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Euler Equation Errors

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  • Sydney C. Ludvigson

    ()
    (Economics New York University)

  • Martin Lettau

Abstract

Among the most important pieces of empirical evidence against the standard representative-agent, consumption-based asset pricing paradigm are the formidable unconditional Euler equation errors the model produces for a broad stock market index return and short-term interest rate. Unconditional Euler equation errors are also large for a broader cross-section of returns. Here we ask whether calibrated leading asset pricing models – specifically developed to address empirical puzzles associated with the standard paradigm – explain these empirical facts. We find that, in many cases, they do not. We present several results. First, we show that if the true pricing kernel that sets the unconditional Euler equation errors to zero is jointly lognormally distributed with aggregate consumption and returns, then values for the subjective discount factor and relative risk aversion can always be found for which the standard model generates identical unconditional asset pricing implications for two asset returns, a risky and risk-free asset. Second, we show, using simulated data from several leading asset pricing frameworks, that many economic models share this property even though in those models the pricing kernel, returns, and consumption are not jointly lognormally distributed. Third, in contrast to the above results, we provide an example of a limited participation/incomplete markets model that is broadly consistent with these empirical facts.

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Bibliographic Info

Paper provided by Society for Economic Dynamics in its series 2005 Meeting Papers with number 487.

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Date of creation: 2005
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Handle: RePEc:red:sed005:487

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  1. R. Mehra & E. Prescott, 2010. "The equity premium: a puzzle," Levine's Working Paper Archive 1401, David K. Levine.
  2. Guo, Hui, 2004. "Limited Stock Market Participation and Asset Prices in a Dynamic Economy," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 39(03), pages 495-516, September.
  3. Stephen Gordon & Pascal St-Amour, 2003. "Asset Returns and State-Dependent Risk Preferences," CIRANO Working Papers 2003s-09, CIRANO.
  4. Ravi Bansal & Amir Yaron, 2000. "Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles," NBER Working Papers 8059, National Bureau of Economic Research, Inc.
  5. Lior Menzly & Tano Santos & Pietro Veronesi, 2004. "Understanding Predictability," Journal of Political Economy, University of Chicago Press, vol. 112(1), pages 1-47, February.
  6. Lettau, Martin & Ludvigson, Sydney C., 2005. "Expected returns and expected dividend growth," Journal of Financial Economics, Elsevier, vol. 76(3), pages 583-626, June.
  7. Fatih Guvenen, 2005. "A Parsimonious Macroeconomic Model for Asset Pricing: Habit Formation of Cross-sectional Heterogeneity?," Finance 0507009, EconWPA.
  8. John Y. Campbell & John H. Cochrane, 1994. "By force of habit: a consumption-based explanation of aggregate stock market behavior," Working Papers 94-17, Federal Reserve Bank of Philadelphia.
  9. Philippe Weil, 1989. "The Equity Premium Puzzle and the Riskfree Rate Puzzle," NBER Working Papers 2829, National Bureau of Economic Research, Inc.
  10. Lettau, Martin & Ludvigson, Sydney, 2005. "Euler Equation Errors," CEPR Discussion Papers 5245, C.E.P.R. Discussion Papers.
  11. Angelo Melino & Alan X. Yang, 2003. "State Dependent Preferences Can Explain the Equity Premium Puzzle," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 6(4), pages 806-830, October.
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  13. Ravi Jagannathan & Yong Wang, 2005. "Consumption Risk and the Cost of Equity Capital," NBER Working Papers 11026, National Bureau of Economic Research, Inc.
  14. Kocherlakota, Narayana R, 1990. " Disentangling the Coefficient of Relative Risk Aversion from the Elasticity of Intertemporal Substitution: An Irrelevance Result," Journal of Finance, American Finance Association, vol. 45(1), pages 175-90, March.
  15. Sydney Ludvigson, 1999. "Consumption And Credit: A Model Of Time-Varying Liquidity Constraints," The Review of Economics and Statistics, MIT Press, vol. 81(3), pages 434-447, August.
  16. Tim W. Cogley & Thomas J. Sargent, 2005. "The Market Price of Risk and the Equity Premium," Working Papers 522, University of California, Davis, Department of Economics.
  17. Campbell, John Y., 2003. "Consumption-based asset pricing," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 13, pages 803-887 Elsevier.
  18. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  19. Hansen, Lars Peter & Singleton, Kenneth J, 1982. "Generalized Instrumental Variables Estimation of Nonlinear Rational Expectations Models," Econometrica, Econometric Society, vol. 50(5), pages 1269-86, September.
  20. Heaton, John & Lucas, Deborah J, 1996. "Evaluating the Effects of Incomplete Markets on Risk Sharing and Asset Pricing," Journal of Political Economy, University of Chicago Press, vol. 104(3), pages 443-87, June.
  21. Luttmer, Erzo G J, 1996. "Asset Pricing in Economies with Frictions," Econometrica, Econometric Society, vol. 64(6), pages 1439-67, November.
  22. Cogley, Timothy & Sargent, Thomas J., 2008. "The market price of risk and the equity premium: A legacy of the Great Depression?," Journal of Monetary Economics, Elsevier, vol. 55(3), pages 454-476, April.
  23. Epstein, Larry G & Zin, Stanley E, 1989. "Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: A Theoretical Framework," Econometrica, Econometric Society, vol. 57(4), pages 937-69, July.
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Cited by:
  1. Sydney Ludvigson, 2008. "The Research Agenda: Sydney Ludvigson on Empirical Evaluation of Economic Theories of Risk Premia," EconomicDynamics Newsletter, Review of Economic Dynamics, vol. 9(2), April.
  2. Lettau, Martin & Ludvigson, Sydney, 2005. "Euler Equation Errors," CEPR Discussion Papers 5245, C.E.P.R. Discussion Papers.
  3. George M. Constantinides & Anisha Ghosh, 2008. "Asset Pricing Tests with Long Run Risks in Consumption Growth," NBER Working Papers 14543, National Bureau of Economic Research, Inc.
  4. Howitt, Peter, 2012. "What have central bankers learned from modern macroeconomic theory?," Journal of Macroeconomics, Elsevier, vol. 34(1), pages 11-22.
  5. Raghu Suryanarayanan, 2006. "Implications of Anticipated Regret and Endogenous Beliefs for Equilibrium Asset Prices: A Theoretical Framework," CSEF Working Papers 162, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
  6. Saziye Gaziog-super-˜lu & Azize Bastıyalı-Hayfavi, 2010. "Stochastic optimization applied to self-financing portfolio: does bequest matter?," Applied Economics, Taylor & Francis Journals, vol. 42(30), pages 3831-3838.
  7. Ravi Bansal & A. Ronald Gallant & George Tauchen, 2007. "Rational Pessimism, Rational Exuberance, and Asset Pricing Models," NBER Working Papers 13107, National Bureau of Economic Research, Inc.

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