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Rare disasters : ウィキペディア英語版
Rare disasters

A rare disaster is an economic event that is infrequent and large in magnitude, having a negative effect on an economy. Rare disasters are important because they provide an explanation of the equity premium puzzle, the behavior of interest rates, and other economic phenomena.
The parameters for a rare disaster are a substantial drop in GDP and at least a 10% decrease in consumption. Examples include financial disasters: The Great Depression and the Asian Financial Crisis; wars: World War I, World War II and regional conflicts; epidemics: Influenza outbreaks and the Asian Flu; and weather events: Tsunamis and Earthquakes; however, any event that has a substantial impact on GDP and consumption could be considered a rare disaster.
The idea was first proposed by Rietz in 1988, as a way to explain the equity premium puzzle. Since then, other economists have added to and strengthened the idea with evidence, but many economists are still skeptical of the theory.
==Model==
The model set forth by Barro is based upon the Lucas's fruit tree model of asset pricing with exogenous, stochastic production. The economy is closed, the amount of trees is fixed, output equals consumption ( ) and there is no investment or depreciation. As ( ) is the output of all the trees in the economy and ( ) is the price of the periods fruit (the equity claim). The equation below shows the gross return on the fruit tree in one period.
:R=\frac}
In order to model rare disasters, Barro introduces the equation below, which is a stochastic process for aggregate output growth. In the model, there are three types of economic shocks:
a.) Normal iid shocks
b.) Type (\tilde_) disasters which involve sharp contractions in output, but no default on debt.
c.) Type (\tilde) disasters which involve sharp contractions in output and at least a partial default on debt.
:\log A_ = \log A_t + \bar + \tilde_+\tilde_
The type ω (\tilde_) models low probability disasters and (\tilde_) is a random iid variable. They are assumed to be independent so they are interchangeable in the equation. Then from the above equation, the magnitude of the contraction from (\tilde_) is determined by the following equation.
:\begin
1 & (e^)\mbox \\
1-b & (1-e^)\mbox \\
\end
In this equation, p is the probability per unit of time that a disaster will occur in each period. If the disaster occurs, b is the factor by which consumption will shrink. The model requires a p that is small and a b that large to correctly model rare disasters. In Barro's analysis, d is also used to deal with the problem of the partial default on bonds.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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