Long-run risk and the persistence of consumption shocks

We propose a decomposition for time series in components classified by levels of persistence. Employing this decomposition, we provide empirical evidence that consumption growth contains predictable components highly correlated with well-known proxies of consumption variability. These components generate a term-structure of sizable risk premia. At low frequencies we identify a component correlated with long-run productivity growth and commanding a yearly premium of approximately 2%. At high frequencies we identify a component with yearly half-life, which contributes to the equity premium for another 2%. Accounting for persistence heterogeneity, we obtain an estimate of the IES strictly above one and robust across subsamples.