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On the Size Distribution of Macroeconomic Disasters*

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  • Robert J. Barro
  • Tao Jin

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.
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Suggested Citation

  • Robert J. Barro & Tao Jin, 2011. "On the Size Distribution of Macroeconomic Disasters," Econometrica, Econometric Society, vol. 79(5), pages 1567-1589, September.
  • Handle: RePEc:ecm:emetrp:v:79:y:2011:i:5:p:1567-1589
    DOI: ECTA8827
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    References listed on IDEAS

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    Replication

    This item has been replicated by:
  • Michal Brzezinski, 2015. "Relative Risk Aversion and Power‐Law Distribution of Macroeconomic Disasters," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(1), pages 170-175, January.
  • More about this item

    JEL classification:

    • E20 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - General (includes Measurement and Data)
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • G01 - Financial Economics - - General - - - Financial Crises
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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    1. On the Size Distribution of Macroeconomic Disasters (ECTA 2011) in ReplicationWiki

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