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Part 1 of ebook Behavioral interactions, markets, and economic dynamics: Topics in behavioral economics provide readers with content about: intergenerational interactions; an equilibrium model of child maltreatment; tough love and intergenerational altruism; behavioral macroeconomics; consumer interdependence via reference groups; time preference in macroeconomics;... Shinsuke Ikeda · Hideaki Kiyoshi Kato Fumio Ohtake · Yoshiro Tsutsui Editors Behavioral Interactions, Markets, and Economic Dynamics Topics in Behavioral Economics Behavioral Interactions, Markets, and Economic Dynamics Shinsuke Ikeda • Hideaki Kiyoshi Kato Fumio Ohtake • Yoshiro Tsutsui Editors Behavioral Interactions, Markets, and Economic Dynamics Topics in Behavioral Economics 123 Editors Shinsuke Ikeda Institute of Social and Economic Research Osaka University Ibaraki, Osaka, Japan Hideaki Kiyoshi Kato Graduate School of Economics Nagoya University Nagoya, Aichi, Japan Fumio Ohtake Institute of Social and Economic Research Osaka University Ibaraki, Osaka, Japan Yoshiro Tsutsui Faculty of Economics Konan University Kobe, Hyogo, Japan ISBN 978-4-431-55500-1 DOI 10.1007/978-4-431-55501-8 ISBN 978-4-431-55501-8 (eBook) Library of Congress Control Number: 2015950212 Springer Tokyo Heidelberg New York Dordrecht London © Springer Japan 2016 This work is subject to copyright All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed The use of general descriptive names, registered names, trademarks, service marks, etc in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made Printed on acid-free paper Springer Japan KK is part of Springer Science+Business Media (www.springer.com) Preface For the purpose of providing new and broader directions for the future development of behavioral economics and finance, this book collects important contributions in behavioral economics/finance and related topics among journal publications of Japanese researchers to date By applying new insights from behavioral economics/finance, we are interested in extending the reach of the standard theories in our own fields A project to edit readings and/or handbooks on behavioral economics/finance for the promotion of economic research came about naturally as a result of our frequent interactions when running academic meetings on behavioral economics, especially those of the Association of Behavioral Economics and Finance (ABEF), the Japanese Economic Association (JEA), and the Nippon Finance Association (NFA) In addition, these meetings gave us access to important works that were motivated by behavioral economics We therefore have compiled and edited a couple of independent volumes in an attempt to capture the many worthy articles that lie within this topic The first, titled Behavioral Economics of Preferences, Choices, and Happiness, focuses on works on behavioral economics; and the second, Behavioral Interactions, Markets, and Economic Dynamics: Topics in Behavioral Economics, on economics-oriented studies on topics in behavioral economics This book is the latter Three features characterize the present book First, it focuses on economic studies examining the interactions of multiple agents or market phenomena using behavioral economics models As current behavioral economics models are not necessarily good at analyzing phenomena from the viewpoints of market equilibrium and agent interactions, this feature of the book will help readers consider new possibilities for behavioral economics models as well as for general economic models In contrast, the other book focuses on more behavioral, single-agent issues, such as decision making, preference formation, and subjective well-being The two books thus are complementary Second, the chapter authors have added newly written addenda to the original articles, in which they discuss their own subsequent works, and provide supplementary analyses, detailed information on the underlying data, and/or recent literature v vi Preface surveys The addendum of each chapter is based on discussion at the Development of Behavioral Economics and Finance Conference held in February 2014 During this conference, participants, including the authors of the book chapters, discussed the original studies to be included in these volumes in light of contributions, limitations, and implications for future research developments We accordingly believe that this work creates a bridge between the original studies and future research development Third, reflecting the diverse fields of the editors, this book as well as the companion volume, captures broad influences of behavioral economics on various topics in economics The topics of this book cover parental altruism, economic growth and development, the relative and permanent income hypotheses, wealth distribution, asset price bubbles, auctions, search, contracts, personnel management, and market efficiency and anomalies in financial markets The remainder of this preface provides a brief introduction to the parts of the book Part I is composed of two chapters that address intergenerational interactions under parents’ altruism In Chap 1, Professor Hideo Akabayashi develops a unique dynamic principal-agent model to endogenously describe a child’s development, his time preference formation, and the parents’ interventions under asymmetric information Akabayashi successfully explains child maltreatment by parents as an equilibrium outcome under their divergent misbeliefs about the child’s ability He also characterizes families that are at risk of child maltreatment In Chap 2, Professors Vipul Bhatt and Masao Ogaki propose another model of parents’ strict intervention behavior toward their children Unlike Akabayashi, they assume perfect information and thereby focus on a positive aspect of parental intervention in the form of “tough love,” where the parent in their model allows the child to suffer in the short run via lower childhood transfers (e.g., allowances) so that she grows up to be more patient in the long run The authors also extend the model to account for the child’s leisure choice to emphasize the distinction between exogenous and endogenous changes in income when examining the redistributive neutrality property of altruism models Part II begins with important research by Professors Hiroaki Hayakawa and Yiannis Venieris in Chap 3, which was originally published in the Journal of Political Economy In 1977, when the field of behavioral economics had not yet appeared, they made contributions that are behavioral-economics oriented First, they address heuristic cognition-saving decision making under bounded rationality Second, they focus on the critical role of social interdependence in endogenous preference formation The authors describe the consumer behavior that identifies with and emulates a chosen reference group for heuristic decision making In doing so, they derive indifference curves under social interdependence based on two axioms and four basic assumptions The implications for consumer theory too are discussed In Chap 4, Professor Hayakawa further extends the ideas in the previous chapter by presenting an axiomatic theory for the analysis of boundedly rational consumer choice To describe heuristic decision making, the author focuses on the important roles of social norms and reference groups as sources of lowcost heuristics and proposes a model of a sequential two-step choice making Preface vii procedure to satisfy physical and social wants Classical theories of consumption externalities developed by Leibenstein, Veblen, and Duesenberry are re-interpreted using the proposed framework In Chap 5, Professors Koichi Futagami and Akihisa Shibata address the effect of consumers’ status/wealth preferences on endogenously determined steady-growth rate When consumer preferences are personally interdependent due to status preferences, effective time preferences are shown to depend on relative wealth holdings producing rich, and sometimes paradoxical, implications for growth and wealth distribution In Chap 6, Professor Katsunori Yamada provides further macroeconomic implications of status preferences He develops a capital-accumulation model with two consumption goods for normal and conspicuous purposes in order to characterize the properties of equilibrium dynamics in the bandwagon-type and snob-type economies The Sombartian oscillating dynamics are duplicated as an equilibrium outcome of the growth-impeding effect of conspicuous consumption This characteristic is seen particularly in the bandwagontype economy Chapter 7, written by Professors Yoshiyasu Ono and Junishiro Ishida, develops a new dynamic behavioral model to describe unemployment due to demand shortage In this process, two behavioral assumptions are incorporated: workers’ concern for fairness, which provides a microfoundation for a behavioral version of the Phillips curve, and the insatiable desire for money, which plays a critical role in producing persistent demand shortage Monetary and fiscal policies are then evaluated in light of their effectiveness in reducing unemployment in the short and long run The four studies in Part III contribute to the literature of time preference in macroeconomics Chapter is based on the Review of Economics and Statistics article written by Professors Masao Ogaki and Andrew Atkeson The authors examine the empirical validity of the models of wealth-dependent intertemporal elasticity of substitution (IES) and the wealth-dependent rate of time preference (RTP) using panel data from India in which there were large fluctuations in consumption data By incorporating the subsistence consumption level, the estimation result shows that IES depends positively on wealth, whereas RTP is wealth-independent In contrast, in Chap Professor Kazuo Ogawa uses aggregate time-series data of Japan, Taiwan, and Korea to show that the RTP of each country’s representative consumer depends on the income level In particular, he compares the empirical validity of the three alternative RTP schedules—flat, upward, and U-shaped—to show that the RTPs of Japan and Taiwan are characterized by a U-shaped schedule The estimated turning points in the two countries are found to be consistent with their historical loci of economic growth Chapters 10 and 11 comprise theoretical contributions to the RTP issue In Chap 10, Professor Shinsuke Ikeda extends an endogenous RTP model to characterize luxury and necessity good consumption in terms of good specific RTP and IES Preferences for luxury are shown to affect capital accumulation and wealth distribution In Chap 11, Professors Ken-ichi Hirose and Ikeda examine the implications of decreasing marginal impatience As is often empirically observed, RTP is decreasing in wealth The authors show its dynamic implications for stability property, multiple equilibria, and the possibilities of consumption-satiated equilibria viii Preface Part IV analyses bubbles and the ensuing crashes Chapter 12, authored by Professors Robert J Shiller, Fumiko Kon-Ya and Yoshiro Tsutsui and published in the Review of Economics and Statistics, investigates why the Japanese stock market crashed between 1989 and 1992 To answer this question, they collect parallel time series data on expectations, attitudes, and theories from market participants in both Japan and the United States for the period 1989–1994 Such a survey is unique, especially in the early 1990s They find a relationship between the crash and changes in both Japanese price expectations and speculative strategies In Chap 13, Professors Shinichi Hirota and Shyam Sunder conduct an economic experiment to explore how investor decision horizons influence the formation of stock price bubbles The experiment consists of long- and short-horizon sessions These sessions differ by receiving either the determined dividend (the long-session) or the expected future price when the subjects exit (the short-session) They find that price bubbles emerge more frequently in the short-horizon session, suggesting that the difficulty of performing backward induction from future dividends is important to the emergence of price bubbles Part V contains three chapters concerning experimental markets It begins with Chap 14, which is authored by Professors Soo Hong Chew and Naoko Nishimura It is well-known that the English and second-price auctions generate the same revenue when bidders have independent private valuations of an auctioned object That is, both auctions exhibit the revenue equivalence theorem However, if the auctioned object involves risk, the theorem breaks down when bidders are non-expected utility maximizers, since submitting one’s valuation is no longer a dominant strategy for them under second-price sealed-bid auctions In this chapter, the authors experimentally examine whether their subjects have expected utility preferences and, if not, whether they exhibit choices consistent with the Allais paradox The authors show that the two experimental auction markets not support the revenue equivalence theorem when they introduce a risky auctioned object Additionally, the English auction yields higher seller revenue than the second-price auction for the subject pool where the Allais type is predominant, as predicted by the theoretical examination under non-expected utility preferences In Chap 15, Professors Yoichi Hizen, Keisuke Kawata, and Masaru Sasaki examine the properties of a committee search, in which a decision is made by a group of multiple agents rather than by a single agent Recently, Albrecht, Anderson, and Vroman (AAV) theoretically analyzed the properties of decision-making in the case of committee search However, there exist no empirical studies on committee search, mainly because of the difficulty in collecting suitable data A unique feature of this chapter is the use of laboratory experiments to collect original data in order to test the AAV’s propositions Specifically, the authors examine the propositions that the average search duration is increasing in the number of votes required to stop committee search and that it is also increasing in the number of group members Overall, the experimental outcomes are consistent with the implications suggested by the AAV model Chapter 16 is authored by Professors Toshiji Kawagoe and Hirokazu Takizawa The authors investigate cheap-talk games with private information using an experiment They find that when the interests of Preface ix the sender and receiver are aligned, informative communication frequently arises While babbling equilibrium play is observed more frequently in conflicting interest cases, a substantial number of players tend to choose truth-telling In other words, they found over-communication, truth bias, and truth-detection bias, which are not predicted by equilibrium refinement theories They explain these results using a level-k model, which is a non-equilibrium theory of players’ initial responses to games that reflect the strategic thinking of players Part VI contains three attempts to extend contract theory by applying the insights of behavioral economics Chapter 17 is Professor Hideshi Itoh’s initial attempt to develop a behavioral contract theory By incorporating players’ other-regarding preferences, such as inequity aversion and status preferences, into the standard moral hazard models of principal-agent relationships, he shows that other-regarding preferences interact with moral hazard in some important ways For example, a principal is worse off when his agent cares about the principal’s income In the presence of symmetric self-regarding agents, the principal is shown to be able to optimally exploit his agents’ other-regarding behaviors by designing contracts appropriately Further development of behavioral contract theory is surveyed in the addendum of the chapter and found in the two subsequent Chaps 18 and 19, both of which are written by Professor Junichiro Ishida In Chap 18, Ishida incorporates self-esteem concerns as a behavioral motive into a simple principalagent framework By specifying the agent as benefiting from having a positive self-image (expected self-attributes), he provides a unique model that describes “self-handicapping” behaviors to withhold effort with the intention of obscuring his own attributes An important implication is that uncertainty reduces agency costs and thereby increases the effort incentive because uncertainty reduces the need for self-handicapping In Chap 19, Ishida again considers a principal-agent model in which the agent does not have perfect knowledge about his innate ability (attributes) When the principal has superior knowledge about the agent’s ability and decides whether to promote the agent based on the private information, promotion decisions act as credible signals of the principal’s evaluation and have the “looking-glass” effect on the agent’s self-confidence The principal’s strategic promotion policy that incorporates the “looking-glass” effect potentially explains why demotions are rare in practice, even when employees’ incompetence level increases, a phenomenon otherwise known as the Peter Principle Part VII contains four chapters on anomalous stock return behavior against market efficiency In Chap 20, Professor Takahiro Azuma, Katsuhiko Okada, and Yukinobu Hamuro examine the media’s influence on stock returns, focusing on investor behavior surrounding revisions of sell-side analysts’ ratings Azuma et al find that media-covered stocks show significantly lower post-announcement returns than non-media-covered stocks A more careful examination of media-covered stocks finds that while downgraded stocks show little difference in post-event returns regardless of the degree of sentiment, upgraded stocks show a difference These results are consistent with the view that heavy-media-coverage stocks are overpriced due to individual investors’ noise trading In Chap 21, Professors Yoshio Iihara, Hideaki Kiyoshi Kato, and Toshifumi Tokunaga document the winner–loser 318 K Hirose and S Ikeda Solution E is characterized by the consumption level c in Eq (11.4) and a strictly positive c , whereas the satiated steady-state solution E by the satiated consumption level c and c D 0: From Assumptions 4–6, both steady-state solutions E and E uniquely exist.7,8 Example For a simple example, specify functions u c/ and ı c/ in quadratic form as:  à 100 u c/ D c 11/2 ; (11.17) 121 and ı c/ D 0:1 c C 0:1; 100 (11.18) respectively These functions can be shown easily to satisfy the regularity conditions Assumptions 1–5 for c 0; 11/.9 The critical consumption level cN that satisfies ı c/ N D equals 10 The resulting U c/-function (Eq (11.5)) satisfies Assumptions and 7, where the satiated consumption level c is uniquely given by 9: 091 The non-satiated steady-state equilibrium E uniquely exists if r Œ0:018; 0:1/.10 For example, when r D 0:05, the steady-state consumption c amounts to 7: 071, which is smaller than satiated level 9: 091, as required by Assumption By analyzing the local dynamics around the two steady-state points, we can show that non-satiated steady-state point E is unstable whereas the satiated point E is saddlepoint stable (see Appendix “Stability of Points E and E in Proposition 1”) Proposition Under Assumptions 1–8, the optimization problem with DMI, given by Eqs (11.1)–(11.3), has two steady-state optimal points: a non-satiated point E , which is unstable, and a satiated point E , which is saddlepoint stable The resulting optimal consumption dynamics are depicted in Fig 11.2, where the top panel illustrates the c; a/-dynamics and the bottom depicts c; / In the bottom panel, we illustrate two cP D schedules One is defined by c; / D r and is locally flat at E The other is upward sloping at E Schedule P D illustrates the relation c; / D As a zero means D u c/ =ı c/, the schedule is exactly the same as depicted in the top panel of Fig 11.1 Steady-state points E c ; / This shows that, even if the felicity function is strictly increasing, satiation can arise under intertemporally nonseparable preference Ryder and Heal (1973) show that habit formation can produce satiated steady-state optimal solutions Satiation has also been reported in happiness studies; see, e.g., Leu et al (1997) and Tsutsui et al (2005) Function (11.17) can be respecified to satisfy the regularity conditions for all c modifying the graph for c 11 10 The exact value of the lower bound is 0:017355 by arbitrarily 11 On Decreasing Marginal Impatience 319 a a a=0 E ** ** E* a* O c* c ** c φ O c ** c* φ ** φ* c E ** c=0 E* φ =0 c=0 saddle-point stable steady-state unstable steady-state Fig 11.2 Optimal consumption dynamics under decreasing marginal impatience with a constant interest rate and E c ; / are determined at the intersections of the P D schedule and the two cP D schedules By assumption, the P D schedule has a unique peak at E The optimal consumption dynamics are indicated by arrows Point E is depicted as unstable whereas E is saddlepoint stable Given an initial value a0 of wealth holding, optimal consumption c.0/ is determined on the optimal trajectory in the c; a/-plane The c; /-dynamics are then generated on the arrowed trajectory in the c; /-plane The optimal consumption dynamics depend crucially on a0 Suppose first that < a0 < a Then, c.0/ is determined as smaller than c ; and thereafter c.t/ and hence a.t/ implode over time Consider, instead, the case that a < a0 < a 320 K Hirose and S Ikeda In this case, c.0/ exceeds c but falls short of c In the interim run, c.t/ grows gradually toward the satiation level c Finally, when a0 > a , a larger c.t/ than c would generate negative marginal utility The optimal solution is thus not to choose greater consumption levels than c , even though they are feasible, but to keep c.t/ equal to the satiation level c As discussed, DMI in a constant interest rate economy leads poor consumers to decumulate wealth toward zero and rich consumers to accumulate wealth up to the satiated level Note that the attained long-run consumption levels (zero or the satiation level) are insensitive to any income shocks, e.g., shocks in a0 and/or r: With constant interest rates, the DMI model may thus not be suitable for analyzing the long-run effects of policy changes This, however, does not imply that we cannot analyze any DMI models We can consider well-behaved models with DMI by introducing some stabilizing decreasing return properties into the production technology and/or consumer preference We next incorporate capital accumulation with the usual decreasing returns technology Decreasing Marginal Impatience and Capital Accumulation 3.1 The Neoclassical Model Consider a stylized neoclassical model with two production factors, labor and capital, a single multipurpose commodity produced using constant-to-scale technology F , and competitive firms Consumers inelastically supply one unit of labor in each instant Their preferences are specified as in the previous section In particular, we assume DMI, ıc c/ < The government spends g by levying capital taxes and lump-sum taxes Letting k represent the capital–labor ratio and f a per capita production function satisfying fk > 0, fkk < 0, and the Inada conditions, we can easily obtain a reduced dynamic system as follows: cP D c; / cc c; / c / fk k/ ı c// PD c; / ; kP D f k/ c c; / ıc c/ ; cc c; / (11.19) g: The solution of this system that satisfies the transversality condition is sufficiently optimal When c c; / > 0, the first equation can be rewritten as: cP D c; / cc c; / c / fk k/ c; // ; where the rate of time preference c; / is given by Eq (11.13) 11 On Decreasing Marginal Impatience 321 As in the previous section, we consider two steady-state equilibria: (i) the nonsatiated, modified golden-rule steady-state equilibrium E c ; k / such that D ı c / fk k ; (11.20) and f k D c C g; (11.21) and (ii) the satiated steady-state equilibrium E c ; k /, where c is given by (11.6); and k is given by f k / D c C g as in Eq (11.21) By analyzing the local dynamics around these two steady-state points, we can show that the non-satiated steady-state point E , as well as the satiated point E , can be saddlepoint stable Lemma 1 Non-satiated steady-state point E is saddlepoint stable if and only if: fk k Satiated steady-state point E ı c < / fkk k =ıc c : (11.22) is saddlepoint stable if and only if: < / fk k : (11.23) Proof See Appendix “Proof of Lemma 1” Figure 11.3a, b demonstrate the determination and the stability properties of the steady-state points E and E , where Eqs (11.20) and (11.21) are depicted by upward sloping schedules With the satiated consumption level c being determined from Eq (11.6), satiated steady-state point E is determined on the schedule of Eq (11.21) Non-satiated steady-state point E is given at the intersection of the two schedules if it exists on the left side of E For point E to be saddlepoint stable, Lemma (1) requires that the gradient of the schedule of (11.21) at E (the left-hand side of Inequality (11.22)) be smaller than that of Eq (11.20) (the righthand side ) From Lemma (2), point E is saddlepoint stable if, and only if, it is located above the schedule of Eq (11.20) Note that ı 0/ D ıN < 1/ whereas, from the Inada condition, we have lim fk k/ D 1: The schedule of Eq (11.20) thus intersects the horizontal axis k!0 at a positive k As the schedule of Eq (11.21) goes through the origin when g is assumed to equal zero for brevity, this implies that the relative magnitudes of ı c / and / fk k /, i.e., whether satiated steady-state point E is located above or below the schedule, Eq (11.20) has critical implications for the existence and stability of the non-satiated and satiated steady-state points, and can be summarized as follows.11 11 In the case that g > 0, Proposition remains valid as far as /fk f N g// > ı 322 K Hirose and S Ikeda a c (20) (21) c ** c E E* * ** saddle-point stable steady state unstable steady state O k* k k ** c b E ** c c 2∗ ** ∗ c (21) (20) E * E1* saddle-point stable steady state unstable steady state O k1* k *2 Fig 11.3 Steady-state equilibria and stability (a) ı.c /fk k / k ** / > /fk k / (b) ı.c k / < Proposition Suppose that ı c / > / fk k / Then, (i) there necessarily exist an odd number of non-satiated steady-state points, which are alternatively saddlepoint stable and unstable, i.e., the first is saddlepoint stable, the second is unstable, , and the last is saddlepoint stable; and (ii) the satiated steady-state point is unstable Suppose that ı c / < / fk k / Then, (i) if there exists a k < k such that ı f k// / fk k/, there exist an even number of steady-state points, which are alternatively saddlepoint stable and unstable, i.e., the first is 11 On Decreasing Marginal Impatience 323 saddlepoint stable, the second is unstable , and the last is unstable; otherwise there exists no non-nonsatiated steady-state point; and (ii) the satiated steadystate point is saddlepoint stable Figure 11.3a depicts the case that ı c / > fk k / by assuming that the nonsatiated steady-state point E is unique From Lemma (1), point E is saddlepoint stable whereas, from Lemma (2), satiated steady-state point E is unstable, as stated by Proposition (1) Insofar as the initial capital stock k0 lies below the satiated stock level k , the economy monotonically converges to the non-satiated steady-state point E Figure 11.3b illustrates the case that ı c / < fk k / ; where two non-satiated steady-state points are assumed to exist As implied by Proposition (2), the first point E1 is saddlepoint stable whereas the second point E2 is unstable Point E is saddlepoint stable When k0 lies below k2 , the economy gradually approaches non-satiated steady-state point E1 , whereas a higher k0 than k2 is followed by monotonic convergence toward satiated steady-state point E : Example As in Example 1, we specify functions u c/ and ı c/ in quadratic forms as Eqs (11.17) and (11.18), respectively, and the production function as: f k/ D Ak0:3 ; A > 0: Assume that g D and D These functions satisfy all the regularity conditions The satiated consumption level is obtained as c D 9:091: The existence of the non-satiated steady-state equilibrium E depends on the value of total factor productivity A From Proposition 2, there exists a non-satiated equilibrium point if and only if for some k < k ; ı f k// / fk k/ and hence ı Ak0:3 0:7 0:3Ak : With a too large A, however, the capital productivity 0:3Ak 0:7 remains larger than ı Ak0:3 for all k < k For the existence of the non-satiated steadystate equilibrium, A must thus be smaller than some critical value, which can be computed as 2:302 in the present example.12 After tedious computation, we can show the following relations For A 0; 1:993/, the non-satiated steady-state equilibrium point E uniquely exists and is saddlepoint stable, as in Fig 11.3a.13 For example, when A D 1:5, c ; k / equals 2:974; 9:786/ : For A 1:994; 2:301/, there are two non-satiated steady-state equilibria, one saddlepoint stable and one unstable, as in Fig 11.3b For example, when A D 2:1; c ; k / is given by 5:335; 22:373/, which is saddlepoint stable, and 8:826; 119:811/, which is unstable For A 2:302, there is a non-nonsatiated equilibrium 12 The exact critical value is 2:30160 13 The exact value of the upper bound is 1:99397 324 K Hirose and S Ikeda With a decreasing return technology, a model of DMI can thus be well behaved in the sense that there exists a non-satiated steady-state point that is saddlepoint stable This enables us to consider the policy implications of DMI by conducting usual comparable statics 3.2 The Effects of Capital Taxation Let us examine the implications of DMI on capital taxation As shown by Chamley (1981), when the rate of time preference is constant, capital shifts away the entire burden of capital taxation in the long run because the long-run after-tax rate of return to capital must equal the constant time preference rate The resulting reductions in the steady-state capital, consumption, and welfare are large With endogenous time preference, Epstein and Hynes (1983) show that capital taxation reduces the steadystate capital stock, but not as much as it would under constant time preference, implying that the reductions in consumption and welfare are mitigated However this depends crucially on the assumption of IMI With DMI, the result is drastically changed, as we shall show below Assume that the economy initially stays at a non-satiated, saddlepoint stable steady-state point From Eqs (11.20) and (11.21), the steady-state capital stock k and the long-run after-tax rate of return to capital r Á / fk k / are determined by: r D/ / fk k Dı f k g : (11.24) As shown in Fig 11.4, / fk k / on the left-hand side can be depicted as a downward-sloping schedule in the r; k/ plane With DMI, the right-hand side, ı f k / g/ ; can also be expressed by a downward-sloping schedule The steadystate capital stock k and the long-run after-tax rate of return to capital r are given at the intersection, say point E0 ; of the two schedules For the initial steady-state point E0 to be saddlepoint stable, from Lemma 1, the / fk k / schedule is steeper than the ı f k / g/ schedule at E0 Following Chamley (1981) and Epstein and Hynes (1983), suppose that the government raises capital tax and pays back the revenue to consumers in a lumpsum manner, by keeping fiscal spending g constant It shifts the / fk k / schedule downward, thereby bringing the steady-state point from point E0 to E1 Consequently, k decreases in response to the tax increase Note that this reduction in k is larger than in the case of constant time preference: if ı were constant, the reduction would stop at k : This property contrasts sharply with the results in Epstein and Hynes (1983) under IMI, in which case the reduction in k caused by capital taxation is smaller than in the case of constant time preference With DMI, a decrease in k makes consumers less patient, which raises the long-run aftertax interest rate irrespective of the capital taxation, and thereby causes a further 11 On Decreasing Marginal Impatience 325 (1 − τ ) f k (k) r E2 E1 E0 τ↑ O g↑ δ ( f ( k) − g ) k′ k Fig 11.4 Steady-state capital stock under decreasing marginal impatience reduction in k From Eq (11.21), in turn, the resulting decreases in steady-state consumption and welfare u c / =ı c / are larger than they would have been under constant time preference Implication With DMI, an increase in capital taxes raises the long-run after-tax interest rate, so that, in contrast to the case of IMI, the resulting decrease in steadystate capital, consumption, and hence welfare are larger than they would have been under constant time preference 3.3 The Effects of Government Spending By using Eq (11.24) and hence Fig 11.4, we can also consider the effect of an increase in government spending financed by lump-sum taxation Suppose that the government increases its spending g permanently by raising the lump-sum tax while keeping the capital tax constant As shown in Fig 11.4, it shifts the ı f k/ g/ schedule upward, thereby bringing the steady-state point from point E0 to E2 along the / fk k/ schedule An increase in g thus raises r and reduces k The fiscal policy makes consumers cut down consumption and raises the rate of time preference under DMI, which leads to a higher r and hence a smaller k These 326 K Hirose and S Ikeda properties differ from the result under constant time preference that either r or k is not affected by an increase in g, and the result under IMI that the g increase lowers r and thereby enlarges k Implication With DMI, an increase in government spending raises the long-run interest rate and harms capital accumulation Conclusions This chapter has demonstrated the implications of DMI for dynamic consumer behavior and macroeconomic policy We have first shown that with DMI, there are multiple steady-state non-satiated and satiated equilibria When the interest rate is constant, the non-satiated steady-state point is necessarily unstable, which leads the rich to accumulate wealth up to a satiated level, while the wealth of the poor shrinks toward zero consumption In a capital economy with decreasing returns technology, both of the non-satiated and satiated steady-state points can be saddlepoint stable Unlike the IMI case, the negative long-run effects of an increase in capital taxes on consumption, capital stocks and hence, welfare, are larger than they would have been under constant time preference An increase in government spending reduces the long-run capital stock There are a number of interesting related issues First, the model of constant interest rate economy can be applied straightforwardly to the analysis of various policy issues in small open economies Second, in a two-country context, DMI leads to various interesting multiple steady-state equilibria, as discussed in Hirose and Ikeda (2004a) Third, the neoclassical model with DMI can be extended to incorporate money and thereby examine the effect of inflation Acknowledgements The authors would like to thank K Futagami, W Jodo, K Koda and two anonymous referees for their helpful comments on an earlier version of this paper A part of this research is financially supported by the Osaka University 21st Century Center of Excellence Program and Grants-in-Aid for Scientific Research C (No.18530137) Appendix Stability of Points E and E in Proposition Local optimal dynamics around the non-satiated steady-state point c ; linearized as: 10 1 rıccc cP c c C @ PADB A; @ c r 0A@ aP a a r ; a / is 11 On Decreasing Marginal Impatience 327 where the coefficient matrix is evaluated at c ; positive characteristic roots: (  r C r2 4rıc c Ã1=2 ) cc ; (  r2 r ; a / This system has three 4rıc c Ã1=2 ) ; and r; cc implying that the non-satiated steady-state point c ; ; a / is unstable Local optimal dynamics around the satiated steady-state point c ; ; a / is linearized as: 10 1 ı r rıccc c c cP C A; @ PADB @0 ı 0A@ a a aP r ; a / This system has where the coefficient matrix is evaluated at c ; characteristic roots r, ı.c /, and ı.c / r, which is negative as ı.c / < ı.c / D r from Assumption The satiated steady-state point c ; ; a / is thus saddlepoint stable Proof of Lemma By linearizing system in Eq (11.19) around the non-satiated steady-state point c ; ; k /, the local dynamic system can be obtained as: c ııccc cP B @ PAD@ c ı kP fk /fkk where the coefficient matrix is evaluated at c ; trace D ı C fk > 0; det: D ı c 10 C@ A cc c c a a A; ; k / For this coefficient matrix: ıc fk / fkk / : cc The linear system thus has one negative and two positive roots if and only if ıc c / fk k / / fkk k / > 0, as stated as the first item in Lemma By linearizing the system equation (11.19) around the satiated steady-state point c ; ; k /, the local dynamic system can be obtained as: ı cP @ PADB @0 kP / fk ııc cc ı 10 c C@ A a fk c a A; 328 K Hirose and S Ikeda where the coefficient matrix is evaluated at c ; ; k / The characteristic roots are fk , ı, and ı / fk The linear system thus has one negative and two positive roots if and only if ı c / / fk k / < 0, as stated as the second statement in Lemma Addendum: Related Studies14 In the text article, we formalize DMI by specifying the subjective discount rate as a function of consumption (or instantaneous utility) Alternatively, it is possible to introduce DMI by assuming that the subjective discount rate is a decreasing function with respect to wealth (e.g., Schumacher 2009) or saving (e.g., Gootzeit et al 2002) Becker and Mulligan (1997) deal with DMI in a “future-oriented capital” model, in which accumulation of the future-oriented capital leads to a lower discount rate, so that wealthier people become more patient In either case, similar economic implications of DMI, as discussed in our article, could be obtained Literature on dynamic macroeconomic theory incorporates DMI for various purposes, such as to analyze growth dynamics in an overlapping generations model (e.g., Sarkar 2007) and in an AK model with borrowing constraints (e.g., Borissov 2013) It has helped investigate asset pricing in an overlapping generations model (e.g., Nath and Sarkar 2006) and to examine equilibrium indeterminacy in response to interest-rate rules (e.g., Chang et al 2011) It also allows us to consider the effects of inflation on capital accumulation (e.g., Chen et al 2008; Gong 2006; Hirose and Ikeda 2004b) Based on the text article, we have been advancing further research on DMI Hirose and Ikeda (2012a,b) investigate implications of DMI in a two-country world economy If both countries exhibit DMI, the steady-state equilibrium is always unstable For saddle-point stability, at least one country needs to exhibit IMI Hirose and Ikeda (2012a) analyze the equilibrium dynamics in a one-good, two-country model where one country has DMI and the other has IMI Hirose and Ikeda (2012b) solve for two-good, two-country equilibrium dynamics with endogenous time preference, and re-examine the Harberger-Laursen-Metzler (hereafter HLM) effect, which states that a terms-of-trade deterioration would cause a reduction in national savings and a current-account deficit Although the HLM effect is invalid for a small country with IMI preference (as shown in Obstfeld 1982), it can be rehabilitated in a two-country economy The terms-of-trade deterioration affects the long-run accumulation of net foreign assets and hence the current account through the following three channels: (a) the income-compensating effect (which is always positive), (b) the welfare-supporting effect, and (c) the interest-income effect In the case where both countries have IMI, the HLM effect can materialize if the negative welfare-supporting effect dominates the positive income-compensating 14 This addendum has been newly written for this book chapter 11 On Decreasing Marginal Impatience 329 Table 11.1 Associations between time preference (discounting) and income Study Hausman (1979) Lawrance (1991) Ogawa (1993) Pender (1996) Ogaki and Atkeson (1997) Samwick (1998) Coller and Williams (1999) Donkers and van Soest (1999) Harrison et al (2002) Kapteyn and Teppa (2003) Ventura (2003) Read and Read (2004) Anderson et al (2004) Ikeda et al (2005) Booij and van Praag (2009) Tanaka et al (2010) Wang et al (2011) Data Field survey (Midwest Research Institute study) PSID National macro data Sample regions U.S Impatience-income Budget association variable Negative Income U.S Negative Japan, Korea, U-shaped (Japan, Taiwan Taiwan) const (Korea) India Negative No association Income National disposable income Net wealth Income Negative Income Positive Income Holland No association Income Experiment Denmark Negative Income Survey (CentERpanel) Holland Negative Income Survey (Bank of Italy Survey of Household Income and Wealth) Non-incentivized choice task Field interview survey Italy Negative Income, wealth U.K Negative Income Vietnam No association Income Experiment Japan Negative NIPO Post-Initial Schooling Survey Experiment Holland Negative Reward income in the experiments Income Vietnam Negative Income 45 countries Negative Income A field household panel survey (ICRISAT) A field household India panel survey (ICRISAT) Survey of Consumer U.S Finance Experiment U.S Survey (CentERpanel) An original international survey effect In the case where one country exhibits DMI and the other exhibits IMI, the HLM effect is necessarily invalid for the IMI country (since the welfare-supporting effect is positive) whereas it may be valid for the DMI country (due to the negative welfare-supporting effect) 330 K Hirose and S Ikeda As for empirical research, it is a matter of controversy as to how time preference and the discount rate relate to the decision maker’s degree of affluence, measured by income and/or wealth However, the majority of previous research reports that the degree of impatience, measured by time preference or personal discount rate, is negatively associated with income and/or wealth Table 11.1 summarizes the previous literature Although it covers only a part of the literature, 12 of the 17 studies listed indicate that richer people are more patient, as per the DMI model Note, however, that the detected associations not capture any causality In particular, since more patient people would have higher saving propensity and hence be wealthier, there could be an endogeneity problem when estimating how time preference relates to income and wealth The previous studies in Table 11.1 not cope with the problem.15 It is an important research topic to tackle this problem and thereby detect causal relationship between time preference and income/wealth References Anderson L, Dietz M, Gordon A, Klawitter M (2004) Discount rates in Vietnam Econ Dev Cult Change 52:873–887 Barro RJ (1999) Ramsey meets Laibson in the neoclassical growth model Q J Econ 114:1125–1152 Becker GS, Mulligan CB (1997) The endogenous determination of time preference Q J Econ 112:729–758 Booij AS, van Praag BMS (2009) A simultaneous approach to the estimation of risk aversion and the subjective time discount rate J Econ Behav Organ 70:374–388 Borissov K (2013) Growth and distribution in a model with endogenous time preferences and borrowing constraints Math Soc Sci 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Q J Econ 97:251–270 Obstfeld M (1990) Intertemporal dependence, impatience, and dynamics J Monet Econ 26:45–76 Ogaki M, Atkeson A (1997) Rate of time preference, intertemporal elasticity of substitution, and level of wealth Rev Econ Stat 79:564–572 Ogawa K (1993) Economic development and time preference schedule the case of Japan and East Asian NICs J Dev Econ 42:175–195 Pender JL (1996) Discount rates and credit markets: theory and evidence from rural India J Dev Econ 50:257–296 Read D, Read NL (2004) Time discounting over the lifespan Organ Behav Hum Decis Process 94:22–32 Ryder HE, Heal GM (1973) Optimal growth with intertemporally dependent preference Rev Econ Stud 40:1–33 Samwick AA (1998) Discount rate heterogeneity and social security reform J Dev Econ 57:117– 146 Sarkar J (2007) Growth dynamics in a model of endogenous time preference Int Rev Econ Financ 16:528–542 Schumacher I (2009) Endogenous discounting via wealth, twin-peaks and the role of technology Econ Lett 103:78–80 Svensson LEO, Razin A (1983) The terms of trade and the current account: the Haberger–Laursen– Metzler effect J Politi Econ 91:97–125 Tanaka T, Camerer CF, and Nguyen Q (2010) Risk and time preferences: linking experimental and household survey data from Vietnam Am Econ Rev 100:557–571 332 K Hirose and S Ikeda Tsutsui Y, Ohtake F, Ikeda S (2005) The reason why you are unhappy ISER Discussion Paper No 630, Osaka University (in Japanese) Uzawa H (1968) Time preference, the consumption function and optimum asset holdings In: Wolfe JN (ed) Value capital and growth: papers in honour of Sir John Hicks Aldine, Chicago Ventura L (2003) Direct measures of time preference Econ Soc Rev 34:293–310 Wang M, Rieger MO, Hens T (2011) How time preferences differ: evidence from 45 countries Norwegian School of Economics Discussion Paper (ISSN: 1500-4066) ... Behavioral Economics of Preferences, Choices, and Happiness, focuses on works on behavioral economics; and the second, Behavioral Interactions, Markets, and Economic Dynamics: Topics in Behavioral Economics, ... DOI 10 .10 07/97 8-4 -4 3 1- 5 550 1- 8 ISBN 97 8-4 -4 3 1- 5 550 1- 8 (eBook) Library of Congress Control Number: 2 015 950 212 Springer Tokyo Heidelberg New York Dordrecht London © Springer Japan 2 016 This work is... of Economics, Keio University, 2 -1 5-4 5 Mita, Minato-ku, Tokyo 10 8-8 345, Japan e-mail: hakab@econ.keio.ac.jp © Springer Japan 2 016 S Ikeda et al (eds.), Behavioral Interactions, Markets, and Economic
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