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     

Ambiguity aversion and the absence of indexed debt

Summary. Following the seminal works of Schmeidler (1989), Gilboa and Schmeidler (1989), roughly put, an agents subjective beliefs are said to be ambiguous if the beliefs may not be represented by a unique probability distribution, in the standard Bayesian fashion, but instead by a set of probabilities. An ambiguity averse decision maker evaluates an act by the minimum expected value that may be associated with it. In spite of wide and long-standing support among economists for indexation of loan contracts there has been relatively little use of indexation, except in situations of extremely high inflation. The object of this paper is to provide a (theoretical) explanation for this puzzling phenomenon based on the hypothesis that economic agents are ambiguity averse. The paper considers a general equilibrium model based on Magill and Quinzii (1997) with ambiguity averse agents, where both nominal and indexed bond contracts are available for trade and all relevant prices are determined endogenously. We obtain conditions which prompt an endogenous cessation of trade in indexed bonds: i.e., conditions under which there is no trade in indexed bonds in any equilibrium; only nominal bonds are traded.Received: 7 April 2003, Revised: 8 March 2004, JEL Classification Numbers: D81, E31, D52, E44.Correspondence to: Sujoy MukerjiWe thank seminar members at Birkbeck, Oxford, Paris I, Southampton and Tel Aviv, the audience at the 00 European Workshop on General Equilibrium Theory, and especially, E.Dekel, I. Gilboa, D. Schmeidler and A. Pauzner for helpful comments. The first author acknowledges financial assistance from an Economic and Social Research Council of U.K. Research Fellowship (# R000 27 1065). The second author thanks financial support from the French Ministry of Research (Action Concertée Incitative).     

Intertemporal substitution, risk aversion and ambiguity aversion

Summary. This paper axiomatizes a form of recursive utility on consumption processes that permits a role for ambiguity as well as risk. The model has two prominent special cases: (i) the recursive model of risk preference due to Kreps and Porteus [18]; and (ii) an intertemporal version of multiple-priors utility due to Epstein and Schneider [8]. The generalization presented here permits a three-way separation of intertemporal substitution, risk aversion and ambiguity aversion.Received: 5 August 2003, Revised: 12 March 2004, JEL Classification Numbers: D80, D81, D90.I am grateful to Larry Epstein for his guidance and invaluable advice, and to a referee for helpful comments and suggestions.     

Ambiguity aversion among student subjects: the role of probability interval and emotional parameters

In the literature on decision-making under uncertainty, it has been shown that decision-makers tend to prefer taking gambles with known-risk probabilities (pure risk) over equivalent gambles with ambiguous probabilities. This article contributes to the ongoing discussion in the literature on cognitive and non-cognitive covariates of ambiguity aversion. Through a series of experiments, it finds that subjects are more ambiguity-averse to prospects with wide probability intervals than to an equivalent prospect with narrow intervals, and that subjects’ inherent trust, happiness and level of optimism affect the level of ambiguity aversion.     

Ambiguous act equilibria

A game-theoretic framework that allows for explicitly randomized strategies is used to study the effect of ambiguity aversion on equilibrium outcomes. The notions of “independent strategies” as well as of “common priors” are amended to render them applicable to games in which players lack probabilistic sophistication. Within this framework the equilibrium predictions of two-player games with ambiguity-averse and with ambiguity-neutral players are observationally equivalent. This equivalence result does not extend to the case of games with more than two players. A translation of the concept of equilibrium in beliefs to the context of ambiguity aversion yields substantially different predictions – even for the case with just two players.     

Monotone risk aversion

Summary. This paper defines decreasing absolute risk aversion in purely behavioral terms without any assumption of differentiability and shows that a strictly increasing and risk averse utility function with decreasing absolute risk aversion is necessarily differentiable with an absolutely continuous derivative. A risk averse utility function has decreasing absolute risk aversion if and only if it has a decreasing absolute risk aversion density, and if and only if the cumulative absolute risk aversion function is increasing and concave. This leads to a characterization of all such utility functions. Analogues of these results also hold for increasing absolute and for increasing and decreasing relative risk aversion.Received: 31 January 2003, Revised: 15 January 2004, JEL Classification Numbers: D81.The views, thoughts and opinions expressed in this paper are those of the author in his individual capacity and should not in any way be attributed to Morgan Stanley or to Lars Tyge Nielsen as a representative, officer, or employee of Morgan Stanley.     

Cost information sharing with uncertainty averse firms

Summary. A homogeneous Cournot duopoly with asymmetric information is analyzed. Every firm learns its own marginal cost parameter, but not the marginal cost parameter of the opponent. Every firm can commit to revealing its private information to the other firm, i.e. to share information. The influence of uncertainty aversion on the readiness of the duopolists to share cost information is analyzed. Uncertainty aversion is modeled according to the Choquet utility theory. It is shown that low uncertainty aversion leads the firms to share information, while high uncertainty aversion leads the firms not to share. A simple economic explanation for this result is given.Received: 5 January 2001, Revised: 7 May 2003, JEL Classification Numbers: D43, D81, D82.I wish to thank Jürgen Eichberger, Volker Krätschmer, Willy Spanjers, seminar participants at Universität des Saarlandes, seminar participants at University College London, participants in the conference of the Verein für Socialpolitik in Mainz 1999 and an anonymous referee for helpful comments. The views expressed in this paper are those of the author and do not necessarily reflect the views of the European Central Bank.     

Risk aversion, moral hazard, and the principal's loss

Summary. In their seminal paper on the principal-agent model with moral hazard, Grossman and Hart (1983) show that if the agent's utility function is , then the loss to the principal from being unable to observe the agent's action is increasing in the agent's degree of absolute risk aversion. Their proof is restricted to the case where the number of observable outcomes is equal to two, and it uses an argument that is specific to that case. In this note, we provide an alternative proof that generalizes their result to any (finite) number of outcomes. Received: March 21, 2001; revised version: June 21, 2001     

Mistaken self-perception and equilibrium

Summary. Motivated by real-world information economics problems and by experimental findings on overconfidence, this paper introduces a general epistemic construction to model strategic interaction with incomplete information, where the players self-perception may be mistaken. This allows us to rigorously describe equilibrium play, by formulating appropriate equilibrium concepts. We show that there always exist objective equilibria, where the players correctly anticipate each others strategies without attempting to make sense of them, and that these outcomes coincide with the equilibria of an associated Bayesian game with subjective priors. In population games, these equilibria can also be always introspectively rationalized by the players, despite their possibly mistaken self-perception.Received: Received: May, 12, 2003; revised version: 3 December 2004, Revised: 3 December 2004, JEL Classification Numbers: J31, D82, D83.I thank Massimiliano Amarante, Eddie Dekel, Massimo Marinacci, Jean Francois Mertens, Giuseppe Moscarini, Paolo Siconolfi, Marciano Siniscalchi, Joel Sobel, and an anonymous referee.     

Least convex capacities

Summary. Debreu proposed the notion of `least concave utility' as a way to disentangle risk attitudes from the certainty preferences embedded in a von-Neumann Morgenstern index. This paper studies preferences under uncertainty, as opposed to risk, and examines a corresponding decomposition of preference. The analysis is carried out within the Choquet expected utility model of preference and is centered on the notion of a least convex capacity. Received: May 7, 1997; revised version: November 5, 1997     

The welfare implications of advertising and extension under uncertainty

This paper specifies an adoption model based upon Bayesian learning and exogenous information generation. Formulae for welfare effects are derived and calibrated using Green Revolution agricultural data. The effects of intervention through the dissemination of new information are then estimated numerically. The simulations indicate that gains to intervention can be substantial. Intervening with slowly adopted marginal technologies is as beneficial as intervening with superior technologies. Taken from Shampine [Am. J. Agric. Econ. 2 (1998).], which examined intervention in the presence of learning externalities, the results suggest that if adoption is slow, and information is the primary constraint, the gains to intervention are generally substantial relative to the costs.     

Advancing economic analysis beyond the equilibrium framework

Twentieth century economics was dominated by the development and refinement of the concept of economic equilibrium. While it is worthwhile to understand the properties of economic equilibrium, equilibrium concepts have dominated economic thought to the point that they have obscured some of the more important issues economists have always strived to understand. At least since Adam Smith’s time, economists have tried to understand the causes of prosperity, and how economic welfare can be enhanced, but these issues are best understood outside the equilibrium framework. The foundations provided by the Austrian school point toward ways that economic analysis can expand beyond the equilibrium framework.

Parametric characterizations of risk aversion and prudence

Summary. Our first main result says that whether one decision maker is more risk averse than another can be determined from their attitudes toward a given two-parameter family of risks. When all risks belong to this family, risk aversion can be compared even when initial wealth is random. Our second main result solves a long-standing problem in mean-variance analysis: what is the interpretation of the concavity of utility as a function of mean and variance? We show that in the case of normal distributions, this utility function is concave if and only if the agent has decreasing prudence. Received: July 29, 1996; revised: October 2, 1998     

Living with ambiguity: prices and survival when investors have heterogeneous preferences for ambiguity

This paper investigates asset prices and the long run wealth of investors in an asset market populated by investors who have heterogeneous preferences over risk and ambiguity. In a dynamic setting I characterize conditions under which investors who are averse to ambiguity will have an effect on long run asset prices. If ambiguity averse investors always believe that the true distribution could be wrong in many possible directions then a necessary condition for their survival is that the market exhibit no aggregate risk, a condition not met by many asset pricing models of interest. However, unlike investors with irrational beliefs, there do exist markets in which ambiguity averse investors survive. I have greatly benefitted from conversations with David Easley, Karl Shell, Ani Guerdjikova, Val Lambson, Kristian Rydqvist, Liyan Yang, Josh Teitelbaum and Jayant Ganguli as well as seminar participants at Cornell University and the Midwest Economic Theory Meetings. I am grateful to the Solomon Fund for Decision Research at Cornell University for support.     

More on parametric characterizations of risk aversion and prudence

Summary. This note provides an alternative proof for the equivalence of decreasing absolute prudence (DAP) in the expected utility framework and in a two-parametric approach where utility is a function of the mean and the standard deviation. In addition, we elucidate that the equivalence of DAP and the concavity of utility as a function of mean and variance, which was shown to hold for normally distributed stochastics in Lajeri and Nielsen [4], cannot be generalized. Received: November 27, 2000; revised version: November 26, 2001 Correspondence to: T. Eichner     

Aggregation under homogeneous ambiguity: a two-fund separation result

Contrary to the common prior model, the construction of a representative agent whose preferences follow the multiple-priors model (1989) requires strong restrictions on sets of priors and on an aggregate endowment process if we permit a large deviation among agents’ degrees of risk aversion. This paper shows that if agents’ felicity functions belong to a family of linear risk tolerance functions with the same marginal risk tolerance, the representative agent always exists at an interior equilibrium without such restrictions, and two-fund separation holdsI am grateful to a referee and to participants at the conference, Uncertainty in Economic Theory, held at Yale University (October 2004) for their valuable comments and suggestions     

Barter, credit and welfare

This paper develops a model to investigate the welfare implications of barter in Russia and other transition economies during the 1990s. We argue that barter is a welfare‐improving phenomenon that acts as a defence mechanism against monetary instability. When firms react to tighter credit markets by switching to barter, the risk they face diminishes, allowing for a higher level of production.     

Electoral competition with uncertainty averse parties

John Nash's work laid the foundations for evolutionary game theory as well as the theory of games with rational agents. The Nash bargaining solution emerges as a natural solution concept in both of these settings.     

Risk aversion in the Talmud

Summary. Evidence is adduced that the sages of the ancient Babylonian Talmud, as well as some of the medieval commentators thereon, were well aware of sophisticated concepts of modern theories of risk-bearing. Received: April 10, 2002; revised version: May 7, 2002 RID="*" ID="*"Presented at the Institute for Mathematical Studies in the Social Sciences-Economics, Stanford University, August 4, 1981. Subsequent to that presentation, the author's attention was drawn to an article by Zvi Ilani, “Models in the Economics of Uncertainty: The Cost of Concluding a Conditional Contract, according to the Talmud and the Halachic Literature,” Iyunim Bekalkala (Investigations in Economics), The Israel Association for Economics, Jerusalem, Nissan 5740 (April 1980), 246–261 (in Hebrew). Inter alia, Ilani treats the Talmudic passage that forms the subject of this paper, and provides a fairly comprehensive review of the medieval commentaries thereon; undoubtedly, he was the first to recognize in print the relevance of this passage to modern economic theories of uncertainty. It is not clear, though, whether or not his understanding of the passage agrees with ours. The current paper appeared in January 2002 in the Research Bulletin Series of the Research Center on Jewish Law and Economics, Department of Economics, Bar Ilan University.     

The role of risk aversion in public goods dilemmas with environmental uncertainty: an experimental analysis

The purpose of this study is to extend earlier research on environmental uncertainty in public goods dilemmas. The present paper reports the results of an experiment designed to examine the effect of risk aversion on public goods provision. A von Neumann–Morgenstern utility function with constant coefficient of relative risk aversion is used to investigate the impact of risk attitudes within a threshold public goods environment. The outcome of the threshold public goods experiment shows that subjects are indifferent to the changes in environmental conditions. Additionally, the analysis indicates that risk aversion is a significant determinant of voluntary public goods contribution level.