Implications of return predictability for consumption dynamics and asset pricing

Two broad classes of consumption dynamics—long-run risks and rare disasters—have proven successful in explaining the equity premium puzzle when used in conjunction with recursive preferences. We show that bounds a-là Gallant, Hansen, and Tauchen that restrict the volatility of the stochastic discount factor by conditioning on a set of return predictors constitute a useful tool to discriminate between these alternative dynamics. In particular, we document that models that rely on rare disasters meet comfortably the bounds independently of the forecasting horizon and the asset returns used to construct the bounds. However, the specific nature of disasters is a relevant characteristic at the 1-year horizon: disasters that unfold over multiple years are more successful in meeting the predictors-based bounds than one-period disasters. Instead, at the 5-year horizon, the sole presence of disasters—even if one-period and permanent—is sufficient for the model to satisfy the bounds. Finally, the bounds point to multiple volatility components in consumption as a promising dimension for long-run risk models.