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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

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 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 commonly used to estimate the parameters correct some, but not all, of the approximation bias.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Technical Working Papers with number 0236.

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Date of creation: Mar 1999
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Handle: RePEc:nbr:nberte:0236

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  1. Quantitative Macroeconomics and Real Business Cycles (QM&RBC)
References listed on IDEAS
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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)
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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)
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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)
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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.
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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!]
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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.
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