@techreport{NBERw15247,
title = "On the Size Distribution of Macroeconomic Disasters",
author = "Robert J. Barro and Tao Jin",
institution = "National Bureau of Economic Research",
type = "Working Paper",
series = "Working Paper Series",
number = "15247",
year = "2009",
month = "August",
doi = {10.3386/w15247},
URL = "http://www.nber.org/papers/w15247",
abstract = {
In the rare-disasters setting, a key determinant of the equity premium is the size distribution of macroeconomic disasters, gauged by proportionate declines in per capita consumption or GDP. The long-term national-accounts data for up to 36 countries provide a large sample of disaster events of magnitude 10% or more. For this sample, a power-law density provides a good fit to the distribution of the ratio of normal to disaster consumption or GDP. The key parameter of the size distribution is the upper-tail exponent, `alpha`, estimated to be near 5, with a 95% confidence interval between 3-1/2 and 7. The equity premium involves a race between `alpha` and the coefficient of relative risk aversion, `gamma`. A higher `alpha` signifies a thinner tail and, therefore, a lower equity premium, whereas a higher `gamma` implies a higher equity premium. The equity premium is finite if `alpha-1>gamma`. To accord with the observed average unlevered equity premium of around 5%, we get a point estimate for `gamma` close to 3, with a 95% confidence interval of roughly 2 to 4.},
}