Temporal Resolution of Uncertainty and Recursive Models of Ambiguity Aversion

Dynamic models of ambiguity aversion are increasingly popular in applied work. This paper shows that there is a strong interdependence in such models between the ambiguity attitude and the preference for the timing of the resolution of uncertainty, as defined by the classic work of Kreps and Porteus (1978). The modeling choices made in the domain of ambiguity aversion influence the set of modeling choices available in the domain of timing attitudes. The main result is that the only model of ambiguity aversion that exhibits indifference to timing is the maxmin expected utility of Gilboa and Schmeidler (1989). This paper examines the structure of the timing nonindifference implied by the other commonly used models of ambiguity aversion. This paper also characterizes the indifference to long-run risk, a notion introduced by Duffie and Epstein (1992). The interdependence of ambiguity and timing that this paper identifies is of interest both conceptually and practically—especially for economists using these models in applications.Economic

Probabilistic Sophistication and Variational Preferences

This paper shows that in the class of variational preferences the notion of probabilistic sophistication is equivalent to expected utility as long as there exists at least one event such that the independence axiom holds for bets on that event. This extends the result of Marinacci (2002) and provides a novel interpretation of his result.Economic

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.Economic

Depth of Reasoning and Higher Order Beliefs

As demonstrated by the email game of Rubinstein (1989), the predictions of the standard equilibrium models of game theory are sensitive to assumptions about the fine details of the higher order beliefs. This paper shows that models of bounded depth of reasoning based on level-k thinking or cognitive hierarchy make predictions that are independent of the tail assumptions on the higher order beliefs. The framework developed here provides a language that makes it possible to identify general conditions on depth of reasoning, instead of committing to a particular model such as level-k thinking or cognitive hierarchy.Economic

Axiomatization and Measurement of Quasi-Hyperbolic Discounting

This article provides an axiomatic characterization of quasi-hyperbolic discounting and a more general class of semi-hyperbolic preferences. We impose consistency restrictions directly on the intertemporal trade-offs by relying on what we call “annuity compensations.” Our axiomatization leads naturally to an experimental design that disentangles discounting from the elasticity of intertemporal substitution. In a pilot experiment we use the partial identification approach to estimate bounds for the distributions of discount factors in the subject pool. Consistent with previous studies, we find evidence for both present and future bias.Economic

Dynamic Random Utility

We provide an axiomatic analysis of dynamic random utility, characterizing the stochastic choice behavior of agents who solve dynamic decision problems by maximizing some stochastic process (U_t) of utilities. We show first that even when (U_t) is arbitrary, dynamic random utility imposes new testable restrictions on how behavior across periods is related, over and above period-by-period analogs of the static random utility axioms: An important feature of dynamic random utility is that behavior may appear history dependent, because past choices reveal information about agents’ past utilities and (U_t) may be serially correlated; however, our key new axioms highlight that the model entails specific limits on the form of history dependence that can arise. Second, we show that when agents’ choices today influence their menu tomorrow (e.g., in consumption-savings or stopping problems), imposing natural Bayesian rationality axioms restricts the form of randomness that (U_t) can display. By contrast, a specification of utility shocks that is widely used in empirical work violates these restrictions, leading to behavior that may display a negative option value and can produce biased parameter estimates. Finally, dynamic stochastic choice data allows us to characterize important special cases of random utility—in particular, learning and taste persistence—that on static domains are indistinguishable from the general model

Dynamic Random Utility

Under dynamic random utility, an agent (or population of agents) solves a dynamic decision problem subject to evolving private information. We analyze the fully general and non-parametric model, axiomatically characterizing the implied dynamic stochastic choice behavior. A key new feature relative to static or i.i.d. versions of the model is that when private information displays serial correlation, choices appear history dependent: different sequences of past choices reflect different private information of the agent, and hence typically lead to different distributions of current choices. Our axiomatization imposes discipline on the form of history dependence that can arise under arbitrary serial correlation. Dynamic stochastic choice data lets us distinguish central models that coincide in static domains, in particular private information in the form of utility shocks vs. learning, and to study inherently dynamic phenomena such as choice persistence. We relate our model to specifications of utility shocks widely used in empirical work, highlighting new modeling tradeoffs in the dynamic discrete choice literature. Finally, we extend our characterization to allow past consumption to directly affect the agent’s utility process, accommodating models of habit formation and experimentation

How Much Would You Pay to Resolve Long-Run Risk?

Though risk aversion and the elasticity of intertemporal substitution have been the subjects of careful scrutiny, the long-run risks literature as well as the broader literature using recursive utility to address asset pricing puzzles have ignored the full implications of their parameter specifications. Recursive utility implies that the temporal resolution of risk matters and a quantitative assessment thereof should be part of the calibration process. This paper gives a sense of the magnitudes of implied timing premia. Its objective is to inject temporal resolution of risk into the discussion of the quantitative properties of long-run risks and related models.Economic