We relate two main representations of the cost of acquiring information: a cost that depends on the experiment performed, as in statistical decision theory, and a cost that depends on the distribution of posterior beliefs, as in applications of rational inattention. We show that in many cases of interest, posterior-based costs are inconsistent with a primitive model of costly experimentation. The inconsistency is at the core of known limits to the application of rational inattention in games and, more broadly, in equilibrium analyses where beliefs are endogenous; we show that an experiment-based approach helps to understand and overcome these difficulties. (JEL D82, D83)

We derive the analogue of the classic Arrow-Pratt approximation of the certainty equivalent under model uncertainty as de…ned by the smooth model of decision making under ambiguity of Klibano¤, Marinacci and Mukerji (2005).We study its scope via a portfolio allocation exercise that delivers a tractable mean-variance model adjusted for model uncertainty.In a problem with a risk-free asset, a risky asset, and an ambiguous asset, we …nd that portfolio rebalancing in response to higher model uncertainty only depends on the ambiguous asset's alpha, setting the performance of the risky asset as benchmark.In addition, the portfolios recommended by our model are not systematically conservative on the share held in the ambiguous asset: indeed, in general, it is not true that greater ambiguity reduces the optimal demand for the ambiguous asset.The analytical tractability of the enhanced Arrow-Pratt approximation renders our model especially well suited for calibration exercises aimed at exploring the consequences of ambiguity aversion on equilibrium asset prices."Crises feed uncertainty.

We find that Epstein's (2010) Ellsberg-style thought experiments pose, contrary to his claims, no paradox or difficulty for the smooth ambiguity model of decision making under uncertainty developed by Klibanoff, Marinacci, and Mukerji (2005). Not only are the thought experiments naturally handled by the smooth ambiguity model, but our reanalysis shows that they highlight some of its strengths compared to models such as the maxmin expected utility model (Gilboa and Schmeidler (1989)). In particular, these examples pose no challenge to the model's foundations—interpretation of the model as affording a separation of ambiguity and ambiguity attitude or the potential for calibrating ambiguity attitude in the model.

We characterize, in the Anscombe–Aumann framework, the preferences for which there are a utility functionu on outcomes and an ambiguity indexc on the set of probabilities on the states of the world such that, for all acts f and g, . The function u represents the decision maker's risk attitudes, while the index c captures his ambiguity attitudes. These preferences include the multiple priors preferences of Gilboa and Schmeidler and the multiplier preferences of Hansen and Sargent. This provides a rigorous decision-theoretic foundation for the latter model, which has been widely used in macroeconomics and finance.

We propose and characterize a model of preferences over acts such that the decision maker prefers act f to act g if and only if E μ φ( E π u○f) ⩾ E μ φ( E π u○g), where E is the expectation operator, u is a von Neumann-Morgenstern utility function, φis an increasing transformation, and μis a subjective probability over the set Πof probability measures πthat the decision maker thinks are relevant given his subjective information. A key feature of our model is that it achieves a separation between ambiguity, identified as a characteristic of the decision maker's subjective beliefs, and ambiguity attitude, a characteristic of the decision maker's tastes. We show that attitudes toward pure risk are characterized by the shape of u, as usual, while attitudes toward ambiguity are characterized by the shape of φ. Ambiguity itself is defined behaviorally and is shown to be characterized by properties of the subjective set of measures Π. One advantage of this model is that the well-developed machinery for dealing with risk attitudes can be applied as well to ambiguity attitudes. The model is also distinct from many in the literature on ambiguity in that it allows smooth, rather than kinked, indifference curves. This leads to different behavior and improved tractability, while still sharing the main features (e.g., Ellsberg's paradox). The maxmin expected utility model (e.g., Gilboa and Schmeidler (1989)) with a given set of measures may be seen as a limiting case of our model with infinite ambiguity aversion. Two illustrative portfolio choice examples are offered. Copyright The Econometric Society 2005.

We analyze a notion of self-confirming equilibrium with non-neutral ambiguity attitudes that generalizes the traditional concept. We show that the set of equilibria expands as ambiguity aversion increases. The intuition is quite simple: by playing the same strategy in a stationary environment, an agent learns the implied distribution of payoffs, but alternative strategies yield payoffs with unknown distributions; increased aversion to ambiguity makes such strategies less appealing. In sum, a kind of “status quo bias” emerges; in the long run, the uncertainty related to tested strategies disappears, but the uncertainty implied by the untested ones does not. (JEL C72, C73, D81, D83)

We provide a new foundation of risk aversion by showing that this attitude is fully captured by the propensity to seize insurance opportunities. In our main results, we first characterize Arrow-Pratt (1963–1964) risk aversion in terms of propensity to full insurance and the stronger notion of risk aversion of Rothschild and Stiglitz (1970) in terms of propensity to partial insurance. We then extend the analysis to comparative risk aversion by showing that the classical notion of Yaari (1969) corresponds to comparative propensity to full insurance, while the stronger notion of Ross (1981) corresponds to comparative propensity to partial insurance. (JEL D81, G22, G52)