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A new methodology for studying the equity premium

Abstract

This paper provides a new framework for the derivation and estimation of consumption and equity premium functions. Applying duality in a dynamic context, we show that equity premium and consumption functions can be easily obtained from the indirect utility function. Our new framework, therefore, does not require explicit specification of underlying consumer preferences.

Using aggregate US data (1929–2000) we estimate the consumption and equity premium functions using a nonparametric technique. We find that the model does well in explaining the observed smooth consumption patterns and does reasonably well in explaining the high mean and volatility of equity premia.

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References

  • Alvarez, F., & Jermann, U. J. (2000). Using asset prices to measure the cost of business cycles (Mimeo). University of Chicago.

  • Appelbaum, E. (1997). Duality in production theory under uncertainty (Discussion Paper). York University.

  • Appelbaum, E. (2006). A framework for empirical applications of production theory expected utility. Journal of Economics and Business, 58(4), 290–303.

    Article  Google Scholar 

  • Appelbaum, E., & Ullah, A. (1997). Estimation of moments and production decisions under uncertainty. Review of Economics and Statistics.

  • Baillie, R. T., & Myers, R. J. (1991). Bivariate GARCH estimation of optimal commodity futures hedge. Journal of Applied Econometrics, 16, 109–124.

    Article  Google Scholar 

  • Basu, P. (1993). Mean reversion in GNP and stock prices: an adjustment cost hypothesis. Kyklos, 46(1), 87–104.

    Article  Google Scholar 

  • Basu, P., Semenov, A., & Wada, K. (2008). Uninsurable risk and financial market puzzles (Working Paper). Durham University.

  • Bera, A. K., & Higgins, M. L. (1993). Arch models: properties, estimation and testing. Journal of Economic Surveys, 7, 307–366.

    Article  Google Scholar 

  • Berg, C. (1963). Topological spaces. New York: MacMillan. Translated by Patterson.

    Google Scholar 

  • Bollerslev, T., Engle, R. F., & Wooldridge, J. M. (1988). A capital asset pricing model with time-varying covariances. Journal of Political Economy, 96, 116–131.

    Article  Google Scholar 

  • Campbell, J. Y. (1994a). Intertemporal asset prices without consumption data. American Economic Review, 83(3), 487–512.

    Google Scholar 

  • Campbell, J. Y. (1994b). Inspecting the mechanism: an analytical approach to stochastic growth models. Journal of Monetary Economics, 33(3), 463–506.

    Article  Google Scholar 

  • Campbell, J. Y., Lo, A., & Mackinlay, C. (1997). Econometrics of financial markets. Princeton: Princeton University Press.

    Google Scholar 

  • Cochrane, J., & Hansen, L. (1992). Asset pricing explorations in macroeconomics. In NBER macroeconomics annual 1992 (pp. 115–165). Cambridge: MIT Press.

    Google Scholar 

  • Deaton, A., & Muellbauer, J. (1992). Economics and consumer behavior. Cambridge: Cambridge University Press.

    Google Scholar 

  • Engle, R. F., Granger, C. W. J., & Kraft, D. F. (1984). Combining competing forecasts of inflation using a bivariate ARCH model. Journal of Economic Dynamics and Control, 8, 151–165.

    Article  Google Scholar 

  • Epstein, L. G., & Zin, S. E. (1991). Substitution, risk aversion, and the temporal behavior of consumption and asset returns: an empirical analysis. Journal of Political Economy, 99, 263–286.

    Article  Google Scholar 

  • Fan, J., & Gijbels, I. (1996). Local polynomial modelling and its applications. London: Chapman and Hall.

    Google Scholar 

  • Faugère, C., & Van Erlach, J. (2006). The equity premium: consistent with GDP growth and portfolio insurance. Financial Review, 41(4), 547–564.

    Article  Google Scholar 

  • Geweke, J. (2001). A note on some limitations of CRRA utility. Economics Letters, 71, 341–345.

    Article  Google Scholar 

  • Hansen, L. P. (1982). Large sample properties of generalized method of moments estimators. Econometrica, 50(3), 1029–1054.

    Article  Google Scholar 

  • Hansen, L. P., & Jagannathan, R. (1991). Implications of security market data for models of dynamic economies. Journal of Political Economy, 99, 225–262.

    Article  Google Scholar 

  • Ibbotson Associates (2002). Stocks, bonds and inflation—2002 yearbook. Chicago: Ibbotson

    Google Scholar 

  • Jagannathan, R., McGrattan, E. R., & Scherbina, A. (2000). The declining U.S. equity premium. Federal Reserve Bank of Minneapolis Quarterly Review, 24(4), 3–19.

    Google Scholar 

  • Kendall, M. G. (1969). The advanced theory of statistics (Vol. 1). New York: Hafner.

    Google Scholar 

  • Kocherlakota, N. R. (1996). The equity premium: it’s still a puzzle. Journal of Economic Literature, 34, 42–71.

    Google Scholar 

  • Kocherlakota, N. R., & Pistaferri, L. (2007). Asset pricing implications of Pareto optimality with private information (Working Paper). University of Minnesota.

  • Kreps, D. M., & Porteus, E. L. (1978). Temporal resolution of uncertainty and dynamic choice theory. Econometrica, 46, 185–200.

    Article  Google Scholar 

  • Lettau, M., & Uhlig, H. (2002). Sharpe ratio and preferences: a parametric approach. Macroeconomic Dynamics, 6(2), 242–265.

    Article  Google Scholar 

  • Machina, M. (1984). Temporal risk and induced preferences. Journal of Economic Theory, 33, 199–231.

    Article  Google Scholar 

  • Mass-Collel, A., Whinston, M. D., & Green, J. R. (1995). Microeconomic theory. London: Oxford University Press.

    Google Scholar 

  • McGrattan, E. R., & Prescott, E. C. (2001). Taxes, regulations, and asset prices (Working Paper 610). Federal Reserve Bank of Minneapolis.

  • Mehra, R. (2003). The equity premium: why is it a puzzle? Financial Analysts Journal, 59(1), 54–69.

    Article  Google Scholar 

  • Mehra, R., & Prescott, E. C. (1985). The equity premium puzzle. Journal of Monetary Economics, 24, 401–421.

    Google Scholar 

  • Pagan, A., & Ullah, A. (1999). Nonparametric econometrics. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • Racine, J. (2003). Portable nonparametric kernel estimation version 1.7.1. Department of Economic, Syracuse University.

  • Reitz, T. (1988). The equity risk premium: a solution? Journal of Monetary Economics, 21, 117–132.

    Article  Google Scholar 

  • Roll, R., & Ross, S. A. (1983). An empirical investigation of arbitrage pricing theory. Journal of Finance, 35, 1073–1104.

    Article  Google Scholar 

  • Santos, M. (1991). Smoothness of the policy function in discrete time economic models. Econometrica, 59(5), 1365–1382.

    Article  Google Scholar 

  • Singh, R. S., & Tracy, D. S. (1977). Strongly consistent estimators of k-th order regression curves and rates of convergence. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, 40, 339–348.

    Article  Google Scholar 

  • Singleton, J. C., & Wingender, J. (1986). Skewness persistence in common stock returns. Journal of Financial and Quantitative Analysis, 335–341.

  • Treynor, J. I. (1994). The invisible cost of trading. Journal of Portfolio Management, 21, 71–78.

    Article  Google Scholar 

  • Ullah, A. (1988). Non-parametric estimation of econometric functionals. Canadian Journal of Economics, 21, 3.

    Google Scholar 

  • Wilks, S. S. (1964). Mathematical statistics. New York: Wiley.

    Google Scholar 

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Correspondence to Elie Appelbaum.

Additional information

We wish to thank the two referees for this journal and M. Tavas for their helpful comments and suggestions. We also wish to thank J. Racine for his help with the non-parametric estimation.

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Appelbaum, E., Basu, P. A new methodology for studying the equity premium. Ann Oper Res 176, 109–126 (2010). https://doi.org/10.1007/s10479-008-0484-1

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  • DOI: https://doi.org/10.1007/s10479-008-0484-1

Keywords

  • Consumption function
  • Equity premium
  • Moments