NATIONAL BUREAU OF ECONOMIC RESEARCH

# On the Size Distribution of Macroeconomic Disasters

## Robert J. Barro, Tao Jin

NBER Working Paper No. 15247
Issued in August 2009, Revised in December 2011
NBER Program(s):Asset Pricing, Economic Fluctuations and Growth, Monetary Economics

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.

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Document Object Identifier (DOI): 10.3386/w15247

Published: Robert J. Barro & Tao Jin, 2011. "On the Size Distribution of Macroeconomic Disasters," Econometrica, Econometric Society, vol. 79(5), pages 1567-1589, 09. citation courtesy of

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