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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 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 Technolog

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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. Quantitative Macroeconomics and Real Business Cycles (QM&RBC)
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  6. John Y. Campbell & N. Gregory Mankiw, 1990. "Consumption, Income, and Interest Rates: Reinterpreting the Time Series Evidence," NBER Working Papers 2924, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  9. 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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  16. 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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  18. repec:fth:harver:1435 is not listed on IDEAS
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  23. 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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  24. 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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  26. 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)
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  28. 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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  29. 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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  30. 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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