Time-Varying Disaster Risk Models : An Empirical Assessment of the Rietz-Barro Hypothesis

This paper revisits the fit of disaster risk models where a representative agent has recursive preferences and the probability of a macroeconomic disaster changes over time. We calibrate the model as in Wachter (2013) and perform two sets of tests to assess the empirical performance of the model in long run simulations. The model is solved using a two step projection-based method that allows us to find the equilibrium consumption-wealth ratio and dividend-yield for different values of the intertemporal elasticity of substitution. By fixing the elasticity of substitution to one, the first experiment indicates that the overall fit of the model is adequate. However, we find that the amount of aggregate stock market volatility that the model can generate is sensible to the method used to solve the model. We also find that the model generates near unit root interest rates and a puzzling ranking of volatilities between the risk free rate and the expected return on government bills. We later solve the model for values of the elasticity of substitution that differ from one. This second experiment shows that while a higher elasticity of substitution helps to increase the aggregate stock market volatility and hence to reduce the Sharpe Ratio, a lower elasticity of substitution generates a more reasonable level for the equity risk premium and for the volatility of the government bond returns without compromising the ability of the price-dividend ratio to predict excess returns