Rare Disasters, Asset Prices, and Welfare Costs

In a previous study, Barro (2006), I used the Thomas A. Rietz (1988) idea of rare economic disasters to explain the equity premium and related asset-pricing puzzles. My quantitative examination of large macroeconomic contractions in 35 countries during the twentieth century suggested a disaster probability of roughly 2 percent per year. The size distribution of GDP contractions during these events ranged between 15 percent (the arbitrary lower bound) and over 60 percent. A simple representative-agent economy, calibrated to accord with this disaster experience, can explain an equity premium of around 4–6 percent and a risk-free real interest rate of 1–2 percent. With power-utility preferences, these results require a coefficient of relative risk aversion of 3–4. The analysis applies in a Lucas-tree economy with i.i.d. production shocks or to an “AK model” with endogenous saving and stochastic depreciation. The present analysis extends the framework to consider additional aspects of asset pricing and to assess the welfare cost of consumption uncertainty. As observed by Ravi Bansal and Amir Yaron (2004), power-utility preferences with a coefficient of relative risk aversion above one generate two implausible predictions. First, an increase in uncertainty raises the price-dividend ratio for equities and, second, a rise in the mean growth rate lowers the price-dividend ratio. More reasonable predictions require an intertemporal elasticity of substitution (IES) above one. In the power-utility framework, however, this property conflicts with a coefficient of relative risk aversion greater than one—a condition needed to match observed equity premia. Therefore, to fit a broad set of asset-pricing “facts,” it is essential to use a preference specification, such as that of Larry G. Epstein and Stanley E. Zin (1989) and Philippe Weil (1990), that delinks the IES from the coefficient of relative risk aversion. Power utility, although attractive for its simplicity, cannot work. The framework is still a representative-consumer model with i.i.d. shocks to production. In this setting, the key asset-pricing conditions under Epstein-Zin-Weil (henceforth, EZW) preferences resemble those with power utility. However, two key differences emerge. First, under EZW preferences, consumption enters into asset-pricing formulas with an exponent that involves the Rare Disasters, Asset Prices, and Welfare Costs