Efficient allocations under ambiguity

Important implications of the expected utility hypothesis and risk aversion are that if agents have the same probability belief, then consumption plans in every efficient allocation of resources under uncertainty are comonotone with the aggregate endowment, and if their beliefs are concordant, then the consumption plans are measurable with respect to the aggregate endowment. We study these two properties of efficient allocations for models of preferences that exhibit ambiguity aversion using the concept of conditional beliefs, which we introduce in this paper. We provide characterizations of such conditional beliefs for the standard models of preferences used in applications.     

On the informational efficiency of simple scoring rules

We study information aggregation in large elections. With two candidates, efficient information aggregation is possible (e.g., Feddersen and Pesendorfer [5], [6] and [7]). We show that this result does not extend to elections with more than two candidates. We study a class of simple scoring rules in voting games with Poisson population uncertainty and three candidates. No simple scoring rule aggregates information efficiently, even if preferences are dichotomous and a Condorcet winner always exists. We introduce a weaker criterion of informational efficiency that requires a voting rule to have at least one efficient equilibrium. Only approval voting satisfies this criterion.     

In search of welfare-improving gifts

Gift giving is thought to decrease welfare. Recipients are sometimes stuck with gifts they would not have purchased because the giver does not perfectly know the recipient's preferences and in-kind gifts cannot be costlessly refunded. Such gifts are welfare reducing compared to giving cash if, in addition, recipients possess full information as to which stores carry their desired goods and the ability to reach these stores costlessly. We replace these two latter assumptions with the more realistic assumptions of uncertainty about the location of goods and search costs. In contrast to existing economic models, gifts in our model enhance expected welfare. Moreover, gift giving cannot be replaced by a profit-maximizing trader nor the introduction of nearby specialty stores carrying gift goods. We use our model to explain a number of stylized facts about gift giving, the organization of retail trade and in-kind government transfers.     

A behavioral characterization of plausible priors

Recent decision theories represent ambiguity via multiple priors, interpreted as alternative probabilistic models of the relevant uncertainty. This paper provides a robust behavioral foundation for this interpretation. A prior P is “plausible” if preferences over some subset of acts admit an expected utility representation with prior P, but not with any other prior Q≠P. Under suitable axioms, plausible priors can be elicited from preferences, and fully characterize them; also, probabilistic sophistication implies that there exists only one plausible prior; finally, “plausible posteriors” can be derived via Bayesian updating. Several familiar decision models are consistent with the proposed axioms.     

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.     

Knightian uncertainty and moral hazard

This paper presents a principal-agent model in which the agent has imprecise beliefs. We model this situation formally by assuming the agent?s preferences are incomplete as in Bewley (1986) [2]. In this setting, incentives must be robust to Knightian uncertainty. We study the implications of robustness for the form of the resulting optimal contracts. We give conditions under which there is a unique optimal contract, and show that it must have a simple flat payment plus bonus structure. That is, output levels are divided into two sets, and the optimal contract pays the same wage for all output levels in each set. We derive this result for the case in which the agent?s utility function is linear and then show it also holds if this utility function has some limited curvature.     

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.     

Over-savings and hyperbolic discounting

Hyperbolic discounting models are widely seen as implying that consumers do not save enough, in accordance with the observed low rates of savings of some households. This paper qualifies this view by showing that hyperbolic consumers may ‘oversave’ in the short run. The result extends to uncertainty on future income and does not depend on whether preferences are present-biased or future-biased. A generalized comparative statics analysis of self-control is introduced, and its relationship to the analysis of uncertainty on discount factors is emphasized.     

Uncertainty averse preferences

We study uncertainty averse preferences, that is, complete and transitive preferences that are convex and monotone. We establish a representation result, which is at the same time general and rich in structure. Many objective functions commonly used in applications are special cases of this representation.     

Preference shocks from aggregation: time series data evidence

Abstract.  We investigate the impact of preference shocks on the aggregate dynamics of the U.S. economy in the context of a neoclassical growth model derived from aggregation. The aggregation result we use is as follows: if markets are complete and if agents have identical preferences of the addilog type, then the heterogeneous‐agent economy where agents are subject to idiosyncratic productivity shocks behaves as if there was a representative consumer who faces shocks to preferences and technology. We estimate the parameters in the aggregation‐based model from the aggregate time‐series data and compute the numerical solution. We find that the preference shocks play an important role in the aggregate labour‐market fluctuations. JEL classification: C73, D90, E21     

Dynamic variational preferences

We introduce and axiomatize dynamic variational preferences, the dynamic version of the variational preferences we axiomatized in [F. Maccheroni, M. Marinacci, A. Rustichini, Ambiguity aversion, robustness, and the variational representation of preferences, Mimeo, 2004], which generalize the multiple priors preferences of Gilboa and Schmeidler [Maxmin expected utility with a non-unique prior, J. Math. Econ. 18 (1989) 141-153], and include the Multiplier Preferences inspired by robust control and first used in macroeconomics by Hansen and Sargent (see [L.P. Hansen, T.J. Sargent, Robust control and model uncertainty, Amer. Econ. Rev. 91 (2001) 60-66]), as well as the classic Mean Variance Preferences of Markovitz and Tobin. We provide a condition that makes dynamic variational preferences time consistent, and their representation recursive. This gives them the analytical tractability needed in macroeconomic and financial applications. A corollary of our results is that Multiplier Preferences are time consistent, but Mean Variance Preferences are not.     

On the robustness of laissez-faire

This paper considers a model economy in which agents are privately informed about their type: their endowments of various goods and their preferences over these goods. While preference orderings over observable choices are allowed to be correlated with an agent's private type, we assume that the planner/government is both uncertain about the nature of this joint distribution and unable to choose among multiple equilibria of any given social mechanism. We model the planner/government as having a maxmin objective in the face of this uncertainty.Our main theorem is as follows: Once we allow for this kind of uncertainty and assume no wealth effects in preferences, the uniquely optimal social contract is laissez-faire, in which agents trade in unfettered markets with no government intervention of any kind.     

Coalitional manipulation and the Pareto rule

This paper examines aggregation procedures that map profiles of individual preferences into choice sets. An aggregation procedure is said to be “manipulable by a coalition” if there is a group of individuals, and a preference profile, such that every member of the group prefers the choice set obtained when they are misrepresenting their preferences, to the one obtained when they are honest. We show that the Pareto rule, which is an aggregation procedure that maps profiles of individual preferences into corresponding sets of Pareto optima, is not manipulable by any coalition of individuals under various behavioural assumptions which relate preferences over choice sets to preferences over alternatives. The non-manipulability of the Pareto rule by a single individual follows as a special case under these behavioural assumptions.     

Construction of a state space for interrelated securities with an application to temporary equilibrium theory

Summary We construct an endogenous state space in an exchange economy with possibly infinite horizon. Every period agents trade securities whose payoffs depend on future dividends and asset prices. We reject the perfect foresight assumption on the ground that agents have not only limited knowledge of other individuals' endowments and preferences, but also limited capacity to compute equilibria. We choose instead absence of arbitrage as the principle which allows agents to determine if a system of future prices is possible. We give an alogrithm to compute the set of nonarbitrage prices every period, with both finite and infinite horizon. We then apply this endogenous structure of uncertainty to an infinite horizon temporary equilibrium model.I would like to thank Professor Donald Brown for his constant help and guidance. I have also greatly benefited from helpful discussions with Professors Jacques Drèze, Bernard Dumas, Mordecai Kurz, Carsten Nielsen, Jan Werner, and Ho-Mou Wu.     

Intertemporal equilibria with Knightian uncertainty

We study a dynamic and infinite-dimensional model with incomplete multiple prior preferences. In interior efficient allocations, agents share a common risk-adjusted prior and subjective interest rate. Interior efficient allocations and equilibria coincide with those of economies with subjective expected utility and priors from the agents? multiple prior sets. A specific model with neither risk nor uncertainty at the aggregate level is considered. Risk is always fully insured. For small levels of ambiguity, there exists an equilibrium with inertia where agents also insure fully against Knightian uncertainty. When the level of ambiguity exceeds a critical threshold, full insurance no longer prevails and there exist equilibria with inertia where agents do not insure against uncertainty at all. We also show that equilibria with inertia are indeterminate.     

Transfers in a polarized country: bridging the gap between efficiency and stability

We consider a political economy model of country whose citizens have heterogeneous preferences for a national policy and some regions may contemplate a threat of secession. The country is efficient if its breakup into smaller countries leads to an aggregate utility loss. We show that in an efficient country whose citizens' preferences exhibit a high degree of polarization, a threat of secession cannot be eliminated without inter-regional transfers. We also demonstrate that if majority voting is used to determine the redistribution schemes within the country, then a high degree of polarization yields the full-compensation scheme as the unique political equilibrium.     

Arrovian aggregation in economic environments: how much should we know about indifference surfaces?

Arrow's celebrated theorem of social choice shows that the aggregation of individual preferences into a social ordering cannot make the ranking of any pair of alternatives depend only on individual preferences over that pair, unless the fundamental weak Pareto and non-dictatorship principles are violated. In the standard model of division of commodities, we investigate how much information about indifference surfaces is needed to construct social ordering functions satisfying the weak Pareto principle and anonymity. We show that local information such as marginal rates of substitution or the shapes “within the Edgeworth box” is not enough, and knowledge of substantially non-local information is necessary.     

Interim efficiency with MEU-preferences

Recently Kajii and Ui (2009) [17] proposed to characterize interim efficient allocations in an exchange economy under asymmetric information when uncertainty is represented by multiple posteriors. When agents have Bewley's incomplete preferences, Kajii and Ui (2009) [17] proposed a necessary and sufficient condition on the set of posteriors. However, when agents have Gilboa-Schmeidler's MaxMin expected utility preferences, they only propose a sufficient condition. The objective of this paper is to complete Kajii and Ui's work by proposing a necessary and sufficient condition for interim efficiency for various models of ambiguity aversion and in particular MaxMin expected utility. Our proof is based on a direct application of some results proposed by Rigotti, Shannon and Stralecki (2008) [24].     

Subjective probability over a subjective decision tree

A state space has been assumed as a primitive for modeling uncertainty, which presumes that the analyst knows all the uncertainties a decision maker (DM) perceives. This is problematic because states are private information of the DM, and hence are not directly observable to the analyst. Dekel et al. [Representing preferences with a unique subjective state space, Econometrica 69 (2001) 891-934] derive, rather than assume, the subjective state space from preference over suitable choice objects.In a dynamic setting, a decision tree, that is, a pair consisting of a state space and a filtration, has been taken as a primitive. This assumption is also problematic—a decision tree should be derived rather than assumed as a primitive. We formulate a three-stage extension of the above literature in order to model a DM who anticipates subjective uncertainty to be resolved gradually over time. We identify also subjective beliefs on the subjective state space.     

A term structure model with preferences for the timing of resolution of uncertainty

Summary In this paper we present a model of the term structure of interest rates with imperfect information and stochastic differential utility, a form of non-additive recursive utility. A principal feature of recursive utility, that distinguishes it from time-separable expected utility, is its dependence on the timing of resolution of uncertainty. In our model, we parametrize the nonlinearity of recursive utility in a way that corresponds to preferences for the timing of resolution. This way we show explicitly the dependence of prices on the rate of information, as a consequence of the nature of utilities. State prices and the term structure of interest rates are obtained in closed form, and are shown to have a form in which derivative asset pricing is tractable. Comparative statics relating to the dependence of the term structure on the rate of information are also discussed.We thank Bob Hodrick and Matt Jackson for their comments. Darrell Duffie is grateful for support from the National Science Foundation under NSF SBR-9409567. This paper presents the first model of an earlier, preliminary working paper titled: Two models of price dependence on the timing of resolution of uncertainty.