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Approximation bias in linearized Euler equations

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Author Info
Sydney Ludvigson
Christina H. Paxson

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Abstract

This paper concerns pitfalls associated with the use of approximations to dynamic Euler equations. Two applications of the approximations are notable. First, tests for precautionary saving motives typically involve regressing consumption growth on uncertainty in expected consumption growth. The parameter estimates are used to measure the strength of precautionary motives, which is also related to the coefficient of relative risk aversion. Another application estimates the sensitivity of consumption growth to the expected real interest rate, with the coefficient on the latter equal to the intertemporal elasticity of substitution in consumption, often the inverse of the coefficient of relative risk aversion. The two literatures yield very different estimates of how prudent or risk averse consumers are or, alternatively, how willing they are to substitute consumption over time. We investigate one possible reason for these apparently contradictory results: both methods of estimation rely on linear approximations of Euler equations. We demonstrate that biases associated with these approximations can be substantial, and that the direction of the biases is consistent with the divergent estimates found in the literature.

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Paper provided by Federal Reserve Bank of New York in its series Research Paper with number 9712.

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Date of creation: 1997
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Handle: RePEc:fip:fednrp:9712

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Keywords: Saving and investment ; Consumption (Economics) ; Interest rates ; Forecasting;

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  1. Quantitative Macroeconomics and Real Business Cycles (QM&RBC)
References listed on IDEAS
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  1. Carroll, Christopher D & Kimball, Miles S, 1996. "On the Concavity of the Consumption Function," Econometrica, Econometric Society, vol. 64(4), pages 981-92, July. [Downloadable!] (restricted)
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  2. Attanasio, Orazio P & Weber, Guglielmo, 1993. "Consumption Growth, the Interest Rate and Aggregation," Review of Economic Studies, Blackwell Publishing, vol. 60(3), pages 631-49, July. [Downloadable!] (restricted)
  3. Hall, Robert E, 1988. "Intertemporal Substitution in Consumption," Journal of Political Economy, University of Chicago Press, vol. 96(2), pages 339-57, April. [Downloadable!] (restricted)
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  4. Campbell, John Y, 1993. "Intertemporal Asset Pricing without Consumption Data," American Economic Review, American Economic Association, vol. 83(3), pages 487-512, June. [Downloadable!] (restricted)
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  5. 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.
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  6. Sydney Ludvigson, 1996. "Consumption and credit: a model of time-varying liquidity constraints," Research Paper 9624, Federal Reserve Bank of New York. [Downloadable!]
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  7. John Y. Campbell & N. Gregory Mankiw, 1989. "Consumption, Income and Interest Rates: Reinterpreting the Time Series Evidence," NBER Chapters, in: NBER Macroeconomics Annual 1989, Volume 4, pages 185-246 National Bureau of Economic Research, Inc. [Downloadable!]
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  8. 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. [Downloadable!] (restricted)
  9. 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.).
  10. Pischke, Jorn-Steffen, 1995. "Individual Income, Incomplete Information, and Aggregate Consumption," Econometrica, Econometric Society, vol. 63(4), pages 805-40, July. [Downloadable!] (restricted)
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  11. Guiso, Luigi & Jappelli, Tullio & Terlizzese, Daniele, 1992. "Earnings uncertainty and precautionary saving," Journal of Monetary Economics, Elsevier, vol. 30(2), pages 307-337, November. [Downloadable!] (restricted)
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  12. Zeldes, Stephen P, 1989. "Optimal Consumption with Stochastic Income: Deviations from Certainty Equivalence," The Quarterly Journal of Economics, MIT Press, vol. 104(2), pages 275-98, May. [Downloadable!] (restricted)
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  13. 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.).
  14. Tony S. Wirjanto, 1995. "Aggregate Consumption Behaviour and Liquidity Constraints: The Canadian Evidence," Canadian Journal of Economics, Canadian Economics Association, vol. 28(4b), pages 1135-52, November.
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  15. 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. [Downloadable!] (restricted)
  16. Skinner, Jonathan, 1988. "Risky income, life cycle consumption, and precautionary savings," Journal of Monetary Economics, Elsevier, vol. 22(2), pages 237-255, September. [Downloadable!] (restricted)
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  17. Campbell, John Y & Deaton, Angus, 1989. "Why Is Consumption So Smooth?," Review of Economic Studies, Blackwell Publishing, vol. 56(3), pages 357-73, July. [Downloadable!] (restricted)
  18. Kuehlwein, Michael, 1991. "A test for the presence of precautionary saving," Economics Letters, Elsevier, vol. 37(4), pages 471-475, December. [Downloadable!] (restricted)
  19. Zeldes, Stephen P, 1989. "Consumption and Liquidity Constraints: An Empirical Investigation," Journal of Political Economy, University of Chicago Press, vol. 97(2), pages 305-46, April. [Downloadable!] (restricted)
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  20. 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. [Downloadable!] (restricted)
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  21. Orazio P. Attanasio & James Banks & Costas Meghir & Guglielmo Weber, 1995. "Humps and Bumps in Lifetime Consumption," NBER Working Papers 5350, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  22. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January. [Downloadable!] (restricted)
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  23. 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.
  24. 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. [Downloadable!] (restricted)
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  25. Abowd, John M & Card, David, 1989. "On the Covariance Structure of Earnings and Hours Changes," Econometrica, Econometric Society, vol. 57(2), pages 411-45, March. [Downloadable!] (restricted)
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  26. 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(1998-1), pages 91-196. [Downloadable!]
  27. Deaton, Angus, 1991. "Saving and Liquidity Constraints," Econometrica, Econometric Society, vol. 59(5), pages 1221-48, September. [Downloadable!] (restricted)
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  28. repec:fth:harver:1435 is not listed on IDEAS
  29. Christopher D. Carroll, 1997. "Death to the Log-Linearized Consumption Euler Equation! (And Very Poor Health to the Second-Order Approximation)," NBER Working Papers 6298, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  30. Deaton, A. & Grosh, M., 1998. "Consumption," Papers 191, Princeton, Woodrow Wilson School - Development Studies.
  31. 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. [Downloadable!] (restricted)
  32. Dynan, Karen E, 1993. "How Prudent Are Consumers?," Journal of Political Economy, University of Chicago Press, vol. 101(6), pages 1104-13, December. [Downloadable!] (restricted)
  33. 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. [Downloadable!] (restricted)
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