Disasters and Recoveries: A Note on the Barro-Rietz Explanation of the Equity Premium Puzzle

In a recent article, Barro (2006) revives the Rietz explanation of the equity premium. Rietz (1988) showed that infrequent, large drops in consumption make the theoretical equity premium large. Barro shows empirically that in the XXth century, disasters are frequent and large enough, and stock returns low enough relative to bond returns during disasters, to make this explanation quantitatively plausible. In this note I revisit this issue, taking into account the empirical fact that many disasters are followed by a recovery. Barro and Rietz assumed that disasters are permanent. Mathematically, they model log consumption per capita as following a unit root process plus a Poisson jump. However a casual look at the data suggests that disasters are often followed by recoveries. In this note I extend the Barro-Rietz model to the case when there is a possible recovery following a disaster. In doing so, I follow Barro’s suggestion that “a worthwhile extension would deal more seriously with the dynamics of crisis regimes” (p. 854). I show that when the intertemporal elasticity of substitution of consumption (IES) is low, the risk premium is larger than what Barro found, reinforcing his point. However, when the IES is relatively high, the equity premium is markedly reduced.