Medical insurance with rank-dependent utility

Summary. A well-known result in the medical insurance literature is that zero co-insurance is never second-best for insurance contracts subject to moral hazard. We replace the usual expected utility assumption with a version of the rank-dependent utility (RDU) model that has greater experimental support. When consumers exhibit such preferences, we show that zero co-insurance may in fact be optimal, especially for low-risk consumers. Indeed, it is even possible that the first-best and second-best contracts are identical. In this case, there is no “market failure”, despite the informational asymmetry. We argue that these RDU results are in better accord with the empirical evidence from US health insurance markets. Received: February 26, 2001; revised version: October 4, 2002 RID="*" ID="*"The authors would particularly like to thank Simon Grant, John Quiggin, Peter Wakker and an anonymous referee for valuable comments and suggestions on earlier drafts. The paper has also benefitted from the input of seminar audiences at The Australian National University, University of Auckland, University of Melbourne and University of Sydney. Ryan also gratefully acknowledges the financial support of the ARC, through Grant number A000000055. Correspondence to:R. Vaithianathan     

Equilibria in incomplete assets economies with infinite dimensional spot markets

The paper studies the two period incomplete markets model where assets are claims on state contingent commodity bundles and there are no bounds on portfolio trading. The important results on the existence of equilibrium in this model assume that there is a finite number of commodities traded in each spot market and that preferences are given by smooth utility functions. With these assumptions an equilibrium exists outside an “exceptional” set of assets structures and initial endowments. The present paper extends these results by allowing for general infinite dimensional commodity spaces in each spot market. These include all the important commodity spaces studied in the literature on the existence of Walrasian equilibrium—in each spot market the consumption sets are the positive cone of an arbitrary locally solid Riesz space or of an ordered topological vector space with order unit or of a locally solid Riesz space with quasi-interior point. The paper establishes that even with our very general commodity spaces there exists an equilibrium for a “very” dense set of assets structures. Our approach is in the main convex analytic and the results do not require that preferences be smooth or complete or transitive. The concepts and techniques studied in this paper have important finite as well as infinite dimensional applications. This paper has benefited from the comments of Martine Quinzii, Wayne Shafer, Manuel Santos and Yeneng Sun. The research of C. D. Aliprantis is supported by the NSF Grants SES-0128039, DMS-0437210, and ACI-0325846. The research of R. Tourky is funded by the Australian Research Council Grant A00103450.     

Ambiguity and the Value of Information: An Almost-objective Events Analysis

Using the concept of almost-objective acts, due to Machina, this paper shows that ambiguity aversion may be defined in terms of the value of information. In particular, for expected utility preferences, the value of information with respect to almost-objective acts is asymptotically equal to zero. I thank Simon Grant, Mark Machina, and an anonymous referee for helpful comments.     

Bayesian estimation of social welfare and tax progressivity measures

This paper examines Bayesian methods of examining posterior distributions of inequality, concentration, tax progressivity and social welfare measures. Use is made of an explicit income distribution assumption and two alternative assumptions regarding the distribution of pre-tax mean incomes within each income group. The methods are applied to a simulated distribution of individual incomes and tax payments. It is possible to identify a minimum acceptable number of income classes to be used. The results suggest support for the use of group means in practical applications, particularly where large sample sizes are available. First version received: August 2000/Final version received: July 2001 RID="*" ID="*"  This research was supported by a Melbourne University Faculty of Economics and Commerce Research Grant. We should like to thank Bill Griffiths and two referees for comments on an earlier draft.     

Parametric continuity of stationary distributions

For Markovian economic models, long-run equilibria are typically identified with the stationary (invariant) distributions generated by the model. In this paper we provide new sufficient conditions for continuity in the map from parameters to these equilibria. Several existing results are shown to be special cases of our theorem. This paper has benefitted from the helpful comments of Kevin Reffett, Rabee Tourky, an anonymous referee and participants at the 13th European Workshop on General Equilibrium Theory, Venice 2004. The second author is grateful for financial support from Australian Research Council Grant DP0557625.     

The impossibility of compromise: some uniqueness properties of expected utility preferences

Summary. We focus on the following uniqueness property of expected utility preferences: Agreement of two preferences on one interior indifference class implies their equality. We show that, besides expected utility preferences under (objective) risk, this uniqueness property holds for subjective expected utility preferences in Anscombe-Aumann's (partially subjective) and Savage's (fully subjective) settings, while it does not hold for subjective expected utility preferences in settings without rich state spaces. Indeed, when it holds the uniqueness property is even stronger than described above, as it needs only agreement on binary acts. The extension of the uniqueness property to the subjective case is possible because beliefs in the mentioned settings are shown to satisfy an analogous property: If two decision makers agree on a likelihood indifference class, they must have identical beliefs. Received: November 15, 1999; revised version: December 29, 1999     

Balancedness and the core in economies with asymmetric information

Summary. A condition is given that is equivalent to balancedness of all NTU-games derived from an exchange economy with asymmetric information when endowments are variable. The condition is applicable to the ex-ante model with expected utilities, but also to the more general model of Arrow-Radner type economies without subjective probabilities. Differences in the interpretation of measurability assumptions between these two models are discussed, and another model with information consistent utility functions is developed in which the result would also hold. Received: December 12, 2001; revised version: November 1, 2002 RID="*" ID="*"I thank two anonymous referees whose comments led to an improvement of the paper.     

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.     

Existence of a competitive equilibrium in a one sector growth model with heterogeneous agents and irreversible investment

Summary. We prove existence of a competitive equilibrium in a version of a Ramsey (one sector) model in which agents are heterogeneous and gross investment is constrained to be non negative. We do so by converting the infinite-dimensional fixed point problem stated in terms of prices and commodities into a finite-dimensional Negishi problem involving individual weights in a social value function. This method allows us to obtain detailed results concerning the properties of competitive equilibria. Because of the simplicity of the techniques utilized our approach is amenable to be adapted by practitioners in analogous problems often studied in macroeconomics. Received: September 13, 2001; revised version: December 9, 2002 RID="*" ID="*" We are grateful to Tapan Mitra for pointing out errors as well as making very valuable suggestions. Thanks are due to Raouf Boucekkine and Jorge Duran for additional helpful discussions. We also thank an anonymous referee for his/her helpful comments. The second author acknowledges the financial support of the Belgian Ministry of Scientific Research (Grant ARC 99/04-235 “Growth and incentive design”) and of the Belgian Federal Goverment (Grant PAI P5/10, “Equilibrium theory and optimization for public policy and industry regulation”). Correspondence to: C. Le Van     

Effects of health information on Nordic meat and fish demand

Increasing public concerns about health risks associated with dietary intakes of cholesterol are expected to have significant impacts on the demand for foods with high fat content. This paper investigates how information about cholesterol, as measured by two newly constructed indices based on published medical research, has affected the demand for meats (beef, chicken and pork) and fish in the Nordic countries (Denmark, Finland, Norway and Sweden). To compare the effects of information across countries and over time, the demand equations for all the countries are estimated within one system, and a complete set of price and expenditure elasticities is estimated. Our findings suggest that health information has affected consumption in a healthy way in all countries studied except for Denmark. We find positive effects on the demand for chicken in Finland, Norway and Sweden and for fish in Finland and Sweden. A negative effect on the demand for beef in Sweden also is found. First version received: May 2001/Final version received: December 2001 RID="*" ID="*"  The authors would like to thank Wen S. Chern and Bj?rn Sl?en for their assistance in the construction of the health information indices. The suggestions of two anonymous referees have also been of great assistance. The EU (contract FAIRS-CT97-3373) and the Research Council of Norway (grant no. 134018/110) provided financial support for this research.”     

A simple axiomatization and constructive representation proof for choquet expected utility

>P>Summary. We provide a set of simple and intuitive set of axioms that allow for a direct and constructive proof of the Choquet Expected Utility representation for decision making under uncertainty. Received: October 29, 2002; revised version: November 13, 2002 RID="*" ID="*" We thank Matthew Ryan for very useful comments and suggestions on related work and for encouraging us to write this note. Correspondence to: S. Grant     

Risk Preferences,Production Risk and Firm Heterogeneity*

A new technique is proposed for deriving the risk preference function under production risk and expected utility of profit maximization. The derivation depends on neither a specific parametric form of the utility function nor any distribution of the error term representing production risk. The proposed risk preference function is flexible enough to test different types of risk behavior and symmetry of the output distribution. Furthermore, our production risk specification allows for inputs with positive and negative marginal risk. The econometric model accommodates production risk, risk preferences and firm heterogeneity simultaneously. Norwegian salmon farming data are used as an application.     

An axiomatic characterization of preferences under uncertainty: Weakening the independence axiom

The independence axiom used to derive the expected utility representation of preferences over lotteries is replaced by requiring only convexity, in terms of probability mixtures, of indifference sets. Two axiomatic characterizations are proven, one for simple measures and the other continuous and for all probability measures. The representations are structurally similar to expected utility, and are unique up to a generalization of affine transformations. First-order stochastic dominance and risk aversion are discussed using a method which finds an expected utility approximation to these preferences without requiring differentiability of the preference functional.     

Consumption externalities and upward-sloping demand

The law of demand states that individual demand curves are negatively sloped. To date, the Giffen Paradox represents the only analytically valid exception to the law under standard assumptions. This article shows that if consumption externalities exist, it is possible for the individual's demand curve to slope upward. In particular, the condition under which demand becomes upward-sloping can be delineated in terms of measures of elasticity of demand. Research grants (Grant #2056/99H and Grant #FRG99-00/II-12) from the Research Grant Council of Hong Kong and the Hong Kong Baptist University are gratefully acknowledged.     

Model selection when estimating and predicting consumer demands using international,cross section data

This paper assesses the ability of five structural demand systems to predict demands when estimated with cross sectional data spanning countries with widely varying per capita expenditure levels. Results indicate demand systems with less restrictive income responses are superior to demand systems with more restrictive income effects. Among the least restrictive demand systems considered, An Implicitly, Directly Additive Demand System (AIDADS) and Quadratic Almost Ideal Demand System (QUAIDS) seem roughly tied for best, while the Quadratic Expenditure System (QES) is a close second. Given differences in the characteristics of AIDADS and QUAIDS, it is concluded the former is better suited to instances where income exhibits wide variation and the latter to cases when prices exhibit considerable variation. First Version Received: November 2000/Final Version Received: February 2002 RID="*" ID="*"  The authors acknowledge the insightful comments of two journal referees and Baldev Raj. Bettina Aten kindly provided the data used in this study. Any errors or omissions remain the responsibility of the authors. Partial financial support of the United States Department of Agriculture – National Research Initiative Grant #97-35400-4752 and the Purdue Research Foundation is gratefully acknowledged. An expanded version of this paper is available from the authors upon request. RID="**" ID="**"  Contact author     

What do uncertainty-averse decision-makers believe?

Summary. This paper introduces the concept of firm belief, which is proposed as a new epistemic model for a wide class of preferences. In particular, firm beliefs are shown to have the following desirable properties: (i) they are derived from preferences according to a plausible rule of epistemic inference; (ii) they satisfy standard logical properties; and (iii) tractable representations of firm belief are available for all (suitably continuous) biseparable preferences [13, 14], including the Choquet expected utility [30] and maxmin expected utility [16] classes. We also use firm belief to construct a generalization of Nash equilibrium for (two-player) normal form games. Received: December 14, 1999; revised version: February 26, 2001     

Extreme inequality aversion without separability

Hammond (J Econ Theory 11, 465–467, 1975), Meyer (J Econ Theory 11, 119–132, 1975), and Lambert (The distribution and redistribution of income Manchester University Press, Manchester, 2001) provide the formal result connecting leximin and the idea of extreme inequality aversion for social preferences of the expected utility type. Using an analogous approach, we show that for social preferences not necessarily satisfying the separability axiom that underlies expected utility theory, the case of extreme inequality aversion is covered by the class of weakly maximin social preferences—i.e., the class of social preferences that give priority to the worst off in all cases in which the worst off is not indifferent. I wish to thank Bart Capéau, Frank Cowell, Peter Lambert, Luc Lauwers, Erik Schokkaert, Frans Spinnewyn, and Bertil Tungodden for valuable comments. Remaining shortcomings are mine. Financial support from the Fund for Scientific Research - Flanders (grant G.0005.04) and the Interuniversity Attraction Poles network funded by the Federal Public Planning Service, Belgian Science Policy (grant P5/21-A) is gratefully acknowledged.     

Economic evolution and the science of synergetics

This paper deals with synergetic methods, which have developed as a sub-field of the self-organisation approach in the natural sciences. Such methods have been used successfully to model structural transitions in physio-chemical contexts. The synergetic approach is explained in a non-technical way and the main elements of the synergetic methodology are introduced. The extent to which such methods can be applied in the presence of historical time series data, which are subject to underlying processes of evolutionary economic change, is assessed. Proposals, concerning more appropriate synergetic methods for evolutionary economic application, are considered.The research from which this paper is derived was supported by an Australian Research Council Large Grant. We would like to thank University of Queensland Emergent Complexity and Organisation in Economics [(ECO)²] Research Group participants-David Anthony, Bryan Morgan and Pradeep Philip-for their comments and criticisms on an earlier draft of this paper (Foster and Wild 1994). We are also grateful to Ulrich Witt for his detailed comments and Gerard Milburn (UQ Physics) for helping us to understand how synergetics is applied in physics. Three anonymous referees also provided invaluable comments on the journal submission. However, the usualcaveat applies.     

Risk and risk aversion when states of nature matter

When uncertainty is associated with some intrinsically relevant states of nature, there is no reason for an agent to base his or her preferences only on probability distribution of claims. We propose a new concept of risk for state-contingent claims that, unlike the standard concept of Rothschild–Stiglitz, does not identify state-contingent claims with their probability distribution. This concept is called mean-independent risk, and we provide a simple characterization in terms of marginal utilities of (non-expected) utility functions that exhibit aversion to mean-independent risk. We study implications of aversion to mean-independent risk on agents’ choices under uncertainty. This research has been supported by the NSF under Grant SES-0099206. I have benefited from numerous conversations with Rose-Anne Dana and illuminating discussions with Tadeusz Miłosz about the theory of subgradients.     

Interim efficient allocations under uncertainty

This paper considers an exchange economy under uncertainty with asymmetric information. Uncertainty is represented by multiple priors and posteriors of agents who have either Bewley's incomplete preferences or Gilboa-Schmeidler's maximin expected utility preferences. The main results characterize interim efficient allocations under uncertainty; that is, they provide conditions on the sets of posteriors, thus implicitly on the way how agents update the sets of priors, for non-existence of a trade which makes all agents better off at any realization of private information. For agents with the incomplete preferences, the condition is necessary and sufficient, but for agents with the maximin expected utility preferences, the condition is sufficient only. A couple of necessary conditions for the latter case are provided.