ROBUSTNESS TO UNCERTAINTY † Sharing Ambiguity By

In a version of the Ellsberg Paradox, the decision-maker is confronted with two urns, each containing 100 balls that are either Red or Blue. She is told that there are 50 of each color in the first (“unambiguous”) urn, but no further information is provided about the second (“ambiguous”) urn. There is a widely exhibited preference to bet on drawing Red (or Blue) from the first urn rather than from the second. Though such rankings are intuitive, they are inconsistent with subjective expected utility theory and, more generally, with reliance onany single probability measure to represent beliefs. Thus, the paradox illustrates the behavioral meaning of the Knightian distinction between risk (measurable or probabilistic uncertainty) and ambiguity (unmeasurable uncertainty). The importance of the Ellsberg Paradox is the intuition that this distinction may be important more generally. In particular, it seems at least plausible to view consumption–savings and portfolio choice decisions as being qualitatively different than the choice of which bet to accept on the outcome of a coin flip; only the latter is a choice between risky prospects. My objective in this paper is to illustrate both the tractability and potential fruitfulness (for addressing the home-bias puzzle, for example) of a macrostyle model that permits aversion not only to risk, but also to ambiguity. I employ a simple two-period heterogeneousagent economy. The time periods are t 2 1 (“today”) and t (“tomorrow”). Uncertainty is represented by the state space V. There are two consumers and consumer i ’s consumption process is ( ct 2 1 i , ct ), wherect 2 1 i is deterministic, ct i is a random variable on V, and each is realvalued. I consider an endowment economy with aggregate endowment ( Yt 2 1, Yt), whereYt is random. The efficient allocation of this endowment is usually posed as a problem of efficient risk-sharing. In particular, it is assumed that consumers’ beliefs are represented by a common probability measure. If it is assumed further that von Neumann-Morgenstern (vNM) indices are (increasing, concave, and) additive across time and that consumers have a common discount factor, then efficient allocations are such that eachct i is an increasing function of Yt. Consequently, consumption is perfectly correlated across consumers, and if preference is homothetic, then consumption growth rates are equal. These predictions are often contradicted dramatically by data, particularly in international settings where consumers represent countries and where individual country growth rates respond to idiosyncratic shocks (see Karen Lewis [1999] for a survey; she terms the observed systematic violation of efficient risksharing the “consumption home-bias puzzle”). The model that I outline continues to assume complete markets and hence focuses on efficient allocations. However, taking Ellsberg seriously, I drop the assumption that it is risk alone that is to be shared. I assume that consumers are not sufficiently confident to assign sharp probabilities to all future states. Rather, following Itzhak Gilboa and David Schmeidler (1989), beliefs are represented by a (nonsingleton) set of priors, and consumption prospects are ranked according to their minimum expected utility as probabilities vary over the set of priors. Thus, consumers view consumption prospects as ambiguous, and the question of interest is: What is the nature of efficient sharing of ambiguity? † Discussants:Lars Hansen, University of Chicago; James Stock, Harvard University; Thomas Sargent, Stanford University and Hoover Institution.