In this paper we supply a new long-run risk valuation model in which the pricing of long-run risk in consumption growth is made consistent with a more realistic description of the persistence and predictability properties of all the relevant time series. The main innovation is the use of a decomposition of time series which classifies innovation shocks on the basis of their half-life. Correspondingly the relation between price variations and the persistent fluctuations in both consumption and cash flows growth is disaggregated across different levels of persistence and the complete term structure of risk-return trade-off is computed. Remarkably the empirical tests performed within our model remove most of the counterfactual implications generated by the original R.Bansal and A.Yaron (2004) model. In particular we find that consumption growth does contain cyclical components that are predictable, while it remains unpredictable at the aggregate level. These predictable components, moreover, are highly correlated with well known structural drivers of consumption variability, such as long-run productivity growth and demographic effects. The estimation of the term structure of risk premia produces evidence that these long-run drivers of consumption are priced by the market and contribute significantly to explain the equity premium. Finally, we propose a new test on the elasticity of intertemporal substitution which properly accounts for the persistence heterogeneity in both the risk free rate and the consumption growth and produces an estimate significant and larger than one.

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