Long Run Risk and the Persistence of Consumption Shocks

Abstract

We propose a methodology based on multiresolution analysis to decompose a time series in components classified by their level of persistence. Using this decomposition to detect the layers with different degrees of persistence in consumption growth, we provide empirical evidence that some of the consumption components are predictable and highly correlated with well known economic proxies of consumption variability. These predictable components generate a term-structure of sizable risk premia in a long-run risk model properly modified to account for the different layers of persistence. A low frequency component correlated with long-run productivity growth commands a premium of up to 2% per year when the risk aversion takes the reasonable value of 7.5 and the IES is 2.5. On the high-frequency side, a component with yearly half-life contributes to another sizable 2%. By accounting for persistence heterogeneity in consumption we obtain, moreover, an estimate of the IES strictly greater than one and robust across subsamples.

Keywords: Long-run risk, Persistence heterogeneity, Temporal aggregation, Consumption predictability

JEL Classification: G12, E21, E32, E44