Rare Disasters and Asset Markets in the Twentieth Century Barro QJE, 2006 Presentation by Serdar Aldatmaz Spring, 2010

Background Mehra-Prescott, 1985 –Equity premium puzzle Rietz, 1988 –Low-probability economic disasters might be the solution

Preview of Results Inclusion of rare disasters into Mehra and Prescott’s model can explain asset- market puzzles –Equity-premium puzzle –Low real rate of return on government bills –Low expected real interest rates during major wars

Outline The Model Review of economic disasters Calibration Results Extensions Concluding Remarks

The Model Lucas Tree Model –Exogenous, stochastic production –Neither investment, nor depreciation Allows for capital formation in the extension –Consumption equals output –Two assets Equity claim on t+1 output Risk-free asset, which partially defaults in disasters

Solution without Rare Disasters Solving for the agent’s maximization problem;

Modelling Rare Disasters u t+1 is i.i.d w/ N(0, σ 2 ) σ and γ are known p is the probability of disaster (constant) b is the size of contraction in case of a disaster

Modelling Default Default occurs with probability q when a v-type disaster occurs Default wipes out the fraction d of the return on the government bill Default does not affect equities and real GDP

Solution of the Model - Price Price of one-period equity claim:

Solution of the Model - Returns Expected rate of return on one-period equity: E t (R e t+1 )=E t (A t+1 )/P t1 Return on government bills: (Assumption: d=b)

Solution of the Model - Equity Premium The difference between the two returns: –Increasing in p & θ & b=d –Decreasing in q

Outline The Model Review of economic disasters Calibration Extensions Concluding Remarks

Economic Disasters

Stock and Bill Returns

Outline The Model Review of economic disasters Calibration Extensions Concluding Remarks

Calibration of Disaster Parameters Probability of disasters –60 occurrences for 35 countries over 100 years p = 1.7% Distribution of b from realized contractions Default probability –25 partial defaults out of 60 events q = 40%

Calibration of Other Parameters σ = 0.02 γ = ρ = 0.03 θ = 3 or 4

Calibration Results

What other puzzles can be explained? Why do expected real interest rates fall during wars? –Perceived probability, p, of future economic disaster increases

Outline The Model Review of economic disasters in the twentieth century Calibration Extensions Concluding Remarks

Duration and Capital Formation Main results do not change when we allow for finite and various length disasters When we incorporate capital formation, invested and depreciation, the model still predicts similar equity premium results based on the calibration

Outline The Model Review of economic disasters in the twentieth century Calibration Extensions Concluding Remarks

Low-probability disasters explain the equity premium puzzle along with other asset market puzzles Future research –Incorporate stochastic variations in p Option prices, insurance premiums, prices of gold etc. –Relax i.i.d assumptions