This paper develops procedures for inference about the moments of smooth functions of out-of-sample predictions and prediction errors when there is a long time series of predictions and realizations. The aim is to provide tools for analysis of predictive accuracy and efficiency and, more generally, of predictive ability. The paper allows for nonnested and nonlinear models as well as for possible dependence of predictions and prediction errors on estimated regression parameters. Simulations indicate that the procedures can work well in samples of size typically available.

At least since Keynes (1935), many economists have had the intuition that the marginal propensity to consume out of wealth declines as wealth increases. Nonetheless, standard perfect-certainty and certainty equivalent versions of intertemporal optimizing models of consumption imply a marginal propensity to consume that is unrelated to the level of household wealth. We show that adding income uncertainty to the standard optimization problem induces a concave consumption function in which, as Keynes suggested, the marginal propensity to consume out of wealth or transitory income declines with the level of wealth.