Rare disasters
Encyclopedia
Rare disasters are economic events that are 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.
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.
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.
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 (i.e. the Great Depression or World War I and World War II) 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, if 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.
(the interest received on fixed income, like bonds) 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 (from .127 to .035) when a rare disaster with the probability of .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 (like the Cuban Missile Crisis or World War II), 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 to forces counteract and lead to ambiguity. As shown left with the risk free rate before and falling after the Great Depression, then falling initially during World War II and then rising afterward.
and Rajnish Mehra
first proposed the Equity Premium Puzzle in 1985. In 1988, Rietz suggested that large and infrequent economic shocks could explain the equity premium (the premium of securities over fixed income assets). However, it was not deemed feasible at the time, because it seemed that such events were too rare and could not occur in reality. The theory was forgotten until 2005, when Robert Barro
provided evidence of nations from around the world from the 19th and 20th century, showing that these events were possible and have happened. Since his papers, others have submitted different ideas regarding rare disasters' impact on other economic phenomenon. However, many economists remain skeptical of how much rare disasters really explain the equity premium and Mehra still expresses doubt as to the validity of the theory.
and supporting evidence. The model Rietz presented did not compensate for a partial default on bond holders do due
rapid inflation. Further, the risk aversion in parameter was used inconsistently in his analysis. For example, a
value of 10 was used to show a 25% drop in consumption, but a value of 1 is used to explain stock returns and
consumption. Finally, more historical evidence was said to have been needed to give the theory proper support. For
example, the perceived probability of a rare disaster should have been low before the atomic bomb was dropped and
must have been higher before the Cuban Missile Crisis
than after. Therefore, real interest rates should have
correlated with these events, but they did not. Mehra concluded that Rietz's scenario was far too extreme to
resolve the puzzle.
Equity premium puzzle
The equity premium puzzle is a term coined in 1985 by economists Rajnish Mehra and Edward C. Prescott. It is based on the observation that in order to reconcile the much higher returns of stocks compared to government bonds in the United States, individuals must have implausibly high risk aversion...
, 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
Consumption (economics)
Consumption is a common concept in economics, and gives rise to derived concepts such as consumer debt. Generally, consumption is defined in part by comparison to production. But the precise definition can vary because different schools of economists define production quite differently...
. Examples include financial disasters: The Great Depression and the Asian Financial Crisis; wars: World War I
World War I
World War I , which was predominantly called the World War or the Great War from its occurrence until 1939, and the First World War or World War I thereafter, was a major war centred in Europe that began on 28 July 1914 and lasted until 11 November 1918...
, World War II
World War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...
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
Rietz
For the musician, seeJulius Rietz.Rietz is a municipality in the Imst district and is located 23 km east of Imst and 4 km west of Telfs on the southern shore of the Inn River. It is a peculiarity that the village has no sun during winter time because of the height of the Stubai Alps. In recent...
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 BarroBarro
Barro is a municipality in Galicia, Spain in the province of Pontevedra....
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.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.The Equity Premium
Much of the equity premium puzzleEquity premium puzzle
The equity premium puzzle is a term coined in 1985 by economists Rajnish Mehra and Edward C. Prescott. It is based on the observation that in order to reconcile the much higher returns of stocks compared to government bonds in the United States, individuals must have implausibly high risk aversion...
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 (i.e. the Great Depression or World War I and World War II) 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, if 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 rateRisk-free interest rate
Risk-free interest rate is the theoretical rate of return of an investment with no risk of financial loss. The risk-free rate represents the interest that an investor would expect from an absolutely risk-free investment over a given period of time....
(the interest received on fixed income, like bonds) 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 (from .127 to .035) when a rare disaster with the probability of .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 (like the Cuban Missile Crisis or World War II), 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 to forces counteract and lead to ambiguity. As shown left with the risk free rate before and falling after the Great Depression, then falling initially during World War II and then rising afterward.
History
Edward C. PrescottEdward C. Prescott
Edward Christian Prescott is an American economist. He received the Nobel Memorial Prize in Economics in 2004, sharing the award with Finn E. Kydland, "for their contributions to dynamic macroeconomics: the time consistency of economic policy and the driving forces behind business cycles"...
and Rajnish Mehra
Rajnish Mehra
Rajnish Mehra is an Indian American economist. He currently holds the E. N. Basha Chair at Arizona State University and is a research associate of the NBER...
first proposed the Equity Premium Puzzle in 1985. In 1988, Rietz suggested that large and infrequent economic shocks could explain the equity premium (the premium of securities over fixed income assets). However, it was not deemed feasible at the time, because it seemed that such events were too rare and could not occur in reality. The theory was forgotten until 2005, when Robert Barro
Robert Barro
Robert Joseph Barro is an American classical macroeconomist and the Paul M. Warburg Professor of Economics at Harvard University. The Research Papers in Economics project ranked him as the 4th most influential economist in the world as of August 2011 based on his academic contributions...
provided evidence of nations from around the world from the 19th and 20th century, showing that these events were possible and have happened. Since his papers, others have submitted different ideas regarding rare disasters' impact on other economic phenomenon. However, many economists remain skeptical of how much rare disasters really explain the equity premium and Mehra still expresses doubt as to the validity of the theory.
Controversy
Rajnish Mehra was skeptical of Reitz's claim that rare disasters explain the equity premium and real interest rate behavior, because the rare disaster that Rietz had specified had never occurred in the U.S. Rietz suggested 25-97% drops, but this has never happened in the United States. Even if this were true, there are several other flaws regarding his model, parameters,and supporting evidence. The model Rietz presented did not compensate for a partial default on bond holders do due
rapid inflation. Further, the risk aversion in parameter was used inconsistently in his analysis. For example, a
value of 10 was used to show a 25% drop in consumption, but a value of 1 is used to explain stock returns and
consumption. Finally, more historical evidence was said to have been needed to give the theory proper support. For
example, the perceived probability of a rare disaster should have been low before the atomic bomb was dropped and
must have been higher before the Cuban Missile Crisis
Cuban Missile Crisis
The Cuban Missile Crisis was a confrontation among the Soviet Union, Cuba and the United States in October 1962, during the Cold War...
than after. Therefore, real interest rates should have
correlated with these events, but they did not. Mehra concluded that Rietz's scenario was far too extreme to
resolve the puzzle.