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The equity premium and the risk-free rate: matching the moments

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  • S.G. Cecchetti
  • P. Lam
  • N.C. Mark

Abstract

This paper investigates the ability of a representative agent model with time separable utility to explain the mean vector and the covariance matrix of the risk free interest rate and the return to leveraged equity in the stock market. The paper generalizes the standard calibration methodology by accounting for the uncertainty in both the sample moments to be explained and the estimated parameters to which the model is calibrated. We develop a testing framework to evaluate the model's ability to match the moments of the data. We study two forms of the model, both of which treat leverage in a manner consistent with the data. In the first, dividends explicitly represent the flow that accrues to the owner of the equity, and they are discounted by the marginal rate of intertemporal substitution defined over consumption. The second form of the model introduces bonds and treats equities as the residual claim to the total endowment stream. We find that the first moments of the data can be matched for a wide range of preference parameter values. But for both models the implied first and second moments taken together are always statistically significantly different from the data at standard levels. This last result contrasts sharply with other recent treatments of leverage in the literature.

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Bibliographic Info

Paper provided by David K. Levine in its series Levine's Working Paper Archive with number 1396.

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Date of creation: 09 Dec 2010
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Handle: RePEc:cla:levarc:1396

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References

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  1. N. Gregory Mankiw, 1986. "The Equity Premium and the Concentration of Aggregate Shocks," NBER Working Papers 1788, National Bureau of Economic Research, Inc.
  2. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, Econometric Society, vol. 50(4), pages 1029-54, July.
  3. Epstein, Larry G. & Zin, Stanley E., 1990. "'First-order' risk aversion and the equity premium puzzle," Journal of Monetary Economics, Elsevier, Elsevier, vol. 26(3), pages 387-407, December.
  4. John Y. Campbell & Robert J. Shiller, 1986. "Cointegration and Tests of Present Value Models," NBER Working Papers 1885, National Bureau of Economic Research, Inc.
  5. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, Econometric Society, vol. 46(6), pages 1429-45, November.
  6. Andrew B. Abel, 1991. "The equity premium puzzle," Business Review, Federal Reserve Bank of Philadelphia, Federal Reserve Bank of Philadelphia, issue Sep, pages 3-14.
  7. Sanford J. Grossman & Robert J. Shiller, 1981. "Consumption Correlatedness and Risk Measurement in Economies with Non trade Assets and Heterogeneous Information," NBER Working Papers 0690, National Bureau of Economic Research, Inc.
  8. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, Econometric Society, vol. 57(2), pages 357-84, March.
  9. Newey, Whitney K & West, Kenneth D, 1987. "A Simple, Positive Semi-definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix," Econometrica, Econometric Society, Econometric Society, vol. 55(3), pages 703-08, May.
  10. Allan W. Gregory & Gregor W. Smith, 1988. "Calibration as Testing, Type I Error in the Equity Premium Puzzle," Working Papers, Queen's University, Department of Economics 725, Queen's University, Department of Economics.
  11. Mehra, Rajnish & Prescott, Edward C., 1985. "The equity premium: A puzzle," Journal of Monetary Economics, Elsevier, Elsevier, vol. 15(2), pages 145-161, March.
  12. Lee, Bong-Soo & Ingram, Beth Fisher, 1991. "Simulation estimation of time-series models," Journal of Econometrics, Elsevier, Elsevier, vol. 47(2-3), pages 197-205, February.
  13. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, Econometric Society, vol. 50(6), pages 1345-70, November.
  14. Pamela A. Labadie, 1988. "The effects of stochastic inflation on asset prices," Discussion Paper / Institute for Empirical Macroeconomics, Federal Reserve Bank of Minneapolis 5, Federal Reserve Bank of Minneapolis.
  15. Cecchetti, Stephen G & Lam, Pok-sang & Mark, Nelson C, 1990. "Mean Reversion in Equilibrium Asset Prices," American Economic Review, American Economic Association, American Economic Association, vol. 80(3), pages 398-418, June.
  16. James M. Nason, 1988. "The equity premium and time-varying risk behavior," Finance and Economics Discussion Series, Board of Governors of the Federal Reserve System (U.S.) 11, Board of Governors of the Federal Reserve System (U.S.).
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