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The Equity Premium and the Risk Free Rate: Matching the Moments

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Author Info
Stephen G. Cecchetti
Pok-sang Lam
Nelson C. Clark

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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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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 3752.

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Date of creation: Jun 1991
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Publication status: published as Journal of Monetary Economics, vol. 31, no. 1, p. 21-46, February 1993
Handle: RePEc:nbr:nberwo:3752

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  1. Newey, Whitney K & West, Kenneth D, 1987. "A Simple, Positive Semi-definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix," Econometrica, Econometric Society, vol. 55(3), pages 703-08, May. [Downloadable!] (restricted)
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  2. Stephen G. Cecchetti & Pok-sang Lam & Nelson C. Mark, 1990. "Mean Reversion in Equilibrium Asset Prices," NBER Working Papers 2762, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  3. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July. [Downloadable!] (restricted)
  4. Andrew B. Abel, 1991. "The equity premium puzzle," Business Review, Federal Reserve Bank of Philadelphia, issue Sep, pages 3-14.
  5. Lee, Bong-Soo & Ingram, Beth Fisher, 1991. "Simulation estimation of time-series models," Journal of Econometrics, Elsevier, vol. 47(2-3), pages 197-205, February. [Downloadable!] (restricted)
  6. James M. Nason, 1988. "The equity premium and time-varying risk behavior," Finance and Economics Discussion Series 11, Board of Governors of the Federal Reserve System (U.S.).
  7. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-84, March. [Downloadable!] (restricted)
  8. Mehra, Rajnish & Prescott, Edward C., 1985. "The equity premium: A puzzle," Journal of Monetary Economics, Elsevier, vol. 15(2), pages 145-161, March. [Downloadable!] (restricted)
  9. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-70, November. [Downloadable!] (restricted)
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  10. Allan W. Gregory & Gregor W. Smith, 1988. "Calibration as Testing, Type I Error in the Equity Premium Puzzle," Working Papers 725, Queen's University, Department of Economics.
  11. Campbell, John Y & Shiller, Robert J, 1987. "Cointegration and Tests of Present Value Models," Journal of Political Economy, University of Chicago Press, vol. 95(5), pages 1062-88, October. [Downloadable!] (restricted)
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  12. Mankiw, N. Gregory, 1986. "The equity premium and the concentration of aggregate shocks," Journal of Financial Economics, Elsevier, vol. 17(1), pages 211-219, September. [Downloadable!] (restricted)
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  13. Grossman, Sanford J. & Shiller, Robert J., 1982. "Consumption correlatedness and risk measurement in economies with non-traded assets and heterogeneous information," Journal of Financial Economics, Elsevier, vol. 10(2), pages 195-210, July. [Downloadable!] (restricted)
  14. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November. [Downloadable!] (restricted)
  15. Sanford J. Grossman & Robert J. Shiller, 1982. "Consumption Correlatedness and Risk Measurement in Economies with Non trade Assets and Heterogeneous Information," NBER Working Papers 0690, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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