This research was supported by the National Science Foundation. We appreciate helpful comments from Xavier Gabaix, Rustam Ibragimov, Chris Sims, Jose Ursua, and Marty Weitzman.
On the Size Distribution of Macroeconomic Disasters
Article first published online: 20 SEP 2011
© 2011 The Econometric Society
Volume 79, Issue 5, pages 1567–1589, September 2011
How to Cite
Barro, R. J. and Jin, T. (2011), On the Size Distribution of Macroeconomic Disasters. Econometrica, 79: 1567–1589. doi: 10.3982/ECTA8827
- Issue published online: 20 SEP 2011
- Article first published online: 20 SEP 2011
- Manuscript received September, 2009; final revision received February, 2011.
- Power law;
- rare disaster;
- equity premium;
- risk aversion
The coefficient of relative risk aversion is a key parameter for analyses of behavior toward risk, but good estimates of this parameter do not exist. A promising place for reliable estimation is rare macroeconomic disasters, which have a major influence on the equity premium. The premium depends on the probability and size distribution of disasters, gauged by proportionate declines in per capita consumption or gross domestic product. Long-term national-accounts data for 36 countries provide a large sample of disasters of magnitude 10% or more. A power-law density provides a good fit to the size distribution, and the upper-tail exponent, α, is estimated to be around 4. A higher α signifies a thinner tail and, therefore, a lower equity premium, whereas a higher coefficient of relative risk aversion, γ, implies a higher premium. The premium is finite if α > γ. The observed premium of 5% generates an estimated γ close to 3, with a 95% confidence interval of 2 to 4. The results are robust to uncertainty about the values of the disaster probability and the equity premium, and can accommodate seemingly paradoxical situations in which the equity premium may appear to be infinite.