Intertemporal Substitution and Recursive Smooth Ambiguity ...

where R t+1 is the market return from periods t to t + 1 that satisfies:where (X t ) is the wealth process.X t+1 = R t+1 (X t − c t ) , (29)When η = γ, the homothetic recursive ambiguity model reduces to the Epstein-Zin-Weil model. In this case, the pricing kernel in (27) or (28) reduces to that in Epstein andZin (1989) and Hansen et al. (2008). Why is our generalized recursive smooth ambiguitymodel useful in explaining asset pricing puzzles? Equation (27) reveals that there are twoadjustments to the standard pricing kernel β (c t+1 /c t ) −ρ . The first adjustment is presentfor recursive expected utility of Epstein-Zin (1989). This adjustment is the second term onthe right-hand side of (27). The second adjustment is due to ambiguity aversion, which isgiven by the last term on the right-hand side of (27). This adjustment has the feature thatan ambiguity averse agent with η > γ puts a higher weight on the pricing kernel when hiscontinuation value is low in recessions. This pessimistic behavior helps explain the equitypremium puzzle and the riskfree rate puzzle and also generates time-varying equity premium.Ju and Miao (2010) study the quantitative implications of the above homothetic specificationusing the pricing kernel in (27), when z is governed by a regime switching process.They show that our model proves successful in explaining many asset pricing puzzles quantitatively.6. Related LiteratureOur paper is related to a small literature on axiomatically founded dynamic models of ambiguity.Our second-order act approach is closely related to KMM (2009a). 19Unlike thatpaper, we adopt a hierarchical Anscombe-Aumann-type domain. This domain allows us toimpose simple and intuitive axioms. More importantly, it permits a separation of intertemporalsubstitution from attitudes toward risk or uncertainty. Our utility representation allowsfor flexible parametric specifications and nests KMM (2009a) model and some other popularmodels in the literature as special cases such as the recursive expected utility model (Krepsand Porteus (1978) and Epstein and Zin (1989)) and the multiplier preference model withhidden states (Hansen (2007) and Hansen and Sargent (2007)). In addition, this representa-19 Hanany and Klibanoff (2009) also provide a dynamic extension of the KMM (2005) model. Theirapproach is non-recursive in that they first define preference over consumption plans and then determineconditional preferences by updating beliefs.29