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Approximation Bias In Linearized Euler Equations

  • Sydney Ludvigson
  • Christina H. Paxson

A wide range of empirical applications rely on linear approximations to dynamic Euler equations. Among the most notable of these is the large and growing literature on precautionary saving that examines how consumption growth and saving behavior are affected by uncertainty and prudence. Linear approximations to Euler equations imply a linear relationship between expected consumption growth and uncertainty in consumption growth, with a slope coefficient that is a function of the coefficient of relative prudence. This literature has produced puzzling results: estimates of the coefficient of relative prudence (and the coefficient of relative risk aversion) from linear regressions of consumption growth on uncertainty in consumption growth imply estimates of prudence and risk aversion that are unrealistically low. Using numerical solutions to a fairly standard intertemporal optimization problem, our results show that the actual relationship between expected consumption growth and uncertainty in consumption growth differs substantially from the relationship implied by a linear approximation. We also present Monte Carlo evidence that shows that the instrumental-variables methods that are commonly used to estimate the parameters correct some, but not all, of the approximation bias. © 2001 by the President and Fellows of Harvard College and the Massachusetts Institute of Technology

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Article provided by MIT Press in its journal The Review of Economics and Statistics.

Volume (Year): 83 (2001)
Issue (Month): 2 (May)
Pages: 242-256

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Handle: RePEc:tpr:restat:v:83:y:2001:i:2:p:242-256
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  1. Christopher D Carroll, 1997. "Death to the Log-Linearized Consumption euler Equation! (And Very Poor Health to the Second-Order Approximation)," Economics Working Paper Archive 390, The Johns Hopkins University,Department of Economics.
  2. Weil, Philippe, 1989. "The equity premium puzzle and the risk-free rate puzzle," Journal of Monetary Economics, Elsevier, vol. 24(3), pages 401-421, November.
  3. Christopher D. Carroll, 1991. "Buffer stock saving and the permanent income hypothesis," Working Paper Series / Economic Activity Section 114, Board of Governors of the Federal Reserve System (U.S.).
  4. Lusardi, Annamaria, 1996. "Permanent Income, Current Income, and Consumption: Evidence from Two Panel Data Sets," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(1), pages 81-90, January.
  5. Deaton, Angus, 1991. "Saving and Liquidity Constraints," Econometrica, Econometric Society, vol. 59(5), pages 1221-48, September.
  6. Miles S. Kimball, 1989. "Precautionary Saving in the Small and in the Large," NBER Working Papers 2848, National Bureau of Economic Research, Inc.
  7. Campbell, John, 1993. "Intertemporal Asset Pricing Without Consumption Data," Scholarly Articles 3221491, Harvard University Department of Economics.
  8. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-57, August.
  9. MaCurdy, Thomas E., 1982. "The use of time series processes to model the error structure of earnings in a longitudinal data analysis," Journal of Econometrics, Elsevier, vol. 18(1), pages 83-114, January.
  10. Campbell, John & Deaton, Angus, 1989. "Why Is Consumption So Smooth?," Scholarly Articles 3221494, Harvard University Department of Economics.
  11. John Y. Campbell & N. Gregory Mankiw, 1989. "Consumption, Income, and Interest Rates: Reinterpreting the Time Series Evidence," NBER Working Papers 2924, National Bureau of Economic Research, Inc.
  12. Sydney Ludvigson, 1996. "Consumption and credit: a model of time-varying liquidity constraints," Research Paper 9624, Federal Reserve Bank of New York.
  13. Fama, Eugene F & French, Kenneth R, 1988. "Permanent and Temporary Components of Stock Prices," Journal of Political Economy, University of Chicago Press, vol. 96(2), pages 246-73, April.
  14. Pischke, Jorn-Steffen, 1995. "Individual Income, Incomplete Information, and Aggregate Consumption," Econometrica, Econometric Society, vol. 63(4), pages 805-40, July.
  15. Giucca, P. & Jappelli, T. & Terlizzese, D., 1992. "Earning Uncertainty and Precautionary Saving," Papers 161, Banca Italia - Servizio di Studi.
  16. Philip Merrigan & Michel Normandin, 1994. "Precautionary Saving Motives: An Assessment from U.K. Time Series of Cross-Sections," Cahiers de recherche CREFE / CREFE Working Papers 29, CREFE, Université du Québec à Montréal.
  17. David I. Laibson & Andrea Repetto & Jeremy Tobacman, 1998. "Self-Control and Saving for Retirement," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 29(1), pages 91-196.
  18. Stephen Zeldes, . "Consumption and Liquidity Constraints: An Empirical Investigation," Rodney L. White Center for Financial Research Working Papers 24-85, Wharton School Rodney L. White Center for Financial Research.
  19. Attanasio, Orazio P, et al, 1999. "Humps and Bumps in Lifetime Consumption," Journal of Business & Economic Statistics, American Statistical Association, vol. 17(1), pages 22-35, January.
  20. John M. Abowd & David Card, 1986. "On the Covariance Structure of Earnings and Hours Changes," NBER Working Papers 1832, National Bureau of Economic Research, Inc.
  21. repec:fth:harver:1435 is not listed on IDEAS
  22. Stephen Zeldes, . "Optimal Consumption with Stochastic Income: Deviations from Certainty Equivalence," Rodney L. White Center for Financial Research Working Papers 20-86, Wharton School Rodney L. White Center for Financial Research.
  23. Wirjanto, T.S., 1993. "Aggregate Consumption Behavior and Liquidity Constraints: The Canadian Evidence," Working Papers 9315, University of Waterloo, Department of Economics.
  24. Epstein, Larry G & Zin, Stanley E, 1991. "Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: An Empirical Analysis," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 263-86, April.
  25. Dynan, Karen E, 1993. "How Prudent Are Consumers?," Journal of Political Economy, University of Chicago Press, vol. 101(6), pages 1104-13, December.
  26. Carroll, Christopher D & Kimball, Miles S, 1996. "On the Concavity of the Consumption Function," Econometrica, Econometric Society, vol. 64(4), pages 981-92, July.
  27. Deaton, Angus, 1992. "Understanding Consumption," OUP Catalogue, Oxford University Press, number 9780198288244, March.
  28. Attanasio, Orazio P & Weber, Guglielmo, 1993. "Consumption Growth, the Interest Rate and Aggregation," Review of Economic Studies, Wiley Blackwell, vol. 60(3), pages 631-49, July.
  29. Kuehlwein, Michael, 1991. "A test for the presence of precautionary saving," Economics Letters, Elsevier, vol. 37(4), pages 471-475, December.
  30. Carroll, Christopher D, 1994. "How Does Future Income Affect Current Consumption?," The Quarterly Journal of Economics, MIT Press, vol. 109(1), pages 111-47, February.
  31. Robert E. Hall, 1981. "Intertemporal Substitution in Consumption," NBER Working Papers 0720, National Bureau of Economic Research, Inc.
  32. 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.
  33. Jonathan S. Skinner, 1987. "Risky Income, Life Cycle Consumption, and Precautionary Savings," NBER Working Papers 2336, National Bureau of Economic Research, Inc.
  34. Karen E. Dynan, 1993. "How prudent are consumers?," Working Paper Series / Economic Activity Section 135, Board of Governors of the Federal Reserve System (U.S.).
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