Economics of an Innovation System: Inside and Outside the Black Box 9781138388536, 9780429425448

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Economics of an Innovation System

Existing literature looks at national innovation systems from the perspective of either “inside the black box” or “outside the black box”. This is the first book that analyzes both the inside and outside of the black box using a general equilibrium framework. The book looks at what is outside the black box and provides models of pathdependent endogenous growth; examines the dynamics of the black box from the intersectoral perspective of the economy; and proposes an innovation flow matrix. It also takes into account both business cycles and endogenous innovation in the unified New Keynesian dynamic stochastic general equilibrium (DSGE) model and examines how business cycles and other policy shocks affect endogenous innovation. The unified treatment of the national innovation system from perspectives both inside and outside the black box using rigorous economic models and empirical analyses makes this an enlightening work, shedding new light on innovation economics. Tsutomu Harada is Professor of Industrial Economics at Kobe University, Japan. He received Ph.D. in economics from Stanford University and Ph.D. in business administration from Kobe University. His research interests include innovation economics, technology management, and strategy.

Routledge Studies in the Economics of Innovation

The Routledge Studies in the Economics of Innovation series is our home for comprehensive yet accessible texts on the current thinking in the field. These cutting-edge, upper-level scholarly studies and edited collections bring together robust theories from a wide range of individual disciplines and provide in-depth studies of existing and emerging approaches to innovation, and the implications of such for the global economy. Automation, Innovation and Economic Crisis Surviving the Fourth Industrial Revolution Jon-Arild Johannessen The Economic Philosophy of the Internet of Things James Juniper The Workplace of the Future The Fourth Industrial Revolution, the Precariat and the Death of Hierarchies Jon-Arild Johannessen Economics of an Innovation System Inside and Outside the Black Box Tsutomu Harada For more information about this series, please visit: www.routledge.com/ Routledge-Studies-in-the-Economics-of-Innovation/book-series/ECONINN

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Economics of an Innovation System Inside and Outside the Black Box

Tsutomu Harada

First published 2019 by Routledge 2 Park Square, Milton Park, Abingdon, Oxon OX14 4RN and by Routledge 52 Vanderbilt Avenue, New York, NY 10017 Routledge is an imprint of the Taylor & Francis Group, an informa business © 2019 Tsutomu Harada The right of Tsutomu Harada to be identified as author of this work has been asserted by him in accordance with sections 77 and 78 of the Copyright, Designs and Patents Act 1988. All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. Trademark notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging-in-Publication Data A catalog record for this book has been requested ISBN: 978-1-138-38853-6 (hbk) ISBN: 978-0-429-42544-8 (ebk) Typeset in Times New Roman by Apex CoVantage, LLC

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Contents

List of figures List of tables Introduction

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PART I

Outside the black box: path-dependent growth

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1 Path-dependent economic growth with technological trajectory

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2 Path-dependent economic progress and regress

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3 Division of labor in innovation between general purpose technology and special purpose technology

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PART II

Dynamics of the black box: intersectoral growth 4 Advantages of backwardness and forwardness with shifting comparative advantage

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5 Changing productive relations, linkage effects and industrialization

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6 Structural change and economic growth with relation-specific investment

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PART III

Inside the black box: innovation mechanism 7 Focusing device as innovation mechanism and cluster growth

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8 Managing innovation probabilities through focusing device

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9 Three-step flow of knowledge communication

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PART IV

Measuring the black box: innovation flow matrix and policy evaluation

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10 Model of intersectoral flow of technology using technology and innovation flow matrices

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11 Estimating innovation flow matrix and innovation linkages in the East Asian region and the United States

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12 Endogenous innovation and macroeconomic shocks in a New Keynesian DSGE model

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References Index

259 273

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Figures

1.1 1.2 5.1 5.2 5.3 5.4 5.5 6.1 8.1 8.2 8.3 11.1 12.1 12.2 12.3 12.4 12.5 12.6 12.7 12.8 12.9

The growth paths The growth paths and convergence clubs Determination of backward and forward linkages Effects of R&D shocks Effects of capital share shocks and an increase of labor share Effects of labor share shock Effects of vertical specialization Determination of forward linkages Innovation trajectories Three types of dynamic strategies Shifts in competitive advantages and innovation trajectories Production structure Preference shock (ebt ) Government expenditure shock (egt ) Investment adjustment cost shock (eit ) Investment-specific technology shock (ect ) Price markup shock (ept ) Wage shock (ew t ) Monetary policy shock (ert ) Productivity shock (est ) Endogenous innovation shock (eat )

33 34 108 110 111 111 113 127 166 167 167 212 248 249 249 250 251 251 252 253 254

Tables

5.1 8.1 8.2 9.1 9.2 9.3 9.4

Correlation between backward and forward linkages Capability management in two-tier technology systems Management of technology systems Descriptive statistics Determinants of boundary spanning individuals (TOBIT) Determinants of the frequency of internal communication Percentage of boundary spanning individuals who communicate with transformers 10.1 Total, direct, and indirect effects 10.2 Indirect effects of key sectors 11.1 Innovation input–output matrix (G0 ) (excluding the USA) 11.2 Innovation input–output matrix (G0 ) (with the USA) 11.3a Innovation backward and forward linkages 11.3b Innovation backward and forward linkages 11.4 Z tests for pairwise differences in innovation forward linkages (without US) 11.5 Z tests for pairwise differences in innovation forward linkages (with US) 11.6 Average growth rate and volatility 12.1 Parameter estimation 12.2 Variance decompositions

101 160 162 182 184 185 186 204 205 222 225 227 228 230 231 232 246 247

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Introduction

1 Inside and outside the black box One thing that is obvious about societies that have achieved certain degrees of industrialization is that innovation has been the critical variable in accounting for the dynamics of the economies and the resulting levels of economic prosperity. Industrial economies have acquired unusual skills in generating, diffusing, and elaborating innovation, and understanding innovation is basic to comprehending economic growth and development. According to Rosenberg (1994), to further investigate the role of innovation in economic growth, two relevant questions must be answered: “what can be said about the manner in which the stock of technological knowledge grows over time? And, to what factors is it responsive, and in what ways?” However, satisfactory answers to these questions have not been provided, at least through formal analysis. What is less obvious than the critical role of innovation is the underlying mechanism of innovation, or inside the black box (Rosenberg, 1982), and its economic implications, which can be referred to as outside the black box. This implies that an integrative approach has to be taken to explore both inside and outside the black box. On the one hand, the existing literature on innovation has studied innovation processes at the firm level, with less attention paid to economic consequences and implications at the economy level. On the other hand, a relatively recent development in the field of endogenous economic growth are studies that have incorporated endogenous innovation in a general equilibrium framework and drawn various economic policy implications. However, the innovation mechanism utilized presupposes a simple innovation function, in which a positive relationship is assumed between R&D investment as an input and the arrival of innovation in a deterministic or stochastic manner. As a result, in the endogenous growth literature, an innovation mechanism is assumed, rather than explored. Instead, the literature has focused on drawing out the economic implications of this simple innovation function. The purpose of this book is to provide several models regarding the economics of the innovation system, which can be applied to analyses of both inside and outside the black box. Of course, it is difficult to simultaneously integrate a detailed description of the innovation process as in the innovation management

2 Introduction

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literature with the complicated system of equations that describe a general equilibrium in an economy. Indeed, parts I and II of this book follow the standard modeling framework of the endogenous economic growth literature. However, from part III, we gradually incorporate a more detailed innovation mechanism into the model. This book attempts, at the least, to move between inside and outside the black box and to draw some implications regarding innovation policies and management. For this purpose, we are interested in developing some empirical models that are subject to data analysis. Therefore, one of the characteristics of this book lies in the balanced approach taken in examining innovation through theoretical and empirical studies as well as from the perspectives of inside and outside the black box. In the remainder of this introductory chapter, we first provide a brief review of the related literature regarding innovation management and innovation economics and draw implications relevant to our research. Thereafter, we point out the perspectives of this book that distinguish its analysis from the related literature. Finally, the outline of this book is described.

2 Innovation management The inside of the black box has been explored primarily in studies within the field of innovation management. However, the approach in this field tends to be more descriptive than analytical. As a result, integrative and consistent theoretical frameworks and models have yet to be developed. Nevertheless, some of the existing studies provide useful insights on exploring inside the black box. As it is not our purpose to conduct an extensive or complete review of the literature, we will focus on two topics in this field that are most relevant to our research: typologies of innovation and innovation process. 2.1 Typologies of innovation Innovation refers to something new that must be reflected eventually in the values and costs of products or services. According to Schumpeter (1934), there are five types of innovation from the perspective of creating new combinations: (1) the introduction of new goods; (2) the introduction of a new method or production process; (3) the opening of a new market; (4) the acquisition of a new source of raw materials or semi-manufactured goods; and (5) the establishment of a new organization of any industry. Rosenberg (1982) pointed out that the common denominators underlying innovation were (1) a greater volume of output or (2) a qualitatively superior output from a given amount of resources. Thus, innovation could be specified in economics as a shift of a production function or product quality. However, what is less obvious are the more specific types of innovation that lead to lower costs or higher quality levels. Although the types of innovations differ considerably in the preceding studies, most of the definitions of innovation tend to involve three key dimensions: (1) technological discontinuity (radical vs. incremental innovation); (2) the

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Introduction 3

place of innovation (products vs. process innovation); (3) the user expectation (sustaining vs. disruptive innovation); and (4) systemic view (architectural vs. modular innovation). Radical and incremental innovations refer to the degree of novelty or technological discontinuity between old and new technologies (Tushman and Anderson, 1986). Thus, the technological development that led from VCRs to DVDs is classified as radical because of the underlying differences between analog and digital technologies. Radical innovation cannot be achieved through current continuous technological trajectories. Rather, it requires new technological disciplines that must be either invented or modified, building upon technologies transferred from other fields. This typology has many implications for practitioners in R&D laboratories because both require different types of search algorithms. However, from the economic modeling perspective, whether an innovation is radical or incremental does not make a fundamental difference in the derivation of their economic consequences, because the qualitative differences are translated into a quantitative difference in terms of the magnitude of a jump parameter l. For example, suppose that the quality level of a current technology is represented by ln, where l > 1. The arrival of innovation can be modeled as an increase in n, i.e., lnþ1 . The radical innovation in this specification merely involves a larger magnitude of l, without significant qualitative differences being generated compared with a smaller magnitude of l – i.e., incremental innovation, unless further assumptions are imposed. Therefore, in economic models at least, the technological discontinuity itself does not generate significant qualitative differences. The place of innovation is sometimes referred to in a dynamic context. Abernathy and Utterback (1978) developed a so-called A–U model. A central idea is that competition takes place in different phases, respectively the fluid, transitional, and specific phases. During the fluid phase, where technological and market uncertainties prevail, many firms enter the market with competing product designs. The competition occurs in terms of the characteristics of these product designs, with much less competition on the basis of quality and cost. In this first phase, many product innovations take place but fewer process innovations. In the transitional phase, a dominant design emerges and the amount of technological variety decreases. The number of competing firms also decreases. In this phase, process innovation becomes much more important, whereas product innovation begins to wither. The nature of competition shifts from model specifications to costs and quality. In the specific phase, the competition has fully shifted to cost and the number of producers has dropped. Innovation in this phase emphasizes incremental process innovation to achieve lower costs within the dominant design. Thus, the locus of innovation shifts from product to process innovation as the dominant design emerges. The dynamics of innovation along with industrial change in this A–U model are primarily based on the historical analysis of the US automobile industry. Although the model fits the early evolution of this industry sector, whether it is generalizable and applicable to other industries has yet to be seen. From the modeling perspective, the distinction between product and process innovation

4 Introduction

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does not have any significant difference. Suppose that product innovation improves product quality V and process innovation lowers its costs C. Then, both improvements can be summarized in a single measure V =C. As long as this measure increases, it enhances the productivity of the firm, which in turn contributes to economic growth. It is irrelevant whether this improvement arises from V (product innovation) or C (process innovation). Therefore, although the A–U model provides useful insights into the dynamics of a specific industry, its relevance to analysis of an economy as a whole seems limited unless further assumptions are imposed. User expectations are also related to types of innovation. According to Christensen (1997), a sustaining innovation has a predicted technological trajectory in which quality and cost improve over time in a smooth and consistent manner. However, an “innovator’s dilemma” sometimes takes place when current users refuse to purchase or adopt new technology. For example, Seagate Technology developed a 3.5-inch hard disk drive in 1984. However, one of the main customers at that time, IBM, refused to adopt that product. As a result, Seagate abandoned the development project. As time went by, new usages were gradually found for 3.5-inch hard disk drives in laptop computers, and they replaced the 5.25-inch hard disk drives even in the main market segment of desktop computers. As a result, eventually, the 3.5-inch hard disk drive dominated the whole market. Christensen (1997) argued that it was the rejection of IBM that forced Seagate to abandon its R&D project. In other words, the customer expectation matters for the decision regarding R&D investment in new technology. Although the 3.5-inch hard disk drive was not a radical innovation, its impact on current technologies was enormous. Of course, if IBM could have correctly predicted the subsequent technological improvement in the 3.5-inch hard disk drive and the emergence of the corresponding market for laptop computers, it would have immediately adopted the new technology. However, owing to technological and market uncertainty, it misjudged these developments. This implies that users sometimes make incorrect judgments regarding new technology in the face of uncertainty. Consequently, even innovators terminate what can be eventually successful R&D projects. It should be noted that disruptive innovation, defined as innovation that the main users are not willing to adopt, has no direct relation to radical innovation. Indeed, according to this typology, the invention of the DVD does not correspond to a disruptive innovation because most users were willing to switch from VCRs to DVDs. It is not technological properties but user expectations that determine the definition of a disruptive innovation. From the modeling perspective, this disruptive innovation could be reflected in a delayed adoption of the innovation by users. In addition, neither users nor producers will be certain about when the adoption might actually take place or whether it will at all. Surrounded by this high level of uncertainty, the presence of disruptive innovation discourages R&D investment. Hence, the simplest way to model disruptive innovation is to raise R&D costs and discount innovation rents. Once again,

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Introduction 5

the economic consequences of this type of innovation are the subject of quantitative, rather than qualitative, differences. Henderson and Clark (1990) proposed a systemic view of technology, whereby a technology system consists of core design concepts and components. A component is defined as a physically distinct portion of the product that embodies a core design concept and performs a well-defined function. According to their model, incremental innovation reinforces core concepts while leaving the linkages between core concepts and components unchanged. In contrast, radical innovation changes not only the linkages but also the core concepts themselves. Although the existing studies have emphasized both radical and incremental innovation, they insist that a substantial portion of innovations take the form of either architectural or modular innovation. Architectural innovation changes the way in which the components of a product are linked together while leaving the core design concepts untouched. Modular innovation overturns core concepts, while the linkages remain intact. Thus, these new typologies take a systemic view on technology and innovation. This systemic view provides useful insights into innovation economics because an economy consists of many industries. As shown by a Leontief input–output model, one of the distinctive characteristics of modern society is mutual interdependence across industry sectors, which in turn implies the systemic nature of technology and innovation. However, the existing studies in innovation economics do not necessarily account for this systemic nature of technology and innovation, at least in their formal models. Therefore, the incorporation of this systemic nature of technology and innovation into economic models constitutes a challenging research agenda. 2.2 Innovation process The innovation process can be defined as the development and selection of ideas and the transformation of these ideas into an innovation. This process consists of certain phases, stages, or activities. Most innovation studies have identified these stages as some form of idea generation; the selection of ideas; turning the selected idea into some product, process, or service (development and testing); and the implementation of the innovation in the market, including mass production, marketing, and sales (see, for example, Cooper, 1986; Andrew and Sirkin, 2007; Hansen and Birkinshaw, 2007; Tidd and Bessant, 2013). One of the representative innovation process models is the stage-gate innovation process, introduced by Cooper (1986), which has distinctive and orderly phases. The process could be used to facilitate and manage innovation by allowing the next stage to start only if a project complied with all the requirements of the prior stage. In each stage, certain criteria are specified to examine a given project. Once a project passes the examination based on these criteria, it can proceed to the next stage. Although this linear approach is useful for the practical management of an innovation process, it is sometimes criticized because its view of the innovation process is too simplistic. Instead, alternative models are

6 Introduction

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proposed that allow for many feedback loops and cycles within the innovation process (Tidd and Bessant, 2013). According to these models, in the early stages, the innovation proceeds in a nonlinear manner, with many feedback loops and cycles, but it becomes more linear, formal, and rigid as it progresses to later stages, as discussed by Cooper (1986). This modification reflects the role of uncertainties in the innovation process. That is, as the process proceeds, uncertainties gradually decrease. To efficiently manage the innovation process, we need to determine appropriate search algorithms to effectively reduce the uncertainty surrounding the innovation process. March (1991) proposed two types of such algorithms: exploitation and exploration. On the one hand, exploitation is a mode of learning that aims to deliver on the opportunities inherent in the current products or services. This learning can be considered analogous to climbing up to the top of a single hill and staying there. On the other hand, exploration pursues the discovery of new opportunities outside the current context, with the corresponding analogy being roaming the misty mountains, rather than a single clear hill. March (1991) pointed out that there is a trade-off between the two modes of learning because they require different organizational designs. In the case of exploitation, the firm should focus on the current performance agenda with strong, clear goals, measures, incentives, accountability, and discipline. In contrast, exploration encourages extensive search beyond the current contexts and celebrates failures, which requires slack resources, lax controls, soft incentives, and qualitative rather than quantitative measures. Thus, the role of innovation management is to increase the underlying innovation probability rather than to rigidly control the process. In the context of exploitation vs. exploration, appropriate organizational settings, such as incentive schemes, management styles, and organization cultures, should be congruent with the corresponding search algorithms, which in turn increases the underlying innovation probability. As an alternative, but not necessarily mutually exclusive, approach, von Hippel (1988) proposed a means of finding market opportunities by systematically tapping the expertise and experience base of lead users. A lead user is defined as the user that experiences needs ahead of the market segment in which they operate, with some lead users seeking to innovate on their own. By tapping the expertise of these lead users, the firm could find invaluable sources of innovation. This lead user research is also instrumental in increasing the innovation probability. The existing studies clearly suggest the importance of analyzing the innovation process through the lens of innovation probability (Harada, 2014a). As innovation is the result of some stochastic processes, its outcomes cannot be controlled in a deterministic manner. When the process starts from basic research through commercialization, it is likely that the success rate (at least if the project is commercialized) would be lower than, say, 30%, depending on the type of technologies and the market conditions. In the pharmaceutical industry, for example, only a small percentage of the basic research projects result in a new drug approval. In this case, failure of the innovation project cannot be attributed

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Introduction 7

to mismanagement of the project. Rather, it is the result of underlying stochastic processes, in which the success probability is extremely low. Therefore, the management of the innovation process should be directed towards increasing the innovation probability of the innovation process. In other words, innovation management should correspond to management of the innovation probability. This perspective provides useful insights for the research in this book.

3 Innovation economics Innovation economics commenced with the seminal work of Joseph A. Schumpeter in 1934. Schumpeter began by analyzing the evolution of the economic system and quickly recognized that this evolution is propelled by the activities of innovative entrepreneurs within the economic sector. Following his work, innovation was recognized as one of the critical factors generating economic development and growth. However, it took more than a half-century for innovation to be fully incorporated into economics. Earlier efforts in neoclassical economics involved incorporating innovation as an exogenous shift in the production function, which could be measured by the Solow residual (Solow, 1956). Dissatisfaction with this neoclassical treatment of innovations as exogenous shocks triggered the emergence of innovation economics in several fields. First, economic historians began to analyze economic development and growth in terms of innovation, leading to the discovery of the path-dependent nature of innovation (David, 1985; Arthur, 1989; Rosenberg, 1994). Second, the inadequacy of the neoclassical treatment of innovation stimulated Nelson and Winter (1982) to propose their so-called evolutionary theory. Third, this theory was applied more directly to innovation itself and analyzed in terms of a national innovation system. This approach focused on the institutional aspects of the innovation system as well as on the knowledge flow across sectors. Finally, in contrast to the neoclassical growth model, the endogenous growth literature incorporated innovation as the outcome of economic activity, rather than as exogenous shocks, and examined how endogenous innovation is accounted for by various economic variables. In what follows, we will briefly review these four fields as representative of innovation economics, at the risk of disregarding other important work on innovation economics. Note that this review is intended to be selective, rather than comprehensive, based on the relevance to our research interests and perspectives in this book (for a more thorough review of this field, see, for example, Fagerberg, 2005). 3.1 Path-dependent nature of innovation The main features of technology and innovation available at any given time can only be understood by a systematic examination of the earlier history out of which they emerged (Rosenberg, 1994). The path dependency of innovation means that important influences upon the eventual outcome can be exerted by temporally remote events, including happenings dominated by historical

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accidents rather than systematic forces. As the famous example of the QWERTY layout in typewriters by David (1985) suggests, the path-dependent effect might select Pareto inferior outcomes owing to its lock-in effects. The underlying stochastic processes do not converge automatically to a Pareto efficient equilibrium. This path-dependent nature of innovation clearly suggests that history matters (David, 1985; Arthur, 1989; Rosenberg, 1994). This implies that any outcomes of innovation should be examined in terms of the path the innovation took over time. Even though state variables are the same between two innovation paths, subsequent dynamics might differ unless their historical paths reaching the current states also coincide. This historical force could be changed within a limited time period, i.e., within a window of opportunity. If this window is closed, the eventual outcomes cannot be altered to move towards more desirable states. Hence, according to the path-dependent nature of innovation, not only a careful examination of history but also the identification of lock-out opportunities is critical to achieving efficiency (Ghemawat, 1991). The path-dependency arguments shed new light on standard economic analyses, in which it is assumed that an ergodic equilibrium will be achieved, regardless of initial conditions. Under increasing returns, the economic process tends to lock-in to certain states as a result of historical accidents or expectations, giving rise to less efficient economic outcomes (Krugman, 1991a). As innovation economics is primarily concerned with the dynamics of technological evolution and innovation, sufficient attention should always be paid to historical paths of technology and innovation. 3.2 Evolutionary theory In the literature on innovation economics, debate continues regarding the adequacy of neoclassical theory in accounting for economic changes. The main arguments stem from proponents of the so-called evolutionary theory. The work of Nelson and Winter (1982) is one of the major contributions to evolutionary economics. These authors focused on the issue of changes in technology and routines, suggesting a Darwinian evolutionary process of economic change. Under this theory, the innovation mechanism consists of the three phases of variation, selection, and retention. The firms in an economy are a collection of heterogeneous organizations guided by routines, the evolutionary economic equivalent of genes. Firms search for innovative or imitative solutions to improve their profits (variation), and, as a result of selection in markets, successful firms grow at the expense of the less successful ones (retention). The process of search (variation), selection, and retention is dynamic in nature because firms may not be able to reach a unique and stable equilibrium point. Thus, evolutionary economics analyzes a process of economic change and innovation that occurs through generating and electing a diversity of ideas with more survival values and shows, mainly through simulation exercises, that orthodox equilibrium and evolutionary outcomes do not correspond with each other. This difference is caused by the fact that, under the latter approach, novel environments may

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Introduction 9

be created as the mix of firms changes, and firms may fail to discover the optimal rules. One of the most important implications of evolutionary economics is its emphasis on interactions across economic agents, such as firms, human resources, and institutions, through routines. As a result, the innovation processes are more likely to be path-dependent over time. During such processes, even the actors involved could not ex ante know the optimal path, and hence, the end result. Of course, mainstream economics does allow for some kinds of interaction. However, at the same time, it is trivial in most cases because an equilibrium is reached immediately under the assumption of perfect foresight or rational expectations (the exceptions include chaotic dynamics). In evolutionary economics, interaction is far more than trivial because multiple paths exist and their selection depends on history, expectations, and other social forces. This makes evolutionary economics complementary to the path-dependent nature of innovation. However, the radical departure of evolutionary economists from mainstream economics, such as their rejection of all the components of the maximization model, has lessened its influence on the mainstream, despite stimulating enormous subsequent work in the field of evolutionary economics. Although we are sympathetic to their views and efforts to make economic models more realistic, complete rejection of maximization and equilibrium models can result in useful results being disregarded and the advantages of mainstream economics being overlooked. In particular, the specific models and simulation exercises of evolutionary economics are likely to be arbitrary, which make it harder to evaluate the effects of policy measures such as taxes, interest rates, and monetary supply. Thus, what remains to be done is not to deny evolutionary economics, but to develop it in a direction that incorporates the advantages of mainstream economics without sacrificing the central evolutionary ideas of variation, selection, and retention loops. In particular, their emphasis on interaction provides a valuable perspective on innovation economics. 3.3 National innovation system The national innovation system literature aims to understand differences in innovation performance and profiles of technological specialization among countries. Following the pioneering work of Freeman (1988), Lundvall (1992), and Nelson (1993), a growing body of literature has developed. The national innovation system refers to the network of institutions in the public and private sectors (Freeman, 1988), the interactions of which determine the innovative performance of national firms (Nelson, 1993). This approach focuses on flows of knowledge and attempts to evaluate and compare the main channels for knowledge flows at the national level, to identify bottlenecks and to suggest policies to improve their fluidity. Obviously, the knowledge flow is derived primarily from interaction between economic agents and institutions. Thus, innovation is the result of a complex interaction, which cannot be generated in a linear sequence but rather through

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Introduction

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feedback loops within the system. The success of firms, and of national economies as a whole, is dependent on their efficiency in gathering and utilizing knowledge through these complex interactions. Learning by interaction plays a critical role here, in addition to learning by doing and using (Lundvall, 1992). This learning takes place primarily among firms, universities, and research institutions, yet each country differs in its own institutional settings, such as the governance structures of firms, university systems, and government-funded research systems. The differences in the characteristics and the relative roles account for different knowledge flows and interaction patterns, which, in turn, affect the outcomes of innovation at the country level. This necessitates taking an institutional view on the national innovation system to analyze the underlying knowledge flow. In other words, intersectoral flows of technology and innovation matter in the analysis of the national innovation system, which is influenced by the embedded institutional settings within the system. However, as Nelson and Rosenberg (1993) pointed out, the concept of a national innovation system is too broad. For instance, the system of institutions supporting innovation in pharmaceuticals may have very little overlap with those supporting innovations in aircraft (Nelson and Rosenberg, 1993). In particular, under this approach, institutions can refer to almost everything, encompassing not only economic agents, such as firms, banks, universities, and public research institutions but also cultural components, such as language, habits, customs, traditions, and social conventions. Consequently, such broad definitions are rarely useful in identifying the key elements in the national innovation system that account for innovation performance. Indeed, Lundvall (1998) addressed this concern by pointing out that focusing on a specific aspect of economic life can result in more fruitful research outcomes than adopting a broad concept that seemingly encompasses everything. This highlights another weakness of this approach, which is the lack of theoretical foundations underlying the national innovation system and the knowledge flows across institutions. Indeed, the more specific dynamics of innovation and institutional change in the national innovation system is not well specified. As a result, at present, this approach remains more descriptive than analytical, although further efforts at analysis have been made (Lundvall, 2007; Chaminade, Lundvall, and Haneef, 2018). More specifically, while this approach emphasizes that learning and interaction is vital to innovation, little discussion has occurred on the nature of knowledge flows and linkages. For this approach to progress, it requires more rigorous microfoundations that account for the knowledge flows across sectors. 3.4 Endogenous growth Endogenous growth theory explains long-run growth as emanating from endogenous economic activities that create innovation (Romer, 1990; Grossman and Helpman, 1991; Aghion and Howitt, 1992). The long-run rate of economic growth, as measured by the growth rate of total factor productivity (TFP), is

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Introduction

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determined by the rate of technological progress, i.e., innovation. The neoclassical growth theory (Solow, 1956; Swan, 1956) assumes that the rate of innovation is determined by a scientific process that is independent of economic forces. Endogenous growth theory challenges this neoclassical view by endogenizing innovation as the result of human capital, knowledge spillovers, and R&D investment. This implies that innovation is not the result of random events and, hence, long-run economic growth can be influenced by economic factors. To facilitate innovation and economic growth, innovation policies to promote more investment in education, knowledge spillovers, and R&D matter. Obviously, these modeling efforts to endogenize innovation are a response to some of the criticisms raised by evolutionary economics against the neoclassical growth theory. Moreover, the literature focuses on positive externalities and spillover effects of knowledge, as in the national innovation system literature. One of its most significant advantages over evolutionary economics and the national innovation system approach lies in its rigorous microfoundations, which enable the model to be examined through empirical analyses. Although it is easy to criticize the rigorous treatment of economic relations based on optimization and rational expectations, at the same time, it avoids elusive and arbitrary model specifications. In reality, it is probable that the choice between abstract but rigorous models and a more realistic but rather arbitrary conceptual framework might depend on the research purpose. If the aim is rich description of historical events and institutional backgrounds, undoubtedly the latter approach should be taken. However, for the purpose of drawing some general propositions and examining the complex relations among economic variables either theoretically or empirically, the former approach would be more appropriate, despite its limitations in terms of strict and unrealistic assumption. Obviously, the endogenous growth literature takes this approach and succeeds in incorporating innovation into its general equilibrium framework. However, from the perspective of our research interests, the endogenous growth literature is missing the interactive aspects of innovation within institutional settings, which has been the central issue in the national innovation system literature. In addition, the path-dependent nature of innovation is disregarded in its standard models. These deficiencies are not the result of theoretical limitations; rather, they reflect research interests that differ from those of the literature that we have reviewed above. Therefore, one of the missions in this book is to incorporate these perspectives on intersectoral linkages and the path-dependent nature of innovation into the framework of the endogenous growth model.

4 Perspective on innovation The purpose of this book is to analyze innovation both inside and outside the black box. The brief literature review above reveals several implications, which in turn assist in illuminating the direction of research in this book. In particular, the following perspectives on innovation could be extracted from the related literature: (1) the innovation probability perspective; (2) the systemic

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Introduction

12

view on innovation; (3) intersectoral relations; and (4) path dependency. Below, we discuss each of these in turn. 4.1 Innovation probability perspective Empirical evidence from several studies in the innovation management literature suggests that organizational practices and inertia make innovative efforts diverge from the innovation probability maximization principle, which in turn requires the effective management of focusing devices (Rosenberg, 1976; Harada, 2014a, 2014b, 2015b). One of the implications of these results is that the effective management of innovation is made possible when innovative activities are appropriately arranged and coordinated in terms of innovation probabilities, instead of relying on elusive concepts such as enactments, routines, and capabilities. In a simple innovation function in which innovation depends on R&D investment, this perspective might seem trivial. Indeed, the common policy implication underlying a number of endogenous growth models is that R&D investment should be subsidized to promote innovation and economic growth. However, once the systemic nature of innovation is taken into account, the priority given to subsidies has to be determined among several competing technology components, the criteria for which could be social welfare, a firm’s profits, and economic growth. The innovation probability perspective focuses on the latter to promote innovation. In particular, when this perspective is applied to the more microlevel of innovation management, we need some conceptual apparatus to evaluate how to improve the underlying innovation probability where technology consists of components, each of which has to be improved over time to facilitate innovation. This book examines this issue in terms of the focusing device. 4.2 Systemic view on innovation This perspective on innovation highlights the importance of conceiving of technology as a system. For example, personal computers (PCs) consist of items, including the central processing unit, the operating system, memory, the motherboard, hard drives, monitors, and keyboards. PC manufacturers purchase most of these from outside suppliers, such as Intel and Microsoft. No existing PC manufacturing firms produce all of them internally. Thus, innovation in the PC industry critically depends on innovation in those PC components. As we have seen, Henderson and Clark (1990) proposed the existence of two types of innovation, architectural and modular innovation, in addition to radical and incremental innovation. These two types of innovation presuppose the existence of a technology system in which components are somehow related to each other under the guide of a core design concept. This systemic nature of technology is not necessarily reflected in a typical innovation function adopted in the endogenous growth literature. Consequently, the innovation policy becomes quite simple to recommend subsidies on R&D and human capital investment. However, once this systemic nature of technology is allowed, more careful

13

Introduction

13

examination is required to determine which technology components should be subsidized to promote the overall innovation. To address this question, technology and its components should be specified as a kind of technology and economic system. The decision on the priority of R&D subsidies should depend on not only pure technological necessities but also the underlying economic forces. In other words, the former should be translated into the latter, which in turn provides some guidance regarding the desirable direction of innovation. The inside of the black box of innovation would be revealed, to some extent, through the lens of this internal technological and economic logic of innovation, which will be modeled as a focusing device in this book. 4.3 Intersectoral relations When we shift our focus from inside to outside the black box of innovation, the systemic view on innovation necessitates paying more attention to intersectoral linkages. Once we admit that technology consists of many components with market frictions, such as transaction costs, it becomes apparent that some of the components are produced outside the boundary of a single firm that produces final products. Indeed, nowadays, it is a major trend in many industries to produce less and outsource more. The complementary relations between the relevant sectors account for one of the characteristics of modern innovation (Rosenberg, 1982). At the level of outside the black box, the systemic nature of innovation could be reflected in intersectoral relations in terms of technology as well as commodities. These intersectoral relations are well accounted for by a standard Leontief economy, in which the input–output matrix describes the flow of commodities across sectors, assuming fixed proportions of factors of production with no substitutability. This rather restrictive assumption is relaxed by Long and Plosser (1983) in a framework of real business cycles, allowing for flexibility among factors of production and dynamic settings. However, much of their effort was directed to reproducing business cycles when innovations are regarded as exogenous random events, as in the case of neoclassical growth models. Subsequent work following the framework of Long and Plosser (1983) shares a similar research interest in accounting for business cycles rather than endogenous innovation. This book attempts to incorporate intersectoral relations mainly from two perspectives. First, we will consider an intersectoral relationship between the general purpose technology (GPT) and special purpose technology (SPT) sectors. Although the role of GPT has been well acknowledged in related literature (Bresnahan and Trajtenberg, 1995; Helpman, 1998), its model specification is relatively limited. This book attempts to fill this gap by developing a model of intersectoral relations between GPT and SPT and analyzing their roles in economic growth. Second, although GPT–SPT relations are vertical, we also consider horizontal intersectoral relations across sectors producing technology components. These intersectoral relations entail not only commodity flows but

14

Introduction

14

also technology and innovation flows. In this book, we will build intersectoral models of economic growth that incorporate both flows and analyze how innovation could be facilitated in the presence of the intersectoral flows of technology and innovation. Moreover, based on the theoretical models, we propose an empirical framework to estimate the flows of technology innovation across sectors, using new concepts of technology and innovation flow matrices, which could provide useful policy implications. 4.4 Path dependency Finally, some of the models in this book explicitly incorporate the pathdependent nature of innovation and examine how innovation is influenced by historical forces. Although not all the models in this book consider the effects of path dependency explicitly, we believe it is of critical importance to allow for the role of history in the dynamics of the economy as a whole. This clearly raises the hurdles for our modeling efforts because it can make the model extremely complicated as a result of the nonergodic nature of the stochastic processes. However, when it is feasible, we attempt to incorporate the pathdependent nature of innovation into this book. We believe that these four perspectives – the innovation probability perspective, the systemic view on innovation, intersectoral relations, and path dependency – constitute an important agenda in the field of innovation economics. Of course, we do not intend to adopt these perspectives simultaneously in all models in this book because of modeling difficulties. Instead, our approach is a more modest one of taking these perspectives on innovation eclectically, rather than exhaustively. Our intention is not to build a comprehensive theory, but rather to develop several different models that account for at least one of these perspectives. In so doing, we hope to fill some gaps between mainstream economics and the related innovation literatures. Therefore, one of the unique features of this book lies in its balanced approach to innovation through the four outlined perspectives, with the aim of articulating innovation both inside and outside the black box.

5 Outline of the book This book consists of four parts. Part I examines what is outside the black box and, thus, provides models of path-dependent endogenous growth. Chapter 1 develops an integrated model of neoclassical and endogenous growth, which accounts for both income inequalities across countries and the convergence hypothesis, while all the growth stylized facts are satisfied. The model in this chapter assumes that an economy industrializes in two stages. In the first stage, the economy starts industrialization through factor accumulation (the Solow stage); after sufficient factor accumulation, it switches to the second stage of endogenous growth through innovation (the AK stage). Therefore, it becomes crucial to determine when switching from the Solow to the AK stage is

15

Introduction

15

implemented. We model this switching problem as a two-stage optimal control and show that the growth rate declines during the Solow stage, while in the AK stage it becomes constant. In addition, we draw several policy implications. Chapter 2 develops a two-stage economic growth model with real options and examines the effects of various subsidy policies. The economic stages are the deterministic and stochastic AK stages, and the economy may shift between the two, depending upon state variables and technological shocks. This model allows for path-dependent economic growth that accounts for both club convergence and divergence across countries. Moreover, it is shown that under certain conditions, a decrease in the subsidy rate facilitates the shift from the deterministic to stochastic AK stages, which is defined as “economic progress”, even in the face of an economic crisis, while more subsidies delay economic progress and promote the shift from the stochastic to deterministic AK stages, which is defined as “economic regress”. Chapter 3 constructs an endogenous growth model that identifies three patterns in the division of labor in terms of innovation between GPT and SPT sectors: (1) the SPT stage; (2) the GPT–SPT joint-research stage; and (3) the autonomous GPT stage. It is shown that the emergence of GPT only has a temporary level effect, and a negative effect on economic growth. However, the new phenomenon of the autonomous GPT stage has a positive influence on both growth and level effects. This result theoretically explains the emergence and resolution of the IT productivity paradox. Part II is concerned with the dynamics of the black box with multiple sectors in the economy. The existence of multi-sectors that are undertaking innovation is assumed, and the interrelation and dynamics of the multi-sector innovation systems as endogenous growth models are examined. Chapter 4 develops a multi-sector endogenous innovation model that is able to account for the dynamics of comparative advantage of each sector within the economy. The model in this chapter assumes that two kinds of learning effects exist in R&D: advantages of backwardness and forwardness. It is shown that if the economy is divided into advanced and backward sectors, in the latter sectors, the advantage of backwardness dominates, leading to cyclic repetition of comparative advantage. However, in the former sectors, the advantage of forwardness becomes more significant, so comparative advantage among these sectors stabilizes. Thus, the direction of learning spillovers has a critical effect on the dynamics of comparative advantage. Given this result, it is shown that only R&D policies for the marginal sector are effective in facilitating economic growth. If a decision is made to facilitate R&D investment within advanced sectors, R&D taxes, rather than subsidies, should be imposed on this marginal sector. Moreover, it is shown that trade liberalization does not affect the intrinsic dynamics of comparative advantage among surviving sectors in the economy if the locus of this marginal sector does not change significantly after trade liberalization. Chapter 5 develops a multi-sector endogenous innovation model that is able to take changing productive relations among sectors into account. It is shown that while productivity and demand shocks do not induce any changes in productive

16

Introduction

16

relations and linkage effects, shocks in the productivity of R&D increase both backward and forward linkages. Key sectors are characterized as having high forward and backward linkages, which are consistent with the definition of key sectors in the existing empirical studies. However, vertical specialization generates not only sectors with high backward and low forward linkages, but also sectors with low backward and high forward linkages. As a consequence of this vertical specialization, the latter sectors become key sectors, in the sense that they have significant effects on business fluctuations. This implies that general purpose technology sectors emerge, and sector-specific policies for these sectors play a critical role in economic development and growth. Chapter 6 develops an intersectoral endogenous innovation model that is able to account for changing productive relations among sectors and examines how the relation-specific investment affects the evolution of industry structure. It is shown that in the steady state, the economy gets stuck in the “growth trap”, where the economy still achieves positive growth, but at the lowest level. The most efficient remedies for the growth trap are to facilitate relation-specific investment among sectors and to decrease the degree of specialization in the economy. Thus, the relation-specific investment is indeed instrumental in improving economic efficiency in the face of the growth trap. These remedies could be implemented by subsidies on relation-specific groups and permanent R&D taxes. Part III investigates inside the black box by developing the economic models. Chapter 7 models a focusing device of innovation in which a cluster has an oring type production function and each technology component endogenously upgrades its quality. We show that provided the magnitude of innovation is the same across technology components, competitive equilibrium is an efficient mechanism by which core technology-driven innovations emerge with expanding inequality among clusters. Our result is in sharp contrast to bottleneckremoving innovation that is widely accepted. The inefficiency arises, however, when low-powered incentives, such as cost plus contracting, are employed to reward innovation. In this case, the corresponding factor price provides erroneous information regarding the potential benefits of innovation, which should be corrected by some form of policy intervention. Chapter 8 analyzes two types of innovation: core-driven and bottleneckremoving innovations in terms of management of focusing device. We show that core-driven innovation should be undertaken when technology components are independent (independent technology system), while bottleneck-removing innovation should be pursued when they are interdependent (interdependent technology system). Different types of focusing device should therefore be adopted based primarily on the degree of interdependence among technology components, which in turn maximizes underlying innovation probabilities. One of the implications of the results is that the effective management of innovation is made possible when innovative activities and corresponding focusing devices are appropriately arranged and coordinated to maximize innovation probability.

17

Introduction

17

Chapter 9 explores the determinants of innovation at a more micro-level within organizations, given the focusing device, in terms of knowledge communication among organization members. Although the related literature points out information gathering and information transmitting functions as main roles of gatekeeper, this chapter further suggests the knowledge transforming function that has to be executed within R&D organizations. We will argue that since the latter function often requires distinctive skills that impede information gathering activities, there emerges a three-step flow of communication instead of a two-step flow of communication. We define persons fulfilling this new role as knowledge transformers, and related testable hypotheses are derived. The latter part of this chapter proposes new measuring methods that identify knowledge transformers and test these hypotheses. Part IV is concerned with measuring the black box. It proposes a new concept of an innovation flow matrix and assesses that matrix. In addition, this part of the book considers both business cycles and endogenous innovation in the unified New Keynesian dynamic stochastic general equilibrium (DSGE) model and examines how business cycles and other policy shocks affect endogenous innovation. Chapter 10 builds a simple general equilibrium model that sheds new light on the mechanism of intersectoral flows of technology. It explicitly models the production of technology using diverse technology components as inputs and proposes technology and innovation flow matrices. The model shows that demand shocks do not cause innovation, while technology shocks as deviations from a balanced growth path induce asymmetric productivity changes across sectors. We also conduct a simple quantitative analysis using recent Japanese R&D data, which shows that most productivity effects remain within the bounds of the sector. We find some important exceptions to this rule, however, in particular for shocks occurring in information technology and precision instruments. Chapter 11 also estimates the innovation flow matrix by taking a different approach from Chapter 10. Using industry-level total factor productivity data, we estimate innovation input–output matrices and examine the properties of innovation linkages for two areas: the East Asian region and the integrated region of East Asia and the USA. Our empirical examination favors unbalanced as opposed to balanced growth and identifies core and bottleneck sectors that are the targets of the unbalanced growth strategy. In particular, we found that sectors with high innovation backward and forward linkages are likely to become bottlenecks. Chapter 12 constructs an endogenous growth model using the framework of New Keynesian dynamic stochastic general equilibrium models incorporating endogenous innovation. This chapter estimates the model parameters using Japanese economic data. Given the estimates, the relationship is evaluated between endogenous innovation and macroeconomic variables, in particular from the perspective of the effects of several macroeconomic shocks on endogenous innovation. The results demonstrate that low interest rate policies discourage endogenous innovation while facilitating investment in existing technologies.

18

Introduction

18

Moreover, it is found that any innovation policies that generate positive productivity gains in terms of future innovation discourage endogenous innovation. These results indicate both a trade-off and complementary relationship between current technologies and future innovation. To facilitate innovation, monetary policy should not include low interest rates, and the government should not subsidize productivity gains through innovation. Instead, higher interest rates and subsidies for current technologies should be facilitated. In this way, the book presents a unified treatment of the innovation system from the perspectives of both inside and outside the black box, based on rigorous economic models and empirical analyses. This work unifies path dependency, multisector dynamics, endogenous growth, and business cycles under several general equilibrium models and, we hope, sheds new light on innovation economics.

6 Acknowledgements I would like to thank my teachers at Stanford, Nathan Rosenberg, Masahiko Aoki, Ken-ichi Imai, and Paul David, for their continuing advice and encouragement. In particular, I owe the greatest intellectual debt to Nathan Rosenberg. I also thank Tadao Kagono, Toshihiro Kanai, Ichiro Tokutsu, Hideo Suehiro, Hideo Kozumi, Hideki Yoshihara, and Kiyonori Sakakibara for their advice and useful comments. In Chapter 12, I have benefitted from technical support and advice from Yasuo Hirose and Masataka Eguchi. Seminar participants at Kobe, Osaka, and Kyoto Universities, Organization Society in Japan, Japan Society for Evolutionary Economics and the International Input–Output Association, are greatly appreciated for their useful comments. This project is financially supported by JSPS KAKENHI (Grant Number 26380506). Finally, I would like to express my greatest appreciation to my parents, Iwao and Ritsuko Harada, my wife, Rumi Harada, and my three children, Yuki, Kako, and Takahiro.

19

Part I

Outside the black box Path-dependent growth

21

1

Path-dependent economic growth with technological trajectory

1 Introduction Although a wide consensus has emerged that income inequalities across countries are attributable to differences in technology rather than differences in human capital accumulation, little work has explored how different technologies are adopted and improved, or how subsequent technical change takes place. Most of the related studies on economic growth and development assume identical production functions across countries, and only the differences in factor endowments, savings rate, or productivity levels are allowed to account for crosscountry differences. However, according to a famous study by Habakkuk (1962), the technological experiences of the US and Britain during the nineteenth century stand in a sharp contrast to each other. That is, US nineteenth-century technological progress can be attributed to a tendency towards labor saving, whereas technological progress in Britain can be attributed to a tendency towards saving capital rather than labor. Habakkuk’s thesis was later reformulated by David (1975) such that relative factor prices influence choices among techniques, but such choices, in turn, have a strong influence upon the path of subsequent technological change due to “local technological spillovers”. As a result, the US selected labor-saving technology, leading to labor-saving technological change, while Britain adopted capital-saving technology and subsequently followed the path of capital-saving technological change. These contrasting “technological trajectories” between the US and Britain and their “path-dependency” are widely accepted among economic historians, but not necessarily among growth and development economists. The purpose of this chapter is to formalize the ideas of “local technological spillovers”, “technological trajectory”, and “path-dependent aggregate growth”, and to show how path-dependence can account for convergence or divergence among multiple countries in the process of economic growth and development. For this purpose, the two-stage optimal control problem is formulated to integrate both the neoclassical Solow and endogenous growth models. The model in this chapter assumes that the economy industrializes in two stages. In the first stage, the economy starts industrialization through factor accumulation (the Solow stage), and after sufficient factor accumulation, it switches to the

22

Outside the black box

22

second stage of endogenous growth through innovation (the AK stage). Therefore, it becomes crucial to determine steady-state growth when the switch from the Solow to the AK stage is implemented. The two stages of economic growth have been modeled in previous studies as well. For example, Matsuyama (1999) argues that two views of growth, one based on factor accumulation and the other based on innovation, are complementary in that they capture different stages of a single growth experience. Matsuyama presents a model where endogenous growing cycles emerge between the neoclassical and endogenous growth phases and the economy perpetually moves back and forth between the two phases. We share the view that the two phases represent different stages of a single instance of economic growth but differ in that we assume the two growth stages are irreversible and the timing of the switch from the first to the second stage is endogenously determined by a social planner. That is, the newly industrializing economy grows through factor accumulation in the first (Solow) stage, but the social planner has the option to switch to the second (AK) stage of innovation-based growth. Once the economy switches to the second stage, there is no incentive to move back to the first stage in the future. Of course, the economy in the second stage continues to grow through factor accumulation, but the engine of growth at this stage is attributed to innovation, instead of investment in capital, enabling the economy to achieve sustainable growth. Irmen (2005) also models two stages of economic growth: extensive growth through capital accumulation and intensive growth through endogenous innovation. In this model, capital accumulation raises the relative wage, which in turn induces labor-saving innovation. However, since this model sticks to the neoclassical framework, economic growth is not sustainable, and the steady-state growth rate converges to zero without population growth. In contrast, we adopt the AK model as the second stage of innovation-based growth that incorporates the embodied technological change and gives rise to positive endogenous growth. Moreover, the model in this chapter differs from the standard AK model in that the level of the capital–labor ratio at the time of the switch accounts for the productivity level. This specification is similar to that of localized learning by doing as proposed by Atkinson and Stiglitz (1969) and David (1975), in which a firm or economy learns over time to improve the productivity of the particular mix of capital and labor that it is currently using. In these models, since the capital–labor ratio is fixed, the capital– output ratio decreases over time without population growth. But according to the growth stylized facts pointed out by Kaldor (1961), it must be steady. In addition, these models yield the de facto Leontief-type production function, which seems extreme. The complete lack of substitutability between inputs is not well justified even in the presence of local spillovers. The model in this chapter allows for factor substitutability so that the capital– labor ratio is allowed to change over time. The localized spillover is assumed to take effect in the learning platform represented by the specific capital–labor ratio at the time of the switch to the AK stage. Basu and Weil (1998) adopt a similar

23

Path-dependent economic growth 23

specification of technology called “appropriate technology”. That is, in the appropriate technology model, the economy improves and learns from the productivity of similar techniques represented by the range of capital–labor mixes. Accordingly, if the economy increases the capital–labor ratio, the range of similar techniques exerting local spillovers changes as well. Thus, in this model, the learning platform changes over time. In contrast, the specification of technology in this chapter implies that this platform remains the same once the economy shifts to the AK stage. Thus, the determination of the switch to the second stage has a path-dependent nature since the timing of the switch determines the subsequent technological trajectory and, hence, its steady-state economic growth. This specification is more in line with Atkinson and Stiglitz (1969) and David (1975), while allowing for factor substitutability between capital and labor and satisfying the growth stylized facts. In this model, latecomers with little capital accumulation tend to grow faster in the Solow stage, but gradually their growth rates decline and converge to the growth rate of advanced countries that follow the same technological trajectory. These results are consistent with the recent experiences of eastern Asian countries such as Japan and Korea. These nations achieved rapid economic growth in the post–World War II period, although their growth rates eventually declined. The initial high-growth rate and its gradual decline could also be attributed to the changing role of international technology transfer. In other words, this could be accounted for by the “advantage of economic backwardness” suggested by Gerschenkron (1962). The idea of the advantage of economic backwardness reflects the fact that latecomers tend to grow faster than the leading countries due to international technology transfer and spillovers, but when the former approaches the technological frontier, they tend to face economic slowdown. This mechanism of catching up is consistent with the evidence for b convergence (Barro and Sala-i-Martin, 1995) or the catch-up hypothesis (Abramovitz, 1986) in advanced countries. Hence, while the model in this chapter satisfies all of the growth stylized facts (Kaldor, 1961) by synthesizing the Solow and AK models, it incorporates the path dependency suggested by Habakkuk and David, which accounts for income differences across countries due to differences in technological trajectories. Also, as in the neoclassical growth models, our model accounts for the convergence and, as in the endogenous growth literature, the savings rate matters in determining the long-run economic growth in this model. The rest of this chapter is organized as follows. Section 2 presents a basic model of two-stage economic growth, and Section 3 considers the policy implications of this model. Finally, Section 4 presents our conclusions.

2 The model In this section, the basic model of this chapter is presented. The model adopts the standard two-stage optimal control techniques proposed by Tomiyama (1985), Tomiyama and Rossana (1989), Makris (2001), and Boucekkine, Saglam, and

24

Outside the black box

24

Vallee (2004) and derives the equilibrium condition for the optimal switching problem between the Solow and AK stages. Consider a continuous-time economy inhabited by a representative agent, the intertemporal utility function of which is U¼

Ð1

ert ln cðtÞdt;

ð1:1Þ

0

where r refers to the time discount factor and cðtÞ denotes the per capita consumption level at time t. Denote the per capita capital by k, the production function in the consumption sector by f ðkÞ and the investment by I. The consumption goods are used either for consumption or as inputs in the production of the capital goods such that y ¼ c þ I ¼ f ðkÞ: The production function in the capital-goods sector is k_ ¼ f ðkÞ  dk  c; where d is the rate of depreciation of capital. There are two stages of economic growth in this model: (1) the Solow stage and (2) the AK stage. These stages represent different production functions and engines of growth. In the Solow stage, the production function takes the form of f ðkÞ ¼ A1 k α ;

ð1:2Þ

where A1 represents the productivity index and 0 < α < 1 is assumed. In order to incorporate the economic advantage of backwardness, we assume A1  A1 ð~k 0 Þ; A0 1 ð~k 0 Þ > 0; where ~k 0 denotes the highest level of per capita capital in the world at the outset of industrialization (t ¼ 0). So, at this stage, any underdeveloped country could take advantage of international technology transfer from the advanced countries. This benefit enhances the steady-state level of capital accumulation, but without switching to the next AK stage, the growth rate declines over time due to decreasing marginal products of capital. In the AK stage, the production function is given by f ðkÞ ¼ A2 k α ; and y

A2 ¼ ðmk1 Þ k 1α ; is assumed. This specification is standard in the AK models, except for the term y ðmk1 Þ . This term represents the effect of the capital–labor ratio at the time of the

25

Path-dependent economic growth 25

switch. We assume m > 0, but y can be either positive or negative. If it is positive, the new and old technological regimes are complementary, but if it is negative, both become substitutable. Thus, the production function in the consumption sector during the AK stage becomes f ðkÞ ¼ ðmk1 Þ k: y

ð1:3Þ

In this model, the initial capital–labor ratio at the time of the switch to the AK stage plays a critical role in subsequent economic growth. The positive values of y would reflect the historical fact pointed out by Rosenberg (1976). He argued that labor-abundant economies are unlikely to generate a stream of capitalsaving innovations, largely because of the stagnation and backwardness of capital-goods industries. Since such capital-goods industries do not provide the necessary skills and aptitudes conducive to innovation, labor-abundant countries are unable to succeed in industrialization. In other words, the lower levels of capital accumulation do not provide sufficient spurs to innovation and growth and, hence, the learning platform. On the other hand, the negative value of y would reflect the mechanism of leapfrogging by follower countries. For example, Brezis, Krugman, and Tsiddon (1993) model the systematic process of leapfrogging in international North– South trade. In their model, leapfrogging takes place as a response to occasional major technological change. When such a change occurs, the new technology does not initially seem to be an improvement for the North, given their extensive experience with old technologies. Thus, the South has a stronger incentive to adopt new technology, and once the new technology proves more productive than the old, the South establishes a new lead. In other words, the disadvantage of forwardness generates leapfrogging, which implies the negative values of y. Note that at this stage, international technology transfer plays only a limited role. As was argued by Basu and Weil (1998), technology improvements diffuse slowly across countries, although knowledge spreads instantaneously and there are no technology adoption costs at this stage. Basu and Weil account for this fact by the “appropriateness” of technology. That is, technology transfer takes place locally, within the neighborhood of the current technology. At the Solow stage, economic growth is enabled by factor accumulation alone, which is likely to be facilitated by international technology transfer in the form of licensing and foreign direct investment (FDI). On the other hand, at the AK stage, indigenous R&D investment becomes an engine of growth where the learning platform plays a significant role. In other words, local adaptation, rather than adoption from abroad, becomes a more important and relevant issue. As a result, the effect of international technology transfer is weakened, and instead, the local conditions at the time of the switch to this stage have a profound effect on the subsequent growth path. However, the above specification differs from the Basu and Weil model in that the appropriateness of technology is determined at the time of the switch to the AK stage, while the latter model assumes that the local spillover depends only on

26

Outside the black box

26

the neighborhood of the current capital level, k. That is, ½k  g; k þ g for some g > 0. So, as the capital level increases, the range of the neighborhood changes as well. We do not adopt this specification, since the initial learning platform seems critical in the subsequent innovation process in many countries. For example, Toyota’s just-in-time system was invented not through the imitation of the Ford system but by benchmarking the US chain-store management. As a result, the subsequent development in the Japanese automobile industry has been significantly different from that in the US automobile industry. Now assume that at date t1  0, the economy does operate the switch. Then, the production function of the capital-goods can be decomposed as follows: k_ ¼ A1 ð~k 0 Þk α  dk  c;

ð1:4Þ

if 0  t < t1 , and y k_ ¼ ðmk1 Þ k  dk  c;

ð1:5Þ

if t1 < t. As is clear from (1.4), the growth rate in the Solow stage would be higher if the initial capital–labor ratio remains low. Thus, during the phase of low capital accumulation, the Solow stage tends to be preferred in order to maximize social welfare and economic growth. But, as is well known, the growth rate declines to zero in the Solow stage in the absence of population growth. In contrast, in the AK stage, the growth rate always remains at the same positive level. Moreover, the growth rate is determined by capital accumulation during the Solow stage. Hence, the social planner has an incentive to switch from the Solow to the AK stage sometime in the future. Two-stage optimal control In this model, the social planner is assumed to determine the timing of the switch from the Solow to the AK stage. This assumption is not at all unrealistic since in most rapidly growing Asian countries, such as China, Indonesia, Singapore, and Korea, the role of government in promoting growth has been significant; such nations are sometimes referred to as “developmental dictatorships”. Although it remains an empirical question as to whether these countries have shifted to the endogenous growth stage, if this shift is to take place, the role of the governments would remain significant. Therefore, the timing of the shift to the AK stage constitutes one of the most important development policies for these countries. This problem can be formulated and solved using a two-stage optimal control technique. Although we closely follow the solution methods described by Boucekkine, Saglam, and Vallee (2004), since the Solow stage does not yield a closed-form solution, we cannot analytically solve this two-stage optimal control problem as in Boucekkine, Saglam, and Vallee. However, since the AK stage does yield a closed-form solution, we can at least characterize the optimal timing of the switch from the Solow to AK stages of economic growth.

27

Path-dependent economic growth 27

The objective function for the social planner can be rewritten as Zt1

Z1 rs

Uðc; t1 Þ ¼

e

ers ln cðtÞdt:

ln cðtÞdt þ

0

ð1:6Þ

t1

The social planner maximizes this objective function with respect to t1 and cðtÞ, subject to (1.4) and (1.5). Boucekkine, Saglam, and Vallee suggest that this problem can be solved in four steps. In step 1, assuming that t1 and the capital–labor ratio at the time of switch, k1 , are given, we solve the optimal control problem in the second stage. That is, maximize Z1 ert ln cðtÞdt;

U2 ðc; t1 Þ ¼ t1

subject to (1.5). In step 2, using the optimal values derived in step 1, maximize Zt1 ert ln cðtÞdt þ U2 ðk1 ; t1 Þ;

U1 ðc; t1 Þ ¼ 0

subject to (1.4). Following Tomiyama (1985), we can formulate the Hamiltonians associated with these Pontryagin problems as H1 ðk; c; t; l1 Þ ¼ ert ln cðtÞ þ l1 ðA1 ð~k 0 Þk α  dk  cÞ;

ð1:7Þ

H2 ðk; c; t; l2 Þ ¼ ert ln cðtÞ þ l2 ððmk1 Þ k  dk  cÞ;

ð1:8Þ

y

where lj refers to the costate variable in the jth stage at time t1 , and Hj represents the Hamiltonian value in the jth stage (j ¼ 1; 2). Then the following optimal conditions have to be satisfied: l1 ðt1 Þ ¼ l2 ðt1 Þ; H1 ðk1 ; t1 Þ ¼ H2 ðk1 ; t1 Þ;

ð1:9Þ ð1:10Þ

where * indicates the optimal value. Equation (1.9) ensures the continuity of the costate variable at time t1 , and Equation (1.10) is the optimality condition that allows an interior switching time to exist. In step 3, a sufficient condition for maximum, @H2 ðk1 ; t1 Þ @H1 ðk1 ; t1 Þ  < 0; @t1 @t1

ð1:11Þ

is checked, and finally in step 4, we examine whether corner solutions of immediate switching or no switching exist or not. The immediate switching is optimal

28

Outside the black box

28

if H1 ðk0 ; 0Þ  H2 ðk0 ; 0Þ: No switching is optimal when H1 ðk1 ; t1 Þ < H2 ðk1 ; t1 Þ holds for every t1 > 0. Step 1: AK stage First, let us examine solutions for the AK stage of economic growth. The optimal control problem in this stage is Z1 ert ln cðtÞdt;

max U2 ðc; t1 Þ ¼ c

ð1:12Þ

t1

subject to (1.5) where k1 and t1 are given. With the corresponding Hamiltonian, (1.8), the first-order necessary conditions are ert ¼ l2 ðtÞ; c ðtÞ

ð1:13Þ

@H2    k_ ¼ ðk ; l2 ; c ; tÞ; @l2

ð1:14Þ

@H l_ 2 ¼  2 ðk  ; l2 ; c ; tÞ; @k

ð1:15Þ

lim l2 ðtÞ  0 and lim l2 ðtÞk  ðtÞ ¼ 0:

ð1:16Þ

t!1

t!1

Solving these conditions, we obtain y

c ðtÞ ¼ rk1 efðmk1 Þ drgðtt1 Þ ; k  ðtÞ ¼ efðmk1 Þ l2 ¼ 

y

drgðtt1 Þ

efðmk1 Þ

y

k1 ;

dgðtt1 Þrt1

rk1

:

ð1:17Þ ð1:18Þ ð1:19Þ

Step 2: Solow stage Next, a solution must be reached for the Solow stage of economic growth. The corresponding optimal control problem is formulated as Zt1 ert ln cðtÞdt þ U2 ðk1 ; t1 Þ;

max U1 ðc; t1 Þ ¼ c; t1

ð1:20Þ

0

subject to (1.4). The initial capital–labor ratio, k0 , at time 0 is assumed to be given. With the corresponding Hamiltonian, (1.7), the first-order necessary

29

Path-dependent economic growth 29

conditions are ert ¼ l1 ðtÞ; c ðtÞ

ð1:21Þ

@H1    k_ ¼ ðk ; l1 ; c ; tÞ; @l1

ð1:22Þ

@H l_ 1 ¼  2 ðk  ; l1 ; c ; tÞ: @k

ð1:23Þ

One difficulty in this step is that no closed-form solution can be derived in the Solow model. Without closed-form solutions, we cannot analytically derive the optimal timing of switching, as is done in Boucekkine, Saglam, and Vallee (2004). However, instead of the optimal timing, we can derive a closed-form solution for the capital–labor ratio at time t1 . From (1.19) and the optimality condition (1.9), we have l1 ðt1 Þ ¼ l2 ðt1 Þ ¼ 

1 rt1 e : rk1

Substituting this in (1.10), we obtain H2 ðk1 ; t1 Þ  H1 ðk1 ; t1 Þ ¼

k1 y rt e 1 ðA1 ð~k 0 Þk1 α1y  my Þ ¼ 0: r

ð1:24Þ

Thus, the optimal interior solution, if it exists, is given by  1

k ¼

A1 ð~k 0 Þ my

1 !1αþy

:

ð1:25Þ

Step 3: sufficient condition Now we are in a position to check whether the interior solution obtained in step 2 is indeed optimal. For the optimal interior solution to exist, the sufficient condition (1.11), @H2 @H1 ðk ; t Þ  ðk ; t Þ < 0; @t1 1 1 @t1 1 1 must hold. Substituting (1.25) into this condition yields 

ert1 y1 @k k ðA1 ð~k 0 Þð1  αÞk11þαy þ ymy Þ 1 < 0: r 1 @t1

ð1:26Þ

30

Outside the black box

30

Note that although the optimal capital–labor ratio at the time of the switch is represented in (1.25), clearly k1 is a non-decreasing function of t1 . During the Solow stage, the longer the period of capital investment, the more capital is accumulated, unless the economy has exhausted its growth potential. That is, if the economy does not switch to the AK stage, the capital is accumulated from k0 up to !1 ~k Þ 1α αA ð 1 0 k ¼ ; d and no further capital investment is made. Note that k0 < k is assumed here. Otherwise, it makes no sense to consider the Solow stage of economic growth in this @k model. Therefore, if k1 < k, clearly we have 1 > 0. As a result, the sufficient @t1 condition requirements are always satisfied as long as y > 0 and 1 1 !1α !1αþy A1 ð~k 0 Þ αA1 ð~k 0 Þ < ; ð1:27Þ my d hold. If y < 0, the sufficient condition, (1.26), requires 1 " #1αþy A1 ð~k 0 Þð1  αÞ > k1 :  ymy Substituting (1.25) in this inequality yields 1  α þ y > 0:

ð1:28Þ

Accordingly, for the optimal interior solution to exist, (1.28) must be satisfied, regardless of the sign of y. Step 4: corner solutions Finally, conditions for corner solutions must be examined. The immediate switching is optimal if H1 ðk0 ; 0Þ  H2 ðk0 ; 0Þ: From (1.24), this implies 1 !1αþy A1 ð~k 0 Þ k0 > ¼ k1 : my

ð1:29Þ

That is, when the initial capital–labor ratio, k0 , exceeds k1 , the social planner immediately switches to the AK stage with no experience of the Solow stage. In this case, the economy has already achieved a higher level of capital

31

Path-dependent economic growth 31

accumulation at time 0 so that it does not have to accumulate capital in the Solow stage. The economy directly shifts to the AK stage. The other corner solution is no switching. The condition for this case is given by H1 ðk1 ; t1 Þ < H2 ðk1 ; t1 Þ; for every t1 > 0. For this to be satisfied, we need k < k : 1

ð1:30Þ

That is, the economy has exhausted its growth potential before reaching the optimal switching point, k1 . If this condition is satisfied, clearly we have H2 ðk1 ; t1 Þ  H1 ðk1 ; t1 Þ ¼

k y  ert1 ðA1 ð~k 0 Þk α1y  my Þ > 0: r

Thus, no switching is optimal if (1.30) is satisfied. In other words, when 1 1 !1α !1αþy A1 ð~k 0 Þ αA1 ð~k 0 Þ > ð1:31Þ my d holds, no switching from the Solow to AK stages takes place (see also (1.27)). Summarizing the above results, we have the following proposition: Proposition 1. The optimal switching from the Solow to AK stages is as follows: (a) If 1  α þ y > 0 and k0
αA1dðk0 Þ > k0 , the economy never switches from the Solow to AK stages. Thus, in this model, initial conditions of k0 , A1 ð~k 0 Þ, m, and y matter in determining the optimal switching time. In order for the interior solution to exist, the negative effect of the old on the new technologies must be modest such that 1  α þ y > 0 holds. Otherwise, there exists no interior solution, and the economy either immediately switches to the AK stage or remains in the Solow stage, depending on the values of k0 and A1 ð~k 0 Þ. If the initial capital– labor ratio is too high, the economy immediately switches to the AK stage,

32

Outside the black box

32

since it does not require a preparation period for the modern endogenous growth stage. On the other hand, if the growth potential in the Solow stage is limited and the economy cannot accumulate capital up to k1 , the economy is unable to switch to the AK stage, and its growth rate converges to zero in the steady state in the absence of population growth. In this case, the policy implication can be drawn that the technology policy should make the old regime (Solow stage) as unproductive as possible in order to enable the economy to switch to the new regime (AK stage). Otherwise, the policy maker has to give up trying to attain the new regime and instead attempts to reinforce the existing old regime. In this model, if the leader country remains in the Solow stage, any countries switching to the AK stage leapfrog the former, which is a rather unrealistic scenario. If the leader country has already switched to the AK stage, the leapfrogging by the follower country becomes possible only if the capital accumulated during the Solow stage is large enough to provide the follower with an advantageous platform (k1 ) to start the new regime of economic growth. In other words, the leapfrogging follower must proceed in a technological trajectory different from that of the leader. Thus, the US leapfrogged Britain after the US adopted a technological trajectory characterized by labor-saving technological change or “the American system of manufacturers” (Rosenberg, 1994), as opposed to the British approach of capital-saving technological change. In contrast, Japan and Korea could not leapfrog the US since they all follow similar technological trajectories. These results also account for the per capita income difference among various countries. First of all, if the economy remains in the Solow stage of economic growth, its growth rate declines to zero in the long run, and growth rate and per capita income diverge from those of advanced countries. Second, even if the economy succeeds in switching to the AK stage, its productivity level is determined by the capital–labor ratio, k1 . Therefore, technological trajectories for countries are determined by the timing of the switch, which in turn depends upon the initial conditions of k0 , A1 ð~k 0 Þ, m, and y. If the technological trajectories differ, growth rates and per capita income levels diverge. Thus, the model in this chapter could account for the convergence clubs and path dependency, which is summarized in the following proposition: Proposition 2. The growth rate in the economy gradually declines and the steady-state growth rate, g, is path-dependent; economies with the same initial conditions share the same path of economic growth (convergence club) such that 1 1  ~ 1αþy  ~ 1α < αA1dðk0 Þ or (a) If 1  α þ y > 0 and either k0 < A1mðky0 Þ 1  ~ 1αþy y ð1αÞy , g ¼ m1þyα A1 ð~k 0 Þ1þyα  d  r: k0 > A1mðky0 Þ  (b) If



1

A1 ð~k 0 Þ 1αþy my

>





1

αA1 ð~k 0 Þ 1α d

> k0 , g ¼ 0.

33

Path-dependent economic growth 33

Growth rate

k03

k02 Higher growing economy

Lower growing economy

k01 Underdeveloped economy

t 11

t 12

t 13

Time

Figure 1.1 The growth paths

Figure 1.1 illustrates the result of this proposition. In this figure, three growth paths are depicted: higher growth, lower growth, and underdeveloped economies. In all of the paths, the growth rate during the Solow stage declines over time. In addition, if the initial conditions are the same among economies, obviously the timing of the switch to the AK stage and the path of economic growth are shared as well. The results of this proposition can easily be extended to allow for local spillovers so that economies with similar (although not necessarily the same) initial conditions form the convergence club. Figure 1.2 illustrates this situation. In this figure, it is assumed that some range of initial conditions exist such that economies having the same range of initial conditions eventually follow the same path of economic growth. In either case, the results in proposition 2 generate both path dependency and the convergence club, which accounts for income inequalities across countries. Due to the perfect-foresight assumption in this model, these income inequalities are attributed to the initial conditions, not the current state variables, such as the capital–labor ratio or productivity levels. These initial conditions might correspond to social infrastructure, as pointed out by Hall and Jones (1999). According to their empirical analysis, differences in physical capital and educational attainment can only partially explain the variation in per capita output, and

34

Outside the black box

34

Growth rate

k03

k03 k02 Higher growing club

k02 k01

Lower growing club

Underdeveloped club

Time

Figure 1.2 The growth paths and convergence clubs

they argue that differences in social infrastructure explain large differences in income across countries. Since the model in this chapter assumes that k1 provides the learning platform in the AK stage, this can be interpreted as social infrastructure that is responsible for a large variation in per capita income across countries.

3 Policy implications Given the above results, this section derives some implications for development strategies. In particular, we are interested in how savings rates influence the path of economic growth and how policy announcements affect the growth path. 3.1 Savings rate Suppose that some policy measures, such as taxes and subsidies, are available, and these change the savings rate in the economy. Such a policy directly affects the production function in the capital-goods sector. These can be reformulated as k_ ¼ ð1 þ s1 ÞA1 ð~k 0 Þk α  dk  c ð0  t < t1 Þ;

ð1:32Þ

y k_ ¼ ð1 þ s2 Þðmk1 Þ k  dk  c ðt1 < tÞ;

ð1:33Þ

35

Path-dependent economic growth 35

where s1 and s2 denote either the subsidy to or tax on the consumption good, depending on their signs. Following the same steps in the previous section, we obtain "

ð1 þ s1 ÞA1 ð~k 0 Þ k1 ¼ ð1 þ s2 Þmy

1 #1αþy

;

ð1:34Þ

g ¼ ð1 þ s2 Þ1αþy ½ð1 þ s1 ÞA1 ð~k 0 Þm1y 1αþy  d  r: 1α

y

ð1:35Þ

From these equations and Proposition 1, the policy effects can be characterized as follows: Proposition 3a. The savings rate affects the switching time as follows: (a) The case of interior solution @t1 @t > 0 and 1 < 0. @s1 @s2 (b) The case of immediate switching A sufficient increase in s1 and decrease in s2 gives rise to t1 > 0. (c) The case of no switching A sufficient increase in s1 and s2 gives rise to t1 < 1. In the cases of the interior solution and immediate switching, the result in the proposition suggests that an increase in the savings rate in the Solow stage delays the timing of the switch, while an increase in the savings rate in the AK stage brings forward this timing. This result is intuitive, since an increase in savings implies an increase in the social welfare in the current stage. But in the case of no switching, increases in savings in both the Solow and AK stages facilitate the switch from the Solow to the AK stage. This implies that a sufficient increase in savings shortens the timing of the switch in this case. Thus, it follows that underdeveloped countries could avoid the development trap by taking policy measures that increase the savings rate in both the Solow and AK stages. Regarding the growth rate, from proposition 2 and (1.35), we can derive the following proposition: Proposition 3b. The savings rate affects the growth rate as follows: (a) The case of switching @g @g < . @s1 @s2 @g @g < . If 1  α < y, 0 < @s2 @s1 If 1  α > y, 0
0 holds by (1.25). Thus, international technology transfer plays a significant role in preparing for the learning platform itself later. But in the AK stage, the learning platform in turn has a direct effect on the rate and direction of technological change, while international technology transfer has no such effects. Its influence is exerted only

38

Outside the black box

38

through the former. Thus, both adoption and adaptation must be carefully examined, designed, and controlled by the government, from a dynamic perspective. 3.4 Policy for switching The above model clearly suggests that the timing of the switch to the AK stage matters. If the underdeveloped country immediately adopts the AK stage at the outset of industrialization, without going through the Solow stage, its growth potential is severely restricted, sometimes causing it to become a member of the underdeveloped club, as shown in Figure 1.2. This is because the initial growth rate in the Solow stage is much higher than that of the AK stage. In order to escape from the underdeveloped club, the country must start from the Solow stage by utilizing the benefits of international technology transfer, and with a learning platform of a sufficiently high level available, the country should switch to the AK stage. However, if the underdeveloped country has already accumulated higher capital stock at the time of industrialization, an immediate switch to the AK stage is desirable, as suggested in Proposition 1. But this scenario seems unrealistic. The switch between the innovation stages has a profound effect not only on the rate and direction of technological change, but also on social welfare. If the switch is either premature or delayed, social welfare can be reduced, since it changes the consumption sequences as well as the growth rate. That is why the timing of the switch must be carefully examined and the change must be executed by a social planner in this model. Thus, developing countries must pay more attention to this timing and the learning platform, which together determine the subsequent growth path after switching to the AK stage. Of course, it remains to be resolved how the switch to the AK stage and the formation of the learning platform can be carried out, managed, and controlled by the government. Indeed, these issues have been neglected in related literature so far. The above analysis emphasizes the importance of the timing of the switch and formation of the learning platform, and it is vital for more detailed empirical studies on these issues to be carried out.

4 Concluding remarks This chapter developed a model of path-dependent economic growth in conjunction with technological trajectory. The model is fundamentally based on the assumption that there exist local technological spillovers that are available to economies with similar technologies (k1 ). Based on this assumption, once an economy switches to the AK stage, the subsequent series of innovations proceed through learning by doing in the same learning platform. The value of k1 , which is determined by the initial condition of k0 at time zero, can also be interpreted as representing a type of social infrastructure, as pointed out by Hall and Jones (1999), or a “learning platform”. In this model, it is not the current levels of state variables such as the capital–labor ratio but the historical

39

Path-dependent economic growth 39

values of k1 and k0 that determine the long-run path of economic growth and the steady-state growth rate. This path-dependent growth model accounts for club convergence, in which club members are assumed to follow the same technological trajectory. Moreover, this model explains why the growth rates of newly developing economies gradually slow down. Since these economies follow the Solow growth path, their growth rate should be higher the lower the capital–labor ratio, but eventually the rate declines. Also, as in the endogenous growth literature, the savings rate and development policies that control the rate are of significance in determining the long-run economic growth in this model. In particular, a stagnant economy that cannot switch to the AK stage should raise the savings rates in both the Solow and AK stages. However, if the economy could switch to the AK stage, the relative impact of the savings rate on economic growth differs between the Solow and AK stages, depending on the magnitude of the complementary effect of the old on the new technology. Of course, it is not necessarily realistic to assume that after the success of the second industrialization (i.e., the switch to the AK stage), economies follow the path indicated in the AK model. Different variations of economic growth stages could be modeled after the Solow stage. Thus, the model in this chapter is regarded as representing the first attempt to model complicated paths of economic growth within a simple framework of two-stage optimal control. But even this simple framework could account for the catch-up hypothesis, large income inequalities, and the path dependency at the same time. It is obviously a subject for future research to model a more realistic, complex path of economic growth after the second industrialization.

2

Path-dependent economic progress and regress

1 Introduction External shocks such as technological change, demand shifts, and policy shifts have played critical roles in the process of economic growth and development. For example, the second industrial revolution, especially in the US, was enabled by a series of innovations in machine-based manufacturing.1 World War I spurred economic growth in the US and Japan during the 1910s,2 and Japanese economic growth during 1950s would have been impossible without the special procurement boom occasioned by the Korean War.3 Conversely, these external shocks sometimes result in economic decline or slowdown, as in the cases of the bursting of the Japanese bubble economy in 1991, the Asian financial crisis in 1997, and the Lehman shock in 2008 (see for example, IMF, 2003, 2009). Although purposive R&D as an engine of economic growth has been extensively studied in endogenous growth literature, little attention has been paid to these external shocks and their relation to the process of economic growth. In contrast, the real business cycle literature focuses on external technological shocks as a cause of economic fluctuation, but in so doing, it assumes away the endogenous aspect of economic growth. This chapter attempts to develop a simple model that integrates these two contrasting views of economic growth and fluctuations. While the previous chapter and Harada (2010b) considered the shift from the Solow stage and the AK stage in a deterministic model, this chapter incorporates uncertainty into the growth model. That is, this chapter models endogenous economic growth, while allowing for recurrent technological shocks that cause economic fluctuation and affect selection between two economic regimes: the deterministic and stochastic AK stages. In the former stage, no uncertainty exists and economic growth is driven by a standard AK model of endogenous growth. However, as financial wealth accumulates, the economy could switch to the latter stage, in which recurrent technological shocks always take place and cause economic fluctuations. Despite this, the average rate of economic growth in this stage is much higher than in the former. Thus, economic growth and development in this model are caused not only by increasing returns and structural change between the two stages, but also by external technological shocks. Indeed, technological shocks

41

Path-dependent economic progress and regress

41

play a significant role in the switching between the two stages, which in turn affects economic slowdown as well as economic growth and development. The purpose of this chapter is to examine the effects of various subsidy policies on economic growth in the two stages and the optimal timing for switching between the two stages. The role of public intervention and subsidies in economic growth has been extensively studied in both the deterministic and stochastic endogenous growth framework (see, for example, Barro, 1990; Turnovsky, 1993; Corsetti, 1997). However, little attention has been paid to the role of taxation and subsidies in the process of switching between the deterministic and stochastic growth stages. We formulate this switching problem by taking a real options approach and evaluate how increases and decreases in the subsidy rates at each stage affect the optimal timing for switching. The real options approach has been extensively studied (Dixit and Pindyck, 1994), but this approach has been limited to partial equilibrium settings such as investment (Abel and Eberly, 1994), project management (McDonald and Siegel, 1985), and exchange rates (Krugman, 1991c). One exception is Dixit and Rob (1994), who examined labor mobility between the two sectors in the face of technological shocks in the general equilibrium framework. But the model used in this chapter differs from the latter in that the process of economic growth and development is explicitly incorporated and solved in three steps: (1) solving the deterministic AK stage; (2) solving the stochastic AK stage; and (3) solving the optimal timing for the switching. The real options approach is utilized in (3) alone, and (1) and (2) must be solved as optimal control and stochastic dynamic programming problems, respectively. Thus, the model used in this chapter consists of a mixture of these three different techniques. It is shown that a decrease in subsidy rates in the deterministic AK stage always facilitates the shift from the deterministic to stochastic AK stages in the face of positive shocks and delays the reversion from the stochastic to deterministic AK stages in the face of negative shocks. In this chapter, “economic progress” is defined as the switch from the deterministic to stochastic AK stages, since the latter stage allows for higher economic growth. Also “economic regress” refers to the reversion from the stochastic to deterministic AK stages. Although these two stages and their economic growth rates are exogenously fixed in this model, the switch between the two is endogenous. Thus, the subsidy policies do affect both “economic progress” and “economic regress” and the resulting economic growth rates. In the stochastic AK stage, the effect of an increase in tax rates on the stochastic part of net output also facilitates economic growth and delays economic decline. Moreover, when technological uncertainty reaches a sufficiently high level in this stage, the effect of a decrease in subsidy rates on net output plays a similar role in promoting economic growth, even in the face of economic crisis, since in this case the subsidies work as a form of insurance. In the standard endogenous growth models (see, for example, Grossman and Helpman, 1991; Aghion and Howitt, 1998a), taxes impede and subsidies promote economic growth. However, once staged economic growth and recurrent uncertainty are

42

Outside the black box

42

incorporated into the model, more taxes and a reduction in subsidies not only enable faster economic growth but also facilitate economic recovery under certain conditions. This is one of the salient findings of this chapter that sheds new light on the negative role of subsidies in promoting economic growth and recovery. In related literature, Boucekkine, Saglam, and Vallee (2004) also studied the two-stage optimal control problem involving the two deterministic AK models, and Chapter 1 examined the switch from the Solow to AK economies using a similar technique. However, the model used in this chapter differs significantly from the aforementioned in that uncertainty is introduced in the stochastic AK stages, and bilateral, rather than unilateral, shifts between the two stages are considered. That is, the model used in this chapter involves examination of not only the shift from the deterministic stage to the stochastic AK stage (“economic progress”) but also the reversion from the latter to the former stage (“economic regress”). Consequently, the model in this chapter examines the effects of various subsidy policies in the context of economic regress as well as economic progress. This also departs from the endogenous growth literature, which focuses primarily on economic growth and has tended to ignore economic decline. The rest of this chapter is organized as follows. Section 2 presents a basic model of two-stage economic growth, and Section 3 evaluates the effects of subsidy policies on economic progress and regress. Finally, Section 4 presents our conclusions.

2 The model 2.1 Preferences and technology Consider a continuous-time economy inhabited by a representative agent, the intertemporal utility function of which is Z1

1R

ert

U¼

cðtÞ dt; 0 < R < 1; 1R

ð2:1Þ

0

where R is the inverse of elasticity of intertemporal substitution, and as we will see later, this must be less than unity. r refers to the time discount factor and cðtÞ denotes the per capita consumption level at time t. In the following notations, t is omitted unless it causes confusion. There are two stages of economic growth in this model: (1) the deterministic AK stage and (2) the stochastic AK stage.4 These stages represent different production functions and engines of growth. In the deterministic AK stage, the production function takes the form of Y ¼ AD K 1b J b ; 0 < b < 1;

ð2:2Þ

where AD , Y , K, and J denote the productivity index, the output, and capital and

43

Path-dependent economic progress and regress

43

labor inputs, respectively, and the subscript D refers to the deterministic AK stage. For the sake of simplicity, the population is assumed to be stationary. Dividing this by J yields y ¼ fD ðkÞ ¼ AD k 1b ;

ð2:3Þ

AD ¼ ZD k b ;

ð2:4Þ

and

is assumed, where y and k are the per capita output and capital, respectively. Thus, the production function in the consumption sector during this stage becomes fD ðkÞ ¼ ZD k:

ð2:5Þ

In the stochastic AK stage, the production function is given by dfS ðkÞ ¼ ½ZS dt þ sdoAS k 1b ; and AS ¼ k b is assumed, where df ðkÞ is the instantaneous output flow, do is the increment to a Wiener process with zero mean and unit variance, and ZS and s are positive constants that denote the instantaneous drift and standard deviation of productivity shocks, respectively. The subscript S refers to the stochastic AK stage. Then, the production function during this stage becomes dfS ðkÞ ¼ ½ZS dt þ sdok:

ð2:6Þ

We assume ZS > ZD in what follows. If the opposite holds, there is no incentive to switch to the stochastic AK stage. Although the latter stage entails high risk, it remains attractive due to its higher returns. As ZS gets higher, the relative advantage of the stochastic AK stage increases. The consumption goods are used either for consumption or capital goods, such that y ¼ c þ I ¼ fi ðkÞ; i ¼ D; S; where I refers to the investment. The capital accumulation is given by k_ ¼ fi ðkÞ  c; where the dot denotes the time derivative. In this specification, capital depreciation is assumed away in order to simplify the algebra and notation, but this does not change the qualitative results below.

44

Outside the black box

44

2.2 The public sector Following Eaton (1981) and Corsetti (1997), we specify a general linear tax function as dT ¼ ti dy þ αskdo; i ¼ D; S;

ð2:7Þ

where T is cumulated tax revenue; ti is a time-invariant tax rate on net output in each stage, which can be called “deterministic tax rate”; and α is a time-invariant tax rate on output exceeding or falling short of its expected level, which can be called “stochastic tax rate”. Note that the latter tax revenue accrues only in the stochastic AK stage, since no stochastic disturbances are assumed in the deterministic AK stage. Budget deficits are financed by issuing consols paying an instantaneous real coupon rate, u. Define B and qB as the number of consols and their prices in terms of consumption good. Then, the dynamics of public debt follow   u dqB dBqB ¼ dT þ BqB þ ; ð2:8Þ qB qB where dqB =qB represents capital gains on consols. Following Corsetti (1997), we make a simplifying assumption of a null government expenditure without loss of generality. To be consistent with this assumption, the time-invariant tax rate should be interpreted as subsidies such that ti < 0. However, α is assumed to be positive. In the presence of positive productivity shocks, it is equivalent to taxes, but in the presence of a negative shock, it becomes subsidies. 2.3 Financial assets We assume that financial assets in this model include equity shares, consols, and claim to labor income. These are freely traded in the competitive markets without transaction costs. Thus, the financial wealth of the representative agent is W ¼ k þ BqB þ HqH ;

ð2:9Þ

where H and qH are units and real price of claims to labor income.5 We assume policy parameters, ti ði ¼ D; SÞ and α, are constant without policy changes. Hence, technology shocks (do) are the only source of uncertainty in the stochastic AK stage. The after-tax equilibrium rate of return on each financial asset takes the form of rj dt þ sj do; j ¼ k; B; H:

ð2:10Þ

That is, the returns on financial assets consist of deterministic (rj dt) and stochastic parts (sj do). The latter parts depend on technology shocks (do) alone. Since technology shocks are the common stochastic element driving the returns of all financial assets, these returns are perfectly correlated.

45

Path-dependent economic progress and regress

45

2.4 Optimal switching In this model, the social planner is assumed to determine the timing of the switch between the deterministic and stochastic AK stages. “Economic progress” refers to the switch from the deterministic to stochastic AK stages, and “economic regress” to the one from the stochastic to deterministic AK stages. So, the model in this chapter differs from the related studies on the staged economic growth in that economic regress is allowed to take place. This economic regress has often been observed in the world, such as “the productivity slowdown” in the US during 1980s, “the lost decade” in Japan during the 1990s, the Asian financial crisis in 1997, and “the Lehman shock” in 2008. Faced with these economic crises, some countries might have experienced structural changes, which could be regarded as the switch from high growing, but volatile economic regime to lower growing, but stable economic regime. This switching problem can be formulated and solved using the real options approach, although the structure of the model in this chapter is more complicated than the standard one. To take this approach, we need to solve the problem in three steps: (1) the optimal solutions in the deterministic AK stage; (2) the optimal solutions in the stochastic AK stage; and (3) the optimal timing of the switch. Note that (1) and (2) are to be solved as if the economy stays there forever. Given these results, the optimal timing could be derived in (3).

2.4.1 Deterministic AK stage First, let us consider the optimal control problem in the deterministic AK stage. We will examine both competitive and socially optimal solutions, since the optimal tax rates internalize the AK externality in the market economy. Since no uncertainty exists and each return should be equal in this stage, the portfolio shares are indeterminate. Without loss of generality, we can assume the wealth consists of equity alone and W0 ¼ k0 at time t ¼ 0. However, at the time of the switch to the stochastic AK stage, we assume the portfolio shares are immediately adjusted to the optimal ones in the stochastic AK stage, which are to be derived below. The objective function can be rewritten as Z1

1R

ert

max UD ¼ c

cðtÞ dt; 1R

ð2:11Þ

0

subject to _ ¼ Wrk  c ¼ Wð1  bÞð1  tD ÞZD  c: W

ð2:12Þ

This is a standard optimal control problem, and solving this gives rð1bÞð1tD ÞZD t R

W ¼ e

W0 ;

ð2:13Þ

46

Outside the black box c¼

r  ð1  RÞð1  bÞð1  tD ÞZD rð1bÞð1tD ÞZD t R e W0 : R

46 ð2:14Þ

In addition, the transversality condition requires r > ð1  RÞð1  bÞð1  tD ÞZD :

ð2:15Þ

Regarding the socially optimal solution, the only difference lies in the fact that the social planner now internalizes the externality without imposing taxes, such that the wealth accumulation proceeds as W_ ¼ WZD  c:

ð2:16Þ

Then, the socially optimal solution becomes W ¼ e c¼

rZD R t

W0 ;

ð2:17Þ

rZD r  ð1  RÞZD W0 e R t : R

ð2:18Þ

Thus, the socially optimal rate of growth is higher in this case, due to the internalization of externality. Then, the optimal tax rates in the market economy should satisfy tD ¼ 1 

1 < 0: 1b

ð2:19Þ

With this production subsidy, the distortion induced by the external effect of capital on labor productivity is completely offset. As a result, the competitive equilibrium achieves the socially optimal allocation. Given this result, the value function in this stage, as if the economy stays in this stage forever, is given by Z1 rt

VD ðW0 Þ¼ max

e 0

 R 1R cðtÞ 1 R dt ¼ W0 : 1  R r  ð1  RÞð1  bÞð1  tD ÞZD 1R ð2:20Þ

For these optimal solutions to exist, once again, we need (2.15) is satisfied. 2.4.2 Stochastic AK stage Next, let us examine solutions for the stochastic AK stage of economic growth. Consider the competitive equilibrium first. Given the initial condition, W1 , at the time of the switch to this stage, t1 , the representative consumer solves

47

Path-dependent economic progress and regress Z1

1R

erðtt1 Þ

max E1 fc;ng

47

cðtÞ dt; 1R

ð2:21Þ

t1

subject to dW ¼ Wnk ½rk dt þ sk do þ WnB ½rB dt þ sB do þ W ð1  nk  nB Þ½rH dt þ sH do  cdt;

ð2:22Þ

and W  0; where nk and nB denote the portfolio share of equity and consols, respectively. Since this stochastic dynamic programming problem has been extensively studied (see Eaton, 1981; Merton, 1990; Corsetti, 1997), and the derivation of the solution of the dynamic problem is long, it is reported in Appendix. We simply state the main results as follows: nk sk þ ð1  nk  nB ÞsH þ nB sB ¼ s;

ð2:23Þ

nk rk þ nB rB þ nH rH ¼ ZS  Gðn1 k  1Þ;

ð2:24Þ

c ¼ GW ;

ð2:25Þ

G¼

i nk ð1  RÞ h r  ZS þ 0:5Rs2 ; nk  ð1  RÞ 1  R

ð2:26Þ

  r  ZS þ 0:5Rs2 ð1  RÞ bðZS  Rs2 Þ þ ð1  bÞg þ R 1  ; nk ¼ r 2  ZS þ 0:5Rs2 bðZS  Rs Þ þ ð1  bÞg þ ð1  RÞ 1R

ð2:27Þ

r  ð1  RÞðZS  0:5Rs2 Þ > 0;

ð2:28Þ

where g  tS ZS  Rs2 ðtS þ αÞ is a certainty equivalent tax rate. According to Corsetti (1997), this is a certainty equivalent tax rate since changes in tS and α alter the equilibrium allocation only through changes in the values of g. Even if tS and α change but g remains constant, the portfolio shares and consumption are not affected, as is obvious from (2.25), (2.26), and (2.27). Also, it should be noted that (2.28) is imposed in order to obtain positive consumption. From (2.22), (2.23), (2.24), and (2.25), the financial wealth follows dW ¼ WðZS  Gn1 k Þdt þ Wsdo; which implies Z1 2 erðtt1 Þ Wt1R dt ¼ W11R =½r  ð1  RÞðZS  Gn1 k  0:5Rs Þ;

E1 t1

ð2:29Þ

48

Outside the black box

48

where the expectation is taken conditional on the initial level of the wealth W1 at time t1 (see Dixit, 1993, p. 13). Next, consider the socially optimal solution. The social planner also maximizes (2.21), but the resource constraint now becomes ci k_ dy  cdt h ¼ ZS  dt þ sdo: ¼ k k k

ð2:30Þ

This problem can be solved using the method described in Appendix. The firstorder condition is c ¼ R1 fðR  1ÞðZS  0:5Rs2 Þ þ rg: k

ð2:31Þ

The optimal tax policy equates this ratio to the competitive equilibrium consumption rate out of total capital, c=Wnk , which is given by (2.25), (2.26), and (2.27). Solving this yields g¼

bðZS  Rs2 Þ : 1b

ð2:32Þ

The optimal tS and α are to be determined to satisfy this equality. Given these results, the expected value in this stage, as if the economy stays here forever, can be derived as Z1

1R

erðtt1 Þ

VS ðW1 Þ  E1

cðtÞ 1R dt ¼ v1R ; S W1 1R

ð2:33Þ

t1

vS 

G 1 1R

1

2 1R ð1  RÞ ½r  ð1  RÞðZS  Gn1 k  0:5Rs Þ

;

ð2:34Þ

where for the integral convergence, we need 2 r  ð1  RÞðZS  Gn1 k  0:5Rs Þ > 0:

But it is easy to check this inequality always holds when (2.28) is satisfied. However, this inequality further needs R < 1 be satisfied, since G > 0 holds. Otherwise, VS < 0 realizes, which implies that the economy never switches to the stochastic AK stage. Moreover, to make the model non-trivial, we need to have VS ðWÞ > VD ðW Þ, at least for higher values of W . If this inequality does not hold, no switching takes place. In what follows, we assume this is always satisfied. 2.4.3 Optimal switching time Now we are in a position to solve the optimal timing of the switch. While the firm is to decide the timing of the switch in a competitive equilibrium, the optimal timing of the switch is to be determined by the social planner who maximizes

49

Path-dependent economic progress and regress

49

the social welfare. Thus, the social planner compares the social welfare between the two stages, (2.20) and (2.33).6 It should also be noted that when tax rates are fixed at the optimal levels, the solution of this switching problem is indeed socially optimal. However, if tax rates are different from the optimal values, the solution of this switching problem becomes socially optimal, conditional on the competitive equilibria in the two regimes. In other words, timing is socially optimal, but the competitive equilibria in the two regimes are not Pareto-optimal. Suppose that if the economy switches from one stage to another; the sunk cost h > 0 must be paid by the social planner. Denote the expected relative value in the stochastic AK stage by vðWÞ. According to the standard real options approach (e.g., Dixit and Pindyck, 1994), this value consists of two parts. The first, v1 ðW Þ, is the added value of being in the stochastic AK stage rather than the deterministic AK stage forever. From (2.20) and (2.33), this is given by v1 ðWÞ ¼ VS ðWÞ  VD ðWÞ;

ð2:35Þ

which is assumed to be positive, as we have described above. This implies the average growth rate in the stochastic AK stage is much higher than in the deterministic AK stage. The other part, v2 ðWÞ, comprises giving up the option of staying in the deterministic AK stage and acquiring in turn the option of staying in the stochastic AK stage, assuming rational expectations about future moves and optimal behavior in each stage, as calculated above. This is given by (see, for example, Dixit and Pindyck, 1994) rv2 ðWÞ ¼

E½dv2 ðW Þ : dt

ð2:36Þ

The intuition for this equation is that the expected return on the asset (option value) is equal to the expected capital gain (the change in the option value). Since W follows the geometric Brownian motion (2.29), using Ito’s lemma, the RHS can be expanded as 2 2 0:5s2 W 2 v2WW ðW Þ þ ðZ  Gn1 k ÞWvW ðWÞ  rv ðW Þ ¼ 0;

ð2:37Þ

where the subscripts W and WW of v2 denote the first and second derivatives, respectively. The general solution to this differential equation is given by v2 ðWÞ ¼ G1 W y1 þ G2 W y2 ;

ð2:38Þ

where G1 and G2 are constants to be determined, and y1 and y2 are roots of the quadratic equation 2 ðxÞ  r  ðZS  Gn1 k Þx  0:5s xðx  1Þ ¼ 0:

ð2:39Þ

Since r > 0, and ðxÞ is negative when the absolute value of x is large of either sign, the roots are real and of opposite signs. Without loss of generality, assume y1 < 0 < y2 . It should also be noted that ð1  RÞ > 0 always holds by (2.28). This implies y1 < 1  R < y2 .

50

Outside the black box

50

From (2.35) and (2.38), we have an expression for the expected relative value of staying in the stochastic AK stage as vðWÞ ¼ v1 ðW Þ þ G1 W y1 þ G2 W y2 :

ð2:40Þ

Then, two conditions must be satisfied for optimality of each switch, that is, value matching and smooth pasting conditions. The value matching conditions are  ¼ h; vðW Þ ¼ h; vðWÞ

ð2:41Þ

 denotes the threshold levels for the optimal switching. That is, where W < W  when W > W, it is optimal to switch to the stochastic AK stage, and when W < W , the economy should regress to the deterministic AK stage, if it stays  no switching takes place. The in the stochastic AK stage. When W < W < W, smooth pasting conditions are given by  Þ ¼ vW ðW Þ ¼ 0: v W ðW

ð2:42Þ

 and W . These two conditions and the limiting argument determine G1 , G2 , W, Consider the switch from the deterministic to stochastic AK stages, first. In  the switching this case, when the asset value hits the upper threshold level, W, takes place. As W goes to zero, the option to switch is very far from being exercised, implying that the term in the negative power of W should be absent. Otherwise, this term goes to infinity, as W goes to zero. Thus, we have vðWÞ ¼ v1 ðW Þ þ G2 W y2 : From the value matching and smooth pasting conditions, we obtain 1R  1Ry2 ; G2 ¼ ð1  RÞy1 2 vS W

 ¼ W



y2 y2  1 þ R

1 1R

ð2:43Þ 1

1R v1 : S ðh þ VD Þ

ð2:44Þ

Following a similar argument, the switch from the stochastic to deterministic AK stages requires the value function as vðWÞ ¼ v1 ðW Þ þ G1 W y1 : Applying the value matching and smooth pasting conditions yields 1Ry1 1R ; G1 ¼ ð1  RÞy1 1 vS W



y1 W ¼ y1  1 þ R

1 1R

ð2:45Þ 1

1R v1 : S ðh þ VD Þ

ð2:46Þ

Note that although y1 < 0, since y1 < 1  R holds, as described above, the first  always holds from (2.44) term on the RHS of (2.46) is positive. Since W < W

51

Path-dependent economic progress and regress

51

 the and (2.46), if the current state variable is in the region of W < W < W, economy could be in either the deterministic or the stochastic AK stage, depending upon its history. That is, if the economy has shifted from the deterministic to stochastic AK stage, the current stage should be the latter, while if it has remained in the deterministic AK stage or reverted from the stochastic AK stage, the current stage should be the deterministic AK stage. Thus, even if the state variable W is the same among economies, their stages could differ. This result is summarized in the following proposition: Proposition 1. The economic stage is determined as follows:  < W, then the economy is in the stochastic AK stage. (a) If W (b) If W < W , then the economy is in the deterministic AK stage.  , then the economy is in either the deterministic or the (c) If W < W < W stochastic AK stage, depending upon its historical path. In other words, economic growth in this model is path-dependent, such that both convergence and divergence could co-exist among several countries in terms of growth rates and stages. Howitt (2000) and Howitt and Mayer-Foulkes (2004) also attempt to account for not only convergence but also divergence in growth rates among multiple countries. In their models, countries that either conduct or implement modern R&D converge to the same growth rate in the long run, but those that do not make R&D investments diverge from those that do. In contrast, in this chapter, the growth rates of countries could differ in the steady state, even if their state variables are the same. This is because history matters in this model. Thus, countries with the same state variables could belong to different growth stages or “convergence clubs”.

3 Subsidy policies In this section, various subsidy policies are examined based upon the above model. In particular, we are interested in how they influence the process of economic progress and regress. Note that, as described above, the tax in this model should be interpreted as subsidies, since the null government expenditure is assumed. To avoid unnecessary confusion, we will use “subsidy” instead of “tax”, except for stochastic taxes, in what follows. A change in the subsidy rate primarily works through the effects on the household’s portfolio allocation, which in turn affects income, consumption, and production. Since the optimal timing of the switch is to be determined by the household in this model, the change in the subsidy rate does shift the optimal timing. In general, more subsidies (lower g) will be associated with lower debt-to-capital ratios (nB =nk ), but this does not necessarily hold in some cases. For example, if R < 1, a decrease in subsidies may reduce the quantity of capital in portfolio, even though the debt-to-capital ratio is declining.

52

Outside the black box

52

3.1 Subsidies in the deterministic AK stage First, let us examine the effect of subsidies in the deterministic AK stage in the context of economic progress and regress. Although a decrease in subsidies obviously reduces the value of this stage, this in turn increases the relative advantage of the stochastic AK stage. As a result, reducing subsidies in this stage always facilitates the shift to the stochastic AK stage. Even in the face of negative shocks, a decrease in subsidies enhances the value of remaining in the stochastic AK stage, which delays reversion to the deterministic AK stage if the economy has already shifted to the former. This result is summarized in the next proposition. Proposition 2. In the deterministic AK stage, a decrease in subsidies always  facilitates economic progress (@ W=@t D < 0) and delays economic regress (@W =@tD < 0). Proof. See Appendix. Note that an announcement of subsidy decreases is effective even if the economy stays in the stochastic AK stage, since this announcement alters the threshold  and W . Therefore, this subsidy policy could be carried out, regardless levels, W of the current economic stage. In addition, although the divergence from the optimal subsidy rate reduces the social welfare in the deterministic AK stage, if the economy remains in the stochastic AK stage, this announcement does not directly affect social welfare, while it delays economic regress. 3.2 Subsidies in the stochastic AK stage Next, consider the subsidy effects in the stochastic AK stage. In this stage, two kinds of subsidies are available, i.e., deterministic (tS ) and stochastic (α) subsidies. The former is provided on the net output, the latter on the stochastic part of net output. The effects of these subsidies on economic progress and regress are as follows: Proposition 3. In the stochastic AK stage, (a) If ZS < Rs2 , then a decrease in deterministic subsidy rates in the stochastic AK stage facilitates economic progress and delays economic  regress (i.e., @ W=@t S < 0, @W =@tS < 0). 2 (b) If ZS > Rs , then an increase in deterministic subsidy rates in the stochastic AK stage facilitates economic progress and delays economic  regress (i.e., @ W=@t S > 0, @W =@tS > 0). (c) An increase in stochastic tax rates in the stochastic AK stage always facilitates economic progress and delays economic regress (i.e.,  @ W=@α < 0, @W =@α < 0). Proof. See Appendix.

53

Path-dependent economic progress and regress

53

Surprisingly, the results indicate that imposing lower subsidies in this stage under certain conditions also facilitates economic progress, but the economic reasoning for these results is quite intuitive. An increase in stochastic tax rates implies that when the economy encounters negative shocks, tax reduction takes place, while more taxes are levied in the presence of positive shocks. Thus, the stochastic tax works as insurance that smooths consumption over time. Since the representative agent is risk averse, an increase in stochastic tax rates always enhances the value of the stochastic AK stage. Second, a decrease in deterministic subsidy rates usually reduces the value of the stochastic AK stage. However, if uncertainty is high enough, a deterministic subsidy also works as insurance since it is provided on the stochastic part of net income as well. Indeed, a certainty equivalent tax rate decreases with a reduction in deterministic subsidy rates under high uncertainty, since @g=@tS ¼ ZS  Rs2 . Thus, a reduction in deterministic subsidies in this situation implies a decrease in taxes in the face of negative shocks (note that subsidies in this case become taxes if do < 0). Due to risk aversion, this reduction in deterministic subsidies increases the value of the stochastic AK stage. If subsidies are introduced in the standard endogenous growth models (see, for example, Grossman and Helpman, 1991; Aghion and Howitt, 1998a), the growth rate must increase, since entrepreneurs with subsidies could make more R&D investment in these models. In contrast, this chapter predicts that reducing subsidies facilitates economic progress and, hence, economic growth. This counterintuitive result is due to the “insurance” function of the subsidies in volatile environments. However, it should be noted once again that a change in the subsidy rates implies a diversion from the Pareto-optimal allocation in the market economy. If the economy is in the deterministic AK stage, these changes do not directly affect the economy until it switches to the stochastic AK stage. The goal of these subsidy policies should be facilitating economic progress or avoiding reversion from the stochastic to the deterministic AK stage, rather than maximizing the expected utility of the representative agent.

4 Concluding remarks This chapter developed a model of path-dependent economic progress and regress and examined the effect of subsidies in two stages. This model differs significantly from existing growth models in that recurrent technological uncertainty and staged growth are introduced. Three main results were obtained. First, the model allows for path-dependent economic growth that accounts for both club convergence and divergence. In this model, even if the state variables are the same across the countries, since optimal switching depends upon not only the state variables but also history, the resulting stages might differ. Club convergence is enabled by similar histories as well as the similar state variable in this model.

54

Outside the black box

54

Second, it is shown that a decrease in the subsidy rate in the deterministic AK stage always facilitates economic progress and delays economic regress. Thus, regardless of whether the economy is in the process of economic growth or decline, an announcement of a reduction in subsidies would appear to be an effective measure in order to facilitate economic progress. Third, an increase in the stochastic tax rates also facilitates economic progress and regress, and a decrease in the deterministic subsidy rates in the stochastic AK stage has a similar effect when technological uncertainty is sufficiently high. This is because stochastic taxes and deterministic subsidies work as insurance, allowing realization of higher social welfare with risk aversion. This negative aspect of subsidies under certain conditions has not received much attention in previous studies. However, in situations in which recurrent uncertainty is significant, this negative role of subsidies should be taken into account in designing growth policies.

Notes 1 During the nineteenth century, “the American system of manufactures” emerged first in the US, in which manufacturing goods were (1) produced by specialized machines; (2) highly standardized; and (3) made up of interchangeable component parts. Rosenberg (1994) describes: “While greater homogeneity of tastes was originally conducive to the introduction of goods produced according to the American system of manufactures, it is also true that, once this technology began to spread, it in turn shaped and influenced tastes in the direction of simplicity and functionality. Furthermore, although American factor endowment pushed in the direction of mechanization, the experience with mechanization in itself brought about an improvement in inventive activity and its more rapid diffusion” (Rosenberg, 1994, p. 119). 2 Usually, high costs of war outweigh its positive economic effects. However, Goldstein (2003) states: “Countries that can fight wars beyond their borders avoid the most costly destruction (though not the other costs of war). For example, the Dutch toward the end of the Thirty Years’ War, the British during the Napoleonic Wars, the Japanese in World War I, and the Americans in both World Wars enjoyed this relative insulation from war’s destruction, which meanwhile weakened their economic rivals” (p. 215). 3 After the adoption of the “Dodge Line”, an anti-inflationary policy in 1949, the Japanese economy encountered economic crisis due to the resulting deflation and money shortage. The recession caused by the Dodge Line was transformed into a boom overnight by the outbreak of the Korean War, and “Japan settled on the road to long-term recovery” (Nakamura, 2003, p. 97). 4 The qualitative results in this chapter remain the same even if exogenous growth rates are assumed under constant returns to scale. However, we adopt the AK endogenous growth framework in this chapter, since it seems more reasonable to allow for endogenous growth rather than exogenous growth. 5 Note that H differs from J, although both are closely related. H is the quantity of claims to labor income, while J is the labor input. 6 If the firm is to determine the timing of the switch, it compares the expected profits between the two stages. In this case, the dynamics of k, instead of W, matter. Thus, the timing in the competitive equilibrium differs from the socially optimal one. However, since the dynamics of k and W are closely related due to the common stochastic element, the resulting economic progress and regress would show similar patterns.

55

Appendix

Solutions for the stochastic AK stage Given the stochastic dynamic programming in the text, the Bellman equation becomes  1R  c 2 þ VW dW þ 0:5VWW dW ; ðA1Þ rV ¼ max E c;n 1R where the subscripts indicate the partial derivatives. Then, we can guess the value function as V ðWÞ ¼

GR W 1R : 1R

ðA2Þ

The first-order conditions with respect to c, nk , and nB give c ¼ GW ;

ðA3Þ

rk  rH ¼ Rðsk  sH Þ½nk sk þ ð1  nk  nB ÞsH þ nB sB ;

ðA4Þ

rB  rH ¼ RðsB  sH Þ½nk sk þ ð1  nk  nB ÞsH þ nB sB :

ðA5Þ

Regarding rk and sk , since rk dt þ sk do ¼

dY  dT ¼ ð1  bÞð1  tS ÞZS dt þ ð1  bÞ½1  ðtS þ αÞsdo; dk

we can immediately obtain rk ¼ ð1  bÞð1  tS ÞZS ;

ðA6Þ

sk ¼ ð1  bÞ½1  ðtS þ αÞs:

ðA7Þ

In the steady states, we have dW dk h ci dq B dq H ¼ ¼ ZS  dt þ sdo ¼ B ¼ H : W k k qB B qH H

56

Outside the black box

56

Substituting this into (2.8) yields c n rB ¼ ZS  þ k tS ZS ; k nB  nk sB ¼ 1 þ ðtS þ αÞ s: nB

ðA8Þ



ðA9Þ

Then, substituting (A6), (A7), (A8), and (A9) into (2.22) gives  c ð1  tS Þbnk ZS þ ; rH ¼ ZS  k 1  nk  nB sH ¼ s þ

b½1  ðtS þ αÞnk s: 1  nk  nB

ðA10Þ

ðA11Þ

Note that while rk and rB were derived explicitly, rH was obtained by substituting rk and rB into the wealth accumulation equation, (2.22). This is because the production function, (2.6), is represented as a function of the per capita capital. From (A6)~(A11), we can calculate nk sk þ ð1  nk  nB ÞsH þ nB sB ¼ s:

ðA12Þ

nk rk þ nB rB þ nH rH ¼ ZS  Gðn1 k  1Þ:

ðA13Þ

Thus, substituting these into (A4), (A5), and (2.22) yields rk  rH ¼ Rsðsk  sH Þ;

ðA14Þ

rB  rH ¼ RsðsB  sH Þ;

ðA15Þ

dW ¼ WðZS  Gn1 k Þdt þ Wsdo:

ðA16Þ

Using (A16), (A1), and (A2), we can derive the expression for G as G¼

i nk ð1  RÞ h r  ZS þ 0:5Rs2 : nk  ð1  RÞ 1  R

ðA17Þ

In order to exclude the negative consumption, we need to have G > 0. By inspection of (A18) below, we can see nk > 1  R is satisfied. Given this result, G > 0 holds if r  ð1  RÞðZS  0:5Rs2 Þ > 0:

ðA18Þ

57

Path-dependent economic progress and regress

57

Finally, using (A17) and g  tS ZS  Rs2 ðtS þ αÞ, we can solve (A14) and (A15) for nk and nB as   r  ZS þ 0:5Rs2 ð1  RÞ bðZS  Rs2 Þ þ ð1  bÞg þ R 1  ; nk ¼ ðA19Þ r  ZS þ 0:5Rs2 bðZS  Rs2 Þ þ ð1  bÞg þ ð1  RÞ 1R nB ¼

Rg

 r : bðZS  Rs2 Þ þ ð1  bÞg þ ð1  RÞ  ZS þ 0:5Rs2 1R

ðA20Þ

Proof of Proposition 2 From (2.20) and R < 1, it is easy to derive @VD =@tD < 0. Since tD appears only  through VD in (2.44) and (2.46), this implies that @ W=@t D < 0 and @W =@tD < 0 always holds. Q.E.D.

Proof of Proposition 3 Differentiating nk with respect to g yields @nk / Rð1  bÞfr  ð1  RÞðZS  0:5Rs2 Þg < 0: @g Substituting (2.26) into (2.34), through some algebra, we obtain vS /

1 R

1

½ð1  RÞfnk  ð1  RÞg nRk 1R

:

Differentiating this with respect to nk yields @vS =@nk > 0. Hence, we have  =@g > 0 @vS =@g < 0. But according to (2.44) and (2.46), this implies that @ W and @W =@g > 0. So, an increase in certainty equivalent taxes always raises the threshold levels. Then, since g  tS ZS  Rs2 ðtS þ αÞ, it is immediate to  < 0. If obtain @g=@α < 0 and @g=@tS ¼ ZS  Rs2 . Hence, we obtain @ W=@α 2  ZS  Rs < 0, @ W=@tS < 0 and @W =@tS < 0 are also satisfied. Q.E.D.

3

Division of labor in innovation between general purpose technology and special purpose technology

1 Introduction The previous chapters and Harada (2010b, 2010c) considered the path-dependent economic growth in terms of several stages under the assumption that a single sector generates innovation and economic growth. From this chapter, we relax this assumption and allow for multi-sectors generating innovation. This chapter establishes an endogenous economic model that involves innovation in the two sectors of general purpose technology and special purpose technology and examines the economic implications of different patterns of interaction between the two sectors. General purpose technology (GPT henceforth), as typified by machine tools, semiconductors, IT, etc., refers to fundamental technology that is utilized in diverse industries. In contrast, special purpose technology (SPT) is technology that is utilized only in specific areas and industries, where both SPT and GPT are utilized in order to produce final goods. Needless to say, the two technologies exist in a complementary relationship, since the SPT level rises if the level of GPT is high. The importance of GPT was pointed out by Rosenberg (1976) in his pioneering study on the machine tool industry. He argued that the GPT sector is extremely important for economic development because GPT plays a central role in the diffusion of technology and thus has a major influence on innovation.1 However, it has been only relatively recently that this proposition has been studied in a formal manner. The partial equilibrium model of Bresnahan and Trajtenberg (1995) was a pioneering work; thereafter, there have been several examples of research that postulated GPT as a driver of endogenous economic growth, such as Helpman and Trajtenberg (1994, 1996, 1998) (HT model henceforth). These models are impressive achievements that formalized the role of GPT; for example, the incorporation of GPT has made it possible to provide an integrated explanation of the relationship between economic growth and business fluctuations. However, in the HT model and subsequent papers extending the HT model, innovation in GPT is assumed to be no more than an exogenous shock, while only innovation in the special purpose technology sector (the SPT sector) is seen as endogenous.

59

Division of labor in innovation

59

This chapter attempts to endogenize both the GPT and SPT sectors and to create a dynamic general equilibrium model that examines the economic implications of different institutional arrangements regarding interaction between the GPT and SPT sectors. Obviously, the economic implications of interaction between GPT and SPT cannot be fully examined without endogenizing innovation processes in both sectors. We distinguish three patterns in the division of labor in innovation between the GPT and SPT sectors – (1) the SPT stage; (2) the GPT–SPT joint-research stage; and (3) the autonomous GPT stage – analyze the characteristics of the market equilibrium for each stage of innovation activities, and elucidate their economic implications. In this analysis, it is shown that the emergence of GPT, as long as it takes the form of joint-research with the SPT sector, only has a temporary level effect, and a negative effect on economic growth when compared with the previous stage. This result is consistent with the IT productivity paradox, in which IT diffusion fails to contribute to economic growth. In addition, the new phenomenon of the autonomous GPT stage has a positive influence on both growth and level effects. This result theoretically supports empirical studies showing that the IT productivity paradox was resolved in the US economy in the 1990s.2 Thus, the model provides a theoretical explanation for both the emergence of the IT paradox and its recent resolution. The rest of this chapter is organized as follows. The next section reviews major studies on GPT, clarifying the differences between models in the early studies and the model proposed here. Sections 3–5 provide detailed explanations of the model: Section 3 explains the model of the SPT stage, Section 4 the model of the GPT–SPT joint-research stage, and Section 5 the autonomous GPT stage. Section 6 compares social welfare and market equilibrium and discusses socially desirable technology policies. Finally, Section 7 concludes the discussion.

2 Review of previous studies Although there has recently been a growing interest in GPT in the economic profession, little work has been done on formalizing the idea.3 Bresnahan and Trajtenberg (1995) first proposed the concept of GPT and developed a model for the conditions of the “dynamic game” between the GPT sector and the SPT sector. However, in that model, only these two sectors exist, while the kinds of influence exerted by the interaction between the sectors on social welfare and consumer behavior are not clarified. The growth effects of GPT in a general equilibrium framework were formally analyzed by Helpman and Trajtenberg (1994, 1996, 1998). In their models, GPT requires complementary inputs before they can be applied in the production process. Complementary inputs developed for previous GPTs are not utilized for a newly arrived GPT. As a result, the sequential arrival of GPTs generates business cycles. Following the HT model, most of the subsequent work on GPT focused attention on the cyclical properties caused by the arrival of GPT. Aghion and Howitt (1998b) partially endogenized the arrival times of successive

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GPTs by adding a second stage of component-building to the innovation process in a basic Schumpeterian model of endogenous growth and attempted to extend the model so as to make it consistent with empirical observations. Petsas (2003) analyzed the dynamic effects of GPT within a scale-invariant Schumpeterian growth model and showed that transitional growth cycles exist even if population growth is introduced. Eriksson and Lindh (2000) modified the HT model by allowing for positive technological externalities in the process of component innovation and only partial replacement of old components with a new arrival of GPT. Following these previous studies, this chapter adopts the framework of a basic Schumpeterian growth model and explores the economic implications of GPT. However, the model in this chapter differs greatly from those in previous studies in the following respects. First, this chapter focuses attention on the growth implications of institutional arrangements regarding patterns of interaction between the GPT and SPT sectors, rather than focusing on growth cycles. This model does not generate growth cycles, since innovations in the GPT and SPT sectors are allowed to proceed simultaneously. Although the growth cycle is an interesting phenomenon, different patterns of interaction between the GPT and SPT sectors also deserve equal attention, as a historical analysis of the US machine tool industry by Rosenberg (1976) persuasively demonstrates. The kind of influence exerted by these institutional factors on the economic growth rate and R&D has become a central topic in innovation research, but one that has not yet been formally analyzed. As noted above, we distinguish three patterns in the division of labor in innovation between the GPT and SPT sectors: (1) the SPT stage; (2) the GPT–SPT joint-research stage; and (3) the autonomous GPT stage. The SPT stage implies that no GPT sectors emerge in the economy so that each SPT sector internally develops production technology. In contrast, the GPT–SPT joint-research stage allows SPT firms to jointly develop production technology with GPT firms. The outcome of this joint research is available to all other SPT sectors, except SPT firms within the same SPT sector. Otherwise, the SPT firm cannot recoup the profits from innovation. Finally, at the autonomous GPT stage, innovation is executed by GPT sectors alone, without the help of SPT firms. Here we attempt to analyze the characteristics of the market equilibrium for each stage of innovation activities and elucidate their economic implications. Thus, this chapter, while derived from the quality ladder model, goes one step beyond previous related research by encompassing endogenous innovation in the GPT sector and the division of labor in innovation between the GPT and SPT sectors. Second, a major difference is that our model incorporates R&D and innovation in both the GPT and SPT sectors, while previous growth cycle models have described innovation only in one sector. More precisely, previous studies such as Aghion and Howitt (1998b) assumed that the arrival of a new GPT followed some stochastic process (a Poisson process), but moments of this stochastic process were exogenously fixed. In contrast, this chapter endogenizes this arrival time by making the arrival rate depend on research intensity, as assumed in a standard one-sector

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Schumpeterian growth model.4 Thus, the arrival times of both GPT and SPT are influenced by the division of labor in innovation between the two sectors.

3 The model This section describes the basic framework of the model and then describes the economic growth model at the SPT stage.

3.1 Household Consider a continuous-time closed economy, assuming that a representative household maximizes the utility function Z1 erðstÞ uðsÞds;

UðtÞ ¼

ð3:1Þ

t

where r > 0 denotes the rate of time preference rate, and uðsÞ is the instantaneous utility function, which is specified as follows: u ¼ ln c; 0 c ¼ exp@

"

ZN ln

X

# 1 yij diA;

N  1;

ð3:2Þ

j

0

where c denotes the consumption level and yij indicates final goods supplied by the jth generation of production technology developed in the ith SPT sector. As is clear from (3.2), the size of the SPT sectors is expressed as N and the household purchases final goods from each SPT sector.The household maximizes (3.1) subject to the intertemporal budget constraint Z1

Z1 e

½RðtÞRðtÞ

e½RðtÞRðtÞ wðtÞdt;

cðtÞdt  BðtÞ þ

t

t

Zt RðtÞ ¼

rðsÞds; 0

where wðtÞ denotes wage income, BðtÞ denotes the household’s stock of assets at time t, RðtÞ represents the discount factor from time zero to t, and rðtÞ indicates the instantaneous discount factor at time t. The first-order conditions of the household’s optimization require that c_ ðtÞ ¼ rðtÞ  r; cðtÞ

ð3:3Þ

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62

and the transversality condition holds lim eRðsÞ BðsÞ ¼ 0:

s!1

In this model, the price of c (the sum of all final goods) is normalized at 1, and the amount of expenditure by the household is equivalent to c. Thus, the demand for the final goods is given by yi ¼

c : Npi

ð3:4Þ

3.2 The SPT sector Assume that each SPT sector produces final goods by the following production function: yi ¼ elj li ;

ð3:5Þ

where elj (j  1) indicates the j generation’s production technology for the final goods, and productivity increases with each succeeding generation. As is clear from the production function, no SPT firms purchase technology from outside the firm. At this stage, since the GPT sector has yet to appear, the technology used in each sector is limited to internally developed technology. Therefore, the model at this stage is essentially the same as the existing quality ladder model. The marginal costs in the SPT sector are given by MC ¼ elj w: Hence, the limit price charged by the jth new quality leader becomes pi ¼ eð1jÞl w:

ð3:6Þ

As is clear from (3.2), the representative household purchases final goods only from an SPT firm that has successfully developed the state-of-the-art technology. As a result, the jth quality leader will be replaced as soon as a winner of the R&D race for the j þ 1th appears. The instantaneous profits of the quality leader, according to (3.4) and (3.6), are given by pS ¼

ð1  el Þc : N

ð3:7Þ

3.3 R&D activities In the SPT sector, a firm that has already succeeded in developing the newest generation of technology produces final goods, while other firms conduct their

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R&D aimed at innovation in the next generation. Following previous studies of the quality ladder model, let us assume that this R&D follows the Poisson process such that the instantaneous probability of an entrepreneurial success is provided by is. For simplicity, assume that the amount of labor is must be allocated to innovation activities to achieve the instantaneous probability is without loss of generality.5 The stock value at time t of a quality leader is equal to the present discounted value of its profit stream subsequent to t, which is given by Z1 eðRðtÞRðtÞÞ eiS ðttÞ pS dt;

vðtÞ ¼ t

where it is assumed that firms in each SPT sector exist up to ½0; 1, and because of the symmetry of the model, the amount invested in R&D by each firm is at the same level. As a result, the probability that a quality leader will not be replaced from time t to time τ is given by eiS ðttÞ. Therefore, this term is multiplied on the right side of the above equation. Differentiating that equation with respect to t, we get the following non-arbitrage condition: rv ¼ v_ þ

ð1  el Þc  iS v: N

ð3:8Þ

This value of v represents the economic value of innovation, while, in order to achieve the instantaneous probability of innovation is , the same amount of labor, is , must be allocated to innovation activities. Since there are no entry barriers to this R&D race, the net value of innovation turns out to be zero in equilibrium, i.e.,iS v  iS w. Needless to say, is > 0 is satisfied whenever this condition holds with equality. Thus, the free-entry condition is given by v  w:

ð3:9Þ

Finally, assuming the total amount of labor is L, we obtain the labor market clearing condition ZN li di þ NiS ¼ L:

ð3:10Þ

0

This completes the model of the SPT stage. Note that, since this specification follows a standard Schumpeterian growth model, the results in what follows suffer from the scale effects that have been criticized by Jones (1995a, 1995b). In addition, a constant population size of L is not a realistic assumption. In the Appendix, we will present a modified model with positive population growth that removes these scale effects. However, this modified model in no way changes the qualitative results below, so we maintain the assumptions of

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64

constant population size and constant returns in R&D technology to avoid unnecessary complications. By solving (3.3), (3.7), (3.8), (3.9), and (3.10), we obtain the following result: Lemma 1. The market equilibrium at the SPT stage is given as follows:   L l l ðe  1Þ  r The amount of R&D investment: i0 ¼ e N l l The growth rate: g0 ¼ le fðe  1ÞL  Nrg, ðel  1ÞL > r: where N

4 GPT–SPT joint-research stage In the model of the SPT stage described above, innovation is carried out only by SPT firms. However, the advanced economies are characterized by the emergence of GPT sectors that provide technology to many SPT sectors, as suggested by Rosenberg (1976). This section analyzes the emergence of GPT sectors that develop technology in joint cooperation with SPT firms where significant learning takes place in the interaction between SPT and GPT sectors. With technological spillovers of GPT to other SPT sectors, GPT sectors play an important role in economic development and growth, according to Rosenberg (1976). This section attempts to formalize the emergence of GPT sectors in the economy and examine its economic implications. 4.1 SPT sector The main difference between the SPT stage and the GPT–SPT joint-research stage lies in the type of R&D that the SPT and GPT sectors carry out. In the joint-research stage, R&D is conducted jointly by GPT and SPT firms. When the joint research succeeds, the GPT firm can provide the new technology to other SPT sectors. However, it is assumed that no technology is provided to direct rivals of its SPT partner.6 While SPT firms do not gain profits through providing the new jointly developed technology to other SPT firms, they can enjoy a monopoly position within their own sector. This monopoly lasts until a rival SPT firm succeeds in developing the latest generation of technology in joint research with another GPT firm. Accordingly, as long as the new technology is not provided to a rival firm in the same sector, the incentive exists to engage in R&D jointly with a GPT firm. This sort of joint R&D between the GPT and SPT sectors reflects the role, pointed out by Rosenberg (1976), that the US machine tool industry played as a transmission center of innovation. Rosenberg argued that the learning process in the economy was facilitated in two steps: (1) new skills and techniques were developed or perfected in response to the demands of specific customers; and (2) once they were acquired, the machine tool industry was the main

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transmission center for the transfer of new skills and techniques to the entire machine-using sector of the economy. This type of learning process implies that GPT firms and specific SPT firms jointly engaged in research in order to resolve specific technical problems, and the new technology produced thereby was then provided to other firms by the GPT firm. Consequently, the aforementioned hypothesis of the GPT-SPT joint-research stage reflects the role of the GPT sector as a transmission center of innovation. From this perspective, the production function of each SPT sector can be specified as RN yi ¼ e 0

jm dml

li  A 1 li :

ð3:11Þ

The difference between (3.5) and (3.11) is that, in the latter, new technology developed by all other SPT sectors is purchased from GPT firms, and all SPT firms use identical production technology. In other words, the new technology that is developed jointly by an SPT firm with a GPT firm is provided to all SPT firms in other SPT sectors. For this reason, compared with the SPT stage, the shift to this joint-research stage causes an improvement in the production technology level used by SPT firms. However, in the long term, it is not necessarily obvious whether this effect becomes significant or not. We will discuss this issue in a later section. With this production function, the marginal costs and limit price are given by MC ¼ A1 1 w; pi ¼ el A1 1 w: The instantaneous profit of a quality leader is now specified as pS ¼

ð1  el Þc : N

Note that this instantaneous profit is equal to the one in the model of the SPT stage, since all SPT firms are assumed to improve their productivity to the same level here. With the utility function of this model, the elasticity of substitution is unity, implying that as long as there is symmetry in the improvement of productivity, no change will occur in the profit. 4.2 GPT sector Next, assume the size of GPT sectors that emerge at this stage to be unity, instead of N, which is smaller than that of SPT sectors. This assumption is consistent with the previous arguments on GPT sectors by Rosenberg (1976), where the US machine tool industry, for example, supplies its products to diverse industries, including textiles, railroads, arms, sewing machines, bicycles, and automobiles. In other words, industrialization was characterized by the introduction of a

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66

relatively small number of broadly similar productive processes to a large number of industries. For simplicity, it is assumed that the marginal costs of newly developed technology are zero for GPT firms that conduct successful joint research. If the newly developed technology takes the form of intellectual assets, such as patents or software, this assumption would be plausible. Obviously, it is also possible to construct a model with positive marginal costs, but it makes the model unnecessarily complicated without providing many insights. With zero marginal costs, the limit price of GPT makes no sense. This is because in terms of costs, there is no disparity with rival firms. Given this situation, it is assumed here that SPT firms always prefer to introduce new, state-ofthe-art technology, as long as the GPT price does not exceed the profits gained by the SPT firm. This assumption is reasonable since if a SPT firm adopts less efficient GPT, the rival firms would instead purchase the latest technology and dominate the whole market. As a result, SPT firms always have an incentive to adopt only the latest GPTs. Thus, the upper limit of the GPT price is set at the profit level of the SPT firm, and its lower limit set at zero. The eventual price level ends up being set somewhere between those two limits, according to the respective bargaining power of the GPT and SPT firms. At this joint-research stage, the level at which the price eventually settles is determined endogenously through market equilibrium. The non-arbitrage condition for the GPT firm, according to a similar argument as above, can be expressed as follows: rv ¼ v_ þ

ð1  el Þc  Npg  ðia þ ig Þv; N

rv ¼ v_ þ Npg  ðia þ ig Þv; where pg refers to the GPT price. Since free-entry conditions for joint R&D activities are assumed here, the expected value of the innovation in the GPT and SPT sectors ends up being the same. If the two were not at the same level, R&D resources would be invested only in projects with higher expected value. Hence, if R&D is carried out by both the GPT and SPT sectors, the expected value of innovation ends up settling at the same level, v. The free-entry condition for R&D activity and the labor market clearing condition are, respectively, v  w; ZN li di þ NiS þ Nig ¼ L: 0

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67

This completes the model of the joint-research stage. and the following results can be derived: Lemma 2. The market equilibrium at the GPT–SPT joint-research stage is given as follows:   1 L l The amount of R&D investment: i1  iS þ ig ¼ l ðe  1Þ  2r ; e þ1 N Nl fðel  1ÞL  2Nrg;, The growth rate: g1 ¼ l e þ1 ðel  1ÞL where > r: 2N @i1 < 0 is satisfied. In other words, an increase @N in the size of the SPT sectors will cause a proportional decline in R&D investment. However, the economic growth rate is not proportionate to N, but rather to N 2 . This is due to the effect of the GPT sector as a transmission center of innovation, making it necessary to pay attention to the fact that an increase in N does not necessarily lead to a decline in the economic growth rate. From this lemma, we see that

4.3 Comparison of the SPT stage with the joint-research stage Now compare the growth rates and economic levels of the SPT stage and the GPT–SPT joint-research stage. First, a comparison of growth rates yields g1  g0 / ðN  el  1Þ½ðel  1ÞL  Nr  N 2 r ð Dg10 Þ: This difference in growth rates can be either positive or negative, depending on the size of L, l, r, and N. For example, take the case of N ¼ 1. In this situation, we get Dg10 ¼ ð1  el ÞðL þ rÞ < 0: In this case, the growth rate of the joint-research stage is smaller than that of the SPT stage, no matter how big L, r, and l are. Now define the following:   1 ðel  1ÞL  l þe þ1 : N  4 r It follows that Dg10 represents an increasing function of N when N  > N, and a decreasing function when N  < N. According to Lemma 2, the upper limit of N is given by l   ðe  1ÞL : N 2r In this case, we get

Dg10 ¼ ðel þ 1Þ

ðel  1ÞL < 0: 2

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68

Accordingly, the shift to the joint-research stage can result in a negative growth effect at the lower and upper limits of N.7 Dg10 is at its largest at N  , but whether the value in that case is positive or negative depends on the size of L, λ, and ρ. At least it can be stated here that, although the growth effect improves slightly as N increases, once it crosses the N  threshold and approaches the maximum, it once again becomes negative. Meanwhile, the level effect turns positive when the shift is made to the jointresearch stage. This result is clear from (3.5) and (3.11) as well. Since the production function of SPT firm increases significantly, the economic level also rises. However, since the growth effect is negative if N stays at a low level or if it approaches its upper limit, the long-term level effect will also be negative. Consequently, when the shift is made to the joint-research stage, the economic level may improve, but in the long run, its level effect attenuates, implying that a higher economic level could be achieved by remaining in the SPT stage. A summary of the above discussion results in the following proposition: Proposition 1. When the level of N is near either its upper or lower limit, the emergence of GPT through joint research causes a decline in the growth rate compared with the SPT stage. For this reason, the economic level increases temporarily right after the shift, but its level effect turns negative in the long run. This proposition suggests that when N is either small or near its upper limit, the economic effect of the emergence of GPT, which Rosenberg (1976) regards as positive, is actually only a temporary shock, and in the long term, both the level effect and the growth effect decline. Of course, it is dangerous to interpret the results of the model and apply them directly to reality. However, it should be noted that this theoretical result stands in sharp contrast to the previous studies by Rosenberg (1976). That is, the emergence of the GPT sector does not increase the economic growth rate but instead may decrease it. This result, which seemingly goes against common sense, must be understood within the general equilibrium framework. Put differently, the division of labor between the GPT and SPT sectors through joint research has the advantage of temporarily giving each SPT firm a significant technological boost. However, the amount of production expands as well, owing to the increase in productivity, leading to a reduction in prices. In this model, the price elasticity of demand is unity, thus offsetting the increase in production by the decrease in price. Moreover, the shift to the joint-research stage increases the total costs of production technology, consisting of all state-of-the-art GPTs available in the economy. As a result, wages decrease, and the value function of innovation v also declines. For this reason, the incentive for innovation declines as well. However, since the economic growth rate is N 2 times the amount of R&D investment, whether or not the growth rate declines in the end depends on the value of N.

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69

Usually, in the initial stages of the emergence of the GPT sector, N is not predicted to have a large value. The availability of GPT expands as time progresses. Thus, according to Proposition 1, in the initial periods, it follows that the growth rate is negative in comparison to the SPT stage, and as N goes on increasing, the growth effect is improved. The increase in N can be accounted for from the perspective of time adjustment processes, as pointed out by David (1990). That is, it takes significant time for GPT to diffuse in an economy, so that the number of SPT sectors adopting GPTs (i.e., N) increases only slowly. However, if Nexpands beyond N  , the growth effect once again starts to decline, and finally turns negative. In that case, the long-term level effect may also turn out to be negative. Consequently, it is clear that the emergence of the GPT sector, as long as it takes the form of joint research, does not necessarily generate a desirable effect in the long run, depending on the size of N. This may be one reason why the diffusion of GPT does not necessarily contribute to productivity growth, as is the case with the IT productivity paradox.

5 Autonomous GPT stage The aforementioned analysis illustrates the negative influence of the emergence of the GPT sectors, one that shares similarities with the IT productivity paradox, which implies that the diffusion of IT has not contributed to an increase in productivity. The emergence of the GPT sectors has given the economy a temporary boost, increasing the stock of GPT. Meanwhile, given the fact that the economic growth rate has decreased, the increase in the stock of GPT does not lead to productivity growth. As a consequence, while GPT has diffused, causing the level of the economy to rise, there is no statistical evidence of its positive effect on productivity, which can be called a “technology paradox”. However, as N increases, the economic growth rate recovers, leading to the possibility of a positive growth effect. Yet, if Nexpands beyond a certain level, it will lead conversely to a negative growth effect. A long-term continuation of the IT productivity paradox could be explained as follows: the initial phase will witness a low level of N, spike rapidly, and then reach its upper limit. At the same time, though, empirical studies in the 1990s and later, such as Brynjolfsson and Hitt (1996), demonstrated the resolution of the IT productivity paradox in many instances. If the findings of such studies are reliable, then it cannot be interpreted as simply an expansion of N. Rather, another sort of mechanism must be at work yielding a different result from that above. 5.1 SPT sector and GPT sector Regarding the resolution of the IT productivity paradox, this chapter attempts to construct a model of the new phase of the economy as the autonomous GPT stage, exploring the characteristics of its equilibrium. The autonomous GPT stage refers to a situation in which new technologies are no longer developed in cooperation

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with the SPT sector, but rather one in which both the GPT and SPT sectors engage in their own R&D separately, so as to produce innovations. The production function of the SPT sector in those circumstances can be formulated as follows: hSi lS þ

yi ¼ e

R1

g

jm dmlg

0

S

li  A2 ehi lS li ;

ð3:12Þ

where hSi  1 refers to the latest generation of technology in the ith SPT sector. For the autonomous GPT stage to have any significance, the condition lg  Nl must be fulfilled. Otherwise, the autonomous GPT stage would lead to a decline in the production technology of each SPT firm, and there would be no incentive in the first place to shift to the new stage.8 Each SPT firm purchases the latest GPT from the GPT sector [0,1]. Additionally, the SPT sector carries out its own innovations. In this case, even when the shift to the autonomous GPT stage takes place, it is assumed that the technological framework used in the joint-research stage (between the SPT and GPT sectors) remains available to SPT firms, and lS  l is guaranteed. By definition, SPT is not available to a wide range of customers, and it is assumed that it cannot be provided to other SPT firms. Accordingly, the technology developed by other SPT firms is not reflected in this production function. Given this production function, the marginal costs (MC) and limit price imposed by the SPT (pi ) are as follows: hi lS w; MC ¼ A1 2 e S

ð1hi ÞlS pi ¼ A1 w: 2 e S

Thereafter, a model can be constructed in a similar manner to the preceding sections. First, the non-arbitrage condition is set as follows: rv ¼ v_ þ

ð1  elS Þc  pg  iS v; N

ð3:13Þ

rv ¼ v_ þ Npg  ig v: However, the difference with the joint-research stage can be found in that the price pg which the GPT sector imposes on the SPT sector is no longer endogenously determined, as described in the previous section, but the GPT firm can determine the price, according to the extent of its bargaining power. For the time being, the price is assumed to be set at a fixed ratio of the wages.

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Specifically, the following equation is assumed: b  pg =w: If no specific restrictions are placed on the bargaining position of the GPT firm, the most reasonable level of b would be the limit price for the SPT firm.9 In other words, the GPT price would be set at the same amount as the profit of the SPT firm. In that case, however, the equality of (3.13) is no longer satisfied, and R&D in the SPT sector would not be carried out. Put differently, if the GPT firm sets the limit price, innovations would only take place in the GPT sector. Such a phenomenon is not unrealistic at all. For instance, in the area of personal computers, innovations are implemented by only a handful of GPT firms, and the bulk of the profits are concentrated there. As the independence of GPT in terms of innovation progresses, the limit price set by the GPT firm is expected to come to the fore. Thus, the following analysis focuses on this particular case of the limit price. Then, the free-entry condition and labor market clearing condition are, respectively, v  w; ZN li di þ NiS þ ig ¼ L: 0

These conditions lead to the following lemma: Lemma 3. The market equilibrium at the autonomous GPT stage is as follows: The amount of R&D investment (SPT sector):  1  e lS lS L lS r  b; 1þ iS ¼ ð1  e Þ  e N N The amount of R&D investment (GPT Sector): ig ¼ Nb  r; The growth: rate: g2 ¼ lS fð1  elS ÞL  elS ðN þ 1  elS Þr  Nbgþ lg NðNb  rÞ:

5.2 Comparison of joint-research stage and GPT autonomy stage A comparison of the market equilibrium in the autonomous GPT stage and in the joint-research stage is set out below. To obtain a clear result, a specific examination of the limit price case will be made. However, the result is not limited to this case alone but is also applicable to instances when the GPT firm has a relatively high level of bargaining power.

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72

First, compare the growth rate in the two stages. When the GPT firm sets the limit price, the GPT price is given by pg ¼

ð1  elS Þc ; N

and (3.13) is no longer satisfied. Consequently, iS ¼ 0, and the growth rate in such a case is as follows: g2 ¼ lg N½ð1  elS ÞL  elS r: This growth rate is different from that of the joint-research stage in that the former is monotonically increasing in N. From Lemma 2, we obtain g2  g1 ¼ lg N½ð1  elS ÞL  elS r 

lN fðel  1ÞL  2Nrg ð D21 Þ: e þ1 l

The magnitude of the growth rate difference in this case varies depending on the size of lg , lS , l, and N. If l is small and lg , lS , and N are large enough (for instance, lg ¼ Nl; lS ¼ l), then D21 > 0 is obtained so that the growth effect is observed in the shift to the autonomous GPT stage. Since lg  Nl and lS  l are assumed above, D21 > 0 turns out to be guaranteed here. This result is intuitive. If lg and lS are both large, then the growth rate will increase as a matter of course. This situation will occur even if no innovation is implemented in the SPT sector. The reason is that, if lS is large, the limit price imposed by the GPT firm grows larger, leading to an increase in the amount of R&D investment by the GPT firm. In addition, in the joint-research stage, the new technology developed by the SPT sector, which has the size of N, must all be purchased, whereas in the autonomous GPT stage, the new technology can be purchased from GPT sectors, which has the size of 1, leading to a reduction in the cost of production technology. This cost-reduction effect becomes ever more prominent as Nincreases. Meanwhile, a comparison of the level effect leads to the following: ln c2  ln c1 / ln

ðL þ rÞðel þ 1Þ þ ln A2  ln A1 þ la ðh  1Þ; 2ðL þ NrÞ

where h  1 refers to the average SPT level in the initial stages. Since we know from Lemma 2 that ðel  1ÞL > r; 2N the first item on the right side of the equation is: ln

ðL þ rÞðel þ 1Þ ðL þ rÞ > ln > 0: 2ðL þ NrÞ L

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Also, since (3.11), (3.12), and the growth effect are all positive, ln A2  ln A1 will always be true. This confirms that the level effect will also be positive as a consequence. Here also, lg and lS have a positive influence on the level effect, while N has a negative effect on the initial level. However, because an increase in N will heighten the growth effect, in the long run it will cause the level effect to increase. Consequently, we arrive at the following proposition: Proposition 2. The transition from the GPT–SPT joint-research stage to the autonomous GPT stage produces a positive growth effect and level effect.

6 Social welfare and technology policies This section will compare the market equilibrium and Pareto-optimal solutions for the different economies in the three stages explored above, so as to derive policy implications.

6.1 SPT stage First, let us seek the socially optimal solution for the SPT stage. Social welfare is expressed as a utility function of a representative household. The social planner’s problem is to maximize the utility function by determining the number of workers to be allocated to production and R&D. Consequently, this problem can be formulated as follows: Z1 maxX ;i U ¼ erðstÞ N½ ln X ðtÞ  ln N þ lIðtÞdt; t

_ s:t: IðtÞ ¼ i; Ni þ X ¼ L: The Hamiltonian is then given by

 LX H ¼ ln X ðtÞ  ln N þ lIðtÞ þ y : N

Solving this problem, we obtain i0 ¼

L r  : N l

From the results of Lemma 1, a comparison of the amount of R&D investment is as follows: i0  i0 /

L el þ1 : rN l

74

Outside the black box

74

Clearly, the right-hand side of this expression is positive when λ is small, and negative when its value crosses a certain threshold. Consequently, the following proposition can be derived: Proposition 3. In the SPT stage, a large value for λ leads to excessive investment, and a small value to insufficient investment. This is basically the same result arrived at in previous research, such as Grossman and Helpman (1991). Their model differs from the one described above in showing that a small λ value also resulted in excessive investment.10 However, the result remains the same here insofar as a large λ value leads to excessive investment. As this SPT stage is basically the same as traditional endogenous economic growth models, this result is not surprising.

6.2 GPT–SPT joint-research stage Next, the socially optimal value for the GPT–SPT joint-research stage can be sought in the same way as above. In this case, the optimization problem is as follows: Z1 erðstÞ N½ ln X ðtÞ  ln N þ lINðtÞdt;

max U ¼ X ;i

t

_ s:t: IðtÞ ¼ i; Ni þ X ¼ L: Solving this equation leads to the following: i1 ¼

L r  : N Nl

From Lemma 2, we obtain  L el þ 1  i1  i1 / 2 þN  : r l On the right side of this expression, any value of l greater than 1.278 makes it a decreasing function of l; a sufficiently large l will thus make the right side negative. In contrast, when l is less than 1.278, it becomes an increasing function. As for the latter case, the sign of the right side is dependent on the values for L, r, and N, so it may not necessarily turn negative. However, in the former case, a sufficiently large l will always result in the sign of the right side becoming negative. Accordingly, the following proposition is obtained: Proposition 4. In the GPT–SPT joint-research stage, excessive investment will occur when l is sufficiently large, or when it is sufficiently small (and L and N are also small). When l falls in an intermediate range

75

Division of labor in innovation

75

between those two poles (and L and N are large), there will be insufficient investment. 6.3 GPT autonomy stage One of the results described above – that excessive investment takes place when λ is large – is consistent with previous research. However, as far as the autonomous GPT stage is concerned, the model presented above differs greatly from the existing endogenous growth model in that it incorporates a distinct division of labor in innovation. This raises the possibility that the socially optimal solution will also differ from the existing one. In the autonomous GPT stage, the social planner’s problem is formulated as follows: Z1 erðstÞ N½lS IS ðtÞ þ lg Ig ðtÞ þ ln X  ln Ndt;

max U ¼

X ;iS ;ig

t

s:t: I_ S ðtÞ ¼ iS ; I_ g ðtÞ ¼ ig ; ig þ NiS þ X ¼ L: In this utility function, R&D stocks in GPT and SPT are in a linear relationship. Consequently, from the social planner’s perspective, it is more efficient not to make investments equally in GPT and SPT, but rather to concentrate investments in the type of technology that has the larger value of λ. In this case, let us assume that lg > lS is satisfied. Given this situation, the socially optimal solution is therefore: i ¼ L 

r : lg

In the case of the autonomous GPT stage, in market equilibrium, both GPT and SPT sectors will invest in R&D unless GPT firms set the limit price. In contrast, the socially optimal solution shows that R&D investment will occur only in the GPT sector. However, as stated above, the reasonable assumption here is limit price so that both the market equilibrium and socially optimal solution make the same predictions about the innovation pattern. The problem is the relative size of the respective amounts invested in R&D by the GPT sector. Lemma 3 shows that the amount invested in R&D, when GPT firms set a limit price, is as follows: i2 ¼ ð1  elS ÞL  elS r: Thus, we obtain i  i g / L þ r 

relS : lg

76

Outside the black box

76

The right side of the expression is an increasing function of lg and a decreasing function of lS . This leads to the following proposition: Proposition 5. The autonomous GPT stage gives rise to insufficient investment when lg is sufficiently large, and excessive investment when it is small. When lS is sufficiently large, it leads to excessive investment, and to insufficient investment when small. In this way, lg and lS generate contrasting results. Whereas the latter is similar to that of the SPT stage and the GPT–SPT joint-research stage, the former is completely the opposite. Consequently, the direction of technology policies once the autonomous GPT stage is reached is completely different from the direction prevailing at other stages. These results lead to the following corollary: Corollary. In the SPT stage and GPT–SPT joint-research stage, a large value of l produces excessive investment, so it is socially desirable to tax R&D investment. In contrast, at the autonomous GPT stage, a large value of lg leads to insufficient investment, making it desirable to provide subsidies to R&D in the GPT sector. When the value of lS is large, however, excessive investment prevails, making taxation more desirable. Thus, the optimal direction for technology policy differs according to the manner in which labor is divided between the GPT and SPT sectors in terms of innovation. Particularly, during the autonomous GPT stage, it becomes desirable to promote R&D in the GPT sector as much as possible, so if the limit price is not set, it will become necessary to restrain R&D in the SPT sector. This result has not been pointed out in the related literature on endogenous growth.

7 Concluding remarks This chapter constructed an endogenous growth model, analyzing the economic effect of the pattern of the division of labor between the GPT and SPT sectors in terms of innovation. What it revealed is that, in a majority of cases, the emergence of GPT, as long as it takes the form of joint-research with the SPT sector, only has a temporary level effect, and a negative effect on economic growth when compared with the previous stage. This highlights the negative aspects of the GPT sector as a transmission center of innovation. In addition, the new phenomenon of the autonomous GPT stage has a positive influence on both growth and level effects. This result theoretically supports the empirical studies showing that the IT productivity paradox was resolved for the US economy in the 1990s. To put it differently, the IT industry in the United States witnessed the development of the autonomous GPT sectors, with an

77

Division of labor in innovation

77

expansion of N and an increase in the size of each step of the quality ladder, thereby resulting in improvements of both growth and level effects, thus resolving the IT productivity paradox. The results of this chapter make it clear that it is possible to explain the emergence and resolution of the IT productivity paradox not merely through the IT productivity paradox as time-consuming adjustment process (David, 1990) but also through a shift in division of labor in innovation between the GPT sector and the SPT sector. Also, the results of this chapter reveal that the direction of optimal technology policies is profoundly different between the SPT stage and GPT–SPT jointresearch stage, on the one hand, and the autonomous GPT stage, on the other. In the first two stages, a larger size of each step of the quality ladder results in excessive investment, requiring taxation in order to restrain investment in R&D. In contrast, in the latter stage, investment will be insufficient if the GPT sector has larger steps of the quality ladder, making it necessary to provide subsidies to or reduce taxes on the GPT sector so as to promote R&D investments in the GPT sector while restraining those in the SPT sector. To the best of our knowledge, little attention has been paid to these kinds of policy implications in the previous studies.

Notes 1 Rosenberg (1976) specifically points out the importance of the capital-goods sector, and that basically corresponds to the GPT sector referred to in this study. 2 For example, refer to Brynjolfsson and Hitt (1996). 3 See Helpman (1998) for a summary of previous research on GPT. 4 There are several papers that combine vertical and horizontal innovations and endogenize both innovation processes (Young, 1998; Dinopoulos and Thompson, 1998; Peretto, 1998; Howitt, 1999). The difference between these studies and this chapter is that the latter endogenizes two-tier vertical innovations in order to focus on the role of GPT. 5 In order to ensure is  1 is satisfied, it might be better to assume Zis labor must be allocated to achieve the instantaneous probability of is where Z > 1. However, this additional assumption does not change the results in the chapter at all, so we assume Z ¼ 1 in what follows for simplicity. 6 If the supply of new technology to rival firms were to be allowed, there would be no incentive for the SPT firm to engage in joint-research. This is because, once the technology is supplied to a rival firm, positive profit could no longer be secured. Of course, if this condition were to be loosened, with new technology being sold to rival firms in the same sector, and with the SPT firm being able to secure the profit, then there would be an incentive for joint R&D. However, to simplify the analysis, it is assumed in this chapter that no new technology is supplied to rival firms in the same sector. 7 The term “growth effect” used here refers to the difference in growth rates between two stages at issue. The term “level effect” is used with the similar meaning. 8 This chapter does not specifically model the shift between stages that occurs endogenously. However, one can postulate, for example, that each SPT firm always attempts to improve the level of production technology. Otherwise, the rival firms dominate the market instead. Thus, a shift will not take place without at least a temporary level effect.

78

Outside the black box

78

9 Here, for convenience, the term “limit price” is also used for prices set at the same level of the SPT firm’s profit. 10 This difference derives from the difference in the specifications related to product quality. In contrast to Grossman and Helpman (1991), where lj is specified, this paper uses elj , producing a trivial difference. However, the basic result remains the same.

79

Appendix

All of the above analysis in this chapter assumes that the size of population, L, remains constant, so that the growth rate depends positively upon L. Thus, as population growth causes the size of the economy to increase over time, R&D resources also grow, leading to a higher growth rate. Although this assumption greatly simplifies the analysis, it may call its empirical relevance into question. As Jones (1995a, 1995b) suggested with time series evidence, these scale effects are not observed with positive population growth. In this appendix, we will present the model with positive population growth, while removing scale effects. Although several mechanisms that remove scale effects have been proposed by several papers, dealing with topics such as R&D cost function increasing in scale (Segerstrom, 1998), product proliferation effects (Young, 1998; Howitt, 1999; Dinopoulos and Thompson, 1998), and the crowding-in effect (Peretto, 1998), among others, we will adopt the assumption of the R&D cost function increasing in scale, since this assumption does not change the basic structure of the above model, and, moreover, it is more consistent with empirical observations, as discussed in Segerstrom (1998). In the above model, the instantaneous probability of innovation is is achieved by the same amount of labor, is allocated to innovation activities. But now it is assumed that is X must be allocated to innovation activities. X measures the difficulty of innovation and is specified as X ¼ h1 L;

ðA1Þ

where h > 0 is satisfied. That is, the difficulty of innovation increases as the population gets larger. The size of population is assumed to grow exponentially, such that L_ ¼ gl > 0: L With these modified assumptions, let us recalculate the equilibrium R&D investment and growth rate in the three stages. First, consider the SPT stage. The assumption of R&D difficulty changes the free-entry condition as v ¼ wX :

ðA2Þ

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Outside the black box

80

Assuming w ¼ 1, we can derive from this condition v_ X_ ¼ ¼ gl: v X Substituting this and (A2) into (3.8) gives r ¼ gl þ

ðh  NiS Þðel  1Þ  iS : N

ðA3Þ

Solving this, we obtain   h i0 ¼ el ðel  1Þ  ðr  gl Þ ; N g0 ¼ lel fðel  1Þh  Nðr  gl Þg: Although this model removes scale effects, compared with Lemma 1, there exist only minor differences between this and Lemma 1. The only differences are that h appears instead of L, and r is corrected by r  gl in this model. As this holds true in the other stages, and the procedure to derive equilibrium remains the same, we omit the rest of the model without scale effects. Instead, we summarize the results of all three stages in the next lemma. Lemma 4. The market equilibrium without scale effects are given as follows: (a) The SPT stage   h l l ðe  1Þ  ðr  gl Þ ; i0 ¼ e N g0 ¼ lel fðel  1Þh  Nðr  gl Þg: (b) The GPT–SPT joint-research stage   1 h l ðe  1Þ  2ðr  gl Þ ; i1  iS þ ig ¼ l e þ1 N g1 ¼

Nl fðel  1Þh  2Nðr  gl Þg: e þ1 l

(c) The GPT autonomy stage  h 1  elS b iS ¼ ð1  elS Þ  elS 1 þ ðr  gl Þ  ; N N X Nb  ðr  gl Þ; ig ¼ X   Nb lS lS lS g2 ¼ lS ð1  e Þh  e ðN þ 1  e Þðr  gl Þ  X   Nb þ lg N  ðr  gl Þ : X

81

Part II

Dynamics of the black box Intersectoral growth

83

4

Advantages of backwardness and forwardness with shifting comparative advantage

1 Introduction Part II takes into account more explicitly intersectoral relations within an economy and analyzes the dynamics of the black box with multiple sectors in the economy. For this purpose, this chapter attempts to study the dynamics of comparative advantage within an economy stemming from endogenous innovation and to examine the effects of trade and R&D policies, such as patent and subsidy policies, on these dynamics. In this chapter, the engines for change in the dynamics of comparative advantage are the “advantage of economic backwardness” (Gerschenkron, 1962) and the “advantage of economic forwardness”. The idea of the former advantage reflects the fact that latecomers tend to grow faster than developed countries due to technological spillovers, but when the latecomers approach the technological frontier, they tend to face an economic slowdown. This mechanism has been adopted by several studies that attempt to account for both convergence and divergence in growth rates among multiple countries (see, for example, Abramovitz, 1986; Howitt, 2000; Howitt and Mayer-Foulkes, 2004). However, these studies do not necessarily account for the shift in comparative advantage within a single country. Thus, although a vast literature exists on the convergence and divergence of growth rates across countries or regions at the aggregated level or on the sectoral econometric analyses of productivity (see, for example, Griffith, Redding, and Reenen, 2003, 2004; Zachariadis, 2003, 2004; Ulku, 2007; López-Pueyo, 2008), little work has been done on the convergence and divergence of productivity at the more disaggregated industrial level. One exception to this is the study of Krugman (1987), who examined the effect of economies of scale on comparative advantage and showed that a small initial advantage tends to be reinforced over time under increasing returns. This could be regarded as the “advantage of forwardness”. However, the focus of Krugman’s work is the effect on trade patterns, and the dynamics of changing comparative advantage within an economy are simply assumed, rather than derived, in this analysis.1 What is missing in the analysis of trade, in general, is to account for the permanent differences in the dynamics of comparative advantage across countries after trade, particularly when an advanced country

84

Dynamics of the black box

84

trades with a backward country. For this purpose, the dynamics of comparative advantage within a country and the trade effect on the latter must be carefully examined. The advantage of forwardness is a relatively new concept to the literature, while that of backwardness has been extensively studied. Nevertheless, the former advantage does play a significant role in the process of technological change. If the advantage of backwardness alone exists, all firms and countries must eventually converge to the same technological level. As a result, no sustainable comparative advantage could emerge. In reality, however, technological gaps do exist among firms and countries in many industries; along certain technological trajectories, several firms, such as Intel and Toyota, have established sustainable comparative advantages over followers. This could be regarded as a manifestation of the advantage of forwardness. This advantage of forwardness is the result of learning by doing and using in the presence of technological tacitness and appropriability. If tacitness and appropriability are not assumed, followers could benefit from the learning spillovers of leading firms and sectors. However, if these barriers exist, increasing returns work only for the leading firms and sectors. For example, advanced technologies are developed for some specific context, which in turn opens the possibility of new applications to other contexts. Therefore, the more technologically advanced firms or sectors are, the more R&D investment is to be made in the next period. As a result, the economic advantage of forwardness arises. The model in this chapter attempts to account for the dynamics of comparative advantage within an economy by incorporating both the “advantage of backwardness” and the “advantage of forwardness”, the relative strength of which is assumed to depend upon the technological distance from a marginal sector in the economy. A sector with the threshold relative productivity level, y, is referred to as a marginal sector in this chapter, and sectors with productivity levels that are lower than or higher than y are defined as backward and advanced sectors, respectively. It is shown that the dynamics of comparative advantage depend on the locus of this marginal sector such that cyclic repetition can be observed among backward sectors, whereas sustainable comparative advantage emerges among advanced sectors in the economy. A growing sector initially enjoys the advantage of backwardness, but this advantage gradually decreases and the advantage of forwardness eventually becomes associated with the sector. These dynamics of comparative advantage remain the same even after trade liberalization. Trade determines which sectors will survive in the economy, but it does not define the dynamics of comparative advantage before or after trade liberalization as long as the threshold level, y, does not change significantly after such liberalization. Moreover, it is also shown that only those R&D policies that significantly change the locus of y are effective and that other R&D policies have limited effects on economic growth. In other words, R&D policies related to the marginal sector alone have a profound effect on economic growth and the dynamics of comparative advantage in the overall economy. Therefore, changes in the locus of y

85

Advantages of backwardness and forwardness 85

provide an explanation for not only the sectoral dynamics before and after trade but also permanent differences in productivity across countries. Thus, R&D policies should be designed to facilitate the shift towards a more desirable overall comparative advantage in the economy. For example, if a backward country attempts to shift towards more productivity growth in its advanced sectors, R&D taxes, rather than subsidies, should be imposed on the marginal sector. On the other hand, R&D subsidies should be provided to the marginal sector when the backward country aims to gain a greater comparative advantage for its backward sectors. This finding also has policy implications regarding conditions under which sectors make the transition from backward to forward. One of the most efficient ways to ensure that backward sectors make the transition to being advanced sectors is to decrease the locus of y below the technological levels of the targeted sectors. This policy, if it is feasible, could be implemented without subsidies. Instead, imposing taxes on the marginal sector enables backward sectors to make the journey toward advanced sectors in the economy. The rest of the chapter is organized as follows. Section 2 describes and solves a basic model, while Section 3 derives the equilibrium dynamics of comparative advantage and examines the effects of trade and R&D policies on these dynamics. Section 4 presents our conclusions.

2 The model This section describes the basic model of this chapter. The economy has a household sector and N final good sectors in an infinite sequence of periods t = 1,2, . . . Three objects of exchange exist: N final goods, labor, and bonds. In each period, markets exist for the three objects of exchange. Let wt be the wage and pbt the bond price at time t. The interest rate from t to t þ 1 is denoted by rtþ1. Expenditure, E, is normalized to unity (E ¼ 1). A bond at t is a claim on expenditure at t þ 1 such that the bond price becomes pbt ¼ 1=ð1 þ rtþ1 Þ. 2.1 The household sector The household sector has an initial endowment of B1 bonds coming due at t = 1 and owns the shares of all firms in the economy. It supplies L units of labor in each period, and L is assumed to be unity without loss of generality. The budget constraint is given by N X i¼1

pit Cti þ

Btþ1 ¼ wt þ Bt þ Pt ; 1 þ rt

ð4:1Þ

where Pt is the profits of firms in N final good sectors, which become zero in equilibrium. The utility function of the household is tt X 1  N X 1 ln Cti ; ð4:2Þ Ut ¼ 1þr t¼t i¼1

86

Dynamics of the black box

86

where Cti denotes consumption of the ith final good at time t and r is the discount rate. Expenditure then follows the Ramsey equation, and by assuming E ¼ 1, we have r ¼ r:

ð4:3Þ

The demand for each final good is then nit ¼

1 ; Npit

ð4:4Þ

where nit denotes the quantity of final good i demanded by the household at time t.

2.2 Final good sectors A firm in each sector has an identical production function except for the productivity level, ait , and it has a capacity limit of one unit of output per period. At date i t þ 1, a firm in the ith sector hires labor ltþ1 and its output is given by the Leontief production function i yitþ1 ¼ min½1; aitþ1 ltþ1 :

ð4:5Þ

Following the standard Ricardian model, the model in this chapter adopts the Leontief production function, which not only makes this model comparable to the aforementioned model but also greatly simplifies the analysis. In addition, we also assume a capacity constraint, allowing for positive economic profits in competitive settings. In the standard endogenous growth literature (e.g., Grossman and Helpman, 1991), some market power is assumed in order to secure innovation rents and justify R&D investment. However, it would be more realistic if several firms, instead of a single firm, were to supply the final goods in each sector. This seems to be supported by the fact that such firms are technologically on a par with each other and some capacity constraint exists that prevents a technological leader from capturing the whole market.2 Thus, this chapter adopts the assumptions of the Leontief production function and a capacity constraint in what follows (see Irmen 2005 for a similar specification). The firm’s labor productivity is equal to aitþ1 ¼ At ð1 þ qit Þ;

ð4:6Þ

where At is an indicator of economy-wide labor productivity at date t, and qit is an indicator of the current relative productivity growth of the firm with respect to all the others. Note that productivity growth depends on both the growth of economy-wide productivity, At , and the growth of the firm’s investment in R&D. Thus, technological spillover effects also influence the level and growth of labor productivity within the firm.3

87

Advantages of backwardness and forwardness 87

Economy-wide labor productivity is a result of past R&D investments by all sectors in the economy, which is specified as 0 X ni qi 1 t t1 B 1 þ qit1 C B C: ð4:7Þ At ¼ At1 @1 þ X nit A 1 þ qit1 Thus, the larger the R&D investment by all sectors, the greater the productivity growth that follows. 2.3 Cost of innovation The firm invests the amount iðqit ; Dit Þ at date t by issuing bonds and increases current productivity by the factor ð1 þ qit Þ available at date t þ 1. Dit denotes the technological gap at date t and is defined as Dit  ait1  y;

ð4:8Þ

where y denotes the standard (threshold) technological level. The sectors where ait1 < y are referred to as “backward sectors” and those where ait1 > y are referred to as “advanced sectors”. The sector where ait1 ¼ y is called a “marginal sector”. The value of y depends on technological tacitness, the degree of patent protection, and other institutional factors such as academic organizations and trade associations. Because whether a sector is advanced or backward depends on the current economy-wide level of productivity, we specify yt ¼ cAt ;

ð4:9Þ

where 0 < c < 1.4 According to this specification, the standard technological level depends solely on the distance from the current frontier technology.5 However, it is obvious that c depends on technological tacitness, the degree of patent protection, and other institutional factors. For example, stronger patent protection implies a decrease in c (smaller advantage of backwardness). Therefore, the cost of innovation is assumed to be a function of the technological gap, indicating the “advantage of economic backwardness” for backward sectors (ait1 < y). However, it is also assumed that as the technological gap decreases, this advantage also declines. Eventually, the advantage of backwardness disappears at ait1 ¼ y, and the advantage of forwardness (or disadvantage of backwardness) emerges thereafter (ait1 > y). Note that in the latter case, the technological gap from the frontier sector increases the R&D costs. Thus, narrowing this gap alone increases the advantage of forwardness. To be consistent with this specification and assure optimal solutions, we assume the following. Assumption 1. iðqit ; Dit Þ is twice continuously differentiable such that @iðqit ; Dit Þ= @qit > 0; @ 2 iðqit ; Dit Þ=@qit 2 > 0:

88

Dynamics of the black box

88

Assumption 2. For all qit  0, @iðqit ; Dit Þ=@Dit  0, @ 2 iðqit ; Dit Þ=@qit @Dit  0 if Dit  0 and @iðqit ; Dit Þ=@Dit < 0, @ 2 iðqit ; Dit Þ=@qit @Dit < 0 if Dit > 0. The second assumption implies that given qit  0, the marginal R&D costs increase up to ait1 ¼ y and decrease afterwards. In other words, the advantage of backwardness prevails where ait1 < y, while the advantage of forwardness emerges where ait1 > y. Assumption 3. @iðqit ; Dit Þ=@qit  @iðqjt ; Djt Þ=@qjt for all Dit < 0 and Djt  0. This assumption suggests that a discontinuous gap exists between backward and advanced (including marginal) sectors. In other words, this assumption implies the advantage of backwardness should not surpass the advantage of forwardness, which seems innocuous in reality. That is, followers could benefit from leaders, but the technological capability of the former would be lower than that of the latter. Although the following analysis could proceed without this assumption, the results become too complicated in this case. How the results below would be altered without this assumption will be considered later. 2.4 Economic intuition The justification for this specification is that while in the stage of underdevelopment, technologically backward sectors gain from some of the spillover effect from more advanced sectors in the economy. Such sectors are able to avoid redundant R&D investment. For example, advanced sectors invest more in the training of human capital, which in turn benefits backward sectors through labor mobility or the emergence of educational institutions as a by-product. Moreover, knowledge spillover effects could play a significant role during this stage of backwardness. According to Rosenberg (1976), the process of industrialization in the US is characterized by “technological convergence” mediated by the US machine tool industry. Due to this technological convergence, the US machine tool industry played the role of a technology diffusion center whereby new skills and techniques were developed or perfected in response to the demands of specific customers, and once they were acquired, the new skills and techniques were transferred to the entire machine-using sector of the economy. This historical evidence obviously supports and justifies the specification that the backward sectors are able to achieve cost-reducing innovation with lower R&D costs. However, it does not seem realistic to assume that the full spillover effect is available to all backward sectors. Instead, the magnitude of any spillover effect would be limited by the tacit nature of advanced technology or patent protection. Hence, this spillover effect is measured by Dit ¼ ait1  y for some y at1 , where at1 denotes the highest level of productivity achieved in the

89

Advantages of backwardness and forwardness 89

economy. Obviously, if at1 < y, the higher value of y implies that backwardness has a greater advantage in the economy. In contrast, if at1 > y, this advantage of backwardness is no longer available, and instead, the advantage of forwardness emerges. Chapter 3 models this stage as “the GPT (General Purpose Technology) autonomy stage” and derives the equilibrium situation in which innovation proceeds mainly in GPT sectors without a significant contribution from other sectors. This result could be interpreted as a reflection of the widening gap between advanced and backward sectors over time. In the context of the model presented in this chapter, this implies that more technologically advanced sectors are able to enjoy learningby-doing effects that lower their R&D costs.

2.5 Equilibrium Given this specification for the R&D cost function, it is optimal for a firm in the ith sector to set i ¼ ltþ1

1 1 : ¼ atþ1 At ð1 þ qit Þ

ð4:10Þ

At date t þ 1, the competitive wage rate is wtþ1 and the firm sells its output at price ptþ1 . R&D investment iðqit ; Dit Þ is financed by an issue of bonds. Therefore, its operating profit is  1 wtþ1 i i  iðqit ; Dit Þ: p  ð4:11Þ ptþ1 ¼ 1 þ rtþ1 tþ1 At ð1 þ qit Þ The firm takes the sequence of real prices, aggregated productivity, and the technological gap, fpt ; wt ; rt ; At ; Dit g, as given and chooses its production plan so as to maximize the sum of the present discounted values of its profits in all periods. Since it is assumed that each sector’s impact on the economy-wide productivity level in the next period through (4.7) is negligible, production plans for different periods are independent of each other. Hence, the firm will choose the production plan that will maximize its profit ptþ1 in period t. The firstorder condition yields 1 wt @iðqit ; Dit Þ  ; 1 þ rtþ1 At ð1 þ qit Þ2 @qit

ð4:12Þ

with strict inequality only if qit  ¼ 0: Now, let us consider the equilibrium at a particular date t. At this date, given the sequence of real prices, aggregated productivity, and the technological gap, fpt ; wt ; rt ; At ; Dit g, firms invest in R&D to maximize their current operating profits. Since each firm produces only one unit of output per period due to the capacity constraint, the set of active firms emerges for each sector at date t,

90

Dynamics of the black box

90

which is given by nit for the ith sector at time t. An equilibrium in this model is then defined as follows. Definition. ðqit  ; nit  ; lti  ; pit ; At Þis a static equilibrium if (a) qit  maximizes pitþ1 ðqit Þ (b) pit ðqit1  Þ ¼ 0 if nit  > 0 and pit ðqit1  Þ < 0 if nit  ¼ 0 1 (c) nit  ¼ i if nit  > 0 Npt X (d) At ¼ nit  X i (e) nit  lti  ¼ 1 i

At date t, a total mass of nit firms enters the market in the ith sector, and since all firms are identical in each sector, they choose the same R&D investment qit  . The first equilibrium requirement is that the firms behave competitively by taking price, wage, and aggregate productivity as given when investing in R&D. With free entry, profits cannot be positive such that each firm earns zero profit when the mass of active firms is positive. Otherwise, profits become negative. The third requirement ensures that the market of the ith sector clears at price pit , and the last requirement suggests the labor market clearing condition. Lemma 1. A unique static equilibrium exists in the economy. Proof: See Appendix. This lemma establishes a unique static equilibrium for each period. Since the cost function is well behaved, a unique optimal level of R&D investment always exists. Price is adjusted to make the profits of firms equal to zero, and the number of firms in each sector is determined to make the labor and final good markets clear. In this static equilibrium, the relations between R&D investment and the total output and its price in each sector are Lemma 2.

@nitþ1 @pitþ1 @qit @qit @qit i > 0, < 0, < 0, > 0 if D  0, < 0 if t @qit @qit @At @Dit @Dit Dit < 0.

Proof: See Appendix. Thus, higher R&D investment leads to more output and a lower price in the next period, which suggests that comparative advantage in R&D investment implies comparative advantage in price and output at the same time. Turning to the behavior of the economy as a whole, a dynamic equilibrium corresponds to a sequence of price, wage, and aggregate productivity that satisfies the following conditions. Definition. ðqit  ; nit  ; lti  ; pit ; wit ; At ; Bt Þ is a dynamic equilibrium sequence if, for all t and 0  i  N,

91

Advantages of backwardness and forwardness 91 (a) it is a static equilibrium X iðqit Þ (b) Btþ1 ¼ ð1 þ rÞ i tþ1 (c) 1 þ B1þr ¼ wt þ Bt :

Lemma 3. Given B1  0, a unique dynamic equilibrium sequence exists in the economy.

3 Dynamics of comparative advantage and R&D policies This section examines the dynamics of comparative advantage in the economy and the effects of trade and R&D policies on these dynamics. 3.1 Dynamics of comparative advantage In this model, movements of comparative advantage are completely described by the R&D investment of firms in each sector. Higher R&D investment leads to a higher share of output, and the current R&D investment in turn depends on the productivity level in the previous period. Proposition 1. (a) Among backward sectors with ait1 < y (Dit < 0), cyclic repetition arises when comparative advantage in the next period is ranked in an order that is the reverse of the order in which comparative advantage in the current period is ranked. (b) Among advanced sectors with ait1 > y, comparative advantage in the economy does not change over time. Proof: See Appendix. The first part of this proposition suggests that comparative advantage among backward sectors changes over time in a cyclical manner. That is, the least productive sector becomes the most productive sector in the next period, while the current leading sector becomes the least productive sector in the next period. Hence, R&D-intensive sectors in the previous period do not have an incentive to invest in R&D in the current period. These cyclical movements are enabled by the advantage of backwardness. The second part of this proposition implies that among advanced sectors, the order of the magnitude of R&D investment in the previous period remains the same as that in the current period. Thus, R&D-intensive sectors in the previous period have more incentive to invest in R&D in the current period. To what extent does this theoretical prediction regarding the dynamics of comparative advantage correspond to reality? In particular, the cyclic repetition among the backward sectors seems counterintuitive. However, some empirical studies show changing comparative advantages in some countries. For example, Balassa and Noland (1989) presented empirical evidence that during the period from

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1967 to 1983, Japan’s pattern of specialization in manufacturing goods changed dramatically from specialization in unskilled labor-intensive goods towards specialization in human capital and R&D-intensive goods, while the US maintained its comparative advantage in physical capital, human capital, and R&D-intensive goods. In contrast to the US, during this period, Japan had not yet reached the mature stage of economic development. Dalum, Laursen, and Villumsen (1998) examined the stability of trade patterns in OECD countries during the period from 1965 to 1992. In this study, it was shown that the “catching-up” OECD countries, including Japan, had a strong tendency towards a decreasing number of initially advantaged sectors and an increasing number of initially disadvantaged sectors, whereas small, high-income countries and the US showed stable patterns of comparative advantage. These results suggest that comparative advantage tends to change more frequently in developing countries (higher y) than it does in developed countries (lower y). Moreover, the term “economy” or “country” might also be extended to refer to a “global industry”.6 For example, the global semiconductor industry has been dominated by the US, Japan, Korea, and Taiwan. At the inception of this industry, the US initiated and dominated the market, but it lost its comparative advantage in this industry to Japan during the 1980s. However, after the bubble economy burst around 1990, Japan lost its comparative advantage, and once again, the US became the dominant producer. So, a cyclic repetition in this industry between the US and Japan can be observed.7 Similar dynamics can also be observed in the global automotive industry, where the comparative advantage of the US has fluctuated over time. These results seem consistent with Proposition 1 in this chapter. Note that the results of Proposition 1 should be altered slightly when Assumption 3 is violated. To be precise, suppose there exist some D t  Dt < 0 and ~ Di  D ~t  D  t such that @iðqi ; Di Þ=@qi < @iðqj ; Dj Þ=@qj holds for all 0D t t t t t t t ~t ~ t , where D and D  t denote the lowest and highest technologiand 0  Djt  D t cal gaps at time t, respectively. Then, cyclic repetition takes place for all ~ t , that is, backward sectors where Di  Dt leapsectors where Dht  D t ~ t . Depending on the locus~ of the frog advanced sectors where 0  Djt  D ~ t might next marginal sector, some of the advanced sectors where 0  Djt  D become backward sectors in the next period. However, all the advanced ~ t < Dj maintain their comparative advantage. Thus, when sectors where D t Assumption 3 is violated, cyclic repetition takes place even among some of the advanced sectors. However, the overall dynamics of comparative advantage, i.e., cyclic repetition and sustainable comparative advantage, still hold in this case. 3.2 Trade effect How does this model account for the dynamics of comparative advantage across national boundaries? Let us consider the effect of trade liberalization on the dynamics of comparative advantage. According to the standard Ricardian

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Advantages of backwardness and forwardness 93

model, trade liberalization selects which sectors will survive. Now, assume that the international spillover of aggregate technology takes place after trade liberalization, and yh < y where yh and y are the threshold productivity levels of Home and Foreign countries before trade liberalization, respectively. This implies that Home is a backward country before trade liberalization, which is quite a realistic assumption. From the specification of (4.9), yh < yw  y holds where yw denotes the world threshold productivity level after trade liberalization, as long as c does not change significantly between Home and Foreign countries. World aggregate productivity after trade liberalization is denoted by Awt, which must equal At at the time of trade liberalization. If c is the same for both countries, yw ¼ y should be satisfied. However, it is highly unlikely that the advantage of backwardness increases in advanced countries after trade with backward countries. Therefore, yw  y is expected to hold in general. Now, the dynamics of Awt follow (4.7), but R&D investment is made by both Home and Foreign countries. It is also assumed that once sectors cease to exist after trade liberalization, R&D investment in such sectors will no longer take place. It then becomes easy to obtain the following result. Proposition 2. (a) Trade liberalization does not change the dynamics of comparative advantage for all surviving sectors where ai < yh or ai  yw. (b) Trade liberalization changes the dynamics of comparative advantage from stability to cyclic repetition for all surviving sectors where yh < ai < yw . Suppose the threshold level does not change significantly after trade liberalization (yh  yw ). Then, although trade liberalization determines which sectors will survive, once the surviving sectors are selected, the dynamics of comparative advantage among these sectors remain the same as before. In this sense, trade does not alter the dynamics of comparative advantage in our model. However, if huge gaps in technology or intellectual property rights exist between Home and Foreign countries, then the dynamics are significantly altered. The social efficiency of trade liberalization in terms of economic growth hinges on which group of sectors, backward or advanced, should increase R&D investment. Obviously, when yh < yw , domestic advanced sectors benefit from trade liberalization due to fewer spillovers.

3.3 The effect of R&D policies So far, the model in this chapter has described the dynamics of comparative advantage. Now let us examine the effects of various R&D policies on these

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dynamics, such as in relation to patent policy and subsidies. In order to obtain unambiguous results, assume the following: Assumption 4.

X

iðqit ; Dit Þ does not significantly change as a result of R&D

i

policies. That is, although R&D policies do change R&D investment in some sectors, the sum of R&D costs in all sectors of the economy is not altered significantly. Given this assumption, consider patent policy first. Strong patent protection, such as increases in the patent breadth and length, implies that the advantage of backwardness becomes restricted, since strict patent policies restrict the ability of backward sectors to utilize advanced technologies. Thus, a strict patent policy has the effect of decreasing y (c), the implication of which is given by the next proposition. Proposition 3. Strict patent policy leads to more R&D investment in the advanced sectors of the economy, while discouraging R&D investment in the backward sectors. Proof: See Appendix. Thus, strict patent policy encourages innovation only in advanced sectors, since it increases the advantage of forwardness by increasing the technological gap, Dit ¼ ait1  y > 0. In addition, backward sectors with productivity near y could benefit from this strict patent policy as well, since these sectors would now belong to the group of advanced sectors. Hence, in the next round of R&D investment, the productivity rankings of these sectors do not have to decline significantly. Strict patent policy also benefits these marginal sectors. Next, consider the effects of sector-specific subsidies. In particular, we are interested in subsidies for the marginal sector (i.e., the y sector). It is assumed that the subsidies are not so large that assumptions 3 and 4 still hold. Then, we obtain the following result: Proposition 4. (a) Subsidies for and taxes on non-y sectors have no significant structural effects on R&D investment. (b) Subsidies for the y sector have permanent structural effects that encourage R&D investment in backward sectors and discourage R&D investment in advanced sectors. (c) Taxes on the y sector have permanent structural effects that discourage R&D investment in backward sectors and encourage R&D investment in advanced sectors. Proof: See Appendix.

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Advantages of backwardness and forwardness 95

Structural effects refer to the changes in the membership of backward and advanced sectors. According to this result, subsidies for and taxes on non-y sectors would not change the membership significantly. Only those sectors that receive R&D subsidies or pay taxes might make the transition from backward to forward or from forward to backward sectors. If the amounts of subsidies and taxes are small, the membership would not be altered at all. As a result, these effects would remain modest. For example, suppose one of the backward sectors receives an R&D subsidy, which would obviously improve its comparative advantage in the next period. However, since this sector remains in the group of backward sectors, the comparative advantage of this sector once again decreases thereafter. Consequently, the effect of the R&D subsidy does not significantly improve the ranking of this sector among the backward sectors. Hence, only subsidies for and taxes on the y sector have permanent structural effects. In this case, although the relative ranking of the marginal sector remains the same after the R&D policies are implemented, its R&D investment differs from investment without the R&D policies, which in turn has a permanent effect on other sectors in the economy. Thus, it makes sense to target this marginal sector when formulating R&D policies. If more R&D investment in the backward sectors is socially desirable, R&D subsidies that benefit this marginal sector should be introduced. However, if social welfare critically depends on the level of productivity among the advanced sectors, R&D taxes, rather than subsidies, should be imposed in this marginal sector.

4 Concluding remarks In this chapter, we developed a multi-sector endogenous growth model that accounts for the dynamics of comparative advantage within an entire economy. We showed that the direction of learning spillovers plays a significant role in generating the dynamics of comparative advantage and made some suggestions regarding desirable R&D policy that would facilitate economic growth. If the level of the marginal sector is high enough, cyclic repetition of comparative advantage is more likely to arise, such that comparative disadvantage becomes a source of comparative advantage in the next period, due to the advantage of backwardness. However, once this threshold level decreases beyond a certain point, no shift in comparative advantage takes place and the relative rank of comparative advantage stabilizes, due to the advantage of forwardness. These intrinsic dynamics of comparative advantage within the economy remain the same even under international trade. Therefore, only R&D policies that affect the locus of the marginal sector play a significant role in the subsequent dynamics of comparative advantage and permanent differences in comparative advantage and economic growth across countries. If the locus of the marginal sector does not change, R&D policies for non-y sectors have only a temporary effect. Thus, to facilitate economic growth, only R&D policies for the marginal sector are justified.

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96

R&D taxes in this case widen the technological gap between advanced and backward groups, while this gap is reduced by R&D subsidies, the effectiveness of which critically depends on the curvature of the R&D cost function and the distribution of firms among advanced and backward sectors. Hence, R&D policies should be designed to take full advantage of learning spillovers in the economy.

Notes 1 Regarding the dynamics of comparative advantage within an economy, Landesmann and Stehrer (2000) demonstrated through simulation exercises that in the course of economic development, the comparative advantage of catching-up economies can increasingly be directed towards the medium- to high-tech sectors rather than remaining in the lower-tech sectors. This is consistent with our findings when the advantage of forwardness dominates. However, in the process of catching up, the advantage of backwardness might play a more significant role. In such cases, cyclic repetition emerges in our model, instead of unidirectional movement towards medium- to high-tech sectors. 2 For example, Teece (1986) argues that innovation rents accrue to the owners of certain complementary assets. Since these complementary assets, such as sales distribution channels, after-sales support networks, and manufacturing plants, are usually relation-specific and limited in terms of supply, a single firm could not own all of the complementary assets that would enable it to capture all of the innovation rents in the market in general. 3 Note that this specification of the firm’s labor productivity gives rise to somewhat unrealistic productivity dynamics. That is, more backwardness leads to more research effort and a higher jump in productivity. However, since we do not examine the implications of dynamic equilibrium, oscillatory behavior does not cause a direct problem regarding the propositions asserted in this model. The alternative specification, such as atþ1 ¼ lat þ ð1  lÞAt ð1 þ qÞ, seems more realistic, but at the cost of extremely complicated algebra. 4 We would like to express our appreciation to the referee for suggesting this specification. 5 This implies that we are interested in how a given y affects the dynamics of comparative advantage, rather than in how y is to be determined endogenously. 6 Similarly, the argument on the dynamics of comparative advantage could be applied to firms belonging to the same sector or industry. 7 Note that at such time, the locus of process innovation in this industry had just shifted from plant operation to semiconductor equipment, which was available mainly from specialized equipment suppliers. As a result, most of the semiconductor equipment was first utilized and tested by the leading producers, and subsequently, more reliable, refined, and less expensive items were sold to followers, which implies a higher value of y.

97

Appendix

Proof of Lemma 1 The cost function is convex, so the optimal solution for qit , given fptþ1 ; wtþ1 ; rtþ1 ; At ; yg always exists. Prices are adjusted to make the profit of firms in each sector equal to zero. Given these prices, consumer demand for final goods is determined according to (4.4). Since the total supply of labor is assumed to be L ¼ 1, from (4.10), the aggregate demand for labor is given by X X ni tþ1 i L1¼ nitþ1 ltþ1 : However, from (4.7), ¼ At ð1 þ qit Þ 0 1 X ni qi tþ1 t B X ni X nitþ1 1 þ qit C B C tþ1 ¼ 1 þ B X ni C At ð1 þ qit Þ Atþ1 ð1 þ qit Þ @ tþ1 A 1 þ qit 1 0 X X nitþ1 C nitþ1 1 X nitþ1 B C¼ B ¼ ; Atþ1 1 þ qit @X nitþ1 A Atþ1 1 þ qit X which implies Atþ1 ¼ nitþ1 : i

This therefore constitutes the static equilibrium in the definition. Q.E.D.

Proof of lemma 2 Since the only difference among the sectors in the LHS of the first-order condition (4.12) is R&D investment qit , more R&D investment implies lower values for the RHS as well as the LHS. From the zero-profit condition and (4.11), the price of wtþ1 output is given by pitþ1 ¼ þ ð1 þ rtþ1 Þiðqit ; Dit Þ: However, the RHS of At ð1 þ qit Þ this equation becomes lower when the RHS of (4.12) is low. Thus, more R&D investment leads to a lower price of output. Moreover, the demand function (4.4) indicates that a lower price of output results in a greater total amount of

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98

output. Regarding the effects of At and Dit , the results immediately follow by applying the implicit function theorem to (4.12). Q.E.D.

Proof of lemma 3 From lemma 2, a unique static equilibrium of ðqit  ; nit  ; lti  ; pit ; At Þ always exists, given the wage and Bt . According to (4.1), (4.4), and the zero-profit condition, B we can derive 1 þ tþ1 ¼ wt þ Bt : Hence, the wage rate sequence is fixed 1þr when bond demand is determined. In equilibrium, bond demand must be equal to aggregate savings, which in turn is given by the total amount of R&D X investment. Thus, the bond market equilibrium condition is Btþ1 ¼ ð1 þ rÞ iðqit ; Dit Þ: i

Accordingly, given the initial condition B1 ¼ 1, a unique sequence of bonds and wages is determined. Q.E.D.

Proof of Proposition 1 From (4.12) and assumptions 1 and 2, we obtain pqq < 0, pqD  0 for Dit  0, dq and pqD > 0 for Dit > 0. By the implicit function theorem, if Dit  0, 0 dD  dq holds, and if Dit > 0, > 0 is established. By Assumption 3, the results dD follow. Q.E.D.

Proof of proposition 2 Following the standard Ricardian model, we assume that after trade liberalization, in the Home country, f1; :::; Ig sectors survive, while fI þ 1; :::; Ng sectors shift to the Foreign country. Since complete separation of R&D and production is not possible, R&D investments in f1; :::; Ig sectors are made in the Home country and R&D investment in fI þ 1; :::; Ng sectors in the Foreign country. Thus, trade liberalization selects the surviving sectors, but after this selection, the dynamics of R&D investment among surviving sectors remain the same as before, which now depend on the locus of yw . The remaining part of the proposition immediately follows. Q.E.D.

Proof of proposition 3 From the definition of a dynamic equilibrium, wt ¼ 1 þ

X

iðqit ; Dit Þ  Bt is

i

obtained. Substituting this and (4.3) into (4.12) yields X 1þ iðqit ; Dit Þ  Bt 1 @iðqit ; Dit Þ i  : 2 1þr @qit At1 ð1 þ qit Þ

ðA1Þ

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Advantages of backwardness and forwardness 99

Since Bt is given, by assumption 2, an increase in Dit increases the RHS for backward sectors while it decreases the RHS for advanced sectors. According to assumption 4, the LHS does not change significantly. Hence, the results in this proposition follow. Q.E.D.

Proof of proposition 4 Since (b) and (c) are obvious, let us consider (a) alone. Suppose a non-y sector receives the subsidy. However, according to assumptions 3 and 4, this subsidy does not change the value of y that would be realized without the subsidy. The subsidy therefore temporarily affects R&D investment through the FOC of (A1), but in the next period, the effect of the subsidy disappears in (A1). Its effect appears only through aggregate productivity A. However, assumption 4 implies that A does not change significantly as a result of the subsidy. Hence, this subsidy has only a temporary effect. Q.E.D.

5

Changing productive relations, linkage effects and industrialization

1 Introduction In many advanced countries, industry structure changes over time. In this process, a few key industries play an important role in economic development and growth as centers of learning. These sectors are sometimes called “GPT” (general purpose technology) sectors (see, for example, Bresnahan and Trajtenberg, 1995; Helpman, 1998; Harada, 2010a; Chapter 3). Multi-sector economic growth models such as product-variety models (Grossman and Helpman, 1991), however, typically assume fixed and symmetric linkages among sectors, and structural changes have not been accounted for explicitly. From a slightly different perspective, Hirschman (1958) argued that the main source of economic development is activities with high potential linkage effects, mainly backward ones. Backward linkages correspond to the stimuli going to sectors that supply the inputs required by a particular activity, whereas forward linkages are the inducements to set up new activities utilizing the output of the proposed activity. If these linkage effects are sufficiently strong, underdeveloped countries are more likely to take off and escape the poverty trap. A number of empirical studies have been conducted to measure the linkage effects and to identify key sectors (Rasmussen, 1956; Chenery and Watanabe, 1958; Schultz, 1977; Dietzenbacher and van der Linden, 1997; Miller and Lahr, 2001). In most of these empirical studies, sectors with high forward and backward linkages have been identified as key sectors. However, it is not necessarily obvious why the key sectors should have both high forward and backward linkages. Table 5.1, for example, shows the correlation between forward and backward linkages in seven advanced countries in 1995, 2000, and 2005. According to this table, the correlations tend to be negative for most countries, while all of the correlations are statistically insignificant. Despite these weak and negative relations, should the key sectors still be identified as having both high forward and backward linkages? Although several theoretical models have been developed that incorporate linkage effects (for example, Krugman, 1991b; Fujita, Krugman, and Venables, 1999), these studies have assumed fixed productive relations among sectors in an economy. As a result, endogenous relations between forward and backward linkages could not be accounted for by these models. In reality, productive relations vary over time. This implies that backward and

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Table 5.1 Correlation between backward and forward linkages Country

1995

2000

2005

Canada France Germany Italy Japan UK US

0.06 0.05 −0.07 0.05 −0.12 0.10 −0.01

−0.02 −0.01 −0.09 0.02 −0.02 0.01 −0.09

−0.03 −0.04 −0.03 −0.01 −0.11 −0.15 −0.15

Sources: OECD input–output tables (www.oecd.org/sti/inputoutput) Note: Backward and forward linkages are measured by Chenery–Watanabe indices.

forward linkages also change. What is required, then, is to account for the dynamics of backward and forward linkages as well as changing productive relations. For this purpose, production functions should entail variable productive relations among intermediate goods.1 Therefore, this chapter attempts to develop a multisectoral general equilibrium model that incorporates endogenous changes in productive relations, characterizes the dynamics of structural change, and derives implications regarding growth-enhancing policies. It is shown that productivity shocks in R&D activities increase both backward and forward linkages, while productivity and demand shocks have no effects on productive relations. Thus, under a strong influence of R&D productivity growth, key sectors are characterized as having high forward and backward linkages, which is consistent with the definition of key sectors in the existing empirical studies. In contrast, labor and capital share shocks generate the negative relationship between forward and backward linkages. Therefore, depending on the types of shocks, the relations between forward and backward linkages differ. Accordingly, the results in Table 5.1 can be interpreted as reflecting these heterogeneous random shocks. Moreover, it is shown that when vertical specialization occurs, as illustrated by Rosenberg (1976) for the case of the US machine tool industry, it generates not only sectors with high backward linkages but also sectors with low backward and high forward linkages. Thus, in contrast to the previous studies, the key sectors are characterized as having high forward and low backward linkages in this case. This implies that GPT sectors now emerge and then become not only leading sectors in economic development and growth but also bottlenecks in the event of negative shocks. It is also shown that an underdeveloped country can escape from the poverty trap when positive demand shocks in general and R&D shocks specific to potential GPT sectors take place. If these shocks are not present, sector-specific policies are necessary that provide subsidies in potential GPT sectors and impose taxes on other sectors. These policies are also an efficient way to get out of an economic slump after industrialization. Besides these results, the model in this chapter could be regarded as a modest attempt to make a bridge between IO analysis and multi-sector business cycle

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literature. As Los (2001) indicated in his model, the theory of endogenous growth could be enriched by IO analysis. To further explore this potential, we start from a multi-sector general equilibrium proposed by Long and Plosser (1983) and modify the model so that productive relations endogenously change as a result of R&D. The equilibrium productive relations are fully captured by an input–output matrix. Hence, this model could account for endogenous changes of the coefficients in input–output matrix. The rest of this chapter is organized as follows. Section 2 describes the basic model of a multi-sector economy, and Section 3 examines the equilibrium properties of this model. Finally, Section 4 concludes this chapter.

2 The model 2.1 Structure of the model In this section, a multi-sectoral general equilibrium model is developed. It builds on a multi-sectoral version of the classic Brock and Mirman (1972) one-sector model. Long and Plosser (1983) also proposed a multi-sectoral model, but ours departs from this by allowing for endogenous changes in productive relations among sectors. In each period, a two-stage game is assumed to be played by firms and a household. In the first stage, firms invest in R&D in order to attain the optimal mix of productive relations by changing the share parameters of the Cobb–Douglas production function. In the second stage, given new share parameters, firms engage in production that is realized in the next period with some productivity shocks, while the household consumes the currently available final goods. 2.2 Consumption and production Consider a discrete time economy inhabited by a representative agent, the intertemporal utility function of whom is given by " # 1 n X X t ð5:1Þ b yi;t ln Ci;t ; U ¼ E0 t¼0

i¼1

where 0 < b < 1 and yi;t  0 for i ¼ 1; :::; n, and Ci;t refers to consumption of commodity i at time t. There are n production sectors that have linear homogeneous technologies: b

Yi;tþ1 ¼ li;tþ1 Li;ti;t

n Y

a

Mij;tij;t ; i ¼ 1; :::; n;

ð5:2Þ

j¼1

where Yi;tþ1 is the per capita total stock of commodity i available at time t þ 1 and li;tþ1 is a random variable realized at time t þ 1. Li;t and Mij;t denote the labor and the quantity of commodity j allocated to the production of commodity

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Changing productive relations

i at time t. It is assumed that bi;t þ

n X

103

aij;t < 1(labor compensation and costs for

j¼1

intermediate inputs taken together are smaller than revenues), and 1  bi;t  n X aij;t represents a level of technological capability, which is idiosyncratic to j¼1

a firm. The commodity allocation is restricted by Yj;t ¼ Cj;t þ

n X

Mij;t þ vj;t ;

j ¼ 1; :::; n;

ð5:3Þ

i¼1

where vj denotes the total amount of R&D investment in the jth sector. The current output is spent on consumption and payments to intermediate goods and R&D investment. Suppose that labor receives the wage rate wt and the ith sector gains profits pi;t at time t. Then, adopting a distributional perspective, (5.3) can also be expressed as Yj;t ¼

n X

Mij;t þ wt Li;t þ pi;t ;

j ¼ 1; :::; n:

ð5:4Þ

i¼1

The labor market clearing condition requires n X

 Li;t ¼ L;

ð5:5Þ

i¼1

 is the total amount of labor in the economy. where L 2.3 Backward and forward linkages As we will see later, backward and forward linkages can be measured by X cib;t ¼ aij;t ; ð5:6Þ j

c ¼ j f ;t

X

aij;t :

ð5:7Þ

i

That is, backward and forward linkages represent the column and row sums of the input–output coefficient matrix At  ½aij;t , which correspond to Chenery– Watanabe indices (Chenery and Watanabe, 1958). The backward linkages in (5.6) measures the total shares of intermediate goods in the production of commodity i, while the forward linkages in (5.7) indicate the relative share of commodity j in the production of commodity i. Note that these Chenery–Watanabe indices measure only the first round of effects generated by the intersectoral relations. Thus, these indices refer to direct backward and forward linkages, and indirect effects are disregarded. As suggested by Rasmussen (1956), in the case of a linear economy, the Leontief inverse, (I-A)-1 must be used, instead of A, to measure both direct and indirect linkage effects. In

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the model in this chapter, (I-LA)-1 should be considered, in which L denotes the lag operator (see (5.16) below). Indeed, Horvath (1998) and Dupor (1999) analyze this matrix in order to characterize the effects of productivity shocks. However, in this model, R&D investment is directly affected by Chenery– Watanabe indices, as we will see later. This implies that endogenously changing productive relations also depend on Chenery–Watanabe indices. Therefore, we focus in what follows on the measures of direct backward and forward linkage effects.

2.4 R&D The model in this chapter departs from Long and Plosser (1983) in that the share parameters aij;t are allowed to change endogenously. Although this specification is not standard in mainstream macro models, productive relations among factors of production are not stable in reality.2 For example, the factor share of IT (information technology) remained relatively small for decades but has now become one of the most important factors of production in many countries. A series of IT innovations has made IT one of the major factors of production. Once IT was revealed to be potentially an efficient factor of production, many firms invested in IT, resulting in more IT-based production systems. Thus, factor shares depend on innovations as well as factor prices. Suppose the ith sector invests in R&D regarding one of its intermediate inputs, j, by vji;t ðrj;ti ; εi;t Þ in the first stage of period t, where rj;ti  0 denotes R&D intensity. Then, the corresponding share parameter of the production function is assumed to be determined as rj;ti aji;t ¼ cjb;t X l : rj;t

ð5:8Þ

l

That is, aji;t is determined to reflect the share of the ith sector’s R&D intensity in the first stage of time t.3 cjb;t appears on the right-hand side since the sum of the right-hand side over all l amounts to the magnitude of backward linkages of the jth sector. The cost of this R&D,vji;t ðrj;ti ; εi;t Þ, is assumed to be strictly convex (a condition that guarantees the existence of a unique optimal solution) and to be paid out of current output Yi;t . εi;t is a R&D productivity shock at time t that X affects R&D costs directly. Thus, vi;t ¼ vji;t holds in (5.3). j

For the time being, we assume that the backward linkages are exogenously given, which greatly simplifies the algebra. Assumption 1. The backward linkages are exogenous such that cib;t ¼ cib : Later, this assumption is relaxed, and endogenous changes in the backward linkages are also examined.

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2.5 Equilibrium We will solve the perfect foresight competitive equilibrium of the economy in this model. This equilibrium is characterized as follows: (1) intermediate suppliers invest in R&D in order to maximize the profits that are realized in the next period, which in turn determines share parameters of the Cobb–Douglas production function and forward and backward linkages; (2) given the share parameters and forward and backward linkages, firms maximize their profits under given prices; (3) the household maximizes a discounted sum of utilities subject to the budget constraint under a given sequence of prices and the distributed profits; and (4) each commodity market is cleared in each period. The first stage corresponds to (1), while in the second stage, (2)–(4) take place simultaneously. Using backward induction, we will first solve the equilibrium in the second stage, (2)~(4) and then the first stage R&D game is to be solved. 2.5.1 Second stage Consider the second stage optimization problem. In this stage, it is assumed that firms take share parameters, demand shocks, and backward and forward linkages as exogenously given. Then, this problem is essentially a multi-sector version of a Mirman and Brock economy, completely characterized by Long and Plosser (1983). Since this second stage does not include externalities and R&D, the second welfare theorem assures that a socially optimal solution coincides with competitive equilibrium. Thus, instead of solving competitive equilibrium, we can derive the equilibrium conditions by solving a pseudo-planning problem, as done by Benhabib and Nishimura (1998), in which the social planner maximizes a discounted sum of utilities subject to (5.2) and (5.3). In doing so, the planner is assumed to take the share parameters that are determined as a result of R&D investment in the first stage as given. Define the value function at time t by V ðSt Þ, which equals the maximum value of a discounted sum of utilities. St  fYt ; lt ; vt g is the state variable with 0 0 0 Yt ¼ ðY1;t ; :::; Yn;t Þ , lt ¼ ðl1;t ; :::; ln;t Þ , and vt ¼ ðv1;t ; :::; vn;t Þ . Note that vt is determined in the first stage. Then, the planner maximizes n nX o yi;t ln Ci;t þ bE½V ðStþ1 ÞjSt  ; V ðSt Þ ¼ max

ð5:9Þ

i¼1

subject to (5.2) and (5.3). Following Long and Plosser (1983), we can solve this dynamic programming problem as4 ! yi;t  Y i;t ; i ¼ 1; :::; n; Ci;t ¼ ð5:10Þ gi;t

M

 ij;t

¼

! bgi;t aij;t Y j;t ; gj;t

i; j ¼ 1; :::; n;

ð5:11Þ

106 Dynamics of the black box n X gj;t ¼ yj;t þ b gi;t aij;t ; i¼1

Li;t ¼ gi;t bi

n X

106

j ¼ 1; :::; n;

ð5:12Þ

!1 gj bj

 L;

i ¼ 1; :::; n;

ð5:13Þ

j¼1

gi;t pi;t ¼  ; Y i;t

ð5:14Þ

where Y i;t  Yi;t  vi:t :

ð5:15Þ

Substituting (5.11) into (5.2) yields  ytþ1 ¼ const þ At yt þ ln ltþ1 ;

ð5:16Þ

0 with  yt ¼ ð ln Y 1;t ; . . . ; ln Y n;t Þ : 0 The productivity shocks, lnlt ¼ ð lnl1;t ; . . . ; lnln;t Þ follow an i.i.d. stochastic process as

ln li;t ð0; s2 Þ;

ð5:17Þ

yi;t represents a demand shock such that yi;tþ1 ¼ yi;t þ utþ1 ;

ð5:18Þ

where Eutþ1 ¼ 0 with the support of yi;t 2 ð0; y, and y > 1. In accordance with related studies (Horvath, 1998; Dupor, 1999), we assume the following: Assumption 2.

X i

ln li;t ¼ 0;

X

yi;t ¼ 1:

i

This assumption implies that the law of large numbers applies to the productivity and demand shocks such that their aggregate effects are negligible. Under these assumptions, it is well known that sectoral shocks become under certain conditions irrelevant in the examination of aggregate business fluctuations (Dupor, 1999). 2.5.2 First stage Next, consider the first stage. (5.2), (5.8), (5.12), and (5.14) imply that the discounted profits arising from the R&D investment are given by 0 1 i X rj;t C X B gj;t cjb;t X l A  vji;t ðrj;ti ; εi;t Þ: ð5:19Þ pi;tþ1 ¼ bð1  bi  cib;t Þ@yi;t þ b rj;t j j l

Each final goods sector maximizes the profits with respect to rj;ti , assuming R&D investments and backward linkages of other sectors are given. When the latter

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conjecture is consistent, the solutions constitute a Nash equilibrium in this game. The first-order conditions are .X @rj;ti rj;tl @v0 ji;t l ð1  bi  cib;t Þbgj;t cjb;t ¼ ; j ¼ 1; :::; n; ð5:20Þ @rj;ti @rj;ti which yield the value of vi;t in (5.15). As is clear from (5.20), in the Nash equilibrium solutions, the share of R&D investment by the ith sector depends on R&D shocks (εi ), the labor share (bi ) and the backward linkage (cb;i ). If the former is favorable and the latter two are small, its share increases, and hence aji ðtÞ becomes higher than for other intermediate sectors. The first-order conditions in (5.20) could be referred to as a forward linkage curve, since they jointly determine the Nash equilibrium magnitudes of forward linkages, given R&D shocks, labor shares, and backward linkages. Backward linkages could be assumed exogenous, depending on the technological properties of intermediate goods, rather than the direct result of optimal decision making, since the share of intermediate goods seems stable over time. For example, it is almost impossible to make the backward linkage of the automobile industry equivalent to the level of the software industry, even if it would be optimal for automobile firms from an economic point of view. Backward linkages could change to some extent, however, due to technological change in intermediate goods. Agriculture was labor intensive in the nineteenth century, but in some advanced countries this sector is more capital intensive nowadays, as a result of invention and improvements in agricultural machinery and chemicals. This is the result of technological change in the machine and chemical industries that took place outside the agricultural sector. Hence, the forward linkages could have some effect on the magnitude of backward linkages. In the following analysis, it is assumed that the backward linkage is to be determined by the total amount of R&D intensity undertaken by producers of intermediate inputs. This could be represented by ! X X cb;i ¼  ril ðtÞ; rli ðtÞ; m ; ð5:21Þ l

l6¼i

where 0  cb;i  1, and m is a capital share shock that increases the share of intermediate goods. Although this model assumes full depreciation in one period, intermediate goods can be regarded as capital when partial depreciation is allowed. Thus, we will refer to m as a capital share shock, instead of an intermediate share shock. This shock could be caused by a shock in core competences or core capabilities of a firm that has been extensively discussed in the management literature (see, for example, Barney, 1997). In this model, we simply assume that changes in core competences are a result of capital share shocks. If this positive shock takes place, reliance on core competences decreases, and hence the backward linkages increase, assuming that the labor share is

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108

constant. Thus, regarding the right-hand side of (5.21), we have the following assumption: . X . . X ril ðtÞ > 0; @ @ rli ðtÞ  0; @ @m > 0: Assumption 3. @ @ l

l6¼i

The first inequality implies that the larger the total sum of R&D intensity in the ith sector made by all intermediate sectors, the larger the backward linkage of the ith sector. As we have already discussed, this specification is quite intuitive. As for the second inequality, it is not so obvious whether the R&D investment by the ith sector itself affects this sector’s backward linkage. However, it is hard to imagine that the total amount of this sector’s R&D decreases the backward linkage. R&D investment in other sectors usually requires adjustments of the existing product, which sometimes induces the purchase of more intermediate goods. Therefore, it would be reasonable to assume that this effect is nonnegative, which implies that this curve becomes upward sloping. The last inequality implies a shock that decreases core competences and obviously shifts  downwards. This curve, , can be referred to as a backward linkage curve since it determines, given R&D intensities and capital share shocks, the magnitude of backward linkages. Since the second argument of this curve corresponds to forward linkages of the ith sector, the backward linkage curve is upward sloping. (5.20) and (5.21) jointly determine the equilibrium magnitudes of forward and backward linkages of the ith sector, as indicated in Figure 5.1.5 The dynamics of industry structure in this model can be described by changes in these equilibriums’ forward and backward linkages. It is worth noting that the competitive equilibrium in the first stage generates excessive R&D investment since a decrease in the current final goods by R&D investment and the resulting reduction in production in the next period are not taken into account by firms in the first stage. This is due to the Cobb–Douglas specification of the production function where the profits do not depend on the Forward linkage

Backward linkage curve

Forward linkage curve

Backward linkage

Figure 5.1 Determination of backward and forward linkages

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109

output level. As a result, firms in the first stage spend more on R&D investment than the socially optimal levels.

3 Dynamics of backward and forward linkages Let us now examine the dynamics of the sectoral structure in terms of backward and forward linkages, as affected by various types of shocks. 3.1 Productivity, demand, and R&D shocks Suppose that positive productivity and demand shocks take place in one sector. Under Assumption 2, these effects are irrelevant for other sectors in the economy. Proposition 1. Under assumption 2, sectoral productivity and demand shocks in the ith sector do not change backward and forward linkages in the economy. Proof: See Appendix. In reality, however, input–output coefficients change over time. How is this fact accounted for by our model? The result of Proposition 1 only suggests that productivity and demand shocks are irrelevant for changing input–output coefficients. Although productivity and demand shocks have been emphasized in the real business cycle and Keynesian models respectively, another shock exists that might have profound effects on aggregate business fluctuations. That is a R&D shock, ε. This R&D shock has not been examined in related literature. However, according to Rosenberg (1982), technological progress in the design and construction of scientific instruments has enormously expanded the observational capabilities of science and technology. For example, improvements in CAD/ CAM, simulation, and medical imaging technologies clearly contribute to the productivity of R&D. Of course, this type of technological progress can be regarded as productivity shocks in scientific instrument sectors. However, even in this case, learning by using arises when these scientific instruments are utilized in R&D activity. These learning effects also constitute R&D shocks. Suppose this positive R&D shock (meaning lower R&D costs) takes place in one sector. Obviously, this R&D shock affects the right-hand side of (5.20), shifting the forward linkage curve upwards, as is shown in Figure 5.2. Proposition 2. Under Assumption 3, positive (negative) sectoral R&D shocks of the ith sector increase (decrease) this sector’s forward and backward linkages. R&D shocks now generate changing sectoral linkages. According to Dupor (1999), if the magnitude of forward linkage is the same for each sector in the economy, the law of large numbers eliminates aggregate business fluctuation even if sectoral shocks take place in each sector. However, when backward

110 Dynamics of the black box Forward linkage

110 Backward linkage curve

Forward linkage curve

Backward linkage

Figure 5.2 Effects of R&D shocks

and forward linkages change over time, sectoral shocks could generate aggregate fluctuations. Moreover, the sector that receives these shocks attempts to increase internal procurement of intermediate products. That is, this sector tends to use more intermediate products from its own and other sectors. As a result of these R&D shocks, key sectors that play a critical role in economic development emerge. These key sectors exert strong forward and backward linkages in the economy so that economic development and structural change are facilitated. This mechanism is what Hirschman (1958) has emphasized in the process of economic development. The result of proposition 2 further maintains that these key sectors are the result of strong R&D shocks. 3.2 Capital share shock Next, consider the effects of capital share shocks. By definition, these shocks increase backward linkages. This implies that the production function becomes more dependent on intermediate products. Therefore, positive shocks shift the backward linkage curve downwards in Figure 5.3. In contrast, negative shocks make the production function more core competences-intensive, which is reflected in the backward linkage curve shifting upwards. Thus, positive shocks reflect capability-saving technological change, while negative shocks correspond to capability-using technological change. Proposition 3. A positive (negative) capital share shock increases (decreases) backward linkages and decreases (increases) forward linkages. 3.3 Labor share shock Similarly, if a labor share increases while the share of core competences remains constant, the backward linkages must decrease. This shifts the backward linkage

111

Changing productive relations Forward linkage

111

Backward linkage curve

Forward linkage curve

Backward linkage

Figure 5.3 Effects of capital share shocks and an increase of labor share

Forward linkage

Backward linkage curve

Forward linkage curve

Backward linkage

Figure 5.4 Effects of labor share shock

curve upward. In this case, since cib þ bi remains unchanged, the forward linkage curve does not shift (see (5.20)). As a result, backward linkages decrease and forward linkages increase, as is shown in Figure 5.4. Proposition 4. A positive (negative) labor share shock decreases (increases) backward linkages and increases (decreases) forward linkages. 3.4 Vertical specialization and general purpose technologies (GPTs) While R&D shocks generate a positive correlation between changes in backward and forward linkages, capital and labor share shocks suggest negatively correlated changes. GPT sectors would be characterized by such a negative correlation. Rosenberg (1976) argued that the GPT sector such as the US machine tool industry is extremely important for economic development because its GPT plays a

112 Dynamics of the black box

112

central role in the diffusion of technology and thus has a major influence on innovation in other sectors (Helpman, 1998).6 This implies in our model that these GPT sectors have strong forward linkages by the definition of GPT.7 Moreover, the emergence of GPT sectors sometimes involves vertical specialization, which in turn generates new sectors using the GPT. This is because the emergence of GPT is mainly a discovery of the generality of purpose of (improved versions of) existing technologies, which previously have been confined within a limited area. In this model, vertical specialization can be regarded as a split of one sector into at least two independent sectors. For example, according to Rosenberg (1976), the US machine tool suppliers sprang from textile firms in the 1840s. The newly established machine tool sector supplied its products to various user sectors such as the bicycle, sewing machine, arms, and automobile industries, as well as the textile industry itself. This implies that separating the machine tool sector from the textiles sector led to lower backward linkages in the first than in the latter sector, at least right after the 1840s. This is caused by the fact that the machine tool sector did not have to purchase the intermediate goods such as yarns necessary for the production of textiles. On the other hand, the backward linkages of the textile sector should have increased because machine tools had to be purchased rather than manufactured. Thus, GPT sectors can be characterized in our model as: (1) having high forward linkages (many user sectors) and (2) having low backward linkages (less dependence on other intermediate sectors in the production of GPT goods). In other words, vertical specialization and the emergence of GPT sectors imply that n increases and newly established sectors have high cf and low cb, while the backward linkages of other sectors increase. As a result of GPTs, the user sectors become more dependent on GPTs, and their own value added per unit of output declines as a result. This suggests that their backward linkages increase, at least temporarily. However, the net effects on their backward linkages are ambiguous since their forward linkage curves also shift (see Figure 5.5 and Appendix). Thus, we obtain the following result: Proposition 5. Vertical specialization generates (1) GPT sectors with low backward and high forward linkages and (2) user sectors with low forward linkages. Proof: See Appendix. Key sectors are now characterized as GPT sectors with low backward and high forward linkages, which differs from those in Proposition 2. Although user sectors still have significant effects, GPT sectors exert stronger influences on the economy. We can establish the following result: Proposition 6. Variance in sectors with the largest forward linkage has the most significant effects on aggregate business fluctuations. Proof: See Appendix.

113

Changing productive relations 113 Backward linkage curve

Forward linkage

Forward linkage curve

Backward linkage

Figure 5.5 Effects of vertical specialization

This result implies that the sectors with high forward linkages become not only leading sectors in economic development and growth but also bottlenecks in the event of negative shocks. It should be noted that this proposition only refers to sectoral variance (variance regarding sectoral shocks across relevant sectors), not directly to sectoral shocks. For example, a productivity shock in the ith sector might have the largest effect on the jth sector’s output. If the jth sector has the largest forward linkages, the impact of productivity shocks in the ith sector turns out to be the most significant. Proposition 6 does not refer to such effects of sectoral shocks. Instead, it mentions the effects of sectoral variance on aggregate business fluctuations. 3.5 Poverty trap According to Horvath (1998), the actual disaggregated input–output matrix is characterized by many zero elements, which in turn generates aggregate fluctuations from sectoral shocks.8 How is this fact accounted for by the model in this chapter? Note that (5.8) implies that a decision not to invest in R&D causes its share in the next period jumping down to zero. Such zero R&D investment occurs when the expected profits from R&D investment are nonpositive. This case could arise if fixed costs are required in order to undertake R&D activity. Thus, suppose the jth sector must pay a fixed cost of Fji when it invests in R&D in the ith technology. The expected profits from R&D can be written as 0 1 i X X X r j;t pi;tþ1 ¼ bð1  bi  cib;t Þ@yi;t þ b gj;t cjb;t P l A  vji;t ðrj;ti ; εi;t Þ  Fji : rj;t j j j l

ð5:22Þ

114 Dynamics of the black box

114

According to Rosenberg (1976), underdeveloped countries remain underdeveloped simply because there are no capital-goods sectors in the economy. This is because the growing productivity of industrial economies is the complex outcome of large numbers of interlocking, mutually reinforcing technologies: The early industrial revolution can only be understood in terms of the interactions of a few basic technologies that provided the essential foundation for other technological changes in a series of ever-widening concentric circles, at the heart of which were a few major innovations in steam power, metallurgy (primarily iron), and the large-scale utilization of mineral fuels. (Rosenberg, 1982, p. 59) Hence, forward linkages from GPT sectors play a critical role in industrialization.9 Suppose potential GPT sectors have already existed in the economy. Then, economic backwardness implies that the input–output matrix has zero columns in potential GPT sectors. In other words, the economy has not yet realized significant technological complementarities among sectors, although potential GPT sectors have already existed, and industrialization is enabled primarily by initiation of R&D investment in potential GPT sectors. In contrast to Proposition 1, demand shocks have macroeconomic effects in this case. Proposition 7. Industrialization is facilitated by (1) positive demand shocks to non-potential GPT sectors; (2) positive capital share shocks to nonpotential GPT sectors; (3) negative capital share shocks to potential GPT sectors; (4) negative labor share shock to potential GPT sectors; (5) positive labor share shocks to potential GPT sectors; (6) negative R&D shocks to non-potential GPT sectors; and (7) positive R&D shocks to potential GPT sectors. The underlying assumption behind this proposition is that industrialization is facilitated by inducing more R&D investment in GPT sectors and establishing their forward linkages, as the argument of Rosenberg (1982) has suggested. This result is reflected in (5.21) and (5.22). The various shocks improve the expected R&D profits of potential GPT sectors, while reducing those of non-potential GPT sectors. This enables potential GPT sectors to overcome the high fixed costs of R&D investment. It should also be noted that sectoral productivity shocks do not have any effects on industrialization in this case as well. This policy implication differs slightly from the Hirschman hypothesis stating that capital intensification facilitates economic development (Hirschman, 1958). To the contrary, Proposition 7 suggests that negative capital share shocks in potential GPT sectors are required, although capital intensification in other sectors is conducive to industrialization in our model. The result in Proposition 7 also differs from the big push theory of Murphy, Shleifer, and Vishny (1989), since policy implications go in an opposite direction between potential GPT and other sectors.10 This also holds true in the case of R&D subsidies.

115

Changing productive relations 115 Proposition 8. R&D subsidies on GPT sectors and R&D taxes on other sectors have favorable effects on industrialization.

Thus, the most efficient development policy is to provide subsidies for potential GPT sectors, while imposing taxes on other sectors. This sector-specific policy would also be an efficient measure in developed countries, since these sectors could turn into bottlenecks under negative shocks. In this case, subsidies for these GPT sectors could mitigate and, in some cases, help recovery from an economic slump associated with negative shocks. Moreover, if some policy measures are available to improve the R&D technology, implementing these policies just in the GPT sectors would be an efficient approach. These policy implications are slightly different from Hirschman (1958), since he put stronger emphasis on backward linkages in the development process. Another implication that can be derived from these results is that rapidly growing economies are more likely to pay the “tax of growth” later, when negative shocks take place in the key GPT sectors in the economy. Faster growth tends to be enabled by positive shocks in these sectors since this is one of the most efficient ways to take off from the poverty trap. However, more reliance on a few GPT sectors at the same time implies the risk of economic slump in the event of negative shocks in these sectors. Hence, faster growth accompanies the “tax of growth” in the future. This result seems consistent with the experience of some Asian countries after the World War II.

4 Concluding remarks In this chapter, we have examined the dynamics of backward and forward linkages in a general equilibrium framework. It was shown that demand and productivity shocks do not have any effects on productive relations and aggregate business fluctuations, while R&D and capital share shocks generate changes in productive relations. R&D shocks generate key sectors with high backward and forward linkages, while capital share shocks give rise to the trade-off between backward and forward linkages. Thus, vertical specialization, caused by the latter shocks, gives rise to GPT sectors with low backward and high forward linkages, which then become not only leading sectors in economic development and growth but also bottlenecks in the event of negative shocks. This emergence of GPT sectors is a double-edged sword in the process of economic development and growth. However, when the economy remains in the underdeveloped stage, demand shocks in general and R&D shocks specific to potential GPT sectors enable the economy to get out of the poverty trap. If these shocks are not present, sector-specific policies that provide subsidies in a sector with the largest forward linkage and impose taxes on other sectors are necessary. These policies are also an efficient way to get out of an economic slump after industrialization.

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116

Notes 1 Several theoretical studies examined the relationships between input–output structures (Rodríguez-Clare, 1996; Ciccone, 2002; Jones, 2011). However, they primarily focus on the multiplier effects with fixed or symmetric productive relations. 2 One of the few exceptions is Kamien and Schwartz (1968). 3 A similar specification is also adopted in Thompson and Waldo (1994). This functional form is used in this model since it is simple and intuitive. Without R&D, the corresponding intermediate good loses its sales in (5.8). Although this may seem strange, if R&D is interpreted to include marketing and sales expenses, the result would make sense. A more general specification is feasible and does not change the results in this chapter, as long as forward linkages depend positively on the relative share of R&D investment. 4 The solutions can be obtained by the so-called lucky guess method, in which the functional form of the value function is conjectured and verified using the first-order conditions. Chow (1997) solves the Long and Plosser model using the Lagrange method instead of dynamic programming. 5 To be precise, a forward linkage curve in this figure must be convex to the origin, due to the implicit function theorem applied to (5.20). 6 GPTs could be regarded as one component of the fundamental economic structure, as suggested by Jensen, West, and Hewings (1988), although the former focuses more on innovational complementarity and the resulting structural changes, and the latter on common denominators behind seemingly different economic structures. 7 This implies that GPT sectors have high levels of R&D investment. Hall and Trajtenberg (2004) found from patent citation data that most of the modern GPT sectors are related to information and communication technologies (ICT). According to Vickery and Wunsch-Vincent (2009), in most of the OECD countries, ICT sectors have higher than average shares of R&D expenditure in GDP. In particular, as a share of GDP, Denmark, Finland, Ireland, and Sweden have the greatest specialization in ICT services R&D. 8 Starting from the US input–output matrix with 523 sectors, Horvath (1998) aggregated these to matrices with 77, 36, 21, and 6 sectors. He found that these become increasingly sparse with disaggregation. While the matrix of dimension 6 has no zero elements, the detailed input-use matrix contains as many 224,410 zeros and only 49,119 nonzero elements. 9 However, the result of Horvath (1998) suggests that even the industries of one of the most developed countries (the US) are not so interlocking at the disaggregated levels. The point here is that even at the disaggregated level, forward linkages from GPT sectors would play a critical role in the process of industrialization. 10 In their model, it is shown that simultaneous industrialization of many sectors of the economy can be profitable even when no sector can break even by industrializing alone. The big push is defined as a simultaneous move from a bad to a good equilibrium.

117

Appendix

Proof of Proposition 1 Note that (5.20) does not directly depend on yj and ln lj;t . Since gi ðtÞ depends on yi , we need to check whether yi affects (5.20). By the law of large numbers, 1X 1X 1X plim yi cb;i ¼ plimyi cb;i ¼ c holds by assumption 2. Thus, n i n i n i b;i demand and productivity shocks do not affect R&D investment. Q.E.D.

Proof of proposition 5 Suppose vertical specialization takes place without any other shocks. With regard to a GPT sector, the backward linkage curve should shift upwards, since its backward linkages decrease as the result of vertical specialization. Because R&D shocks do not take place in this case, the forward linkage curve remains the same as before. Thus, the GPT sector has higher cf and lower cb. Regarding other sectors, the emergence of the GPT sector implies that their backward linkages should increase by definition of a GPT. Moreover, the R&D game now has one more competitor that shifts the forward linkage curve downward. As a result, these user sectors now have lower cf , but the net effects on cb are ambiguous. Q.E.D.

Proof of proposition 6 Consider the variance of the aggregate output at t þ 1 before stochastic shocks at time t have occurred. Assume no demand shocks take place. From (5.16), the aggregate output can be written as X 2 X yi;tþ1 ¼ cf ;j Varðyj;t Þ þ ns2 : Var i

j

Thus, the sector with the highest value of cf ;j has the largest effect on the aggregate variance at time t þ 1. Q.E.D.

6

Structural change and economic growth with relation-specific investment

1 Introduction All factors of production are heterogeneous. The heterogeneity that matters is not physical heterogeneity, but heterogeneity in use. The process of economic development and growth involves grouping and regrouping of various factors of production, and as an economy proceeds on the path of economic progress, increasing specialization and complexity in the use of the factors of production result. The process of increasing specialization and concomitant grouping and regrouping of factors of production needs to be modeled in order to elucidate their economic consequences. However, most of the related work on economic development and growth typically assumes the homogeneity of factors of production and production functions. As a result, although increasing specialization could emerge in these models, such as the product-variety model in the endogenous growth literature (see, for example, Grossman and Helpman, 1991), its effect appears only through symmetry, leading to no heterogeneity in use among sectors and firms in the economy. This chapter further develops the intersectoral model in the previous chapter by allowing for relation-specific investment among sectors in the economy, forming relation-specific groups. Relation-specific investment has been extensively studied by transaction cost economics (Williamson, 1985, 1996) and incomplete contract literature (Grossman and Hart, 1986; Hart and Moore, 1990). However, its economic implications have been examined only at the micro-level. How do increasing specialization and changing productive relations affect the formation of relation-specific groups? What are the economic consequences of these relation-specific groups? These research questions constitute the main motivation of this chapter. It is shown that in the steady state, the economy gets stuck in the “growth trap” where the economy still achieves positive growth but at the lowest level. The most efficient remedy for the growth trap is to facilitate relation-specific investment among sectors and to decrease the degree of specialization in the economy. Thus, the relation-specific investment is indeed instrumental in improving economic efficiency in the face of the growth trap. These remedies could be implemented by subsidies on relation-specific groups and permanent R&D taxes. Therefore, it is the mixture of subsidies on

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relation-specific groups and permanent R&D taxes that enable the economy to escape from the growth trap and improve both social welfare and economic growth. The rest of this chapter is organized as follows. Section 2 reviews related literature and describes the main motivation of this chapter. Section 3 develops the basic model of an intersectoral growth economy, and Section 4 examines the effect of relation-specific investment. Section 5 characterizes the evolution of industry structure, and Section 6 presents our conclusion.

2 Related literature Before looking at the model used in this chapter in any detail, let us first review the related literature on intersectoral economic growth, structural changes, and relation-specific groups. In this way, we can clearly describe the motivation of this chapter and its empirical background. First of all, this chapter is primarily concerned with intersectoral economic growth that accompanies changing structural relations. On the one hand, while some multi-sector endogenous growth models explore multiplier effects associated with intersectoral relations (Rodríguez-Clare, 1996; Ciccone, 2002; Jones, 2011), they do not account for changes in the intersectoral relations. On the other hand, input–output literature focuses more on the asymmetric nature of intersectoral relations represented by input–output tables. However, even if more general production technologies are adopted over the Leontief type (see, for example, ten Raa and Mohnen, 1994; Rose and Casler, 1996; Liew, 2000), they do not incorporate the dynamics of intersectoral relations at all. One exception to this neglect of changing productive relations is found in Harada (2015a), and in the previous chapter, where an intersectoral growth model is presented with structural changes induced by R&D. This chapter builds upon the previous chapter and extends the model to incorporate relationspecific groups within an industry structure. We believe this extension is critical to understanding the process of economic change because relation-specific groups, or “business groups”, are a prominent feature of the industrial organization of many emerging economies, including Brazil, Chile, Hong Kong, India, Indonesia, Malaysia, Pakistan, South Africa, South Korea, and Taiwan (Ghemawat and Khanna, 1998). Some empirical studies on business groups suggest that business group membership positively affects firm profitability and productivity (see, for example, Keister, 1998). Although such evidence does not directly show the positive effect of business groups on economic growth, given that many East Asian countries such as Japan, Korea, Hong Kong, Indonesia, Malaysia, and China can be characterized by the presence of business groups and high economic growth, at least historically, it can be inferred that business groups do have some positive effects on economic development and growth. Business groups can be defined in a variety of ways. For example, Granovetter (1995) defines business groups as “collections of firms bound together in some formal and/or informal ways, characterized by an ‘intermediate’ level of binding”, excluding, “on the one hand, a set of firms bound merely by short-term strategic

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alliances and, on the other, a set of firms legally consolidated into a single one” (p. 95). This definition clearly implies that business groups include many forms of inter-firm relations, ranging from formal arms-length legal contracts to relational contracts grounded in family, ethnicity, society, religion, and region. Among the various business groups, we are specifically interested in the Japanese keiretsu. The term keiretsu has been applied to a variety of Japanese interfirm ties. In general, keiretsu is defined as a cluster of independently managed firms maintaining close and stable economic ties, cemented by a governance mechanism such as a presidents’ club, partial cross-ownership, and interlocking directorates (Grabowiecki, 2006). Calder (1993) argues that keiretsu groups “have been a key element in Japan’s rapid industrial development and transformation since the 1950s” (p. 142). As an economic analysis of keiretsu, Qiu and Spencer (2002), inspired by the user–supplier relationship in the Japanese automobile industry, model keiretsu as an institution facilitating relation-specific investment and draw implications for various policies aimed at opening the Japanese market for intermediate goods such as auto parts. They show that a VIE (voluntary import expansion) reduces relation-specific investment, raising the keiretsu cost of production. This in turn leads to a reduction in Japanese auto output and hence to a reduction in the total Japanese demand for parts. Thus, although the US share of the Japanese parts’ market would rise due to the import of a greater range of parts, it is possible that the total value of US parts exported to Japan would fall. Ahmadjian and Oxley (2006) analyzed a more detailed institutional mechanism of keiretsu: the extensive use of partial equity stakes in suppliers by Japanese automobile assemblers. That is, auto assemblers hold partial equity stakes in their suppliers in situations where the suppliers are likely to be most vulnerable to assembler opportunism. They showed that on average, Japanese automobile assemblers hold shares in 20% of the suppliers in their sample, and onethird of the equity ties involve stakes of less than 5%. In addition, Dyer (2009) mentioned that Toyota owns roughly 28% of the shares of its top ten major supplier partners. With partial equity stakes, automobile assemblers outsource customized, relation-specific auto parts from several alternative suppliers at the same time. Using the hostage model of Williamson (1985); Ahmadjian and Oxley (2006) argued that the use of partial equity stakes can be understood as hostage-based governance mechanisms to make credible commitments. Other related studies pointed out that pervasive trust is the central feature of Japanese supply relationships (e.g., Dore, 1983; Sako, 1992; Dyer 2009), together with the role of reciprocity, repeated interaction, and reputation effects in sustaining cooperation (Smitka, 1991; Holmstrom and Roberts, 1998; Klein, 2000). A common thread linking these diverse views is that Japanese supply networks involve governance mechanisms that facilitate relation-specific investment and innovation from a more dynamic perspective, and these mechanisms

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could be understood in terms of general economic logic, rather than as countryspecific anomalies.1 However, they have been relatively disregarded in transaction cost economics. As Hodgson (1998) pointed out, standard transaction cost economics overlooks the dynamic aspects of learning, innovation, and technological development and primarily focuses on static, cost-minimizing efficiency. Of course, this focus on the latter is reasonable because the presence of relationspecific investment can create a hold-up problem and resulting inefficiency (Williamson, 1985, 1996; Grossman and Hart, 1986; Hart and Moore, 1990). In response to this inefficiency, a number of theoretical models (including the above studies on keiretsu) exist that analyze the optimal governance to mitigate the hold-up problem. What is required, then, is to integrate both static and dynamic perspectives in a consistent model. However, this chapter does not aim to develop the model of governance mechanism that facilitates relation-specific investment and innovation. Instead, building upon these related studies on keiretsu and other inter-firm relations, and assuming optimal governance is adopted by stakeholders in existing inter-firm relations, this chapter attempts to draw out the macroeconomic implications of relation-specific investment for economic growth. In other words, we are interested in examining the dynamic effects of relation-specific investment on innovation and structural change. In this respect, Adam Smith suggested that an increase in the size of the market allows for more specialized work to be undertaken in the operation of a pin factory, and this results in greater overall output of pins per unit of input. Stigler (1951) reformulated this dictum as the relationship between market size and vertical integration. Thus, in the early stages of economic development, firms would be vertically integrated because the level of production is too small to support specialized firms and fixed costs. However, as demand grows, firms vertically separate the stages that are subject to increasing returns, and as demand declines, the process reverses itself. It should be noted that vertical integration and separation in this hypothesis refer to the patterns of task partitioning or specialization, and do not necessarily imply an ownership structure. As Williamson (1975) suggested, even though blast furnace and rolling mill stage processes are integrated technologically and spatially, they could be owned by separate firms. The ownership structure is determined by the level of asset specificity or relation-specific investment. Thus, transaction cost economics and incomplete contract literature further elaborated Stigler’s hypothesis such that vertical integration and separation are determined by the level of asset specificity, which, in turn, is limited by the extent of the market. Stigler’s hypothesis might suggest that economic growth and resulting market size positively affect relation-specific investment. Hence, this hypothesis only reveals the causality that economic growth facilitates this investment, but not the other way around. The main contribution of this chapter is to examine this reverse causality under the general equilibrium framework of intersectoral endogenous growth.

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3 The model 3.1 Structure of the model In this section, an intersectoral general equilibrium model is developed. The model in this chapter relies on Harada (2015a, 2015c), chapter 5, and Long and Plosser (1983) because these models generate closed-form solutions for asymmetric intersectoral productive relations under dynamic settings, while most of the multi-sector endogenous growth models assume only symmetric productive relations among sectors. However, the model in this chapter departs from Long and Plosser (1983) in that endogenous changes in productivity shocks as well as productive relations among sectors are allowed. It also differs from chapter 5 because relation-specific groups are examined in this model. In each period, a two-stage game is assumed to be played by firms and a household. In the first stage, firms invest in R&D in order to attain the optimal mix of productive relations by changing the share parameters of the Cobb–Douglas production function. In the second stage, given new share parameters, firms engage in production that is realized in the next period with some productivity shocks, while the household consumes the current final goods. 3.2 Consumption and production Consider a discrete time economy inhabited by a representative agent, the intertemporal utility function of which is given by " # 1 n X X t ð6:1Þ U ¼ E0 b yi ln Ci;t ; t¼0

i¼1

where 0 < b < 1 and yi;t  0 for i ¼ 1; :::; n are assumed, and Ci;t refers to consumption of the commodity i at time t, respectively. There are n production sectors that have linear homogeneous technology as b

Yi;tþ1 ¼ li;tþ1 Li;ti;t

n Y

a

Mij;tij;t ; i ¼ 1; :::; n;

ð6:2Þ

j¼1

where Yi;tþ1 is the per capita total stock of commodity i available at time t þ 1 and li;tþ1 is a random variable, which is realized at time t þ 1. Li;t and Mij;t denote respectively the labor and the quantity of commodity j allocated to the n X aij;t < 1 and 1  production of commodity i at time t. It is assumed that bi;t þ bi;t 

n X

j¼1

aij;t represent a level of technological capability idiosyncratic to a firm.

j¼1

This capability is assumed to be fixed in this model because allowing for capability change makes the model intractable. In addition, capability building is not a major concern in this chapter.

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To simplify the analysis, this chapter takes a representative agent approach that is commonly adopted in macroeconomics so that the terms “firm” and “sector” are used interchangeably. It should therefore be noted that “intersector” also means “inter-firm” in this chapter. The commodity allocation is restricted by Yj;t ¼ Cj;t þ

n X

Mij;t þ vj;t ;

j ¼ 1; :::; n;

ð6:3Þ

i¼1

where vj denotes the total amount of R&D investment in the jth sector. The current output is spent on consumption and payments to intermediate goods and R&D investment. Suppose the labor receives the wage rate wt and the ith sector gains the profits of pi;t at time t. Then, from the distributional perspective, (6.3) can also be expressed as Yj;t ¼

n X

Mij;t þ wt Li;t þ pi;t ;

j ¼ 1; :::; n:

ð6:4Þ

i¼1

The labor market clearing condition requires n X

 Li;t ¼ L;

ð6:5Þ

i¼1

 is the total amount of labor in the economy. where L 3.3 Backward and forward linkages As we will see later, from this specification, backward and forward linkages can be respectively measured by cib;t ¼

X

aij;t ;

ð6:6Þ

aij;t :

ð6:7Þ

j

cjf ;t ¼

X i

That is, backward and forward linkages represent the column and row sums of the input–output coefficient matrix At  ½aij;t  (see Chenery and Watanabe, 1958).2 The backward linkages in (6.6) measure the total shares of intermediate goods in the production of commodity i, while the forward linkages in (6.7) indicate the relative share of commodity j in the production of all commodities. In this model, R&D investment is directly affected by these indices, as we will see later. This implies that endogenously changing productive relations also depend on the backward and forward linkages.

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3.4 R&D In this model, the share parameter of aij;t is allowed to change endogenously. In other words, the model in this chapter adopts the endogenous production function. Although this specification is not standard in mainstream macro models, productive relations among factors of production are not stable in reality. For example, the factor share of IT (information technology) had remained relatively small for decades, but has now become one of the most important factors of production in many countries. A series of IT innovations has made IT one of the major factors of production. Once IT was revealed to be potentially an efficient factor of production, many firms invested in IT, resulting in more IT-based production systems. Thus, factor shares depend on innovations as well as factor prices. Suppose the ith sector makes an R&D investment in one of its factors of production, j, by vji;t ðrj;ti Þ and K in the first stage of time t, where rj;ti  0 denotes R&D intensity and K is the fixed costs of R&D. Then, the share parameter of production function is assumed to be determined as oji rj;ti aji;t ¼ cjb;t X ; ojl rj;tl

ð6:8Þ

l

where 0  oji  1 denotes technological weight in the determination of aji;t . For example, if oji ¼ 0, commodity i is never used in the production of commodity j, regardless of its R&D effort by its intrinsic technological properties. In contrast, if oji ¼ 1, commodity j must use commodity i as input for its production as long X aji;t ¼ cjb;t always as the latter makes R&D investment (rj;ti > 0). Note that i

holds in this specification.3 Thus, aji;t is determined to reflect the share of the ith sector’s R&D intensity in the first stage of time t. For example, an automobile firm faces several alternatives for the material of some parts, including steel, aluminum, and plastics. The optimal choice depends more on the relative technical performance of each material, which in turn depends on R&D investment. R&D in this sense could also include improvements to intangibles that increase sales. For example, R&D investment might increase a reputation for high quality that contributes to an increase in sales. In this case, further R&D investment by the ith supplier provides sales advantages, leading to an increase in the share parameter aji;t. As R&D in this model is primarily concerned with sales increases rather than with cost reduction, no labor-saving biases are assumed to simplify the algebra. cjb;t appears on the RHS since the sum of the RHS for all l amounts to the magnitude of backward linkage of the jth sector. The cost of this R&D,vji;t ðrj;ti Þ, is assumed to be strictly convex, a condition that guarantees the existence of a unique optimal solution, and to be paid out of the current output, Yi;t . Thus, vi;t ¼ X ðvji;t þ KÞ holds in (6.3). j

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We assume the backward linkages are exogenously given, which greatly simplifies the algebra. Assumption 1: The backward linkages are assumed to be exogenous such that cib;t ¼ cib : Although this assumption could be relaxed, it only complicates the algebra without providing further insight. So, throughout this chapter, we will maintain this assumption. 3.5 Equilibrium We will solve the competitive equilibrium of the economy in this model. This equilibrium is characterized thusly: (1) intermediate suppliers invest in R&D in order to maximize the profits that are realized in the next period, which in turn determines share parameters of the Cobb–Douglas production function and forward and backward linkages; (2) given the share parameters and forward and backward linkages, firms maximize their profits under given prices; (3) the household maximizes a discounted sum of utilities subject to the budget constraint under a given sequence of prices and the distributed profits; and (4) each commodity market is clear in each period. The first stage corresponds to (1), while in the second stage, (2)~(4) take place simultaneously. Using backward induction, we will solve the equilibrium in the second stage, (2)~(4), first, and then the first stage R&D game is to be solved. 3.5.1 Second stage Consider the second stage optimization problem. At this stage, it is assumed that firms take share parameters, productivity shocks, and backward and forward linkages as exogenously given. Since this second stage does not include externalities and R&D, the second welfare theorem assures that a socially optimal solution coincides with competitive equilibrium.4 Thus, instead of solving competitive equilibrium, we can derive the equilibrium conditions by solving a pseudo-planning problem, as done by Benhabib and Nishimura (1998), in which the social planner maximizes a discounted sum of utilities subject to (6.2) and (6.3). In so doing, the planner is assumed to take as given the share parameters that are determined as a result of R&D investment in the first stage. Define the value function at time t by V ðSt Þ that amounts to the maximum value of a discounted sum of utilities. St  fYt ; lt ; vt g is the state variable 0 0 0 with Yt ¼ ðY1;t ; :::; Yn;t Þ , lt ¼ ðl1;t ; :::; ln;t Þ , and vt ¼ ðv1;t ; :::; vn;t Þ . Note that vt is determined in the first stage. Then, the planner maximizes V ðSt Þ ¼ max

X n i¼1

 yi ln Ci;t þ bE½V ðStþ1 ÞjSt  ;

ð6:9Þ

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subject to (6.2) and (6.3). Following Long and Plosser (1983), we can solve this dynamic programming problem as ! y i Ci;t ¼ ð6:10Þ Y i;t ; i ¼ 1; :::; n; gi;t  ij;t

M

¼

! bgi;t aij;t Y j;t ; gj;t

n X gj;t ¼ yj þ b gi;t aij;t ;

i; j ¼ 1; :::; n;

ð6:11Þ

j ¼ 1; :::; n;

ð6:12Þ

i¼1

Li;t ¼ gi;t bi

n X

!1 gj bj

 L;

i ¼ 1; :::; n;

ð6:13Þ

j¼1

pi;t ¼

@V ðSt Þ gi;t ¼ ; Y i;t @ Y i;t

ð6:14Þ

where Y i;t  Yi;t  vi:t ;

ð6:15Þ

and pi;t denotes utility-denominated price. Substituting (6.11) into (6.2) yields ytþ1 ¼ const: þ At yt þ ln ltþ1 ;

ð6:16Þ

0 where yt ¼ ð ln Y 1;t ; :::; ln Y n;t Þ . 0 The productivity shock, ln lt ¼ ð ln l1;t ; :::; ln ln;t Þ , is assumed to depend positively on R&D, which is to be shown later.

3.5.2 First stage Next, consider the first stage. From (6.2), (6.8), (6.12), and (6.14), the discounted profits arising from the R&D investment are given by 0 1 i X oji rj;t C X B pi;tþ1 ¼ bð1  bi  cib Þ@yi;t þ b gj;t cjb X ðvji;t ðrj;ti Þ þ KÞ: A l o r j j jl j;t l

ð6:17Þ Each final goods sector maximizes the profits with respect to rj;ti , assuming R&D investments and backward linkages of other sectors are given. When the latter conjecture is consistent, the solutions constitute Nash equilibrium in this

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game. First-order conditions are @o r

i ji j;t

ð1  bi  cib;t Þbgj;t cjb;t

X

ojl rj;tl ¼

l

@rj;ti

@v0 ji;t ; @rj;ti

j ¼ 1; :::; n;

ð6:18Þ

which gives the value of vi;t in (6.15). As is clear from (6.18), in the Nash equilibrium solutions, the share of R&D investment by the ith sector depends on the learning index, Aji;t , the labor share, bi , and the backward linkage, cb;i . If the former is favorable and the latter two are small, its share increases, and hence aji ðtÞ becomes higher than other intermediate sectors. The first-order conditions (6.18) could be referred to as a forward linkage curve, since they jointly determine the Nash equilibrium magnitudes of forward linkage, given R&D shocks, labor shares, and backward linkages. Since the magnitude of backward linkage is exogenously fixed, (6.18) determines the equilibrium magnitude of forward linkage of the ith sector, as indicated in Figure 6.1. It is clearly seen that the negative relation between backward and forward linkages exists. Thus, the sectors that purchase only a small amount of intermediate goods tend to dominate intermediate markets as suppliers in this model. DenoteX the total amount of R&D at time t by Rt. Then, the average productiv ity lt ¼ ln li;t =n is now specified as i

 ltþ1 ¼  lt þ zðRt Þ;

z0 ð Þ > 0:

ð6:19Þ

That is, the deterministic productivity in the economy is determined by the accumulated amount of aggregate R&D investment. If R&D investment is not undertaken, the deterministic growth rate drops to zero. In order to make explicit the dependence of Rt on the number of sectors making positive R&D, denote it by Rt ðnÞ. Obviously, n is equal to the number of sectors Forward linkage

Backward

Forward linkage curve

Backward linkage

Figure 6.1 Determination of forward linkages

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in the economy, since the incumbent sector must have at least one customer sector to which its own intermediate product is supplied. If there are no zero elements in the input–output matrix, ni ¼ n holds for all i. Then, it is easy to confirm that the LHS of (6.18) increases first as n increases, but eventually, it decreases. Lemma 1. Suppose there are no zero elements in A. There exists some ^n > 1 such that Rt ðnÞ decreases in n for n > ^n. Proof: See Appendix.

4 Entry and relation-specific investment In the previous section, no new entry and relation-specific investment are allowed in the model. In this section, we will allow for creation of new sector and relation-specific investment. 4.1 Entry In each period, there is one outside producer that can exploit an entry opportunity.5 When entry occurs, a new entrant obtains its ye and backward linkage by random  , respecdraws from the uniform distribution functions ye 2 ½y; y, cb;e 2 ½c b ; c b tively. In this model, entry implies creation of a new sector that may hurt expected profits of incumbent intermediate sectors. In some cases, incumbent sectors are replaced by a new entrant, and if they cannot find any user sectors that generate non-negative expected profits of R&D, they completely disappear. However, we assume that this replacement takes place if and only if a new entrant earns positive profits while some of the incumbent sectors cannot gain non-negative profits after entry. Assumption 2. A new entrant cannot enter the market if its expected profits are negative after entry, assuming that all incumbent sectors remain in the market. So, for example, suppose a new entrant and one incumbent sector cannot earn positive profits after entry, and if one of them drops out of the market, the remaining sector could earn positive profits. In this case, it is assumed that a new entrant cannot enter the market. Thus, for new entry to be justified, the non-negative profit condition is required as petþ1 ðnÞ  0:

ð6:20Þ

and the equilibrium number of sectors must satisfy nÞ  0 > petþ1 ðn þ 1Þ: petþ1 ð

ð6:21Þ

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This implies that the lowest backward linkage entrant (c b ) with y cannot earn non-negative profits at n þ 1 and can earn non-negative profits at n. If (6.21) is not satisfied, new entry may or may not take place depending on a random draw of backward linkages. However, once this condition is satisfied, no further entries take place since the lowest backward linkage entrant with y could earn the largest profits among potential entrants. If its expected profits are negative, all other potential entrants can never obtain positive profits. Lemma 2. ^ n  n: Proof: See Appendix. This lemma holds regardless of the presence of zero elements in the input–output matrix. Note that the value of n is not unique since it depends on history due to assumption 2 and the random draws. Suppose some sectors emerge that terminate R&D investment to at least one of the sectors in the economy. Denote the number of sectors in the economy at this moment by ~ n. Then, we obtain the following result: Lemma 3. ~ n  n: Proof: See Appendix. This lemma ensures that zero elements in the input–output appear before the creation of new sectors ceases. Thus, the equilibrium level of specialization does not necessarily maximize social welfare, since zero elements in the input–output table appear in equilibrium. Indeed, the next proposition confirms this conjecture. Proposition 1. If b is large enough, there exists the optimal level of specialization n  1 such that n < n. Proof: See Appendix. Therefore, in equilibrium, excessive specialization always emerges.

4.2 Relation-specific investment The preceding discussion assumes that no rigidity exists among intersectoral relations in the economy. In other words, intersectoral relations are elastic to changes in shocks and the degree of specialization, and grouping and regrouping among the related sectors could take place as a result. However, in reality, some of the intersectoral relations involve more rigid, long-term contracts rather than a series of spot contracts, as is observed in the multi-tiered structure of parts suppliers in the Japanese automobile industry.

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Toyota, for instance, divides purchased components into three groups according to the degree of asset specificity: (1) general purchasing; (2) special purchasing; and (3) specialty factory purchasing (Nishiguchi, 1994). Components of general purchasing can be made by and brought in from any supplier. Components of special purchasing and specialty factory purchasing, however, require a certain degree of relation-specific facility and training. Thus, Toyota has established close financial or capital ties with those subcontractors. Toyota has also organized those special purchasing and specialty factory purchasing suppliers into hierarchies. The suppliers on the first tier deal directly with Toyota and the second-tier suppliers, who in turn deal with the third-tier suppliers. All of the suppliers in the first tier form an association called Kyohokai, and Toyota obtains competitive bids from selected members in this association. Once a supplier is selected for the production of a specific part, the supplier makes a corresponding relation-specific investment and supplies the part for the entire model period. To become a member of Kyohokai, a supplier must have an annual transaction value with Toyota of more than 1 billion yen, and its quality and cost performance must meet and surpass the specific criteria set by Toyota. With approval from Toyota, a candidate supplier can join Kyohokai. Following this example of relational contracts and supplier association, we allow for these relational contracts in the model by assuming that each sector could make relation-specific investments to improve its quality by building up long-term relationships. Although the presence of relation-specific investments creates a hold-up problem and resulting underinvestment (Grossman and Hart, 1986; Hart and Moore, 1990), reputation effects and the formation of supplier association can safeguard against the ex post expropriation of quasi rents (Baker, Gibbons, and Murphy, 2002). Moreover, as Ahmadjian and Oxley (2006) explained, the extensive use of partial equity stakes by Toyota in major suppliers of Kyohokai can be understood as hostage-based governance mechanisms to ensure credible commitments. As this chapter is not directly concerned with exploring the specific governance structures that reduce transaction costs, we simply assume that the formation of relation-specific group mitigates the hold-up problem. Instead, we examine the macroeconomic implications of relation-specific investment that accompany appropriate governance.6 Suppose that the jth sector, as a purchaser of intermediate products, decides to allow for intermediate suppliers to make relation-specific investment, Fj, which is a sunk cost that cannot be recovered after the investment. Once this investment is undertaken, other suppliers cannot join an R&D race (competitive bidding) in the jth sector. Intermediate goods are supplied only by those who make relation-specific investment. The gains for intermediate suppliers lie in the exclusion of rivals without relation-specific investment, which improves the probability of increasing their supplies to the jth sector. Since the relation-specific investment is made, it is reasonable to assume the following:

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Assumption 3. Once relation-specific investment is made, the intermediate producer cannot supply its intermediate products to other sectors in the economy. That is, member sectors lock-in to the relation-specific groups so that their own technologies now become relation-specific as well. In reality, it is true that some firm could make relation-specific investment to several users at the same time. Yet, in this case, it could be regarded as if several distinct intermediate sectors exist within the firm. Note that in this relation-specific investment, the jth sector sacrifices its productivity since the number of intermediate products decreases in producing its own output. However, according to (6.14), a decrease in output is compensated for by an increase in price under the Cobb–Douglas specification. As a result, its profits remain unaffected. In order to ensure the jth sector’s incentive to allow for relation-specific investment, it is assumed that this payment goes to the jth sector. Thus, relation-specific investment implies membership fees in this model.7 Denote the group of relation-specific suppliers in the jth sector by Sj. To keep the model as simple as possible, the number of relation-specific suppliers, m, is assumed to be exogenously given.8 That is, when a relation-specific group is formed, the number of suppliers in the group should be equal to m. Suppose this group is formed at time t in the jth sector and one of the members is the ith sector. From Assumption 3, the expected R&D profits for the ith supplier in each period become 0

~i;tþ1 p

1 i o r ji j;t C B  bð1  bi  cib Þ@yi;t þ bgj;t cjb X A  vji;t ðrj;ti Þ  K: ojl rj;tl

ð6:22Þ

l

For the relation-specific investment to become feasible, it is necessary that ~ i;tþ1  Vi;tþ1  Fj V

ð6:23Þ

~ i;tþ1 and Vi;tþ1 denote the expected discount values of holds for all j 2 Si , where V staying in the group and not joining the group forever, respectively. If the economy reaches the steady state and no more changes are expected at time t, (6.23) can be written as ~i;tþ1  pi;tþ1  ð1  bÞFj : p

ð6:24Þ

Note that these conditions imply that the formation of the relation-specific group requires the consent of all members. Of course, we can relax these conditions and, instead, assume the user sector only provides a take-it-or-leave-it offer to potential members; as long as at least one member accepts, the relation-specific

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group is established. In either specification, the results of the following analysis remain almost the same. The user sector always has the incentive to form a relation-specific group, and suppliers agree to join the group as long as (6.23) is satisfied. Indeed, this condition is satisfied for large n if Fj and forward linkages are not sufficiently large. This is easily confirmed. Since (6.17) decreases in n while (6.22) remains the same as long as n > m, under free entry, the latter profits eventually surpass the former profits. Note that for large values of Fj , some sectors exist that cannot form relationspecific groups and their R&D races are open to all sectors in the economy. To make the model non-trivial, it is assumed that there exist several sectors that do not form relation-specific groups.

5 Evolution of industry structure In this section, we will examine the evolution of industry structure in the economy. In particular, we are interested in endogenous relations among the degree of specialization, the formation of relation-specific groups, and aggregate growth and cycles. 5.1 Dynamic relations According to Proposition 1, although a trade-off exists between social welfare and economic growth in this model, the equilibrium level of specialization is excessive so that social welfare is not at the optimal level. However, once relation-specific investment is allowed, then, how does an increase in the equilibrium level of specialization affect the formation of relation-specific groups? The next result shows that its effect is positive. Proposition 2. There exists some _ n > 1 at which relation-specific groups begin to emerge, and an increase in the equilibrium level of specialization facilitates relation-specific investment. Proof: See Appendix. According to this result, increasing specialization facilitates the formation of relation-specific groups. This is due to the fact that increasing specialization exerts negative effects on the expected R&D profits of incumbent sectors. This reduction in the profits induces them to join relation-specific groups. This formation of relation-specific groups in turn has positive effects on increasing specialization. Proposition 3. The emergence of relation-specific groups increases the number of sectors in the economy (n), social welfare, and the growth rate in the steady state. Proof: See Appendix.

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Thus, relation-specific groups have a positive effect on social welfare and economic growth in the steady state. In this case, the trade-off between social welfare and economic growth is mitigated. Therefore, relation-specific investment is instrumental in improving economic efficiency even in terms of macroeconomic consequences. 5.2 Policy implications From the perspective of development policy, the formation of relation-specific groups is also conducive to escaping from the poverty trap. For example, the rapid growth that has occurred in Asian countries such as Korea, Singapore, Malaysia, and Indonesia has the common feature that the rapid development of a few business groups supported by the government has played a critical role. The result in this chapter confirms the positive role of relation-specific groups in facilitating economic growth. Once the number of sectors increases up to n, the growth rate stabilizes and no further progress in specialization takes place. This state could be referred to as the “growth trap” in contrast to “poverty trap”, since the economy has already experienced industrialization. To escape from this growth trap, what kinds of policies are required? The available policy in this model is to enhance y by some fiscal or monetary policies, although they are not explicitly formalized here. The next proposition shows that any temporary policies affecting y may serve to deteriorate social welfare in the long run. Proposition 4. Any temporary policies are likely to have positive effects on economic growth, but their effects on social welfare are ambiguous. Proof: See Appendix. While temporary policies are effective in facilitating economic growth, this does not necessarily imply social welfare also increases. Hence, if some policy intervention is implemented, it must be a permanent measure rather than a temporary one. Proposition 5. (a) Subsidies on F increase the equilibrium number of sectors, social welfare and the growth rate. (b) Permanent taxes on K decrease the equilibrium number of sectors in the economy, but increase social welfare and the growth rate. (c) Subsidies on F and permanent taxes on K increase both social welfare and the growth rate. Note that subsidies and taxes on F could be temporary because membership fees are to be paid only once. According to this result, both subsidies for F and taxes

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on K increase economic growth and social welfare when the economy gets stuck in the growth trap. Although we cannot determine which policy generates higher social welfare, the mixture of these two policies achieves the highest social welfare. This is because this mixture enables the number of non-relation-specific sectors to approach n , while the number of relation-specific sectors increases. This result stands in a sharp contrast to the existing literature on endogenous economic growth that emphasizes permanent R&D subsidies in facilitating economic growth and social welfare.

6 Concluding remarks In this chapter, we have examined the evolution of industry structure from the perspective of the degree of sectoral specialization, relation-specific groups, social welfare, and economic growth. It is shown that in the steady state, the economy gets stuck in the “growth trap” where the economy still achieves positive growth but at the lowest level. Any temporary policies could have path-dependent adverse effects in the long run. Thus, the only remedies for the growth trap are to facilitate relation-specific investment among sectors or to decrease the degree of specialization in the economy. Thus, the relation-specific investment with appropriate governance is indeed instrumental in improving economic efficiency in the face of the growth trap. These remedies could be implemented by subsidies on relation-specific groups and permanent R&D taxes. Therefore, it is the mixture of subsidies on relationspecific groups and permanent R&D taxes that enable the economy to escape from the growth trap and improve both social welfare and economic growth.

Notes 1 The mechanisms analyzed in the related literature that facilitate relation-specific investment and innovation are not necessarily comprehensive. Inter-firm relations in the Italian industrial districts, for example, seem to reflect a different governance mechanism from the keiretsu relation. 2 The concepts of backward and forward linkages were first proposed by Hirschman (1958). 3 This model therefore does not assume that relation-specific investment must potentially take place across any pairs of sectors. This case can be ruled out by setting oji ¼ 0. However, note that in some sectors, extensive use of diverse intermediate goods is observed. The products of these sectors are referred to as CoPS (complex product systems) in the related literature (see, for example, Miller et al., 1995 and Hobday, 1998). 4 Note that R&D and production decisions are split in this model. The second welfare theorem applies to the production stage alone. 5 This assumption can be relaxed to include many entrants. However, it does not add a new insight to the results of this chapter while complicating algebra. 6 Note that our analysis does not critically depend on the specific governance mechanism of Toyota. As long as relation-specific investment is facilitated under some inter-firm groups, the results hold.

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7 It is more intuitive to charge additional membership fees f in addition to relationspecific investment F. But this does not change the model at all. To avoid unnecessary notations, it is simply assumed that the membership fees amount to relation-specific investment here. 8 A standard model of transaction cost economics focuses on bilateral relations between user and supplier, which implies that m ¼ 1 is assumed. It is not difficult to extend the model to allow for endogenous m, but this only complicates the model without adding new insight. So, we simply assume m is fixed.

Appendix

Proof of Lemma 1 The total amount of R&D investment in the ith sector, Rit ðnÞ, is determined by (6.18). Differentiating the LHS with respect to n reveals that there exists some ~ ni > 1 such that it increasesX and decreases for n  ^ni and for n > ^ni, respectively. Rit ðnÞ decreases in n only if n  ^n. Q.E.D. Define ^ n  max ^ni : Then, i

i

Proof of lemma 2 As is clear from (6.21), in equilibrium, no R&D fields exist that provide nonnegative expected profits even to the most efficient (lowest backward linkage) entrant. This implies each sector has already reached the stage of decreasing returns to specialization. Otherwise, new entry takes place. This proves the result of lemma 2. Q.E.D.

Proof of lemma 3 Suppose not. Then, new entrants could undertake R&D with respect to at least one of the sectors in the economy, which is a contradiction. Q.E.D.

Proof of Proposition 1 Denote the average growth rate in each sector in the steady states by g. Suppose the economy is in the steady states at time t. Then, from (6.1) and (6.10), the utility is decomposed as U¼

1 X t¼0

 bt ðC

n X

yi þ gtÞ;

ðA1Þ

i¼1

 represents the constant part of the consumption. Differentiating with where C respect to n yields 1 @Ut X  y þ g0 tÞ:  bt ðC @n t¼0

ðA2Þ

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From Lemma 1, g0 < 0 if n  ^n, and there exists some _ n  ^n such that g0 > 0 if _ =@n < 0 for n > ^n and n  n. Hence, as long as b is large enough, @Ut _ @Ut =@n > 0 for n < n. Since Ut is continuous, it follows that there exists n that maximizes social welfare. Q.E.D. some _ n  n  ~

Proof of proposition 2 According to the proof of Lemma 1, for n  ^ni, an increase in n raises pji;tþ1 . Thus, no incentive exists for intermediate suppliers to make relation-specific investment. Only after n goes beyond ^ni , some sector might find it profitable to make relationspecific investment in the ith sector, since now pji;tþ1 decreases in n. Therefore, n  min^ni > 1 at which relationthere exists some _ n where ^n ¼ max^ni  _ specific investment appears. Obviously, since n  ^n by lemma 2, an increase in n facilitates relation-specific investment. Q.E.D.

Proof of proposition 3 Regarding the growth rate, members in relation-specific groups achieve positive expected profits of R&D even under the steady state by excluding rivals. Therefore, the steady-state growth rate in this economy should be higher. Next, denote the set of sectors forming relation-specific groups by I. Then, the total number of intermediate producers that lock-in to specific user sectors is mI. The number of remaining non-specific sectors is n  mI. Since mI does not significantly affect the expected profits of R&D for each of non-specific sectors, in the steady state, the number of these sectors is almost the same as that without relation-specific groups. Denote the steady-state number of sectors in the latter by  n. Then, the steady-state number of sectors in the economy with relationspecific investment is given by mI þ n. Since the growth rate is higher with relation-specific investment, more sectors imply higher social welfare. Q.E.D.

Proof of proposition 4 Suppose the number of non-relation-specific sectors and the total number of nbp , respectively. Denote the total sectors before temporary policies are nbp nr and  ap number of sectors after policies as n . Obviously, any increase in y improves the expected R&D profits, which raises n and the number of relation-specific groups by proposition 2. Thus, we have nap > nbp . Once y returns to the original level after the temporary policy ceases to take effect,  nap also declines. Some of the newly formed groups now face the violation of (6.23), but they do not dissolve the groups since the membership fees have already been paid. Only some of the non-relation-specific sectors disappear due to deterioration of R&D profits. Note that the relation-specific groups do not affect the expected R&D profits of non-relation-specific sectors. Thus, when temporary policies cease to have any effect, the number of non-relationspecific sectors return to the original level of nbp nr , while the number of relation-specific sectors remains the same.

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Although the expected values of R&D have deteriorated by the time temporary policies come to an end, the FOC of R&D investment for relation-specific groups is the same as that before the introduction of temporary policies (see (6.22)). Regarding non-relation-specific sectors, their FOCs also remain the same. Thus, the total amount of R&D becomes higher than the level before temporary policies due to an increase in the number of relation-specific sectors. Hence, the growth rate should increase as a result. The effects on social welfare are ambiguous. For one thing, temporary policies enhance economic growth, which has a favorable effect on social welfare. However, temporary policies hurt the total expected profits of relation-specific groups, which implies that the total income of a representative household declines. Thus, the net effects remain ambiguous. Q.E.D.

139

Part III

Inside the black box Innovation mechanism

141

7

Focusing device as innovation mechanism and cluster growth

1 Introduction Part III explores inside the black box by modeling the innovation mechanism as a “focusing device”. The role of a “focusing device” in the process of technological change is frequently observed in reality, but it has not yet been incorporated into a formal model of economic growth. According to Rosenberg (1976), technological change is induced by certain constraints imposed by the existing technology or social events such as wars and strikes. In this process, the ordinary messages of the marketplace (i.e., increasing profits, reducing costs, etc.) are general and not sufficiently specific. Instead, technological imbalances provide clear signals that call attention decisively to the existence of certain problems, guiding technological change in specific directions. Such an inducement mechanism is called a “focusing device” that forcefully focuses attention in specific directions and plays a significant role in the process of technological change. Following Rosenberg, several distinct concepts have been proposed that describe the innovation process. These concepts include reverse salient (Hughes 1983) and development blocks (Dahmén 1989). However, they all share the view that technological change proceeds by removing bottlenecks in a technological system. However, the standard neoclassical and endogenous growth literature does not fully incorporate the role of focusing devices into formal models. As a result, technological change in such models proceeds in response only to the signals of the marketplace without any biases. Although the importance of demandside forces in determining the direction of technological change should not be ignored, supply-side factors must also be taken into account to properly explain the direction of technological change. This chapter is a first attempt to formalize the idea of the focusing device in the process of technological change and examine how the focusing device affects patterns of economic growth. In particular, we are interested in economic “clusters” where different kinds of technology components constitute a production system. According to Porter (1998, p. 78), industrial clusters are defined as a “geographic concentration of interconnected companies and institutions in a particular field”. Porter suggests that a firm’s competitive advantage will not be determined chiefly by greater efficiencies in the sourcing of inputs, but rather

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by the ability of firms to exploit the resources available in the “cluster” or network of local individuals and companies in which they operate. Although the concept of clusters is very fascinating, no formal analysis of clusters has been proposed. As a result, the specific mechanism of cluster growth and how it affects competitive advantage remain elusive. This chapter adopts the o-ring production function (Kremer, 1993) and regards a final good firm as a cluster in which interconnected technology components are concentrated. In other words, a cluster is specified in this chapter as an o-ring production function that is assumed to appear at the cluster level and functions as if it maximizes the total profits of the cluster. Note that this definition of a cluster is slightly different from Porter’s in that technology components are not necessarily geographically concentrated, but technologically concentrated. Moreover, we are interested in innovation of a cluster as a whole, while Porter emphasizes a firm’s competitive advantage through exploiting resources available from a cluster. The technological interconnectedness in a cluster becomes a focusing device that induces each technology component to upgrade its quality level, which contributes to the overall growth of the cluster. Thus, this chapter accounts for the pattern of cluster growth in terms of a focusing device in which technical imbalance plays a critical role. In this model, it is shown that high quality technology components are provided with a strong incentive to undertake R&D so that technological divergence emerges among and within clusters. In contrast to the mechanism of a focusing device that primarily necessitates the improvement of bottleneck technologies, the model in this chapter suggests that the direction of technological change is the reverse. That is, advanced (core) technologies are more likely to be improved than bottleneck technologies.1 Therefore, bottleneck technologies are least rewarded when they upgrade their quality. If we allow for changes in the magnitude of the advantages of backwardness and the degree of free mobility of technology components, the matching patterns of clusters could be either self-matching or cross-matching. Self-matching refers to the matching of technology components of the same quality level, while crossmatching refers to that of technology components of different quality levels. However, in all cases, higher quality components have the strongest incentive to undertake R&D. As a result, cluster growth tends to be driven by advanced technology rather than by bottleneck technology. When low-powered incentives for innovation are adopted within organizations or clusters, factor prices lead to erroneous information regarding the potential benefits of technology component innovation. Hence, some policy intervention is required to correct this biased information. The rest of this chapter is organized as follows. Section 2 reviews related literature on the topics of the direction of technological change. Section 3 presents a basic model of a focusing device, and Section 4 examines the effects of the advantages of backwardness, free mobility of technology components, and different feedback mechanisms on cluster growth and derives policy implications. Finally, Section 5 presents our conclusions.

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2 Related literature In this section, related literature on the direction of technological change is reviewed. Like other economic activities, inventive activity is responsive to market forces. The prospects for innovation rents can be resolved into demand forces and supply forces that determine the expected payoff for a successful inventive effort. In examining the railroad industry, Schmookler (1966) found a close correspondence between increases in the purchase of railroad equipment and components and slightly lagged increases in patenting activity. Schmookler found similar relationships in building and petroleum refining. Furthermore, for a large number of industries in the years before and after World War II, he found a very high correlation between capital-goods inventions in a given industry and the volume of sales of capital goods to that industry. Therefore, he concluded that, in both the short and long run, demand considerations represent the decisive determinant of the allocation of inventive effort. The findings of Griliches (1957) were also similar. He found that the entry of hybrid corn seed producers into different portions of the national market was closely related to expected demand, as measured by each region’s market density. Another direction of the research that attempts to substantiate the demand-pull forces in the direction of technological change is found in induced innovation literature, which was first suggested by Hicks (1932) and subsequently developed by Fellner (1961), Kennedy (1964), and Samuelson (1965), among others. In this literature, innovation is induced by a change in factor prices. A rise in a factor price induces inventive activity to save the corresponding factor, leading to factor-saving technological change. Thus, the change in factor prices induces not only factor substitution, but also a shift in the production function. Without exceptions, the corresponding formal model was developed in a reduced form, assuming the existence of an artificial construct, the “innovation possibility frontier” (IPF). In this model, the resources are to be optimally allocated among the alternative innovation possibilities depicted by the IPF. Nordhaus (1973) criticized the entire literature on induced innovation, since it lacked microfoundations. Does the innovation possibility frontier exist in reality? What is the theoretical justification for the shape and position of the IPF? These questions have still to be answered by the proponents of the induced innovation model. Recent work on the direction of technological change has focused on skillbiased innovation, rather than the demand-pull vs. technology push theories. This is because the rise in the skill premium has coincided with the rapid implementation of information technologies (IT) in the work place. A number of microeconometric analyses and case studies reveal a statistical correlation between IT and the employment share of skilled workers (Bartel and Lichtenberg, 1987) or wage share (Autor, Katz, and Krueger, 1998) across industries. The theoretical justification for these skill-biased innovations is attributed to technology-skill complementarity (Acemoglu, 2002; Aghion, 2002; Hornstein, Krusell, and Violante, 2005). By incorporating this complementarity, the skill-biased innovation

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is accounted for. It should be noted, however, that once complementarity is introduced into a model, the direction of technological change is exogenously determined. Thus, what is determined by these models is not the direction of technological change per se but the speed of innovation along a given direction. In this respect, although the endogenous growth literature has not addressed the direction of technological change as well, they still provide useful benchmark models that incorporate endogenous innovation into the general equilibrium framework (see, for example, Grossman and Helpman, 1991; Aghion and Howitt, 1998a). Using the product-variety model of the new growth literature, Acemoglu (1998, 2002) made an important contribution to advance the ideas of induced innovation towards a general equilibrium model. This model allowed for both capital- and labor-augmenting technological change and showed that, in the long run, labor-augmenting technological change dominates, such that the capital share and interest rate remain stable, while the wage rate increases steadily due to labor-augmenting technological change and capital deepening. The important assumptions that lead to this result are the constancy of labor and the accumulation of capital. Since, in the steady state, the factor shares must be kept constant, this implies that wage rate and labor productivity increase over time. Otherwise, the constancy of factor shares cannot be maintained, due to the accumulated capital. Therefore, this model succeeded in providing microfoundations for the theory of induced innovation. However, supply-side constraints are not incorporated into this model so that technological change proceeds in response to market forces alone. But this type of market-pull hypothesis was criticized by Rosenberg (1976), since economic incentives to reduce costs or increase sales always exist in business operations, and precisely because such incentives are so diffuse and general, they do not explain the particular sequence and timing of inventive activity. He cited several examples of historical evidence showing that supply-side constraints primarily generated by technological imbalance among complementary technologies provide a much clearer guide to the direction of technological change. Nevertheless, this does not necessarily imply that the market-pull hypothesis should be completely abandoned. On the contrary, Mowery and Rosenberg (1979) suggested that both demand- and supply-side influences are crucial to understanding the innovation process, and criticized the exclusive preoccupation with only one set of these forces. Since then, while some integrated models have been proposed, such as the “chain-linked model” (Kline and Rosenberg, 1986), that somehow incorporate both supply and demand forces, no formal models have been developed. Hence, how these two forces interact in guiding and shaping the direction of technological change remains an open question. The model in this chapter explores this question and formally shows that market-pull forces do play a critical role in determining the direction of technological change. We provide a theoretical framework that accounts for the endogenous direction of technological change by directly examining the technological interrelations among different technology components and translating implicit technological signals into competitive factor prices. The main determinant of

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competitive prices is marginal productivity of innovation, which in turn reflects technological interdependence among technology components. Thus, our model builds a theoretical bridge between economic factors (demand-pull) and technological constraints (technology-push) so that the mechanism of innovation can be understood from an economic perspective.

3 The model In this section, a model of focusing device is developed. The cluster produces output according to an o-ring type production function. As described above, the o-ring production function is assumed to emerge at the cluster level as if it maximizes total profits.2 Kremer (1993) proposes an o-ring production function that incorporates the fact that mistakes in any of a series of tasks can dramatically reduce the product’s value. In this chapter, we suppose that the production function represents a technological system that consists of a series of interrelated technology components (alternatively put, component technologies). Thus, the series of tasks are regarded as a series of technology components in our model, and these components are provided by specialized suppliers. Innovation in this model refers to the quality improvement of these components, and the inducement mechanism of these quality improvements represents a focusing device. Competitive equilibrium is defined as an assignment of technology components to clusters, a set of factor price schedules for technology components, pðqÞ, and wage such that clusters maximize profits and the markets clear for labor. In addition, we will consider the endogenous quality improvements of each technology component. 3.1 Cluster Consider a discrete time closed economy with n commodities, which are produced by clusters. There is an indefinite supply of potential clusters, all of which have the production function yj ¼ Aljα

m Y

qi;j ;

ð7:1Þ

i¼1

where the subscript j refers to the jth cluster, A and lj denote the productivity level and labor employed in this cluster, qi;j is the quality level of technology component i, and 0 < α < 1. As is clear from this specification, one unit of each technology component is provided by a specialized supplier. This is because each technology component represents a technology field rather than specific parts and materials, the quality of which accounts for the total output in this production function. For example, NC machine tools consist of several mechanical and electrical components, such as an NC device, bearing, spindle, motor, cast iron, transfer arm, and worktable. But these parts could be

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reclassified in terms of technology components, such as motion control, electromechanical design, high precision machining, measuring, feeding, materials, and IT technologies. The o-ring production function in this model represents the latter case. It is assumed that a “library” exists in the economy that holds an infinite number of “books” in the form of technological knowledge, which is referred to as technology components.3 Although the number of technology components is finite, since the quality improvement of each component continues endlessly in this model, the library should have an infinite number of books. A supplier of technology components borrows this book on behalf of its cluster. Other suppliers can also borrow the same book at the same time due to the reproducibility of knowledge. The borrowed books are read and understood by suppliers so that acquired knowledge continues to be used after returning the books. However, a supplier cannot borrow all the books in the library. To borrow a book of a certain quality level, the supplier must have attained the equivalent quality level by R&D investment. When the R&D succeeds, the supplier is qualified to borrow the target book. Otherwise, the supplier cannot read and understand the book. The supplier of technology component i in the jth cluster with the quality level of qi;j receives a payment of pðqi;j Þ from the cluster, pays the borrowing costs of ð1  xÞpðqi;j Þ, and makes xpðqi;j Þ as a profit where 0 < x  1. It is assumed x is the same for all suppliers in the economy. Note that x ¼ 1 is allowed, in which case the borrowing costs are zero. However, x ¼ 0 must be ruled out in order to ensure the supplier has an incentive to make R&D investment.4 To simplify the notation, let us assume x ¼ 1 in what follows. The membership of these specialized suppliers in each cluster is assumed to be fixed from the beginning, an assumption that will be relaxed later. Clusters are risk neutral, and there is a fixed supply of labor, L, such that a labor market clearing condition requires n X

lj ¼ L;

ð7:2Þ

j¼1

where the number of the clusters, n, is determined in equilibrium. Obviously, the total amount of output is equal to Y¼

n X

yj :

ð7:3Þ

j¼1

The jth cluster maximizes its current profits as max Aljα

fqi;j g; lj

m Y i¼1

qi;j 

m X

pðqi;j Þ  wlj ;

ð7:4Þ

i¼1

where pðqi;j Þ denotes the price of technology component i with the quality level of qi;j , and w is the wage rate. Since each supplier provides one unit of technology

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component in this model, its factor price alone is subtracted in (7.4). It should also be noted that the supplier of technology component j is different from the jth cluster itself. The former j refers to the technology field, while the latter refers to the cluster. The final price of the jth cluster is normalized to be unity. The FOCs with respect to qh;j and lj are respectively Aljα

m Y

qi;j ¼ p0 ðqh;j Þ;

ð7:5Þ

i6¼h

lj ¼ ðαAw1

m Y

1

qi;j Þ1α :

ð7:6Þ

i¼1

Substituting (7.6) for the labor market clearing condition, (7.2), we obtain L¼

n X

ðαAw1

j¼1

m Y

1

qi;j Þ1α :

ð7:7Þ

i¼1

Thus, the wage rate is adjusted to satisfy this equation. 3.2 Quality of technology component Each specialized supplier provides one unit of technology component inelastically to a cluster to which it belongs. Suppose there are g ð mÞ types of technology components in the economy. With appropriate permutation, it is assumed that s also refers to the ranking of the quality level such that qð1Þ > > qðsÞ > > qðgÞ : These quality levels are represented by a quality ladder (see, for example, Aghion and Howitt, 1992), qðsÞ ¼ qmðsÞ ;

ð7:8Þ

where q > 1 and mðsÞ takes positive values, representing the current quality level of technology component of type s. Obviously, we need to have mð1Þ > > mðsÞ > > mðgÞ:

ð7:9Þ

We refer to the technology component of the highest quality, type 1, as an advanced (core) technology, whereas the technology component of the lowest quality, type g, is referred to as a bottleneck technology. Note that this type of technology component differs from qi;j in (7.1). The latter classification is made in terms of technological field (qi;j ), while the former is made in terms of technological quality (qðsÞ ).5 For example, engine and brake technologies in an automobile represent different technological fields. A highpower engine requires a more sophisticated braking system such as ABS.

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These quality levels of the engine and brakes refer to technological quality. Thus, technology components can be viewed from these two different perspectives. Since the Y production function (7.1) yields positive cross derivatives @ 2 yj =@qi;j @ qk;j > 0, if perfect matching is allowed, technology components k6¼i

of the same quality level are matched together in equilibrium (Becker, 1991; Kremer, 1993). 3.3 Factor price for technology component Now, let us derive the factor price schedule for technology components. From (7.5) and (7.6), we can derive6 p0 ðqh Þ ¼ ðαα Awα

m Y

1

α

qi Þ1α qh 1α :

ð7:10Þ

i6¼h

Suppose this cluster adopting ‘ types of technology components, each of which ‘ X mðsÞ ¼ m. If the quality level of the hth self-matches with mðsÞ partners with s¼1

technology component is l type (qh ¼ qðlÞ ), using (7.8), (7.10) is rewritten as ‘ P 1 α 1α

mðsÞmðsÞ

1þ s¼1 ð1αÞmðlÞ

p0 ðqh Þ ¼ ðαα Aw Þ qh

:

ð7:11Þ

Integrating this with a zero-profit condition yields the factor price schedule of technology component h as pðqh Þ ¼ pðqðlÞ Þ ¼ ð1  αÞyðlÞy; yðlÞ ¼

mðlÞ X ‘

;

ð7:12Þ ð7:13Þ

mðiÞmðiÞ

i¼1

where

X

mðsÞyðsÞ ¼ 1. Thus, we can confirm the cluster indeed earns zero

s

profits, since αy is paid to labor, and higher quality components receive more payments. Hence, we obtain the following result: Lemma 1. pðqð1Þ Þ > > pðqðgÞ Þ holds.

3.4 Quality improvement The above analysis assumes that the quality level is fixed. Now, we will relax this assumption and allow for endogenous quality improvement for each

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technology component within a cluster. Suppose the current quality level of a specialized supplier belonging to a cluster is mðsÞ. When R&D succeeds, quality jumps from mðsÞ to mðsÞ þ 1. Denote the amount of R&D investment by e. With this R&D level, the probability of quality improvement realized in the next period is given by iðeÞ with @i=@e > 0 and @ 2 i=@e2 < 0. In other words, R&D investment increases the probability of innovation with decreasing returns. The expected gains from innovation, W, can be specified in various ways. To keep the model as simple as possible without loss of generality, we simply assume that this is the increasing function of DpðqmðsÞþ1 Þ  pðqmðsÞþ1 Þ  pðqmðsÞ Þ. Even if we specify the functional form of W by introducing further assumptions, it is obvious that W 0 > 0 still holds. For our purpose, it is sufficient to ensure its positive reliance on the expected price increase. In addition, the latter in turn depends on quality improvements in other technology components. Thus, it is also assumed that consistent expectation prevails regarding R&D activities of other technology components. Then, the expected profits of quality improvement are 1

V ðqðsÞ ; eÞ ¼ ð1 þ rÞ iðeÞWðDpðqmðsÞþ1 ÞÞ  e;

ð7:14Þ

where r denotes the rate of interest. It is easily confirmed that DpðqmðsÞþ1 Þ increases the quality level. The FOC with respect to e is 1

ð1 þ rÞ i0 ðeÞWðDpðqmðsÞþ1 ÞÞ ¼ 1:

ð7:15Þ

Denote the optimal R&D level for the current quality level of qðsÞ as e ðqðsÞ Þ. Then, we can immediately derive the following result: Lemma 2. e ðqð1Þ Þ > > e ðqðgÞ Þ holds. That is, quality improvement is more frequently observed in the higher end of the quality ladder. This implies that technological divergence is magnified over time among different clusters and among different components within a cluster. Proposition 1. With a small difference in the quality level, technology divergence prevails over time within and among clusters. Although Becker (1991) and Kremer (1993) primarily focus on self-matching, we need to pay more attention to cross-matching once endogenous quality improvement is incorporated. The cross-matching implies that technical imbalance exists among technology components. Hence, it provides a significant impetus for quality improvement, but the direction of technological change differs from the one suggested by Rosenberg (1976).

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Proposition 2. Innovation proceeds to improve technology components of higher quality. As a result, technical imbalance is expanding over time. We will consider the economic implications of this result in the next section. The total amount of R&D investment is represented by X ei ; ð7:16Þ E¼ i

where i is assigned to each of specialized suppliers existing in the economy. This completes the description of the basic model in this chapter.

4 Cluster growth In this section, we will examine the patterns of cluster growth under various conditions and derive some policy implications. More specifically, three conditions are to be introduced to the model: (1) advantages of backwardness; (2) free mobility of technology components; and (3) different feedback mechanisms. We are interested in how these conditions alter the equilibrium patterns of cluster growth. 4.1 Advantages of backwardness According to lemma 2 and proposition 2, the cluster growth rate increases over time with expanding technology gaps among and within clusters. However, this result does not seem to be supported by several empirical studies, suggesting an economic slowdown among advanced countries. For example, the historical evidence clearly shows that latecomers tend to grow faster than advanced countries, but when the latecomers approach the technological frontier, they tend to face an economic slowdown. Lemma 2 is not supported by this historical fact. The process of catching up, forging ahead, and falling behind has been accounted for by the advantages of backwardness (see, for example, Abramovitz, 1986; Howitt, 2000; Howitt and Mayer-Foulkes, 2004; Harada, 2012). This economic advantage arises due to spillover effects from the frontier countries or technologies. Thus, only backward countries could enjoy this spillover, providing a spur to rapid growth. To incorporate the advantages of backwardness into the model, let us suppose the probability of innovation of type s is specified as iðe; qð1Þ  qðsÞ Þ;

ð7:17Þ

with @2i > 0: @e@ðqð1Þ  qðsÞ Þ

ð7:18Þ

This inequality reflects the advantage of backwardness. That is, as the technology gap increases, the marginal increase in the probability of innovation also

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increases. Hence, technology components of the lower quality are able to take advantage of the higher probability of innovation. One typical example of this advantage is imitation in which the probability of innovation becomes closer to unity. However, as the technology gap becomes narrower, this advantage decreases. As a result, the rate of quality improvement converges to the same level over time. Proposition 3. When the advantages of backwardness are sufficiently significant, cluster growth reduces its own growth rate by narrowing technology gaps among technology components within a cluster. Of course, in the real world, no convergence within clusters is observed. Therefore, the advantages of backwardness are not sufficiently significant to allow a complete convergence, as suggested in proposition 3. However, up to a certain technological distance from the frontier, these spillovers work effectively. Hence, we conjecture that partial convergence to a certain range of levels would be feasible in reality. Within this range, technology components of the higher quality levels are more likely to attract R&D investment. 4.2 Migration In the preceding analysis, it is assumed that technology components stay in the matched cluster forever. In this subsection, this assumption is relaxed so that we allow specialized suppliers to migrate into different clusters. It is assumed that new immigrants provide a take-it-or-leave-it offer to the cluster, and if the cluster accepts, these immigrants could join the cluster. However, since m is fixed, some incumbent technology component must be replaced. Thus, the assumption of free mobility is equivalent to the situation in which re-matching takes place in the economy within and among clusters in every period. Suppose a cluster adopting ‘ types of technology components, each of which ‘ X mðsÞ ¼ m. This cluster faces a new self-matches with mðsÞ, partners with s¼1

immigrant of qðhÞ . Obviously, as long as h < ‘, the output of this cluster and payments to technology components increase by replacing the technology component of the lowest quality with the new immigrant of qðhÞ . Immigrants always have the incentive to find a new cluster that pays a higher factor price, and the latter has the incentive to replace inefficient suppliers with more productive immigrants. Therefore, the higher quality clusters attract other high-quality technology components in different low-quality clusters. As a result, under perfect matching, technology components of the same quality gravitate towards each other (self-matching). Hence, we obtain the following result: Proposition 4. With free mobility of technology components, all clusters maintain self-matches such that high quality clusters grow more rapidly than low quality clusters.

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Thus, under free mobility, neighbor immiserizing growth arises in which high quality technology components move to the most productive clusters, and these clusters alone enjoy rapid growth. In this equilibrium, technology gaps expand over time among clusters, but within a cluster, self-matching prevails as long as matching partners are available. 4.3 Feedback mechanism Next, let us introduce a feedback mechanism in the focusing device and see how the design of the feedback mechanism affects innovation in a cluster. The feedback could be regarded as the impact of bad performance on a system that makes it necessary to modify and improve the current state of the system. Thus, when feedback in a system is significant, divergence from an expected performance should be corrected immediately. The strength of feedback depends on the timing and correctness of the information obtained from the results and responsiveness to this information. In this chapter, we will model the feedback mechanism as the responsiveness to performance, which is determined by the magnitude of innovation. If the magnitude of innovation is small, this implies that the difficulty and cost of innovation are low. Therefore, it is easier to respond to poor performance by quality improvement. In contrast, if the magnitude of innovation is large, the responsiveness to performance remains limited. The magnitude of quality improvement in this model is given by q. This specification assumes that regardless of quality levels, the magnitude of quality jump is the same. However, in reality, technological change in high-tech fields is often characterized as radical innovation, while incremental innovation is more likely to be undertaken in low-tech fields.7 Thus, the magnitude of innovation varies among technological fields and qualities. Suppose the magnitude of innovation is given by qðsÞ ¼ qGs mðsÞ ;

ð7:19Þ

where Gs > 1 represents the magnitude of innovation for technology component of type s. This also represents the responsiveness to performance as a feedback mechanism. Moreover, @ 2 i=@e@Gs < 0 is assumed. That is, the larger the magnitude of innovation, the more difficult it is to succeed in innovation. However, it is also assumed that this difficulty does not increase significantly  where G and G  respectively represent lower and upper limits over G < G < G of G. Then, without difficulty, from (7.15), we obtain the following result: Lemma 3.

de ð ;GÞ dG

> 0.

As a corollary of this lemma, we can derive the following: Proposition 5. The larger the magnitude of innovation, the more advanced the quality level of the corresponding technology components such that G1 > > Gg holds.

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Thus, more innovations are likely to be observed in advanced technologies in the form of radical innovation, while incremental innovation occurs less frequently in bottleneck technologies. The result of lemma 2 is preserved here. One of the implications from this result is that the difference between bottleneck and advanced technologies could be attributable to different magnitudes of innovation and built-in feedback mechanisms. To use the terms of Hirschman (1967), when the “latitude” is narrow, implying a low tolerance for poor performance, the corresponding task has to be performed in a clearly defined and correct manner. Otherwise, it cannot be performed at all or is exposed to a considerable level of risk. However, as far as innovation is concerned, narrow latitude impedes, rather than facilitates, R&D activities due to weaker economic incentives. Therefore, we infer that advanced technologies have achieved their high-quality levels due to the adoption of a weaker feedback mechanism. 4.4 Policy implications We have seen that in this economy, high-quality components are more likely to be improved so that technological gaps expand over time. This type of innovation process can be regarded as core-driven innovation. On the other hand, if the advantages of backwardness are sufficiently significant, bottleneck technologies tend to be improved more frequently than advanced technologies, a situation that can be referred to as “bottleneck-removing innovation”. According to Rosenberg (1976), technological change proceeds in the latter manner by upgrading bottleneck technologies rather than improving already advanced technologies. However, recent arguments regarding general purpose technologies (GPTs) suggest that innovation tends to be driven by advanced technologies such as GPT (see, for example, Helpman, 1998). Chapter 3 identifies three stages of innovation, i.e., (1) the SPT (special purpose technology) stage; (2) the GPT–SPT joint-research stage; and (3) the autonomous GPT stage, and shows that in the autonomous GPT stage, innovation is primarily driven by GPT, not SPT. How does the model in this chapter account for these contrasting patterns of innovation? Our result hinges on the specification of innovation in (7.8) and (7.19). However, when the magnitude of innovation for each technology component is D, which is constant and independent of the current quality level, and the current quality level is q, the quality increases from q to q þ D by innovation. In this case, the marginal productivity of innovation is the highest for bottleneck technology (see (7.1)). Then the market price reflects the marginal productivity so that the incentive for innovation is maximized. As a result, bottleneckremoving innovation, as suggested by Rosenberg (1976), will prevail. Hence, the effect of current quality on the magnitude of innovation determines whether core-driven or bottleneck-removing innovation occurs. If the magnitude of innovation hinges on the current quality level, core-driven innovation emerges. Otherwise, bottleneck-removing innovation prevails.

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In reality, core technologies in high-tech fields advance in large steps so that technological gaps expand over time. In low-tech fields, the technology components are more likely to advance incrementally in a balanced manner. Thus, the model in this chapter is consistent with technology components in high-tech fields. Obviously, many final and intermediate goods consist of both high-tech and low-tech components. Therefore, it is of critical importance to select and facilitate innovation of technology components with the highest marginal productivity. However, within organizations and clusters, sometimes the appropriate incentive for innovation is not provided. For example, low-powered incentives such as cost plus contracting (Williamson, 1985) are likely to be adopted. Under this type of pricing scheme, it is difficult to impose selective innovation policies as the potential benefits of innovation for each technology component are obscured. Indeed, Dedehayir and Mäkinen (2008) discuss in their empirical study of the PC gaming industry how game developers, in order to guarantee success, tend to launch products with a focus on factors other than technological bottlenecks or reverse salience. They pointed out that the ability to gage the magnitude of reverse salience in technological subsystems is likely to increase innovation performance. This argument suggests that conventional incentive schemes do not provide correct information that reflects the true economic value of innovation. One way to get around this is to design a more appropriate feedback mechanism. That is, an increase in the magnitude of innovation in technology components with lower-powered incentives could enhance their R&D incentives and facilitate innovation. In this case, the cluster should pursue more radical rather than incremental innovation to facilitate innovation in less advanced technologies. The feedback mechanism should be modified to allow for wider latitude for poor performance. This policy raises the R&D incentive for such technologies because the larger magnitude of innovation is attractive within the cluster, leading to stronger social pressure to succeed in innovation. Another policy to facilitate innovation is to provide R&D subsidies. Since factor prices in lower-powered incentives do not reflect the true economic value of innovation, some policy intervention should be implemented to correct this bias. The direct measure for this is R&D subsidies.

5 Concluding remarks In this chapter, we have modeled a focusing device mechanism using an o-ring production function and the effects of this mechanism on cluster growth. We have shown that depending on the magnitude of the advantages of backwardness and the degree of free mobility of technology components, the matching patterns of clusters could be either self-matching or cross-matching. However, in all cases, higher quality components have the strongest incentive to undertake R&D. As a result, cluster growth tends to be driven by advanced technology rather than by bottleneck technology.

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The inefficiency arises, however, within many organizations and clusters when they adopt low-powered incentives, such as cost plus contracting, for innovation. In this case, the pricing scheme provides the wrong incentive in terms of technological change. As a result, technological change proceeds to further improve component technologies with lower marginal productivity of innovation. Thus, it is necessary to redirect the focus of R&D by providing appropriate incentives. One of the reasons that the advantages of backwardness work effectively in rapidly growing economics is that these spillovers correct the misdirected incentive and provide an appropriate guide for efficient technological change. When clusters succeed in catching up and forging ahead, they also need to undertake this redirection through the provision of subsidies or through different incentive schemes that induce more R&D investment in technologies with low-powered incentives. If these clusters are falling behind, this is attributable to the fact that they fail to implement this redirection.

Notes 1 Advanced and core technologies are used interchangeably in this chapter. 2 Under this assumption, individual firms (specialized suppliers) correspond to firms in a standard economic model that have a conventional production function such as a CES, although the latter’s production structure is not explicitly modeled in this chapter. 3 This metaphor has a certain empirical relevance. For example, the law of gravity was discovered by Newton, but this law is not his creation. The fact of gravity and its law already existed, and was only discovered by him. In other words, the book on the law of gravity was held by a library, but only Newton was capable of reading and hence borrowing it at that time. 4 The idea of this library metaphor is to justify the positive profits for a supplier in the transaction of knowledge without introducing further arbitrary assumptions regarding its cost structure. The positive profits in turn incentivize R&D investment. 5 This view is similar in spirit to the hedonic approach in product differentiation literature, although the former focuses on quality rather than characteristics. 6 To simplify the notation, we drop the subscript j in the following analysis. However, it should be noted that factor prices are cluster-specific. 7 According to OECD (1994) classification, high-tech industries are defined as having a R&D turnover ratio more than 5%, while low-tech industries have less than 0.9%. For radical innovation to be commercialized, initiation of new areas of scientific research is required. This was the case with the transistor, the laser, the computer, and nuclear fission. See Brooks (1994) for a more detailed argument. Thus, radical innovation is more likely to take place in high-tech (R&D intensive) sectors.

8

Managing innovation probabilities through focusing device

1 Introduction Today, it is widely accepted that the growth of technological knowledge is fundamental to the improvement of economic performance. According to Rosenberg (1994, p. 9), to further investigate the role of innovation in economic growth, two relevant questions must be answered: “What can be said about the manner in which the stock of technological knowledge grows over time?” And “To what factors is it responsive, and in what ways?” Satisfactory answers to these questions still have not been developed, at least through formal analysis. In industrial organization literature, the relationship between competition and innovation has been extensively studied both theoretically and empirically, stimulated by the famous Schumpeter hypotheses that emphasize a trade-off between innovation and static efficiency.1 However, since innovation has generally been modeled as an improvement of a single technology, rather than of multiple technologies, the direction of innovation has been relatively disregarded. Instead, the rate of innovation has been formalized and analyzed as the incentive problem of R&D investment. Thus, institutional factors that enhance this incentive, such as market power, patents, and regulation, were shown to increase the rate of innovation (see, for example, Aghion and Howitt, 2008). This chapter departs from these studies in that technology is regarded as a system of multiple component technologies and the direction of technological change among them is explicitly examined.2 Rosenberg (1976) argued that the innovative efforts of entrepreneurs are directed to ease “the most restrictive constraint on their operation” (p. 125). The restrictive constraints or technical bottlenecks force entrepreneurs to focus their attention on these areas because that is the compelling and obvious need. This allocation mechanism of innovative efforts was referred to as the “focusing device” by Rosenberg (1976), and it generates specific signals indicating precise directions in which technological efforts can be usefully focused. Hughes (1983) also proposed a similar concept of the “reverse salient” in studying the evolution of technology systems. Reverse salients are components that have fallen behind or are out of phase with other system components. Such components represent bottlenecks or backward elements that prevent the further advance of the system. The nature of these reverse salients can be technical,

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economic, organizational, or political (Hughes, 1987, p. 73). Reverse salients that cannot be overcome within the context of the existing system may bring about radical innovations and a shift in prevailing technological regimes. They therefore play the role a focusing device in the process of innovation, though the underlying economic mechanism has not yet been fully analyzed. In contrast, Harada (2014c) and Chapter 7 developed a model of focusing device in which the final good firm that purchases technology components adopts a pricing scheme, which in turn provides specialized suppliers with the incentive for R&D. It was shown that equilibrium factor prices are based on productivity, and that this reward scheme generates core-driven innovation. However, core-driven innovation stands in sharp contrast to the type of innovation pointed out by Rosenberg (1976) and Hughes (1983). Harada (2014a) therefore constructed an alternative model that results in bottleneck-removing innovation. The purpose of this chapter is to provide a much more simplified framework of focusing devices that generate different patterns of innovation, i.e., core-driven and bottleneck-removing innovations, and discuss the managerial implications. Focusing devices are the mechanisms that determine the direction of innovation, which in turn consists of underlying technology systems, incentives, governance, and strategies. We show that core-driven innovation should be undertaken under an independent technology system, when the technology components are independent. Bottleneck-removing innovation should be pursued when the components are interdependent, under an interdependent technology system. Thus, different types of focusing device should be adopted primarily based on the degree of interdependence among technology components. This management of innovation activities maximizes underlying innovation probabilities. One of the implications of the results is that the effective management of innovation is made possible when innovative activities and corresponding focusing devices are appropriately arranged and coordinated to maximize innovation probability (the innovation probability maximization principle), instead of relying on elusive concepts such as enactments (Weick, 1979), resources (Wernerfelt, 1984), routines (Nelson and Winter, 1982), and capabilities (Teece, Pisano, and Shuen, 1997). Thus, managing innovation probabilities is a key to dynamic efficiency of the firm. The rest of this chapter is organized as follows. Section 2 presents a basic model of focusing devices, examines their effects on the rate and direction of innovation, compares the relative dynamic efficiencies, and discusses the implications. Section 3 generalizes management of focusing devices as innovation probability maximization and discusses several managerial challenges. Finally, Section 4 presents our conclusions.

2 Core-driven vs. bottleneck-removing innovation 2.1 Technology system In this section, we will present a simple conceptual model of a technology system and show how interdependence of technology components affects the

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direction of innovation. Since the model is based on Chapter 7, we will just sketch the model. We suppose a technology system consists of several technology components. For example, the railway vehicle technology system includes safety, drive control, power system, braking, vehicle motion, vehicle vibration, vehicle strength, energy control, communication, and transmission. Each technology component is in turn divided into more detailed subcomponents. Suppose the value of innovation is V , and the probability of success of innovation for the ith technology component is denoted by pðri ; ai Þ ¼ qðri Þ  ai ;

ð8:1Þ

where ri measures the amount of R&D investment and ai is the intrinsic difficulty of R&D in this technology component. qðrÞ increases with R&D investment and is strictly concave to ensure interior solutions. If pðri Þ  0, we assume pðri Þ ¼ 0 to rule out negative probabilities. Suppose a technology system consists of k technology components. The heterogeneity across technology components is incorporated by assuming different values of aj for j ¼ 1; . . . ; k: For ease of exposition, we assume a1 < < ak . The first and the kth technology components are referred to as core and bottleneck technologies, respectively. This is because core technology usually implies a higher innovation probability while a bottleneck technology suffers from a lower innovation probability. To keep the model as simple as possible without loss of generality, we assume the function form of qðrÞ is the same for all technology components. Now, we introduce two types of interaction among technology components: (1) independent technology components (modular type) and (2) interdependent technology components (complex products and systems (CoPS) type), and examine how the intensity of R&D investment is affected by these different interaction patterns. 2.2 Independent technology components First, consider the case of independent multiple technology components. Suppose there are k kinds of technology components. If each technology component is independent, the probability that at least one technology component succeeds in innovation is given by pðr1 ; . . . ; rk Þ ¼ 1 

k k Y Y ð1  pðnj ; qj ÞÞ ¼ 1  ð1  qðri Þ þ ai Þ: j¼1

ð8:2Þ

j¼1

The expected profits from innovation are pðr1 ; . . . ; rk ÞV 

k X

rj :

ð8:3Þ

j¼1

When ai is low (core technology), the expected gains from its innovation are higher than other technology components with higher values of aj (bottleneck

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technology) because its marginal impact on the total innovation probability (8.2) is higher.3 Therefore, it is more efficient to invest in core technology more intensively than bottleneck technology. As a result, core technologies are more likely to discover a new technology in this case. Proposition 1. In the case of independent technology components, coredriven innovation should prevail such that r1 > > rK and pðr1 ; a1 Þ > > pðrK ; ak Þ. In other words, if each technology component has an independent effect on the total innovation probability, technology components with higher innovation probabilities should be intensively explored. Consequently, core-driven innovation prevails and technology divergence is more likely to expand over time. This result is consistent with innovation processes of general purpose technologies (GPT) such as machine tools and information technologies (see Helpman. 1998, for a systematic analysis).

2.3 Interdependent technology components As a number of case studies of innovation suggest, innovation proceeds within larger sociotechnological systems consisting of interdependent technology components (Rosenberg, 1976; Hughes, 1983). Miller et al. (1995) and Hobday (1998) argued that while most innovation studies have examined mass-manufactured goods, a large number of industries supply high-cost, technology-intensive, customized, capital goods, such as flight simulation systems, bridges, chemical plants, robotics equipment, and submarines. They are systemic in the sense that they work through the interplay of many interacting components. They defined these technology systems as CoPS. In these CoPS, bottlenecks, rather than core technologies, play a more critical role. In this case, it is therefore reasonable to introduce interdependence across heterogeneous technology components. The innovation function can be specified as pðr1 ; . . . ; rk Þ ¼

k Y j¼1

pðnj ; qj Þ ¼

k Y

ðqðrj Þ  aj Þ:

ð8:4Þ

j¼1

This multiplicative form implies that the total innovation probability is severely damaged if the innovation probability of any one technology component decreases. For example, if pðnj ; qj Þ ¼ 0, the total innovation probability also becomes zero. In the additive specification of (8.2), this will not happen. In this case, R&D investment in other technology components with positive innovation probabilities does not make sense because the total innovation probability does not change as long as pðnj ; qj Þ ¼ 0 is maintained. Thus, increasing pðnj ; qj Þ becomes the top priority.4 As a result, bottleneck technologies should receive more R&D investment than core technologies in the interdependent case.

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Proposition 2. In the case of interdependent technology components, bottleneck-removing innovation should prevail such that r1 < < rk . Note that in this proposition, we cannot establish pðr1 ; a1 Þ < < pðrK ; ak Þ even if n1 < < nk holds. This is because more diversity does not necessarily lead to a higher innovation probability of the corresponding technology component owing to the intrinsic difficulty aj. But the firm attempts to increase the innovation probability of bottleneck technologies as much as possible to increase the total innovation probability. Consequently, bottleneck-removing innovation prevails and technology convergence is more likely over time. This pattern of innovation is consistent with historical evidence provided by Rosenberg (1976) and Hughes (1983) in which bottlenecks or reverse salients play a critical role in determining the direction of innovation.

2.4 Application to capability management in two-tier technology systems These results can also be applied to capability management in more complex technology systems. To illustrate this, let us define core capability as technology components with the highest innovation probability, and peripheral capability as those with the lowest innovation probability. Standard capability management emphasizes core capabilities to be invested and improved, rather than peripheral ones. However, Proposition 1 suggests that this management is effective if and only if the underlying technology system is independent. If technology components are interdependent, it is peripheral capabilities that must be highlighted in managing innovation processes. Thus, even in capability management, to derive effective managerial implications, innovation probability should be the basic unit of analysis in the face of uncertainty. In more complicated cases, suppose a technology system consists of two tiers of subsystems. The first and second tiers are either independent or interdependent. Then, we have four types of technology system, as shown in Table 8.1. Core capabilities should be highlighted only in the case that a technology system consists of independent technology components. When an interdependent tier is included, peripheral capabilities should be prioritized in R&D investment at that tier. For example, suppose the first and second tiers consist of independent Table 8.1 Capability management in two-tier technology systems Types of technology systems

Management focus

Upper tier

Lower tier

Upper tier

Lower tier

Independent Independent Interdependent Interdependent

Independent Interdependent Independent Interdependent

Core Core Peripheral Peripheral

Core Peripheral Core Peripheral

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and interdependent technology components, respectively. While the first tier is managed primarily to increase core capabilities, peripheral capabilities should be improved in the second tier. Without introducing innovation probability as a measure for capability management, these subtle differences could not be derived.

3 Management of innovation probability 3.1 Innovation probability maximization If the direction of innovation follows the optimal trajectory, as specified in propositions 1 and 2, this implies that the total innovation probability is also maximized. Thus, the optimality of innovation trajectory depends on whether the underlying innovation probability is maximized or not. We will refer to this as the innovation probability maximization principle. According to this principle, effective management of innovation is conceived as management of innovation probabilities. The previous section suggests that the patterns of interaction across technology components matter in this management. By contrast, the literature on R&D management typically focuses on knowledge (Kogut and Zander, 1992; Henderson and Cockburn, 1994; Fleming, 2001), capabilities (Teece, Pisano, and Shuen, 1997; Nerkar and Paruchuri, 2005), communications (Allen, 1977; Harada, 2003), or structures (Clark, 1985; von Hippel, 1990; von Zedtwitz and Gassmann, 2002; Argyres and Silverman, 2004; Zhang, Baden-Fuller, and Mangematin, 2007) without much reference to innovation probabilities. But those factors are primarily conducive to the management of operational issues in which significant uncertainty does not exist. When stochastic processes must be effectively controlled, management of innovation should be directly concerned with the underlying innovation probabilities to be increased by corresponding innovative moves. Thus, innovation probability should be the unit of analysis in the face of uncertainty, and other factors such as knowledge and capabilities are instruments in the management of innovation probabilities. In other words, knowledge and capabilities should be efficiently utilized to increase innovation probabilities. However, in reality, the innovation probability maximization principle is sometimes difficult to implement owing to organizational practices, different pricing schemes, and a lack of attention to innovation probabilities. If these obstacles are significant, the management of innovation probabilities consistent with propositions 1 and 2 inevitably necessitates the management of focusing devices. Focusing devices can be defined as mechanisms of innovation that indicate the direction of innovation, such as technical signals, pricing schemes, and feedback loops. Harada (2014c) formalized focusing devices in terms of factor prices of technology components in which core technologies are priced highest, generating core-driven innovation, as suggested in Proposition 1. If technology components are supplied through markets with equilibrium factor

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prices, this implies that innovation probability maximization is discouraged under the interdependent technology system. Even if technology components are internally procured, divergence from innovation probability maximization can still take place. To overcome or transgress a reverse salient, it is crucial that firms are capable of defining them as a set of critical problems (Hughes, 1983). However, this capacity to identify reverse salients under CoPS is not always available. Rather, it must be developed and improved over time. For example, Dedehayir and Mäkinen (2008) discussed in their empirical study of the personal computer (PC) gaming industry that game developers, to guarantee success, tend to launch products with a focus on factors other than technological bottlenecks. They pointed out that the ability to gage the magnitude of bottleneck severity in technological subsystems is likely to increase innovation performance. This argument suggests that conventional incentive schemes do not provide correct information that is conducive to innovation probability maximization. Similarly, Geyer and Davies (2000) suggested in their analysis of railway projects in the United Kingdom and Germany that successful innovation in market-based railway operations increasingly depends on dynamic systems integration and effective coordination between railway projects and the operational railway network. However, a fragmented market structure in the operational railway system makes it extremely difficult to build and maintain these links. Systematic efforts are required to establish some feedback loops between the two. These arguments clearly suggest that management of innovation probabilities should entail the management of focusing devices. The innovation mechanism that determines the direction of innovation should be corrected as soon as it diverges from the innovation probability maximization principle. More specifically, it is one of the most important challenges in the management of innovation to identify core and bottleneck technologies and direct innovative efforts so as to maximize innovation probability. Table 8.2 summarizes the management challenges of technology systems discussed in the previous section. This table indicates that incentives, governance, and strategies must be congruent with the underlying technology system to maximize innovation probability. Complementary sets of incentives, governance, and strategies constitute an efficient focusing device that achieves Table 8.2 Management of technology systems

Innovation Incentive Governance Strategy Advantage Disadvantage

Independent system

Interdependent system

Core-driven Performance-based Internal development Cost-reducing, quality-improving Core strength Rigidity

Bottleneck-removing Marginal productivity-based Relational outsourcing Hybrid Flexibility Core weakness

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dynamic efficiency of the firm. In what follows, we will consider these management challenges. 3.2 Incentives First, management of focusing devices requires appropriate incentive schemes that facilitate desirable innovation. In market transactions, core technology is usually characterized by high quality relative to other technology components. Bottleneck technology is usually rewarded less than other technology components, as otherwise suppliers of technology components, including both employees and outside suppliers, are not motivated to improve quality. On the contrary, they have more incentive to reduce quality because the corresponding payment increases as a result. Bottleneck technology should therefore be rewarded less than other technology components. This is the equilibrium price schedule in the model of focusing device in Harada (2014c). In the case of independent technology components, since core technology must be primarily developed, higher rewards should be provided to suppliers of core technology to facilitate innovation. A decrease in the innovation reward obviously reduces the incentive to make R&D investments in core technology, and hence, discourages innovation. In the case of interdependent technology components, however, the difficulty arises in incentive schemes. According to proposition 2, the optimal incentive scheme should be a reversed version of core-driven innovation, i.e., a marginal productivity-based reward. Consequently, suppliers of bottleneck technology are less motivated to invest in R&D. The management challenge here is to introduce a marginal productivity-based reward scheme in the firm without discouraging innovation and providing an incentive to downgrade quality. However, this is sometimes very difficult to implement via selective intervention (Williamson, 1985) because employees and suppliers of high quality technology components face high reservation utility. If they are rewarded less, they will leave the firm. To respond to this challenge, the firm often introduces a different reward scheme for bottleneck technologies. For example, if core technology is internally procured, bottleneck technology is outsourced so that the negative effect on employees’ incentive to make R&D investment is mitigated by separating the reward schemes. Alternatively, the firm can adopt a fixed reward scheme so that all technology components are equally motivated for innovation. But this cannot resolve the potential problem of incentive incompatibility because employees in charge of bottleneck technology could have more bargaining power than other employees, demanding more nonpecuniary incentives such as promotion and budget. Once again, this might discourage innovative activities of other employees to some extent. Ideally, if the incentive scheme can feasibly reward lower quality, this facilitates bottleneck-removing innovation. Otherwise, the firm must introduce either different governance for bottleneck technology or a fixed reward scheme as second best alternatives.

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3.3 Governance We must now examine the governance required for core and other technologies to fix the appropriate reward scheme for bottleneck technology. Core technology reflects the core capability of the firm, and the resource-based view of management recommends that core technology should be internally procured. If it is outsourced, this implies competitors can also get access to core technology, leading to a decline in competitive advantage. To outperform competitors, the firm must own valuable, rare, inimitable, and well-organized resources and capabilities (Barney, 1991). Obviously, core technology satisfies this criterion. From the perspective of transaction cost economics (Williamson, 1985), internalization of core technology implies relation-specific investment in core technology is also facilitated. As a result, innovation in core technology is facilitated. In this case, if the firm pursues core-driven innovation, it should adopt a performance-based (average productivity) reward scheme. In other words, innovation in high quality technology components will be rewarded more. Employees in charge of core technology will become highly motivated to innovate. However, from the perspective of innovation probability maximization, it is not always desirable to internalize core technology. Although transaction cost minimization is efficient from a static perspective, another aspect needs to be considered from a more dynamic perspective, namely, to maximize the total innovation probability. To clarify this, suppose the ith technology component is currently outsourced and the firm is now considering whether it internalizes this technology component or not. When a technology component is outsourced, outside suppliers make the corresponding R&D investment. If this technology component requires relation-specific investment to the firm, outside suppliers have less incentive to make the R&D investment, which could be reflected in a lower value of V in (8.3). For example, the firm uses packaged software from the outside supplier, but its productivity increases if the software is more customized. The firm must internally develop the customized software because outside suppliers have no incentive to do so. If the firm succeeds in the customization, it increases the value of its technology system (V ) so that VI > VO holds where subscripts I and O denote internal procurement and outsourcing, respectively. From a static perspective, this decision is optimal as VI > VO , from the relation-specific investment. Now, assume that the innovation probability of the ith technology component is exogenously given when it is outsourced. If many outside suppliers investing in R&D in this technology component exist in the market, the corresponding innovation probability is expected to be higher than the innovation probability of the firm. Assume also that innovation increases V over time and the growth rates under outsourcing and internal procurement are mO and mI , respectively, with mO > mI . The expected sum of the future gains from innovation is higher under outsourcing than under internal procurement if the gap between the innovation probabilities (mO and mI ) is sufficiently large.5

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In particular, GPT components are most likely to be outsourced since outside GPT suppliers provide them with lower prices through economies of specialization (Rosenberg, 1976). The emergence of GPT sectors provides the firm with the option of outsourcing with higher level and growth effects (Harada, 2010a). While internal procurement could be efficient from the static perspective, it could be inefficient from the dynamic perspective. Under certain conditions, the firm faces a trade-off between commitment (relation-specific investment) and innovation probability. In other words, the trade-off emerges between static and dynamic efficiencies. For the latter, the innovation probability maximization principle should be more pronounced. If core technology has to be outsourced owing to more rapid pace of innovation outside the firm, the reward scheme simply becomes market prices. As we mentioned above, core technology is rewarded more than other technology components in markets. Thus, if the firm intends to implement core-driven innovation, a market pricing scheme is complementary. However, outsourcing also involves the risk of losing competitive advantage because competitors can also get access to the same core technology. This is indeed what is observed in the PC industry in which core technologies such as operating systems and MPU are outsourced respectively to Microsoft and Intel so that product differentiation in this industry remains harder to achieve. In this case, a technology component with the second highest quality might become the source of competitive advantage. But if this technology component is also subject to a rapid pace of innovation in the market, it must be outsourced once again to maximize innovation probability. This technology component cannot be the source of competitive advantage, as long as outside suppliers are available to competitors. Eventually, if the firm pursues core-driven innovation and gains sustainable competitive advantage, technology components as the source of competitive advantage must be internalized to block imitation by competitors. By contrast, if the firm pursues bottleneck-removing innovation with the interdependent technology components, bottleneck technology becomes the source of competitive advantage. Once again, the optimal governance should be determined based on the innovation probability maximization principle. If outside suppliers provide the bottleneck technology with a rapid pace of innovation, the firm should obtain it from outside suppliers. If competitors regard the same technology component as a bottleneck and pursue bottleneck-removing innovation, outsourcing implies the loss of competitive advantage. In this case, the second lowest quality technology component becomes the source of competitive advantage. Eventually, bottleneck technology as the source of competitive advantage must be either internalized or outsourced to suppliers establishing a specific relation to the firm. Regarding outsourcing to a relation-specific supplier, note that bottleneck technology is priced lowest in the markets. In contrast to core technology, outside suppliers also face less incentive to invest in R&D. On the other hand, the firm pursuing bottleneck-removing innovation has the incentive to invest heavily in R&D in the bottleneck technology. Consequently, the firm can

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provide sufficient incentives and governance mechanisms such as relational contracts. In this case, competitors cannot get access to the same bottleneck technology. This relational contract is likely to be unfeasible in the case of core technology because the opportunity costs of core technology in the market are high, so that the firm cannot provide sufficient incentive to these suppliers. Suppose the marginal productivity-based reward scheme cannot be implemented in the firm. When a bottleneck technology is either internally procured or outsourced to relation-specific contractors, higher quality technology components should be outsourced and rewarded according to market prices. The remaining lower quality technology components are rewarded based on a fixed reward scheme in the firm. When the bottleneck technology is outsourced to relation-specific contractors, more incentives should be provided to those contractors to facilitate R&D investment. 3.4. Competitive strategies Innovation probability maximization leads to sustainable competitive advantage or dynamic efficiency over time. To fully exploit dynamic efficiency, the corresponding competitive strategy must be congruent with the underlying focusing device. In contrast to competitive strategies proposed by Porter (1980, 1996),6 Harada (2014a) introduced the concept of dynamic strategies that refer to innovation trajectories of given competitive strategies. For example, the competitive space represented in Figure 8.1 is specified by two axes: quality and cost advantage. A consumer chooses a bundle of these two properties of the product from the set of available alternatives. Its utility is assumed to be well behaved and the profits of the firm are in proportion to the utility level achieved by its product. If the firm is positioned on A in this competitive space (see Figure 8.2), this position is equivalent to Porter’s competitive strategy. However, innovation enables Quality

Cost advantage

Figure 8.1 Innovation trajectories

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Quality Quality improving Strategy

Hybrid Strategy

A

Cost reducing Strategy

Cost advantage

Figure 8.2 Three types of dynamic strategies

Quality

U’

U’

U B’

U

A’ time T+1 A B time T

Cost advantage

Figure 8.3 Shifts in competitive advantages and innovation trajectories

the firm to shift its own position to somewhere that increases the consumer’s utility. In Figure 8.2, three types of innovation trajectories are identified: (1) quality-improving; (2) cost-reducing; and (3) hybrid strategies. Harada (2014a) argued that while the hybrid strategy is associated with Porter’s stuckin-the-middle strategy, which pursues both differentiation and cost leadership simultaneously, this dynamic strategy alone generates dynamic efficiency. Figure 8.3 shows that the quality-improving strategy of AB is inferior to the hybrid strategy of AA’ because U’ > U holds. Indeed, this figure indicates that

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both positions of A and B provide the same utility to the customer. Paradoxically, if quality-improving innovation continues from A to B, its competitiveness remains the same, whereas if it stops somewhere before reaching B, the firm improves its competitive advantage. However, as long as the firm stays in the trajectory of AB, it cannot gain competitive advantage over competitors in AA’. Therefore, the firm should eventually shift to the hybrid strategy at some point in time even if it currently pursues either cost-reducing or qualityimproving strategies. Now, suppose the firm adopts a hybrid strategy. Then, the corresponding technology system should be interdependent because a balanced innovation trajectory must be realized under this strategy. If the firm is currently advancing in cost performance, its next target of innovation should be quality-improving because the hybrid strategy pursues cost reduction and quality improvement simultaneously. This simultaneous pursuit is only possible by bottleneckremoving innovation. On the other hand, if the firm pursues either cost-reducing or quality-improving strategies, it should focus on innovation in cost reduction or quality improvement, respectively. Obviously, an independent technology system is complementary to these dynamic strategies because it generates core-driven innovation. Thus, our results in propositions 1 and 2 clearly suggest that structure (technology system) follows strategy (dynamic strategy) consistently. If the firm shifts its dynamic strategy between a hybrid and single strategy, the underlying technology system must also be altered to one that is complementary to the new dynamic strategy. 3.5. Endogenous technological interdependence So far, we have simply assumed that technology systems can be classified as either independent or interdependent technology components. This interdependence among technology components is primarily determined by the technological properties of the underlying architecture of the product (Henderson and Clark, 1990). Although the effect of architecture is significant on the degree of interdependence among technology components, the firm could affect this interdependence to some extent by changing incentive schemes and dynamic strategies. For example, automobile firms are usually equipped with an interdependent technology system because an automobile is composed of many interdependent parts and materials. According to Table 8.2, automobile firms must pursue a hybrid strategy with bottleneck-removing innovation. Toyota seems to follow this innovation path with relation-specific keiretsu suppliers. However, Honda, BMW, and Mercedes put more emphasis on distinguishing features of their own cars, such as design, engine performance, quality, and usage. Thus, their dynamic strategies are quality-improving, rather than hybrid. This clearly implies that these automobile firms succeed in generating unique focusing devices that are not implied by the underlying (pure) technology system.

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Although their technology systems are also subject to high degrees of interdependence among technology components, they put more emphasis on the independent nature of product properties that appeal to customers, a type of focusing device can be endogenously determined in the competitive strategy space, even if the firm and competitors share the same technology system. Hence, we should distinguish the strategic technology system from the pure one. The former is the endogenously designed innovation mechanism, while the latter is the exogenously predetermined technical relationships across technology components. Obviously, the former alone matters in managing innovation probabilities.

4 Concluding remarks In response to the two questions raised by Rosenberg (1994), we have developed a simple framework of focusing devices. We have shown that core-driven innovation should be undertaken with independent technologies, while bottleneckremoving innovation should be pursued under the interdependent technology system. These results provide an answer to the first question of Rosenberg (1994) about the manner in which the stock of technological knowledge increases. In the process of innovation, we inevitably face the trade-off between static and dynamic efficiency implied in the Schumpeter hypotheses. Thus, institutional designs such as the boundary of the firm must be evaluated in terms of the innovation probability maximization principle, in addition to the transaction cost minimization principle. A standard economic institutional analysis such as transaction cost economics is primarily concerned with static efficiency, represented by underinvestment in relation-specific assets (Williamson, 1985). However, dynamic consideration modifies this preoccupation with static efficiency in favor of dynamic efficiency. Thus, Rosenberg’s (1994) second question, about the factors to which technological knowledge is responsive, can now be answered by pointing out not only economic factors such as factor prices but also institutional factors that reflect either the transaction cost minimization principle or the innovation probability maximization principle. This chapter illustrates the need to shift our attention towards the latter in the evaluation and design of institutions. The results obtained in this chapter have several implications. They suggest that R&D management literature that emphasizes knowledge and capabilities should be evaluated in terms of the effects on innovation probabilities and used to increase innovation probabilities, based on these evaluations. This is because the existing studies on R&D management lack appropriate measures. As illustrated in Table 8.1, even in capability management, to derive effective managerial implications, innovation probability should be the basic unit of analysis in the face of uncertainty. In terms of the literature on focusing devices, this chapter has formalized the informal arguments in Rosenberg (1976) and Hughes (1983) and integrated their concepts of bottlenecks and reverse salients with the core-driven innovation suggested by Harada (2014c) in a very simple framework of focusing devices. A

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number of case studies on innovation processes have been built upon the framework of reverse salients (Geyer and Davies, 2000; Prencipe, 2000; Fransman, 2001; Mulder and Knot, 2001; Christiansen and Buen, 2002; Markard and Truffer, 2006; Dedehayir and Mäkinen, 2008). However, these arguments seem valid only in interdependent technology systems such as CoPS. Thus, the model in this chapter provides a more balanced view on the innovation processes. Finally, let us make a few remarks on dynamic capabilities. Dynamic capabilities are the ability to build, integrate, or reconfigure other resources and capabilities (Teece, Pisano, and Shuen, 1997), which consists of routines (Zollo and Winter, 2002). Innovation probability is also concerned with building, integrating, and reconfiguring other resources and capabilities as long as they are related to innovation. However, innovation probability should be clearly distinguished from dynamic capabilities, because innovation probability is not a routine. It is one aspect of controlled stochastic processes and changes over time. Innovation probability is the outcome of stochastic events and actions, which in turn might reflect dynamic capabilities. This chapter was not interested in linking innovation probability and dynamic capabilities. As Williamson (1999) suggested, the related work has not yet succeeded in operationalizing dynamic capabilities. Dynamic capabilities, as the framework of management of innovation, are too elusive to provide specific prescriptions regarding innovation activities. Instead of relying on dynamic capabilities, we therefore believe that it is more instructive to make innovation probabilities the basic unit of analysis for innovation strategy and management.

Notes 1 The Schumpeter hypotheses state that (1) innovation increases more than proportionately with firm size; and (2) innovation increases with market concentration. See Cohen and Levin (1989), Reinganum (1989), and Griliches (1984) for a survey and theoretical and empirical studies on the hypotheses. 2 Acemoglu (1998, 2002) also succeeded in providing a microfoundation for the theory of induced innovation under a general equilibrium framework. However, his model did not incorporate supply-side constraints so that technological change proceeds in response to market forces alone. By contrast, this chapter focuses more on the supply-side constraints. k Y ð1  qðrj Þ þ aj Þq0 ðri ÞV. If 3 More formally, the marginal productivity is calculated as j6¼i

ai is minimized, this is maximized. 4 More formally, the marginal productivity is calculated as

k Y

pðrj ; aj Þq0 ðri ÞV: If ai is

j6¼i

maximized, so is this. 5 More formally, this condition is given by VO =r  mO > VI =r  mI where r denotes a discount factor. 6 Porter (1996) defined competitive strategy as “the creation of a unique and valuable position, involving a different set of activities”.

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1 Introduction Chapters 7 and 8 discussed the role of the focusing device as an innovation mechanism. Even though the appropriate focusing device is institutionalized, it does not automatically guarantee any success in innovation. What needs to be examined, given some focusing device, is spontaneous knowledge communication among organization members. Although the success of technological innovation, or knowledge creation in general, can be ultimately attributed to individual commitment, passion, and creativity (Polanyi, 1962, 1967), organizational knowledge creation critically depends upon communication and information processing capacities of the organization (March and Simon, 1958; Cohen and Levinthal, 1990). Among the various methods of information processing, oral communication with individuals inside and outside the organization is considered the primary medium through which engineers and scientists import and digest technical information within the organization (Allen, 1977). Not surprisingly, numerous studies have been conducted on the nature and role of oral communication in the successful completion of scientific and technological innovation. In particular, a two-step flow of communication and the role of gatekeeper have received extensive attention in the past decades (Achilladelis, Jervis, and Robertson, 1971; Allen, Tushman, and Lee, 1979; Carter and Williams, 1957; Tushman and Katz, 1980; Katz and Tushman, 1981). The purpose of this chapter is to reexamine the pattern of technological communication flow in the research organization with a new measurement approach. In contrast to the past studies on the gatekeeper phenomenon (Allen, 1977; Allen and Cohen, 1969; Frost and Whitley, 1971; Taylor and Utterback, 1975; Tushman, 1977; Walsh and Baker, 1972; Whitley and Frost, 1973), this study found that there exists a three-step flow of communication among engineers in the organization. In this new pattern of information processing, outside technical information is transferred to the organization via boundary spanning individuals. However, these individuals do not frequently communicate with other members in the organization. Instead, it was found that boundary spanning individuals are connected to internal communication stars (knowledge transformers) through which external information is translated and transformed into organization

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specific knowledge and subsequently transmitted to other members in the organization. Thus, the usual definition of gatekeeper (being both external and internal communication star) cannot be applied in this study. It is argued that these findings can be interpreted as general rather than deviant in the recent trend of technological innovation. In addition to these findings, our empirical approach differs from the related studies in other ways. Most of the past studies examined communication patterns through the statistical analyses of mean differences using an arbitrary operational definition of gatekeepers. Instead, this chapter will rely on multiple regression models that use more appropriate measurements of communication frequencies. From a broader perspective, this chapter is also closely related to a recent growing literature on knowledge management. Knowledge management addresses the generation, representation, storage, transfer, transformation, application, embedding, and protecting of organizational knowledge (Hedlund, 1994). In this literature, special attention has been paid to the distinction between tacit and explicit knowledge (Hedlund, 1994; Nonaka, 1994). In particular, tacit knowledge is considered one of the primary sources of competitive advantage, and the management of tacit knowledge arises as a challenging research agenda in this field. However, although several management tools have been suggested especially by practitioners and consultants, such as creation of a knowledge base of best practices built on interactive groupware technology, most of the related academic literature remains highly conceptual and theoretical, which makes it hard to test their arguments empirically and draw out managerial implications. The work of Nonaka and Takeuchi (1995) is exceptional. They proposed a middle-up-down model of organizational knowledge creation. In this model, knowledge is created by middle managers, who are often leaders of a team or task force, through a spiral conversion process involving both the top and the front-line employees. Thus, this process puts middle managers at the intersection of the vertical and horizontal flows of information within the company. In this regard, this chapter is closely related since our study is mainly concerned with the flow of information within an organization. However, our model of knowledge transformers differs from the middle managers in Nonaka and Takeuchi (1995) in that knowledge transformers emerge as a result of spontaneous knowledge communication within an organization, who do not necessarily coincide with the middle managers. Moreover, while their middle-up-down model relied exclusively on conceptual arguments and case studies, this study attempts to develop and empirically investigate the model of knowledge transformers, based on the actual information flow, without assuming ex ante who is at the intersection of the vertical and horizontal flows of information within an organization. Thus, the contribution of this chapter is threefold: the finding of the three-step flow of communication, the new estimation approach to communication studies in the organization, and the development of a new knowledge management model supported by empirical tests.

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2 Hypotheses One critical aspect of the innovation process is the ability of the innovating unit to gather information from external areas, transfer, and process within the organization. Oral communication is an important medium by which information and new ideas are transmitted across and within organizations. The related research has consistently demonstrated that oral contacts, rather than written materials, are the primary means used by engineers and applied scientists to discuss and transfer technical information and knowledge (Allen, 1977). Oral communication permits individuals to synthesize complex ideas rapidly and to give one another immediate feedback. Thus, this method of communication provides an efficient medium for information processing, and frequent oral communications are considered to contribute to improved problem solving and higher R&D performance (Baker, Siegman, and Rubenstein, 1967; Myers and Marquis, 1969; Ebadi and Utterback, 1984).

2.1 The emergence of gatekeepers Although oral communication is such an efficient medium, this remains expensive and costly, especially in the field of technical communication. If actors do not share a common coding scheme and technical language, their work-related communication will be less efficient and more costly (March and Simon, 1958; Dearborn and Simon, 1958; Katz and Kahn, 1966; Zenger and Lawrence, 1989). This lack of a common coding scheme usually leads to communication impedance. This communication impedance is associated with errors in the interpretation of messages. Communications across communication boundaries without knowledge on the part of one or both communicators of the other’s coding system may lead to misperceptions and an incomplete understanding of the message. The nature of a subunit’s work is a basic determinant of the cost of communicating. Work that is organizationally defined and operationalized is associated with local norms, values, and languages. This local orientation in tasks in turn generates a communication boundary that insulates the unit from outside areas. As we will argue later, development work in an R&D organization is typically locally oriented and holds localized coding schemes that make it difficult to communicate across organizations. While the evolution of local coding schemes impedes efficient communication outside the organization, the evolution of local coding schemes helps deal with local information processing requirements (Katz, 1982; Katz and Allen, 1982). Not only can large amounts of information be transmitted with relatively few symbols, but misinterpretations between actors are also minimized. Thus, the problem arises as to how organizations can effectively be linked to external information areas without impairing internal efficiency of communication. One way to deal with the difficulties of communicating simultaneously across and within organizations is through gatekeeping (Allen, 1977; Allen

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and Cohen, 1969). Individuals who are capable of understanding and translating contrasting coding schemes are called gatekeepers. With the help of gatekeepers, external information can flow into the organization in a two-step process. Gatekeepers are able to gather and understand external information, and then they are able to translate this information into terms that are meaningful and useful to other organization members. Thus, gatekeepers are strongly connected to external sources of information and are at the same time consulted frequently by other organization members. This flow of technical information implies that gatekeepers must be capable of understanding and translating contrasting coding schemes, and they must be strongly connected to both internal colleagues and external domains (Allen, 1977; Allen and Cohen, 1969). Thus, there exist at least three functions in communication networks: (1) outside information search; (2) translation of different coding schemes; and (3) internal communication. These functions are fulfilled by gatekeepers in order to overcome the trade-off between internal and external communication efficiencies faced by the organizations (Katz and Tushman, 1981; Tushman and Katz, 1980). Some studies have shown that the existence of gatekeepers is critical to high performance in development work (Tushman and Katz, 1980; Katz and Tushman, 1981) since they are able to resolve the communication impedance without sacrificing the efficiency of internal communication with local coding schemes. Hence, the total performance of development work turns out to be critically dependent upon a few key individuals: gatekeepers. 2.2 The effect of organization tenure The two-step flow of communication depends upon the existence of contrasting coding schemes that impede the efficiency of oral communication. Translation between contrasting coding schemes requires a special capability that is hard to obtain and thereby not common among organization members. The scarcity of this capability among organization members accounts for an inverse relation between extra-organizational communication and R&D performance found by several studies (Allen, 1977; Baker, Siegman, and Rubenstein, 1967; Shilling and Bernard, 1964). In order to acquire this translation capability, individuals have to be familiar with not only external coding schemes but also the local language shared among organization members. Clearly, it takes several years to get familiar with the latter language. The longer the organizational tenure, the more familiar with the local coding scheme. Thus, the translation capability requires a certain period of organizational experience. In contrast, information gathering activity is negatively related to the organizational tenure. Members with long organizational experience are likely to have fewer incentives to communicate outside the organization since it threatens to disrupt comfortable and predictable work practice and patterns of behavior (Katz, 1982; Katz and Allen, 1982; March and Simon, 1958). This tendency

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explains the not-invented here (NIH) syndrome found by Katz and Allen (1982). Thus, information translation and gathering capabilities seem mutually incompatible due to the contrasting effects of organizational tenure, which gives the following hypothesis: Hypothesis 1. The longer the organizational tenure, the more difficult to fulfill the function of information gathering. This hypothesis implies there is a potential difficulty with serving as a gatekeeper since information translation capability requires a certain amount of organizational experience. The gatekeeping function can be fulfilled by the same individual only when the amount of time for acquiring the translation capability is not long enough to diminish the tendency for external communication. Even in this case, however, information gathering capability remains mutually incompatible with internal communication capability. The internal communication capability includes the ability to attract organization members for technical discussion and communication. The internal communication stars are those individuals who are frequently approached and communicated with by other members in an organization. To serve as an internal communication star, once again it requires a longer period of organizational experience. As tenure in the organization increases, individuals attain a better understanding of organizational routines (March and Simon, 1958). Thus, organization members seek to have communication with others whose tenure in the organization is at least as great as their own (Zenger and Lawrence, 1989), particularly because useful advice, suggestion, and knowledge specific to the organization are likely to be obtained from those individuals with long tenure. This gives the following hypothesis: Hypothesis 2. Internal communication stars are likely to have longer organizational tenure than other members. Both Hypotheses 1 and 2 suggest the difficulty of obtaining gatekeepers in the organization, since organizational tenure tends to facilitate the emergence of internal communication stars in the organization while it impedes their external communication activities. As a result, we can obtain the following hypothesis: Hypothesis 3. Internal communication stars are less likely to communicate outside the organization. While this hypothesis has been repeatedly pointed out and empirically tested in the form of NIH syndrome, most of the previous studies on the role of gatekeepers seem to assume from the beginning that the capabilities required for gatekeepers are somehow available for a limited number of individuals in an organization. A few studies have reported that gatekeepers were not identified in some R&D organizations, but they have not explained why gatekeepers do not emerge in the communication network in the presence of contrasting

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coding schemes. The above argument suggests that the organizational tenure accounts for the difficulty of acquiring the capabilities necessitated for gatekeepers. The question arises, then, as to what alternative communication patterns are to be observed without the gatekeepers. 2.3 The effect of organization specific routines Once the organization faces the difficulty of capability acquisition required for the gatekeepers, one way to deal with this problem is through specialization: boundary-spanning individuals to deal with external communication and individuals to deal with internal communication. The necessity for this type of specialization especially arises when the organization is endowed not only with local coding schemes but also with organization specific routines. The organization specific routines involve rules and procedures employed implicitly and explicitly by the organization. While these types of routines may usually be described by local coding schemes, in some cases the routines can be expressed in quite general terms. Nevertheless, those routines still remain specific to the organization unless they are commonly adopted by other organizations. Thus, although organization specific routines and local coding schemes are closely related, they have to be carefully distinguished. Organization members cannot carry out the work efficiently without carefully paying attention to the routines (Nelson and Winter, 1982). Thus, the routines, whether specific to the organization or not, play an important role in any organizations to execute the current jobs smoothly. If those routines are specific to the organization, it implies that organization members have to spend substantial time getting acquainted with them. As a result, it is likely that only organization members with long tenure are well versed in organization specific routines. Accordingly, in the presence of organization specific routines as well as local coding schemes, those who are acquainted with both of them are capable of not only translating the outside information into the local coding schemes but also transforming this translated information into the knowledge consistent with the routines. Let us call these organization members knowledge transformers. These knowledge transformers need to be endowed with a knowledge transforming capability in addition to an information translation capability. Although both capabilities are closely related, the former differs from the latter in that new information is modified in order to fit with the existing organization routines. In the traditional gatekeeping function, external information is simply translated into organization specific language without adjusting to the current stock of organization routines. Thus, a knowledge transforming capability seems to require a longer period of organizational experience than an information translation one. As a result, it gets more difficult to acquire capabilities required for efficient internal communication in the presence of organization specific routines, which underscores the importance of Hypothesis 2. Therefore, the organization specific routines, together with local coding schemes, account for the difficulty of obtaining gatekeeping capabilities

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(external information search, translation, and transformation) simultaneously. Moreover, it also suggests the alternative pattern of communication. As pointed out above, external information is critical to organizational performance in R&D organizations (March and Simon, 1958; Cohen and Levinthal, 1990). But this information alone is of little use to the organization if their ideas cannot be incorporated into actual organizational routines. Thus, knowledge transformers capable of transforming external information into organization specific knowledge consistent with its routines are likely to be internal communication stars in R&D organizations with high performance. However, those knowledge transformers do not necessarily coincide with boundary spanning individuals (those who gather the outside information). Indeed, due to Hypothesis 3, knowledge transformers are more likely to be internal communication stars without frequent outside contacts. Boundary spanning individuals tend to be young organization members rather than senior members such as knowledge transformers. In consequence, without gatekeepers in the organization, a three-step flow of communication emerges in the presence of organization specific routines and local coding schemes. Hypothesis 4. There exists a three-step flow of communication in an organization without gatekeepers: (a) Young boundary spanning individuals bring new outside information directly to knowledge transformers. (b) Knowledge transformers transform this information into organization specific knowledge consistent with the routines and coding schemes. (c) That knowledge is transmitted to other organization members via knowledge transformers. The proposition that boundary spanning individuals are not internal communication stars was also maintained by Roberts and O’Reilly (1979). They reported that boundary spanning individuals are frequently isolated and often low performing. However, this three-step flow of communication differs from this proposition in that the boundary spanning individuals are closely connected to knowledge transformers. In addition, the traditional definition of gatekeeper cannot be applied in this case. The functions of a gatekeeper – information search and internal communication – are now performed by different individuals.1 This specialization can be a remedy for the difficulty of obtaining gatekeeping capabilities in the presence of organization specific routines as well as local coding schemes. It is important to note that this three-step flow of communication with knowledge transformers is not at all the only alternative to a two-step flow of communication. However, in the presence of organization specific routines, it is our contention that this three-step flow is instrumental in gaining high performance in R&D organizations due to the efficient way of information flow and distribution. Of course, it may still be possible to identify gatekeepers even in the

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presence of organization specific routines. In such a case, a two-step flow of communication via gatekeepers may be superior to a three-step flow of communication with knowledge transformers. However, as discussed above, not all organizations can afford gatekeepers with organization specific routines. As for organizations facing the difficulty of identifying gatekeepers, it is more likely and even more efficient that they turn to utilizing knowledge transformers in a flow of technical information instead of relying exclusively on gatekeepers. Thus, a three-step flow of communication can replace a two-step flow in the presence of not only local coding schemes but also of organization specific routines. 2.4 Type of R&D activities In the empirical part of this chapter, we are concerned with a communication pattern of an R&D organization that focuses on product development engineering with little emphasis on research. The discussion so far can be applied primarily to the case of development activities. In the case of research activities, the benefits and problems of utilizing outside information are somewhat different from those of development activities. Senior researchers usually stay in closer contact with external technical knowledge than senior development engineers. This is due to the more universal nature of research as opposed to technology (Allen, 1977). Moreover, in research organizations, researchers do not have the same need for the local coding schemes as engineers since the terminology and standards in research are not organizationally dependent. In addition, the importance of organization specific routines is significantly diminished here due to, once again, the universal nature of research. Thus, gatekeepers or knowledge transformers are of little use in research as opposed to development engineering organizations. In contrast, product and process development engineers have the most diverse information needs both within and outside the organization. The development of new products and processes require new ideas and up-to-date technological information. Moreover, development activities must operate within the existing organization routines such as rules, procedures, and standards. The rapid pace of technological change outside the organization and the heavy burden of daily design work make it difficult for most engineers to keep track of new outside technological information. In addition, the local nature of technology necessitates the evolution of local coding schemes, which is likely to impede external communication. Thus, in development organizations, a communication pattern both within and outside the organization plays a critical role in gaining high performance. In particular, the existence of organization specific routines as well as local coding schemes is conducive to the emergence of knowledge transformers rather than gatekeepers. Therefore, it is important to identify which types of R&D activities are engaged in the organization. The above argument concerning knowledge transformers and gatekeepers is only applicable to development activities.

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3 Settings and methods This study was carried out at the R&D division of a medium-sized Japanese machine tool firm. This firm produces a wide variety of machine tools such as NC lathe, machining center, and special machine tools, but all the products share a common technological core; mechatoronics technology consisting of mechanical and electronics technologies. This R&D facility primarily conducts product development work as opposed to basic research and technical service. It consists of three sections that work on the generation of new knowledge in the focused technical areas (i.e., mechanical design, electrical design, and system design) relevant to the development of new machine tools. These three technical areas in the facility serve as important sources of technical knowledge, expertise, and feedback. Most of the development activities on these areas in this facility involve the application of known facts and theory to solve a particular technical problem through exploratory study, design, and testing of new components or systems. In addition, while the pace of technological change in the field of mechatoronics technology remains moderate, machine tool firms in this industry introduce new products frequently into the market so that each firm has to keep track of new product developments outside the firm to be competitive. Thus, the type of R&D activities in our sample involves new product development activities with primary focus on the application of known facts and theory to solve a particular technical problem. As a result, this facility develops a number of organization specific routines in order to carry out experimentation, design, and testing efficiently. Moreover, since these development activities are closely related to the existing product line of the firm, there exist the firm specific coding schemes as well as the routines in this facility. This facility has four management levels – group leader, first-line manager, section leader, and division head. Only the division head concentrates on management activities; the other lower levels of management engage in daily R&D activities. Questionnaires were distributed to all of the division’s 63 engineers and engineering managers except for the division head. All questionnaires were returned.

3.1 Internal technical communication To collect communication data, we distributed a list of engineers in this division to all participants in this study. Each engineer was asked to check those engineers whom he approaches to discuss technical issues in his work at least once a week. In order to check the reliability of the respondents’ answers, we interviewed all respondents and asked whether they were indeed approached by engineers who had reported to approach them at least once a week. Surprisingly, most of the answers were confirmed in this interview (93%). We dropped the answers that were not confirmed. INTERNAL COMMUNICATION was defined as the total number of engineers who approached an individual engineer at least once a week. Thus, if

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the engineer is approached by three colleagues at least once a week, this measure takes on the value of 3. The higher value of this measure implies that the corresponding engineer is an internal communication star. 3.2 Boundary spanning activities In addition, each engineer was asked to name researchers and engineers outside the firm with whom he discusses technical issues and check how often he meets in a year. EXTERNAL COMMUNICATION was defined as the sum of this communication frequency. For example, if an engineer meets two outside engineers once a year and one researcher fourth times a year, this measure amounts to 1 × 2 + 4 × 1 = 6. In a similar manner, we also asked each engineer to name researchers and engineers of user firms with whom he discusses technical issues and check how often he meets them in a year.2 USER COMMUNICATION was defined as the sum of this communication frequency. While EXTERNAL COMMUNICATION was concerned with outside researchers and engineers who belong to outside institutions such as rival firms, universities, and trade associations, USER COMMUNICATION focused on those engineers who belong to user firms. Note that in those measures, we were not concerned with whether engineers approached or were approached by outside researchers for technical communication. Either case was counted as external technical communication or user communication. Since both measures took rather higher values compared to other variables, each measure was reevaluated by 4 values (0, 1, 2, 3). The cutoff points of these values were based upon the quartile of each measure’s empirical distribution.3 The other variable indicating the level of boundary spanning activities was CONFERENCE, which measures the number of meetings sponsored by professional societies that each engineer attended in the past year.4 3.3 Engineer’s characteristics The measures of engineers’ characteristics used in this study were JOURNAL, PATENT, PAPER, DEGREE, TENURE, and MANAGER. JOURNAL indicated the number of professional periodicals each engineer subscribes to and regularly reads. This measure can be also used as one indicating the level of boundary spanning activities (Allen, 1977). However, since this study is primarily interested in oral communication with outside domains, it was regarded as a measure of engineers’ characteristics. PATENT measures the number of patents that each engineer holds, including those pending. PAPER measures the number of papers published in professional journals since an engineer joined this organization. DEGREE is a dummy variable indicating whether an engineer holds master’s or doctoral degrees. TENURE is the number of years since an engineer joined this research division.

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Although we also collected data on each engineer’s age, this variable was highly correlated with TENURE. This result was expected since this firm only hires recent college graduates, and no engineers had prior experiences in other firms. Thus, we only used the variable TENURE. Since this measure took higher values, the log of this variable was used in the statistical analysis.5 MANAGER is a dummy variable indicating that an engineer’s position is the first-line manager or at a higher level. Table 9.1 represents the descriptive statistics of these variables. It should be noted that CONFERENCE, JOURNAL, PATENT, PAPER, and DEGREE are highly correlated, which may cause a multicollinearity problem in the regression analysis below. To deal with this problem, principal component analysis was used as a data reduction technique to determine if these variables formed a common dimension. This analysis extracted a single factor, EXPERTISE2, using a cutoff eigenvalue of 1.0. In addition, since only CONFERENCE indicated the level of boundary spanning activities among those highly correlated variables, we also extracted a single factor, EXPERTISE1, from JOURNAL, PATENT, PAPER, and DEGREE. It should be noted that Table 9.1 shows that INTERNAL COMMUNICATION is highly correlated with TENURE, while its correlations with EXTERNAL COMMUNICATION and USER COMMUNICATION are not significant. This result is consistent with Hypotheses 2 and 3. In contrast, TENURE is not significantly correlated with most of the variables indicating boundary spanning activities, which does not necessarily support Hypothesis 1. However, these results should be interpreted with caution because the correlation matrix does not control for the effects of other variables. In order to obtain more sophisticated results, we need to resort to multiple regression analysis, which will be described next.

3.4 Estimation methods According to Hypothesis 1, boundary spanning activities are negatively related to organizational tenure. This can be tested by estimating the following regression model:  þ m; X ¼ ZZ

2 Þ m ð0; s

ð9:1Þ

 represents explanwhere X denotes the level of boundary spanning activities, Z atory variables including organizational tenure, and m is a measurement error. Thus, Hypothesis 1 can be tested by estimating the corresponding unknown parameter in Z, which is expected to be negative. To test Hypotheses 2 and 3, it is of critical importance to identify internal communication stars in the organization. The previous studies used a number of slightly different criteria to empirically define internal communication stars such as the top fifth of an internal communication distribution (Allen, 1977; Tushman and Katz, 1980; Katz and Tushman, 1981) and one standard deviation

.17 .07 .35*** .29*** .46*** .33*** .15 .39*** .40*** .40*** .40***

1

3

.28** .42*** .23* .43*** .12 .24* .29** .21* .25** .08 .06 .15 .31** .04 −.12 .28*** .24** .34*** .25***

2

.49*** .73*** .73*** .55*** .11 .15 .80***

4

.36*** .93*** .97*** .41*** .11 .18

5

.40*** .37*** .19 .21* .38***

6

Correlation 8

9

10

.93*** .48*** .51*** .20 .09 .01 .25** .21* 07. .41*** .16 .27*** .15 .25***

7

N = 63 * p < 0.1 ** p < 0.05 *** p < 0.01

a

Note: EXPERTISE1 summarizes the data of JOURNAL, PATENT, PAPER, and DEGREE. Similarly, EXPERTISE2 summarizes these data and CONFERENCE.

2.88 1.25 1.07 5.12 1.20 7.81 20.24 0.27 0.61 0.46 1.80 1.80

Means s.d.

1 INTERNAL COMMUNICATION 2.35 2 EXTERNAL COMMUNICATION 0.87 3 USER COMMUNICATION 0.98 4 CONFERENCE 1.44 5 JOURNAL 0.62 6 PATENT 2.46 7 PAPER 3.30 8 DEGREE 0.08 9 TENURE 2.78 10 MANAGER 0.29 11 EXPERTISE1 −2.69 12 EXPERTISE2 −2.69

Measures

Table 9.1 Descriptive statistics

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183

above the mean of communication frequencies (Allen and Cohen, 1969; Frost and Whitley, 1971). However, these criteria are somewhat arbitrary, and different cutoff frequencies may lead to different statistical results. Moreover, the information loss when using a categorical identification of communication stars may also lead to imprecise interpretations. One way to deal with these problems is not to identify internal communication stars. Similar to the above regression model (9.1), communication frequency can be used as a dependent variable. In this manner, the problems of arbitrariness and information loss can be avoided. In addition, after identifying internal communication stars, most of the related studies relied on a comparison of means of various variables between communication stars and non-stars. However, this type of statistical analysis did not control for the influences of other related variables, suggesting that completely different results might be obtained after excluding these influences. In order to overcome this potential problem, we estimated the following multiple regression model: y ¼ X b þ Zg þ ε;

ε ð0; s2 Þ

ð9:2Þ

where y denotes internal communication frequency, and Z represents control variables such as organizational tenure. b and g are unknown parameters to be estimated. ε indicates a measurement error. According to Hypothesis 2, internal communication stars tend to have long organizational tenure. This implies that the parameter corresponding to organizational tenure in g has a positive value. Hypothesis 3 predicts that internal communication stars are less likely to communicate outside the organization. If gatekeepers exist in the organization, b has to take a positive value; otherwise, internal communication stars (knowledge transformers) are unlikely to be boundary spanning individuals. Thus, this parameter constitutes our primary concern in the empirical analysis. Note that due to the definitions of the level of boundary spanning activities and communication frequency in this study, the multiple regression estimations in (9.1) and (9.2) have to be carefully designed. Since boundary spanning activities and communication frequency take only non-negative values when these variables are used as dependent variables, the estimations have to rely on Tobit rather than OLS in order to obtain statistically consistent estimates.

4 Results Table 9.2 presents the regression results for (9.1), which estimates the determinants of boundary spanning activities. Hypothesis 1 states that boundary spanning individuals are likely to have short organizational tenure. However, in the case of USER COMMUNICATION, the coefficients for TENURE are positively significant. Although this result obviously contradicts Hypothesis 1, it should be noted that the coefficients for MANAGER are negatively significant. Since

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Table 9.2 Determinants of boundary spanning individuals (TOBIT) Measures

JOURNAL PATENT PAPER DEGREE EXPERTISE1 TENURE MANAGER Constant

(1)

(2)

(3)

(4)

External communication

User communication

1.024*** 0.106 −0.026 −0.832

0.160 0.030 0.6E-02 −0.107

0.657 −1.648 −2.913

(5)

(6)

Conference 5.771*** 1.541** −0.405 11.552*

0.438** 0.253** 0.909 1.259*** 1.303*** −3.421 −0.781 −1.329*** −1.252*** −11.060 −3.024 −2.763** −2.732** −7.998

4.622*** −0.048 −3.458 −10.884

a

N = 63 * p < 0.1 ** p < 0.05 *** p < 0.01

this organization uses a seniority system, the ages of managers are higher than those of non-managers in general. It may be that senior engineers who are not in a management position communicate heavily with users. This result seems to reflect the firm’s policy for marketing and customer relations rather than the effect of tenure on communication frequency.6 Hence, the effect of TENURE on USER COMMUNICATION should be disregarded in the test of Hypothesis 1. As for EXTERNAL COMMUNICATION and CONFERENCE, TENURE does not make significant contributions to the explained variation in the levels of these boundary spanning activities. Once again, this implies that Hypothesis 1 is not completely supported. Thus, the results in Table 9.2 suggest that boundary spanning activities are not associated with the length of organizational tenure in this organization. Table 9.3 presents the regression results for (9.2), which examines the characteristics of internal communication stars. In contrast to Table 9.2, Table 9.3 shows that organizational tenure is positively related to internal communication frequency in all models. This supports Hypothesis 2, which states that internal communication stars (knowledge transformers) are likely to have longer organizational tenure. Those frequently approached by organization members have a long experience in the organization. The results also suggest that of the four boundary spanning activities, only CONFERENCE has related to the frequency of internal communication. However, once variables measuring engineers’ characteristics are included in the regression model, CONFERENCE also loses its significance as shown in columns (4) and (5). Moreover, its magnitudes decrease sharply when those variables are introduced into the regression. This implies that the impact of CONFERENCE on internal communication frequency is limited once the relevant variables are controlled.7 These results suggest that internal communication

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185

Table 9.3 Determinants of the frequency of internal communication

Measures

(1)

(2)

Technical expertise

(3)

(4)

(5)

(6)

Information Full model gathering

EXTERNAL 0.144 COMMUNICATION USER −0.574 COMMUNICATION CONFERENCE 0.260** JOURNAL 0.238 PATENT 0.505*** PAPER −0.131* DEGREE 0.534 EXPERTISE1 0.879*** EXPERTISE2 TENURE 2.263** 3.063*** 3.483*** MANAGER 1.861 1.868 1.877 Constant −5.252* −6.537** −7.653**

0.216

0.218

0.210

−0.846

−0.734

−0.731

0.080 0.101 0.518** −0.134* −0.061

0.075

0.772 0.860*** 2.824** 3.581*** 3.580*** 1.318 1.358 1.365 −6.031** −7.424** −7.310**

a

N = 63 * p < 0.1 ** p < 0.05 *** p < 0.01

stars do not actively engage in boundary spanning activities. Although Hypothesis 1 is not supported, this result is consistent with the one found in Table 9.2. Since internal communication stars need to have a long experience in the organization, it is quite likely that these engineers are not boundary spanning individuals with short organizational tenure. Thus, the analysis shown in Table 9.3 supports not only Hypothesis 2 but also Hypothesis 3, which states that gatekeeping functions are fulfilled by different individuals: boundary spanning individuals and knowledge transformers. As a result, it follows that there exists a three-step flow of communication in this organization as stated in Hypothesis 4. However, a division of labor between boundary spanning individuals and knowledge transformers is only a necessary condition for the three-step flow of communication. We need to examine whether boundary spanning individuals communicate directly with knowledge transformers in the organization in order to demonstrate the three-step flow of communication. If they communicate with other organization members rather than knowledge transformers, the flow of technical information in this organization turns out to follow more than or less than three steps. In order to examine this case, we have to rely on the categorical definition of knowledge transformers and boundary spanning individuals, which may contradict our position of using the multiple regression. Yet, it should be noted that our criticism regarding the categorical definition is mainly concerned with the effects of other variables on communication frequency or vice versa. In this case, we do not have to rely on the categorical definitions of gatekeepers or internal

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communication stars, and the analysis can be improved using the continuous variable such as communication frequency. However, for the purpose of testing whether boundary spanning individuals communicate directly with knowledge transformers, we have to identify, first of all, who are boundary spanning individuals and knowledge transformers in the organization. So, it should be noted that while the following analysis suffers from the arbitrary definition of boundary spanning individuals and knowledge transformers, the analysis still serves to give some information on whether there exists a three-step flow of communication in the organization. To check whether the communication pattern follows the three-step flow, Table 9.4 presents the percentage of boundary spanning individuals who communicate with knowledge transformers. Engineers are defined as knowledge transformers or boundary spanning individuals when they have a value of one standard deviation above the mean of the corresponding variable. For example, if an engineer’s internal communication frequency is over one standard deviation above the mean, he is regarded as an internal communication star. According to this criterion, eight engineers are identified as knowledge transformers, and only one of them satisfies the criterion of a boundary spanning individual as well. Once again, this result supports Hypothesis 3. Regarding Hypothesis 4, although the average tenure of boundary spanning individuals is not significantly below that of all organization members, more than 60% of the boundary spanning individuals communicate with knowledge transformers in each of the three boundary spanning activities. Since the number of knowledge transformers identified in this analysis is eight out of the total 63 engineers, the probability of communicating with those knowledge transformers by chance amounts to 12.7%. As shown in the z statistics in Table 9.4, the probability is significantly larger than 12.7% that these boundary spanning individuals communicate with knowledge transformers. Hence, part (a) of Hypothesis 4 is supported here, except that boundary spanning individuals are young. Thus, it can be inferred from this result that boundary spanning individuals bring new information directly to knowledge transformers, and then knowledge transformers transmit it to other organization members: the three-step flow of communication. Table 9.4 Percentage of boundary spanning individuals who communicate with transformers Boundary spanning activities

Number of BSIa

Communicate with transformers (%)

Z statistics H: p = 0.127 K: p > 0.127

EXTERNAL COMMUNICATION USER COMMUNICATION CONFERENCE

13

61.5

5.29

10 4

60.0 75.0

4.49 3.74

a

BSI stands for boundary spanning individuals.

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5 Concluding remarks 5.1 Different results The results of this study show that there exists a three-step flow of communication in the organization without gatekeepers. Except for one engineer, no knowledge transformers actively engage in boundary spanning activities. Instead, the information gathering activities are performed by a different set of engineers, who bring outside information directly to knowledge transformers. This pattern of communication is in sharp contrast to the two-step flow of communication suggested in previous studies. The different results may be due to the different statistical procedures used to identify the communication patterns. In previous studies, gatekeepers were defined using a comparison of boundary spanning activity means between internal communication stars and other members. However, in this comparison, there were possible influences from other related variables. Thus, it is quite likely that after controlling for these influences, boundary spanning activities of internal communication stars may not be significantly different from those of noninternal communication stars. Moreover, slightly different and arbitrary criteria were used in past studies to identify internal communication stars. This study dealt with these potential problems by using a multiple regression analysis and communication frequency as the dependent variable. Another explanation for the different results may be that new methods of product development require outside technological information to be transformed into organization specific knowledge before it can be effectively utilized in organizations. In particular, successful product development projects are currently carried out using overlapping development steps and multifunctional teams that usually include supplier involvement at earlier stages than when the previous studies on communication were conducted 20 years ago (Imai, Nonaka, and Takeuchi, 1985; Clark and Fujimoto, 1991). This type of product development is expected to shorten the development time, but at the same time it requires a high level of coordination and cooperation among product development members. In these situations, while outside technical information is of critical importance, it has to be quickly modified and adapted to development (i.e., organization) specific routines. If not, attempting to incorporate the new information into development projects may cause serious confusion due to overlapping development steps. Hence, the recent emphasis on overlapping development stages and other methods of product development may require a division of labor between boundary spanning individuals and knowledge transformers, thus giving rise to a three-step flow of communication. In addition, Japanese lifetime employment and seniority systems may have some effect on the emergence of knowledge transformers in this organization. Since none of the engineers in this organization have working experience in other firms, organization specific knowledge probably plays a particularly important role in daily R&D activities. If engineers from other firms were constantly

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entering this organization, the importance of organization specific knowledge might not be so significant. In such a case, the two-step flow of communication might be observed in this organization. In any event, this study strongly suggests that the role of gatekeepers should be examined critically in R&D organizations. Since organizational knowledge creation in large measure depends upon communication and information processing capacities of the organization, proper management of communication flows in the organization is crucial. If there emerge knowledge transformers in the organization, their capacities of knowledge transformation should be frequently examined and promoted through appropriate job rotation and facilitating communication with boundary spanning individuals, which may be overlooked in the organization with a two-step flow of communication. 5.2 Integration into problem solving activities In this chapter, we have examined the roles of gatekeepers and knowledge transformers in information gathering and distribution activities. Yet, while they greatly contribute to high performance of an R&D organization, as we have discussed above, it is important to note that information gathering and distribution are only the first step to management of technology and knowledge. However important and valuable information gathered from outside areas is, the information alone does not generate high organizational performance without integrating it into each member’s problem solving activities in an R&D organization. In the case of a two-step flow of communication, outside information is distributed via gatekeepers. On the one hand, the advantage of this information channel lies in a shorter step of information flow, as compared with a three-step flow of communication. As a result, more precise information is likely to be transmitted to other organization members, leading to their efficient problem solving activities. In this case, the integration into problem solving activities approximately equates with information gathering and distribution with local coding schemes because it is usually left to each organization member how to utilize the outside information provided by gatekeepers in an R&D organization. The type of technical communication discussed in this chapter is the result of spontaneous behavior of each organization member. It completely differs from administrative communication along with a formal authority system of an organization. The role of gatekeepers here is limited to getting rid of communication impedance caused by contrasting coding schemes, which in turn leads to stimulating, rather than controlling, the creativity of organization members. On the other hand, in the presence of organization specific routines, it is getting more difficult to identify those gatekeepers. Even if the gatekeepers are identified in the organization, other organization members may soon find it difficult to utilize the outside information transmitted by gatekeepers without further suggestion and guidance as to how to utilize that information within the organization. For efficient problem solving activity to be carried out, the

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outside information has to be further transformed so as to be consistent with organization specific routines. Without this knowledge transformation capability, any gatekeepers might not be able to contribute to problem solving activities inside the organization. Thus, the emergence of knowledge transformers further facilitates the integration of information gathering and distribution into each member’s problem solving activities, providing further suggestion and guidance concerning the outside information gathered by boundary spanners All in all, the roles of gatekeepers and knowledge transformers somewhat differ in terms of the integration into problem solving activities. Knowledge transformers not only translate the outside information into local coding schemes as gatekeepers but also transform it so as to be consistent with organization routines. Thus, knowledge transformers turn out to be more involved in the integration of information gathering and distribution into each member’s problem solving activities. 5.3 Limitation Finally, we would like to point out some of the limitations in this study that require future research. First of all, the results in this study were based on a single organization with a small sample (63 engineers). So, caution must be exercised in generalizing to other organizations. Second, although the knowledge transforming function was hypothesized in this study, no data were available that can directly test the importance of this function. These data should also be collected in the future. In spite of these limitations, we strongly believe that the findings in this chapter serve to shed new light on technology management in R&D organizations. In particular, the emergence of knowledge transformers and the resulting three-step flow of communication deserve much attention since they are in a sharp contrast to gatekeepers and a two-step flow of communication. Moreover, the conditions that give rise to this new phenomenon of the three-step flow of communication are not at all specific to the small sample of our study. It seems that a number of R&D organizations take advantage of the evolution of organization specific routines. We have argued that in the presence of such routines, knowledge transformers are likely to emerge in an R&D organization. We hope our findings stimulate the related empirical studies that examine our hypotheses in various organizations in the future.

Notes 1 Translation of different coding schemes might be carried out by both boundary spanning individuals and knowledge transformers. However, the latter will be more efficient due to longer organizational experience. 2 User firms refer to those that purchased machine tools this research division developed. 3 We also estimated regression models in this chapter using the raw data for these measures. The results concerning the hypotheses remained the same. 4 We also collected the data of the number of papers each engineer presented at professional societies in the last year. However, it turned out that only two engineers had

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opportunities to present their own papers at professional societies, and other members did not have such opportunities. Thus, we did not include this variable in our analysis. 5 Once again, we estimated regression models using the raw data for TENURE. The results remained the same. 6 Our interview with this firm’s managers confirmed this conjecture. 7 To check the interaction effect between CONFERENCE and engineers’ characteristics, we estimated a model that included the interaction term of CONFERENCE and EXPERTISE2 into column (5). The results suggested that only EXPERTISE1 had a positive impact, and CONFERENCE and the interaction term were not significant.

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Part IV

Measuring the black box Innovation flow matrix and policy evaluation

193

10 Model of intersectoral flow of technology using technology and innovation flow matrices

1 Introduction Part IV is concerned with measuring the black box by estimating a new concept of an innovation flow matrix. In this chapter, the theoretical foundation of this innovation flow matrix is developed that accounts for complementarity among heterogeneous technologies. This complementary relation constitutes a major characteristic of technological change (Rosenberg, 1982). The importance of complementarity implies that sufficient attention should be paid to intersectoral effects of technological change. For example, it is acknowledged that a few key industries, called general purpose technology (GPT) sectors, play an important role in generating economic development and growth (see, for example, Bresnahan and Trajtenberg, 1995; Helpman, 1998; Harada, 2010a, chapter 3). However, the endogenous growth literature has not yet fully incorporated the intersectoral effects of technological change into its formal models. Although a product-variety version of the endogenous growth literature (Grossman and Helpman, 1991) is a multi-sector model, it assumes a fixed and identical input structure for all sectors, so that asymmetric intersectoral effects of technological change are excluded a priori. The literature on input–output analysis takes the intersectoral relations in commodity transactions into account. In addition, a large number of empirical input–output-based studies have shifted the attention from commodity transactions to R&D spillovers. They have constructed technology flow matrices showing intersectoral technology flows (or intersectoral spillovers) (Scherer, 1984; DeBresson, 1996; Keller, 1997; Kortum and Putnam, 1997; Verspagen, 1997; Meyer, 2002; Nomaler and Verspagen, 2008; Montresor and Marzetti, 2009; Düring and Schnabel, 2000; Gehringer, 2012).1 These matrices trace the intersectoral technology flows on the basis of patent citations, industrial publications, and university patenting (Meyer, 2002). Alternatively, sectorlevel R&D data and coefficients of input–output tables are used to approximate technology flows (see, for example, Keller, 1997; Montresor and Marzetti, 2009). These empirical studies have succeeded in revealing the importance of intersectoral technology flows in generating economic growth. However, their microfoundations are still ambiguous, because they are not built upon a general equilibrium framework.

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Although some attempts have been made to fill the gap between input–output analysis and the endogenous growth literature (Los, 2001; Harada, 2015a; chapter 5), an input–output model that completely accounts for the intersectoral aspect of technological relations with a rigid microfoundation remains undeveloped. The empirical work by ten Raa and Wolf (2000) is one of a few exceptions, in that it derived the intersectoral spillover relations from a standard neoclassical general equilibrium framework. However, this chapter differs from their work in the sense that we explicitly model the production of technology in sectors and regard R&D spillovers as the result of technology transactions across sectors, rather than as external economies. One of the advantages of this approach lies in the new theoretical perspective on intersectoral technology flows (see, for example, Harada, 2015a and Chapter 5) and its computational ease and simplicity. This chapter aims to build a bridge between endogenous growth and input– output literature by using an intersectoral general equilibrium model that directly focuses on the propagation patterns of technology and innovation across sectors. This model assumes that an economy stays on a balanced growth path from the beginning, which is the result of an endogenous growth mechanism. In addition, this model assumes that the technology and innovation flow matrices relate technology and innovation to each intermediate sector. Then, we introduce the production structure of technology, in which technology is a system consisting of many (technology) components (for example, automobile technology consists of material, mechanical, electronics, chemical, and information and communication technologies as technology components). So, the latter technology components are used as inputs to produce the technology. Meanwhile, technology and innovation flow matrices determine the intersectoral technology flows. In this model, technology is not given but is produced through technology transactions. Based on this technology production structure, we can empirically evaluate how productivity shocks (as deviations from a balanced growth path) are propagated across sectors, which has been overlooked in the endogenous growth literature. Moreover, we are able to reveal the underlying microfoundation for technology and innovation flow matrices. Hence, the model in this chapter blends both endogenous growth and input–output models in a consistent manner. However, our model is not a mere blend of these two approaches. First, it sheds new light on the mechanism of intersectoral technology flows by explicitly modeling the production of technology using diverse technology components as inputs. In other words, while related models leave aside the mechanism of technology production, the model in this chapter focuses on this production structure. Second, we conceptually distinguish between technology and innovation flow matrices. In this study, “technology flow matrix” refers to the pattern of technology transaction without innovation. In other words, this matrix describes the transaction patterns of technology components for each technology (for example, it describes how automobile technology is produced using mechanical, electronics, chemical, and IT technology components as inputs). At this stage, no

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innovation takes place in each technology component. Once innovation occurs in some technology component, an “innovation flow matrix” describes how a given innovation is propagated across sectors. This matrix is required because innovation might change the current transaction pattern of technology components. For example, in the production of automobile technology, innovation in information technology components might reduce the demand for mechanical technology components. These matrices should be conceptually distinguished from a standard input–output matrix because the latter primarily describes commodity transactions rather than technology transactions themselves, though both are closely related.2 Third, our technology and innovation flow matrices do not necessarily refer to technology spillovers alone; they also describe the pattern of intersectoral technology flows as a result of economic activity across sectors where the value of each technology component is evaluated at factor prices and no free lunch is assumed. In short, the main contribution of this chapter is to reveal the economics of technology production and intersectoral technology flows in a general equilibrium framework. As a quantitative exercise based on this model, its theoretical predictions are examined using recent Japanese R&D investment data collated at the two-digit standard industrial classification (SIC) code level. These data indicate that technology shocks are generally localized within sectors, whereas asymmetric intersectoral effects are observed in GPT sectors such as IT, precision instruments, and motor vehicles. The rest of this chapter is organized as follows. In Section 2, a basic model of intersectoral technology flows is described, and its equilibrium properties are derived. Section 3 examines the intersectoral effects of technology shocks along with a simple quantitative analysis using recent Japanese R&D data. Section 4 presents the conclusions.

2 The model In this section, a model of intersectoral technology flows is developed, based on Harada (2018b). This model differs from the related literature as the production of technologies is explicitly specified. 2.1 Outline of the model Consider a discrete time closed economy with one final product (commodity) and n technology components, the latter being produced by intermediate (technology component) sectors. An intermediate sector supplies one unit of technology to itself and to other intermediate sectors, as well as to the commodity producer. Both the intermediate and commodity sectors use labor and technology components as inputs. Thus, in this economy, physical intermediate inputs are assumed away to simplify the analysis and focus attention on technology and innovation aspects of the economy. Because technology exists in a non-physical form that is similar to blueprints (i.e., knowledge), technology components are

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regarded as representing knowledge. Knowledge is duplicated without additional costs. Therefore, the quantity of technology components has no relevance and the quality level alone matters in this economy. We assume that the economy is already on a balanced growth path that is caused by some endogenous R&D investment, as described in the endogenous growth literature. Although it is not difficult to explicitly incorporate this endogenous growth aspect into the model, we prefer to maintain the assumption of the balanced growth path from the beginning. The reasons for this are twofold: first, this assumption makes the model less complicated and easier to understand, and second, the growth endogeneity has no direct implication to our empirical exercise. Because the balanced growth path has already been well accounted for by the related literature, we will focus on the intersectoral technology flows and innovation along the balanced growth path. In other words, the model in this chapter is concerned with the propagation mechanism of a given innovation rather than the innovation mechanism per se. In each period, a technology component has to be produced by the corresponding intermediate sector. Each technology component is produced by using labor and its own and other technology components as inputs. Because this model is directly concerned with the production of technology, a change in the quality level is referred to as “technological change” or “innovation”. This is caused by demand or technology shocks, which are deviations from the balanced growth path. As long as the prices and production functions of the intermediate sectors remain the same, innovation does not take place as the quality of each component is fixed. Given the result of past innovation, each sector produces technology of a specified quality. The commodity sector uses the produced technology components and labor for the production of the commodity. Thus, two stages of production prevail in this economy. In the first stage, a commodity producer announces the demand for each technology component. Following this announcement, the technology components are produced by intermediate sectors. In the second stage, the commodity producer produces the commodity and supplies it to the household. Perfect foresight is assumed, such that the realized quality level of each technology component in the first stage is correctly predicted by the intermediate sectors and the commodity producer. It is also assumed that the technology components and the commodity are produced according to an o-ring type production function. Kremer (1993) proposes an o-ring production function that incorporates the fact that mistakes in any series of tasks can dramatically reduce the product value. In this chapter, we suppose that the production function represents a technological system. This consists of a series of interrelated technology components or component technologies. Thus, in our model the series of tasks are regarded as a series of technology components that are provided by their own sector as well as other sectors in an economy. In this model, because the economy is assumed to stay on a balanced growth path, equilibrium consists of static assignment of quality levels, prices, labor, and

Model of intersectoral flow of technology

197

197

consumption across intermediate and commodity sectors. More specifically, equilibrium is defined as: 1 2 3 4 5 6

determination of factor prices for technology components paid by intermediate sectors; determination of quality levels for technology components; determination of factor prices for technology components paid by a commodity producer; labor assignment for each intermediate sector and commodity producer; labor market clearing condition; determination of consumption of a commodity by a representative household.

These prices, payments, and labor employment and consumption are to be determined such that the intermediate and commodity sectors maximize their profits and the representative household maximizes intertemporal utility while satisfying the labor market clearing condition. Note that because the quantity of technology components and commodity has no relevance in this model, the market clearing condition matters only for labor. 2.2 Production of technology There is an indefinite supply of potential firms in the intermediate sectors, and all have the production function qj ¼ Aj ljα

n Y

qi;j ;

ð10:1Þ

i¼1

where the subscript j refers to the jth sector, Aj and lj denote the productivity level and labor employed in this sector, qi;j is the quality (technology) level of the technology component i used in the production of the jth technology component, and 0 < α < 1. As we described above, each technology component is assumed to represent specific knowledge corresponding to its technology field. Therefore, the production function (10.1) specifies the production of knowledge in which technical knowledge is produced using the variety of knowledge as inputs. When the technology component as knowledge is produced, it is supplied to its own sector, other intermediate sectors, and the commodity sector.3 To simplify the notation and algebra, capital is not included in this production function. This exclusion is justifiable because its inclusion does not affect the qualitative results of this chapter. In addition, we are primarily interested in empirically examining intersectoral flow of productivity shocks, which are independent of capital and labor inputs (as the Solow residuals indicate). To highlight and analyze these intersectoral innovation flows more explicitly, we take the knowledge perspective in which each technology component is

198

Measuring the black box

198

regarded as representing specific knowledge. Indeed, many final and intermediate products consist of a number of parts and materials. Consequently, the increasing division of knowledge and labor prevails to such an extent that most of the products cannot be produced without outsourcing. From the knowledge perspective, this implies that each product is produced using the diverse knowledge. Therefore, the production function (10.1) reflects this division of knowledge in the production of knowledge. The critical difference here is that the intersectoral model in this chapter allows for the diversity of technological interdependence among technology components, while the multi-sector endogenous growth model that is used in the literature only assumes a fixed symmetric interdependence. Knowledge is assumed to be protected by a patent so that it cannot be used without payment to the corresponding supplier (i.e., owner). The supplier of technology component i in the jth sector with the quality level of qi;j then receives a payment of pðqi;j Þ from the sector. The risk neutral jth sector maximizes the profits as  j Aj l α max P j q;l

n Y

qi;j 

X

pðqi;j Þ  wlj ;

ð10:2Þ

i

i¼1

 j denotes the quality adjusted price of the jth technology component. As where P  j is derived from the sum of payments received from intermediate we will see, P sectors and the commodity sector (see (10.19)). Meanwhile, w is determined to equate a labor market clearing condition (see (10.16)). Hence, it would be reasonable to assume that each intermediate sector takes them as given. However, the payment given to the ith supplier,pðqi;j Þ, is directly determined by the choice of the quality level, qi;j . Therefore, each sector maximizes its profits with respect to qh;j and lj in (10.2), taking into account that pðqi;j Þ is affected by its own choice. The first-order conditions are:  j Aj l α P j

n Y

qi;j ¼ p0 ðqh;j Þ;

ð10:3Þ

i6¼h

lj ¼

αAj Pj w

1

n Y

1 !1α

qi;j

:

ð10:4Þ

i¼1

From (10.1) and (10.4), we have wlj ¼ αPj ;  j qj . This suggests that the labor budget share is α. where Pj ¼ P

ð10:5Þ

Model of intersectoral flow of technology

199

From (10.3) and (10.4), we derive 1 !1α n Y α 0 α α p ðqh;j Þ ¼ α Aj Pj w qi;j qh;j 1α :

199

ð10:6Þ

i6¼h

2.3 Factor price Intermediate suppliers provide one technology component unit inelastically to each intermediate sector and the commodity producer. Suppose that the quality levels are represented by a quality ladder (see, for example, Aghion and Howitt, 1992) qi;j ¼ qmi;j ;

ð10:7Þ

where q > 1 and mi;j takes positive values, representing the current quality level. Using (10.7) and (10.6), it is rewritten as n P n P mi;j

mi;j

jw Þ q p0 ðqh;j Þ ¼ ðαα Aj P 1 α 1α

mh;j þ i¼1 1α

i¼1 1þð1αÞm

 j w Þ qh;j ¼ ðαα Aj P 1 α 1α

h;j

:

ð10:8Þ

We assume free entry into each intermediate sector so that each supplier earns zero profits. Following Kremer (1993), we have integrated this marginal condition with respect to qh;j and obtain the factor price schedule of technology component h as  j qj ¼ ð1  αÞyh;j Pj ; pðqh;j Þ ¼ ð1  αÞyh;j P mh;j ; yh;j ¼ X n mi;j

ð10:9Þ ð10:10Þ

i¼1

 j qj and where Pj  P

X

yh;j ¼ 1. Therefore, we can confirm that the sector

h

indeed earns zero profits because αPj is paid to labor and higher quality components receive more payments. 2.4 Technology and innovation flow matrices As we have described above, each technology component represents knowledge and can be duplicated without additional costs. Hence, the allocation of a technology component across sectors does not require the equality of supply and demand. Instead, we assume that it is allocated to each sector as mi;j ¼ Wi;j mi ;

ð10:11Þ

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Measuring the black box

200

where Wi;j > 0 is the degree of technology transfer from the ith technology comn X mh;i measures the total quality ponent to the jth intermediate sector and mi  h¼1

level of the ith component. The magnitude of Wi;j  0 is determined based on technological interdependence between the two components and the absorptive capacity of the jth sector. Therefore, it is assumed to be constant in this model. Note that this magnitude must be non-negative. If it is negative, then the jth sector has no incentive to use the ith technology component as an input. In this case, Wi;j becomes zero. Because duplication costs are zero, we X do not require Wi;j ¼ 1. j

Without productivity shocks, the matrix C ¼ ½Wi;j  can be referred to as a technology flow matrix. In other words, this matrix shows the technological interdependence among technology components in a steady state. However, when productivity shocks take place, the innovation linkages cannot be measured by C. To see this, from (10.7) and (10.11) the productivity growth can be derived as ^ qi ; qi;j ¼ Zi;j Wi;j ^

ð10:12Þ

_ where ^ denotes the growth rate (e.g., q^  q=q; q_  @q=@t), and Zi;j represents the impact of innovation of the ith component on the current productivity of the jth sector. If Z > 0, innovation is complementary to the current productivity. Conversely, if Z < 0, then it is substitutable and has a negative effect on the current productivity. Finally, Z ¼ 0 implies that there is no innovation effect. From (10.1) and (10.12), we obtain 2 3 2 30 2 3 2^ 3 ^l g1;1 g1;n 2 ^q1 3 ^ q1 A1 1 7 6 7 6 7 6 . 7 6 6 7 6 . .. 7 .. .. 7 6 .. 7 6 . 7¼6 7; 7 þ α6 ... 7 þ 6 .. 76 . . 4 . 5 6 4 . 4 5 4 5 4 5 . 5 ^l ^n ^ ^qn qn gn;1 gn;n A n where gi;j  Zi;j Wi;j . In matrix notation, this is rewritten as ^ ¼A ^ þ αL ^ ^ þ G0 Q: Q

ð10:13Þ

G0 indicates how productivity shock in each sector is related to the others. ^ yields Solving this for Q ^ þ αLÞ: ^ ¼ ðI  G0 Þ1 ðA ^ Q 1

ð10:14Þ

In this equation, ðI  G0 Þ is a familiar form of a standard Leontief model and corresponds to an innovation flow matrix. This matrix allocates productivity shocks to each intermediate sector and determines quality levels in a new steady state. Then, the allocation of a technology component across sectors follows a technology flow matrix, Y. If technological interdependence and

Model of intersectoral flow of technology

201

201

absorptive capacity do not change after productivity shocks, Y remains the same as before. One implication of this equation is that growth rates critically depend on this innovation flow matrix. For example, even if several countries face the same technology shocks, their growth rates will differ if their innovation flow matrices are not the same. Moreover, the innovation flow matrix immediately reveals the following result: Proposition 1. Sectoral technology shocks induce sectoral innovation asymmetrically. 1

The technology shocks induce asymmetric innovation unless ð1  G0 Þ ¼ 1 0 ð1  G0 Þ . For example, even if technology shocks take place in the jth sector, this sector may not be able to increase quality levels substantially. Instead, other sectors could gain from the shocks and significantly increase quality levels. To correctly predict the impact of technology shocks, we need 1 to empirically evaluate ðI  G0 Þ . Impacts cannot be theoretically predicted unless G is fully endogenized in the model. 2.5 Household and commodity The representative household maximizes its intertemporal utility function with a discount rate r. Suppose a representative household has a standard constant relative risk aversion type utility function. Because the economy is assumed to be in a steady state, and assuming that the interest rate is equal to r, then expenditure is constant over time. In each period it is spent on the consumption of a commodity alone with no saving. The commodity is produced according to the production function of Y ~b ~ qj ; ð10:15Þ Y ¼L j

~ denotes the labor used for the production of the commodity and ~qj is the where L quality level supplied by the jth sector. From the analysis above, bE goes to labor ~ þ LÞ  wL  and ð1  bÞE is spent on technology components where E ¼ wðL n X  denotes the total amount of labor in this economy. lj . L and L ¼ j¼1

Because labor can move freely between the production of a commodity and technology components, the equilibrium condition requires L 1b ¼ : ~ b L The labor market clearing condition becomes  L ¼ ð1  bÞL:

ð10:16Þ

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Measuring the black box

202

Using the result from (10.9), the payment to the jth technology component by the commodity sector is ~ j ¼ ð1  bÞ~yj wL  ¼ ~yj wL; P ð10:17Þ

X nh mh is the jth sector’s share of the total quality level with where ~ yj  nj mj h X ~ yj ¼ 1, and nj denotes the jth sector’s quality level used in the production of j

the commodity. From (10.17), we have X ~ j ¼ wL: P

ð10:18Þ

j

That is, the total amount of the final demand is equal to the total labor costs in the production of technology components.

2.6 Equilibrium To derive Pj , those of other sectors must also be determined. From (10.9), we have X ~j: yj;i Pi þ P ð10:19Þ Pj ¼ ð1  αÞ i

Therefore, we can construct 2 2 3 y1;1 P1 6 6 . 7 . 6 . 7 ¼ ð1  αÞ6 6 .. 4 . 5 4 Pn

yn;1

a system of equations as 3 2 3 ~1

y1;n 2 P1 3 P 76 7 6 7 .. .. 76 .. 7 þ 6 .. 7; 6 7 . . 7 54 . 5 4 . 5



yn;n

Pn

ð10:20Þ

~n P

where, as we have already seen in (10.10), yi;j denotes the budget share of the ith technology component in the production of the jth technology component with X yi;j ¼ 1. In matrix notation, we rewrite this as i

~ P ¼ ð1  αÞYP þ P:

ð10:21Þ

Solving this for P yields 1 ~ P ¼ ðI  ð1  αÞYÞ P:

ð10:22Þ

It is noted that if the labor share of the jth sector is equal to the final demand ~ j ¼ wlj for all j), then it causes a singularity problem in (10.22) because (i.e., P ~ Pj ¼ αPj holds in this case. To exactly identify P, the total value of technology components should not be proportional to its total quality level in at least one

Model of intersectoral flow of technology

203

203

~ and l ¼ ðl1 ; ; ln Þ are linearly independent. We assume that sector. That is, P this linear independence holds here. This assumption is also familiar in standard input–output analysis.4 Equation (10.22) suggests the total value of a technology component, Pj , is not ~ j . This result is directly proportional to the quality level Wj and its final demand P 1 shown as ðI  ð1  αÞYÞ in (10.22). To correctly predict the effect of final 1 demand, we should evaluate the values of ðI  ð1  αÞYÞ . This prediction cannot be based on purely theoretical arguments unless G is endogenously determined by the model. Because the effect of productivity change is completely determined by (10.14), we can derive the following result: 0

Proposition 2. A change in factor prices does not induce innovation. According to (10.22), price changes only affect the distribution of revenues with quality levels remaining constant because each intermediate supplier is assumed to supply quality inelastically and constant returns to scale prevail in the production function. In equilibrium, qi and qi;j are determined by (10.11) and (10.14). Prices are specified by (10.17) and (10.22) with 2n þ 1 unknown parameters and 2n equa~ The amount of tions. Imposing w ¼ 1, we can determine the values of P and P. labor is obtained by (10.5). The market clearing condition is satisfied by (10.16). This completes the description of the model in this chapter.

3 Quantitative analysis We have seen that demand shocks cannot induce innovation, while technology shocks induce asymmetric innovation linkages among intermediate sectors. In this section, we empirically examine the implications of these results by measuring the intersectoral effects of technology shock as an illustration of quantitative analysis based on the model that is developed in this chapter. We examine the intersectoral effects of technology shocks using recent Japanese R&D data. A firm belonging to a particular sector can make R&D investments in several technology fields. A firm may conduct research in other technology fields, as well as its own field, because of technological complementarity. The “Survey of Research and Development” is published annually by the Ministry of Internal Affairs and Communications in Japan; it reports R&D statistics for expenditure across different sectors at the two-digit SIC level. We use these data in our study to construct the corresponding innovation flow matrix. For this purpose, following the common assumption of endogenous growth literature, we make a simplifying assumption that R&D is proportional to the magnitude of productivity gain captured by its investor. The data on sectoral R&D 1 expenditure can then be used to calculate ð1  G0 Þ (this is described in detail in the Appendix).

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Measuring the black box

204 1

Based on the calculated ð1  G0 Þ , Table 10.1 shows total, direct, and indirect effects of innovation. The total effect is measured by a column sum of this matrix. The direct effect refers to the effect of technology shock on its own sector, whereas the indirect effect measures the effect on other sectors. The former is indicated in diagonal elements and the latter calculated as a column sum of off-diagonal elements. Table 10.1 shows these effects. Table 10.1 indicates that the direct effects are close to 100% for all sectors. This dominates the indirect effects in all sectors. The results are quite intuitive because a technology shock in one sector directly improves productivity in that sector. There are strong multiplier effects in pharmaceutical, IT equipment, and motor vehicle sectors. Regarding indirect effects, the table shows that IT equipment has the highest indirect effects, of 9.7%, compared with other sectors. This implies that a technology shock in IT enhances the sum of the productivities of other sectors by 9.7%, thus identifying a significant effect of the IT sector.

Table 10.1 Total, direct, and indirect effects Sectors/Technology fields 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

Agricultural, forest, and fishing products Mining Building construction and civil engineering Food products Textile products Pulp and paper products Printing and publishing Chemicals (fertilizer, inorganic, organic) Chemical fiber Oils and paints Drugs and medicines Other chemical products Petroleum and coal Rubber products Ceramic and stone, and clay products Iron and steel Non-ferrous metals Fabricated metal products General machinery Household electrical appliances Other electric equipment Information and communication equipment Motor vehicles Aircraft Rolling stock Other transport equipment Precision instruments Electricity and gas Software and information processing

Total

Direct

Indirect

1.00073 1.00079 1.0101 1.01532 1.00177 1.00265 1.00161 1.03927 1.00286 1.00741 1.13924 1.03739 1.00284 1.01164 1.00915 1.01081 1.00854 1.00561 1.078 1.03958 1.04963 1.27498 1.26757 1.00458 1.00093 1.00526 1.06698 1.00674 1.0365

1.0002 1.00075 1.00865 1.01395 1.00123 1.00228 1.00113 1.02612 1.00129 1.00669 1.12849 1.0122 1.00244 1.01093 1.00731 1.00982 1.00627 1.00323 1.05663 1.00334 1.02265 1.17753 1.22592 1.00066 1.00012 1.00163 1.02065 1.00582 1.01975

0.000529 4.21E-05 0.001449 0.00138 0.00054 0.000374 0.000472 0.013145 0.001568 0.00072 0.010753 0.025185 0.000399 0.00071 0.00184 0.00099 0.002278 0.002384 0.021366 0.036244 0.02698 0.097453 0.041651 0.003919 0.000807 0.003632 0.046331 0.00092 0.016752

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Model of intersectoral flow of technology

205

The second highest layer of indirect effects is on precision instruments (4.6%), followed by motor vehicles (4.2%) and household electrical appliances (HEAs) (3.6%). Surprisingly, precision instruments exert the highest effect next to IT. This result is somewhat expected because motor vehicles and HEAs are key Japanese industries. Therefore, there are two main results of our calculation of the matrix. First, the effects of technology shocks are generally localized within each sector. This implies that technology shocks are asymmetric because they are sector specific. Second, a few sectors exert significant intersectoral effects. Table 10.2 shows the details of indirect effects of IT, precision instruments, motor vehicles and HEAs on other sectors to see whether the latter effects are asymmetric or not. Table 10.2 suggests that their effects are asymmetric and localized in some sectors. For example, IT has strong indirect effects on machinery, electronics, and precision instruments but other sectors gain little indirect benefits from the IT sector. These results confirm the asymmetric effects of technology shocks as well as their localized nature. Table 10.2 Indirect effects of key sectors Sectors/Technology fields

IT

Precision

Motor

HEA

1 Agricultural 2 Mining 3 Building construction 4 Food products 5 Textile products 6 Pulp and paper products 7 Printing and publishing 8 Chemicals 9 Chemical fiber 10 Oils and paints 11 Drugs and medicines 12 Other chemical products 13 Petroleum and coal 14 Rubber products 15 Ceramics 16 Iron and steel 17 Non-ferrous metals 18 Fabricated metal products 19 General machinery 20 Household electrical appliances 21 Other electric equipment 22 IT equipment 23 Motor vehicles 24 Aircraft 25 Rolling stock 26 Other transport equipment 27 Precision instruments 28 Electricity and gas 29 Software and information

5.54D-10 4.44D-07 0.000467 5.39D-06 0.000677 1.18D-07 0.001268 0.003285 0.000657 0.000402 3.95E-05 0.000136 0.000108 4.51E-05 0.001711 0.000815 0.005323 0.000203 0.039623 0.000143 0.016834 – 0.000167 6.16E-05 6.40D-07 5.8E-05 0.02387 1.56E-05 0.001537

7.03D-10 3.33D-08 6.92E-05 6.83D-06 6.75E-05 2.34D-07 6.56E-05 6.94E-05 6.58E-05 0.000214 0.000333 0.000447 7.77D-07 4.5E-05 7.23D-06 6.67E-05 5.56E-05 6.76E-05 0.041135 1.86E-05 0.000127 0.002856 0.00039 5.19E-05 8.99D-06 8.33E-05 – 1.6E-05 6.3E-05

1.41D-10 3.34D-08 6.23D-06 1.37D-06 0.000681 5.01D-08 2.36D-06 0.000148 0.000509 0.000364 0.000125 8.85E-05 3.98D-07 0.000161 0.00055 0.000284 0.00116 0.001135 0.00465 7.76E-05 0.029656 0.001866 – 8.81E-05 2.85D-06 3.11E-05 5.59E-05 2.20D-06 5.30D-06

3.62D-11 1.32D-08 1.31E-05 3.52D-07 2.84E-05 6.10D-09 3.35E-05 9.62E-05 1.75E-05 3.26E-05 2.91E-05 7.59D-06 2.87D-06 1.21E-05 4.56E-05 2.24E-05 0.000143 9.26E-05 0.001778 – 0.00207 0.031098 1.42E-05 2.19D-06 4.36D-08 2.37D-06 0.00066 7.19D-07 4.1E-05

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Measuring the black box

206

Therefore, our crude empirical analysis indicates that most sectors are localized within their own sectors, whereas some GPT sectors exert significant intersectoral effects. However, the latter effects are also localized in some sectors. These results appear to support Proposition 1 (i.e., the asymmetric nature of innovation effects).

4 Concluding remarks In this chapter, we have developed an equilibrium model of intersectoral technology flows using an o-ring production function. Its equilibrium is described by 1 1 three matrices: Y, ðI  G0 Þ in (10.14), and ðI  ð1  αÞYÞ in (10.22). Y is the technology flow matrix, specifying the quality levels of all sectors in the 1 economy; ðI  G0 Þ is the innovation flow matrix determining the growth 1 dynamics of the economy; and ðI  ð1  αÞYÞ specifies their factor prices. One of the advantages of this model is that it allows for complete general equilibrium specification. Hence, it avoids some of the criticism made about standard input–output analysis and its extreme assumptions on linear production functions and partial equilibrium properties.5 Moreover, the model in this chapter differs from related literature in that technology production and transaction are explicitly specified. Therefore, it is able to shed new light on intersectoral productivity spillover from a different perspective. In other words, this is the result of economic activities as well as technological properties. Another advantage of this model is that its analytical simplicity and tractability with minimum computational burden makes it easier to implement empirical studies. Conversely, a disadvantage of this model lies in the empirical precision of its R&D table, such as Table 10.1. The justification for this calculation is attributed to the common assumption of endogenous growth literature, which states that R&D is proportional to productivity gain. However, this assumption must also be tested by resorting to other measures of productivity, such as TFP. Therefore, the validity of empirical analysis critically depends on the proximity between R&D and productivity gain. Despite this limitation, we still believe that the empirical study based on the existing R&D table provides useful insights regarding innovation policy. That is, effective innovation policies could be formulated and implemented based 1 upon the empirical evaluation of the inverse matrix, ð1  G0 Þ . These policies could more precisely take into account the intersectoral effects that are illustrated by our investigation. Economic growth and technological change have attracted much attention among mainstream economists for decades. Although a number of sophisticated models have been proposed, little attention has been paid to intersectoral relations and the propagation mechanism of technological change. However, as Rosenberg (1982) points out, one of the characteristics of modern technological change is complementarity among heterogeneous technologies. Therefore, to further explore inside a black box, input–output analysis regarding

207

Model of intersectoral flow of technology

207

intersectoral technology flows should be taken into serious account both theoretically and empirically. In other words, economic growth should be more precisely analyzed in terms of the intersectoral effects summarized by technology and innovation flow matrices where multiplier, weak, or independent intersectoral effects could emerge. This chapter is a first attempt at providing a theoretical justification for technology and innovation flow matrices with simple quantitative analysis. More theoretical and empirical studies are needed. These studies could lead to more effective innovation policy.

Notes 1 Several other terms are used besides “technology flow matrix”, such as “knowledge flow matrix”, “invention input–output matrix”, “innovation flow matrix”, and “R&D flow matrix”, most of which refer to the same concept. For surveys, see Evenson and Johnson (1997), Mohnen (1997), and Los and Verspagen (2007). In this chapter, we conceptually distinguish between technology and innovation flow matrices. 2 Hence, the approach to construct technology flow matrix based on the input–output matrix cannot be justified. This was also pointed out by Evenson and Johnson (1997). 3 It may seem logically impossible that a sector produces its own output using part of its output as an input. One interpretation is that the sector needs to use some of its output to test quality levels. It should be noted that the results in this model do not depend on qj;j > 0. 4 Suppose X , F, and A represent total output, final demand, and input–output matrix. We 1 can derive X ¼ ð1  AÞ F. If F ¼ ZX for some Z > 0, this equation is unsolvable 1 unless ðI  AÞ Z ¼ I always holds. 5 Of course, some input–output models also address these criticisms (see, for example, Ten Raa and Mohnen, 1994; Rose and Casler, 1996; Liew, 2000).

Appendix

Data source For the construction of G0 , we collected data from the “Survey of Research and Development” published annually by the Ministry of Internal Affairs and Communications in Japan (www.stat.go.jp/english/data/kagaku/index.htm). This survey collects data on intramural R&D expenditure by Japanese industries. Data for 2011 were analyzed.

Matching between sectors and technology fields The data show the distribution of R&D expenditure, by sector, over 30 technology fields. It is primarily classified at a two-digit SIC level. To achieve a one-toone alignment between sectors making R&D investment and technology fields, the technology field titled “other manufactured products” was dropped from our matrix as it was difficult to identify the corresponding sectors. All other technology fields were identified in the sectors appearing in the dataset. Most sectors are classified at the two-digit SIC level, although “chemical fiber”, “household electrical appliances”, “aircraft”, “rolling stock”, and “precision instruments” are matched with the corresponding sectors at the three-digit level.

Construction of the innovation flow matrix Following the common assumption in the endogenous growth literature, we make a simplifying assumption that states that R&D investment is proportional to the magnitude of productivity growth. Under this condition, suppose the total amount of R&D investment in the ith technology field by all sectors is Ri . If the jth sector makes R&D investment in this field by Ri;j, then this sector gains the productivity growth of ðRi;j =Rj Þ^qj . However, as the quality levels and the difficulty of R&D are not the same across different technology fields, we have attached some weight to this ratio. For this weight, we used the ratio Rj =R, where R denotes the total R&D investment in the economy. The magnitude of productivity growth that can then be gained by the jth sector in the ith technology field is gi;j ¼ Ri;j =R. Based on this specification, G0 was calculated.

209

11 Estimating innovation flow matrix and innovation linkages in the East Asian region and the United States

1 Introduction There is growing recognition that innovation policy is of critical importance if advanced countries are to recover from economic downturn and thrive in a highly competitive global economy, and if developing countries are to promote and sustain economic growth. While growing interest in innovation policies has recently emerged, little attention has been paid to complementarity among heterogeneous technologies.1 According to Rosenberg (1982), the complementarity constitutes a major characteristic of technological change. This implies that sufficient attention should be paid to the intersectoral spillover effects of innovation in implementing innovation policies. Indeed, according to Hirschman (1958), the lack of interdependence and linkage among various industries is one of the most typical characteristics of underdeveloped economies. Economic development and growth inevitably accompany the evolution of intensified intersectoral relations. Because technological change plays a critical role in this process, as suggested by the endogenous growth literature (see, for example, Grossman and Helpman, 1991; Aghion and Howitt, 1998a), a sector’s technological interdependence must be properly understood to implement development and growth policies that promote innovation. While several studies measure intersectoral spillover effects in a few specific industries (see, for example, Bernstein and Nadiri, 1988; Jaffe, 1989; Jaffe, Trajtenberg, and Henderson, 1993), there is little empirical research that comprehensively evaluates intersectoral (technological) spillover effects within a country or region. Coe and Helpman (1995) and Badinger and Egger (2008) estimated international research and development (R&D) spillovers in a sample of countries associated with the Organization for Economic Co-operation and Development (OECD),2 but their R&D spillover measures were aggregated into a few variables so that more specific intersectoral spillover effects were not revealed. Dietzenbacher (2000) conducted one of a few empirical studies that analyzes technological spillover effects by disentangling them into product and process innovations under an input–output framework.3 However, the model assumes a standard Leontief economy, and the chapter evaluates the overall spillover effects of each sector.4 This approach means that the spillover effects between

210

Measuring the black box

210

two sectors could not be recovered.5 Similarly, while both Bos, Goderis, and Vannoorenberghe (2014) and Wolff and Nadiri (1993) share a similar research interest with the present chapter, their empirical analyses were more concerned with overall spillover effects and made no attempt to reveal intersectoral spillover effects in innovation. The purpose of this chapter adopts an innovation flow matrix developed in the previous chapter and evaluates the properties of innovation linkages among manufacturing sectors under a multi-sector general equilibrium framework. As is described in the previous chapter, “innovation linkages” refer to the effect of sector-specific innovations on productivity growth within an economy or region. For example, an increase in productivity in the ith sector affects productivity growth in other sectors, which in turn exerts some influence on the original sector. In this chapter, we estimate innovation linkages in East Asian countries and draw implications for growth strategies in the East Asian region and in the United States by taking a different estimation approach from Chapter 10. In particular, we are interested in measuring innovation backward and forward linkages. The concepts of backward and forward linkages were originally proposed by Hirschman (1958). Backward linkages refer to the stimuli going to sectors that supply the inputs required by a particular activity, whereas forward linkages are the inducements to set up new activities that utilize the output of the proposed activity. If these linkage effects are sufficiently strong, underdeveloped countries are more likely to recover from poverty. A number of empirical studies have been conducted to measure the linkage effects based on input– output matrices and to identify key sectors (Chenery and Watanabe, 1958; Rasmussen, 1956; Schultz, 1977; Dietzenbacher and van der Linden, 1997; Miller and Lahr, 2001). However, these intersectoral linkages are concerned with commodity transactions, which differ from innovation linkages. This chapter defines “innovation backward linkages” of the ith sector as the increase in productivity growth in this sector that results from productivity growth in other sectors. “Innovation forward linkages” refer to the effect of productivity growth in this sector on productivity growth in other sectors.6 In other words, the former regards the sector as a user of innovation and measures the magnitude of benefits received from intersectoral spillover effects. The latter regards the sector as a supplier of innovation and measures its contribution to productivity growth in other sectors. These linkage effects can be evaluated using an innovation flow matrix in which intersectoral spillover effects in innovation are described.7 In the empirical section of this chapter, the properties of innovation linkages are examined from the following two perspectives. First, we test whether a (regional) balanced growth policy is more conducive to the promotion of innovation than a (regional) unbalanced one. Note that the balanced growth policy tries to promote innovation in all sectors equally, while the unbalanced policy primarily supports innovation in selected sectors (Rosenstein-Rodan, 1943;

211

Innovation flow matrix & innovation linkages

211

Hirschman, 1958; Streeten, 1959; Murphy et al., 1989). If the balanced growth policy is innovation-promoting, then a uniform, balanced growth policy should be implemented. Otherwise, a sector-specific, unbalanced growth policy should be pursued. The indicator used for this test is the difference in innovation forward linkages across sectors. The outcome of our empirical examination indicates that policy should favor unbalanced growth over a balanced growth. Second, after the unbalanced growth strategy is selected, the specific targets of the growth strategy should be identified. We identify targets in terms of “core” and “bottleneck” sectors. Core sectors refer to high-growth sectors that have high innovation forward linkages, while bottleneck sectors are low-growth sectors that have high innovation backward linkages. The unbalanced growth strategy should promote innovation in core and bottleneck sectors, and these sectors can be identified only through measuring innovation linkages. We constructed the innovation flow matrix using industry-level TFP (Total Factor Productivity) data for Japan, Korea, China, and the United States and examined the properties of the innovation linkages in these countries. Japan, Korea, and China are included as they represent East Asian countries that have experienced high economic growth and development in the past. Moreover, the three economies have close ties, with official negotiations on a trilateral free trade pact having recently been attempted. Indeed, it is predicted that Japan, Korea, and China will soon form an integral economic region (see, for example, Wong, 2006). In addition, these countries have established strong economic relations with the United States beyond their regional boundaries. It is therefore critical to examine the underlying innovation relations in not only the East Asian region but also the integrated region of East Asia and the United States and to ascertain the difference between the two. Innovation-promoting multi-regional growth strategies can be derived from the estimates of an innovation flow matrix in a target region. If the target differs, the corresponding innovation flow matrix and innovation linkages also differ, leading to different growth strategies. Hence, it should be noted that the empirical analysis in this chapter is conducted using the pooled samples of the two regions selected for the study. The remainder of this chapter is organized as follows. Section 2 develops a basic theoretical model that provides a framework for the following empirical studies. Section 3 empirically estimates innovation flow matrices and innovation linkages and derives policy implications. Finally, Section 4 presents conclusions.

2 The model In this section, we develop an innovation flow model. Although we basically follow the model described in the previous chapter and Harada (2016), we reproduce it here for readers who have not read the previous chapter. Consider a discrete time closed economy (region) with n commodities and n technology components, the latter being produced by intermediate (technology component) sectors.8 Thus, two stages of production prevail in this economy. In the first

212

Measuring the black box

Commodity sectors

Intermediate sectors

212 y1

yn

q1

qn

q1

qn

Figure 11.1 Production structure

stage, technology components are produced by intermediate sectors through intersectoral technology transactions. In the second stage, commodity sectors purchase technology components and produce outputs. The production structure of the model is illustrated in Figure 11.1. 2.1 Commodity production The jth commodity is produced using capital, labor, and the jth technology component as inputs. Its production function is given by b Lαj;t1 ; yj;t ¼ qj;t Kj;t1

ð11:1Þ

where the subscripts j and t refer to the jth sector and time, and Kj and Lj denote the amounts of capital and labor used in this sector, respectively. It is assumed that the production of a given commodity takes one period to complete, so that the subscripts on the RHS variables are t  1, instead of t. As capital accumulation is not our primary concern, no capital depreciation is assumed to simplify the model. As we will see, constant returns to scale prevail in this production function with respect to Kj , Lj , and qij . qj corresponds to the productivity level of production technology in a standard production function, but this production technology must be procured at each period by purchasing one unit of technology from the jth intermediate supplier. In contrast, a standard production function assumes that production technology is available without costs once a production function is given. Thus, while the standard input–output model is primarily concerned with commodity production and its transaction flow, the model in this chapter departs from the latter in that the production of technology is taken into account. That is, the production technology in each commodity sector must be produced at each time by the corresponding intermediate supplier that purchases relevant technology components from other intermediate suppliers. This assumption

213

Innovation flow matrix & innovation linkages

213

reflects the fact that manufacturing plants must continuously procure engineering services and technical support from internal engineering departments or external contractors for their operation. This can be understood as the purchasing of relevant technology components from intermediate sectors. Although we conceptually distinguish between intermediate and commodity sectors, it is possible that a commodity producer owns the corresponding intermediate sector as well. That is, production technology could be internally produced by a commodity producer itself, rather than being purchased from an intermediate supplier. Indeed, because no relation-specific investment is assumed in this model and constant returns to scale prevail in both intermediate and commodity sectors, as we will see, the ownership structure does not matter. Thus, we suppose that each commodity producer and intermediate supplier behaves independently, while solving the equilibrium as if the commodity producer owns the corresponding intermediate sector.

2.2 Production of production technology The intermediate sector supplies one unit of technology component to its own and other intermediate sectors, in addition to the corresponding commodity producer. That is, each technology component is produced using technology components of its own and other sectors as inputs.9 Because this model is directly concerned with the production of production technology, a change in the quality level of the technology component is referred to as “technological change” or “innovation”. This change is caused by technology shocks in each intermediate sector. Although endogenous innovation can be easily incorporated into the model (see Chapters 7 and 8 for this application), we maintain the assumption of exogenous technology shocks in this chapter because our empirical study does not require the explicit endogeneity of innovation. We assume that technology components are produced according to an o-ring type production function. Kremer (1993) proposes an o-ring production function that incorporates the fact that mistakes in any series of tasks can dramatically reduce the product’s value. In his model, production consists of many tasks, all of which must be successfully completed for the product to have full value. It is assumed that highly skilled workers cannot substitute for lowskilled workers. Skill refers to the probability that a worker will complete a task successfully. Chapter 7 extended the o-ring production function to the model of production of production technology and its endogenous innovation. This chapter follows this basic model and assumes that the production function of production technology represents a technological system.10 This consists of a series of interrelated technology components. High quality technology components cannot be substituted for low quality ones. Thus, in our model, the series of tasks are regarded as a series of technology components, which are provided by their own sector as well as other intermediate sectors in an economy.

214

Measuring the black box

214

Production technology that is utilized in the jth commodity sector is produced in the jth intermediate supplier according to11 n Y qj;t ¼ Aj qij;t1 ; ð11:2Þ i¼1

where qij;t1 is the quality level of the technology component i at time t  1 that is used in the production of the jth technology component at time t, and Aj denotes the intrinsic productivity level, the growth rate of which is assumed to be constant. Because it seems more reasonable to assume that the current technology is produced using the previous technology components rather than contemporaneous ones, once again, a one-period lag is imposed in (11.2). In this specification, one unit of each technology component is produced by its own and other technology components. The jth technology component produced in this production function is, in turn, supplied to its own and other technology components, in addition to the jth commodity producer. In the following equations, time subscripts are omitted to simplify the notation. The risk neutral commodity producer maximizes max Pj;t Aj L; K; q

n Y

b qij;t1 Kj;t1 Lαj;t1 

X

pðqij;t1 Þ  rt1 Kj;t1  wt1 Lj;t1 ;

i

i¼1

where Pj;t denotes the price of the jth commodity, pðqij;t1 Þ is the factor price of the ith technology component,12 and rt1 and wt1 refer to the rental and wage rates, respectively. The first-order conditions are: 1 !1α n Y 1 b ; Lj;t1 ¼ αAj Pj;t wt1 qij;t1 Kj;t1 i¼1

Kj;t1 ¼

1 j;t t1

bAj P r

n Y

1 !1b

α j;t1

;

qij;t1 L

i¼1 b Lαj;t1 Pj;t Aj Kj;t1

n Y

qij;t1 ¼ p0 ðqhj;t1 Þ:

i6¼h

Further solving these equations for

n Y

qij;t1 yields 1 !1αb n Y Aj Pj;t qij;t1 ; i¼1

b

1b

1 1αb 1αb Þ ðαw1 Lj;t1 ¼ ðbrt1 t1 Þ

i¼1

1α

1 1αb t1

Kj;t1 ¼ ðbr Þ

α

1 1αb t1

ðαw Þ

Aj Pj;t

n Y

1 !1αb

qij;t1

i¼1

0

α

1 1αb t1

p ðqhj;t1 Þ ¼ ðαw Þ

b

1 1αb t1

ðbr Þ

Aj Pj;t

Y i6¼h

; 1 !1αb

qij;t1

1

1

q1αb hj;t1 :

ð11:3Þ

Innovation flow matrix & innovation linkages

215

Labor and capital market clearing conditions are X X   Lj;t1 ¼ L; Kj;t1 ¼ K; j

215

ð11:4Þ

j

 and K  denote the total amounts of labor and capital, respectively. r and where L w are determined to satisfy these conditions in equilibrium. 2.3 Factor price of the technology component Intermediate suppliers provide the technology component inelastically to each intermediate supplier. Suppose that the quality levels are represented by a quality ladder (see, for example, Aghion and Howitt, 1992) qij;t1 ¼ emij;t1 ;

ð11:5Þ

where mij;t1 takes positive values representing the current quality level. Substituting (11.5) into (11.3) gives13 P 0

α

1 1αb t1

p ðqhj;t1 Þ ¼ ðαw Þ

m i6¼h ij;t1

b

1 1αb ð1αbÞmhj;t1 hj;t1 t1

ðbr Þ

q

1

1

Pj;t 1αb :

Integrating this yields the factor price schedule of technology component h as pðqhj;t1 Þ ¼ ð1  α  bÞyhj;t1 Ej;t ;

ð11:6Þ

mhj;t1 ; yhj;t1 ¼ X n mij;t1 i¼1

where Ej;t  Pj;t yj;t is the output value of the jth commodity, and

X

yhj;t1 ¼ 1.14

h

Thus, the commodity producer earns zero profits, as αPj;t and bPj;t are paid to labor and capital, respectively. The jth intermediate sector receives X X pðqhj;t1 Þ from the jth commodity producer and pðqj‘;t1 Þ from other inter‘6¼j

h

mediate sectors, which in turn are allocated to each intermediate sector supplying to the jth technology component. The net gains are ! X X X pðqhj;t1 Þ þ pðqj‘;t1 Þ ¼ pðqjj;t1 Þ þ yjj;t1 pðqj‘;t1 Þ: yjj;t1 h

‘6¼j

‘6¼j

The LHS represents the revenues of the j th sector, and the RHS refers to the sum of the payments made to that sector. These two accounts should be equal. If production of the jth technology component does not require its own technology component, the net gains are zero.

216 Measuring the black box

216

2.4 Household The representative household maximizes its utility function ut ¼

n X

ln yj;t ;

ð11:7Þ

 þ rt1 K:  Pj;t yj;t ¼ wt1 L

ð11:8Þ

j¼1

subject to Et ¼

n X j¼1

As wt1 and rt1 are determined in (11.4), the amount of expenditure is also determined in this equation. Assuming Et ¼ 1, we can specify the demand for each commodity as yj;t ¼

1 : nPj;t

ð11:9Þ

This implies that Ej;t  Pj;t yj;t ¼ 1=n. Then, we can determine all factor prices in (11.6). The remaining unknown variables are rt1 , wt1 , and Pj . But we have already derived two market clearing conditions in (11.4), and n equations in (11.9). Because yj;t in (11.9) can be represented as 1 !1αb n αþb Y b α 1 1αb 1 1αb yj;t ¼ ðαwt1 Þ ðbrt1 Þ qij;t1 Pj;t1αb ; ð11:10Þ i¼1

we have n þ 2 unknown variables and equations. This completes the model.

2.5 Allocation of the technology component Now, let us derive the innovation flow matrix from this theoretical model. In this model, each technology component is assumed to be supplied by independent suppliers. However, because each technology component exists in a non-physical form similar to blueprints, it is assumed that its output is duplicated without additional costs. Hence, the allocation of a technology component across sectors does not require the equality of supply and demand. Instead, we assume that it is allocated to each sector as mij;t1 ¼ Wij mi;t1 ;

ð11:11Þ

where Wij  0 is the degree of technology transfer from the ith technology component to the jth intermediate sector, and mi measures the total quality level of the ith component. The magnitude of Wij is determined based on technological interdependence between the two components and the absorptive capacity of the jth X Wij ¼ 1. Note sector. Because duplication costs are zero, we do not require j

Innovation flow matrix & innovation linkages

217

217

that Wij should be positive, because the firm does not purchase the ith technology component if Wij < 0. The matrix of Wij can be referred to as the technology flow matrix. 2.6 Innovation flow matrix From (11.5) and (11.11), the productivity growth can be derived as ^ qi;t1 ; qij;t1 ¼ gij ^

ð11:12Þ

_ where ^ denotes the growth rate (e.g., ^q  q=q; q_  @q=@t), and gij measures the effects of innovation in the ith sector on that of the jth sector. If g > 0, innovation is complementary to current productivity growth; however, if g < 0, innovation is substitutable and has a negative effect on current productivity growth. Finally, g ¼ 0 implies that there is no innovation effect. If innovation in the ith sector is neutral in the sense that Wij remains intact, we should have ^ qij ¼ Wij ^qi from (11.5) and (11.11). In this case, gij ¼ Wij holds. However, innovation often changes the complementary relations between two technologies. Therefore, some innovation in the ith sector might have a substitution effect on innovation in the jth sector. For example, the introduction of a fully automated manufacturing plant improves productivity, but it may impede process innovation, because skilled workers and foremen, who are responsible for improvement in cost and quality, would be replaced by high-tech equipment. In this case, we should have Wij  0 > gij . Note that both Wij and gij refer to the technological impacts of the ith sector on the jth sector. However, Wij represents the effect of the productivity level of the ith sector on that of the jth sector. In other words, Wij refers to the productivity spillover effect. However, gij measures the impact of productivity change (i.e., innovation) of the ith sector on that of the jth sector. This represents the innovation spillover effect. Thus, the difference between Wij and gij is accounted for by whether the spillover effects imply productivity relations or innovation relations. The matrix of gij can be referred to as the innovation flow matrix. From (11.2) and (11.12), this matrix can be represented as X ^ j;t þ ^ qj;t ¼ A gij ^qi;t1 : i

Thus, we obtain 2

^ q1;t

3

2

^ 1;t A

3

2

g11

6 7 6 7 6 .. 7 6 . 7 6 .. 6 . 7 ¼ 6 .. 7 þ 6 4 5 4 5 4 . ^ n;t ^ qn;t gn1 A



..

.



3 30 2 ^q 1;t1 6 7 .. 7 7 6 .. 7 7: . . 56 4 5 ^qn;t1 gnn g1n

218

Measuring the black box

218

In matrix notation, this is rewritten as ^ t1 : ^ t ¼ at þ G0 Q Q

ð11:13Þ

G0 corresponds to an innovation flow matrix. This matrix indicates how productivity growth in each sector is related to the others. In particular, we are interested in the backward and forward linkages of this innovation flow matrix. Let us refer to them as innovation backward and forward linkages to differentiate them from corresponding linkages derived from a (commodity) input–output matrix. The innovation backward and forward linkages are respectively calculated as Ibj ¼

n X

gij ;

i¼1

Ifj ¼

n X

gji :

i¼1

The former measures the direct increase of productivity growth in the jth technology component when all technology components increase their productivity level. As is clear from (11.13), a sector with high innovation backward linkages tends to enjoy higher productivity growth when all sectors experience productivity growth. Conversely, the innovation forward linkage measures the effect of the productivity growth in the jth technology component on all sectors. In other words, the innovation forward linkage indicates the benefits provided by the jth technology component to all sectors. By definition, a sector with high innovation forward linkages does not necessarily enjoy higher productivity growth, although this sector contributes to productivity growth in other sectors.

2.7 Balanced vs. unbalanced growth The innovation forward linkage represents a marginal effect on economic growth. If the innovation forward linkages are the same across sectors, there is no reason to select a specific sector as a target of growth policy. Instead, it would be desirable to increase productivity in all sectors in a balanced manner without generating inequality. However, if the innovation linkages are different, it would be more innovation-promoting to focus on the sector with the maximum innovation forward linkages and provide subsidies. The idea that a significant advance in a few sectors is more successful than small advances in many sectors simultaneously is suggested by proponents of “unbalanced growth” (Hirschman, 1958; Streeten, 1959), as opposed to “balanced growth” (Rosenstein-Rodan, 1943; Murphy, Shleifer, and Vishny, 1989). According to Streeten (1959), the conditions favoring unbalanced growth include the

Innovation flow matrix & innovation linkages

219

219

following: (1) indivisibilities are important; (2) expansion costs are important; (3) higher incomes are created than would be by balanced growth; and (4) incentives to invent and to apply inventions are strengthened. If these conditions are satisfied, then the choice of investment priorities would be a stimulus for growth. That is, the growth policy should focus on the sectors that generate the strongest stimuli for growth. In this model, (3) and (4) can be evaluated by innovation forward linkages. Suppose that, currently, no innovation takes place in all sectors, and each sector generates innovation ^q ¼ 1 by the fixed amount of R&D investment, . To make subsequent analysis as simple as possible, assume that ^q ¼ k is achieved by the R&D investment of k. That is, the innovation production function is linearly dependent on R&D investment. Assume that the social planner has a budget of n. Under a balanced growth policy, the social planner subsidizes all sectors equally, so that each sector receives  and its growth rate is ^q ¼ 1. In contrast, under an unbalanced growth policy, the social planner selects m sectors (m < n), whose innovation forward linkages are higher than other sectors, and subsidizes these. Hence, each selected sector receives n=m and achieves ^q ¼ n=m. X ^yj;t. SubFrom (11.7), the growth rate in this economy can be measured by j

stituting (11.9) into (11.10) and rearranging yields ^ j;t / ^yj;t ¼ P

n X

^qij;t1 :

ð11:14Þ

i¼1

From (11.12), the economic growth rate in the economy is represented by X j

^yj;t /

n X i¼1

gij ^qi;t1 ¼

n X i¼1

^qi;t1

n X j¼1

gij ¼

n X

^qi;t1 Ifi :

ð11:15Þ

i¼1

Obviously, the magnitude of the ith sector’s innovation effect is proportional to Ifi . Hence, we can derive the following: Proposition. Both balanced and unbalanced growth policies achieve the same growth rate if and only if Ifi ¼ Ifj for all i ¼ j. Otherwise, an unbalanced growth policy will achieve a higher growth rate. Of course, this proposition is derived from the perspective of economic growth alone. The unbalanced growth policy might generate income inequality, and this might induce some welfare loss. This proposition does not take into account these effects on welfare. If Ifi ¼ Ifj holds for all i ¼ j, both growth policies would be equally innovation-promoting. In this case, however, balanced growth would be more favorable in terms of social welfare as it does not generate inequality.

220

Measuring the black box

220

3 Empirical analysis Having presented the theoretical background of the model, we are now in a position to conduct an empirical analysis of the proposition of balanced vs. unbalanced growth strategies. For this purpose, we need to construct an innovation flow matrix.

3.1 Data For the construction of G0 , we extracted the industry-level TFP data from the International Comparison of Productivity among Asian Countries (ICPA) database of the Research Institute of Economy, Trade, and Industry (RIETI) in Japan (www.rieti.go.jp/en/database/d03.html). This database provides the relevant data on Japan, Korea, Taiwan, China, and the United States. Because TFP data are not available for a few industries in Taiwan, we removed Taiwan from the study and only constructed innovation flow matrices for Japan, Korea, China, and the United States. The data cover the years 1980–2000 for most countries. We selected 15 sectors consisting of chemicals, petroleum and coal products, leather, stone/clay/glass, primary metal, fabricated metal, machinery, electrical machinery, motor vehicles, transportation equipment and ordnance, instruments, rubber and miscellaneous plastics, miscellaneous manufacturing, transportation, and communication. Most of these sectors belong to manufacturing industries. Other manufacturing sectors in this database include food, textile, apparel, lumber, furniture, paper, and printing. These sectors were deleted from the sample because they generally belong to low-tech fields. The service sector consists of electric utilities, gas utilities, trade, finance and real estate, other private services, and public services in the dataset. This sector is excluded from the analysis because the classification of the services sector is rather crude compared with those in the manufacturing sector. Therefore, to estimate rigid innovation linkages, the following empirical analysis focuses only on the 15 manufacturing sectors. In the estimation of innovation linkages, we also need to take into account the magnitude of utilization of technologies in each sector’s innovation activity. For example, suppose some sector does not use machinery technology in undertaking its own innovation. In this case, spillover effects from that technology component on the sector’s innovation should not be expected, at least directly. To control for the magnitude of utilization of technology components, we use R&D expenditure ratio on each technology component as the proxy for the magnitude of utilization of that technology. Although this type of data is not publicly available in general, the “Survey of Research and Development” published annually by the Ministry of Internal Affairs and Communications in Japan reports R&D statistics for expenditure across different sectors at the two-digit SIC level. We use the data for 2002 to control for the magnitude of utilization of technology components in each sector in the evaluation of innovation backward and forward linkages.15

Innovation flow matrix & innovation linkages

221

221

More specifically, suppose the amount of R&D expenditure in the ith technology component by the jth sector is Rji . Then, the sector’s total R&D expenditure, X excluding its own sector’s technology, amounts to Rjj ¼ Rji . We exclude Rjj i6¼j

in this sum because it is obvious that the sector’s technology is fully utilized for its own innovation. Define the R&D ratio of the ith technology component as zji  Rji =Rjj . This measures the magnitude of utilization of the ith technology component in the sector’s innovation. Then, the ith sector’s TFP growth to be utilized in this sector is zji ^qi . We use these transformed values as explanatory variables in the following regression analysis. 3.2 Estimating innovation flow matrices and innovation linkages Using TFP growth data on 15 sectors in Japan, Korea, and China, we can construct the innovation flow matrix G0 by regression analysis that represents intersectoral innovation linkages. The regression equation is derived from (11.13) as ^ t ¼ at þ G0 Q ^ t1 þ ε; Q

ð11:16Þ

where ε is the error term. Note that we have 16 unknown parameters to be estimated for each sector, including constant terms, while the data cover approximately 20 years for each country. To circumvent the insufficient number of observations, matrix coefficients were estimated using the pooled sample. Because this sample is an unbalanced panel data, we conducted both fixed and random effect regressions. In all 15 sectors, the Hausman specification test selected random effect models. Table 11.1 reports the results. Although we do not interpret these estimates in detail because of space limitations, it should be mentioned that no common pattern can be observed across the 15 sectors. For example, while many sectors have several significant estimates, the electrical machinery and communication sectors receive no significant effects from productivity growth in other sectors. In addition, some coefficients are negative and significant, indicating substitutable effects of productivity growth. However, more than half of significant coefficient estimates are positive. Besides the statistical significance, it should be pointed out that not all sectors affect TFP growth in other sectors due to zero R&D investment. As described above, when no R&D investment in that technology is made, we excluded the corresponding TFP growth from regression analysis. Therefore, the result shows that quite a few sectors do not interact with other sectors in terms of contributing to the latter’s innovation. In other words, the result reflects localized interaction across sectors (Horvath, 2000). Note that this estimation assumes the existence of a common innovation flow matrix across the three countries in the East Asian region, controlling for the influence of country-specific factors. However, as we have mentioned before, each country has already established strong economic ties with the United States. Hence, it is of equal importance to construct the innovation flow

8.489 (12.000)

0.537 (0.729) −20.284 (7.620) 0.659 (1.748) – –

−3.186 (19.413) –

–

–

–

–

–

30.121 (13.297)

2.279 (2.065) −10.765 (11.523) 1.264 (0.506) – (51.372) 0.251 (1.930) −91.628 (44.036) −0.519 (1.612) –

1.067 (0.300) −0.508 (1.164) 0.225 (0.120) −0.600 (2.233) – (14.371) –

−0.171 (0.133) 0.432 (0.135) −12.994 (4.843) 26.303 (26.536) – –

Leather

Petro. 4.222 (1.935) – – −4.006 (2.623) 0.330 (2.358) −0.024 (0.811) −1.261 (0.385) 8.637 (21.582) 3.226 (2.742) 5.327 (211) 302.409 (96.902) 686.016 (1165) 9.727 (6.270) 2.015 (10.425) −2.250 (11.403)

– −0.267 (0.169) 20.926 (0.153) 2.469 (4.189) −4.398 (2.177) −186.645 (227) 2.930 (1.051) −42.926 (9.362) 1.066 (3.979) 3650.780 (10519) 1.295 (0.839) −55.674 (57.145) 6.081 (2.099)

P. metal 0.726 (0.362) –

Clay

−47.194 (63.589) 1.524 (6.652) 0.132 (0.161) 0.812 (0.744) −1.348 (0.762) 1.418 (1.084) 153.309 (3.305) −2.004 (1.775) −21.575 (47.887) 1.004 (0.497) −539.495 (241) 90.576 (26.440)

2.185 (11.579) −0.250 (0.235) –

F. metal

29.058 (15.170) −6.530 (942) 8.073 (6.353) 0.001 (0.211) 1.676 (1.818) 0.967 (0.839) 4.083 (133) −0.499 (0.262) 8.522 (20.171) 0.186 (1.088) −12.498 (3.694) 5.592 (0.078)

–

−9.059 (21.257) –

Machine

−2.405 (2.465) −0.794 (227) 54.505 (48.644) −173.413 (148) 0.140 (0.136)

54.333 (55.605) 0.957 (2.405) 0.056 (0.198) 0.293 (0.706) 59.253

0.069 (24.154) 33.637

–

1.898 (7.108) –

Electrical

Note: The number of observations is 53. The dependent variable is productivity growth. All coefficients are estimated by random effect models. Standard errors are shown in parentheses. Constant terms are omitted. Data source: ICPA database.

Communication

Transportation

Misc. manufacturing

Rubber

Instrument

Transportation Equipment

Motor vehicle

Electrical machinery

Machinery

Fabricated metal

Primary metal

Clay & glass

Leather

7.192 (11.749) −1.016 (1.244) 14.029 (43.995) 5.572 (3.558) –

0.009 (0.216) 18.055 (8.334) 24.978 (10.376) −3.116 (1.739) –

Chemical

Petroleum

Chem.

Variable

Table 11.1 Innovation input–output matrix (Γ0 ) (excluding the USA)

– –

– –

−4.486 (12.202) 0.269 (0.143) 43.559 (48.389) – 7.452 (18.527) −0.706 (1.209) 353.197 (205)

−2.124 (3.084) −0.791 (0.362) − 115.622

204.481 (216) −0.054 (0.275) –

−29.039 (16.059) 4.100 (8.254) 1.252 (0.523) −2.247 (14.700) 0.039 (0.145) −0.100 (0.370) −1.799 (11.468) –

1.467 (1.244)

2.112 (3.530) –

−0.238 (0.179) –

0.637 (0.457) −23.004 (12.822) 3.126 (3.675) –

–

–

27.998

–

–

– (25.270) –

Inst.

Tran. eq.

49.682 (16.915) −41.521 (21.468) 224.852 (145) 0.858 (0.475) −1.391 (2.345) 0.206 (12.569) −0.429 (0.232) 0.854 (1.201) 0.996 (2.314) − 0.211

– (1086) –

–

0.211 (2.199) –

Rubber

−0.178 (0.475) 0.458 (0.565) −0.656 (0.995) 3.063 (1.248) 2.811 (9.900) −5.016 (6.397) −6.540 (2.348) −0.103 (0.126) −23.525 (10.584) −44.246 (62.574)

–

18.304 (6.370) 534.823

19.512 (7.290) –

Misc.

35.448 (17.031) −0.077 (0.142) 297.278 (184)

5.640 (11.221) 0.507 (1.017) −11.296 (44.343) –

308.055 (197) 0.085 (0.248) –

– (327) –

–

–

–

Trans.

0.144 (0.171)

−5.433 (4.708) 209.731 (396) 140.672 (262) –

−30813 (36438) −455.735 (460) 4.018 (8.197) 0.338 (0.332) −5.251 (26.525) –

138.125

–

1664.010 (1783) –

Comm.

Note: The number of observations is 53. The dependent variable is productivity growth. All coefficients are estimated by random effect models. Standard errors are shown in parentheses. Constant terms are omitted. Data source: ICPA database.

Communication

Transportation

Misc. manufacturing

Rubber

Instrument

Transportation Equipment

Motor vehicle

Electrical machinery

Machinery

Fabricated metal

Primary metal

Clay & glass

Leather

1.387 (3.316) –

115.622 (92.532) –

Chemical

Petroleum

Motor

Variable

Table 11.1 (Continued)

223

224

Measuring the black box

224

matrix for the integrated region of East Asia and the United States. The results are reported in Table 11.2. The overall pattern of the matrix in this table seems to remain the same as before. Once again, the electrical machinery and communication sectors have no significant coefficients. In other sectors, however, statistical significance and sign conditions differ slightly from those in Table 11.1. To see the difference more clearly, we calculated the innovation backward and forward linkages and examined their significance using a z-test. Table 11.3a shows the results. Comparing the two samples, no difference exists in terms of statistical significance and sign condition. All other linkages show the same pattern between the two samples. Thus, even if the United States is added to the East Asian countries, the properties of innovation linkages remain almost the same. This implies that growth strategy in the East Asian region should not be significantly altered even if this strategy is extended to include the United States. Surprisingly, the data show no significant innovation backward and forward linkages in the electrical machinery sector. This is probably because of the fact that, while this sector should have positive innovation backward and forward linkages in terms of commodity and technology linkages, it has received and exerted little influence in terms of innovation linkages. Obviously, the linkages in this sector are significantly related to process technologies in other sectors, but appear to be less related to product innovation. This result might reflect the fact that product innovation becomes more important than process innovation in terms of productivity growth.16 Regarding innovation backward linkages, transportation equipment has positive effects. This is reasonable because this sector requires a variety of technology components to complete its products. Hence, its innovation backward linkages result in positive effects. Regarding innovation forward linkages, chemical and primary metal have strong effects with no innovation backward linkages. However, while chemical exerts positive effects, primal metal negatively contributes to other sectors’ innovation. This is probably due to the fact that innovation in materials first leads to replacement of current products using previous metal. In the short run, this substitution effects dominate. In the longer run, however, this innovation is fully incorporated into new products, leading to more TFP growth. Therefore, we expect that if more time lag is allowed, innovation in the primary metal sector will positively affect TFP growth in other sectors. The remaining significant sectors are rubber and transportation, which are significant in both innovation backward and forward linkages. In particular, rubber sectors have positive effects on both linkages, indicating that this sector is a key to innovation in our dataset. In contrast, the transportation sector exerts positive innovation backward linkages, but its effects on innovation forward linkages are negative. As mentioned above, since transportation requires a variety of technology components, it is reasonable that this sector’s backward linkages are positive. However, its negative innovation forward linkages imply that improvement in transportation service exerts substitution effects on other sectors, at least in the

6.910 (10.677)

0.618 (0.610) −17.285 (6.807) 0.847 (1.456) – –

−0.272 (18.113) –

–

–

–

–

–

–

–

21.469 (13.860)

2.947 (1.902) 3.382 (11.855) 0.912 (0.502) – (49.358) −1.067 (1.844) −64.012 (45.548) −0.280 (1.529) –

0.784 (0.309) −0.153 (1.124) 0.138 (0.108) −1.068 (2.409) – (13.184) –

Leather

–

– −2.864 (2.817) 0.270 (1.941) −0.015 (0.831) −0.896 (0.370) 24.512 (22.762) 1.679 (2.825) 8.224 (187) 193.623 (97.190) 577.593 (1281) 2.364 (6.437) 2.715 (10.809) −12.869 (11.735)

3.738 (2.107) –

P. metal 0.577 (0.368) –

−0.251 (0.169) 18.272 (0.149) 2.527 (4.034) −2.716 (1.974) −78.772 (222) 1.885 (1.013) −29.489 (9.661) −1.631 (3.713) 4444.790 (10798) 0.933 (0.802) −47.833 (55.587) 4.444 (2.088)

Clay

−79.588 (58.218) 3.899 (5.749) 0.206 (0.140) 0.680 (0.620) −1.126 (0.689) 0.880 (0.971) 190.806 (2.998) −1.754 (1.512) −46.008 (45.009) 0.511 (0.428) −266.441 (213) 66.259 (23.963)

4.248 (10.908) −0.137 (0.197) –

F. metal

20.326 (14.230) 2.293 (824) 13.743 (5.763) 0.009 (0.182) 2.382 (1.675) 0.596 (0.772) 1.684 (123) −0.526 (0.231) −3.179 (19.550) −1.300 (0.986) −7.478 (3.401) −0.657 (6.109)

–

−3.301 (20.492) –

Machine

−3.072 (2.229) −42.447 (225) 15.565 (45.006) −113.100 (138) 0.026 (0.482)

71.777 (51.179) 0.950 (2.069) 0.140 (0.189) 0.178 (0.654) 23.894

−1.571 (23.405) 342.843

–

2.764 (6.967) –

Electrical

Note: The number of observations is 72. The dependent variable is productivity growth. All coefficients are estimated by random effect models. Standard errors are shown in parentheses. Constant terms are omitted. Data source: ICPA database.

Communication

Transportation

Misc. manufacturing

Rubber

Instrument

Transportation Equipment

Motor vehicle

Electrical machinery

Machinery

Fabricated metal

Primary metal

Clay & glass

Leather −9.753 (4.798) 3.595

−0.155 (0.136) 0.407 (0.126) –

−0.082 (0.192) 17.518 (7.086) 20.913 (8.083) −3.151 (1.662) – (24.938) 7.651 (10.546) −0.851 (1.014) 12.181 (39.365) 4.807 (3.117) –

Chemical

Petroleum

Petro.

Chem.

Variable

Table 11.2 Innovation input–output matrix (Γ0 ) (with the USA)

225

−1.868 (2.796) −0.529 (0.347) –

−20.827 (15.064) 6.322 (7.737) 0.516 (0.428) −3.457 (13.900) 0.132 (0.133) 0.048 (0.342) 6.923 (10.207) –

– –

– –

6.039 (15.051) −0.645 (1.006) 347.673 (175)

−3.445 (10.284) 0.212 (0.118) 27.058 (39.817) –

240.935 (184) 0.030 (0.194) –

1.526 (1.016)

1.763 (2.765) –

−0.186 (0.138) –

0.497 (0.331) −23.268 (10.275) 2.594 (2.868) –

–

–

22.374

–

–

– (21.255) –

Inst.

Tran. eq.

44.180 (15.411) −29.293 (17.296) 196.797 (131) 0.499 (0.418) −1.337 (2.075) −0.126 (10.652) −0.396 (0.220) 0.506 (1.071) 1.320 (2.132) –

– (1006) –

–

−0.312 (2.071) –

Rubber

0.051 (0.416) 0.506 (0.438) −0.780 (0.867) 2.774 (1.066) 2.303 (8.420) −5.043 (5.245) −6.435 (2.055) −0.055 (0.101) −20.209 (9.255) −34.053 (53.830)

–

13.657 (4.737) 525.281

18.825 (6.286) –

Misc.

29.762 (13.928) 0.001 (0.120) 166.939 (159)

4.950 (9.492) 0.966 (0.844) 25.527 (36.870) –

158.022 (170) −0.114 (0.176) –

– (255) –

–

–

–

Trans.

0.162 (0.140)

−3.745 (3.449) 103.231 (318) 171.921 (200) –

−27165 (26678) −399.937 (356) 0.188 (6.088) 0.256 (0.251) 3.317 (20.069) –

114.600

–

2211.040 (1417) –

Comm.

Note: The number of observations is 72. The dependent variable is productivity growth. All coefficients are estimated by random effect models. Standard errors are shown in parentheses. Constant terms are omitted. Data source: ICPA database.

Communication

Transportation

Misc. manufacturing

Rubber

Instrument

Transportation Equipment

Motor vehicle

Electrical machinery

Machinery

Fabricated metal

Primary metal

Clay & glass

Leather

0.551 (2.819) –

137.270 (94.429) –

Chemical

Petroleum

Motor

Variable

Table 11.2 (Continued)

227

Innovation flow matrix & innovation linkages

227

short run. Therefore, facilitating innovation in this sector might cause a short-run productivity slowdown. Finally, note that the communication sector has no significant innovation backward and forward linkages. However, in our alternative empirical analysis using simple TFP growth data as explanatory variables, this sector generated positive innovation forward linkages; this result is consistent with the fact that the IT revolution contributed to positive economic growth (see, for example, Brynjolfsson and Hitt, 1996). The difference arises due to the fact that four sectors do not make R&D investment in communication technology in our dataset. Therefore, the result in Table 11.3a does not take into account these sectors’ effects in the regression analysis. As far as this sector is concerned, non-adjusted data might be more realistic in evaluating innovation linkages Table 11.3a Innovation backward and forward linkages Sector Chemical Petroleum Leather Clay & glass Primary metal Fabricated metal Machinery Electrical machinery Motor vehicle Transportation equipment Instrument Rubber Misc. manufacturing Transportation Communication

Without US

With US

backward

forward

backward

forward

55 (36491) 10 (32) −69 (49) 3396 (10559) 1014 (1168) −361 (310) 30* (16) 29 (978) 86 (94) 604** (302) 12 (32) 234* (139) 499 (1066) 636** (274) −29123 (36675)

1800*** (50) 18 (33) 45 (48) 662 (10522) −30767*** (1170) 183 (332) −38 (35) 25 (993) 19 (96) 181 (303) 319*** (29) 4414*** (148) 248 (1089) −803*** (274) 747 (36490)

50 (26723) −6 (30) −37 (51) 4313 (10841) 798 (1286) −128 (277) 25 (15) 298 (866) 125 (95) 618** (252) 5 (27) 212* (123) 497 (987) 386* (231) −24964 (26843)

2375*** (44) 18 (31) 35 (49) 584 (10801) −26815*** (1285) 145 (295) −28 (34) 132 (878) 22 (98) 197 (259) 237*** (24) 4946*** (134) 226 (1008) −452* (237) 568 (26722)

Note: The asterisks *, **, and *** means significance levels at 10%, 5%, and 1%, respectively. Standard errors are shown in parentheses.

228

Measuring the black box

228

Table 11.3b Innovation backward and forward linkages Sector Chemical Petroleum Leather Clay & glass Primary metal Fabricated metal Machinery Electrical machinery Motor vehicle Transportation equipment Instrument Rubber Misc. manufacturing Transportation Communication

Without US

With US

backward

forward

backward

forward

0.539 (0.836) 0.307 (0.518) 0.805*** (0.233) 0.711** (0.295) 0.735** (0.318) 0.403* (0.224) 0.313 (0.296) 0.733 (0.516) 0.142 (0.235) 0.037 (0.374) 1.120*** (0.402) 0.645 (0.403) 0.167 (0.223) 0.592** (0.286) 0.196 (0.765)

2.031*** (0.705) 0.620* (0.373) 2.184*** (0.812) −0.530 (0.807) −0.418 (0.873) 2.602** (1.204) −0.424** (1.204) −0.251 (0.598) 3.786*** (0.984) 0.339 (0.664) −0.932 (0.620) −2.224** (0.959) 1.495* (0.856) −2.263*** (0.730) 1.429*** (0.408)

0.529 (0.730) −0.074 (0.490) 0.785*** (0.246) 0.585* (0.302) 0.578** (0.275) 0.441** (0.192) 0.357 (0.273) 0.726 (0.472) 0.205 (0.206) 0.224 (0.301) 0.814** (0.342) 0.562 (0.374) 0.311 (0.196) 0.383 (0.272) 0.363 (0.586)

1.729*** (0.617) 0.906*** (0.308) 2.027*** (0.618) −0.682 (0.732) −0.100 (0.724) 2.649** (1.047) −0.521 (0.938) −0.126 (0.528) 3.153** (0.858) 0.458 (0.568) −0.857 (0.514) −2.211*** (0.846) 0.739 (0.692) −1.279** (0.636) 0.905** (0.359)

Note: The asterisks *, **, and *** means significance levels at 10%, 5%, and 1%, respectively. Standard errors are shown in parentheses.

because almost all sectors in the economies receive some spillover effects from communication technology even though some of the sectors do not make R&D investment in this technology. Therefore, we should also pay attention to the latter in interpreting the results of innovation linkages. Although we cannot discuss more in detail due to space limitations, we show the result of innovation backward and forward linkages in the alternative regression analysis in Table 11.3b. 3.3 Evaluating growth strategies Given these estimates of innovation linkages, we are now in a position to compare the magnitudes of such linkages in balanced and unbalanced growth

229

Innovation flow matrix & innovation linkages

229

strategies. To achieve this, the difference in innovation forward linkages across the sectors must be tested. We calculated the z-statistics for the pairwise difference between two sectors in innovation forward linkages. Tables 11.4 and 11.5 show the results in the samples without and with the United States, respectively. These tables clearly suggest that many pairs of sectors are statistically different in innovation forward linkages. In particular, innovation forward linkages of the chemical, primary metal, instrument, rubber, and transportation sectors are significantly different from those of many other sectors. These sectors also exerted strong innovation forward linkages in Table 11.3a. Thus, sectors with significant innovation forward linkages tend to be differentiated from many other sectors in the pairwise difference of innovation forward linkages. These results imply that an unbalanced growth strategy should be pursued in both regions. Suppose some kind of unbalanced growth strategy is chosen to be implemented in these regions. The next question to arise is which sectors should become the targets of this unbalanced strategy. In development strategy, Hirschman (1958) suggested that investment should be promoted in the sectors that induce more investment in other sectors. In the innovation input–output analysis, this implies that sectors that induce more innovation should be subsidized to increase productivity growth. In other words, sectors with high innovation forward linkages should become the targets. If we select sectors on the basis of the 5% significance level, the target sectors consist of chemical, instrument, and rubber while excluding the primal metal sector due to its negative sign. In addition, in our alternative regression analysis, the communication sector generated strong innovation forward linkages. To further characterize these sectors, Table 11.6 lists the growth rate and volatility of these sectors. As the average growth rates for the 15 sectors are 1.54% and 1.72% for with and without the US samples, respectively, only the communication sector achieves higher productivity growth than the average in both regions. The instrument sector achieves higher growth than the average in the East Asian region, but slightly less than the average in the integrated region. Therefore, the core sector becomes communication in both regions. The other sectors – chemical, instrument, and rubber – are characterized as bottleneck sectors owing to their lower growth rates. The growth strategy should maintain the current growth rates of the core sectors, while promoting more productivity growth in the bottleneck sectors. In the case of core sectors, more emphasis might be placed on removing current trade barriers and facilitating trade liberalization in the target region to boost innovation in the region as a whole. Innovation can diffuse without commodity trade, but its linkages will be magnified if it is actually purchased. For example, trade restrictions during the Edo era and in World War II blocked the import of foreign commodities to Japan, with negative impacts on productivity growth. The removal of foreign import restrictions after the Meiji restoration and again after World War II provided the spur for economic growth. Hence, trade barriers that impede commodity and innovation flows should be removed for the purpose of promoting innovation. In the case of bottleneck sectors,

Petro

Leather Clay

P metal F metal

Machine Elec

Motor

Trans eq Instru

Rubber Misc.

Trans

Com

Note: Z statistics are reported in the table. The asterisks *, **, and *** mean significance levels at 10%, 5%, and 1%, respectively.

Chemical 29.8*** 25.5*** 0.1 27.8*** 4.8*** 30.1*** 1.8** 16.4*** 5.3*** 25.8*** −16.7*** 1.4 9.3*** 0.3E-01 Petroleum – −0.4 −0.6E-01 26.3*** −0.5 1.1 −0.7E-02 −0.9E-02 −0.5 −6.9*** −29.0*** −0.2 3.0*** −0.2E-01 Leather – −0.6E-01 26.3*** −0.4 1.4 0.2E-01 0.2 −0.4 −4.9*** −28.0*** −0.2 3.0*** −0.2E-01 Clay & glass – 3.0*** 0.5E-01 0.7E-01 0.6E-01 0.6E-01 0.5E-01 0.3E-01 −0.4 0.4E-01 0.1 −0.2E-02 Primary metal – −25.4*** −26.3*** −20.1*** −26.2*** −25.6*** −26.6*** −29.8*** −19.4*** −24.9*** −0.9 Fabricated metal – 0.7 0.2 0.5 0.3E-02 −0.4 −11.6*** −0.6E-01 2.3** −0.2E-01 Machinery – −0.6E-01 −0.6 −0.7 −7.8*** −29.2*** −0.3 2.8*** −0.2E-01 0.8 −0.2E-01 Electrical – 0.6E-02 −0.2 −0.3 −4.4*** −0.2 machinery Motor vehicle – −0.5 −3.0*** −24.9*** −0.2 2.8*** −0.2E-01 Transportation – −0.5 −12.5*** −0.6E-01 2.4** −0.2E-01 equip Instrument – −27.1*** 0.7E-01 4.1*** −0.1E-01 Rubber – 3.8*** 16.7*** 0.1 Misc. – 0.9 −0.1E-01 manufacturing Transportation −0.4E-01

Variable

Table 11.4 Z tests for pairwise differences in innovation forward linkages (without US)

Petro

Leather Clay

P metal F metal

Machine Elec

Motor

Trans eq Instru

Note: Z statistics are reported in the table. The asterisks *, **, and *** mean significance levels at 10%, 5%, and 1%, respectively.

Trans

Com

1.8** 1.9**

−0.2E-01 −0.1E-01

–

−0.1E-01

0.1E-01 2.9*** −0.1E-01 4.6*** ,19.8*** 0.2 – 0.7 −0.1E-01

−0.2 −0.3E-01

2.13** 11.7*** 0.7E-01 −0.2 2.0** −0.2E-01 −0.2 2.0** −0.2E-01 0.3E-01 1.0E-01 0.6E-03 −16.6*** −20.2*** −1.0 −0.8E-01 1.6 −0.2E-01 −0.3 1.8* −0.2E-01 0.6 −0.2E-01 −0.7E-01

Rubber Misc.

Chemical 44.6*** 35.4*** 0.2 22.7*** 7.5*** 43.3*** 2.6** 22.0*** 8.3*** 42.6*** −18.2*** Petroleum – −0.3 −0.5E-01 20.9*** −0.4 1.0 −0.1 −0.4E-01 −0.7 −5.6*** −35.8*** Leather – −0.5E-01 20.9*** −0.4 1.1 −0.1 0.1 −0.6 −3.7*** −34.4*** Clay & glass – 2.5** 0.4E-01 0.5E-01 0.4E-01 0.5E-01 0.3E-01 0.3E-01 −0.4 Primary metal – −20.4*** −20.8*** −17.3*** −20.8*** −20.6*** −21.0*** −24.6*** Fabricated metal – 0.6 0.1E-01 0.4 −0.1 −0.3 −14.8*** Machinery – −0.2 −0.5 −0.9 −6.4*** −36.0*** Electrical – 0.1 −0.7E-01 −0.1 −5.4*** machinery Motor vehicle – −0.6 −2.1** −29.7*** Transportation – −0.2 −16.3*** equip Instrument – −34.6*** Rubber – Misc. manufacturing Transportation

Variable

Table 11.5 Z tests for pairwise differences in innovation forward linkages (with US)

231

232

Measuring the black box

232

Table 11.6 Average growth rate and volatility Sector Sector average Chemical Petroleum Leather Clay & glass Primary metal Fabricated metal Machinery Electrical machinery Motor vehicle Transportation equipment Instrument Rubber Misc. manufacturing Transportation Communication

Without US

With US

Growth

Variance

Growth

Variance

0.017 0.013 0.010 0.008 0.013 0.006 0.009 0.018 0.042 0.016 0.013 0.020 0.012 0.005 0.005 0.066

0.003 0.007 0.006 0.002 0.002 0.002 0.001 0.001 0.004 0.001 0.002 0.004 0.004 0.001 0.002 0.007

0.015 0.011 0.009 0.007 0.012 0.007 0.008 0.023 0.044 0.012 0.010 0.017 0.013 0.006 0.005 0.048

0.002 0.005 0.006 0.001 0.002 0.001 0.001 0.001 0.003 0.001 0.002 0.003 0.003 0.001 0.001 0.006

more policy intervention is needed to promote productivity growth by subsidizing R&D investment. Among the targets of unbalanced growth strategy, only the rubber sector also has significantly positive innovation backward linkages, but it suffers from lower growth rates. Thus, the innovation backward linkages seem to exert a negative effect on productivity growth among the target sectors. This occurs because high innovation backward linkages are sensitive to productivity changes in other sectors. When other sectors enjoy positive growth, sectors with high innovation backward linkages also experience a positive effect. Conversely, in the case of productivity decline, the productivity of those sectors is negatively affected. Over the 20 years of data, these sectors may have experienced even more negative effects. Thus, paradoxically, sectors with high innovation forward and backward linkages tend to become bottlenecks. As we have seen, an unbalanced growth strategy that aims to improve productivity growth in these core and bottleneck sectors should be implemented. However, because the coverage of the strategy extends beyond national boundaries, it would be difficult to implement. In particular, without policy coordination across the countries, an innovation-promoting unbalanced strategy cannot be put into practice. For example, one country cannot be expected to subsidize R&D investment in another country unless that R&D is undertaken by domestic firms. However, the country can indirectly subsidize R&D in another country by removing trade barriers. In turn, such indirect subsidization has positive repercussions in domestic sectors. Policy coordination in implementing a growth strategy will always involve practical difficulty, but the difficulty can be avoided with a proper understanding of the innovation flow matrix and innovation linkages in the target region.

233

Innovation flow matrix & innovation linkages

233

4 Concluding remarks This chapter developed the underlying theoretical model for an innovation flow matrix and derived the implications for growth strategy. Our empirical investigation in four countries – the United States, Japan, Korea, and China – revealed that innovation linkages are sometimes negative but quite a few sectors show positive and significant innovation linkage effects. The estimated innovation linkages of the two regions – the East Asian region and the integrated region of East Asia and the United States – showed similar patterns. The empirical tests favored an unbalanced growth strategy, and communication is identified as a core sector, while chemical, instrument, and rubber are bottlenecks. In particular, rubber showed lower growth with positive and significant innovation backward linkages. This result implies that sectors having both high innovation backward and forward linkages are likely to become bottlenecks in the process of economic growth. The unbalanced growth strategy should place more emphasis on removing current trade barriers and facilitating trade liberalization in the core sectors of the target region. In the case of bottleneck sectors, more policy intervention is needed to promote productivity growth by subsidizing R&D investment. Although a practical difficulty always exists in implementing a growth strategy across national boundaries, policy coordination still seems feasible as long as the findings from the innovation flow matrix are shared. Chapters 10 and 11 are a first attempt at providing a theoretical justification for innovation input–output analysis with simple quantitative analysis. More theoretical and empirical studies are needed. In particular, this chapter assumes that some common innovation linkages have existed across the East Asian region for over 20 years (1980–2000). This assumption is quite bold, but it is necessary owing to the limited number of observations. Construction of the innovation flow matrix without the need for such an assumption remains an important challenge for future research. In addition, this chapter focuses exclusively on TFP growth and does not address factor growth, such as physical and human capital accumulation patterns. The impact of these growth drivers on the estimation of innovation linkages should also constitute a future research agenda, as this would deepen our understanding of the properties of regional innovation systems, ultimately leading to more effective growth policy.

Notes 1 For example, according to the OECD innovation strategy (OECD, 2010), the following five priorities for government action promote innovation: (1) empowering people to innovate; (2) unleashing innovation in firms; (3) creating and applying knowledge; (4) applying innovation to address global and social challenges; and (5) improving the governance and measurement of policies for innovation. Although they definitely constitute crucial policy guidelines for innovation, complementarity among technologies has not been taken into account in the form of explicit policy implications.

234

Measuring the black box

234

2 International R&D spillover effects were measured in these studies by regressing foreign R&D capital on domestic TFP. 3 Process innovation is defined in this study as “more output can be produced with the same amounts of the different inputs, affecting the coefficients column-wise. This implies a shift of the production function and the isoquant”. Produce innovation means that “in each of the n production processes, the same amount of output can be obtained with a smaller amount of this product as an input”. See Dietzenbacher (2000, p. 28). 4 Dietzenbacher (2000) evaluated spillover effect of innovation as “the percentage of the total output change that occurs in sectors i other than the innovated sector k”. See Dietzenbacher (2000, p. 32). 5 For example, suppose the effect of innovation in the ith sector on innovation in the jth effect of the ith sector is denoted by gij, which is referred to as intersectoral spilloverX sector on the jth sector. The overall spillover effect is measured by gij. Then, we j

cannot recover X each intersectoral spillover effect gij (j ¼ 1; . . . ; n) from the aggregate value of gij . j

6 For example, suppose an improvement in DRAM (dynamic random access memory) increases the productivity of personal computer (PC) and videogame sectors that use DRAM. Innovation backward linkages of the PC (videogame) sector measure its productivity gain as a result of DRAM improvement. Innovation forward linkages correspond to the sum of productivity gains in PC and videogame sectors. 7 In what follows, we simply use the term “intersectoral spillover effects” instead of “intersectoral spillover effects in innovation”. These spillover effects measure how innovation in one sector affects innovation in other sectors and vice versa. See also endnote 4. 8 The intermediate sectors in this model do not produce intermediate goods. Instead, they produce technology components that are transformed to production technologies of commodity sectors. 9 Thus, each intermediate supplier can be upstream because it supplies its technology components to other intermediate suppliers. It can also be downstream because it purchases technology components from other suppliers. 10 This specification departs from the standard specification under the input–output analysis such as dynamic TFP model in Kuroda and Nomura (2004). However, we employ the o-ring function in this chapter for the following reasons. First, the o-ring function allows characterization of the equilibrium structure of the technology system consisting of many technology components, whose innovation could also be endogenously determined. Second, this production function gives rise to closed-form solutions. Third, it provides the underlying economic structure behind the innovation matrix, rather than implicitly assuming some TFP spillovers. 11 The technology component q is treated as if it is an intermediate good in this model. 12 According to Figure 11.1, the jth technology component is supplied to the ith intermediate supplier, who in turn supplies the production technology to the ith commodity sector. However, as described above, because of constant returns, it makes no difference to assume that the ith commodity producer behaves as if it directly purchases the jth technology component. 13 Note that e disappears in the following equation because it is represented in terms of qhj;t1 . 14 This integration is made to derive the solution that satisfies (11.3) and zero profits. The imposition of this integration condition is not implied by the model. Rather, this corresponds to the “guess” method of deriving value function in dynamic

235

Innovation flow matrix & innovation linkages

235

programming. It is easy to check that the solution satisfies both. p is strictly convex with respect to the q that ensures an optimum exists. 15 Since the oldest electrical data publicly available is 2002 version, we used this dataset. 16 In this context, process innovation refers to technical change in production technologies for a given product, while product innovation means technical change in that product.

12 Endogenous innovation and macroeconomic shocks in a New Keynesian DSGE model

1 Introduction What determines the rate and direction of innovation in an economy? How do macroeconomic policies affect innovation? The first question has been explored in both the economic history (David, 1975; Rosenberg, 1976, 1982) and endogenous growth literature (Aghion and Howitt, 1998a; Segerstrom, Anant, and Dinopoulos, 1990; Acemoglu, 2009; Galor, 2011). In particular, the latter formalizes endogenous innovation as a result of R&D and succeeds in showing how government taxes and subsidies influence the rate of endogenous innovation. However, the endogenous growth models typically assume away fluctuations in output, consumption and labor employment, market frictions, and monetary policies such as the Taylor rule, all of which constitute major research topics in the New Keynesian dynamic stochastic general equilibrium (DSGE) literature (Christiano, Eichenbaum, and Evans, 2005; Smets and Wouters, 2003, 2007). The second question should be addressed by the New Keynesian DSGE models, but they only consider productivity shocks without incorporating endogenous innovation. Hence, it remains ambiguous as to how monetary policy and other macroeconomic shocks affect endogenous innovation in an economy. The purpose of this chapter is to incorporate endogenous innovation into a standard New Keynesian DSGE model in an attempt to answer these two questions regarding innovation. Unlike the models presented in the endogenous growth literature, the model in this study allows for capital accumulation, business cycles, market frictions, and monetary policies. In addition, unlike the scenarios outlined in the New Keynesian DSGE literature, this study enables Schumpeterian entrepreneurs to undertake innovation leading to endogenous innovation in an economy, in addition to productivity shocks. Moreover, we also incorporate labor and investment shocks to generate more subtle business fluctuations. In this setting, we can evaluate how endogenous innovation is affected by other macroeconomic variables. In this study, we first develop a New Keynesian DSGE model with endogenous innovation and then estimate the model parameters using Japanese economic data. Given the estimates, we evaluate the relationship between endogenous innovation and macroeconomic variables. We find that while endogenous innovation and output respond similarly to most of the shocks, they react in opposite directions

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to wage shocks and monetary policy shocks. This implies that policies that increase wage rates and interest rates facilitate endogenous innovation at the cost of the output level. However, note that endogenous innovation has a permanent effect in terms of the productivity level. Thus, the long-term effect of these policies on output is positive, although the short-term effect is negative. This result suggests that the zero interest rate policy in Japan in recent years might have had a negative effect on both endogenous innovation and output, although its short-term effect on output could have been positive. The result also suggests that any innovation policies that generate positive productivity gains in terms of future innovation discourage endogenous innovation, while positive productivity shocks to current production technologies encourage endogenous innovation. In other words, R&D investment and the productivity shock of endogenous innovation are negatively correlated, suggesting that innovation policies should take into account this salient relationship between two types of productivity gains. These results clearly suggest both a trade-off and complementary relationship between current technologies and future innovation. The rest of this chapter is organized as follows. In Section 2, we present the basic New Keynesian DSGE model. Section 3 describes the empirical analysis based on the proposed model. Section 4 concludes.

2 The model The model presented in this study blends the New Keynesian DSGE model (Christiano, Eichenbaum, and Evans, 2005; Smets and Wouters, 2003, 2007) and the Schumpeterian endogenous growth model (Aghion and Howitt, 1992, 1998a; Grossman and Helpman, 1991). More specifically, we follow the DSGE model in Hirose and Kurozumi (2012) in relation to the former and Phillips and Wrase (2006) regarding the latter. Although Phillips and Wrase (2006) also incorporate endogenous innovation into their macroeconomic model, their model is primarily based on the real business cycle literature (see Cooley, 1995; King and Rebelo, 1999; Rebelo, 2005 for a review of this literature) without market frictions. Anzoategui et al. (2016) provide an exception by incorporating endogenous innovation into the New Keynesian DSGE model and examining how endogenous innovation accounts for business cycles in the US. However, this study differs from Anzoategui et al. (2016) in that we model endogenous innovation in terms of the Schumpeterian competition, implying new interpretation of the Calvo mechanism, and put more emphasis on the effects of macroeconomic shocks on endogenous innovation, rather than on the effects of endogenous innovation on business fluctuation. In this respect, Harada (2018a) also presents an integrated model of the Schumpeterian endogenous growth and a New Keynesian DSGE, but the current study differs from that of Harada (2018a) by incorporating wage stickiness in addition to price stickiness and adding more macroeconomic shocks, such as preferences, government expenditure, investment adjustment costs, investment-specific technology (IST), and endogenous innovation shocks.

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Measuring the black box

238

Thus, the model presented in this study enables a more comprehensive analysis of the effects of these shocks on endogenous innovation. 2.1 Households There is a continuum of households h 2 ½0; 1 in this economy. Each household purchases consumption goods Cj;t and one-period riskless bonds Bj;t , and supplies Z1 one kind of differentiated production labor service Lh;t ¼ Lh;t ðf Þdf to interme0

diate goods, firms, and R&D labor services Nh;t to entrepreneurs. Each household maximizes their lifetime utility function as follows: " # 1s 1þx 1 X A1s εlt L1þZ A1s εnt Nh;t h;t t b ðCh;t  yCh;t1 Þ t t   ; ð12:1Þ b εt Et 1s 1þZ 1þx i¼0 where Et is the expectation operator conditional on all information available in period t and 0 < b < 1 is the discount factor. Utility is positively related to the consumption goods relative to an external habit variable y and negatively related to the supply of labor services. εbt is a shock to the discount factor, which affects both the marginal utility of consumption and the marginal disutility of labor. Following Erceg, Guerrieri, and Gust (2006), Ats1 is added to ensure balanced growth in the economy, where At denotes total productivity, which is specified later. Note that consumption is not indexed by h because the existence of state-contingent securities ensures consumption and asset holdings are the same for all households in equilibrium. εlt and εnt are shocks to labor and R&D labor supply, respectively. Maximization is subject to the following sequence of budget constraints: Z1 Bt Bt1 Ct þ Ih;I þ ¼ Wt ðLh;t þ Nh;t Þ þ Zt Ut Kt1 þ Rt1 þ Tt þ Pi;t di Pt Pt 0 Z Z Z Z P Pi;t1 QRi;t1 di þ PPi;t1 QPi;t1 di  Pi;tR QRi;t di  PPi;t QPi;t di; þ i2success

i2fail

ð12:2Þ subject to the law of motion of capital "  i 2 # w ε I t t ; Kt ¼ ð1  dðUt ÞÞKt1 þ εct It 1  1 2 a It1

ð12:3Þ

where Pt is the general price level, It is the gross investment in capital, Rt is the nominal interest rate, and Wt is the real wage rate. Zt is the return on capital and Ut denotes the rate of utilization of capital stock Kt . Following Christiano, Eichenbaum, and Evans (2005) and Smets and Wouters (2003), we incorporate

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the convex friction costs associated with variations in the use of the installed capacity, represented in the last term on the right-hand side of (12.3). dðUÞ is the depreciation rate of capital with the properties of d0 > 0, d@ > 0, 0 < d < 1, and m ¼ d0 =d@ > 0, where m is the steady-state capital utilization rate. This dependence on the capital utilization rate is adopted in Greenwood, Hercowitz, and Huffman (1988). Following Justiniano, Primiceri, and Tambalotti (2010), εct is incorporated as the IST shock that measures exogenous variations in the efficiency with which the final good can be transformed into physical capital. εit is a shock specific to the investment adjustment costs. Households own equity shares of production firms and entrepreneurs from the previous period. After observing all relevant prices and the probabilities of successful innovation by the current entrepreneurs, households choose the amount of equity shares to hold until the next period, when the results of research are known by households. Thus, in terms of the budget constraint, Pi;tR and QRi;t are the price and quantity, respectively, of equity shares issued by entrepreneurs undertaking innovation in the ith sector. These shares are purchased by households, whose proceeds in turn X are used by entrepreneurs to hire R&D labor Nt. This implies that Wt Nt ¼ Pi;tR QRi;tþ1 holds in equilibrium. The dividends on i

equity shares held by the household in the previous period amount to successful entrepreneurs’ profits Pi;t (i 2 success) in the current period. PPi;t and QPi;tþ1 are the price and quantity, respectively, of equity shares issued by the production firm in the ith sector. Therefore, if the entrepreneur succeeds in innovation, the equity shares of the production firm in the corresponding sector will not pay dividends in the next period. However, if the entrepreneur fails in innovation, the production firm will pay dividends in the next period. The first-order conditions associated with the household problem with respect to Ct , Btþ1 , Ut , Ni;t , Kt , It , QRtþ1 , and QPtþ1 yield Gt ¼ εbt ðCt  yCt1 Þ

s

s

 bhεbtþ1 ðCtþ1  yCt Þ ;

ð12:4Þ

Gt ¼ bEt Gtþ1 ; Rt

ð12:5Þ

Zt ¼ qt d0 ðUh;tþ1 Þ;

ð12:6Þ

A1s εnt Ni;tx ¼ Gt Wt ; t

ð12:7Þ

Qt ¼ bEt fGtþ1 Ztþ1 Uh;tþ1 þ Qtþ1 ð1  dðUh;tþ1 ÞÞg;

ð12:8Þ

"

 2  # w εit It εit It εit It Gt  Q ε 1  1 w 1 2 a It1 a It1 a It1 " #  2  i i εtþ1 Itþ1 Itþ1 c εtþ1 1 ; ¼ wbEt Qtþ1 εtþ1 a It a It c t t

ð12:9Þ

240

Measuring the black box " # Gtþ1 Pi;tþ1 þ PPi;tþ1 ¼ 1; Et ð1  oÞb Gt PRi;t # Gtþ1 Pi;tþ1 þ PPi;tþ1 ¼ 1; Et ob Gt PPi;t

240 ð12:10Þ

"

ð12:11Þ

where Gt denotes the Lagrange multiplier and Qt corresponds to Tobin’s Q, which measures the price of capital to be purchased from capital producers in this model. Households supply differentiated labor in a market structure of monopolistic competition. This service is sold to a representative firm that aggregates these different types of labor into a single labor input as 8 1 91þmwt 0 is the magnitude of innovation, which is assumed to be the same for all intermediate goods sectors. We assume that innovation is patented to block the imitation of new technology by rival firms. However, the previous technology becomes available to rival firms. Cost minimization conditions yield real marginal costs of 1 Wt‘ MCi;t‘ ¼ a εt αA‘i;t

!α 

1α Zt ; 1α

ð12:23Þ

where ‘ ¼ F; S. The superscripts F and S emphasize the failure and success of innovation, respectively. Hence, WtS ¼ Wt and WtF ¼ Wt . The capital–labor ratio is identical among successful entrepreneurs and incumbent intermediate goods firms, and is given by Uf ;t Kf ;t1 ð1  αÞWt‘ ¼ : Lf ;t αZt

ð12:24Þ

Suppose a successful entrepreneur turns into a production firm at the beginning of period t, setting their price to maximize max Et PSi;t

1 X j¼0

" # j  Gtþj PSi;t Y ptþk1 Zp S ðboÞ p  MCi;tþjjt Yi;tþj ; Gt Ptþj k¼1 p j

ð12:25Þ

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subject to "

PSt Y ptþk1 Zp Ytþj ðf Þ ¼ p Ptþj k¼1 p j

#mptþj Ytþj ;

ð12:26Þ

where S denotes the success of innovation, 1  o is the probability of innovation S in period t, which will be specified later, and MCi;tþjjt is the real marginal cost in period t þ j for the firm whose price was last set in period t. Zp 2 ½0; 1 is the weight of price indexation to past inflation relative to steady-state inflation. Note that while 1  o is endogenous in this model, its value remains constant in steady states. We assume that the steady-state value of 1  o is known to successful entrepreneurs and they use it in the calculation of (12.25). The firm takes as given the paths of MCi;tþjjt , Ytþj , and Ptþj . The first-order condition yields " #mptþj j  1 X Y ptþk1 Zp p j p Gtþj S Et ðboÞ mtþj MCi;tþjjt Yi;tþj p G p t tþk k¼1 j¼0  Pt ¼ : ð12:27Þ " # p j  1 Zp p mtþj þ1 X Y G p j tþj tþk1 Et ðboÞ ðmptþj  1Þ Ytþj ptþk G p t k¼1 j¼0 The aggregate price is reduced to 2 " # p3 j  1 Zp p mt X Y p p m tk 5; dt ¼ ð1  oÞ4ðPt Þ t þ oj Ptj ptkþ1 p k¼1 j¼1 Z1 where dt ¼

ðPi;t =Pt Þ

ð12:28Þ

p

mt

di represents the price dispersion of intermediate goods.

0

2.4 R&D investment A Schumpeterian entrepreneur exists in each intermediate goods sector and undertakes R&D. The entrepreneur issues equity shares QRi;tþ1 to finance R&D investment. The result of the R&D investment is revealed at the end of the period. Successful entrepreneurs become intermediate goods producers in the next period. These entrepreneurs hire R&D labor in period t to maximize the expected gains from innovation ð1  ot ÞEt b

Gtþ1 ½Pi;tþ1 þ PPi;tþ1 QPi;tþ1   Wt Ni;t ; Gt

ð12:29Þ

subject to Wt Ni;t  Pi;tR QRi;tþ1 . The innovation probability is assumed to be proportional to the amount of R&D labor 1  ot ¼ kNi;tw ;

ð12:30Þ

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Measuring the black box

244

where k is sufficiently large to induce R&D investment and 0 < w < 1 represents R&D efficiency incorporating diminishing returns. We assume that only one entrepreneur exists in each intermediate goods sector.1 Due to the symmetry condition, P , QPi;tþ1 , and Pi;tþ1 are the same across all of the intermediate goods Ni;t , Pi;tþ1 sectors. The first-order condition is Gtþ1 ½Ptþ1 þ PPtþ1 QPtþ1  ¼ Wt : ð12:31Þ Gt Moreover, o remains constant over time in the steady state. Hence, aggregated endogenous productivity growth is given by wkNtw1 Et b

ln At =At1 ¼ a þ ln εat ;

ð12:32Þ

where a  ð1  oÞl and εat is an exogenous shock specific to endogenous innovation. 2.5 Central bank The monetary authority sets the nominal interest rate using the Taylor rule (Taylor, 1993) ( ) ! 3 ptj 1X Yt n n n þ y ln  þ εrt ; ln logRt ¼ r logRt1 þ ð1  r Þ logR þ p 2 j¼0 p Yt ð12:33Þ where r is the degree of interest rate smoothing, R is the steady-state nominal interest rate, p and y are the degree of interest rate policy responses to inflation and the output gap, respectively, and Yt is the potential output specified by n

Yt ¼ εat ðUKAt1 Þ

1α

α

ðAt LÞ  At ;

ð12:34Þ

Where U, K, and L are the steady-state values of aggregate labor and capital stock. The monetary policy shock εrt is governed by a stationary first-order autoregressive process. 2.6 Market clearing condition The market clearing condition for final goods is Yt ¼ Ct þ It þ gAt εgt ;

ð12:35Þ

where εrt is a shock to government expenditure. This completes the description of the model presented in this study. We also assume that all equity markets clear, so that the number of shares held for each sector and type of firm is equal to the number of shares outstanding, such that QPi;t ¼ QRi;t ¼ 1:

ð12:36Þ

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Endogenous innovation & macroeconomic shocks

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2.7 Exogenous shocks Each exogenous shock follows the univariate first-order autoregressive process ln εxt ¼ rx ln εxt1 þ ext ;

ð12:37Þ

where x ¼ fb; n; a; w; c; i; g; s; p; rg and rx 2 ½0; 1Þ. ext is white noise with zero mean and variance s2x . Note that εwt and εPt are specified in the Appendix. 2.8 Solution The model presented in this study allows for a balanced growth in output and consumption per household as a result of endogenous innovation. To undertake the steady-state analysis, we need to detrend relevant variables for all endogenous variables to be stationary. We transform the relevant variables as yt  Yt =At ; ct  Ct =At ; kt  Kt =At ; it  It =At ; gt  Ast Gt wt  Wt =At ; pPt  PtP =At ; and pRt  PtR =At : The other untransformed variables are also expressed in lowercase letters below to emphasize the fact that all endogenous variables are stationary. Next, we log-linearize the relevant first-order conditions. For this purpose, sector-specific variables must be aggregated over Rall of the Rintermediate sectors. We define these aggregated variables as, yt  yi;t di; kt  ki;t di; nt  R R R R ni;t di; lt  li;t di; mct  mc‘i;t di; and at  a‘i;t di. Using the local approximation method (Uhlig, 1995), we derive the system of equations described in the Appendix. A hat on a variable denotes the logarithmic deviation of the original variable with respect to its steady-state value (i.e., x^t = ln xt – ln x). 2.9 Estimation method We use Bayesian methods to characterize the posterior distribution of the parameters to be estimated and the Kalman filter to evaluate a likelihood function of the system of equations, and apply the Metropolis–Hastings algorithm to generate draws from the posterior distribution of the parameters. The posterior draws enable us to make inferences regarding the parameters, variance decomposition, and Kalman smoothed estimates. It should be noted here that since the marginal costs are detrended, all of the transformed marginal costs are the same across intermediate goods sectors. Even ^ t ¼ Et A ^ ‘ ; due if At 6¼ A‘i;t ; their expected growth rates should coincide such that A i;t to the same amount of R&D investment across entrepreneurs and the law of large ^ Fi;t ¼ mc ^ t holds in the steady-state. ^ St ¼ mc numbers. Hence, mc 2.10 Data Following Sugo and Ueda (2008), we use data from nine quarterly Japanese time series, i.e., per capita real GDP, per capita real consumption, per capita real investment, real wages, labor hours, the consumer price index, the overnight

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Measuring the black box

246

Table 12.1 Parameter estimation Parameter

Distribution

Mean

90% interval

s y Z w m  gw o gP x Z L p Rn r p y rz rb ri rg rw rp rr rn rc rs

gamma beta gamma gamma gamma gamma beta beta beta gamma gamma norm gamma gamma beta gamma gamma beta beta beta beta beta beta beta beta beta beta

1.163 0.445 2.278 6.383 8.615 0.071 0.138 0.809 0.562 2.014 0.139 0.033 0.196 0.483 0.803 1.530 0.227 0.070 0.987 0.323 0.989 0.082 0.775 0.224 0.303 0.817 0.423

[0.744, 1.529] [0.363, 0.535] [1.261, 3.264] [4.301, 8.522] [5.956, 10.859] [0.054, 0.088] [0.008, 0.259] [0.765, 0.851] [0.2541, 0.860] [1.819, 2.166] [0.085, 0.185] [-0.044, 0.112] [0.107, 0.282] [0.420, 0.544] [0.755, 0.852] [1.406, 1.649] [0.172, 0.281] [0.008, 0.132] [0.978, 0.996] [0.210, 0.442] [0.982, 0.996] [0.012, 0.147] [0.694, 0.852] [0.105, 0.339] [0.048, 0.546] [0.500, 0.970] [0.046, 0.802]

call rate, and the relative price of investment goods (see also Hirose and Kurozumi, 2012). The sample period is from 1981:1Q to 1998:4Q because the effect of zero lower bounds on nominal interest rates emerged later, and thus is not taken into account in the model presented in this study. We follow Sugo and Ueda (2008) to calibrate d ¼ 0:06, α ¼ 0:63, and Zw ¼ 0:2. Prior distributions of parameters are summarized in Table 12.1.

3 Empirical analysis In this section, we estimate the relevant parameters appearing in the system of equations in the Appendix and evaluate the effects of stochastic shocks on endogenous variables. In particular, we are interested in examining how these shocks affect the rate of endogenous innovation. 3.1 Parameter estimates The posterior estimates of the structural parameters are also reported in Table 12.1. The estimates are quite similar to those of Sugo and Ueda (2008) and

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Hirose and Kurozumi (2012). Therefore, we leave the detailed interpretation of most of the estimates to these related studies. Instead, we only mention the estimate of the probability of innovation, 1  o, because this is a new parameter. This estimate is 0.191, implying that 19% of existing intermediate goods are to be replaced by new intermediate goods. 3.2 Variance decomposition Next, we analyze the driving forces behind fluctuations by examining the variance decomposition of the main macroeconomic variables implied by the estimated model. Table 12.2 reports the contribution of each shock to the variance of the observed growth rates of macroeconomic variables over the period 1981:1Q to 1998:4Q. It should be noted that both the preference shock ebt and the government demand shock egt account for a significant portion of the variations in most of the macroeconomic variables. This implies that demand shocks in both households and the government play a critical role in generating business fluctuations. In addition, the investment adjustment cost shock eit contributes to variances in output, consumption, and investment, while the shock to IST remains of modest importance in generating variations in these variables. As far as the model presented in this study is concerned, the latter shock does not show a significant propagation mechanism, which stands in sharp contrast to the result of Justiniano, Primiceri, and Tambalotti (2010). However, because our main interest lies in endogenous innovation, we only mention this difference here and do not explore this issue further in this study. 3.3 The effects of shocks on endogenous innovation Now, let us examine the effects of various shocks on endogenous innovation, which can be measured by changes in R&D labor. Figures 12.1 to 12.9 show

Table 12.2 Variance decompositions Variables Variance c R p q z i k u l w y

52.0489 1.4269 1.4644 8.0893 20.5607 195.0143 1119.868 868.3141 10.9638 17.4916 8.9024

Percentage owing to: ebt

eit

egt

ewt

ept

ert

eat

26.14 72.63 47.56 3.79 51.74 51.07 90.24 89.08 17.95 17.91 20.01

1.36 0.86 0.78 31.46 11.95 26.04 1.55 1.47 4.19 1.69 18.39

67.53 10.02 14.88 4.07 4.62 1.52 4.24 6.07 30.42 1.99 23.69

0.26 0.61 1.27 0.58 0.28 0.45 0.12 0.12 2.66 2.68 1.37

2.42 8.14 26.15 28.51 13.5 7.54 0.11 0.25 12.15 40.77 20.2

0.22 1.6 0.04 3.07 1.15 0.19 0.03 0.03 1.58 0.01 0.85

1.46 0.59 0.01 6.07 0.04 0.03 8.66 0.49 0.18 15.54 12.81 0.18 10.4 6.28 0.08 8.45 4.72 0.01 2.35 1.36 0 1.89 1.09 0 30 1 0.05 33.57 1.26 0.12 11.86 3.56 0.06

ect

est

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Measuring the black box

248

impulse response functions of major macroeconomic variables, including R&D labor. Figure 12.1 indicates the effects of a preference shock, ebt . This shock obviously increases consumption, which in turn generates temporary increases in output and labor. However, both output and labor decrease quickly. In contrast, while R&D labor shows a similar increase in response to a positive preference shock, it maintains positive responses over the long term. This implies that a preference shock facilitates endogenous innovation. Figure 12.2 show the effects of a government expenditure shock, egt . Output increases in response to this positive shock, which demands more labor. In contrast, households’ consumption and investment decrease. R&D labor shows a pattern of responses similar to Figure 12.1, indicating positive effects on endogenous innovation. Thus, positive shocks related to consumption of both households and the government lead to more endogenous innovation. Hence, demand shocks affect the rate of endogenous innovation. Figures 12.3 and 12.4 both show shocks related to investment. A positive shock in the investment adjustment cost in Figure 12.3 suggests sharp declines in not only investment, but also output, labor, and R&D labor. This indicates that endogenous innovation is damaged by this type of shock. In contrast, a positive IST shock increases output, investment, and eventually consumption, while

Figure 12.1 Preference shock (ebt )

Figure 12.2 Government expenditure shock (egt )

Figure 12.3 Investment adjustment cost shock (eit )

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Measuring the black box

250

Figure 12.4 Investment-specific technology shock (ect )

labor decreases. Regarding R&D labor, this shock leads to more employment of R&D labor, facilitating endogenous innovation. Hence, endogenous innovation is facilitated when shocks are positively related to increased investment. Figure 12.5 depicts impulse responses to a price markup shock, ept . A positive price markup shock leads to an increase in price, which curtails households’ consumption and hence reduces output, investment, labor, and R&D labor. Similarly, Figure 12.6 shows a wage shock, ewt , which reduces consumption, output, investment, and labor. However, R&D labor increases as a result of wage increases. This is because leisure is replaced by R&D labor, rather than production labor, as a result of higher wages. In this case, production labor should decline because the final goods firms demand less labor in response to a decline in consumption. By contrast, R&D labor is not directly affected by the decrease in consumption. Its demand depends on the future stream of profits, rather than realized profits. Consequently, a positive wage shock facilitates endogenous innovation, while a positive price markup curtails it. A positive monetary policy shock increases interest rates in this model. Figure 12.7 indicates that a higher interest rate is conducive to less output and consumption. As a result, investment and labor decline. Once again, in this case, R&D labor increases because production labor is replaced by more R&D labor. In other words, higher interest rates discourage investment in current

Figure 12.5 Price markup shock (ept )

Figure 12.6 Wage shock (ewt )

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Measuring the black box

252

Figure 12.7 Monetary policy shock (ert )

production but facilitate future innovation by encouraging more R&D investment. This suggests that low interest rate policies reinforce existing technologies at the cost of future innovation. This result implies that not only Japan but also the US might face a potential problem in withholding innovation and economic growth following the Great Recession in December 2007, which was followed by a period of extremely low interest rates (Iiboshi, Matsumae, and Nishiyama, 2014). The extended period of low interest rates prompted scholars to incorporate a zero lower bound (ZLB) constraint on the nominal interest rate in a nonlinear manner (Boneva, Braun, and Waki, 2016; Fernández-Villaverde et al., 2015; Gavin, et al., 2015; Gust et al., 2017; Nakata, 2016; Ngo, 2014). However, very little attention has been paid to the effect of low interest rates on growth in the neighborhood of the ZLB. Our results suggest that in addition to the estimation issue considering the ZLB in a New Keynesian framework, the growth consequences should also be pronounced as a result of the low interest rates. Of course, the relationship between interest rates and endogenous innovation is critically dependent on the assumptions used in the model presented in this study. In particular, the model does not allow for financial intermediaries financing R&D investment. Once this possibility is incorporated in the model, a different relationship might emerge between interest rates and endogenous innovation. Nevertheless, the substitution of current technologies for future innovation as a

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Endogenous innovation & macroeconomic shocks

253

result of higher interest rates seems quite intuitive and highlights the importance of this relationship in future research, a topic that has been neglected to date in the literature. Regarding productivity shocks, the model presented in this study allows for two different types of productivity shocks. The first type is incorporated through the production function in (12.22). This productivity shock is concerned with current technology and production. The second type is added to endogenous innovation in (12.32). Thus, this type of productivity shock is related to future technologies, rather than reinforcing the current production function. The effects of these productivity shocks show a sharp contrast with respect to R&D labor. While output, consumption, investment, and labor show similar hump-shaped responses to these shocks (although the directions of the initial jumps differ), R&D labor reacts in an opposite manner. Figure 12.8 indicates that a positive productivity shock leads to an increase in R&D labor. This implies that higher productivity from the current production function facilitates R&D investment because future technologies might well utilize this productivity gain via a spillover effect. Hence, entrepreneurs also benefit from the current productivity shock, leading to more R&D investment. In contrast, Figure 12.9 shows that R&D labor responds negatively to a positive endogenous innovation shock. Since this type of shock strengthens the productivity gains from future innovation, it acts as a substitute for, rather

Figure 12.8 Productivity shock (est )

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Measuring the black box

254

Figure 12.9 Endogenous innovation shock (eat )

than complementing, the incentive to increase investment in R&D. This is a somewhat surprising result, suggesting that any innovation policies that generate this type of positive productivity shock in relation to future innovation discourage R&D investment and hence endogenous innovation and the resulting economic growth. Therefore, innovation policies should focus on productivity gains from current technologies rather than productivity gains from future technologies. Obviously, direct R&D subsidies to entrepreneurs facilitate endogenous innovation. However, the result implies that indirect R&D subsidies aimed at productivity gains from future technologies should be avoided to facilitate R&D investment and endogenous innovation. We believe that this policy implication is a new contribution to the literature. In summary, we find that while endogenous innovation and output respond similarly to shocks to preferences, government demand, investment adjustment costs, ISTs, price markups, productivity, and endogenous innovation, they react in opposite directions to wage shocks and monetary policy shocks. Thus, policies that increase wage rates and interest rates facilitate endogenous innovation at the cost of the output level. However, because endogenous innovation has a permanent effect in terms of the productivity level, the long-term effects of these policies on output will be positive despite the negative short-term effects. This result suggests that the zero interest rate policy in Japan in recent

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Endogenous innovation & macroeconomic shocks

255

years might have had a negative effect on both endogenous innovation and output, although the short-term effect on output might have been positive.

4 Concluding remarks In this study, we proposed an integrated model of endogenous innovation and a New Keynesian DSGE and examined the effects of several exogenous shocks on endogenous innovation using Japanese economic data. The model presented in this study differs from those presented in the endogenous growth and New Keynesian DSGE literature because they operate as independent research fields without mutual dialog. The unique feature of the model presented in this study is the bridge it provides between these two fields by incorporating endogenous innovation into a New Keynesian DSGE model with several market frictions. This integration allows us to examine the relationship between various macroeconomic variables and endogenous innovation. In particular, two findings are noteworthy. First, we found that low interest rate policies discourage R&D investment and endogenous innovation, while facilitating investment in existing technologies. This suggests a trade-off between increasing current consumption and production and facilitating future innovation. The former requires a low interest rate monetary policy, whereas the latter favors a high interest rate policy. Thus, the monetary authority should make a deliberate trade-off decision between current consumption and production and endogenous innovation. In other words, a trade-off between level and growth effects should be taken into account when formulating monetary policy. Second, our results suggest that any innovation policies that generate positive productivity gains in terms of future innovation discourage endogenous innovation. Thus, if the policy target is to facilitate endogenous innovation, it should not subsidize productivity gains from future technologies but instead should focus on reinforcing productivity gains from current technologies. Once again, we face a trade-off between current and future technologies, but the causal relationship requires more sophisticated examination. That is, endogenous innovation is facilitated when current technologies are reinforced, but it is discouraged when future technologies are reinforced. Obviously, current and future technologies compete in the economy through entrepreneurs’ R&D activity. Nevertheless, future technologies are reinforced only if current technologies are subsidized to obtain positive productivity shocks. Therefore, innovation policies should take into account this salient relationship between the two types of productivity gains. These results clearly suggest both a trade-off and complementary relationship between current technologies and future innovation. To facilitate endogenous innovation and economic growth, innovation policy should acknowledge the somewhat complicated relationship between current technologies and future innovation. Of course, these results are critically dependent on the modeling assumptions outlined in this study. In particular, this model does not allow for financial

256

Measuring the black box

256

intermediation between entrepreneurs, final goods producers, and financial institutions. Incorporating this new relationship might change the effects of a monetary policy shock on endogenous innovation. Clearly, this is an important area for future research.

Note 1 We have also modeled the case of constant returns with respect to N in the innovation function (12.30), where the number of entrepreneurs is irrelevant. The empirical results do not change significantly from the case of diminishing returns.

257

Appendix

 1

y a

 1b

y ^g as t

   y y a ln εbt ¼ s ^ct  ð^ct1  ln εt Þ þ 1  a a     by y y a b ln εtþ1 ; þ s s ^ctþ1 þ ln εtþ1  ^ct  1  a a a

ðA1Þ

^ t  ptþ1 ; ^gt ¼ ^gtþ1  s ln εatþ1 þ R

ðA2Þ

^gtþ1tþ1 ¼ ^ pPt  ^pRt ;

ðA3Þ

^ ^ t; nt ¼ ^ pRt ¼ w

ðA4Þ

^ t  ln εnt ; x^ nt ¼ ^gt þ w

ðA5Þ

^t  w ^ t1 þ p ^t þ p ^t  Zw p ^tþ1  Zw p ^t1 þ ln εat ¼ ba1s ð^ ^t w wtþ1  w 1  xw ð1  bxw a1s Þmw ^ ^ t þ ln εbt Þ þ ln εwt ; ðZlt  ^gt  w xw mw þ Zð1 þ mw Þ  ^k ¼ 1  d ð^k  ln εa Þ  z ^u þ 1  1  d ð^i þ ln εc Þ; t t1 t t t a a t a þln εatþ1 Þ þ

ðA6Þ

ðA7Þ

^ qt ¼  ln εct þ wð^it  ^it1 þ ln εat þ ln εit Þ  bwa1s ð^itþ1  ^it þ ln εatþ1 þ ln εit Þ; ðA8Þ ^ qt ¼ ^gtþ1  ^gt  s ln εatþ1 þ

b ðz^z þ ð1  dÞ^qtþ1 Þ; as tþ1

ðA9Þ

^ utþ1 ¼ φð^zt  ^qt Þ;

ðA10Þ

c i g ^yt ¼ ^ct þ ^it þ ln εgt ; y y y

ðA11Þ

^ t ¼ α^ mc wt þ ð1  αÞ^zt  ln εst ;

ðA12Þ

258 Measuring the black box

258

^ ^ t  ^zt ; ut þ ^k t1  ^lt  ln εat ¼ w

ðA13Þ

^yt ¼ ð1 þ Þfα^lt þ ð1  αÞð^ut þ ^k t1  ln εat Þg

ðA14Þ

^t1 ¼ ba1s ð^ ^t Þ þ ^t  Zp p ptþ1  Zp p p

ð1  oÞð1  boa1s Þ ^ t þ ln εpt ; mc o ðA15Þ

! ( ) 3 1X n n  ^ ^ ^ Rt ¼ r Rt1 þ ð1  r Þ p p þ y ð^yt  ^yt Þ þ ln εrt ; 4 j¼0 tj

ðA16Þ

^yt ¼ ð1  αÞð1 þ Þ ln εat ;

ðA17Þ

w where ln εwt  1x xw

0

ð1bxw a1s Þmw mw þZð1þmw Þ

ð^ mwt þ lnεlt Þ; ln εpt  1o ð1  boa1s Þ o

lnm φ  d ð1Þ=d}, and   F=y. p t

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273

Index

Note: Page numbers in italics indicate figures and page numbers in bold indicate tables on the corresponding pages. Abernathy, W. 3 advantages of backwardness and forwardness 23; cluster growth and 150–151; concluding remarks on 95–96; cost of innovation and 87–88; dynamics of comparative advantage and R&D policies with 91–95; economic intuition and 88–89; final good sectors 86–87; household sector 85–86; introduction to 83–85; model 85–91 Aghion, P. 59–60 Ahmadjian, C. 120, 130 AK model: announcement and 36–37; basics of 23–34; concluding remarks on 38–39; international technology transfer vs. local technological spillovers and 37–38; introduction to 22–23; policy for switching and 38; policy implications 34–38; tax rate increases and 41–42; two-stage optimal control in 26–34, 33–34 AK stage (endogenous growth through innovation) 22, 24; announcement and 36–37; concluding remarks on 39; deterministic 43, 45–46, 52; external shocks and 41; international technology transfer vs. local technological spillovers and 37–38; policy for switching and 38; savings rate and 34–35; stochastic 41–42, 43, 46–48, 52–53, 55–57; in two-stage optimal control 28–29; see also AK model Allen, T. J. 175 allocation of technology component in innovation flow matrix 216–217

American auto industry 3–4 American system of manufactures 54n1 Anzoategui, D. 237 appropriate technology 23 architectural vs. modular innovation 3, 5 Atkinson, A. B. 22 A-U model 3–4 automobile industry 3–4, 120–121 autonomous GPT stage 69–73; social welfare and technology policies in 75–76 backward linkages 103–104, 107, 108, 210; dynamics of 109–115, 110–111, 113; relation-specific investment and 123 balanced vs. unbalanced growth 218–219 Balassa, B. 91–92 Basu, S. 22–23, 25 Becker, G. 149 Benhabib, J. 125 β convergence 23 BMW 168 Bos, M. 210 bottleneck-removing vs. core-driven innovation 157–161, 160 bottleneck technology 142, 153, 211; incentives in 163 Boucekkine, R. 23–24, 26–27, 42 boundary spanning activities 180 Bresnahan, T. 58, 59 Brezis, E. S. 25 Brock, W. A. 102 Brynjolfsson, E. 69

274

Index

budget deficits 44 business groups 119–120 Calder, K. E. 120 capability management in two-tier technology systems 160, 160–161 capital-labor ratio: AK model 22–23, 25–34, 38–39 capital share shock 110, 111 Cark, K. B. 5, 12 catch-up hypothesis 23 central bank in New Keynesian DSGE model 244 chain-linked model 144 Chenery-Watanabe indices 103, 104 Christensen, C. M. 4 cluster growth 150–154 Cobb-Douglas production function 102, 105, 122, 125, 131 comparative advantage 83–84; concluding remarks on 95–96; dynamics of R&D policies and 91–95; model 85–91 competitive strategies 166–167, 166–168 consumption and production 102–103, 122–123 cooper 55, 56 core-driven vs. bottleneck-removing innovation 157–161, 160 corner solutions in AK model 30–31 Corsetti, G. 44 cost of innovation in comparative advantage model 87–88 Dalum, B. 92 David, P. A. 8, 21, 22, 23, 69 Davies, A. 162 Dedehayir, O. 154, 162 demand-pull vs. technology push theories 143, 145 demand shocks 109–110, 110 deterministic AK stage 43, 45–46; subsidies and 52 development blocks 141 Dietzenbacher, E. 209 division of labor: autonomous GPT stage and 69–73; comparison of SPT stage with joint-research stage and 67–69; concluding remarks on 76–77; GPT-SPT joint-research stage 64–69; household optimization and 61–62; introduction to 58–59; model on 61–64; R&D activities and 62–64, 79–80; review of previous studies on 59–61; social welfare and

274 technology policies and 73–76; SPT sector and 62 Dixit, A. 41 Dodge Line 54n3 Dupor, B. 104, 109 Dyer, J. 120 dynamic stochastic general equilibrium see New Keynesian DSGE model Eaton, J. 44 economic intuition 88–89 economics, innovation 7–11 endogenous innovation 10–11; see also AK stage (endogenous growth through innovation); New Keynesian DSGE model endogenous technological interdependence 168–169 engineer’s characteristics 180–181 entry and relation-specific investment 128–132 Erceg, C. J. 238, 240 Eriksson, C. 60 estimation methods in knowledge flow 181–183, 182 evolutionary theory 8–9 exogenous shock in New Keynesian DSGE model 245 exploitation algorithm 56 exploration algorithm 56 external shocks see shocks, external factor price: in intersectoral flow of technology model 199; for technology components 148, 215 feedback mechanism and cluster growth 152–153 Fellner, W. 143 final good sectors: in comparative advantage model 86–87; in New Keynesian DSGE model 241 flow of knowledge communication see knowledge flow fluid phase of innovation 3 focusing devices 156; application to capability management in two-tier technology systems 160, 160–161; cluster growth and 150–154; clusters and 145–147; competitive strategies 166–167, 166–168; concluding remarks on 154–155, 169–170; core-driven vs. bottleneck-removing innovation and 157–161, 160; endogenous

275 technological interdependence of 168–169; factor price for technology component and 148; incentives and 163; independent technology components 158–159; interdependent technology components 159–160; introduction to 141–142, 156–157; management of 161–169, 162, 166–167; model 145–150; policy implications of 153–154; quality improvement and 148–150; quality of technology component and 147–148; related literature on 143–145; technology system 157–158 foreign direct investment (FDI) 25 forward linkages 103–104, 108, 210; dynamics of 109–115, 110–111, 113; relation-specific investment 123 freeman 9 gatekeepers 173–174 general purpose technology (GPT) 13, 58–59; autonomous stage 69–73, 75–76; concluding remarks on 76–77; outsourcing of 165–166; poverty trap and 113–115; review of previous studies on 59–61; -SPT joint-research stage 64–69; vertical specialization and 111–113, 113 Gerschenkron, A. 23 Geyer, A. 162 global industry 92 Goderis, B. 210 Goldstein, J. S. 54n2 governance 164–166 GPT-SPT joint-research stage 64–69; concluding remarks on 76–77; GPT autonomy stage compared to 71–73; social welfare and technology policies in 74–75 Granovetter, M. 119 Greenwood, J. 239 Griliches, Z. 143 Grossman, G. M. 74 growth effect 73, 77n7 growth paths 32–34, 33, 33–34 Guerrieri, L. 238 Gust, C. J. 238 Habakkuk, H. 21, 23 Hall, R. E. 33, 38–39 Harada, T. 40, 58, 119; on focusing devices 157, 163, 166, 169; on innovation flow

Index

275

matrix 195, 211; New Keynesian DSGE model and 237 Helpman, E. 58, 59, 74 Henderson, D. W. 240 Henderson, R. M. 5, 12 Hercowitz, Z. 239 Hicks, J. 143 Hirose, Y. 237, 247 Hirschman, A. O. 100, 110, 115, 153, 209, 210 Hitt, L. 69 Hobday, M. 159 Hodgson, G. M. 120–121 Honda 168 Horvath, M. 104, 113 household sector: in comparative advantage model 85–86; in innovation flow matrix 216; in New Keynesian DSGE model 238–241; optimization model 61–62 Howitt, P. W. 51, 59–60 Huffman, G. 239 Hughes, T. P. 156, 157, 169 IBM 4 incentives 163 independent technology components 158–159 industrial clusters 141, 145–147 industry structure and relation-specific investment 132–134 innovation: economics of 7–11; endogenous (See endogenous innovation); introduction to 1–2; pathdependent nature of 7–8; perspectives on 11–14; process of 5–7; typologies of 2–5; underlying mechanism of 1 innovation flow matrix 95; allocation of technology component in 216–217; balanced vs. unbalanced growth and 218–219; commodity production and 212–213; concluding remarks on 233; data for 220–221; empirical analysis of 220–232; estimating innovation linkages and 221–228, 222–223, 225–228; evaluating growth strategies in 228–232, 230–232; factor price of technology component in 215; household sector in 216; intersectoral flow of technology 199–201, 207n1–2, 208; model 211–219, 212; production of production technology in 213–215; productivity growth in 217–218

276

Index

innovation management 2–7 innovation possibility frontier (IPF) 143 innovation probability 11, 12; competitive strategies 166–167, 166–168; concluding remarks on 169–170; core-driven vs. bottleneck-removing innovation and 157–161, 160; endogenous technological interdependence 168–169; governance and 164–166; incentives and 163; introduction to 156–157; management of 161–169, 162, 166–167; maximization of 161–163, 162 innovation process 5–7 input-output analysis see intersectoral flow of technology inside the black box innovation 1; innovation management 2 Intel 84 interdependent technology components 159–160 intermediate goods firms in New Keynesian DSGE model 242–243 internal technical communication 179–180 international technology transfer vs. local technological spillovers 37–38 intersectoral flow of technology 206–207; equilibrium in 202–203; factor price in 199; household and commodity in 201–202; introduction to 193–195; model outline 195–197; production of technology and 197–199; quantitative analysis in 203–206, 204–205; technology and innovation flow matrices in 199–201, 207n1–2, 208 intersectoral relations 12, 13–14 intersectoral spillover effects 210 Irmen, A. 22 Japanese auto industry 120–121 Jones, C. I. 33, 38–39, 63, 79 Justiniano, A. 247 Kaldor, N. 22 Katz, R. 175 keiretsu groups 120–121, 134n1, 168 Kennedy, C. 143 knowledge flow 9–10; boundary spanning activities in 180; concluding remarks on 187–189; effect of organization specific routines on 176–178; effect of organization tenure on 174–176; emergence of gatekeepers in 173–174;

276 engineer’s characteristics in 180–181; estimation methods 181–183, 182; hypotheses of 173–178; internal technical communication in 179–180; introduction to 171–172; R&D and 178; regression results for 183–186, 184, 185, 186; settings and methods in 179–183, 182 Kremer, M. 145, 149, 213 Krugman, P. 83 Krugman, P. R. 25 Kurozumi, T. 237, 247 Kyohokai 130 labor share shock 110–111, 111 Laursen, K. 92 leapfrogging 32 learning platform 38–39 Leontief input-output model 5, 22 Levin, A. T. 240 limit price 78n9 Lindh, T. 60 linkages 100–102, 101; balanced vs. unbalanced growth and 218–219; dynamics of backward and forward 109–115, 110–111, 113; in innovation flow matrix 217–218; innovation flow matrix and 210–211; introduction to backward and forward 103–104; in multi-sectoral general equilibrium model 102–109, 108 local technological spillovers 21 Long, J. B. 13, 102, 104, 122 lucky guess method 116n4 Lundvall, B.-Å. 9, 10 Mäkinen, S. J. 154, 162 Makris, M. 23 management, innovation 2–7 March, J. G. 56 market clearing condition in New Keynesian DSGE model 244 market-pull hypothesis 144 Matsuyama, K. 22 Mayer-Foulkes, D. 51 Mercedes 168 migration and cluster growth 151–152 Miller, R. 159 Mirman, L. J. 102 Mowery, D. C. 144 multi-sectoral general equilibrium model 102–109, 108; concluding remarks on 115; dynamics of backward and forward

277 linkages in 109–115, 110–111, 113; proof of propositions in 117 Murphy, K. M. 114 Nadiri, I. M. 210 Nash equilibrium 127 national innovation system 9–10 Nelson, R. R. 7, 8, 9, 10 neoclassical growth model 7 New Keynesian DSGE model 257–258; central bank in 244; components of 237–246, 246; concluding remarks on 255–256; data in 245–246, 246; effects of shocks on endogenous innovation in 247–255, 248–254; empirical analysis of 246, 246–255, 248–254; estimation method for 245; exogenous shock in 245; final goods firms in 241; households in 238–241; intermediate goods firms in 242–243; introduction to 236–237; market clearing condition in 244; parameter estimates in 246–247; R&D investment in 243–244; solution 245; variance decomposition in 247, 247 Nishimura, K. 125 Noland, M. 91–92 Nonaka, I. 172 Nordhaus, W. D. 143 optimal switching time: path-dependent economic growth with technological trajectory 38; path-dependent progress and regress 48–51 O’Reilly, C. A., III 177 organization specific routines 176–178 organization tenure 174–176 outside the black box innovation 1; perspectives on 11–14 outsourcing 165–166 Oxley, J. 120, 130 Pareto efficient equilibrium 8 patent protections 94 path-dependent economic growth with technological trajectory: AK model and 22, 23–34; announcement and 36–37; concluding remarks on 38–39; international technology transfer vs. local technological spillovers and 37–38; introduction to 21–23; policy for switching and 38; policy implications 34–38; savings rate and 34–35

Index

277

path-dependent nature of innovation 7–8, 14 path-dependent progress and regress: concluding remarks on 53–54; deterministic AK stage 43, 45–46, 52; financial assets 44; introduction to 40–42; model 42–51; optimal switching 45–51; optimal switching time 48–51; preferences and technology 42–43; public sector 44; stochastic AK stage 41–42, 43, 46–48, 52–53, 55–57; subsidy policies 51–53 Petsas, I. 60 Phillips, K. L. 237 place of innovation 2–3 Plosser, C. I. 13, 102, 104, 122 porter 141–142, 166 positive productivity shocks 44, 107–108 poverty trap 113–115, 133 Primiceri, G. E. 247 probability, innovation 56–57 process innovation 234n3 production of production technology 213–215 productivity shocks 101, 109–110, 110, 253–254, 253–254 products vs. process innovation 3–4 Qiu, L. D. 120 quality improvement 148–150 quantitative analysis in intersectoral flow of technology 203–206, 204–205 QWERTY keyboard layout 8 radical vs. incremental innovation 2 Ramsey equation 86 Rasmussen, N. P. 103 R&D 62–64, 79–80, 97–99; comparative advantage and 83–96; consumption and production and 102–103; dynamics of comparative advantage and policies regarding 91–95; economic intuition and 88–89; equilibrium and 89–91; focusing devices and (see focusing devices); knowledge flow and type of 178; multi-sectoral general equilibrium model and 104–109; in New Keynesian DSGE model 243–244; patent protections and 94; poverty trap and 113; relationspecific (see relation-specific investment); shocks 109–110, 110 relation-specific investment: backward and forward linkages and 123; concluding

278

Index

remarks on 134; consumption and production and 122–123; entry and 128–132; equilibrium in 125–128, 127; evolution of industry structure and 132–134; introduction to 118–119; model 122–128; policy implications of 133–134; proof of propositions of 136–138; R&D 124–125; related literature on 119–121 reverse salients 141, 156–157 Ricardian model 86, 92–93, 98 Rob, R. 41 Roberts, K. H. 177 Rosenberg, N. 1, 2, 25, 54n1, 60, 144, 157, 206; on complementarity 209; on constraints on technological change 141, 149, 153; on GPT sector and vertical specialization 111–112; on GPT-SPT joint-research stage 64, 65, 68; on investigation of role of innovation in economic growth 156, 169; on marketpull hypothesis 144; on poverty trap 114; on R&D shocks 109; on technological convergence 88; on vertical specialization 101 Rossana, R. 23 Saglam, C. 23–24, 26–27, 42 Samuelson, P. A. 143 savings rate 34–36 Schmookler, J. 143 Schumpeter, J. A. 2, 7, 60, 61, 156 Seagate Technology 4 Segerstrom, P. S. 79 Shleifer, A. 114 shocks, external 40–41, 45; capital share 110, 111; effects of, on endogenous innovation 247–255, 248–254; labor share 110–111, 111; productivity, demand, and R&D 109–110, 110 skill-biased innovation 143–144 Smith, Adam 121 social welfare and technology policies 73–76 Solow residual 7 Solow stage 21–22, 23, 24, 26, 32; announcement and 36–37; concluding remarks on 39; international technology transfer vs. local technological spillovers and 37–38; policy for switching and 38; savings rate and 34–35; in two-stage optimal control 28–29; See also AK model

278 special purpose technology (SPT) 13, 58–59; autonomous GPT stage and 69–73; comparison of SPT stage with joint-research stage and 67–69; concluding remarks on 76–77; GPT-SPT joint-research stage 64–69; production function of 62; R&D activities of 62–64; review of previous studies on 59–61; social welfare and technology policies and 73–74 specific phase of innovation 3 Spencer, B. J. 120 spillover effects 209–210, 217–218, 234n2, 234n4–5, 234n7 stage-gate innovation process 55–56 Stigler, G. J. 121 Stiglitz, J. E. 22 stochastic AK stage 41–42, 43, 46–48; solutions for 55–57; subsidies in 52–53 Streeten, P. 218–219 subsidy policies 51–53 Sugo, T. 245, 246 sustaining vs. disruptive innovation 3, 4 systemic view on innovation 3, 5, 11–13 Takeuchi, H. 172 Tambalotti, A. 247 tax rate increases 41–42 Taylor rule 244 technological convergence 88 technological discontinuity 2, 3 technological quality 147–148 technological trajectory 21, 32; see also path-dependent economic growth with technological trajectory technology components: allocation in innovation flow matrix 216–217; factor price for 148, 215; independent 158–159; interdependent 159–160 technology-push constraints 145 technology systems 157–158; application to capability management in two-tier 160, 160–161; endogenous technological interdependence of 168–169; governance of 164–166; incentives in 163; management of 161–163, 162 Teece, D. J. 96n2 ten Raa, T. 194 three-step flow of knowledge communication see knowledge flow Tomiyama, K. 23

279 total factor productivity (TFP) 10–11, 211 Toyota 84, 130, 168 trade effect and comparative advantage 92–93 Trajtenberg, M. 58, 59 transitional phase of innovation 3 Tsiddon, D. 25 two-stage optimal control in AK model 26–34, 33–34 typologies of innovation 2–5 Ueda, K. 245, 246 unbalanced growth 218–219 user expectations 3, 4 Utterback, J. 3

Index

279

Vallee, T. 23–24, 26–27, 42 Vannoorenberghe, G. 210 variance decompositions in New Keynesian DSGE model 247, 247 VCR to DVD innovation 3, 4–5 vertical specialization 101, 111–113, 113 Villumsen, G. 92 Vishny, R. W. 114 von Hippel, E. 56 Weil, D. N. 22–23, 25 Williamson, O. E. 121, 170 Winter, S. G. 7, 8, 10 Wolff, E. N. 194, 210 Wrase, J. 237