Sujoy Mukerji

Recursive smooth ambiguity preferences

This paper axiomatizes an intertemporal version of the Smooth Ambiguity decision model developed in Klibanoff, Marinacci, and Mukerji (2005). A key feature of the model is that it achieves a separation between ambiguity, identified as a characteristic of the decision makers subjective beliefs, and ambiguity attitude, a characteristic of the decision makers tastes. In applications one may thus specify/vary these two characteristics independent of each other, thereby facilitating richer comparative statics and modeling flexibility than possible under other models which accomodate ambiguity sensitive preferences. Another key feature is that the preferences are dynamically consistent and have a recursive representation. Therefore techniques of dynamic programming can be applied when using this model.

Ambiguity aversion and incompleteness of financial markets

It is widely thought that incomes risks can be shared by trading infinancial assets. But financial assets typically carry some riskidiosyncratic to them, hence, disposing incomes risk using financial assetswill involve buying into the inherent idiosyncratic risk. However, standardtheory argues that diversification would reduce the inconvenience ofidiosyncratic risk to arbitrarily low levels. This argument is less robustthan what standard theory leads us to believe: ambiguity aversion canexacerbate the tension between the two kinds of risks to the point thatclasses of agents may not want to trade some financial assets. Thus,theoretically, the effect of ambiguity aversion on financial markets is tomake the risk sharing opportunities offered by financial markets lesscomplete than it would be otherwise.

Understanding the nonadditive probability decision model

SummaryThe pioneering research of Schmeidler [19] [20] and others identified behavioral axioms that underlie preferences consistent with the maximization of Choquet expected utility. However, these theories do not clarify the link between the epistemics of the decision makers (DM) problem and his choice. This paper shows that if the DM isaware that his anticipation and perception of future contingencies is incomplete, then his subjective beliefs will be described by a nonadditive probability specification. Further, if the DM acts with a certain notion of caution given the incompleteness in his understanding of the environment, his preferences over acts may have a Choquet expected utility representation. The model developed here thus provides a justification of such beliefs and preferences based on “procedural rationality”. The formalism also allows a simple characterization of how belief representation may change as the DM acquires a clearer picture of the contingency space underlying the uncertain environment.

Ambiguity and the Historical Equity Premium

This paper assesses the quantitative impact of ambiguity on historically observed financial asset returns and growth rates. The single agent, in a dynamic exchange economy, treats the conditional uncertainty about the consumption and dividends next period as ambiguous. We calibrate the agents ambiguity aversion to match only the first moment of the risk-free rate in data and measure the uncertainty each period on the actual, observed history of (U.S.) macroeconomic growth outcomes. Ambiguity aversion accentuates the conditional uncertainty endogenously in a dynamic way, depending on the history; e.g., it increases during recessions. We show the model implied time series of asset returns substantially match the first and second conditional moments of observed return dynamics. In particular, we find the time-series properties of our model generated equity premium, which may be regarded as an index measure of revealed uncertainty, relates closely to those of the macroeconomic uncertainty index recently developed in Jurado, Ludvigson, and Ng (2013).

On the Smooth Ambiguity Model: A Reply

Epstein (2009) describes three Ellsberg-style thought experiments and argues that they pose difficulties for the smooth ambiguity model of decision making under uncertainty developed by Klibanoff, Marinacci and Mukerji (2005). We revisit these thought exeperiments and find, to the contrary, that they either point to strengths of the smooth ambiguity model compared to other models, such as the maximum expected utility model (Gilboa and Schmeidler, 1989), or, in the case of one thought experiment, raise criticisms that apply equally to a broad range of current ambiguity models.

Ambiguity aversion and the absence of indexed debt

Summary.Following the seminal works of Schmeidler (1989), Gilboa and Schmeidler (1989), roughly put, an agent’s subjective beliefs are said to be ambiguous if the beliefs may not be represented by a unique probability distribution, in the standard Bayesian fashion, but instead by a set of probabilities. An ambiguityaverse decision maker evaluates an act by the minimum expected value that may be associated with it. In spite of wide and long-standing support among economists for indexation of loan contracts there has been relatively little use of indexation, except in situations of extremely high inflation. The object of this paper is to provide a (theoretical) explanation for this puzzling phenomenon based on the hypothesis that economic agents are ambiguity averse. The paper considers a general equilibrium model based on Magill and Quinzii (1997) with ambiguity averse agents, where both nominal and indexed bond contracts are available for trade and all relevant prices are determined endogenously. We obtain conditions which prompt an endogenous cessation of trade in indexed bonds: i.e., conditions under which there is no trade in indexed bonds in any equilibrium; only nominal bonds are traded.

Ordering ambiguous acts

We investigate what it means for one act to be more ambiguous than another. The question is evidently analogous to asking what makes one prospect riskier than another, but beliefs are neither objective nor representable by a unique probability. Our starting point is an abstract class of preferences constructed to be (strictly) partially ordered by a more ambiguity averse relation. First, we define two notions of more ambiguous with respect to such a class. A more ambiguous (I) act makes an ambiguity averse decision maker (DM) worse off but does not affect the welfare of an ambiguity neutral DM. A more ambiguous (II) act adversely affects a more ambiguity averse DM more, as measured by the compensation they require to switch acts. Unlike more ambiguous (I), more ambiguous (II) does not require indifference of ambiguity neutral elements to the acts being compared. Second, we implement the abstract definitions to characterize more ambiguous (I) and (II) for two explicit preference families: α-maxmin expected utility and smooth ambiguity. Thirdly, we give applications to the comparative statics of more ambiguous in a standard portfolio problem and a consumption-saving problem.

Ellsberg's two-color experiment, portfolio inertia and ambiguity

Results in this paper relate the observation of an interval of prices at which a decision maker (DM) strictly prefers to hold a zero position on an asset (termed “portfolio inertia”) to the DMs perception of the underlying payoff relevant events as ambiguous, as the term is defined in [Econometrica 69 (2001) 265]. The connection between portfolio inertia and ambiguity is established without invoking a parametric preference form, such as the Choquet expected utility or the max–min multiple priors model. This allows us to draw an observable distinction between portfolio inertia that may arise purely due to first-order risk aversion type effects, such as those which could arise even if preferences were probabilistically sophisticated, and portfolio inertia that involves ambiguity perceptions.

A survey of some applications of the idea of ambiguity aversion in economics

Abstract Subjective uncertainty is characterized by ambiguity if the decision maker has an imprecise knowledge of the probabilities of payoff relevant events. In such an instance, the decision makers beliefs are better represented by a set of probability functions than by a unique probability function. An ambiguity averse decision maker adjusts his choice on the side of caution in response to his imprecise knowledge of the odds. This paper attempts a (selective) survey of some of the achievements of the research program which has analyzed important economic phenomena using a methodology that departs from standard paradigm by explicitly allowing for ambiguity aversion. We specifically look at applications, and implications, of ambiguity aversion in three areas: design of bilateral economic contracts, the trade in financial contracts and financial markets and finally, strategic decision making in auctions. We also indicate the possible relevance of these findings to recent research in AI.

Perceived Ambiguity and Relevant Measures

We axiomatize preferences that can be represented by a monotonic aggregation of subjective expected utilities generated by a utility function and some set of i.i.d. probability measures over a product state space, S1. For such preferences, we define relevant measures, show that they are treated as if they were the only marginals possibly governing the state space and connect them with the measures appearing in the aforementioned representation. These results allow us to interpret relevant measures as reflecting part of perceived ambiguity, meaning subjective uncertainty about probabilities over states. Under mild conditions, we show that increases or decreases in ambiguity aversion cannot affect the relevant measures. This property, necessary for the conclusion that these measures reflect only perceived ambiguity, distinguishes the set of relevant measures from the leading alternative in the literature. We apply our findings to a number of well-known models of ambiguity-sensitive preferences. For each model, we identify the set of relevant measures and the implications of comparative ambiguity aversion.