Rare disaster
In economics, a rare disaster is a collapse 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 1997 Asian financial crisis; wars: World War I, World War II, and regional conflicts; epidemics: influenza outbreaks and the Asian Flu; weather events; and earthquakes and tsunamis; 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 number 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 equation below shows the gross return on the fruit tree in one period.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 disasters which involve sharp contractions in output, but no default on debt.
c.) Type disasters which involve sharp contractions in output and at least a partial default on debt.
The type ω models low probability disasters and 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 is determined by the following equation.
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.
Applications
Since Rietz and Barro, the rare disaster framework can be used to explain many events in finance and economics.Equity premium
Much of the equity premium puzzle can be explained by the rare disaster scenarios proposed by Barro and Rietz. The basic reasoning is that if people are aware that rare disasters may occur, but the disaster never occurs during their lives, then the equity premium will appear high.Barro and subsequent economists have provided historical evidence to support this claim. Using this evidence, Barro shows that rare disasters occur frequently and in large magnitude, in economies around the world from a period from the mid-19th century to the present day.
Further, the evidence shows that in the long run the risk premium is around 5.0% in most countries. However, when looking at specific periods of time this premium may be higher or lower. For example, if a data set of the period of the Great Depression is observed, then the equity premium will be about 0.4%, because the Great Depression was a rare disaster.
Risk-free interest rate behavior
The risk-free interest rate may also be explained by rare disasters. Using data in the United States, the rare disaster model shows that the risk-free rate falls by a large margin when a rare disaster with the probability of 0.017 is introduced into the data set.Furthermore, Barro defends the criticisms about the behavior of the risk free rate raised by Mehra with respect to the Great Depression and events such as dropping the Atom Bomb in World War II. He reasons that two effects go into people's expectation of rare disasters-the probability of a rare disaster and the probability of default. In an event that has the possibility of nuclear war, the probability of a disaster would rise and therefore, decrease interest rates. However, the probability of government default on bonds also increases, because of the possible destruction of countries, which raises the rate on bonds. These two forces counteract which leads to ambiguity. As shown left with the risk free rate rising before and falling after the Great Depression, then falling initially during World War II and then rising afterward.