Using conditional moments of asset payoffs to infer the volatility of intertemporal marginal rates of substitution

Abstract

Previously Hansen and Jagannathan (1990a) derived and computed mean-standard deviation frontiers for intertemporal marginal rates of substitution (IMRS) implied by asset market data. These frontiers give the lower bounds on the standard deviations as a function of the mean. In this paper we develop a strategy for utilizing conditioning information efficiently, and hence improve on the standard deviation bounds computed by Hansen and Jagannathan. We implement this strategy empirically by using the seminonparametric (SNP) methodology suggested by Gallant and Tauchen (1989) to estimate the conditional distribution of a vector of monthly asset payoffs. We use the fitted conditional distributions to calculate both conditional and unconditional standard deviation bounds for the IMRS. The unconditional bounds are as sharp as possible subject to robustness considerations. We also use the fitted distributions to compute the moments of various candidate marginal rates of substitution suggested by economic theory, and in particular the time-nonseparable preferences of Dunn and Singleton (1986) and Eichenbaum and Hansen (1990). For these preferences, our findings suggest that habit persistence will put the moments of the IMRS inside the frontier at reasonable values of the curvature parameter. At the same time we uncover evidence that the implied IMRS fails to satisfy all of the restrictions inherent in the Euler equation. The findings help explain why Euler equation estimation methods typically find evidence in favor of local durability instead of habit persistence for monthly data.