Long Run and the Temporal Aggregation of Risks

Abstract

The long-run risk model introduced by R.Bansal and A.Yaron (2004) assumes the existence of a small predictable component in consumption growth and an elasticity of intertemporal substitution of the representative agent larger than one for the substitution effect to dominate the income one. Previous tests fail to detect predictability in mean consumption growth fluctuations and the estimated value for the elasticity of intertemporal substitution is smaller than one. We argue that these apparent inconsistencies are due to a severe error-in-variables problem generated by the heterogeneity in the persistence levels of shocks to consumption growth. In this paper the original long run risk model is extended introducing a novel persistence based decomposition which can be considered as a refined permanent-transitory decomposition where the transitory shock is further split into orthogonal components. This new decomposition provides an effective method to represent a time series as a linear combination of innovations classified by their level of persistence and their time of arrival. Correspondingly the relations between equity return variations, cash flow risk and persistent fluctuations in the consumption mean are disaggregated across different levels of persistence and the complete term structure of risk return tradeoffs is computed. Quite remarkably, the empirical tests performed within this extended setup find evidence of consumption growth predictability, produce sizeable estimated for the equity premia and explain the value premium as an effect of the differential exposure of cash flows to consumption risk.