Agent Based Models for Economic Policy Advice: Sonderausgabe von Heft 2+3/Bd. 228 Jahrbücher für Nationalökonomie und Statistik 9783110508840, 9783828204478

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Agent-Based Models for Economic Policy Advice

Herausgegeben von Blake LeBaron, Waltham, MA, USA und Peter Winker, Gießen

Mit Beiträgen von Axhausen, Kay W., Zürich Beuck, Ulrike, Berlin Chen, Yu, Berlin Dawid, Herbert, Bielefeld Demary, Markus, Kiel Gemkow, Simon, Bielefeld Grether, Dominik, Berlin Haber, Gottfried, Klagenfurt Harting, Philipp, Bielefeld

Lucius &c Lucius • Stuttgart 2008

Kabus, Kordian, Bielefeld Nagel, Kai, Berlin Neugart, Michael, Bozen Rieser, Marcel, Berlin und Zürich Veit, Daniel, Mannheim Weidlich, Anke, Mannheim Wersching, Klaus, Bielefeld Westerhoff, Frank H., Bamberg

Anschrift der Herausgeber des Themenheftes Blake LeBaron The Abram L. and Thelma Sachar Professor of International Economics International Business School Brandeis University, Mailstop 32 Waltham, MA 0 2 4 5 4 - 9 1 1 0 USA E-Mail: [email protected] Professor Dr. Peter Winker Justus-Liebig-Universität Gießen Licher Straße 64 3 5 3 9 4 Gießen E-Mail: [email protected]

Bibliografische Information der Deutschen Nationalbibliothek Die Deutsche Nationalbibliothek verzeichnet diese Publikation in der Deutschen Nationalbibliografie; detaillierte bibliografische Daten sind im Internet über http://dnb.d-nb.de abrufbar ISBN 978-3-8282-0447-8

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Jahrbücher f. Nationalökonomie u. Statistik (Lucius & Lucius, Stuttgart 2008) Bd. (Vol.) 228/2+3

Inhalt / Contents Abhandlungen / Original Papers Blake LeBaron, Winker, Peter, Introduction to the Special Issue on Agent-Based Models for Economic Policy Advice Weidlich, Anke, Daniel Veit, Agent-Based Simulations for Electricity Market Regulation Advice: Procedures and an Example Nagel, Kai, Dominik Grether, Ulrike Beuck, Yu Chen, Marcel Rieser, Kai W. Axhausen, Multi-Agent Transport Simulations and Economic Evaluation Westerhoff, Frank H., The Use of Agent-Based Financial Market Models to Test the Effectiveness of Regulatory Policies Demary, Markus, Who Does a Currency Transaction Tax Harm More: Short-Term Speculators or Long-Term Investors? Dau/id, Herbert, Simon Gemkow, Philipp Harting, Kordian Kabus, Michael Neugart, Klaus Wersching, Skills, Innovation, and Growth: An Agent-Based Policy Analysis Haber, Gottfried, Monetary and Fiscal Policy Analysis With an Agent-Based Macroeconomic Model

141-148 149-172 183-194 195-227 228-250

251-275 276-295

Jahrbücher f. Nationalökonomie u. Statistik (Lucius & Lucius, Stuttgart 2008) Bd. (Vol.) 228/2+3

Introduction to the Special Issue on Agent-Based Models for Economic Policy Advice Guest Editors: Blake LeBaron, Waltham, MA, USA, and Peter Winker, Giessen* JEL C15, C63, C69 Agent-based models, economic policy advice, validation.

Summary This special issue of the Journal of Economics and Statistics is devoted to the use of agent-based models for economic policy advice. It presents a collection of research papers in different fields of applications. Special emphasis is laid on discussing the potential and possible limitations of agent-based models for economic policy advice. The editorial provides an overview on the role of agent-based modeling in economic policy referring also to the papers presented. Furthermore, it highlights the strength of the approach, i.e., the explicit microfoundation and the modeling of heterogenous agents. Finally, we also report on current limitations of the method with regard to economic policy advice and point at some areas deserving further research.

1

Agent-based modelling in economic policy advice

Agent-based models gained increasing interest since the 1990s for modeling the interaction of large numbers of possibly heterogenous agents. Often, the agents' properties are not fixed in advance, but are subject to ongoing change, which might be triggered by interaction with other agents or through learning mechanisms. Early research in this area shows that these types of models are capable of reproducing empirical features of markets that would have been more difficult if not impossible with more traditional approaches. Consequently, agent-based models became an accepted tool in economic analysis over the last two decades. Special issues of several journals have been devoted to their development and application (Tesfatsion 2 0 0 1 a , 2 0 0 1 b , Lux/Marchesi 2 0 0 2 , Judd/Page 2 0 0 4 , Gilbert/Abbott 2 0 0 5 , Scalas 2 0 0 5 , Markose 2 0 0 6 , Fagiolo et al. 2 0 0 7 ) . 1 Given their theoretical appeal by an explicit micro foundation and the possibility to model institutional design quite easily, it is not surprising that they are starting to appear more frequently in policy analysis.

* The guest editors are grateful to the contributors and the anonymous referees. The handbook edited by Tesfatsion/Judd (2006) also provides a nice overview on research activities in the domain. Actual information on projects and publications can be obtained from the website on agent-based computational economics (http://www.econ.iastate.edu/tesfatsi/ace.htm) run by Leigh Tesfatsion.

1

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The focus of this special issue is on applications of agent-based models resulting in explicit policy recommendations. Apart from presenting examples to demonstrate the versatility of the approach and the various fields of possible applications, the papers also highlight the specific potential of the method and possible limitations. An introduction to these issues will be given in Sections 2 and 3. Definitely, this special issue cannot claim to provide a full review on applications of agent-based models in economic policy applications. Nevertheless, it covers a broad spectrum of applications ranging from specific markets with a focus on institutions and the interaction of agents to rather aggregate issues. The contributions to this special issue start with two papers devoted to specific well described networks, those for electricity (Weidlich/Veit 2008) and road traffic (Nagel et al. 2008). The specifics of the electricity sector are the technical constraints imposed by existing plants and networks, links between several markets and the oligopolistic structure on the supply side. Given the complexity of the market, classical economic methods are not well suited to provide advice to decision makers. Weidlich and Veit (2008) demonstrate the potential of agent-based modeling in this context. They discuss how to build a suitable model and which approaches might be used for validation. The model is used to analyze the dynamics of emissions trading, the impact of changes in settlement mechanisms, and plant divestiture measures on prices. While the complexity of the electricity market comes from the supply side, it is the interaction of a large numbers of interacting heterogenous agents on the demand side which complicates the analysis of policy measures in the study of traffic. Nagel et al. (2008) describe the limitations of traditional approaches and demonstrate the versatility of an agent-based approach. In particular, it becomes possible to model demand at the individual level taking into account personal characteristics like income or time constraints which will affect the demand. A model is constructed using the geographic and sociodemographic input data for the Zurich metropolitan area. The simulation of the agent-based model allows them derive the effects of time-dependent tolls which might not apply to the complete geographical area considered. Two of the papers in the volume deal with financial markets. Both are concerned with problems of excess volatility and trading in a financial market, and several proposed policy solutions for this. Westerhoff (2008) deals with several different policy tools, and uses a relatively transparent simple framework as a basis for his analysis in all of the cases. His model includes traders relying both on fundamental and technical indicators, and his policy tools include transaction taxes, central bank interventions, and trading halts. In all cases market volatility is reduced, and the price tracks the fundamental more closely. The author does some extensive checking of the model's robustness over different parameter values. Demary (2008) also looks at a financial markets as constructed from a set of interacting agent strategies. His approach has a more complex set of strategies, and policy analysis is only conducted through the mechanism of a transaction tax. The tax again is able to reduce volatility, but it increases the frequency of a few very large price movements in the tail of the distribution. Both of these papers are generally able to validate their models by generating price series with many characteristic features of actual time series. However, in the case of Demary (2008) a different set of parameters is necessary for the transaction tax policy to be effective. The last two papers use agent-based modeling approaches to analyze macroeconomic issues such as the effects of fiscal and monetary policy or the link between skills, innova-

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tion and growth. While applications to specific markets, in particular financial markets, have a modeling history, models allowing for macroeconomic analysis represent a recent extension of the scope of agent-based modeling. In fact, we are not aware of comparable work in the literature. The results presented in Dawid et al. (2008) are part of a larger research agenda funded by the EU Commission with the ambitious aim to develop an agent-based software platform for the simulation of the European economy which might be used for analyzing economic policy designs (http://www.eurace.org/). The present application focuses on skills and innovation. Given a geographical dimension of the model and workers' heterogeneity with respect to skill levels, the effect of different policies aimed at increasing workers' general skill levels is analyzed. Haber (2008) introduces an agent-based model of a national economy including several relevant actors like households and firms, and also government agencies setting monetary and fiscal policy. Special emphasis is put on a detailed modeling of the monetary sector to capture the effect of institutional settings on the monetary transmission mechanism. The model is used to demonstrate how different models of expectation formation can be easily integrated in an agent-based environment and how this might affect the outcome of typical monetary and fiscal policies. Obviously, the issue of validation becomes even more pronounced for such a comprehensive model. The author indicates that the results of policy evaluations might depend on the appropriate choice of the baseline.

2

Advantages of using agent-based models

Agent-based approaches strive for a kind of micro level reality that is often not present in other policy analysis approaches. Modeling begins at the individual level with decision making that respects possible limitations in both information gathering and information processing. In many agent-based models the institutional details become critical to the behavior of the model as they may play a major role in directing individual behavior. One big advantage for policy making is that the behavior of agents in the model can be very open to change. The key role for adaptation in these models is critical for policy making, since they provide a very detailed test bed for how agents will react to policy changes. The policy maker can explore many policy options and watch how agents adapt to each new situation. An important aspect of this policy testing is that many of the agent reactions to new policies might not have to be preprogrammed in by the researcher. Agents may discover new and interesting behaviors which were not even considered by the policy maker ex-ante. This aspect of surprise is often referred to as "emergent behavior" in the agent-based world. This emergence might come in the form of trading strategies in financial markets, commuter patterns on roads, or firm to firm agreements in industrial organization. Emergence can even take place in the appearance of new institutions as well as individual behavior. In most real world social systems interactions between individuals play a critical role. These can be through congestion externalities on roadways (Nagel et al. 2008), the spreading of diseases, counter party risks in financial markets, or information links on the web. Agent-based models are well designed to handle any of these situations, since they can specifically model agent interactions in any arbitrary space. This space might be geographic as in traffic simulations and electric power grids (Sun/Tesfatsion 2007, Weidlich/Veit 2008), or more abstract such as web page linkages. In all cases the impact of social interactions on behavior fits nicely into the agent modeler's tool kit. It is important

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to realize that social systems where interactions are important may often be an area where rough summaries of the data which try to represent groups of individuals as statistical aggregates may fail since the laws of large numbers are not working. It is also possible that the structure of the interconnections is too rich to be captured by a simple statistical model. Infection models are a good example of this. Vaccination strategies may depend critically on the social connections in the population, and how people are linked to others. Getting these structures wrong in a simplified statistical model could lead to very bad policy choices. Finally, the interaction structures that develop may themselves be the interesting object of study. An example might be the types of cross holdings that emerge in a financial market under different policy choices. One of the early roles of agent-based methods has been to compare results with more traditional modeling approaches. This is also important in the policy making world. In macroeconomic modeling the representative agent has been a kind of standard for some time even though it does impose some extreme assumptions needed for it to be a useful simplification of the world (Kirman 1992). Agent-based models are able to provide a robustness check on the representative agent by directly testing how realistic it is in many different situations. It can also add value in areas where the representative agent models do poorly in replicating empirical features, as in financial data (Demary 2008, Westerhoff 2008). They can speak to policy in some places where representative agent models remain completely silent. One example of this would be a trading tax. In this case tax revenues, and the impact on prices depend critically on how the tax impacts the individuals needs and desires to trade with each other. Representative agent approaches would be unable to answer any of these policy questions. Another case would be where the policy maker is explicitly interested in cross sectional distributions as in income distributions or firm sizes. The use of modern computing power in agent-based approaches cannot be underestimated. It allows both for the precise description of individual behavior along with very realistic representations of institutions. This can be done in a fashion which is free from simplifications necessary for analytic tractability. This is important in cases where the policies under study are very explicit, and where approximations might yield incorrect policy recommendations. Examples of this would be market reforms in electric power trading (Weidlich/Veit 2008), or traffic models (Nagel et al. 2008), but also the transmission of monetary policy (Haber 2008). The policies and institutions in these cases can often be described in detail, and it is not clear if approximations will suffice. For traffic one can now model using detailed maps of a city as opposed to some general representative circular city. Agent-based models, along with modern computer power, and detailed data sets allow for a level of realism that was previously out of reach.

3

Limitations of the approach

Agent-based modeling approaches bring great promise to the policy world, but it is also important to realize there are still important limitations and restrictions on what they are able to do. It is important for people involved in evaluating and implementing policy to realize these limitations. Also, it is important for agent-based modelers themselves to be honest about just how far they can push their new tools. The first, and most obvious, problem involves computational complexity. It is not just that agent-based approaches are computer driven, but that they may involve computer

Introduction to the Special Issue on Agent-Based Models for Economic Policy Advice • 145

tools which push the limits of tractability and analyzability for researchers. Some models can be very complex with inner workings depending on techniques borrowed from computer science such as genetic algorithms and artificial neural networks. These all involve many design choices and may include many low level parameters for which economic intuition is almost nonexistent. A recent book on agent-based modeling, Miller and Page (2007), stresses the construction of simple and tractable models for which computer experiments can give a complete picture of what is happening. This transparency is probably a good recommendation for basic theory, but it may not be possible in realistic policy settings. Agent-based modelers should remember that they need to carefully balance realism with simplicity and tractability just as any policy modeler should. It also must be true that policy makers will have a greater comfort level with more traditional models. They have many years of experience of tweaking the dials, and know what to expect. On the other hand, agent-based models are novel, involve many tools policy makers may not be used to, and can generate some very unexpected results. This unfamiliarity may pose a big problem in using these new tools. A key question for policy makers has been the validation of agent-based models. Can these models be reliably tested and validated so that one is comfortable with recommended policies going forward? Obviously this is an issue for more traditional models as well as agent-based approaches (Fagiolo et al. 2007: 190). However, some problems get amplified in the agent-based world. All models with learning and adaption suffer a problem of over parametrization, and over-fitting. Certain learning mechanisms may be far from reality, but they do a good job of fitting past data. They would not be useful measures of effective policies in the future. Agent-based models arguably have more of these parameters, and less is known about their true values, and importance. In finance an example might be a type of trend following strategy. These strategies may look good in terms of fitting features from the data, but unless they reflect real trader strategies they can be very misleading for policy makers. Over-fitting is not the only problem for agent-based models. Their basic properties, and computational nature may make them difficult models to estimate. The computational problems are obvious. If a model requires a day just to generate one run for a given set a parameters then traditional estimation, which would sweep through many sets of parameters maximizing some objective with the data, might be very time consuming. 2 Also, the behavior of the model might be very sensitive to different parameters, changing dramatically for small changes in parameters. This could lead to radically different policy recommendations driven only by slightly different behavioral descriptions of the underlying agents. 3 Modelers must be careful to make sure their policy recommendations are relatively robust. Finally, some of the data necessary for appropriate validation may be difficult to obtain. It may involve detailed information about the trading strategies of investors, or time series on the purchasing patterns of consumers, or even spatial information on drivers' locations. Fortunately, in our modern electronic world these data sets are becoming more

2

3

For an early attempt to solve this problem see Gill/Winker (2003), for an update Winker et al. (2007). The paper by Demary (2008) in this volume presents a typical situation of this type. For a discussion of validation issues see also Windrum et al. (2007) and M o s s (2008).

146 • B. LeBaron and P. Winker

available. However, the use of most o f these will involve privacy issues that will have to be dealt with. Another important source for micro level data comes from controlled laboratory experiments. Subject to the usual caveats about their realism, experiments offer important information on individual behavior which agent-based models can and should take advantage of along with more traditional m a c r o level information.

4

Conclusion

Agent-based models are clearly still a very new approach to policy analysis, but there are many things about them that make them a promising tool for the future. They are based on strong micro foundations, since they start with individual decision makers. Adaptive agents seek to optimize, as best they can, with limited information about the world around them. It is possible that this simple adaptive behavior may find strategies that would not be expected by traditional means of policy analysis. In this way the agent-based model may be a useful tool for finding ways a policy might fail. As mentioned, there are also many difficulties which justify some o f the skepticism given to these models. In some cases their empirical validity may be very weak, and the behaviors of agents at the micro level may have little connection to reality. It would be foolish to use such a model to implement policy, even though it might still produce some useful thought experiments. All these difficulties put greater demands on agent-based modelers. They need to set high standards in terms of documentation and clarity in their approaches. A lot of attention needs to be paid to sensitivity analysis both in terms of parameters, but also general assumptions about learning mechanisms. Obviously, replicability is crucial, along with easy to use and implement computer code. Finally, the very practical aspect of how to communicate the ideas in agent-based models to policy makers has to be considered. This may not be as easy as in the case of more traditional models, where a simple table or graph might do. It is possible that well designed movies, or even user interfaces to runable software will be necessary to make a point. Once one has a working and well tested model it is an interesting question just how it should be used for policy analysis. It might be used as a traditional large scale model where the simulation replicates the world, and the policy maker performs experiments by adjusting the dials on the computer. This might be the case in areas such as traffic simulation, and electric power markets, where the modeler has a pretty faithful replication of the slice of the real world that is under study. It is important to note that there might still be other ways for agent-based approaches to be of use which fall short of full scale simulations. In one case they run in parallel to more traditional tools, but their role could either be to point out flaws in the baseline model under large policy shifts, or to get a better picture of the dynamics in the extreme tails. They might end up ceding analysis of minor policy changes, or forecasting in the center of the distribution to more traditional approaches. Finally, they may exist only as thought experiments on their own. It is important to realize that these computational models may be useful simply by influencing the users of more traditional models, even if the agent-based model itself is never all that realistic. In this way they are simply thought experiments as many economic theories are. They just happen to rely on computational methods to get their points across. We hope that the examples gathered in this special issue demonstrate the potential o f agent-based models in policy analysis. However, it also becomes apparent that much

Introduction to the Special Issue on Agent-Based Models for Economic Policy Advice • 147

m o r e research is required, particularly with regard to validation and estimation of the models, t o move t h e m into the set of s t a n d a r d tools for economic policy analysis. To summarize, agents-based models might not be "the new w a y of doing economics", but provide a n additional and highly interesting tool for doing applied economics.

References Dawid, H., S. Gemkow, P. Harting, K. Kabus, M. Neugart, K. Wersching (2008), Skills, Innovation, and Growth: An Agent-Based Policy Analysis. Jahrbücher für Nationalökonomie und Statistik 228: 251-275. Demary, M. (2008), Who Does a Currency Transaction Tax Harm More: Short-Term Speculators or Long-Term Investors? Jahrbücher für Nationalökonomie und Statistik: 228-250. Fagiolo, G., C. Birchenhall, P. Windrum (2007), Empirical validation in agent-based models: Introduction to the special issue. Computational Economics 30: 189-194. Gilbert, N., A. Abbott (2005), Introduction: Special issue on social science computation. American Journal of Sociology 110: 859-863. Gilli, M., P. Winker (2003), A global optimization heuristic for estimating agent based models. Computational Statistics and Data Analysis 42: 299-312. Haber, G. (2008), Monetary and Fiscal Policy Analysis with an Agent-Based Macroeconomic Model. Jahrbücher für Nationalökonomie und Statistik 228: 276-295. Judd, K.L., S.E. Page (2004), Editorial: Special issue on computational models in public economic theory. Journal of Public Economic Theory 6: 195-202. Kirman, A.P. (1992), Whom or what does the representative agent represent? Journal of Economic Perspectives 6: 117-136. Lux, T., M. Marchesi (2002), Editorial: Special issue on heterogeneous interacting agents in financial markets. Journal of Economic Behavior and Organization 49: 143-147. Markose, S. (2006), Editorial: Special issue on developments in experimental and agent-based computational economics (ace). Journal of Economic Interaction and Coordination 1: 119127. Miller, J.H., S.E. Page (2007), Complex Adaptive Systems: An Introduction to Computational Models of Social Life. Princeton University Press, Princeton, NJ. Moss, S. (2008), Alternative approaches to the empirical validation of agent-based models. Journal of Artificial Societies and Social Simulation 1 1 : 5 . Nagel, K., U. Beuck, D. Grether, Y. Chen, M. Rieser, K.W. Axhausen (2008), Multi-Agent Transport Simulations and Economic Evaluation. Jahrbücher für Nationalökonomie und Statistik 228: 173-194. Scalas, E. (2005), Editorial: Special issue on market dynamics and quantitative economics. Physica A: Statistical Mechanics and its Applications 355: XI-XII. Sun, J., L. Tesfatsion (2007), Dynamic testing of wholesale power market designs: An opensource agent-based framework. Computational Economics 30: 291-327. Tesfatsion, L. (2001a), Introduction to the computational economics special issue on agentbased computational economics. Computational Economics 18: 1-8. Tesfatsion, L. (2001b), Introduction to the journal of economic dynamics and control special issue on agent-based computational economics. Journal of Economic Dynamics and Control 25: 281-293. Tesfatsion, L., K.L. Judd (2006), Handbook of Computational Economics. Vol. 2 of Handbooks in Economics Series. North-Holland/Elsevier. Amsterdam. Weidlich, A., D. Veit (2008), Agent-Based Simulations for Electricity Market Regulation Advice: Procedures and an Example. Jahrbücher für Nationalökonomie und Statistik 228: 149-172. Westerhoff, F. (2008), The Use of Agent-Based Financial Market Models to Test the Effectiveness of Regulatory Policies. Jahrbücher für Nationalökonomie und Statistik 228: 195-227. Windrum, P., G. Fagiolo, A. Moneta (2007), Empirical validation of agent-based models: Alternatives and prospects. Journal of Artificial Societies and Social Simulation 10: 8.

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Winker, P., M. Gilli, V. Jeleskovic (2007), An objective function for simulation based inference on exchange rate data. Journal of Economic Interaction and Coordination 2: 125-145. Blake LeBaron, The Abram L. and Thelma Sachar Professor of International Economics, International Business School, Brandeis University, Mailstop 32, Waltham, MA 02454-9110, USA. E-Mail: [email protected] Professor Dr. Peter Winker, Justus-Liebig-Universität Gießen, Licher Straße 64, 35394 Gießen, Germany. Phone: +49(0)6419922641. E-Mail: [email protected]

Jahrbücher f. Nationalökonomie u. Statistik (Lucius & Lucius, Stuttgart 2008) Bd. (Vol.) 228/2+3

Agent-Based Simulations for Electricity Market Regulation Advice: Procedures and an Example Anke Weidlich and Daniel Veit, Mannheim JEL C63, D43, L49 Agent-based computational economics, Simulation, electricity markets, C 0 2 emissions trading, market interrelations.

Summary This paper discusses the use of agent-based simulation models for regulatory advice in electricity market regulation. It briefly introduces the necessary procedures and the state-of-the-art of the methodology, and outlines its possible range of application. In a second part, the paper presents an agent-based simulation model developed by the authors. The model can be applied for analyzing different market designs and market structures in order to derive evidence for regulatory advice. This is exemplified through the analysis of two settlement rules in the balancing power market and of several divestiture scenarios of the German electricity sector.

1

Introduction

The electricity sector is characterized by technical constraints, multiple interlinked markets, and an oligopolistic structure with vertical integration. Asymmetric information, imperfect competition, strategic interaction, collective learning, and the possibility of multiple equilibria are further difficult aspects that characterize the electricity sector, like economies in general (Tesfatsion 2006). The ensemble of these aspects make electricity markets rank among the most complex of all commodity markets operated at present, and push most classical economic modeling methods to their limits. The complexity of the electricity sector and its high importance for a competitive economy calls for new modeling methods that help gaining insights into the dynamics of power markets. The agent-based (AB) modeling methodology, or more specifically the field of Agent-Based Computational Economics (ACE), provides more flexibility for properly representing relevant complex and may help to overcome some of the limits of traditional modeling methods, like e.g. too strict assumptions. With ACE research, the focus in economic analysis is shifted from rational behavior and equilibrium towards heterogeneity and adaptivity. The tremendous availability of computational resources made it possible to set up large-scale and detailed computational models that allow a high degree of design flexibility. Populations of heterogeneous agents, feedback from interaction, and dynamic processes make up the core of computational economic models. Although it constitutes a change in economic modeling paradigm, the agent-based approach does not need to be seen in sharp contrast with analytical modeling. Like Gulyas (2002) argues, an agent-based implementation is "rather a matter of degree than a binary choice". When moving from top-down approaches in which firms or other actors are represented on an aggregate level, via an entity-level representation of actors, down

150 • A. Weidlich and D. Veit

to the introduction of autonomous agents as actor representatives, frontiers between the modeling paradigms are fluent. However, with each step towards an agent-based implementation, the modeler gains flexibility, as more aspects, like e.g. heterogeneity of agents, can be accounted for. During the last decade, many agent-based simulation models of electricity markets have been developed. A majority of these approaches use reinforcement learning algorithms for representing the adaptive behavior of players in the market, e.g. Sun/Tesfatsion (2007), Nicolaisen et al. (2001), Bower/Bunn (2001); the use of genetic algorithms (e.g. Cau/Anderson (2003) or learning classifier systems (e.g. Bagnall/Smith 2005) is less frequent in AB electricity market modeling. While earlier models represent the electricity sector as one single, strongly simplified market, some recent models comprise several markets (Sun/Tesfatsion 2007), and explicitly model interrelations between them (Ruperez Micola et al. 2006). In most models, the agent's learning task is to set profit-maximizing offer prices or markups. Capacity withholding strategies are mostly not modeled explicitly; however, setting a high offer price can also be interpreted as (economic) withholding. Another observation from surveying the agent-based electricity simulation literature is that the majority of models still neglect transmission grid constraints (although recent developments go into the direction of taking transmission into account, e.g. Sun/Tesfatsion (2007), and most models represent the demand side as a fixed, price-insensitive load. ACE models serve for explaining, understanding, and analyzing socio-economic phenomena. Among the ACE research strands that Tesfatsion (2006) identifies, most electricity related research can be categorized into the normative strand. Agent-based simulation models are used as fully controllable virtual laboratories for testing economic design alternatives in order to determine the policies, institutions, or processes that perform best in an environment of selfish agents. This approach follows the postulation formulated by Roth (2002) that markets should be designed by using engineering tools, such as experimentation and computation. More specifically, most AB electricity market models center around questions of market power and market mechanisms. The comparison between pay-as-bid and uniform pricing is a very popular research question analyzed with AB approaches. Another important research issue for AB electricity modelers is the assessment of market power potential under different market structures or market mechanisms. In this paper, the potential of agent-based modeling for analyzing market structures and market designs with the aim of advising decision makers in the electricity sector is discussed. Procedures of model building and model validation are presented, and current weaknesses of the methodology are pointed out in Section 2. In Section 3, an example of an agent-based electricity sector simulation model developed by the authors is described, and simulation results from this model are presented. Finally, Section 4 concludes and gives an outlook on further research directions to be conducted in the agent-based electricity market simulation field. 2

Procedure of agent-based modeling for regulation advice

In the following, the state of the art of the methodology is briefly discussed, with a special focus on its applications to electricity market modeling. Some basic concepts that characterize and motivate the use of agent-based approaches are presented in Section 2.1. The

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model building process is described in Section2.2. Section 2.3 discusses the important issue of (empirical) model validation. 2.1 Concepts and motivation for ACE models According to Axtell (2000), one main motivation for agent-based models is the dissatisfaction with rational agents. Thus, he argues, all agent-based models involve some form of boundedly rational agents. In fact, many economists argue that people, although they might try to be rational, have natural limits to perception and information collection, memory, and computational capacity, and can consequently rarely meet the requirement of information or foresight that rational models impose. A realistic assumption in electricity market modeling is that agents do not have all information necessary for making an optimal choice of an action to take in order to maximize profits. Instead, they can learn to behave profitably through repeated interaction with the environment they are placed in. Consequently, the most prominent approach of modeling bounded rationality that can be found in the AB electricity market modeling literature is the gradual amelioration of activities through learning, dynamic adaptation, or evolution. Learning and adaptation are obvious representations of human behavior in complex economic situations. As for their realism and usefulness for modeling agents in many economic systems, Batten (2000) postulates that [l]earning and adaptation should not be addenda to the central theory of economics. They should be at its core, especially in problems of high complexity. Another essential element of agent-based modeling is heterogeneity. AB modelers are not restricted to equally sized or symmetric firms, or to other constraints that arise from the limits of analytical modeling. Instead, every agent making up the modeled economy can be designed independently. The economy then evolves as a result of the interplay of these heterogeneous agents, i.e. from the bottom-up. Heterogeneity is an important characteristic of real-world electricity markets. Generator agents differ in size and spatial position, they own and operate different generating technologies (e.g. fossil, nuclear or renewable power plants) with different marginal costs and technical attributes, or they have different strategic characteristics (e.g. vertically integrated or not). During the process of trading, they further differentiate from each other through the individual experience they gain from trading. While no agent has complete information about the global state, each of them accumulates some knowledge of which strategies might be more or less successful when competing with the rest of the population. On this basis, each agent decides how best to act subsequently in order to maximize profits. By this means, aggregate system behavior, such as collusion, might be observed. Agent-based simulation is a natural and intuitive way of representing this agent heterogeneity, as it offers much more flexibility in defining each individual market participant than do analytical modeling methods. 2.2 Model building There are only few guidelines proposed for the design and implementation process of agent-based simulation models. As a start, basic principles of simulation procedures used in other disciplines also apply to agent-based simulation. Law (2007) for example provides helpful guidance for building simulation models and analyzing output data;

152 • A. Weidlich and D. Veit

Gilbert/Troitzsch (2005) describe simulation methodologies in the social sciences, including some hints for agent-based modeling. According to Tesfatsion (2002), the ACE modeling procedure can be described as follows: After having (i) defined the research questions to resolve, the ACE modeler (ii) constructs an economy comprising an initial population of agents and subsequently (iii) specifies the initial state of the economy by defining the initial attributes of the agents (e.g. type characteristics, learning behavior, knowledge about itself and other agents); the modeler then (iv) lets the economy evolve over time without further intervention - all events that subsequently occur must arise from the historical time-line of agent-agent interactions, without extraneous coordination; this procedure is followed by (v) a careful analysis of simulation results and an evaluation of the regularities observed in the data. In AB electricity simulations, the most common agents that make up the population are generators, load serving entities, and a market or system operator. Depending on the research questions, the simulation can also contain regulator agents, a transmission system representation, retail customers, or others. Agents can also be composed of other agents, thus permitting hierarchical constructions, like e.g. utilities. At the subsequent step of model building, that is model description and publication, AB electricity market modelers proceed in heterogeneous ways. It would be helpful if some standard way of model description, as it is conventional for other economic methodologies, became accepted for AB modeling in the medium-term. This description should include information about the number of runs conducted, the applied parameter values, and all other model details that allow for reproducing the described simulations. In order to make agent-based simulations better understandable and publishable, Richiardi et al. (2006) give some practical suggestions towards a standardized methodological protocol of AB simulations; they propose to: - include references to the theoretical background of the economic phenomenon that is investigated, including simulation and non-simulation literature; - state the main features of the simulation model (treatment of time: discrete or continuous, treatment of fate: stochastic or deterministic, coordination structure: centralized or decentralized, and others) clearly and immediately in order to facilitate understanding and model comparison; - follow well-defined processes for data analysis, including accepted calibration, validation and sensitivity analysis techniques; - use standard modeling languages such as the Unified Modeling Language (UML) for describing the static and dynamic properties of the model and use AB modeling toolkits, in order to make models more easily replicable. Moreover, making model source codes publicly available would greatly benefit the research field, because researchers could revise and check the implementations of others and could also reuse parts of them 1 .

1

For a positive step into this direction see Leigh Tesfatsion's site at http://www.econ.iastate.edu/tesfatsi/ElectricOSS.htm.

Agent-Based Simulations for Electricity Market Regulation Advice • 153

2.3 Validation of agent-based simulation models

The difficulty of validating ACE model outcomes against empirical data remains one of the challenges for the ACE methodology. 2 Only few guidelines for calibrating and validating agent-based simulation models have yet been defined. While standard verification and validation techniques for simulation models (e.g. described by Sargent 2005, Gilbert/Troitzsch 2005, or Law 2007) can and should also be applied for AB simulations, it is difficult to establish credibility in the implemented agent behavior. Many models presented in the agent-based electricity modeling literature are not empirically validated. In their survey of the relevant literature, Weidlich/Veit 2008a illustrate this finding, which is consistent with other surveys of agent-based electricity market models that we are aware of, such as Shun-Kun/Jia-Hai (2005) who present some selective papers and nicely show how the ACE methodology is ranged within other methods of economics, or Sensfuf? et al. (2007) who also take into account models of long-term decision making in the power industry. The researchers who report about the (empirical) validation of their AB electricity market model Macal/North 2005 are one example) proceeded in heterogeneous ways. Very recently, the need for reliable validation techniques has obviously been recognized. AB researchers have analyzed and suggested procedures and guidelines for calibrating and validating agent-based simulation models, e.g. Windrum et al. (2007), Marks (2008), Richiardi et al. (2006), Midgley et al. (2007), and a whole journal special issue is devoted to this topic (Fagiolo et al. 2007). These general suggestions should now be assessed from the perspective of their usefulness for electricity modeling purposes. The development of guidelines for assuring the reliability and validity of AB electricity models would greatly benefit the research quality and diminish the heterogeneity of approaches in this field. It is a necessary step for reducing skepticism and ensuring the quality of the methodology. Windrum et al. (2007) review some empirical validation techniques that could be used to ensure validity of AB models. They first examine how the output of an AB simulation can be analyzed. The model outcome is characterized by a set of statistics that are computed from data generated by the model data generation process. As most processes in AB simulations are stochastic in nature, several simulation runs with varying random number seeds are necessary. By exploring a sufficiently large number of points in the space of initial conditions and parameter values, and by computing a set of statistics at each point, one can gain an understanding of the behavior of the model data generation process. In order to ameliorate the problem of empirical model validation, LeBaron (2006) makes three suggestions (his focus is on financial markets): The first is to attempt to construct an AB model such that it replicates empirical features which are not well replicated by standard models. The second one is to put as many parameters as possible under evolutionary control in order to find optimal values for crucial parameters. The third suggestion is to use insights gained from experimental economics in order to build more realistic learning dynamics.

2

It should be noticed that some researchers argue that AB models are only suitable for qualitative analysis. This would entail that AB models can solely test theories in the form of causal relationships, and calibration would be less an issue. Validation could not be grounded on a comparison with empirical data in this case (see Pyka/Fagiolo 2005, or Windrum et al. 2007 for this discussion). In contrast, most of the latest papers on AB model validation consider empirical validation.

154 • A. Weidlich and D. Veit

Moss/Edmonds (2005) propose to cross-validate AB models. They argue that the micro level of an AB model is best investigated qualitatively while the macro level should be investigated using quantitative methods. When the agents' behavior and interaction on the micro level is able to generate the macro level phenomena sharing the statistical characteristics of data from the real-world system, then the model is cross-validated: the micro level behavior is validated qualitatively by domain experts, and the macro level data is validated by comparing statistical properties of numerical outputs from the model with statistics of the real-world system. Werker/Brenner (2004) propose an advanced methodology for calibrating and validating AB simulation models based on Critical Realism. It proceeds in three steps which involve (i) setting possible model specifications (parameters, interactions), where the assumptions on which the model is built should be induced from empirical data whenever this is possible; a set of several plausible models with certain parameter ranges results from this first step; (ii) running each model specification many times and comparing the tested model specifications to empirical observations, rejecting model specifications that are not confirmed by the empirical data; finally, (iii) identify the underlying mechanisms driving the part of the world that should be described and explained using abduction. In this paper, we want to advertise for a two-level validation which considers both the micro and the macro level of an agent-based model. Micro-validation entails ensuring that the applied learning algorithm (or other behavioral representation) adequately reflects the behavior of the agents. Some papers describing AB electricity market models do not report on a careful micro-validation. In the described models, learning or adaptation is implemented in very heterogeneous ways. The choice of the learning algorithm itself is often not argued and justified; most authors do not answer the question why a specific learning model has been chosen and how good it performs in comparison to alternative behavioral representations. In contrast to this modeling practice, the implications of using specific learning models should be analyzed carefully before simulation outcomes are interpreted on a higher level of abstraction. It should be carefully tested - if necessary with a simplified scenario - whether bidding behavior patterns of the agents in the electricity market correspond to a desirable behavior, or to a behavior that can be expected in real-world markets. During the macro-validation procedure, macro variables that result from the interaction of the agents participating in the modeled markets are analyzed. In electricity market models, these macro-variables are usually market prices that result from the agents' interactions, given the data input that characterizes the supply and demand side, and the market structure and rules. The simulated macro variable values are then compared to empirically observed values in order to verify if simulation outcomes resemble those observed at the real-world electricity markets. Law (2007) proposes several procedures for comparing real-world observations and simulation output data, such as the basic or the correlated inspection approach, the confidence-interval approach or the time-series approach. These are also applicable to AB electricity market simulations. 3

Example: An agent-based simulation model of electricity and emissions trading

As an example of an agent-based simulation model that can be applied for economic policy advice, we present here a model that represents the German electricity sector. It comprises three markets, which play an important role in short-term wholesale power trading:

Agent-Based Simulations for Electricity Market Regulation Advice • 155

a day-ahead electricity market at which hourly contracts for physical power delivery on the following day are traded, a market for positive minute reserve (balancing power market), where capacity that is held in reserve for regulating imbalances is procured by the transmission system operators, and an exchange for CO2 emission allowances. The model has been developed within the research project Power ACE and represents the part of the implementation that is concerned with short-term wholesale power trading; some concepts of the whole implementation are described in Weidlich et al. (2008). Following the agent-based paradigm, all relevant parts of the electricity sector simulation model are modeled as agents. The set of agents comprises market operators, electricity generators, load serving entities, and CO2 market participants. Market operators collect supply and demand bids from registered agents and carry out the market clearing. Generator agents operate power plants and sell their generation output either on the dayahead electricity market or - if their power plants meet the technical requirements for delivering minute reserve - on the balancing power market, and buy or sell CO2 emission allowances if they operate fossil fuel fired plants. They are characterized by their power plant portfolios, where each plant is defined through several parameters such as its (constant) marginal generation cost, the net installed capacity, no-load costs, or its emission factor, denoting how much CO2 emissions are associated with every MWh of output. Load serving entities demand electricity on the day-ahead market; they represent a fixed, price-insensitive hourly load. CO2 market participants other than the generator agents constitute the external demand and supply of allowances. They are characterized by their demand or supply quantities and a valuation at which they like to sell or buy CO2 emission allowances. As depicted in Figure 1, all agents inherit basic methods from one abstract super class (PowerACEAgent). The three markets are subclasses of the MarketOperator class, and

Figure 1 U M L class diagram of agents in the simulation model

156 • A. Weidlich and D. Veit

market participants inherit parts of the Trader agent class. In order to ensure that agents can submit correctly formed bids, they implement the corresponding interface of the market (DayAheadBidder, BalancingBidder, C02Bidder). Agents of the AdaptiveGenerator class are able to trade on all three markets, and they can act strategically on the two electricity markets. Agents of the LoadServingEntity type do not act strategically. The model implementation uses the Recursive Porus Agent Simulation Toolkit (Repast), which is a JAVA-based class library that facilitates agent-based simulations. 3 A presentation of the simulation model is also given in Weidlich/Veit (2008b), in which results from other simulation scenarios are presented. The model description provided in the following reproduces parts of this previous paper and presents results from new simulation runs. 3.1 Simulated markets

The day-ahead market (DAM) is modeled as a sequence of 24 simple call markets for every delivery hour of the following day. Each agent i submits offers for each of its G, generating units g. As in the simulations presented here the balancing power market is cleared first, the available capacity that an agent can govern in the day-ahead market depends on the trading results on this first market. The capacity an agent has committed on the balancing power market is subtracted from the net installed capacity qnet of this plant, resulting in the available capacity qava'1. One supply offer consists of a quantity and the price at which the quantity is offered. The agent formulates the offers according to the output of the reinforcement learning algorithm (see Section 3.2 for a description of agent learning), thereby finding the best actions over a two-dimensional action domain. The price dimension allows offer prices from 0 to 100 EUR/MWh, in 21 discrete steps; the offer quantity that agents can choose ranges from fractions of /? = 0 to 100 % of the available capacity, in six discrete steps. The set of offers submitted to the day-ahead market by agent i for delivery hour h, which contains separate offers for each generating unit g ( b f f ^ ) is denoted B ^ f M and is defined as follows: (1) with

DAM

n

— ft

nava'1

f> sold and by deployed minute reserve qBPM,depi s j j j e quantities a r e multiplied with the emission factor cog of plant g, quantifying the CO2 emissions associated with every M W h of power output. C0ltemit

/ 24

( V^,,

6 DAM,sold . V^ ,,

G, \h=1

k=l

\ BPM,depl \ /

The remaining allowance budget that an agent has at its disposal at time t (day of the year y) is divided by the remaining days for which the allowances were issued, in order to calculate a daily budget. This budget is subtracted from the allowance quantity needed for power generation, thus resulting in the bid/offer quantity that agent i submits to the C O 2 market operator. In consequence, if an agent's budget for the current day is larger than the need for allowances, his bid quantity becomes negative, which corresponds to a selling offer. CO2, bud -C02M _ -C01,emit,i _ "t,i q ** ~q 365 - i - 1

,¿s W

Bids on the C O 2 allowance market contain a volume of allowances that is offered or asked, a bid price, and the compliance period (cp) for which the allowance should be valid (for simplicity, and because no speculation is considered, the compliance period is always equal to the current period). Buying bids have positive volumes, and selling offers have negative volumes. All agents submit one single daily bid on the allowance market, representing their requirement or surplus calculated over all power plants they own. bC02M =

(jC02MqC01Mcp^

(7)

The CO2 emission allowance market is modeled as a sealed bid double auction. Demand and supply bids are summed up to form supply and demand functions in the same way as on the day-ahead electricity market, and the uniform market clearing price is determined by the intersection of both curves. The remaining allowance budget is updated at the end of each trading day by subtracting the amount of allowances used for emitted CO2 quantities from the current budget and by adding the resulting trading volumes (positive for bought allowances, negative for sold volumes) to it. The budget at time t = 0 is the initial allowance quantity issued for year y through the grandfathering procedure. 5

If the deployment of minute reserve becomes necessary, this would occur one day after trading on the balancing power market. For simplicity, it is assumed that minute reserve quantities actually deployed are already known on the trading day. In real-world practice, only around 2 % of procured minute reserve capacity is actually deployed for frequency regulation (Bundesnetzagentur 2006} so these quantities are negligible.

Agent-Based Simulations for Electricity Market Regulation Advice • 159

Agents do not act strategically on the market for CO2 emission allowances - they do not set bidding strategies through reinforcement learning. However, the costs incurred from allowance prices influence trading strategies on the electricity markets, as specified in the following section. 3.2 Agent learning and market interrelations

For each market in which they act strategically, agents choose new actions from instances of a reinforcement learning algorithm, and then formulate their bids according to this chosen action. Agents learn strategies separately for the day-ahead and for the balancing power market. Moreover, strategies for each bidding block on the balancing power market and for each hour on the day-ahead market are learned separately. While optimizing their supply offers, agents consider opportunity costs that they could have achieved on the other market if they had sold their capacity there. Prices for CO2 emission allowances are also included into the reinforcement as opportunity costs, because a generator would always have the opportunity to solely sell certificates, thereby realizing a profit. The three markets that form the electricity sector simulation model are interrelated through the agents' bidding strategies. A power generator has the choice to offer his generating capacity on the DAM or on the BPM for the following day (for those plants that fulfill the technical requirements to deliver minute reserve), and has to trade off between these two options. After market clearing on the first market, an agent can offer his remaining unsold capacity on the second market. Through varying the offer quantity on the day-ahead market, agents can influence and optimize their joint strategy on both power markets. The behavioral representation of the agent's search for profit maximizing strategies is modeled with Q-learning (Watkins 1989) and variants of the Erev/Roth (1998) algorithm. For this learning algorithm, different states have to be defined. In the simulations applying Q-learning, the states are based on bid prices and trading success. Bid prices are categorized as low (lower than or equal to one third of the maximum admissible bid price), high (higher than or equal to two thirds of the maximum admissible price) or medium (all remaining prices). A bid is further categorized as marginal or intra-marginal, in which case it is a successful bid, or as extra-marginal for a bid that was not successful. All combinations of bid prices and success form the six states that are differentiated in this model. Reinforcements R that are fed back to the update function of the learning algorithm are calculated for both power markets after all markets have cleared on the current trading day. They are based on the profit n earned on the respective market. Reinforcements are set relative to the maximum possible profit 7cmax that an agent can earn on the market. Consequently, the range of possible reinforcements 0 < R < 1 is the same for all learning tasks; initial Q-values or propensities are set to Qo = 1. Maximum profits depend on variable costs cvar of the power plant deployed, and are different across plants. Agents that own a portfolio of generating units set and learn offers separately for each plant. The reinforcement for learning the bidding strategy of one plant, however, contains some information about the performance of the whole portfolio. The influence of the whole portfolio profit on the reinforcement is set through the portfolio integration parameter y. Throughout the simulations presented here, it is set to y = 0.5. Reinforcements on the day-ahead market are defined as follows:

160 • A. Weidlich and D. Veit

_ , , = I1

K

h,i,g

,

W l t h

-

,„, V ) • nb,,,g

/

DAM DAM,sold h,.,g = 4b,,,g

DAM,mix

_

net

C02M,opp h,i#

„var

/

G

DAM,max

/

i,g

fo\ (»)

^ BPM,opp h,,,g ~

c

j}DAM,max

.var

i i m

)-PBk^'cap-rttgM

(11)

CC>2,emit

~

C

CO!M,opp b,,,g

P

c™«=%MR c

i,g n DAM h -

n

E< „DAM h,i,g

, „. + f

C

nCOlM ' ^t(b)

(

(

9

i z

)

)

The reinforcement for trading on the balancing power market is defined in a similar manner as on the day-ahead market. If no minute reserve energy is actually delivered, profits are only defined by capacity prices and by no load costs (nolc), i.e. the cost for keeping the power plant in a stand-by state. For the calculation of nBFM 0 captures how sensitive the mass of traders is to selecting the most attractive strategy. The higher e, the more agents will select the strategy with the highest fitness. For e = 0, all agents are divided evenly across the strategies, while for e = oo, all agents select the strategy with the best performance. In this sense, we may interpret e as a (bounded) rationality parameter. 2.3 Calibration, dynamics and stylized facts

Unless otherwise stated, we make use of the following parameter setting: a = 1, b = 0.04, c = 0.04, d = 0.975, e = 300, a" = 0.01, u 0.50 \ * 0.151 1250

2500 time

3750

5000

1250

2500 time

Figure 3 The dynamics of the model for different seeds of random variables in the time domain. Design and parameter setting as in figure 1 We may measure all variables precisely. In reality, it is basically impossible to calculate the fundamental value of an asset. Within our setup, this task is quite simple We may control for all exogenous shocks and simulate special events. For instance, if we are interested in how a certain policy operates during a major shift in fundamentals, we may simply define such a shift in fundamentals.

204 • F. H. Westerhoff

1 ^

°- 7 0.0

200 -0.7

-0.7 0

1250

2500

3750

5000

0

1250

time

1250

2500

3750

5000

3750

5000

time

3750

5000

1250

time s

2500

2500 time

0.85

j 0.50 (l

- r)2 + (Rt)"(Wt

-

std\\

(8)

where R = (1 + r) and R* = (1 + r*) are the gross returns on the domestic and foreign bond, while st is the bilateral exchange rate between both countries. The first part is the return on the foreign asset on which a tax on foreign currency transactions r £ [0,1] is levied, while the second term measures the costs of borrowing in the domestic country. For n = 1 and r = 0 this budget constraint collapses to the one proposed by DeGrauwe/ Grimaldi (2006). If we assume wealth to be normally distributed we can simplify the portfolio selection problem by maximizing the certainty equivalent u(w;)«sl-) = E j _ 1 [ w ; ] - | v a r i _ 1 [ w ; ]

(9)

234 • M. Demary

subject t o the same budget constraint. M a x i m i z a t i o n yields agent i's d e m a n d function for foreign currency for the has investment horizon n _ '

E't[WjJ

_ (R*t)"(l-r)2E;[st+„]-(Rt)"5f

" W J W U "

Sajt

(1U)

Thus, trader i's d e m a n d is decreasing in his degree of risk aversion, in a higher risk of fluctuations in his wealth o f t , decreasing in the transaction tax rate r, and increasing in the expected profit. For n — 1 and x = 0 the d e m a n d function collapses t o the one used in DeGrauwe/Grimaldi (2006). Following Brock/Hommes (1997) we assume t h a t the risk evaluation is the same for all agents and constant over time, the d e m a n d function simplifies t o =

- r) 2 E' f [5 t+ „] - (Rt)"st),

(11)

with = I / ¿ a 2 . This simplified d e m a n d function only depends on the domestic and foreign interest rates, the currency transaction t a x as well as the current and the for the future expected exchange rate. The trader's d e m a n d for foreign currency possesses a term which depends on the agent's individual forecasting model of the future exchange rate. The set of possible forecasting models will be tackled in the next subsection.

2.3 Traders' forecasting models We assume t h a t the true data generating process for the exchange rate is u n k n o w n t o the agents and t h a t they have t o a p p r o x i m a t e it by rules of t h u m b . Therefore they use ad-hoc rules for forecasting. We assume t h a t t w o types of forecasting rules are used. A rule which reacts on trends in the exchange rate is commonly called chartist rule or technical trading rule. T h e other technique called fundamentalist forecasting rule looks for over- and undervaluations of the exchange rate with respect t o its arbitrage free f u n d a m e n t a l value s[ and expects a reversion back t o it. The fundamentalist forecasting rule for the one-step-ahead prediction of the exchange rate can be written as EÌ[5(+i-sJ=j/-(sf-st).

(12)

According t o this equation k n o w n as error correction model f r o m the econometrics literature, this rule predicts an exchange rate change such that x/-100 % of the disequilibrium st — st, which is the deviation of the realized exchange rate s, f r o m the arbitragefree exchange rate s{, will be corrected by the subsequent exchange rate change. N o t e t h a t the t w o step ahead forecast assumes that */-100 % of the remaining disequilibrium (1 — x f ) • (sf — st) will be corrected by the subsequent exchange rate change and so on. From this consideration follows, t h a t the «-step ahead forecast will be Eft[st+n - s,+B_i] = Kf{ 1 - zZ)""1 • (4 ~ st)-

(13)

For n = 1 this forecasting model collapses t o the one used in DeGrauwe/Grimaldi (2006), Lux/Marchesi (2000), Chiarella/He (2002) and Brock/Hommes (1997).

Who Does a Currency Transaction Tax Harm More • 235

The expected exchange rate change E([s • lncfet°" else,

where 0 < 1 is a parameter, and Irtc^ a n is the mean individual (labor) income of an agent over the last T periods. By definition the saving propensity fulfills 0 < k < 1. The implications of this consumption rule are as follows: if an agent has a current cash on hand that is below the fraction 0 of mean income, he spends all available liquidity and nothing is saved. If cash on hand exceeds

(

IM M( w )l( H ttî 1)M*

w * MC

-0.40 -0.60 1 2 3 4 5 6 7 8

9 1 0 1 1 1 2 1 3 1 4 1 5 1617 1819 20 2122 23 24 25 26 27 28 29 30 Period

• GDP growth - * - A v g . Retail IR

HB— Inflation

Consumption

—*—Public Deficit

Unemployment

Figure 3 Time-paths for the fiscal policy experiment (averages of all 3 0 rounds)

Monetary and Fiscal Policy Analysis With an Agent-Based Macroeconomic Model • 293

0.40 0.30 0.20 « c sro 0.10 CO 0.00 -0.10 c .2 to -0.20 > s -0.30 -0.40 -0.50 *••

1 2 3 4 5 6 7 8 9 1011121314 151617 1819 20 2122 23 24 25 26 27 28 29 30 Period •

GDP growth

)( Avg. Retail IR

-»-Inflation )l< Public Deficit

—Ér-Consumption —•—Unemployment

Figure 4 Time-paths for the monetary policy experiment

5

Conclusions

If carefully designed, macroeconomic agent-based models are suitable for the analysis of all different kinds of macroeconomic policy issues which are known from traditional model-based exercises. But in addition to this, a large number of more sophisticated questions can be answered, ranging from distributional issues to the feedback effects on microeconomic levels. The effects of expectations on the results and the general effectiveness of economic policy have been shown in this paper. In this sense, agent-based macroeconomic policy analysis further reduces the destructiveness of the traditional Lucas critique because the behavioral patterns of the agents dynamically adjust to changes in policy regimes and policy instruments. From this point of view, the agent-based approach offers superior policy analysis performance, especially for applications which do not depend on accurate forecasts of the levels of certain economic indicators but need to address all types of change and evolution. Clearly, this is an advantage mainly for dynamically evolving economic systems, but also the performance of policy analysis exercises for highly-industrialized countries in the Euro area can be raised by including features of the monetary sphere which are neglected in traditional models. The simulations presented here could give some indication of the effectiveness of fiscal and monetary policies when the expectations in the model are more elaborated: Fiscal policy tended to be less effective while the effectiveness of monetary policy could be improved. Apart from the results presented above, several possible applications of such a model could be investigated, e.g.: - the effects of changes in micro-variables (deep variables in the utility and production functions, market structure...); - the effects of innovation;

294 • G. Haber - the effects of different types of learning and different degrees of rationality; - policy analysis in highly dynamic economies, such as the transition economies or emerging markets, where no useful econometric (or other) models can be constructed due to problems with short and unreliable time-series; - institutional changes in wholesale and/or retail banking; - the effects of monetary (and fiscal) policy in the light of financial disturbances (such as the US sub-prime crisis); - the distribution effects of macro-policy measures. At the same time, there are some specific limitations to this kind of model analysis. As mentioned above, the calibration of the baseline cannot be fully validated so the results might depend on the choice of an appropriate baseline. Moreover, even if the elements of the economic system can be modeled in more detail than in traditional approaches, the results still (partly) depend on the general structure of the model and on the question as to which interactions between agents may take place. Another possible drawback might also be seen as an advantage: The results of the agentbased models are highly stochastic so each batch run of the model produces a large number of "different possible worlds". In some of the simulation setups, these different worlds may look very different - identical initial values of all the system parameters might lead to positive growth in one simulation run and to a "hard landing" of the economy in another. Thus, either result should only be interpreted in a strictly stochastic sense, or the robustness of the results should be thoroughly checked by further evaluating the statistical properties of the distribution of the time-paths. The next steps in developing AS1 will be the full utilization of geographical properties and the multi-country setup. Moreover, more sophisticated expectation formation mechanisms (such as the inclusion of an embedded econometric model) will be implemented and the sub-models for individual markets will be improved.

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Ökologieorientiertes Management Um-(weltonentiert) Denken in der BWL von Edeltraud Günther mit 90 Abbildungen, 104 Tabellen und vielen Anwendungsbeispielen Aus der Reihe wisu-texte (hrsg. von Rainer Lange)

2008. XX/387 S.( kart., € 29,90. UTB 8383. ISBN 978-3-8252-8383-4 Unsere natürliche Umwelt entwickelt sich zu einem ökonomisch knappen und somit entscheidungsrelevanten Parameter. Doch auch die ökologische Knappheit wird langsam zum Entscheidungsparameter in der Unternehmenspraxis. Dieses Lehrbuch greift beide Entwicklungsströme auf und zeigt, wie durch ein Umdenken in der klassischen Betriebswirtschaftslehre Entscheidungen ökologieorientiert getroffen werden können, aber auch wie eine Erweiterung betriebswirtschaftlicher Instrumente um Umweltdimensionen nachhaltige Entscheidungen unterstützen kann. Die Autorin geht davon aus, dass die bereits in der Betriebswirtschaftslehre bestehenden Instrumente genutzt werden können, aber veränderte, z. B. längerfristige Perspektiven und daraus folgende neue Unternehmensziele zu anderen Entscheidungen führen. Studenten erhalten durch dieses Lehrbuch einen umfassenden Einblick in die Betriebliche Umweltökonomie. Praktiker können gerade durch die Anwendungsbeispiele konkrete Handlungsanweisungen ableiten. Die Autorin ist B.A.U.M.-Umweltpreisträgerin 2008.

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