire baseline sequence of global GDP is put in by hand. A third, and more fundamental, reason is that past predictive performance may not be a good indicator of future predictive performance in the case of climate policy. Unlike the fundamental physical principles that underlie climate models, which derive their authority from a myriad of successful applications across vastly different spatial and temporal scales, the structural assumptions that underpin our models of economic growth and technical progress have had only patchy predictive success in other economic applications. They are enormously valuable explanatory tools (e.g. much of economic growth theory uses models to explain historical differences in growth outcomes between countries), but their utility as quantitative predictive tools is far less established. Thus, even if we were able to calibrate our models so that they replicate growth outcomes over the previous century reasonably well, we do not have high confidence that we have identified the true dynamics that govern long-run changes in the global economy. Calibration does not imply out-of-sample predictive power. Millner and McDermott (2016) provide further discussion of the difficulty, and importance, of attempting to confirm the structural modeling assumptions that IAMs rely on.

4 See Knutti et al. (2017) for a recent discussion of weighting climate models. 5 It is well known that temporary temperature shocks are statistically associated with changes in both the

level of economic output, and the pace of economic growth (Dell et al., 2012; Heal and Park, 2016). However these relationships are deduced using data from relatively short time periods (50 years), over which the climate was approximately stationary. They are at best indicative of what might happen if the distribution of shocks changes.

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The lack of availability of unique objective PDFs poses methodological questions for the economic analysis of climate policies. In practice the analyst must choose a framework for policy analysis that represents the state of our knowledge (or lack thereof) in as complete and honest a manner as possible. The tendency in the economic literature on climate change has been to adopt the expected utility framework for analyzing climate policies. In order to apply this framework to the climate problem it is necessary to make subjective judgments about how to transform all the known limitations and ambiguities in the scientific literature on climate science and impacts into a unique mapping between policy choices and probability distributions over outcomes. This process invariably does violence to the available data, mixing largely arbitrary subjective judgments about how to combine alternative models with more objective (conditional) probabilities that arise when fitting models to data. There are however alternative decision tools, involving “multiple priors,” that explicitly recognize that we generally do not have the quality of information needed to define a unique objective PDF. We investigate the possibility of applying these approaches in the climate context below.

1.2 UNCERTAINTY AND BIODIVERSITY We understand generally that the loss of biodiversity has an economic cost, which can be thought of as the loss of various contributions that biodiversity makes to the economy. We probably don’t understand fully these contributions, but they include the value of biological resources in bioprospecting, the insurance value of biodiversity, its value in enhancing productivity of natural ecosystems, and its value as the origin of all domesticated plants and animals (see e.g. Heal, 2016). Consider the first of these: many important pharmaceutical products are derived from plants and insects, and pharmaceutical companies routinely scan extracts from such sources as possible drug leads. Aspirin is probably the most famous plantderived drug, occurring naturally in the bark of willow trees. After decades and billions of dollars of research, the pharmaceutical industry has not come up with anything that is clearly better than aspirin as a painkiller and anti-inflammatory. In addition, aspirin reduces the risks of heart attack and stroke, and recent research (Drew et al., 2016) suggests strongly that regular use of aspirin reduces the risk of a range of common cancers. A more contemporary example is Glucobay, a drug sold by Bayer that lowers blood glucose levels in diabetics and is in great demand in view of the growing menace of diabetes. Its key ingredient is a natural sugar called Acarbose, which reduces the absorption of glucose into the bloodstream. In a US patent application Bayer revealed that a bacterial strain that originates from Kenya’s Lake Ruiru had genes that enable the synthesis of Acarbose, and subsequently confirmed that this was being used to manufacture Acarbose. In the two decades since 1990 Bayer has sold at least Euro 4 billion of Glucobay. A rather different example of the value of biodiversity comes from the development of the polymerase chain reaction (PCR), central to the amplification of DNA specimens for analysis, used in forensic tests for criminal investigations and in many processes absolutely central to the biotechnology

1 Introduction

industry. The PCR technique, which takes a minute sample of DNA and multiplies it manyfold so that there is enough to conduct extensive chemical tests, requires an enzyme resistant to high temperatures. A bacterium Thermus aquaticus containing such an enzyme was discovered in the Lower Geyser Basin of Yellowstone National Park, and has since been found in similar habitats around the world. The enzyme derived from it is now central to the rapidly growing biotechnology industry. It is not much of an exaggeration to say that the biotechnology industry could not have taken off without an obscure bacterium found only in a few hot springs. Several research groups have developed models of the value of biodiversity in bioprospecting, including Simpson et al. (1996), Rausser and Small (2000), and Costello and Ward (2006). Each of these gives very different distributions of the value of biodiversity conservation for bioprospecting. In economic terms, genetic variation is a resource, something we can work with and develop, because it provides a pool of within-species differences on which we can draw when seeking to develop new varieties better adapted to particular places or tasks. Genetic variation is in fact a form of natural capital, allowing us to develop new varieties with valuable properties. Developing crop varieties resistant to disease is an insurance application for genetic diversity within a species. Different examples of the same species have different degrees of susceptibility to any particular disease, allowing us to breed varieties resistant to diseases or to conditions such as drought or heat. If a farmer plants a single crop variety and a disease to which it is susceptible strikes, the entire crop is destroyed. If instead he plants varieties differing in their disease susceptibility, there is some insurance against complete crop loss. The Irish potato famine of the nineteenth century illustrates the hazards of growing a single variety of potato, in that case Solanum tuberosum, vulnerable to a variety of potato blight then rampant in Europe. Genetic variation within species has historically been the source of almost all agricultural progress. It took us from hunter-gatherers to farmers, and in the 20th century it allowed us to increase food production to match the increase in world population from 1 to 7 billion. But today’s food crops are genetically homogeneous, with the same varieties of most major crops grown worldwide, so the within-species variation we have drawn on in the past is disappearing. Institutions such as the International Rice Research Institute (IRRI) maintain seed banks to supplement the diversity we have in the fields; the IRRI has been critical in cases like the outbreak of the grassy stunt virus, which destroyed much of the Asian rice crop and was resistant to all attempts to neutralize it. A previously noncommercial variety of rice resistant to the grassy stunt virus – extinct in the wild – was found at the IRRI and crossbred with commercial varieties. This prevented further drastic crop losses, and showed that species diversity may provide our only protection against disastrous new diseases.6 Brock and Xepapadeas (2003) is a pathbreaking quantitative study of the economic 6 If the population of a species is reduced, then the genetic variation within it is lessened too. Smaller popu-

lations typically have less variation, less potential for innovative new varieties and more risk of inbreeding. So even the partial loss of a population, well short of extinction, can have an economic cost.

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value of genetic diversity in plants, and models the contribution that genetic diversity can make to the yield of an optimally-managed agricultural system. It establishes a framework within which such values can be computed, but the work of extending the model beyond a simple example, establishing parameter values and producing quantitative estimates, remains to be carried out. In the meantime we have only some very approximate estimates to work with (Heal, 2016).7 We conclude that in both of our case studies – climate change and biodiversity loss – we face deep uncertainties that are not readily described by unique, scientifically rigorous, objective, probability distributions. For some key aspects of climate change – such as the equilibrium climate sensitivity – we have a range of PDFs to work with, but for others we have little more than expert’s guesses. And for biodiversity loss, we have a range of analytical estimates for the value of biodiversity in bioprospecting, but seldom (if ever) any objective likelihood information. For the agricultural value of biodiversity we have an analytical framework but little in the way of empirical estimates. In order to make decisions based on such information, we arguably need an uncertainty calculus that is suited to incomplete and qualitative information about the likely consequences of our actions.

2 ALTERNATIVES TO EXPECTED UTILITY In this section we develop formal alternatives to the standard expected utility approach to decision under uncertainty. Before delving into mathematical details however, we discuss intuitive conceptual arguments that are often used to motivate a departure from expected utility theory when decision makers are faced with deep uncertainty.

2.1 PROBABILITIES AND CONFIDENCE Probabilities may either denote relative frequencies, as in a game of chance, or subjective degrees of belief. In the context of climate change, biodiversity, and many environmental applications, the interpretation generally has to be the latter, as we have argued above. One of the main issues we want to discuss is whether it is reason-

7 Tilman et al. (2001) demonstrated the connection between biodiversity and ecosystem productivity: they planted similar plots of land with different varieties of grassland plants – some with many species, some with fewer. Each plot was planted with the same mix year after year and each year the experimenters noted the amount of available nutrients that the plants took up and the amount of biomass grown. Biomass, the total dry weight of the plants, is also a measure of the amount of carbon from the atmosphere that is photosynthesized into carbohydrate. Over about twenty years, the more species-diverse plots performed 270% better than the less-diverse ones. Furthermore, the plots that were more diverse were also more robust in the face of weather fluctuations. Subsequent research has confirmed these findings and the centrality of biodiversity to the functioning of natural systems. As with the previous case, we have no systemic models of the value of diversity in this context.

2 Alternatives to Expected Utility

able to require that decision makers’ beliefs about the consequences of environmental policies with highly uncertain consequences always be represented by unique PDFs. Formalization of choice under uncertainty in economics began with the work of von Neumann and Morgenstern (1944), who assumed that uncertainty can be characterized by an objectively known set of probabilities that is agreed by all observers. Their analysis thus builds on the relative frequency interpretation of probability, showing that if decision makers’ preferences over lotteries obey certain axioms they will act as if maximizing their expected utility. In later work that has since become the mainstream approach (Savage, 1954) probabilities are not assumed a priori, but derived from a primitive set of axioms on preferences over ‘acts’, i.e. maps between states and outcomes. Savage proves a representation theorem implying that anyone whose behavior satisfies these axioms must behave as if she maximizes some subjective expected utility functional. We repeat: the existence of a complete subjective probability distribution follows from Savage’s axioms, which do not presuppose the existence of probabilities. Proponents of the subjective expected utility paradigm identify rational choice with consistency with the Savage axioms. The crucial axiom in Savage’s approach is the so-called “sure thing principle,” which we discuss in detail below. This, plus the other axioms, necessarily implies that agents must behave as if they have unique PDFs over all possible outcomes and can assign probabilities to any events, no matter how little information they have to draw on. Despite the appeal of Savage’s approach, scholars have always questioned whether it is reasonable to adopt a definition of rationality that requires rational agents to be able to assign a unique probability to absolutely any event. As Gilboa et al. (2009) [GPS] argue, Will the US president six years hence be a Democrat? The Bayesian approach requires that we be able to quantify this uncertainty by a single number; we should be able to state that our subjective belief for this event is, say, 62.4% or 53.7%. Many people feel that they do not have sufficient information to come up with such an accurate probability estimate. Moreover, some people feel that it is more rational not to assign a probabilistic estimate for such an event than to assign one. Choosing one probability number in the interval [0,1] would be akin to pretending that we know something that we don’t.

They go on to argue that The Bayesian approach is lacking because it is not rich enough to describe one’s degree of confidence in one’s assessments. For any probability question it requires a single probability number as an answer, excluding the possibility of replies such as “I don’t know” or “I’m not so sure”. A paradigm of rational belief should allow a distinction between assessments that are well-founded and those that are arbitrary.

If we accept this critique, it follows that we must drop one or more of Savage’s axioms when defining ‘rational’ choice. One possibility, of course, is to drop the completeness axiom and accept that preferences over uncertain prospects may be

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incomplete, with decision-makers (DMs) having no preferences over some sets of alternatives. Bewley (1986) adopts this approach, replacing completeness with an inertia assumption and accepting that DMs may pronounce some pairs of alternatives to be “incomparable”. His approach, like those based on ambiguity theory that we will develop further below, implies that DMs work with multiple probability distributions and prefer one alternative to another if and only if it gives a greater expected utility for all probability distributions in some set of distributions (see also Galaabaatar and Karni, 2013). An alternative to dropping the completeness axiom is to drop Savage’s “sure thing principle,” and this is the approach we investigate in detail below.

2.2 FORMAL DEVELOPMENT All of the decision-making frameworks we shall talk about are developed axiomatically. Rules of behavior that are believed to be compelling desiderata of rational choice are posited, and a mathematical representation of behavior that is consistent with these rules is deduced. In all cases there are some essential axioms whose role is technical, and other axioms that embody the intuitive essence of the approach. For example, all frameworks have a largely technical axiom requiring preferences to be continuous in some sense. Also most of them have an axiom implying that preferences are non-trivial, i.e. the decision-maker does not rank all alternatives equally. Clearly we need such an assumption for the problem to be interesting. In the review of alternative decision theories that follows we will focus on the axioms that embody the intuitive essence of each approach, and neglect the technical axioms that are needed for the mathematics, but which play a secondary role in giving the framework its distinguishing characteristics. The von Neumann Morgenstern approach to decision-making under uncertainty is developed in the context of preferences over lotteries, a lottery being a list of outcomes, and a probability of occurrence for each item on the list: Definition 1. A simple lottery l is a list of N exclusive and exhaustive outcomes  1, . . . , N with associated probabilities (p1 , p2 , . . . , pN ) , n pn = 1, pn ∈ [0, 1], where pn is the probability of outcome n occurring. Probabilities are assumed to be objectively given and can be interpreted as the relative frequencies of outcomes in repeated experiments. It is assumed that preferences over simple or compound lotteries (lotteries over lotteries) depend only on the outcomes and their probabilities, and not in any way on the process used to arrive at these outcomes and probabilities. So we take the set of alternatives to be the set of all simple lotteries L over the set of outcomes. If there are three alternatives, the set of lotteries is just the set of numbers in R 3 that are non-negative and sum to one: this is the triangle joining the points (1, 0, 0), (0, 1, 0), (0, 0, 1). Agents are assumed to have a preference ordering  over L. This ordering is, as we indicated above, as-

2 Alternatives to Expected Utility

sumed to be continuous.8 The key assumption in developing this framework is an independence assumption: Definition 2. The preference relation  on the space of simple lotteries L satisfies the independence axiom if for all l, l  , l  ∈ L and a ∈ (0, 1) we have l  l  ⇐⇒ al + (1 − a) l   al  + (1 − a) l  . In words, if we mix two lotteries in the same proportions with a third one, preferences between the two resulting mixtures should be the same as preferences between the two original lotteries. This axiom has a sharp geometric interpretation. As we noted above, with three alternatives a simple lottery can be represented by a point in R 3 in the triangle (1, 0, 0), (0, 1, 0), (0, 0, 1). More generally case of N alternatives it is a point  in the  N :  p = 1 . The independence in the N − 1-dimensional simplex  = p ∈ R+ n n axiom implies that preferences over lotteries can be represented by parallel straight lines (planes, hyperplanes depending on the dimension) on the simplex. This means that preferences are linear in the probabilities, and given this we can fairly readily prove the following: Proposition 1. [von Neumann Morgenstern expected utility theorem] Suppose that the preference relation  on L satisfies the continuity and independence properties. Then  admits a representation in the expected utility form, that is we can assign numbers un to each outcome 1, . . . , N in such a manner that for any two lotteries  ) we have l = (p1 , . . . , pN ) , l  = (p1 , . . . , pN l  l  ⇐⇒

 n

un pn ≥



un pn .

n

We now contrast this result with the Savage approach to decision under uncertainty. Unlike von Neumann and Morgenstern, Savage does not assume an objectively given set of probabilities over outcomes. In his approach probabilities are subjective, and are a consequence of choice behavior that is consistent with primitive behavioral axioms, in a manner similar to the approach developed by De Finetti (1937). The Savage result thus works where von Neumann–Morgenstern’s doesn’t, i.e. where no 8 The preference relation  on the space of lotteries L is continuous if for any l, l  , l  ∈ L the sets

 a ∈ [0, 1] : al + (1 − a) l   l  ⊂ [0, 1]

 and

  a ∈ [0, 1] : l   al + (1 − a) l  ⊂ [0, 1] are closed. So the set of combinations of l, l  that are at least as good as l  is a closed set, as is the set of combinations that are no better than l  . As in the deterministic case, this requirement rules out lexicographic preferences where the agent places all emphasis on the probability of one particular outcome – for example on the risk of death being zero.

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objective probabilities are available. This is clearly a very important advance, particularly in the contexts that we have discussed above. Primitive concepts in Savage’s framework are states and outcomes. The set of states S is an exhaustive list of all scenarios s that might unfold. Knowing which state occurs resolves all uncertainty. An event is any subset A ⊂ S. The set of outcomes is X, with typical member x ∈ X. An outcome specifies everything that affects the chooser’s well-being. The objects of choice are acts, which are functions from states to outcomes, and are denoted by f ∈ F, f : S → X. The state s that will be realized after an act f has been selected is uncertain, but the agent does know that if the state s occurs then the outcome will be f (s) if she chooses act f . Acts whose payoffs do not depend on the state of the world s are constant functions in F . We will use the notation x ∈ F to indicate the constant function in F whose outcome is always equal to x ∈ X. Suppose f, g are two acts and A is an event: then we define a new act by  g (s) , s ∈ A, g fA (s) = f (s) , s ∈ Ac where Ac denotes the complement of the set A. Intuitively this composite act coincides with f everywhere except on A, where it coincides with g. Within this framework Savage’s two key axioms are the following: Axiom P2 (Sure Thing Principle). Preferences between two acts f, g depend only on events where the values of f and g differ: Let A be an event, and suppose f = g on Ac , so that f and g differ only on A. Now consider two new acts f  , g  that are equal to f, g respectively on A, and equal to one another on Ac , i.e. f  (s) = f (s), g  (s) = g(s) for s ∈ A f (s) = g(s), f  (s) = g  (s) for s ∈ Ac Then P2 requires: f  g ⇔ f   g. An intuitive interpretation of P2 is provided by GPS. Consider the following four bets: 1. 2. 3. 4.

If horse A wins you get a trip to Paris, and otherwise you get a trip to Rome If horse A wins you get a trip to London and otherwise a trip to Rome If horse A wins you get a trip to Paris and otherwise a trip to Los Angeles If horse A wins you get a trip to London and otherwise a trip to Los Angeles

Clearly 1 and 2 are the same if A loses, as are 3 and 4. Generally one’s choices between these options will depend on the value one assigns to alternative outcomes

2 Alternatives to Expected Utility

and beliefs about their likelihood of occurring. Presumably however, the chance of A winning is the same in each case, so the choice between 1 and 2 depends on one’s preferences between Paris and London. The same is true for 3 and 4. Axiom P2 thus requires consistency between preferences over the pairs of bets 1, 2 and 3, 4: 1  2 ⇔ 3  4. If two acts are equal on a given event, it does not matter what they are equal to. So it doesn’t matter if when the horse loses you get Rome or LA. It is hard to argue with this axiom viewed in isolation. Nevertheless, when taken together with the rest of Savage’s axioms, it requires agents to be able to assign subjective probabilities to any events however unlikely or unusual, as we noted in the introduction. The second axiom we highlight gives further insight into how Savage’s primitive axioms for choice between acts gives rise to a probabilistic preference representation: Axiom P4. For every A, B ⊂ S and every x, y, z, w ∈ X with x y, z w, z yAx  yBx ⇔ wA  wBz

Here is an interpretation of this axiom. We have four alternatives, x, y, z, w with x y and z w. And we have two subsets of the set of all states, two events, A and B. We look at yAx , which is y modified to be x on the event A. x is preferred to y so this is an improvement on y. The axiom says that we prefer yAx to yBx (that is, prefer y upgraded on A to x to y upgraded on B to x) if and only if we prefer w similarly upgraded to z. Why would we prefer to upgrade y and w on A rather than on B? Presumably because we think A is more likely than B. So Axiom P4 encodes some notion of the relative ‘likelihood’ of the two events A and B. This axiom clearly plays an important role in introducing subjective probabilities into the Savage formalism. There are other essentially technical assumptions, including an axiom roughly analogous to continuity, but it is the two above that give Savage’s theory its main characteristics. With this set of assumptions Savage proves Proposition 2. [Savage] Assume that X is finite. Then  satisfies the Savage axioms if and only if there exists a probability measure μ on states S and a non-constant utility function u : X → R such that for every f, g ∈ F ,   f  g ⇔ u (f (s)) dμ (s) ≥ u (g (s)) dμ (s) S

S

Furthermore μ is unique and u is unique up to positive linear transformations. Savage’s theory has been the economists’ workhorse since the 1960s, and is the default approach to choice under uncertainty in environmental economics and in economics generally. But as we noted above, there are reasons to think that it is limited in important ways, and in particular has a limited capacity to reflect some important aspects of the information available to us on environmental problems. So we next turn to the other candidates for addressing these issues, referred to generally as “multiple priors” models. They are models of decision-making in which the decision-maker

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recognizes the ambiguity inherent in the problem she wishes to solve and instead of working with a single PDF, she works with all of the PDFs consistent with the information available to her. A prominent approach is that of Gilboa and Schmeidler (1989), who work within the same conceptual framework as Savage but of course use a different set of axioms. In particular, they drop Savage’s second axiom, the sure thing principle.9 Their axiom set contains several technical axioms as usual, including a continuity axiom. In addition it includes an independence axiom similar to that used by von Neumann and Morgenstern, and an explicit invocation of uncertainty aversion: Axiom GS5. Independence: For every act f, g ∈ F, ∀ constant h ∈ F, ∀α ∈ (0, 1), f  g ⇔ αf + (1 − α) h  αg + (1 − α) h Axiom GS6. Uncertainty Aversion. For every f, g ∈ F, ∀α ∈ (0, 1) f ∼ g ⇒ αf + (1 − α) g  f The axiom GS5 is similar to but weaker than the von Neumann Morgenstern independence axiom, because the axiom applies only to constant third alternatives h. The uncertainty aversion axiom GS6 is unique; it implies that if we are indifferent between f and g then we regard any strictly convex combination of the two as at least as good as either. This sounds a lot like risk aversion – a mixture of two acts, which hedges some of the uncertainty associated with each act, is weakly preferred to each act itself. With this set of assumptions, and other technical conditions, GS prove the following result: Proposition 3. [Gilboa–Schmeidler] The preference  satisfies the above axioms if and only if there exists a closed convex set of probabilities  and a non-constant function u : X → R such that for every f, g ∈ F   f  g ⇔ min u (f (s)) dp (s) ≥ min u (g (s)) dp (s) p∈ S

p∈ S

C is unique and u is unique up to a positive linear transformation. This result does not require Savage’s “sure thing principle”, nor does it need his axiom P4 about probabilities. What this result says is the following: for each act, look at the probability distribution in the set  that yields the lowest expected utility for that act, and evaluate the act using these probabilities. Then choose the act with 9 Amartya Sen, John Rawls, and others have argued that axioms can only be fully evaluated when one

knows their implications – they are reasonable only if they have reasonable implications. Arguably, alternatives to the Savage axioms are attractive in situations where imprecise probabilities seem to occur naturally because they do not require us to behave as if we know things we don’t. We discuss this more fully below.

2 Alternatives to Expected Utility

the largest evaluation, i.e. the act with the largest minimum expected utility across the set of probabilities . What is important from our perspective is that the idea of multiple priors emerges naturally from this framework. Just as primitive axioms over acts yield subjective probabilities in the Savage framework, so the GS axioms require beliefs to be described by a set of probabilities. In addition, the GS axioms require decision-makers to respond to the multiplicity of priors in a specific way, i.e. by focusing on the worst prior for each act. This result is remarkable in that it uses the same basic machinery as the Savage result, and a simple (indeed simpler) set of axioms, to arrive at a radically different representation of agents’ beliefs that does not collapse all uncertainty into a single probability distribution. Obviously one can conceive of many other ways of reacting to a multiplicity of priors. A more flexible alternative to GS that is widely used is that proposed by Klibanoff et al. (2005) (henceforth KMM). The KMM result is in some senses less ‘primitive’ than the Savage and GS results, although it too can be seen as a consequence of a set of axioms on preferences over Savage acts, albeit over an enriched state space that includes lotteries over states. The idea is relatively simple. KMM assume a set  of ‘objective’ von Neumann–Morgenstern lotteries p over the state space. Preferences over acts, conditional on a lottery p being realized, are represented by a vNM Expected Utility functional, with utility function U . They then assume a set of ‘second order acts’, which map lotteries (not states) into consequences. Preferences over second order acts are also assumed to have a subjective expected utility representation, with some subjective probability μ(p) on lottery p, and some utility function  over consequences. Now given an objective PDF p, an act f induces a lottery pf over the set of consequences, whose value can be captured by a certainty equivalent cf (p). These certainty equivalents take values in the space of outcomes, and are an increasing function of Ep U (f (s)). Since there are many possible priors p, each act f generates a lottery over the outcomes cf (p). Preferences over such ‘second order’ acts have a subjective expected utility representation with utility  by assumption, so we must be able to represent preferences over acts by subjective expected utilities over certainty equivalents. This is effectively the content of their result: Proposition 4. [Klibanoff, Marinacci, and Mukherji] There exists a set of PDFs  with generic element p, a utility function U : S → R, a ‘second order’ utility function  : U → R, and second order subjective probabilities μ(p), such that for all f, g ∈ F ,    U (f (s))p(s)ds μ(p)dp f  g ⇐⇒ p∈ s∈S    U (g(s))p(s)ds μ(p)dp ≥ p∈

s∈S

The subjective probability μ(p) on PDFs p is unique, and  is unique up to positive affine transformations.

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Just as in conventional expected utility theory, if  is concave, this implies that the decision maker is averse to the spread in expected utilities across the set of PDFs , i.e.  < 0 implies    U (f (s))p(s)ds μ(p)dp p∈ s∈S   U (f (s))p(s)ds μ(p)dp ≤ p∈ s∈S   U (f (s)) μ(p)p(s)dp ds = s∈S

p∈

The expectation over s on the right hand side of this inequality

is just a standard compound lottery, so that the effective probability on state s is p∈ μ(p)p(s)dp. Thus, if  is concave, the decision maker would always prefer it if his ‘subjective’ uncertainty μ(p) could be made ‘objective’ – he is averse to subjective uncertainty over conditionally objective PDFs in the set of priors . In more common terminology, he is ambiguity averse. Speaking loosely and intuitively, the KMM approach involves applying a von Neumann Morgenstern framework twice, once to each of the individual models or distributions p and then secondly over the set of expected utilities that emerges from these distributions. Concavity of the U functions, the von Neumann Morgenstern utilities, would reflect the normal aversion to risk, and concavity of the  function would reflect aversion to not knowing the expected utility, which is only known conditional on a particular distribution. The KMM approach converges to the GS approach as the second order utility function  becomes more and more concave. A KMM decision-maker who is infinitely averse to uncertainty about expected utilities is a GS decision-maker. We have now reviewed the traditional expected utility model and modern alternatives to it that allow decision-makers to express lack of confidence in their probabilistic beliefs. In particular, these new tools allow a distinction to be drawn between objective probabilities and subjective judgments, and are naturally suited to dealing with decision problems in which several plausible probabilistic descriptions of the world present themselves to us. Arguably, these features of the new decision models make them well suited to environmental problems such as climate change and biodiversity, as we seldom have objective probabilistic knowledge of the consequences of policy choices in these applications. But is it ‘rational’ to dispense with the appealing axioms that underpin Savage’s subjective expected utility theory? Perhaps violation of the sure thing principle (for example) is too high a price to pay in order to have a decision framework that admits a distinction between objective probabilities and arbitrary subjective judgments? Next we digress slightly and try to put this movement away from the expected utility framework into historical context. The key issue we must address is the extent to which a given axiom system (in this case the Savage axioms) can be thought of as providing a universal and unassailable definition of ‘rationality’. While there can be no ultimate answer to this question – it is

2 Alternatives to Expected Utility

in large part a matter of definition – the history of science does suggest that placing one axiom system on a pedestal can sometimes be a barrier to progress.

2.3 IS AMBIGUITY AVERSION RATIONAL? Not everyone agrees on whether the models of decision under ambiguity developed above should be used in normative applications. As we have emphasized, the EU approach requires that agents be able to assign a precise probability to any event. In many areas of environmental economics this seems to do violence to the facts. For example, we don’t know the equilibrium climate sensitivity, and we have multiple PDFs over its possible values, which we cannot sensibly condense into a single PDF. In other areas, such as the cost of biodiversity loss, our knowledge is even less precise. One response to this is to adopt a decision framework which takes multiple probabilistic descriptions of reality as its raw material, and which allows us to distinguish between subjective judgments and conditionally objective probabilities (i.e. probabilities that arise from constraining models with data, assuming that the model is a ‘correct’ description of the world). The approaches we have discussed above achieve this at the cost of dropping Savage’s “sure thing” principle. While some eminent decision theorists have argued that EU theory is not a universally applicable standard of rational choice (Binmore, 2009; Gilboa et al., 2008), others strenuously adhere to the Savage framework (Sims, 2001; Al-Najjar and Weinstein, 2009; Al-Najjar, 2015). Our view of this debate is that, much like the debate about the appropriate value of welfare parameters, it is something that reasonable people can reasonably disagree about. Nevertheless, it is important to be clear what the arguments for and against the normative status of ambiguity aversion are. We now discuss some of these. It is sometimes asserted that models of decision under ambiguity are merely descriptive theories of people’s behavior in the face of ambiguity, as was memorably described by Ellsberg (1961). Briefly, in one version of Ellsberg’s choice experiment a DM is asked whether she would prefer betting on a red or black ball being drawn from urn 1, which contains 50 red and 50 black balls, or from urn 2 which contains 100 balls, each of which is red or black, but whose proportions are not known. Most people are indifferent between betting on red or black in both Urn 1 and Urn 2. However, when asked whether they would prefer to bet on a red ball being drawn from urn 1, or a red ball being drawn from urn 2, many people prefer to bet on urn 1. The important point here is that according to the Savage approach, being indifferent between red and black in Urns 1 and 2 reveals that the DM must have a subjective probability that red and black are equally likely in both urns. Since the subjective probabilities and payoffs are the same for bets on both urns, from the perspective of the Savage axioms these two urns are indistinguishable, and it is irrational to prefer betting on a red ball being drawn from Urn 1 to a red ball being drawn from Urn 2. And yet, many people do prefer betting on the Urn with known composition to that with unknown composition, i.e. they are ambiguity averse. An ability to explain behavior in Ellsberg’s choice experiments is certainly an attractive feature of the decision theoretic tools developed above, but this is clearly not

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a reason to believe that these tools have normative legitimacy. A compelling argument against the normative validity of the behavior Ellsberg observes was provided by Raiffa (1961). He asks us to choose a color in Urn 2 by flipping a fair coin, say choose red if the coin lands on heads. Clearly our chance of matching the ball drawn from Urn 2 using this strategy is now an ‘objective’ 50% – the coin flip is either ‘right’ or ‘wrong’. Raiffa thus uses a randomization device (the coin) to turn an ambiguous situation (unknown probabilities) into a risky one (known probabilities). According to Raiffa, this shows that preferring to bet on Urn 1 is irrational. We do not deny the force of this argument in the context of Ellsberg style choice problems. It is however important to realize that the argument turns on the high degree of symmetry in the stylized Ellsberg examples. This symmetry gives rise to a natural prior on the space of possible probability distributions that describe the composition of Urn 2, i.e. that all distributions are equally likely. Raiffa’s coin is simply a device for bringing this symmetry to the fore. But, as David Schmeidler (quoted in Gilboa, 2009) says: ‘Real life is not about balls and urns.’ What is the natural prior for the probability of war in the South China Sea in 2050? Of course, there is none. The key normative argument for deviating from subjective expected utility theory is that it forces us to treat situations that are manifestly different from an informational perspective as if they were identical. Savage’s theory admits no distinction between arbitrary subjective judgments and objective probabilistic knowledge (e.g. known relative frequencies of events). In practice it seems desirable for policy analysts to be able to make use of multiple conflicting probabilistic models of how the world works, while acknowledging that their policy recommendations rely on subjective judgments about how to weight alternative models. These judgments clearly do not have the same character as objective probabilities. The models of decision under ambiguity described above provide such tools. A more technical set of objections to giving up the Savage axioms concerns the extensions of ambiguity averse decision rules to dynamic contexts (e.g. Al-Najjar and Weinstein, 2009). Extending static decision frameworks to dynamic contexts requires us to specify how information sets are updated, and how preferences at different nodes of decision trees are related. This aspect of intertemporal decision-making is pinned down by invoking additional axioms: dynamic consistency (conditional plans, once made, are not revised due to the mere passage of time), and consequentialism (preferences depend only on nodes of the decision tree that are reachable from the current node). There is a tight connect between the sure thing principle and dynamic consistency (Epstein and Le Breton, 1993), implying that ambiguity averse decision rules cannot be made to respect dynamic consistency on a universal domain of decision trees. However, dynamic consistency may be respected for any particular decision tree. Epstein and Schneider (2003) and Mukerji (2009) pursue this approach in the GS and KMM models respectively. See Mukerji (2009), Siniscalchi (2009), Machina and Siniscalchi (2014) for further details and discussion. It is very likely that some readers may feel that giving up the elegant Savage axioms, in particular the sure thing principle, is too high a price to pay for the additional epistemic nuance that the ambiguity models provide. That is a legitimate normative

2 Alternatives to Expected Utility

perspective, although ultimately not one we agree with. As we have argued above, axioms cannot be evaluated in isolation, but must be judged by their implications when combined with other axioms. If an axiom system leads to conclusions we are not prepared to accept, it must be revised – a process that the philosopher John Rawls refers to as reflective equilibrium (Rawls, 1971). While the appeal of the Savage axioms is undeniable, their implications are, to our eyes, unpalatable in situations in which information is imprecise or incomplete. In our view, the Savage axioms are best seen as a recipe for translating arbitrary choice problems into choices over bets that look like coin tosses or rolls of a die. This is an elegant and powerful trick, but the sleight of hand comes at a high price. In executing this recipe we are required to behave as if we knew things (i.e. the relative frequencies of events) that we often do not. For some commentators the Savage (or worse, von Neumann–Morgenstern) axioms provide a definition of rational behavior in the face of uncertainty in all situations. We would argue, however, that concepts of rationality can (and should) evolve, as our understanding of the implications of axiom systems deepens. The history of science demonstrates that adopting an inflexible view of the nature of reality based on preconceived notions of mathematical elegance can be a barrier to progress. The same may well be true of normative theories of rationality. To illustrate, consider the following example: It is an elementary fact of geometry, known to schoolchildren the world over, that the sum of the angles in a triangle is equal to 180 degrees. This fact is a direct consequence of the five axioms of Euclid’s Elements: 1. Any two points can be connected by a straight line. 2. Any line segment can be extended indefinitely in a straight line. 3. Given any straight line segment, a circle can be drawn having the segment as radius and one endpoint as its center. 4. All right angles are equal to one another. 5. Given any straight line and a point not on it, there exists exactly one straight line which passes through that point and never intersects the first line. These axioms are so self-evident that doubting them was seen as a symptom of madness by learned minds for almost 2000 years after Euclid. The Elements became the gold standard of rational thought throughout that period. Nevertheless, as the centuries rolled by it was occasionally suggested that the fifth axiom, the so-called ‘parallel postulate’, seemed less satisfying than the others. It was more complex, and some argued that it should be possible to derive it as a consequence of the other four more primitive axioms. Several attempts were made, but no one could find a proof. Then, in the 18th century, a Jesuit priest named Giovanni Girolamo Saccheri adopted a novel approach. His strategy was simple: assume that the parallel postulate does not hold, and derive a contradiction. It was known that the parallel postulate is equivalent to the fact that the angles of a triangle sum to 180 degrees, so Saccheri considered two cases: either the angle sum of a triangle is greater, or less than 180 degrees.

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FIGURE 2 Illustration of non-Euclidean geometries. Reprinted with permission from the Encyclopædia Britannica, © 1997 by Encyclopædia Britannica, Inc.

Saccheri set about deriving the consequences of these assumptions, which he was sure would lead to a self-evident contradiction. He first considered the case where the angle sum exceeds 180 degrees, and quickly derived a contradiction with the second axiom – the assumption implied that straight lines would have to be finite. He saw this as a victory, as the second axiom was seen as self-evidently true. Next he considered the case where the angle sum of a triangle is less than 180 degrees. He derived proposition after proposition based on this flawed initial assumption, but could not find a contradiction. Finally, exasperated, he asserted that ‘the hypothesis of the acute angle is absolutely false; because it is repugnant to the nature of straight lines’. Today we recognize Saccheri’s many propositions not as a failed attempt to vindicate the parallel postulate and Euclid’s Elements, but as an inadvertent first step towards a new, non-Euclidean, geometry. The sum of the angles of a triangle can be less, or indeed greater, than 180 degrees. In so-called elliptical geometries, the angle sum is greater than 180, all parallel lines eventually meet, and just as Saccheri discovered, straight lines cannot be extended indefinitely. In hyperbolic geometries, the angle sum is less than 180, and there are many lines that pass through the same point and are parallel to a given line. These non-Euclidean geometries are now a part of the mathematical mainstream, and have a myriad of applications in diverse areas of science. Most famously, non-Euclidean geometry lies at the heart of Einstein’s General Theory of Relativity (Fig. 2). There are two lessons we wish to draw from this remarkable episode in the history of science, one intellectual, the other, for want of a better word, sociological. The intellectual lesson is this: although relaxing the parallel postulate leads to a new and deeper understanding of geometry, the old Euclidean geometry is still a vital part of our analytical toolkit. It turns out that all smooth geometries are approximately Euclidean on small enough spatial scales. If we zoom in to the surface of a sphere or a hyperboloid, the curvature of the surface becomes negligible, and we reclaim the old Euclidean geometry to a very good approximation. The message of this fact is that even if one axiom system is superseded by another, this does not render the original axioms useless. For some problems accounting for the non-Euclidean effects of

3 Application to Environmental Policy Choices

surface curvature is crucial (e.g. in applications of General Relativity to cosmology, astrophysics, and the technologies underpinning Global Positioning Systems), while for others, we can safely rely on our tried and trusted Euclidean tools. Suggesting that ambiguity aversion may be a normatively legitimate stance in no way invalidates the expected utility approach in applications where objective probabilities are available, or as a parsimonious modeling tool in descriptive applications. The sociological lesson is this: history teaches us that viewing a single axiom system as the universal standard of truth or rationality can be a barrier to progress. Had the mathematicians who followed Euclid been less dogmatic in their adherence to the Euclidean axioms, non-Euclidean geometry, and its many applications, might have been discovered hundreds of years earlier, perhaps paving the way for further advances in other areas. While Euclid’s axioms concern the nature of consistent geometrical spaces, the parallels to our discussion of consistent theories of rational choice are obvious.

3 APPLICATION TO ENVIRONMENTAL POLICY CHOICES The next step is to show how these new ideas can be applied to the analysis of environmental choices. For this we develop a simple static model of the optimal choice of an environmental policy, and show how the multiple priors framework can be applied. We then briefly review more sophisticated environmental applications of the decision frameworks discussed above from the literature.

3.1 A SIMPLE ANALYTICAL MODEL We focus on a class of problems in which there are several alternative models of the relationship between a policy choice that the DM has to make, and the outcome that is of value to the DM. The DM does not know which of these models is correct. She can however assign subjective second-order probabilities to each model being correct. There are many possible interpretations of this framework: in keeping with our earlier discussions we could, for example, be thinking of an integrated assessment model of climate policy choice where the equilibrium climate sensitivity is unknown and there are several alternative distributions over its possible values, each corresponding to a different underlying climate model. A different interpretation could be that we are concerned with modeling the allocation of resources to biodiversity conservation. The consequences of biodiversity loss are unknown and there are again multiple models of how biodiversity affects human welfare. We assume that each alternative model can be identified with the value of a key parameter S of the underlying system – this could be the equilibrium climate sensitivity or the cost of biodiversity loss. A model is a distribution pm (S) over this parameter, indexed by m, and the set of such distributions of S is . The level of the chosen policy variable – think for example of greenhouse gas abatement or tropical

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forest conservation – is a, and the utility level associated with this level depends on the parameter S and is denoted U (a, S). For each model or distribution

pm (S), the expected utility associated with policy level a is given by EUm (a) = U (a, S) pm (S) dS. The correct distribution is of course not known. We assume that the policy maker has KMM preferences. Thus, there exists a second order probability distribution over the set of distributions , with the weight on distribution pm (S) given by μm . So the DM’s overall objective is to choose policy a so as to  max  [EUm (a)] μm (1) a

m

where  is a concave function. We can think of the probabilities pm (S) within each expected utility calculation as scientific probabilities from some model of a physical or economic process, and the μm as subjective judgments about how to weight alternative models. The first order conditions for (1) are

  dEUm

μˆ m a ∗ =0 (2) da a=a ∗ m where a ∗ is the optimal abatement level and the μˆ m (a) are “ambiguity-adjusted” second order probabilities:   (EUm (a ∗ )) μm μˆ m a ∗ =   ∗ n  (EUn (a )) μn

(3)

In the case of ambiguity neutrality (i.e.  (x) is a constant), the first order condition is 

d( m μm EUm )

∗ =0 da a=a

i.e. uncertainty over which ‘model’ is correct is treated as a standard compound lot tery, which reduces the set of priors  to a single prior given by m μm pm (S). When  (x) is concave however (i.e.  is decreasing), (3) shows that the decision-maker’s first order condition effectively places more weight on models that have low expected utilities, through the ambiguity adjusted second order weights. Indeed, all else equal, an increase in the concavity of  always places more weight on models with low expected utility models in the first order conditions. If  (x) is very steeply decreasing (i.e.  is strongly concave), then priors that predict really poor outcomes will receive most of the weight in the first order condition. In the limit of very large concavity, only the prior with the lowest expected utility enters the first order condition, and we recover the GS model of ambiguity aversion. It is important to realize that the ambiguity adjusted second order weights (3) that appear in the first order condition depend on the endogenous variable a. Thus, the

3 Application to Environmental Policy Choices

FIGURE 3 Comonotonicity [left] and anti-comonotonicity [right].

fact that an increase in ambiguity aversion places more weight on models with low expected utilities in the first order condition does not imply that increasing ambiguity aversion has an unambiguous effect on optimal policies. Conditions that allow us to sign the effect of increased ambiguity aversion on policy choice are provided in a result by Millner et al. (2013): d 2 EUm da 2

< 0 for all m, and assume that for every fixed   m value of a the sequences {EUm (a)} and dEU are anti-comonotonic [comonoda tonic] in m. Then an increase in ambiguity aversion increases [decreases] the optimal level of the policy variable a. Proposition 5. Suppose that

Fig. 3 gives examples of anti-comonotonic and comonotonic sequences of expected utilities and marginal expected utilities. Policy intensity (e.g. conservation, greenhouse gas abatement) a is plotted horizontally and a set of expected utilities EUm is plotted vertically for a set of three distinct models. Anti-comonotonicity means that for each policy value the models with high expected utility have low derivatives of expected utility with respect to policy, and vice versa. When the anticomonotonicity condition holds an increase in policy will reduce the spread of expected utilities across models, so that a rise in aversion to ambiguity will increase optimal abatement. This simple model illustrates the basic workings of ambiguity aversion in static optimization models. Applying such models to environmental problems, in particular in more sophisticated dynamic contexts, is a topic of ongoing research. We next review some of the recent work in this area.

3.2 APPLICATIONS IN THE LITERATURE There is an emerging, but not yet extensive, literature on ambiguity in environmental economics; the idea is more firmly established in macroeconomics and finance. Most of the applications to dynamic environmental problems have focused on some aspect of climate policy. In an early paper, Lange and Treich (2008) survey the effects of

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ambiguity aversion on optimal policy choices in a simple two period discrete time model motivated by climate policy. Using a simple two period model, Chambers and Melkonyan (2017) show that the subjective expected utility, maxmin expected utility and incomplete expected utility theories can lead to radically different policy recommendations. Millner et al. (2013) develop the KMM framework used in the previous section and apply it to the ranking of exogenous dynamic climate abatement policies using Nordhaus’s DICE integrated assessment model, and the set of distributions over the ECS depicted in Fig. 1. They find that ambiguity aversion can have a substantial positive effect on the welfare benefits of greenhouse gas abatement if damage functions are steep. Lemoine and Traeger (2016) analyzes the consequence of ambiguity aversion in a climate model in which there are tipping points (regime changes in a complex dynamical system) whose locations are unknown. In their model ambiguity aversion increases the optimal tax on CO2 emissions, but only a little. Asano (2010) uses the Gilboa–Schmeidler approach to study the optimal timing of climate policy in a model that incorporates irreversibility, model uncertainty, and strong ambiguity aversion. A slightly different formulation of ambiguity aversion, known as ‘multiplier preferences’, has been developed by Hansen and Sargent (2001), and is becoming increasingly popular in macroeconomics. Macroeconomists have long recognized that it is often not possible to know the ‘correct’ model of the evolution of the economy and that as a result they must contend with multiple possible models. In this sense, the challenges they face are similar to those faced by economists concerned about climate change or biodiversity loss. Under the Hansen–Sargent approach, the analyst chooses a ‘best guess’ model or distribution, but is not sure that this distribution is correct. So the analyst allows for possible model misspecification and evaluates policy options according to her best guess as well as other distributions that are ‘similar’ to this guess. Distributions that are far from the best guess distribution are penalized by adding a non-negative cost term to the DMs objective function, which depends on a measure of the distance between the distribution and the best guess. Policy makers are assumed to have strong ambiguity aversion, and thus evaluate each action using the distribution that is most pessimistic for that action across the set of models in consideration, as in the Gilboa–Schmeidler framework. The multiplier preferences approach makes sense if there is a clear preferred model but we are not sure about some of its details. However, if there are several rather different models that are all serious candidates for the ‘best’ model, then this approach is not so attractive. That is, it may be a good approach for macroeconomists who think they more or less know the true model and only need to consider small variations around it, but it is not clear that it is appropriate for environmental issues, climate change in particular. However there is a return for this assumption – a tractable framework that allows us to identify analytical solutions to complex dynamic optimization problems, at least in the case of linear-quadratic models. Xepapadeas (2012) and Athanassoglou and Xepapadeas (2012) apply the Hansen– Sargent multiplier preference approach to climate problems. They consider models in which output produces a pollutant according to a stochastic process, taken to be

4 Conclusions

a Brownian motion. Possible misspecification of this process is captured, as in the macroeconomic work, by adding a weighted error term to the stochastic process, and then conducting a min-max expected utility calculation. By the magic of the linear-quadratic model assumption, this complex dynamic optimization problem permits analytical solutions. Vardas and Xepapadeas (2010) use this approach to study biodiversity management under model uncertainty. The effects of ambiguity and ambiguity aversion on social discount rates, essential inputs to the cost-benefit analysis of marginal environmental projects, have also been studied. Traeger (2014) studies the consequences of allowing for ambiguity about consumption growth rates or policy payoffs on the choice of a social rate of discount. Gierlinger and Gollier (2017) study the related question of how ambiguity affects equilibrium interest rates in a Lucas tree model, finding a term structure that is qualitatively different from the ambiguity neutral case.

4 CONCLUSIONS We have argued that profound uncertainty is endemic to the field of environmental policy. Arguably, traditional approaches to decision-making under uncertainty based on expected utility maximization are out of their depth in this area, as they force us to act as if we know things (i.e. unique probabilities) that we know we do not. Alternative decision frameworks based on the explicit recognition of multiple priors are naturally suited to the information we in fact possess about the consequences of environmental policy choices. These frameworks allow us to reflect our lack of confidence in our ability to discern between alternative probabilistic views of the world. The virtue of this approach is that it explicitly acknowledges the limitations of our knowledge, and allows us to exhibit preferences that are sensitive to this lack of knowledge. Applying these tools to environmental policy choice leads to new policy conclusions, which would be lost if all available information were forced into a single PDF.

REFERENCES Al-Najjar, N.I., 2015. A Bayesian framework for the precautionary principle. The Journal of Legal Studies 44 (S2), S337–S365. Al-Najjar, N.I., Weinstein, J., 2009. The ambiguity aversion literature: a critical assessment. Economics and Philosophy 25 (Special Issue 03), 249–284. Aldy, J.E., Viscusi, K., 2014. Environmental risk and uncertainty. In: Machina, M., Viscusi, K. (Eds.), Handbook of the Economics of Risk and Uncertainty, vol. 1. North-Holland, pp. 601–649. Arrow, K.J., Fisher, A.C., 1974. Environmental preservation, uncertainty, and irreversibility. The Quarterly Journal of Economics 88 (2), 312–319. Asano, T., 2010. Precautionary principle and the optimal timing of environmental policy under ambiguity. Environmental and Resource Economics 47 (2), 173–196. Athanassoglou, S., Xepapadeas, A., 2012. Pollution control with uncertain stock dynamics: when, and how, to be precautious. Journal of Environmental Economics and Management 63 (3), 304–320.

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Index A

B

Abatement costs, 240, 244–246, 251, 264, 272, 445 pollution, 240, 244–246, 251 Acute respiratory infections, 147 Adaptation, 33, 75, 123, 203, 207, 221, 239, 269, 319 costs, 33, 208, 215 strategy, 195, 212 Adjustment costs, 48, 92, 98, 202, 336, 355 Agricultural outcomes, 199, 205, 310, 319 profits, 318 sector, 206, 211, 319 Air conditioning, 218, 320 Air pollution, 150, 162, 176, 196, 304, 310, 324 ambient, 147, 174, 315 exposure, 146, 163, 218 indoor, 147, 159, 166, 171, 175 local, 292, 312, 316 outdoor, 147, 152, 174 regulations, 305, 315 Air quality, 74, 123, 287, 312, 315, 323 Alpha diversity, 70 Ambiguity aversion, 8, 160, 359, 457, 461 Amenity benefits, 290 Anthropocene, 269 Anthropogenic biosphere change, 62, 65 Anthropogenic climate change (ACC), 63, 318, 320, 325, 326 Asset market, 90, 95, 107 Asset prices, 94, 97, 112, 129, 131 equations, 111 natural, 130 natural capital, 87 stock, 91, 112 Assets, 23, 31, 70, 86, 95, 103, 125, 241, 247 Assimilative capacity, 65 Asymmetric information, 233, 243 Atmosphere, 6, 35, 46, 247, 269, 318, 365–371, 379 Atmospheric carbon concentration, 338, 365, 367, 370, 372, 377, 385, 444 Atmospheric carbon stocks, 88 Average exposure effect estimator (AEEE), 287, 302, 315, 324 Average source effect estimator (ASEE), 287, 300, 311 Average treatment effect (ATE), 294 Averting behaviors, 151–162, 176

Balanced growth, 352 Baltic Sea, 106, 121, 129 Banking, 241, 247, 261 Baseline human capital, 160, 176 Baseline model, 8, 16 Baseline temperature, 24 Behaviors household risk-averting, 154 individual, 233, 243 prosocial, 424 Benchmark model, 8, 32, 37, 336, 362, 371, 377 Bifurcations, 35, 76 Biodiversity, 2, 62, 70–76, 240, 249, 270, 275, 399, 446, 456, 461 anthropogenic, 61, 62, 70, 72, 76 change, 71 conservation, 447, 461 loss, 269, 440, 446, 457, 461 offsets, 240, 249 portfolio, 70, 73, 75 Bioeconomic model, 131 full dynamic, 121 Biomass, 3, 448 Budget, 367, 416 cumulated carbon, 13 world carbon, 26 Bureaucrats, 149, 177, 179, 180, 184

C Cap-and-trade markets, 314, 322 Capital assets, 86, 98, 102, 134 natural, 92, 98, 107, 125, 130 depreciation, 98, 352 gains, 88, 93, 96, 98, 99, 101, 107, 108, 111–113, 116, 121, 126, 129 markets, 90, 94, 106, 210 incomplete, 167 international, 218 prices, 101 natural, 87, 96, 130 stocks, 70, 87, 91–95, 98, 104–108, 111, 116–119, 121–125, 130, 321, 365 aggregate, 360 decoupled, 125 distinct natural, 133 explicit, 102 initial, 108, 353, 387

469

470

Index

multiple coupled, 111 multiple interacting, 121 non-environmental, 119 residual, 102 society’s, 86 underlying, 104, 118, 124 underlying natural, 123 Capital–output ratio, 335, 341, 350, 358 Carbon circulation, 365 Carbon concentration, 338, 367, 372, 377, 385 Carbon cycle, 24, 338, 365, 379 Carbon dioxide, 323, 365 Carbon emissions, 13, 15, 63, 237, 257, 258, 360, 365, 369, 377, 379, 413 cumulated, 13 Carbon leakage, 256, 262, 271 Carbon monoxide, 312, 316 Carbon prices, 262, 272 Carbon sequestration, 74, 125 Carbon taxes, 247, 253–261, 263, 273, 377, 380, 384, 387 Carrying capacity, 65, 121 Causal models, 397, 406 Central authority, 33, 245 Chebyshev polynomials, 109 Childhood diarrhea, 147 Choice experiments, 157, 166 Clean air, 157, 272, 292 Clean Air Act (CAA), 236, 251, 287, 301, 312, 322 Clean Water Act, 236 Climate adaptation, 212, 219 Climate change, 4, 12, 19, 28–35, 75, 102, 117, 144, 180, 194–223, 233, 241, 245, 253, 260, 269, 274, 319, 325, 334–339, 358, 363, 366–371, 382, 387, 391, 440–448, 456, 464 costs of, 337 global, 33, 271, 323, 388 impacts, 8, 200, 204, 327 long-run, 320 policy, 21, 45, 317, 323 potential role, 31 regional, 368 slow rapid, 218 Climate clubs, 272 Climate dynamics, 20, 24, 27, 29 Climate economics, 11, 20, 32, 195 Climate models, 32, 196, 336, 364, 383, 441, 444, 464 downscaled, 208 global, 441 temperature dynamics, 14 Climate policy, 249, 260, 272, 337, 354, 359, 390, 441, 445, 464 Climate regulation, 74

Climate science, 14, 39, 48, 194, 441, 446 Climate scientists, 14, 21, 39, 183, 375 Climate sensitivity, 8, 12, 24, 103, 203, 208, 338, 367, 382 Climate shocks, 209, 213, 222 Climate system, 13, 23, 196, 338, 440 Closed-form solutions, 374, 377, 379 CO2 emissions, 257, 366, 464 Coal, 20, 35, 221, 238, 247, 258, 263, 274, 315, 360, 362, 363, 372, 378, 381, 385–387, 390 Collective action, 33, 233, 270, 397, 409, 417, 423 Common pool resource (CPR), 232, 234, 239, 246, 408, 413, 421 Communal forest management, 417 Communities, 70, 126, 132, 160, 177, 233, 248, 396, 409, 420–425 local, 179, 183, 202, 232, 240, 422 Community forest management (CFM), 405, 415, 421 Community Led Total Sanitation (CLTS) interventions, 170 Community management, 415, 422 Conceptualizing natural capital, 88 Conditional independence assumption (CIA), 402, 424 Conservation instruments, 396–399, 412, 416, 422 Conservation interventions, 396, 417, 423 Consumption, 3, 13, 22, 29, 70, 104, 116, 125, 148, 153, 158, 195, 200, 219, 232, 237, 243, 268, 286, 339, 350–356, 364, 378, 388, 443 Consumption discount rate, 29 Contingent valuation method (CVM), 157 Continual bioeconomic equilibrium, 121 Control groups, 286, 288, 296, 302, 317, 401 Control units, 288, 295, 304, 314, 324, 401 Corporate taxes, 255 Cost benefit analysis (CBA), 12 Cost effectiveness analysis (CEA), 13 Countries, 25, 31, 146, 148, 197, 206, 245, 249–274, 287, 301, 312, 316, 319, 324, 336, 341, 361, 369, 387, 404, 411, 417, 426, 445 Brazil, 196, 211, 218, 404, 413, 419 Chile, 404, 415 China, 163, 206, 211, 222, 268, 271, 315, 400, 406 Costa Rica, 399, 404, 413, 419 Denmark, 256, 264, 265 Ecuador, 404, 412, 420, 423 Finland, 254 Germany, 215, 264 higher-income, 243, 268, 271 India, 167, 171, 178, 206, 211, 239, 271, 315 Indonesia, 166, 176, 400, 413 lower-income, 198, 248, 252, 271

Index

Mexico, 118, 120, 128, 400, 404–406, 413, 415–419, 421, 423, 425 middle income, 144, 183, 403 Nepal, 163, 423, 425 Norway, 149, 177, 254, 256, 264 Peru, 404, 415, 419 poor, 197, 370 Sweden, 254–257, 263–265, 380, 389 Thailand, 413, 414, 419 the UK, 256, 267 the United States, 163, 179, 207, 211, 214, 236, 239, 243, 252, 259, 261, 263, 312, 314, 318, 335, 339 Countryside, 194, 210, 214, 217 Countryside natural capital, 217 Credit institutions, 241 Crops, 196, 200–211, 319, 323, 447 Cross-stock effects, 99, 121, 129 Cultural services, 71, 74 Cumulated carbon response parameter (CCR), 13 Cumulative carbon budgeting, 4, 11, 19, 29, 39 Current value Hamiltonian (CVH), 96 Cycles, 63, 132

D Damage elasticity, 382 Damage functions, 5, 8, 12, 19, 25, 35, 39, 45, 246, 370, 379, 442, 464 Damage reservoir, 35 Decentralization, 246, 396, 403, 415, 420, 425 policies, 409, 418, 425 reform, 420 Decentralized market institutions, 21 Decision-makers (DMs), 7, 32, 36, 64, 75, 250, 261, 410, 450, 455, 464 Deforestation, 152, 248, 271, 404, 411–415, 419–421 Depreciation rate, 357, 378 Deterministic model, 38, 101, 118, 153, 359 Developed countries, 25, 145, 361 least, 197 Developing countries, 206, 218, 388 Developing world, 194, 202, 211, 217, 273, 388 Diarrhea, 144–148, 151–153, 162, 164, 168, 171, 172, 174, 176, 177 DICE model, 25, 34, 365, 375, 445 Diesel, 258, 389 Difference-in-difference (DID), 174, 296, 307 Discount rates, 8, 19, 29, 48, 96, 104, 112, 116, 159, 233, 241, 380, 388, 443 Diseases, 64, 144–152, 158, 183, 195, 447 malaria, 146 Distortionary taxes, 238, 377 Dividends, 93, 101, 116, 239, 253 double, 237

Domestic environmental issues, 275 Donors, 177, 179, 182 Double dividend, 237, 238 Downwind locations, 287, 298, 314 Durable capital, 207 Dynamics climate model, 14

E Earnings, 195, 213, 292, 313, 321 Ecological damage, 249 Ecological modeling, 32 Ecological systems, 3, 62–64, 73, 93, 113, 132, 243, 416, 425 Ecology, 63, 71, 76, 148, 182 human, 144, 152 Economic activity, 336, 349, 370, 389, 442 Economic agents, 2, 65, 222 Economic costs, 316, 319, 446 Economic damages, 320, 338, 383 Economic development, 180, 220, 275 Economic efficiency, 244 Economic growth, 32, 62, 65, 86, 219, 370, 445 Economic program, 70, 76, 89–106, 110, 115–123, 132 Economic systems, 2, 63, 209, 440 Economists, 13, 21, 61, 70, 86, 97, 107, 118, 132, 144, 167, 174, 181, 196, 213, 233, 260, 269, 335, 374, 396–403, 407, 418, 426, 453, 464 environmental, 73, 127, 133, 244, 264, 288, 324, 337 Economy closed, 31, 351 human, 2, 269 real-world, 374 Ecosystems, 2, 32, 67–75, 125–132, 147, 239, 269, 413, 422 coupled, 3, 33 health, 272 income, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114–128, 130, 132, 134 local, 274 management, 3, 9 productivity, 448 services, 3, 71, 86, 94, 98, 106, 117, 122, 125, 132, 232, 240, 248, 269, 413 wealth, 106, 128 Effects heterogeneous, 415 moderating, 411, 417 price, 99, 299, 326 Elasticity, 197, 206, 259, 356, 443 Emission taxes, 262

471

472

Index

Emissions, 3, 13, 23, 46, 166, 171, 179, 196, 222, 237, 251, 260, 271, 287, 366, 378, 384, 441, 443 cumulative, 28 price, 260 uncertainty, 441 Emissions trading scheme (ETS), 254, 256, 260–262 Endogenous technical change, 339, 384 Energy, 241, 255, 337, 339, 361, 371, 389 market, 384, 389 prices, 339, 349 real price of, 337, 361 renewable, 241 representative, 21 share, 18, 337, 350, 361, 389 sources, 46, 242, 361, 372, 381, 391 tax, 21, 254 use, 18, 22, 268, 337, 348–350, 377, 380 Energy balance climate models (EBCMs), 23, 34 Energy-budget models, 368 Enforce policies, 243 Environment, 62, 65, 89, 127, 144, 161, 182, 234, 238, 252, 267, 268 natural, 65, 161, 234 Environmental amenities, 122, 133, 146, 157 conditions, 66, 72, 183, 201 conservation, 395–400, 411 damage, 245, 251 economics, 31, 94, 124, 183, 246, 286, 288–295, 300, 308, 321, 369, 440, 453, 463 exposures, 153, 170, 175, 286 goods, 62, 119, 248, 286, 288, 306, 311, 323 hazards, 146, 148, 175, 180 health, technologies, 144–146, 150, 151, 155, 158, 159, 161–163, 166, 167, 171, 174, 175, 177–180, 183, 184 justice, 150, 251 management, 152 perturbations, 72 policies, 232, 239, 251, 254, 270, 273, 286, 309, 314, 321, 449, 461 national, 273, 311 protection, 148, 155, 246, 413 quality, 116, 122, 146, 154, 160, 236 refugees, 216 regulations, 220, 234, 245, 292, 316, 323 risk reductions, 145, 150, 155, 156, 163, 166, 181 risks, 144, 148, 155–163, 167, 171, 174–183 service provision, 149, 180, 248 taxes, 237, 258, 265 Environmental health, 144, 148, 161, 175, 181 damages, 149

risk reductions, 150, 179 risks, 153, 177, 182 technologies, 144, 150, 159, 167, 171, 178 Environmental risk reducing technologies, 167 Epidemiological externalities, 175 Equilibrium climate sensitivity (ECS), 444 competitive, 4, 21, 338, 355, 360, 371, 379, 386 conditions, 29, 177, 376 market, 3, 355, 372 natural, 66 permit price, 322 price, 261, 388 price changes, 197 solution, 18 value, 39 Evil agent, 8 Exchange values, 91 Existence value, 4 Exogenous prices, 106 Expected utility, 153, 155, 216, 448, 456, 462 households maximize, 153 marginal, 155, 463 maxmin, 7, 455, 464 Expected utility model, 440 External validity, 182, 408, 412, 426 Externality damage, 377 Externality spillovers, 287, 293, 298, 304, 324

F Factors institutional, 412, 420 time-invariant, 403 Farmer climate adaptation, 210, 211, 213, 215 Farmers, 117, 194, 210, 213, 238, 246, 319, 447 poor, 194, 209 small, 210 Fees, 237, 262 Fenichel and Abbott shadow price, 129 Fertilizer, 202, 326 Finite supply, 362, 390 Fish stocks, 86, 121, 129, 235 Fisheries, 2, 66, 120, 129, 235, 248 Fluctuating environmental conditions, 73 Forestry, 272, 421 Forests, 63, 236, 248, 270, 400–425, 462 Fossil fuels, 17, 24, 35, 41, 221, 239, 242, 251, 255, 349, 375, 385, 389 Fuel prices, 255, 258, 361 higher, 259 Fuel taxes, 253, 258, 259 Fuels, 71, 151, 255, 389 Functional diversity (FD), 72, 75

Index

G Gamma diversity, 71 Gases, 21, 45, 260 Gasoline, 238, 251, 258, 389 General Circulation Models (GCMs), 196 General equilibrium effects, 125, 181, 195, 209, 216, 325 Genetic variation, 447 Genuine savings, 104 German regulations, 266 Global average temperature, 14, 25, 29, 41 Global markets, 245, 387 Global mean temperature (GMT), 16 Global warming potential (GWP), 21 Goods, 71, 74, 88, 120, 125, 150, 202, 334, 352, 386 capital, 98, 357 health-producing, 291, 299 marketed, 119 Government subsidies, 118, 208 Greater Yellowstone Area (GYA), 63 Green technology, 222, 385 Greenhouse gases (GHGs), 3, 12, 21, 35, 45, 196, 203, 247, 365, 441 emissions of, 15, 34, 74, 194, 196, 221, 255, 268, 318, 325

H Habitats, 93, 121, 152, 249 Hamiltonian, 18, 46 current value, 5, 17, 19, 96 Harmful environmental exposures, 153 Hazardous airborne pollutants (HAPs), 316 Health biomarkers, 174 Health burdens, 145, 183 environmental, 150, 183 Health impacts, 145, 160, 171, 182, 314 Health production, 154, 160 Health risks, 153, 176 changing environmental, 184 environmental, 146, 153, 177, 182 multiple, 176 reducing environmental, 182 Hedonic price models, 112, 123 Hot spot research, 35 Household averting behavior, 154 Household income, 167, 195, 405, 417 Household production, 119, 122–128, 144, 154, 155, 158, 160, 167, 175, 177, 183 Household wealth, 419 Households, 65, 120, 144–183, 194, 212, 219, 237, 251, 287–294, 303, 316, 320, 401, 412, 417–425 risk averse, 178 Housing market, 123, 312, 317 Housing prices, 317

Housing values, 310, 312, 316, 323 Human behavior, 77, 93, 108, 115, 118, 125, 132, 161, 396 Human capital, 3, 86, 89, 131, 150, 160, 174, 180, 194, 211, 214, 219, 222 accumulation, 219 Human health, 144, 147–152, 181 Human populations, 64, 248 Human wellbeing, 243

I Identification problems, 292 Illnesses, 153, 155, 157 Improved cookstoves, 146, 152, 159, 167, 174 Improved water sources, 152 Inclusive wealth, 76, 87, 91, 104, 131 Income, 90, 97, 116, 120, 128, 131, 156, 167, 174, 194, 198, 211, 259, 268, 356, 388, 404, 419 flows, 86, 90, 92, 95, 110, 126 index, 93, 102 inequality, 211 real, 93 Individual tradable quota (ITQ), 129 Individual transferable quota (ITQ), 66, 128 Indoor air pollution, 147, 151, 159, 166, 171, 175 Indoor residual spraying (IRS), 157 Infant health, 316 Infant mortality, 174 Infection externalities, 158, 160 Infections, 150, 176, 179 Infectious disease risk, 217 Infectious diseases, 144–150, 153, 159, 162, 181, 217 Informal community institutions, 409 Informal institutions, 88, 412, 419, 422 Information asymmetries, 245, 396 Input markets, 125, 355 Institutional arrangements, 90, 92, 235 Institutional mechanism, 409, 423 Institutional moderators, 408, 416–419, 423 Institutions community, 409, 416, 423 decentralized market, 21 formal market, 90 international, 87 local, 396, 417 market, 21, 90 real-world imperfect, 88 Instrumental variables, 174, 195, 297, 309, 325, 401 International capital markets, 218 climate negotiations, 249 environmental agreements, 271 environmental organizations, 397

473

474

Index

institutions, 87, 447 International Forestry Resources and Institutions (IFRI), 415 International Rice Research Institute (IRRI), 447 International trade, 217, 327 International treaties, 242, 271 Intertemporal welfare, 87, 98, 100, 106 Interventions, 62, 64, 145, 160, 170, 174, 182, 386, 403, 405, 416, 419 Invested capital, 98 Investment, 3, 89, 99, 155, 207, 210, 214, 218, 232, 239, 256, 260, 336, 351, 355, 407, 425 Irreversibilities, 5, 440, 464 Irreversible damages, 265

L Labor market, 157, 288, 355 Labor market outcomes, 310 Labor productivity, 195, 315, 342, 370, 442 Labor shares, 346, 357 Laissez-faire, 373, 378, 381 Lakes, 4 Land markets, 90, 125, 210 Land parcel, 213, 222 Land tenure, 412 Land values, 292, 318 local, 219 Leakage, 271, 389, 403, 405, 422 Least developed countries (LDC), 198, 211, 217 cities, 215 nations, 215, 218 Lindahl–Samuelson condition, 289, 321 Linearization, 358 Literature review, 306 Lobbies, 238, 249, 251, 259–261, 263, 265 Local, 23, 31–33, 35, 67, 68, 74, 91, 106, 116, 123, 130, 133, 148, 150, 156, 157, 159, 177–179, 183, 194, 195, 202, 205–207, 209, 213, 216–220, 232, 233, 236, 240, 242, 245, 246, 249, 250, 258, 265, 272, 274, 287, 289, 292, 297, 302–306, 310–312, 315, 316, 318, 323–327, 388, 390, 395–399, 404–406, 411, 413, 417–425 climate, 23, 31–36, 74, 148, 150, 194, 195, 202, 205–207, 209, 213, 218–220, 245, 272, 274, 318, 325, 326, 387, 388, 390 conditions, 209, 218, 220, 318, 325, 326 regime, 206 shocks, 195, 209, 318 community institutions, 423 damages, 31, 35, 245, 387 institutions, 150, 156, 250, 395–399, 417–424 regulation, 35, 74, 220, 240, 246, 265, 272, 292, 311, 312

taxes, 33, 35, 150, 219, 242, 249, 258, 397 Local labor markets, 216 Local leaders, 177, 218 Local officials, 218 Local people, 396 Local public goods, 157, 218, 287, 302, 324 Local resource users, 413, 424 Local temperatures, 23, 32, 315, 388 Local welfare, 398, 406 Local well-being, 424 Locals, 123, 289, 404 Locations downstream, 287 downwind, 287, 298, 314 Logarithmic utility, 18, 19, 25, 27, 371, 378, 380, 388 Lotka–Volterra model, 66 Lotteries, 440, 449, 455 Low and middle income countries (LMICs), 144–150, 153–157, 161, 167, 175, 179

M Macroeconomics, 7, 334, 337, 351, 374, 440, 464 Malaria, 144–148, 153, 157, 162, 171, 176 carrying mosquitos, 152 eradication programs, 171, 174 vaccines, 166 Management policies, 48, 128 Marginal benefits, 158, 177 Marginal costs, 155, 158, 177, 180, 244, 290, 306, 311, 321, 362, 390 general-equilibrium, 321 social, 47 Marginal economic agent, 223 Marginal price, 98 Marginal private cost, 289, 321 Marginal social benefit, 287–291, 306, 309, 317 Marine protected areas, 248, 400, 411, 415 Market allocation, 244, 363 Market asset prices, 90 Market commodities, 87, 157 Market economy, 336, 339, 379 Market equilibrium, 291, 355, 372 Market failures, 106, 232–235, 239, 243, 250 Market goods, 120, 125, 127, 195 Market imperfections, 88, 149 Market prices, 90, 102, 237, 322, 369 Market production, 120 Market transactions, 127 Maximizing agent, 9, 17, 37 Meat consumption, 253, 268 Metapopulation models, 32 Methane, 21, 45, 196, 272, 365 Mickey-Mouse model, 378 Migration, 207, 214, 387

Index

international, 215 rural to urban, 214 Model uncertainty, 7, 38, 441, 464 Models box, 25 business-cycle, 358, 375 carbon-cycle, 336, 365, 369, 375 complex, 374 general-equilibrium, 336 hedonic, 157, 166 long-run, 352, 364, 378 positive, 381, 440 quantitative, 375, 378 standard, 289, 327 structural, 119, 365 travel cost, 116, 163 Moderators, 398, 408, 416, 424 Monopoly, 233, 244, 363 Mortality rates, 315, 319, 326 Multi-region modeling, 387 Multiple risks, 145, 175

N Nash equilibrium, 5, 17, 44 dynamic, 40 National accountants, 91, 128 accounts, 127, 339, 385 institutions, 418 policies, 256, 272, 311 Natural assets, 70, 87, 91, 125 Natural capital, 6, 62, 75, 86–134, 217, 447 asset prices, 91, 100, 115, 121 flow, 89 pricing, 91, 99, 102, 107, 120, 132 shadow prices, 91, 119, 129 stocks, 86, 91–99, 108, 118–127, 132 valuation, 86, 89, 108, 116–119, 122–127, 131 wealth, 87, 118 Natural disasters, 146, 148, 158, 180, 211–214, 217, 219, 222 Natural ecosystems, 2, 67 Natural experiments, 174, 195, 212, 293, 401 Natural gas, 221, 360 Natural hazards, 71, 149 Natural resources, 2, 65, 86, 194, 248, 270, 360, 397, 411, 418, 422 exhaustible, 75 non-renewable, 391 Nature, 8, 17, 73, 108, 132, 144, 148, 177, 232, 238, 250, 338, 359, 364, 409, 459 Negative externalities, 27, 232, 248, 267 Net benefits, 90, 93, 119 Net economic benefits, 182 Net income, 119, 127

Net profits, 200, 205 Network externalities, 234 Neyman–Rubin model, 396, 426 Nitrogen oxides (NOx ), 263, 314 Non-convexities, 100, 181, 232 Non-differentiability, 92, 100 Non-point source pollution (NPSP), 246 Noncompetitive markets, 233

O Objective function, 65, 178, 464 Oceans, 25, 270, 365–369, 411 Oil, 263, 348, 360–365, 372, 378, 379, 381, 388 Oil market, 259, 363 Oil price, 388 Omitted variables bias (OVB), 206, 313 Optimal allocation, 378, 381 Optimal control, 3, 46 Optimal public good provision, 289 Optimal tax, 21, 26, 377–382, 384, 464 Ordinary least squares (OLS), 292 Outdoor air pollution, 147, 152, 174, 176 Output markets, 117, 125, 355 Ozone, 312

P Packages DYNARE, 376 TEFFECTS, 403 Paleoclimate reconstructions, 196 Parameter selection, 356, 374 Parameterized damage function, 13, 39 Payments, 233, 238, 248, 253, 263, 396, 412, 415, 423 collective, 417, 422 Payments for ecosystem services (PES), 238, 240, 399 program, 406, 412, 417, 422 Perfect market, 234 Permit prices, 254, 261 Persistent weather shocks, 213 Perturbations, 67, 72, 367 environmental, 72 Pest regulation, 74 Pigouvian taxes, 238, 262 Planetary boundaries, 250, 269, 270, 272–275 Planning problem, 371 Policy failures, 234, 243 Policy instruments, 13, 232, 234, 242, 246, 250, 265, 270, 399 traditional, 236, 269 Policymakers, 129, 132, 182, 246, 254, 258, 264, 374 Political economy, 146, 175, 177, 182, 218, 235, 243, 249, 259, 263, 311

475

476

Index

Political institutions, 243 Political processes, 249 Politicians, 149, 177–184, 235, 245, 258, 273 Pollutants, 3, 9, 244, 260, 270, 274, 312, 464 Polluters, 239, 249, 261 Polluting firms, 263, 287 Polluting industries, 262, 308, 315 Pollution, 3, 49, 51–53, 144, 146, 147, 149–152, 154, 157, 159, 162, 163, 166, 170, 171, 174–177, 181, 182, 195, 196, 218, 236, 239, 240, 244–246, 249, 251, 252, 262, 271, 272, 274, 287–289, 291, 292, 298, 299, 302–305, 309–317, 322, 324, 325, 328, 399 abatement, 289, 299 capacity, 3 abatement costs, 240, 244 ambient, 176, 312, 315 control, 262, 399 exposure, 146, 147, 163, 218, 287, 298, 310, 324 local air, 310 local, 292 sources, 305, 325 spillovers, 314, 324 taxes, 245, 249 victims of, 239, 249, 252 Polymerase chain reaction (PCR), 446 Poorer households, 303 Poorest rural households, 179 Population growth, 198, 221, 352, 357, 380, 391 Portfolio choice problem, 73 Portfolio effects, 72 Potential outcomes, 287, 294, 299, 317, 325, 397, 400, 408, 416 Poverty, 184, 211, 273, 404, 414, 419, 425 Precautionary principle, 20, 250, 265 Precipitation, 35, 74, 196–201, 317, 404 Preference methods revealed, 126, 157, 158, 166 stated, 126, 156, 157, 163, 166 Preference relation, 451 Preference surveys, 126, 158 Preference techniques, 126 Prevailing institutions, 117, 120 Price elasticities, 259, 267 Price instrument, 253 Price mechanism, 100, 246 Price subsidies, 159, 161 Price-type instruments, 237, 253 Private capital, 98 Private good, 289–292, 302, 303, 306, 322 Producer surplus, 94, 120 Producers, 178, 197, 210, 240, 244, 289, 362, 388

Production, 2, 18, 74, 93, 98, 125, 128, 202, 204, 207, 221, 232, 237, 240, 243, 255, 271, 289, 361, 372, 389 agricultural, 215 Production function, 6, 119, 202, 357, 361, 372, 387 Productivity, 73, 99, 125, 147, 158, 180, 220, 309, 310, 315, 326, 342 marginal, 98, 290 total factor, 70, 76, 102, 220 Productivity benefits, 290, 316 Profits, 22, 93, 116, 201, 220, 318, 356 Program evaluations, 401, 406, 410, 424 Property rights, 66, 86, 89–91, 126, 146, 210, 232, 233, 235–237, 239, 240, 247, 252, 273, 397–399, 406, 416, 419, 421, 422 Public goods, 90, 212, 232, 243, 286, 287, 289–294, 298–306, 315, 318, 321, 324, 325, 400 exposure, 291, 297 provision, 289 spillovers, 287, 299

Q Quantitative analytical IAMs, 378 Quantitative IAM, 371 Quasi-experimental methods, 118, 162, 181, 288, 308, 318, 324 Quotas, 4, 209, 239, 337, 390

R Randomized controlled trial (RCT), 406 Rational choice, 339, 449, 457, 461 Rationality, 449, 456 Real interest rate, 362, 387 Recreation demand models, 124 Recursive equilibrium, 360, 376 Refunded emission payments (REP), 263 Regression discontinuity (RD), 297 Regulating services, 71, 74, 75 Renewable natural resources, 248, 397 Renewable resources, 4 Reproducible capital, 90 Reserves, 40, 275, 362, 414, 422 safety, 17, 38 Resilience, 62, 67, 75, 241, 269 Resource allocation, 247, 461 Resource management, 2, 32 natural, 2, 247, 418, 421 Resource problems, 251, 260 standard exhaustible, 16, 40 Resource stocks, 117, 124 natural, 397, 399 Resources ecosystem, 234, 269 finite, 247, 336, 364

Index

Respiratory infections, 146, 147, 153, 162 Revenue recycling, 238, 264 Revenues, 21, 130, 238, 252, 262, 373 Ricardian models, 205 Rice, 201, 206, 447 RICE model, 34, 336, 367, 375 Rights-based policies, 239 Risk averting technologies, 146 Risk management, 241 Risk reducing technologies, 150 environmental, 167 Risk reductions, 150, 177 Robust control, 7, 16, 27, 42, 103 Robust control theory, 9, 20 Rural Indian households, 177 Rural people, 210, 215–217

S Sanitation, 159, 167, 178, 218 Savage axioms, 449, 453–459 Scarce environmental resources, 245 Scarce resources, 210 Scientific uncertainty, 250, 441 Service flows, 76, 89, 123, 132 Services, 62, 71, 74, 89, 119, 124, 150, 166, 178, 195, 202, 219, 232, 240, 251, 263, 269, 389 cultural, 2, 71 non-market, 116, 125 provisioning, 71 regulating, 71, 74 Shadow prices, 19, 40, 44, 47, 48, 70, 87–89, 91, 93, 95–102, 104, 106–110, 112, 113, 119–121, 126, 128, 129, 131, 322 function, 40, 100, 108, 128 marginal, 126 optimal, 91, 101 recovering, 88, 102 Shadow values, 5, 46, 103, 118, 125, 129 Simple analytical model, 461 Single exposures, 176 Single stock, 65, 97, 98, 101, 108, 110, 112 Smoking, 267 Social benefit-cost analysis, 94, 133 Social capital, 210, 412, 423 Social cost of carbon (SCC), 241, 261, 325, 371, 378, 442, 443 Social marketing, 171 Social norms, 234, 417, 424 Social preferences, 159, 246, 396, 443 Social welfare, 86, 93, 94, 179, 233, 240, 246, 251, 443 Social well-being, 76 Socially mis-priced markets, 291

Society, 35, 89, 93, 98, 119, 146, 148, 233, 244, 250–255, 269, 272, 386 Sorting models, 95, 174 Spatial transport phenomena, 4, 11, 23, 35 Spatial units, 206, 411 Species, 63, 66, 70–75, 119, 125, 130, 447 competition, 2 distinct, 71 Spillover likelihoods, 287, 304–306, 317, 324 Spot price, 89, 247 Stable equilibrium, 67 Stable unit treatment value assumption (SUTVA), 408 Standard capital theory, 88 Standards versus taxes, 246 Steady state, 3, 44, 106, 114, 128, 355, 367, 375 best, 44 Stochastic dynamics, 92, 102 Stochastic stock dynamics, 103 Stock asset price, 112 changes, 101, 104, 357 consumption, 4 dynamics, 53, 92, 95, 103 Subjective expected utility, 440, 449, 455, 458, 464 Subpopulations, 182, 297, 317, 401 Subsidies, 159, 167, 177, 222, 235, 237, 244, 251, 259, 264, 377, 387, 397, 400 fossil fuel, 259 price, 159 Suppliers, 171, 177 Supranational policies, 236 Sustainability, 62, 66, 86, 100, 128, 171, 182 criterion, 87 measuring, 119, 128 Sustainable development, 86 Sustainable management, 130, 241, 400, 422 SUTVA violation, 300, 302, 306, 314 Swedish taxes, 256 System climate-economy, 442 coupled, 3, 62, 75 Earth, 269 federal, 233 linear, 366, 376 natural, 63, 66, 194 natural resource, 67 over-determined, 115 social, 64, 442 social-ecological, 416 stability, 69 Systematic reviews, 163, 167, 171, 397, 403–405

T Tax revenues, 238, 254, 262

477

478

Index

Taxation, 98, 240, 254, 260, 268 Taxes, 3, 6, 21, 22, 33, 35, 48, 53, 97, 98, 150, 219, 236–239, 242, 244–246, 249, 251–264, 268, 269, 273, 337, 354, 355, 373, 377, 381, 388–390, 397 emission, 262 local, 150, 258 pollution, 249 value-added, 255 Temperature, 13, 23, 34, 43, 74, 103, 194–200, 207, 220, 292, 310, 315, 320, 325, 365–372, 379, 441 dynamics, 16, 43 Temperature response, 28, 207, 368 Temperature-mortality relationship, 320 Tipping points, 6, 35, 101, 269, 338, 366, 379, 464 Total factor productivity (TFP), 102 Tough regulation, 265 Toxic plant, 317 Tradable permit instruments, 249 Trade, 245, 251, 256, 261, 271, 327, 389 Tradeoffs, 109, 127, 151, 159, 166, 215, 386 Traffic control policies, 315 Transaction costs, 89, 202, 396 Transportation costs, 90, 125, 389 Treaties, 270 Treatment assignment, 286, 293 Treatment effects, 296, 402, 408, 417 population average, 294 Treatment of interest, 297 Treatment spillovers, 288 Trichloroethylene (TCE), 264 Trust, 210, 396, 409, 417, 423 Twin exposures, 176

U Unauthorized deforestation, 420 Uncertainty, 7, 12, 16, 32, 103, 195, 245, 251, 261, 270, 274, 299, 336, 358, 368, 375, 439–456, 459, 462 additive, 38 aversion, 454 high structural, 7 multiplicative, 16, 38 scientific, 250, 441 socio-economic, 441 subjective, 440, 456 Unemployment, 238, 257, 351 Uniform world-wide price, 27 United Nations Framework Convention on Climate Change (UNFCCC) Kyoto Protocol, 271 Unpaid externalities, 259

Unregulated market equilibrium, 3 Urban district heating, 256 Urbanization, 102, 195, 219 Utility function, 4, 17, 29, 39, 48, 156, 234, 289, 353, 455

V Valuation contingent, 166 ecosystem services, 73, 132 marginal, 119 non-market, 122, 182 Violence, 210, 217, 446, 457 Von Neumann Morgenstern expected utility theorem, 451 Von Neumann Morgenstern independence axiom, 454

W Warmer climate, 205, 387 Water, 118, 125, 128, 152, 157, 170, 178, 179, 182, 194, 218, 232, 239, 246, 252 contamination, 150, 170, 176 pollution, 144, 149, 152, 157, 162, 163, 176, 195, 218, 311 abatement, 287 regulations, 315 quality, 71, 170, 236, 240, 315 Waxman–Markey policy, 323 Wealth, 75, 86, 91, 107, 127–133, 167, 235, 255, 360, 419 metrics, 105, 129 Weather, 201–207, 317 local, 209, 318, 326 shocks, 195, 202, 203, 213, 318, 319, 387 Weighted average source effect estimator (WASEE), 305, 324 Welfare, 13, 86, 97, 104, 119, 197, 260, 263, 292, 404 social, 86, 93, 150, 179, 233, 240, 251, 443 weights, 25–27, 30 Wholesale electricity prices, 291 Workers, 213, 220, 288, 292, 313, 321 low skill, 216 World capital markets, 31 World Health Organization, 144 World market price, 27, 389 World quality adjusted prices, 220 World trading market, 27 Worst case model, 16

Z ZIP codes, 208, 317