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 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.     

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     

Condorcet cycles in bipartite populations

Summary. Simple majority voting between pairs of alternatives is used to aggregate individual preferences. The occurence of Condorcet cycles is limited thanks to a principle of homogeneity on individual preferences. The restrictions induced on the domain of the latters are weak: among the n! possible orderings of n alternatives, more than one half are admissible within a domain. The resulting aggregated preference has then a neglectable probability of showing up cycles. We show moreover that the set of individual preferences can be `naturally' partitioned into two such domains. Received: June 17, 1996; revised version: April 15, 1997     

Social responsibility promotes conservative risk behavior

Previous studies show that group risk taking can be more conservative than individual risk taking. Two common, but untested reasons for this greater caution are the influence of social responsibility and a tendency to conform to the preferences of others. We study changes in risk taking in simple settings, where another’s risk taking can sometimes be observed, and where decisions affect not only one’s own payoffs but sometimes also affect those of a passive, second party. We find that social responsibility leads to more conservative risk behavior in group decision making. Conformism has a more symmetric effect: observing the choice of another tends to lead both individual and social decisions toward whatever the other’s expressed risk preference is. Direct tests fail to link the social behavior we observe to the social preference for distributional fairness common in decision-making under certainty.     

From sure to strong diversification

This paper presents a characterization of weak risk aversion in terms of preference for sure diversification. Similarly, we show that strong risk aversion can be characterized by weakening preference for diversification,as introduced by Dekel (Econometrica 57:163,1989), in what we call preference for strong diversification. We are grateful to Jean-Yves Jaffray, Peter Wakker and anonymous reference for very helpful suggestions and comments.     

Risk and intertemporal substitution: Livestock portfolios and off-take among Kenyan pastoralists

Most decisions involve variability in two dimensions: uncertainty across states of nature and fluctuations over time. The stakes involved in tradeoffs between these variability dimensions are especially high for the poor who have difficulty managing and recovering from shocks. We assume Epstein and Zin recursive preferences and estimate risk aversion and intertemporal substitution as distinct preferences using data from Kenyan herders. Results suggest that the assumption implicit in additive expected utility models that relative risk aversion (RRA) is the inverse of the elasticity of intertemporal substitution (EIS) is flawed. Specifically, our RRA and EIS estimates are consistent with a preference for the early resolution of uncertainty, which we believe is driven importantly by the instrumental value of early uncertainty resolution. This same preference pattern is consistent with asset smoothing in response to a dynamic asset threshold.     

Discrepancies between ex ante and ex post efficiency under identical subjective probabilities

Summary. Starr (1973) showed that, if people have different subjective probabilities, ex ante and ex post efficiency conflict. Conversely, under the simple preferences that he considered, the discrepancy between ex ante and ex post efficiency disappears when subjective probabilities are identical. Here I consider identical subjective probabilities, but more general preferences. First, risk attraction is admitted. Second, I dispense with the double requirement (dubbed IZU) of additive separability and state-independence of the utility of zero-date consumption, an unrealistic requirement when modeling the investment in durable goods. I find that, under IZU, and as long as ex post preferences satisfy the natural assumption of quasiconcavity (and satisfy some technical qualifications), an ex ante efficient allocation is indeed ex post efficient, but the converse is not necessarily true under risk attraction. If, on the other hand, IZU is violated, then one can have ex ante efficient allocations that are not ex post efficient, and vice-versa, even under risk aversion. Received: June 25, 1999; revised version: March 2001     

A solution to the random assignment problem on the full preference domain

We consider the problem of allocating a set of indivisible objects to agents in a fair and efficient manner. In a recent paper, Bogomolnaia and Moulin consider the case in which all agents have strict preferences, and propose the probabilistic serial (PS) mechanism; they define a new notion of efficiency, called ordinal efficiency, and prove that the probabilistic serial mechanism finds an envy-free ordinally efficient assignment. However, the restrictive assumption of strict preferences is critical to their algorithm. Our main contribution is an analogous algorithm for the full preference domain in which agents are allowed to be indifferent between objects. Our algorithm is based on a reinterpretation of the PS mechanism as an iterative algorithm to compute a “flow” in an associated network. In addition we show that on the full preference domain it is impossible for even a weak strategyproof mechanism to find a random assignment that is both ordinally efficient and envy-free.     

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.     

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.     

Parimutuel contests with strategic risk-sensitive bettors

Existing models in the parimutuel betting literature typically explain betting data by either assuming a single, representative bettor with certain risk preferences or by assuming that a number of risk neutral bettors compete strategically within a game theoretic framework. We construct a theoretical framework of parimutuel markets in which we model both strategic interaction and individual bettor risk preferences, distinguishing between sophisticated insiders and recreational outsiders. We solve this model analytically for the optimal insider betting amount in a static symmetric Nash equilibrium. A new data set of 126 million individual horse race bets in New Zealand from 2006 to 2014 allows us to calibrate the model. We find that insiders (those betting $100 or more) outperform outsiders by 7.5% in terms of realized returns. The best fit of the model to the data is obtained when insiders are assumed to be risk neutral and to have an information advantage of 0.08 in probability terms. This finding provides empirical support for the common assumption of risk neutrality in strategic interaction models of parimutuel betting.     

Optimal Pollution Abatement Under ‘Sustainable’ and Other Social Time Preferences

This paper analyses optimal pollution abatement expenditure and the pricing of pollution under alternative social time preferences, including ‘sustainable’ preferences, defined as those that are consistent with two axioms of sustainable development introduced by Chichilnisky (Land Econ 73:467–491, 1997). These axioms state essentially that neither the welfare of present nor future generations ought to be favoured over the other in determining the socially optimal path of economic development. The method is to calibrate a modified Ramsey model of optimal global growth and saving, where pollution is generated by the global output of goods and services. Pollution in turn reduces output. The simulation results illustrate how sensitive the optimal pollution price and abatement expenditure can be over time to assumptions about the social time preference rate. They also show that ‘sustainable’ preferences impose a lower burden on future generations in terms of the pollution price and abatement expenditure. Hence there is a case for governments to make explicit their value judgments about intergenerational welfare, in the context of their notion of sustainable development, when setting target pollution abatement levels and pollution prices over time.     

Diversification, convex preferences and non-empty core in the Choquet expected utility model

Summary. We show, in the Choquet expected utility model, that preference for diversification, that is, convex preferences, is equivalent to a concave utility index and a convex capacity. We then introduce a weaker notion of diversification, namely “sure diversification.” We show that this implies that the core of the capacity is non-empty. The converse holds under concavity of the utility index, which is itself equivalent to the notion of comonotone diversification, that we introduce. In an Anscombe-Aumann setting, preference for diversification is equivalent to convexity of the capacity and preference for sure diversification is equivalent to non-empty core. In the expected utility model, all these notions of diversification are equivalent and are represented by the concavity of the utility index. Received: July 27, 1999; revised version: November 7, 2000     

Attitude toward imprecise information

This paper presents an axiomatic model of decision making under uncertainty which incorporates objective but imprecise information. Information is assumed to take the form of a probability–possibility set, that is, a set P of probability measures on the state space. The decision maker is told that the true probability law lies in P and is assumed to rank pairs of the form (P,f) where f is an act mapping states into outcomes. The key representation result delivers maxmin expected utility (MEU) where the min operator ranges over a set of probability priors—just as in the MEU representation result of Gilboa and Schmeidler [Maxmin expected utility with a non-unique prior, J. Math. Econ. 18 (1989) 141–153]. However, unlike the MEU representation, the representation here also delivers a mapping, , which links the probability–possibility set, describing the available information, to the set of revealed priors. The mapping is shown to represent the decision maker's attitude to imprecise information: under our axioms, the set of representation priors is constituted as a selection from the probability–possibility set. This allows both expected utility when the selected set is a singleton and extreme pessimism when the selected set is the same as the probability–possibility set, i.e., is the identity mapping. We define a notion of comparative imprecision aversion and show it is characterized by inclusion of the sets of revealed probability distributions, irrespective of the utility functions that capture risk attitude. We also identify an explicit attitude toward imprecision that underlies usual hedging axioms. Finally, we characterize, under extra axioms, a more specific functional form, in which the set of selected probability distributions is obtained by (i) solving for the “mean value” of the probability–possibility set, and (ii) shrinking the probability–possibility set toward the mean value to a degree determined by preferences.     

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.     

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.     

A new definition of and role for preferences in positive economics

Positive economic models aim to provide truthful explanations of significant (aspects of) economic phenomena. While the notion of ‘preferences’ figures prominently in micro-economic models, it suffers from a remarkable lack of conceptual clarity and rigor. After distinguishing narrow homo economicus models (self-interest maximization) from broader ones (preference satisfaction) and rehearsing the criticisms both have met, I go into the most promising attempt to date at addressing them, developed by Hausman. However, his definition of preferences as ‘total comparative evaluations’, I argue, plays into the general disregard that economists have for human psychology. My alternative definition of preferences as ‘overall comparative evaluations’ – and hence as one of the many factors that influence people’s behavior – allows for more adequate causal explanations of people’s dutiful, committed, and norm-guided actions. Against Hausman but in agreement with Sen, it also allows for (motivated) counterpreferential choice.     

A theory of (relative) discounting

We derive a representation theorem for time preferences (on the prize-time space) which identifies a novel notion of relative discounting as the key ingredient. This representation covers a variety of time preference models, including the standard exponential and hyperbolic discounting models and certain non-transitive time preferences, such as the similarity-based and subadditive discounting models. Our axiomatic work thus unifies a number of seemingly disparate time preference structures, thereby providing a tractable mathematical format that allows for investigating certain economic environments without subscribing to a particular time preference model. This point is illustrated by means of an application to sequential bargaining theory.     

Bribe-proof rules in the division problem

The division problem consists of allocating an amount of a perfectly divisible good among a group of n agents with single-peaked preferences. A rule maps preference profiles into n shares of the amount to be allocated. A rule is bribe-proof if no group of agents can compensate one of its subgroups to misrepresent their preferences and, after an appropriate redistribution of their shares, each obtains a weakly preferred share and all agents in the misrepresenting subgroup obtain a strictly preferred share. We characterize all bribe-proof rules as the class of Pareto efficient, strategy-proof, and weakly replacement monotonic rules. This class is larger than the set of sequential allotment rules identified in Barberà et al. [Barberà, S., Jackson, M., Neme, A., 1997. Strategy-proof allotment rules. Games Econ. Behav. 18, 1–21].