Ebook Behavioral interactions, markets, and economic dynamics: Topics in behavioral economics - Part 1

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
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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 8 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. 9 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 do 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 do 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

x

Preface

effect in the Japanese stock market. Surprisingly, the well-known stock return
regularity that is a characteristic of American and other nations’ stock markets,
momentum, is not observed in Japan. Instead, a significant short-term return
reversal exists for the portfolio of the formation period of 1 month. Iihara et al.
argue that investor overreaction may be a possible cause for the 1-month return
reversal. Although a number of studies have examined Japanese stock markets since
this paper was first written, no momentum effect has been reported except the
conditional momentum effect in our addendum. Either the Japanese market is more
efficient or our theoretical model is still immature or both. In Chap. 22, Professors
Katsuhiko Okada, Nobuyuki Isagawa, and Kenya Fujiwara examine the Japanese
stock market response to additions to the composition of the Nikkei Stock Average.
This study is an extension of several U.S. studies that focus on stock price effects
associated with a change in the composition of the S&P 500 index. All these studies
find stock price increases for the added firms. Since the price increase is temporary,
a large demand shock such as the excess demand of index arbitragers for shares of
the newly added firms moves the price. This finding implies that the demand curve
is downward sloping, which is inconsistent with the market efficiency assumption of
a horizontal demand curve. In Chap. 23, one of the long-lived anomalies, the Sellin-May effect, is carefully re-examined using Japanese stock return data. Although
Professors Shigeki Sakakibara, Takashi Yamasaki, and Katsuhiko Okada document
a similar stock return seasonality, the pattern is not exactly the same. Sakakibara et
al. find stock returns are higher for the first 6 months of the year even though the
Sell-in-May effect implies that stock returns are higher from November to April. For
some reason, Japanese markets do not respond to this global market trend in a timely
fashion. The authors call this anomaly the “Dekanshobushi effect.” Interestingly,

this anomaly still exists.
Ibaraki, Japan
Nagoya, Japan
Ibaraki, Japan
Kobe, Japan

Shinsuke Ikeda
Hideaki Kiyoshi Kato
Fumio Ohtake
Yoshiro Tsutsui


Acknowledgements

We thank Emi Kurimune and Azusa Ohishi of the Research Center of Behavioral Economics, Osaka University, for all the hard work, and Springer Japan
for their support for this project. We appreciate the financial support from the
Joint Usage/Research Center Project of the Institute of Social and Economic
Research, Osaka University (project title: Overview and Future Issues of Behavioral
Economics in Japan, 2014 and 2015), which was granted from the Ministry of
Education, Culture, Sports, Science and Technology.

xi



Contents

Part I

Intergenerational Interactions

1

An Equilibrium Model of Child Maltreatment . . . . .. . . . . . . . . . . . . . . . . . . .
Hideo Akabayashi

3

2

Tough Love and Intergenerational Altruism . . . . . . . .. . . . . . . . . . . . . . . . . . . .
Vipul Bhatt and Masao Ogaki

43

Part II

Behavioral Macroeconomics

3

Consumer Interdependence via Reference Groups .. . . . . . . . . . . . . . . . . . . .
Hiroaki Hayakawa and Yiannis Venieris

4

Bounded Rationality, Social and Cultural Norms,
and Interdependence via Reference Groups . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 101
Hiroaki Hayakawa

5

Keeping One Step Ahead of the Joneses: Status,
the Distribution of Wealth, and Long Run Growth .. . . . . . . . . . . . . . . . . . . . 141
Koichi Futagami and Akihisa Shibata

6

Macroeconomic Implications of Conspicuous
Consumption: A Sombartian Dynamic Model . . . . . .. . . . . . . . . . . . . . . . . . . . 163
Katsunori Yamada

7

On Persistent Demand Shortages: A Behavioural Approach .. . . . . . . . . 191
Yoshiyasu Ono and Junichiro Ishida

Part III
8

81

Time Preference in Macroeconomics

Rate of Time Preference, Intertemporal Elasticity
of Substitution, and Level of Wealth . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 229
Masao Ogaki and Andrew Atkeson

xiii

xiv

9

Contents

Economic Development and Time Preference Schedule:
The Case of Japan and East Asian NICs . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 249
Kazuo Ogawa

10 Luxury and Wealth .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 273
Shinsuke Ikeda
11 On Decreasing Marginal Impatience .. . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 311
Ken-ichi Hirose and Shinsuke Ikeda
Part IV

Bubbles and Crash

12 Why Did the Nikkei Crash? Expanding the Scope
of Expectations Data Collection .. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 335
Robert J. Shiller, Fumiko Kon-Ya, and Yoshiro Tsutsui
13 Price Bubbles Sans Dividend Anchors: Evidence
from Laboratory Stock Markets . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 357
Shinichi Hirota and Shyam Sunder
Part V

Experimental Markets

14 Revenue Non-equivalence Between the English

and the Second-Price Auctions: Experimental Evidence . . . . . . . . . . . . . . . 399
Chew Soo Hong and Naoko Nishimura
15 An Experimental Test of a Committee Search Model . . . . . . . . . . . . . . . . . . 419
Yoichi Hizen, Keisuke Kawata, and Masaru Sasaki
16 Equilibrium Refinement Versus Level-k Analysis:
An Experimental Study of Cheap-Talk Games
with Private Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 453
Toshiji Kawagoe and Hirokazu Takizawa
Part VI

Behavioral Contract Theory

17 Moral Hazard and Other-Regarding Preferences . .. . . . . . . . . . . . . . . . . . . . 483
Hideshi Itoh
18 Contracting with Self-Esteem Concerns . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 519
Junichiro Ishida
19 Optimal Promotion Policies with the Looking-Glass Effect . . . . . . . . . . . 543
Junichiro Ishida
Part VII

Market Efficiency and Anomalies

20 Is No News Good News? The Streaming News Effect
on Investor Behavior Surrounding Analyst Stock Revision
Announcement .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 567
Takahiro Azuma, Katsuhiko Okada, and Yukinobu Hamuro


Contents

xv

21 The Winner–Loser Effect in Japanese Stock Returns .. . . . . . . . . . . . . . . . . 595
Yoshio Iihara, Hideaki Kiyoshi Kato, and Toshifumi Tokunaga
22 Addition to the Nikkei 225 Index and Japanese Market
Response: Temporary Demand Effect of Index Arbitrageurs .. . . . . . . . 615
Katsuhiko Okada, Nobuyuki Isagawa, and Kenya Fujikawa
23 The Calendar Structure of the Japanese Stock Market:
The ‘Sell in May Effect’ Versus the ‘Dekansho-Bushi Effect’ . . . . . . . . . 637
Shigeki Sakakibara, Takashi Yamasaki, and Katsuhiko Okada
Erratum . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .

E1

Index . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 663



About the Editors

Shinsuke Ikeda is a professor at the Institute of Social and Economic Research
(ISER), Osaka University, and serves as the director of the Research Centre of
Behavioral Economics in ISER. He got a B.Com. of Kobe University in 1980
and a Ph.D. (Doctor) of Osaka University (economics) in 1997. He was the
former president of the Association of Behavioral Economics and Finance. He
published articles on behavioral economics, macroeconomic dynamics, and asset
pricing in Journal of Finance, Journal of Health Economics, Journal of International
Economics, Journal of Monetary Economics, International Economic Review, etc.
His work on behavioral economics is incorporated into the book The Economics of
Self-Destructive Choices, Springer, to appear in 2015.

Hideaki Kiyoshi Kato is a professor of finance at Graduate School of Economics,
Nagoya University, Nagoya, Japan. Before joining Nagoya University, he taught at
Kobe University. He received his Ph.D. degree from the University of Utah in 1985.
He has published several books and more than 30 articles in the leading finance
journals such as Review of Financial Studies, Management Science, Journal of
Financial Economics, Journal of Financial and Quantitative Analysis, International
Review of Finance, Japan and the World Economy, Pacific Basin Finance Journal,
Journal of Portfolio Management, Journal of Financial Research, Journal of Banking
and Finance, and Journal of Futures Markets on subjects including the market
efficiency and anomalies, stock options, investor behavior, dividend policy, equity
offerings, and stock index futures. He is currently an associate editor of Pacific Basin
Finance Journal and International Review of Finance.
Fumio Ohtake is Osaka University distinguished professor and a professor in the
Institute of Social and Economic Research at Osaka University and an executive
vice president of Osaka University. He earned his M.A. and a Ph.D. from Osaka
University in 1985 and 1996, respectively, and a B.A. from Kyoto University in
1983. He is the president of the Association of Behavioral Economics and Finance,
and an executive director of the Japanese Economic Association. His research topics
are behavioral economics, labor economics, income distribution, and household
xvii


xviii

About the Editors

behavior. He is also a recipient of the 2005 Nikkei Prize for Excellent Books in
Economic Science; the 2005 Suntory Prize for Social Science and Humanities;
the 2005 Economist Prize; the 2006 Ishikawa Prize of the Japanese Economic
Association; and the 2008 Japan Academy Prize.

Yoshiro Tsutsui is a professor of economics at Konan University. He had previously taught at Nagoya City University and Osaka University. He was awarded
a Ph.D. (economics) from Osaka University. He was the first president of the
Association of Behavioral Economics and Finance, and the president of Japan
Society of Monetary Economics. His primary areas of teaching and research are
behavioral economics and banking and finance. Currently, his research includes
happiness study, time discounting, international linkage of stock prices, and regional
banking and finance. His publications appeared in journals including Review of
Economics and Statistics, Journal of Financial and Quantitative Analysis, Journal
of Banking and Finance, Journal of Risk and Uncertainty, Regional Science and
Urban Economics, and Journal of Research in Personality. In 1988, his book,
The Financial Markets and Banking Industry: Economic Analysis of Industrial
Organization (Toyokeizai-Shinpo Sha, in Japanese) was awarded the Nikkei Prize
for Excellent Books in Economic Science.


Part I

Intergenerational Interactions


Chapter 1

An Equilibrium Model of Child Maltreatment
Hideo Akabayashi

Abstract We propose a dynamic equilibrium model of human capital development
of a child that can explain why a parent-child relationship might lead to child
maltreatment. Assuming that a parent cannot observe a child’s human capital
accumulation or effort, and that the child’s time preference develops endogenously,
an unstable path of the parent’s beliefs regarding the child can persist in equilibrium

when the parent faces a high degree of uncertainty in inferring the child’s human
capital. The parent with an initial high estimate of the human capital then tends to
underestimate the child’s effort, which results in persistently punitive—abusive—
nteractions.
Keywords Human capital production • Parental intervention • Family education • Child development • Time preference

1 Introduction
The purpose of this chapter is to propose a dynamic equilibrium model of a
child’s human capital formation and the parents’ style of interactions with the child
and thereby explain complicated phenomena in modern families, such as child
maltreatment (abuse).1 This is probably the first rational choice model of child
maltreatment in economic literature that is consistent with recent views on child
maltreatment.

The original article first appeared in the Journal of Economic Dynamics and Control 30: 993–1025,
2006. A newly written addendum has been added to this book chapter.
1

The terms “maltreatment” and “abuse” are used interchangeably throughout this chapter, although
the former is usually intended to cover a wider range of behavioral patterns such as abuse and
neglect, both emotional and physical.
H. Akabayashi ( )
Faculty of Economics, Keio University, 2-15-45 Mita, Minato-ku, Tokyo 108-8345, Japan
e-mail:
© Springer Japan 2016
S. Ikeda et al. (eds.), Behavioral Interactions, Markets, and Economic Dynamics,
DOI 10.1007/978-4-431-55501-8_1

3

4

H. Akabayashi

Parental interactions with the child change over the course of a child’s development. My calculations from the National Longitudinal Survey of Youth—Child
Supplement in 1988 suggest that, on an average, a mother spanks her 5-year-old boy
once a week and praises him 6 times a week, whereas the frequencies reduce to 0.7
times a week and 4 times a week, respectively, when he turns 7. Generally, there is
a tendency for a mother to intervene less often as a child grows older. This may be
explained by an older child’s improved ability to control him or herself with better
foresight, thus, the frequency with which the parent needs to intervene is reduced.
We can say that the average path of interactions is stable in this sense, and a dynamic
model should help us explain this formally.
However, there is a growing concern regarding the causes of deviations from such
a path in some families, especially in extreme cases of child maltreatment. Until
recently, such deviations, characterized by parents’ increasing interventions and
a child’s developmental delay, have frequently been ascribed psychopathological
explanations. Nonetheless, very few studies have succeeded in differentiating
between abusers and nonabusers on the basis of traditional measures of personality
disturbances (Wolfe 1987, p. 45). In recent explanations, it is common to view
child abuse “along the hypothetical continuum that establishes the polar opposites
of abusive and healthy parenting styles” and as a “process between parent and child,
within both the familial context and the larger social structure” (Wolfe 1987, p. 40
and p. 48). In this sense, most professionals no longer believe that child abuse is
pre-programmed in “crazy parents,” but view it as an outcome of the continuous
breakdown of normal parent-child relationships. The model presented in this chapter
allows us to interpret such a deviation as an unstable equilibrium path of parent-child
interactions.2
The principal-agent framework is used to describe a family consisting of an

altruistic parent and a growing child. The key assumptions are: (1) a child’s
human capital develops through his or her own effort under parental influence and
interventions, (2) a child’s rate of time preference is a decreasing function of the
human capital, (3) the parent cannot directly observe the child’s human capital and
the parent’s observation errors can be reduced by spending additional time with the
child, and (4) the parent updates her beliefs regarding the child’s human capital level
using available information.
The dynamic equilibrium process of the parent’s beliefs about the child’s human
capital indicates that the parental beliefs may diverge. It is then suggested that the
parent with a high initial expectation about the child’s ability tends to maintain
an unreasonably high expectation about the child’s behavior, which leads to a
persistently negatively biased assessment of the child’s effort. The parent’s optimal
interactions with the child tend to be punitive rather than positive, thereby providing
an explanation of child maltreatment.

2

Therefore, child abuse as a direct result mental illness, frustration, stress from divorce and
unemployment, unattractiveness of the child, and the parents’ own upbringing is beyond the scope
of this chapter. Sexual abuse is not explained either.


1 Child Maltreatment

5

Theoretical results and implications, including the role of parental expectations,
are found to be mostly consistent with the recent views on child maltreatment in
psychological literature. Although the model presented here is not intended to be a
comprehensive theory of child maltreatment or parent-child interactions, the results

suggest that interpretations based on rational choice and equilibrium are highly
useful for better understanding those phenomena.
A static model of parent-child relationships as the principal-agent model was
first proposed by Akabayashi (1996), which focused on the conflicts between
parents and children stemming from the fact that children’s efforts are unobservable
and that children tend to be myopic. It was shown that, in equilibrium, altruistic
parents choose to provide incentives (e.g., praise and punishment) in order to
influence the child’s development, formalizing psychologists’ views of parent-child
relationships.3 This chapter considers the dynamic interrelationships between the
development of a child’s characteristics, the accumulation of human capital, and
parental expectations in order to determine how a child’s characteristics develop
and how parental actions toward the child change over time.

2 Issues of Child Maltreatment
There has been an increasing interest in the prevention and treatment of child abuse.
The most recent incidence rate of child maltreatment is 42 per 1,000 children
(Sedlak and Broadhurst 1996). Abused children not only have been found to have
emotional and behavioral problems, such as higher rates of aggression, acting
out, and hyperactivity, but also problems in cognitive development and social
competence.4 To the extent that these developmental elements predict their future
socio-economic status, how a child is reared must be regarded as an important input
to the production of human capital.
There are numerous theories that researchers use for explaining why parents
might abuse children.5 It is probably impossible to construct a single model that
explains the various aspects and causes of child abuse, because it is a “multi-

3

The conflict between an altruistic parent and a selfish child has been widely discussed in the family
economics literature (Bergstrom 1997). Weinberg (2001) developed a similar model that includes

the effects of parental income on the choice between pecuniary and non-pecuniary methods of
punishment. Using state level panel data, Paxson and Waldfogel (2002) empirically found that
child maltreatment is correlated with the father’s absence, poverty, and unemployment.

4

Appelbaum (1977) found a delay in language development among abused children. Erickson et al.
(1989) states, “disproportionate numbers of abused children have been found to perform below the
average range on IQ tests.” Wolfe (1987) states, “from preschool age and beyond, studies have
found that abused children are significantly more likely than their peers to show delays related to
cognitive development and deficits in academic performance and intellectual functioning.”

5

“Psychological Theories of Child Maltreatment” gives a brief explanation of competing theories
of child abuse.


6

H. Akabayashi

dimensional” (Wolfe 1987, p. 59) phenomenon and the points of emphasis depend
on the approach selected. Recent approaches, labeled as the social-cultural approach
or the social-interactional approach, view child abuse as a consequence of a “process” of interactions between parents, children, and their socio-economic situation,
rather than as a psychopathological consequence of the parents’ predetermined
characteristics. In this chapter, while placing child abuse in the broad context of
the developmental consequences of the parent-child relationship, the focus is on
the role of a parent’s expectation of the child’s development in causing an abusive
relationship.

The importance of the parent’s expectation of a child in an abusive relationship
has been extensively documented in literature. For instance, Zigler and Hall (1989,
p. 64) wrote, “Parents who have unrealistically high expectations of their child are
more likely to abuse than are parents who have a good understanding of the sequence
of child development.” Wolfe (1987, p. 87) states, “Practitioners observed that many
abusive incidents involved senseless attempts by the parent to force a child to behave
in a certain manner that was beyond the child’s developmental limitations.”
Focusing on this aspect, here child abuse is defined as “a dynamic parentchild relationship where the parent unreasonably overestimates the child’s ability,
tends to form a negatively biased view of the child’s behavior, and maintains or
excessively increases negatively-biased (“punitive”) interactions.”6 We define the
parent’s “interactions” as encompassing all physical, verbal, and psychological
interactions with the child.7 Although, initially, a parent’s estimate of the child’s
characteristics may be inaccurate, this estimate generally converges to the true
value as the parent collects information about the child. However, even after
many observations of the child’s behavior, some parents continue to possess an
unreasonable belief about the child’s characteristics and tend to build a negatively
biased view of the child’s self-control or effort. To highlight this idea, we consider
the child’s rate of time preference as a key determinant of the child’s developmental
characteristics, and we assume that this rate of time preference is related to the
child’s maturity or “basic human capital.”8 The study investigates the reasons for

6

As will be clear in the following sections, “negatively biased” interactions mean only that utility
transfer from a parent to a child tends to be smaller than the expected amount based on the
predetermined incentive schedule and not that parents transfer a negative amount of utility.

7

Therefore, this definition does not necessarily imply “physical” abuse. Some researchers are

beginning to define child abuse in such a sense, which is broader than that commonly used. Wolfe,
for example, states that, “Child abuse, according to this [social-psychological] perspective, can
be viewed as an extreme disturbance of child rearing, which is to say it is not necessarily an
individual disorder or psychological disturbance. Abusive families are ones in which the usual
balance between positive and negative interactions and between discipline and emotional bonding
has not been achieved” (1987, p. 18).
8

Here “basic” human capital broadly represents the degree of maturity that encompasses personality and cognitive abilities, rather than skills or knowledge that are directly productive and
observable in the market. In the subsequent sections, a mature child means a child with a high level
of basic human capital. Henceforth, “basic” is dropped for simplicity.


1 Child Maltreatment

7

the biased parental belief regarding the child not converging to the true value and
remaining negatively-biased along with the manner in which this occurs.

3 The Model
3.1 Law of Motion of a Child’s Human Capital
Let us suppose a family consists of one parent and one child and denote the child’s
human capital at the beginning of period t by ht , where t = 1,. . . ,T C 1. T C 1
is the period when a child becomes independent of the parent and starts relying
only on the value of his or her own human capital accumulated over the previous
periods. A child’s initial human capital or “potential ability,” h1 , is assumed to be
given and positive. A child’s human capital at subsequent periods is assumed to be
determined by the child’s human capital level in the immediate past, the level of
effort, the parent’s time spent with the child, and the family environment including

the parent’s human capital level. We assume that the parent and the child know that
the law of motion of human capital is described by the following linear process9 :
h

C1

D .1

ı/h C 's H C a ;

for

D 1; : : :; T;

(1.1)

where H is the parent’s human capital (assumed to be positive and constant over
time), s 2 (0,1] is her (normalized) time spent with a child, and a is the child’s
effort level. We assume that ı is strictly positive and less than 1 so that the first
term represents the depreciation of human capital. The second term represents the
parent’s investment in the child’s human capital (or “education”), which is a function
of the time spent by the parent and her human capital level. The third term represents
the child’s own investment in human capital (or “learning by own effort”). ' and
are presumably positive marginal effects of “education” and “effort” on human
capital, respectively. We assume that is less than 1 ı so that the effect of effort is
smaller than the effect of past human capital. By applying (1.1) repeatedly, we have
T
P
hT C1 D .1 ı/T t C1 ht C
.1 ı/T .'s H C a /; for arbitrary t < T C 1:

Dt

9

Additivity and linearity in choice variables in the production process are imposed to avoid
unnecessary complication. These restrictions ignore a productive complementarity between the
child’s current human capital and the parent’s time spent with the child or the child’s effort. The
assumption that both the parent and the child know the process may also seem unrealistic; however,
this is the standard assumption in the classical Kalman filter literature, and increasing the number
of unobservables would unnecessarily complicate the analysis. The point is that the current setup
is sufficient for explaining essential features that characterize child maltreatment without further
complications.