A Statistical Inquiry into the Plausibility of Recursive Utility ∗

We use purely statistical methods to determine if it is plausible that the pricing kernel can be represented as the intertemporal marginal rate of substitution of a representative agent in an endowment economy whose preferences are determined by recursive utility. Specifically we investigate regression implications of recursive utility such as the implication that the R-square of a log-linear regression of the pricing kernel on endowment growth and the return to wealth is one. We make no assumptions other than that a unique pricing kernel exists and that our payoffs span the factors that determine it. We introduce a Bayesian statistical method that treats the pricing kernel as a latent variable and extracts it and its transition density from real payoffs on twenty-four Fama-French portfolios, on bonds, and on payoffs formed by interacting these payoffs with conditioning information available to agents when portfolios are formed, notably labor income growth. Our priors are formed from an examination of a long simulation of a Bansal-Yaron economy. Using both monthly data and annual data, we determine the posterior distributions of the R-squares of various regressions and compare these posteriors to the R-squares that should have obtained were the pricing kernel determined by recursive utility. These regressions are invariant to seasonal adjustment. We find that the data support recursive utility.