Rare disaster: Difference between revisions
No edit summary |
→History: ref fmt, sp Tags: Mobile edit Mobile web edit Advanced mobile edit |
||
(45 intermediate revisions by 27 users not shown) | |||
Line 1: | Line 1: | ||
{{Short description|Large and rare economic collapse}} |
|||
{| style="margin: 0 0 1em 1em; border: 1px solid #BEBEBE; background-color:#f9f9f9; clear:right; float:right;" cellpadding=0 cellspacing=0 |
|||
{{Economics sidebar}} |
|||
|- |
|||
In [[economics]], a '''rare disaster''' is a [[economic collapse|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 history|economic phenomena]]. |
|||
| style="font-size: 120%; background:#ccccdd; border-bottom: 1px solid #BEBEBE; padding: 5px 5px 3px 5px;" align="center"|'''[[Economics]]''' |
|||
|- |
|||
|style="text-align: center; background:#FFFFFF; "|[[Image:GDP nominal per capita world map IMF 2007.PNG|185px]]<br/> |
|||
|- |
|||
|<div class="NavFrame" style="border-style: none; padding: 0px; text-align: center; border-left: 0px; border-right: 0px; border-top: 0px; border-bottom: 0px;" cellpadding=0 cellspacing=0><div class="NavHead" style="border-style: none; padding: 0px; background:#FFFFFF; text-align: left; font-size: 11px; height:1.9em;"> '''[[Economies of present-day nations and states|Economies by region]]''' </div><div class="NavContent" style="border-style: none; padding: 0px; background-color:transparent; font-size: 90%; text-align: center; display:none; border-top: 1px solid #BEBEBE;"> |
|||
[[Economy of Africa|Africa]]{{·}} [[Economy of North America|North America]]<br> |
|||
[[Economy of South America|South America]]{{·}}[[Economy of Asia|Asia]]<br> |
|||
[[Economy of Europe|Europe]]{{·}}[[Economy of Oceania|Oceania]]<br> |
|||
</div></div> |
|||
|- |
|||
! style="background:#ddddee; font-size: 95%; border-top: 1px solid #BEBEBE; border-bottom: 1px solid #BEBEBE; padding: 0 5px 0 5px;" | [[Topic outline of economics|Outline of topics]] |
|||
|- |
|||
! style="background:#ddddee; font-size: 95%; border-top: 1px solid #BEBEBE; border-bottom: 1px solid #BEBEBE; padding: 0 5px 0 5px;" | [[JEL classification codes|General classifications]] |
|||
|- |
|||
| style="font-size: 90%; padding: 0 5px 0 5px;" | <center> |
|||
[[Microeconomics]]{{·}} [[Macroeconomics]]<br/> |
|||
[[History of economic thought]]<br/> |
|||
[[Economic methodology|Methodology]]{{·}} [[Heterodox economics|Heterodox approaches]] |
|||
|- |
|||
! style="background:#ddddee; font-size: 95%; border-top: 1px solid #BEBEBE; border-bottom: 1px solid #BEBEBE; padding: 0 5px 0 5px;" | [[JEL classification codes#Mathematical and quantitative methods JEL: C Subcategories|Techniques]] |
|||
|- |
|||
| style="font-size: 90%; padding: 0 5px 0 5px;" | |
|||
<center> |
|||
[[Mathematical economics|Mathematical]]{{·}} |
|||
[[Econometrics]] |
|||
<br/> |
|||
[[Experimental economics|Experimental]]{{·}} [[National accounts| National accounting]] |
|||
|- |
|||
! style="background:#ddddee; font-size: 95%; border-top: 1px solid #BEBEBE; border-bottom: 1px solid #BEBEBE; padding: 0 5px 0 5px;" | [[JEL classification codes|Fields and subfields]] |
|||
|- |
|||
| style="font-size: 90%; padding: 0 5px 0 5px;" | |
|||
<center> |
|||
[[Behavioral economics|Behavioral]]{{·}} [[Cultural economics|Cultural]]{{·}} [[Evolutionary economics|Evolutionary]]<br> |
|||
[[Economic growth|Growth]]{{·}} [[Development economics|Development]]{{·}} [[Economic history|History]]<br> |
|||
[[International economics|International]]{{·}} [[Economic system]]s<br> |
|||
[[Monetary economics|Monetary]] <span style="color:blue">and</span> [[Financial economics|Financial]]<br> |
|||
[[Public economics|Public]] <span style="color:blue">and</span> [[Welfare economics]]<br> |
|||
[[Health economics|Health]]{{·}} [[Labour economics|Labour]]{{·}} [[Managerial economics|Managerial]]<br> |
|||
[[Business economics|Business]]{{·}}[[Information economics|Information]]{{·}}[[Game theory]]<br/> |
|||
[[Industrial organization]] {{·}} [[Law and economics|Law]]<br> |
|||
[[Agricultural economics|Agricultural]]{{·}} [[Natural resource economics|Natural resource]]<br>[[Environmental economics|Environmental]]{{·}} [[Ecological economics|Ecological]]<br> |
|||
[[Urban economics|Urban]]{{·}} [[Rural economics|Rural]]{{·}} [[Regional science|Regional]] |
|||
|- |
|||
| style="background:#ddddee; font-size: 95%; border-top: 1px solid #BEBEBE; border-bottom: 1px solid #BEBEBE; padding: 0 5px 0 5px;" align="center"|'''[[:Category:Economics lists|Lists]]''' |
|||
|- |
|||
| style="font-size: 90%; padding: 0 5px 0 5px;" align="center"| |
|||
[[List of scholarly journals in economics|Journals]] · [[List of important publications in economics|Publications]]<br/> |
|||
[[:Category:Economics|Categories]] · [[List of economics topics|Topics]] · [[List of economists|Economists]] |
|||
<br> |
|||
</div></div> |
|||
|- |
|||
| <div class="NavFrame" style="border-style: none; padding: 0px; text-align: center; border-left: 0px; border-right: 0px; border-top: 0px; border-bottom: 0px;" cellpadding=0 cellspacing=0><div class="NavHead" style="border-style: none; padding: 0px; background:#ddddee; border-top: 1px solid #BEBEBE; text-align: center; font-size: 11px; height:1.9em;">'''[[Economic ideology|Economic ideologie]]s''' </div><div class="NavContent" style="border-style: none; padding: 0px; background-color:transparent; font-size: 90%; text-align: center; display:none; border-top: 1px solid #BEBEBE; "> |
|||
[[Anarchist economics|Anarchist]]{{·}} [[Capitalism|Capitalist]]<br> |
|||
[[Communist economy|Communist]]{{·}}[[Corporatism|Corporatist]]<br> |
|||
[[Economics of fascism|Fascist]]{{·}}[[Georgism|Georgist]]<br> |
|||
[[Islamic economics|Islamic]]{{·}}[[Laissez-faire]]<br> |
|||
[[Market socialism|Market socialist]]{{·}}[[Mercantilism|Mercantilist]]<br> |
|||
[[Protectionism|Protectionist]]{{·}} [[Socialist economics|Socialist]]<br> |
|||
[[Syndicalism|Syndicalist]]{{·}}[[Third Way (centrism)|Third Way]]<br> |
|||
</div></div> |
|||
|- |
|||
| <div class="NavFrame" style="border-style: none; padding: 0px; text-align: center; border-left: 0px; border-right: 0px; border-top: 0px; border-bottom: 0px;" cellpadding=0 cellspacing=0><div class="NavHead" style="border-style: none; padding: 0px; background:#ddddee; border-top: 1px solid #BEBEBE; text-align: center; font-size: 11px; height:1.9em;">'''[[Economy|Other economies]]''' </div><div class="NavContent" style="border-style: none; padding: 0px; background-color:transparent; font-size: 90%; text-align: center; display:none; border-top: 1px solid #BEBEBE;"> |
|||
[[Anglo-Saxon economy|Anglo-Saxon]]{{·}} [[Feudal]]<br/> |
|||
[[Global economy|Global]]{{·}} [[Hunter-gatherer]]<br/> |
|||
[[Newly industrialized country]]<br/> |
|||
[[Palace economy|Palace]]{{·}}[[Plantation economy|Plantation]]<br/> |
|||
[[Post-capitalism|Post-capitalist]]{{·}}[[Post-industrial economy|Post-industrial]]<br/> |
|||
[[Social market economy|Social market]]{{·}}[[Socialist market economy|Socialist market]]<br/> |
|||
[[Token economy|Token]]{{·}}[[Traditional economy|Traditional]]<br/> |
|||
[[Information economy|Information]]{{·}} [[Transition economy|Transition]] |
|||
</div></div> |
|||
|- |
|||
| style="background:#ccccdd; font-size: 85%; border-top: 1px solid #BEBEBE; padding: 0 5px 0 5px;" align="center"| [[Image:Portal.svg|15px]] [[Portal:Business and economics|Business and Economics Portal]] |
|||
|- |
|||
! style="background:#ccccdd; font-size: 95%; padding: 0 5px 0 5px;" | {{tnavbar|Economics sidebar}} |
|||
|}<noinclude> |
|||
[[Category:Economics templates|{{PAGENAME}}]] |
|||
[[pt:Predefinição:Infobox Economia]] |
|||
[[zh:Template:Economics sidebar]] |
|||
</noinclude> |
|||
The parameters for a rare disaster are a substantial drop in [[GDP]] and at least a 10% decrease in [[consumption (economics)|consumption]]. Examples include [[financial crisis|financial disaster]]s: the [[Great Depression]] and the [[1997 Asian financial crisis]]; wars: [[World War I]], [[World War II]], and regional conflicts; [[epidemic]]s: influenza outbreaks and the Asian Flu; weather events; and [[earthquake]]s and [[tsunami]]s; however, any event that has a substantial impact on GDP and consumption could be considered a rare disaster. |
|||
'''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 idea was first proposed by [[Rietz]] in 1988,<ref name="The equity risk premium a solution">{{cite journal|last1=Rietz|first1=Thomas|title=The equity risk premium a solution|journal=Journal of Monetary Economics|date=1988|volume=22|issue=1|pages=117–131|doi=10.1016/0304-3932(88)90172-9}}</ref> 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. |
|||
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]], [[Asian Financial Crisis]]), wars([[World War I]] and [[World War II]], Regional conflicts), epidemics(Influenza Outbreak, Asian Flu), 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== |
==Model== |
||
The model set forth by [[Barro]] is based upon the Lucas's fruit tree model of asset pricing with exogenous, stochastic production. |
The model set forth by [[Robert Barro|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 ( {{math|<VAR>A</VAR> <sub>''t'' + 1</sub> {{=}} <VAR>C</VAR> <sub>''t''</sub>}} ) and there is no investment or depreciation. As ( {{math|<VAR>A</VAR> <sub>''t'' + 1</sub>}} ) is the output of all the trees in the economy and ( <math>{P_t}</math> ) is the price of the periods fruit (the equity claim). The equation below shows the gross return on the fruit tree in one period.<ref name= "Barro10">{{cite web|last=Barro|first=Robert|title= Rare Disasters and Asset Markets in the Twentieth Century|url=http://www.economics.harvard.edu/faculty/barro/files/equity%20premium%2012-1-05.pdf|publisher=The Quarterly Journal of Economics|pages= 10–20|accessdate=2009-03-09|archive-url=https://web.archive.org/web/20100709152623/http://www.economics.harvard.edu/faculty/barro/files/equity%20premium%2012-1-05.pdf |archive-date=9 July 2010 |url-status=dead}}</ref> |
||
:<math>R=\frac{A_{t+1}}{P_{t1}}</math> |
|||
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: |
|||
<math>R=\frac{A_{t+1}}{P_{t1}}</math> |
|||
a.) Normal [[iid]] shocks<br> |
|||
In order to model rare disasters Barro introduces the below equation, which is a stochastic process for aggregate output growth. In the model there are three types of economic shocks. |
|||
b.) Type (<math>\tilde{w}_{t+1}</math>) disasters which involve sharp contractions in output, but no default on debt.<br> |
|||
c.) Type (<math>\tilde{v}</math>) disasters which involve sharp contractions in output and at least a partial default on debt. |
|||
:<math>\log A_{t+1} = \log A_t + \bar{g} + \tilde{u}_{t+1}+\tilde{v}_{t+1}</math> |
|||
a.) Normal [[iid]] shocks<br /> |
|||
b.) Type <math>\tilde{w}_{t+1}</math> disasters which involve sharp contractions in output but no default on debt.<br /> |
|||
c.) Type <math>\tilde{v}</math> disasters which involve sharp contractions in output and at least a partial default on debt<br /> |
|||
The type ω (<math>\tilde{v}_{t+1}</math>) models low probability disasters and (<math>\tilde{u}_{t+1}</math>) 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 (<math>\tilde{v}_{t+1}</math>) is determined by the following equation. |
|||
<math>\log A_{t+1} = \log A_t + \bar{g} + \tilde{u}_{t+1}+\tilde{v}_{t+1}</math> |
|||
<br /> |
|||
The type ω (<math>\tilde{v}_{t+1}</math>) models low probability disasters and <math>\tilde{u}_{t+1}</math> 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 <math>\tilde{v}_{t+1}</math> is determined by the following equation. |
|||
<math>\begin{cases} |
:<math>\begin{cases} |
||
1 & (e^{-p})\mbox{ no disaster} \\ |
|||
1-b & (1-e^{-p})\mbox{ disaster} \\ |
|||
\end{cases}</math |
\end{cases}</math> |
||
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. |
|||
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== |
==Applications== |
||
Since Rietz and Barro, the rare disaster framework can be used to explain many events in finance and economics. |
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 puzzle can be explained by the rare disasters scenarios proposed by Barro and Rietz. The basic reasoning is that if people are aware that rare disasters(i.e the Great Depression or WW1 and WW2) may occur, but the disaster never occurs during their lives, then the equity premium will appear high. |
|||
===Equity premium=== |
|||
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 1800s to the present day. |
|||
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 (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.<ref>Barro, Robert. "RARE DISASTERS AND ASSET MARKETS IN THE TWENTIETH CENTURY" pg3-12</ref> |
|||
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.<ref name="Barro10"/> |
|||
===Risk Free Interest Rates=== |
|||
The Risk Free Interest Rate(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. <ref>Barro, Robert. "RARE DISASTERS AND ASSET MARKETS IN THE TWENTIETH CENTURY" pg22-27</ref> |
|||
===Risk-free interest rate behavior=== |
|||
[[File:riskfree.png|260px|right|thumb]] |
|||
The [[risk-free interest rate]] (the interest received on fixed income, like bonds issued by extremely safe entities, typically governments) 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 0.127 to 0.035) when a rare disaster with the probability of 0.017 is introduced into the data set.<ref name="Barro10"/> |
|||
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 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.<ref name="Barro10"/> |
|||
==History== |
==History== |
||
[[Prescott]] and [[Mehra]] first proposed the |
[[Edward C. Prescott]] and [[Rajnish Mehra]] first proposed the equity premium puzzle in 1985. In 1988, Rietz<ref name="The equity risk premium a solution"/> suggested that large and infrequent economic shocks could explain the equity premium (the premium of equity 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.<ref>pp. 2–3</ref> 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.<ref>pp. 4–11</ref> 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.<ref name=MehraHist>{{cite web|author=Rajnish Mehra|title=The Equity Premium Puzzle: A Review|url=http://www.academicwebpages.com/preview/mehra/pdf/FIN%200201.pdf|journal=Foundations and Trends in Finance|date=2008|volume=2|issue=1|pp=1–81|website=|accessdate=2009-03-09}}</ref> |
||
==Controversy== |
==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 to 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 due to rapid inflation. Further, the risk aversion 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.<ref name=MehraHist/> |
|||
Rajnish Mehra was skeptical of Reitz 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 united states. Rietz suggested 25-97% drops but this has never |
|||
==See also== |
|||
happened in the United States. Even if this was true there are several other flaws regarding his model, parameters, |
|||
*[[Rare events]] |
|||
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.<ref>Mehra, Rajnish. The Equity Premium Puzzle. A Solution? pgs 2-4</ref> |
|||
==References== |
==References== |
||
{{Reflist}} |
|||
===Notes=== |
|||
{{reflist|2}} |
|||
===Bibliography=== |
===Bibliography=== |
||
* |
*{{cite web|author=Rajnish Mehra|date=February 2003|title=The Equity Premium: Why Is It a Puzzle?|url=http://wwwdocs.fce.unsw.edu.au/economics/news/VisitorSeminar/RMehra.pdf|website=|accessdate=2009-03-09}} |
||
*{{cite web|author=New Economist|date=September 30, 2005|title=New Economist on Barro and the Equity Premium Puzzle|url=http://economistsview.typepad.com/economistsview/2005/09/new_economist_o.html|publisher=Mehra|website=|accessdate=2009-03-09}} |
|||
* {{citeweb|author=Rajnish Mehra and Edward C. Prescott(1988)|title=THE EQUITY RISK PREMIUM: A SOLUTION?|url=http://www.academicwebpages.com/preview/mehra/pdf/EP%20Solution.pdf|publisher=Journal of Monetary Economics|work=|accessdate=2009-03-09}} |
|||
* {{cite web|author=Robert Barro(2005)|title=RARE DISASTERS AND ASSET MARKETS IN THE TWENTIETH CENTURY|url=http://www.economics.harvard.edu/faculty/barro/files/equity%20premium%2012-1-05.pdf|publisher=|work=|accessdate=2009-03-09}} |
|||
* {{cite web|author=Ranjnish Mehra(2003)|title=The Equity Premium: Why Is It a Puzzle?|url=http://wwwdocs.fce.unsw.edu.au/economics/news/VisitorSeminar/RMehra.pdf|publisher=|work=|accessdate=2009-03-09}} |
|||
* {{cite web|author=New Economist(2005)|title=New Economist on Barro and the Equity Premium Puzzle|url=http://economistsview.typepad.com/economistsview/2005/09/new_economist_o.html|publisher=Mehra|work=|accessdate=2009-03-09}} |
|||
{{DEFAULTSORT:Rare Disasters}} |
|||
* {{cite web|author=Mehra(2008)|title=The Equity Premium Puzzle: A Review|url=http://www.academicwebpages.com/preview/mehra/pdf/FIN%200201.pdf|publisher=Mehra|work=|accessdate=2009-03-09}} |
|||
[[Category:Economic collapses]] |
Latest revision as of 00:01, 13 March 2024
Part of a series on |
Economics |
---|
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,[1] 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
[edit]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 ( A t + 1 = C t ) and there is no investment or depreciation. As ( A t + 1 ) 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.[2]
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
[edit]Since Rietz and Barro, the rare disaster framework can be used to explain many events in finance and economics.
Equity premium
[edit]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 (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, 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.[2]
Risk-free interest rate behavior
[edit]The risk-free interest rate (the interest received on fixed income, like bonds issued by extremely safe entities, typically governments) 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 0.127 to 0.035) when a rare disaster with the probability of 0.017 is introduced into the data set.[2]
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 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.[2]
History
[edit]Edward C. Prescott and Rajnish Mehra first proposed the equity premium puzzle in 1985. In 1988, Rietz[1] suggested that large and infrequent economic shocks could explain the equity premium (the premium of equity 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.[3] 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.[4] 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.[5]
Controversy
[edit]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 to 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 due to rapid inflation. Further, the risk aversion 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.[5]
See also
[edit]References
[edit]- ^ a b c d Barro, Robert. "Rare Disasters and Asset Markets in the Twentieth Century" (PDF). The Quarterly Journal of Economics. pp. 10–20. Archived from the original (PDF) on 9 July 2010. Retrieved 2009-03-09.
- ^ pp. 2–3
- ^ pp. 4–11
- ^ a b Rajnish Mehra (2008). "The Equity Premium Puzzle: A Review" (PDF). Foundations and Trends in Finance. pp. 1–81. Retrieved 2009-03-09.
Bibliography
[edit]- Rajnish Mehra (February 2003). "The Equity Premium: Why Is It a Puzzle?" (PDF). Retrieved 2009-03-09.
- New Economist (September 30, 2005). "New Economist on Barro and the Equity Premium Puzzle". Mehra. Retrieved 2009-03-09.