Intertemporal Substitution and Recursive Smooth Ambiguity ...

Segal (1987, 1990) and Seo (2009). Segal uses the anticipated utility model and considersobjective lotteries, while the Ellsberg paradox is often viewed as a phenomenon associatedwith subjective uncertainty. Seo does not provide a formal definition of ambiguity aversionand characterizations of ambiguity attitude. We provide such an analysis and characterizethe link between ambiguity aversion and reduction of compound lotteries. Our result thatambiguity aversion is identical to risk aversion in the first stage is similar to Theorem 5in Ergin and Gul (2009) who refer to risk aversion in the first stage as second-order riskaversion.Maccheroni, Marinacci, and Rustichini (2006b) provide a dynamic extension of the staticvariational model of ambiguity developed by Maccheroni, Marinacci, and Rustichini (2006a).The static variational model includes multiple-priors model and the multiplier preferencemodel of Hansen and Sargent (2001) as special cases. The dynamic extension does notseparate intertemporal substitution from attitude toward risk or ambiguity. Variationalpreferences are also subject to the limitation concerning the separation of ambiguity fromambiguity attitude.Our model is also related to the literature on recursive utility under risk or uncertainty(Chew and Epstein (1991), Epstein and Zin (1989), Klibanoff and Ozdenoren (2007), Krepsand Porteus (1978), and Skiadas (1998)). This literature does not deal with ambiguity. Inthe framework of Klibanoff and Ozdenoren (2007) or Skiadas (1998), preferences depend onthe filtration. Unlike their framework, we take the filtration as given and, thus, cannot makecomparisons of representations across filtrations.Recursive utility models allow for preferences for the timing of the temporal resolutionof uncertainty. As is well known in the literature on recursive expected utility preferences, anonlinear time aggregator is needed to permit nonindifference to the timing of the temporalresolution of uncertainty. Strzalecki (2009) shows that even without a nonlinear aggregator,or with standard discounting, most dynamic models of ambiguity aversion (including themodels discussed above) result in timing nonindifference. In particular, decision makerswith such preferences prefer earlier resolution of uncertainty. The only model of ambiguityaversion that exhibits indifference to timing is the multiple-priors utility model. Our paperdoes not study this issue. Presumably, Strzalecki’s analysis can be applied to our setting.Finally, like most papers in the literature on dynamic models, we follow a recursiveapproach and maintain dynamic consistency. This approach is normative appealing andcomputationally simple in applications because the usual dynamic programming method canbe applied. This approach typically shares the drawback of lacking a ‘reduction’ or ‘closure’31