Nest-monotonic two-stage acts and exponential probability capacities

This paper examines conditions for Choquet expected utility (CEU) to satisfy both the reduction of two-stage acts and the recursion axioms, which are taken for granted in economics. A key idea of this paper is to consider nest-monotonic two-stage acts, which share their rankings of states with those of their reduced one-stage acts. Our main theorem shows that the axioms, one of which is restricted to nest-monotonic two-stage acts, and consequentialism are satisfied if and only if the preference is exponential CEU, which is such that the probability capacity is an exponential transformation of a probability measure. This result indicates that within a specified range of decision problems, exponential CEU is the only form of CEU that derives indifference to the timing of information resolution. Furthermore, the relation between first- and second-stage exponential CEU is characterized both by the f*-Bayesian updating rule and by comonotonic dynamic consistency. Conditions to establish the law of iterated expectation for CEU are also discussed.     

Risk aversion and prudence in the large

The familiar measures of absolute and relative risk aversion constructed by Pratt and Arrow, along with the measures of absolute and relative prudence inspired by Leland and later developed by Kimball, are local instruments based on the first and second derivatives of utility at a specific level of wealth. As such, they are applicable only to infinitesimal risks—those for which differential calculus is a suitable analytical tool. Consequently, they may not accurately gauge preferences regarding the larger risks typically encountered in practice. To address this problem, the present paper develops more general, closed-form index measures of risk aversion and prudence that are applicable to either large or small risks. The new measures are exact in that they do not rely on approximations, they can be implemented empirically without knowledge of the functional form of utility, and they do not require information regarding pre-existing wealth.     

Migration decisions under ambiguity: Migration distance effects revisited

There is ample evidence that distance has a strong negative effect on migration. Despite its significance in migration decisions, scholars rarely explore the migration distance effect deeper than the first level of interpretation derived from the simple neoclassical theory of migration. This study revisits the migration distance effect in the spirit of Knightian distinction between risk and uncertainty. To this end, this study attempts to construct estimates of the risk premium migrants are willing to pay to avoid the risk associated with migration distance. The results show that the magnitude of the distance effect is not rationalized by risk aversion in the Arrow–Pratt sense (Arrow, 1965, The theory of risk aversion, Yrjo Jahnssonin Saatio, Helsinki, Finland, 90; Pratt, 1964, Econometrica, 32, 122). In particular, the risk premium demanded by distant rural residents is unjustifiably higher compared with that of those living closer to urban areas in their migration decisions. The results suggest that the migration distance effect is analogous to the equity home bias puzzle and the Ellsberg paradox in that the assumption of subjective expected utility can lead to seemingly irrational human behaviors. Some of the findings in this study shed light on the role of subjective aspects such as perception, confidence, and pessimism in migration decisions, which have been neglected in the literature.     

Greater downside risk aversion in the large

In this paper, we advance a definition of greater downside risk aversion that applies to both large and small changes in risk preference, and thereby complements the results for small changes reported previously. We show that a downside risk-averse transformation of a utility function results in a function that is more downside risk averse in the same manner that a risk-averse transformation increases risk aversion. Our demonstration is conducted first by using the compensated approach introduced by Diamond and Stiglitz [P. Diamond, J. Stiglitz, Increases in risk and in risk aversion, J. Econ. Theory 8 (1974) 337-360] and then by using an adaptation of the risk premium approach taken by Pratt [J. Pratt, Risk aversion in the small and in the large, Econometrica 32 (1964) 122-136].     

INTERTEMPORAL UTILITY SMOOTHING: THEORY AND APPLICATIONS

This paper reviews models of intertemporal choice designed to be consistent with a phenomenon called a preference for spread; that is, where a decision‐maker prefers to spread good and bad consumption evenly over time. We closely examine the notion of utility smoothing adopted in these models as a source of the preference for spread. The paper also reviews extensions of these models where a strong aversion to volatility involved in a utility sequence causes preferences to be nonmonotone. Furthermore, to gain a better understanding of the behaviour implied by these models, we apply them to the Diamond growth model.     

Real estate and relative risk aversion with generalized recursive preferences

This paper investigates how real estate wealth affects the household’s attitude toward risk, and derives the closed-form expressions for risk aversion with generalized recursive preferences. We find three channels through which real estate wealth affects risk aversion, and these channels are absent in the traditional measure of relative risk aversion as in Arrow (1965) and Pratt (1964). First, illiquidity and fluctuations in real estate value increase consumption risk, thereby increasing risk aversion. Second, real estate as an asset provides a cushion for absorbing negative shocks to households, reducing risk aversion. Third, an increase in real estate prices lowers the profit of the firm that uses real estate as a factor of production, induces a decline in the real wage, and causes a rise in consumption risk. This channel increases risk aversion. We study how these channels as a whole determine relative risk aversion using a basic real business cycle model with generalized recursive preferences and compare the results with the case of expected utility preferences. Finally, we explore the implications of the firm’s and the household’s real estate holdings and illiquidity of real estate on the risk premiums for equity and real estate.     

Ambiguity Made Precise: A Comparative Foundation

The theory of subjective expected utility has been recently extended to allow ambiguity to matter for choice. We propose a notion of absolute ambiguity aversion by building on a notion of comparative ambiguity aversion. We characterize it for a preference model which encompasses some of the most popular models in the literature. We next build on these ideas to provide a definition of unambiguous act and event and show the characterization of the latter. As an illustration, we consider the classical Ellsberg 3-color urn problem and find that the notions developed in the paper provide intuitive answers. Journal of Economic Literature Classification Number: D81.     

Wealth effects and agency costs

We analyze how the agent's initial wealth affects the principal's expected profits in the standard principal–agent model with moral hazard.We show that if the principal prefers a poorer agent for all specifications of action sets, probability distributions, and disutility of effort, then the agent's utility of income must exhibit a coefficient of absolute prudence less than three times the coefficient of absolute risk aversion for all levels of income, thus strengthening the sufficiency result of Thiele and Wambach (1999). Also, we prove that there is no condition on the agent's utility of income alone that will make the principal prefer richer agents. Moreover, we show that, for an interesting class of problems, the principal prefers a relatively poorer agent if agent's wealth is sufficiently large. Finally, we discuss how alternative ways of modeling the agent's outside option affects the principal's preferences for agent's wealth.     

A Definition of Uncertainty Aversion

A definition of uncertainty or ambiguity aversion is proposed. It is argued that the definition is well-suited to modelling within the Savage (as opposed to Anscombe and Aumann) domain of acts. The defined property of uncertainty aversion has intuitive empirical content, behaves well in specific models of preference (multiple-priors and Choquet expected utility) and is tractable. Tractability is established through use of a novel notion of differentiability for utility functions, called eventwise differentiability.     

Bliss,Catastrophe, and Rational Policy

Lotteries with infinite expected utility are inconsistent with the axioms of expected utility theory. To rule them out, either the set of permissible lotteries must be restricted (to exclude, at a minimum, “fat-tailed” distributions such as that underlying the St. Petersburg Paradox and power laws that are popular in models of climate change), or the utility function must be bounded. This note explores the second approach and proposes a number of tractable specifications leading to utility functions that are bounded both from above and below. This property is intimately related to that of increasing relative risk aversion as first hypothesized by Arrow (1965).     

Preservation of “more risk averse” under expectations

The preservation of risk aversion properties of utility functions under expectation operations is of interest in the study of derived utility functions in sequential decision problems and in problems with multiple (contemporaneous) sources of uncertainty. The purpose of this note is to present sufficient conditions for the Pratt relation “more risk averse” to be preserved under expectations.     

Completing the State Space with Subjective States

We define an opportunity act as a mapping from an exogenously given objective state space to a set of lotteries over prizes, and consider preferences over opportunity acts. We allow the preferences to be possibly uncertainty averse. Our main theorem provides an axiomatization of the maxmin expected utility model. In the theorem we construct subjective states to complete the objective state space. As in E. Dekel et al. (Econometrica, in press), we obtain a unique subjective state space. We also allow for preference for flexibility in some of the subjective states and commitment in others. Journal of Economic Literature Classification Number: D81.     

Disclosure policies in all-pay auctions with bid caps and stochastic entry: The impact of risk aversion

We investigate how risk aversion affects the organizer's disclosing the actual number of bidders in an all-pay auction with an exogenous bid cap and stochastic entry. With an exogenous probability of participation, the organizer prefers fully concealing the number of participating bidders when bidders are risk neutral. However, this result does not hold with risk aversion. Specifically, whether the organizer prefers fully concealing or fully revealing information depends on the number of potential bidders, the probability of participation, and the size of bid caps. A special case of endogenous entry shows that the organizer's preference is similar to the risk-neutral case.     

Almost-objective uncertainty

Summary. Every subjective state space with Euclidean structure contains almost-objective events which arbitrarily closely approximate the properties of objectively uncertain events for all individuals with event-smooth betting preferences - whether or not they are expected utility, state-independent, or probabilistically sophisticated. These properties include unanimously agreed-upon revealed likelihoods, statistical independence from other subjective events, probabilistic sophistication over almost-objective bets, and linearity of state-independent and state-dependent expected utility in almost-objective likelihoods and mixtures. Most physical randomization devices are based on events of this form. Even in the presence of state-dependence, ambiguity, and ambiguity aversion, an individuals betting preferences over almost-objective events are based solely on their attitudes toward objective risk, and can fully predict (or be predicted from) their behavior in an idealized casino.Received: 17 July 2003, Revised: 12 November 2003, JEL Classification Numbers: D81.I am grateful to Kenneth Arrow, Erik Balder, Hoyt Bleakley, Richard Carson, Eddie Dekel, Larry Epstein, Clive Granger, Simon Grant, Peter Hammond, Jean-Yves Jaffray, Edi Karni, Peter Klibanoff, Duncan Luce, John Pratt, Chris Tyson, Uzi Segal, Peter Wakker, Joel Watson, Nicholas Yannelis, anonymous referees and especially Ted Groves and Joel Sobel for helpful comments. This material is based upon work supported by the National Science Foundation under Grant No. 9870894.     

Decreasing Impatience: A Criterion for Non‐stationary Time Preference and "Hyperbolic" Discounting

Despite recent interest in hyperbolic discounting, there has been little discussion of exactly what property of time preferences is instantiated by hyperbolic or quasi‐hyperbolic functional forms. The paper revives an earlier proposal in Prelec (1989) that the key property is Pratt–Arrow convexity of the log of the discount function, which corresponds to decreasing impatience(DI) at the level of preferences. DI provides a natural criterion for assessing the severity of departure from stationarity in that greater DI is equivalent to more choices of dominated options in two‐stage decision problems, as well as greater convexity of the log of the discount function. Inefficient choices may arise as intentional precommitments, or as unintended reversals of preference by “naïve” agents.     

Stochastically independent randomization and uncertainty aversion

Summary.   This paper proposes a preference-based condition for stochastic independence of a randomizing device in a product state space. This condition is applied to investigate some classes of preferences that allow for both independent randomization and uncertainty or ambiguity aversion (a la Ellsberg). For example, when imposed on Choquet Expected Utility (CEU) preferences in a Savage framework displaying uncertainty aversion in the spirit of Schmeidler [27], it results in a collapse to Expected Utility (EU). This shows that CEU preferences that are uncertainty averse in the sense of Schmeidler should not be used in settings where independent randomization is to be allowed. In contrast, Maxmin EU with multiple priors preferences continue to allow for a very wide variety of uncertainty averse preferences when stochastic independence is imposed. Additionally, these points are used to reexamine some recent arguments against preference for randomization with uncertainty averse preferences. In particular, these arguments are shown to rely on preferences that do not treat randomization as a stochastically independent event. Received: February 10, 2000; revised version: March 30, 2000     

Risk and regret aversions on optimal bank interest margin under capital regulation

This paper examines the bank's optimal loan rate (and thus the bank's interest margin) under more stringent capital regulation when the bank is not only risk-averse but also regret-averse. Risk-averse preferences are characterized by an option-based utility function that includes disutility from the dislike of bank equity risk. Regret-averse preferences feature an option-based utility function that includes disutility from having chosen ex-post suboptimal alternatives. We show that an increase in bank capital requirement results in an increased margin under risk aversion dominating regret aversion, whereas it results in a reduced margin under regret aversion dominating risk aversion. The former holds when risk aversion domination stems from increasing risk-averse preference, but not from decreasing regret-averse preference, while the latter holds when regret aversion domination results from either decreasing risk-averse or increasing regret-averse preference. Risk aversion, as such, makes the bank more prudent and less prone to risk-taking, while regret aversion, as such, makes the bank less prudent and more prone to risk-taking.     

Two-persons efficient risk-sharing and equilibria for concave law-invariant utilities

Efficient risk-sharing rules and equilibria between two agents with utilities in a class that contains the rank dependent expected utility (RDU) are fully characterized. Specific attention is given to the RDU. Call-spreads and contracts with mixed regimes are shown to be efficient. Closed-form solutions are obtained for several examples.      

Greater prudence and greater downside risk aversion

Variation in the degree of downside risk aversion across decision makers has implications for efficient risk sharing. However, except for small differences in risk preferences, there is no index, analogous to the Arrow-Pratt index of risk aversion, that depends only on local properties of the utility function and indicates the degree of aversion to downside risk. A measure that does depend only on local properties of the utility function u, the index of prudence p=−u^?/u^″, is related to downside risk aversion, which is indicated by a positive value for u^?. Although we show that the degree of prudence is not an accurate indicator of the degree of downside risk aversion, we nonetheless demonstrate that a uniform increase in prudence accompanied by a uniform increase (decrease) in risk aversion is sufficient to indicate greater downside risk aversion, provided prudence is greater (less) than three times the degree of risk aversion.     

Justifiable preferences

We characterize preferences over acts that can be represented by a utility function and a multiple-prior, such that an act f is preferred to act g if there is a prior under which the expected utility induced by f is higher than that induced by g. These preferences are referred to as justifiable preferences. We further introduce a generalized model of ambiguity that involves a collection of multiple-priors, namely, multiple multiple-priors and incorporate Bewley?s Knightian model in justifiability: f is preferred to g if, according to at least one set of priors, f is unanimously preferred to g.