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Estimating Euler Equations

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  • Orazio P. Attanasio

    (University College London)

  • Hamish Low

    (University of Cambridge)

Abstract

In this paper we consider conditions under which the estimation of a log-linearized Euler equation for consumption yields consistent estimates of the preference parameters. When utility is isoelastic and a sample covering a long time period is available, consistent estimates are obtained from the log-linearized Euler equation when the innovations to the conditional variance of consumption growth are uncorrelated with the instruments typically used in estimation. We perform a Montecarlo experiment, consisting in solving and simulating a simple life cycle model under uncertainty, and show that in most situations, the estimates obtained from the log-linearized equation are not systematically biased. This is true even when we introduce heteroscedasticity in the process generating income. The only exception is when discount rates are very high (e.g. 47% per year). This problem arises because consumers are nearly always close to the maximum borrowing limit: the estimation bias is unrelated to the linearization and estimates using nonlinear GMM are as bad. Across all our situations, estimation using a log-linearized Euler equation does better than nonlinear GMM. Finally, we plot life cycle profiles for the variance of consumption growth, which, except when the discount factor is very high, is remarkably flat. This implies that claims that demographic variables in log-linearized Euler equations capture changes in the variance of consumption growth are unwarranted. (Copyright: Elsevier)

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File URL: http://dx.doi.org/10.1016/j.red.2003.09.003
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Bibliographic Info

Article provided by Elsevier for the Society for Economic Dynamics in its journal Review of Economic Dynamics.

Volume (Year): 7 (2004)
Issue (Month): 2 (April)
Pages: 405-435

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Handle: RePEc:red:issued:v:7:y:2004:i:2:p:406-435

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References

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  1. 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.
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  15. 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.
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  17. Hansen, Lars Peter & Singleton, Kenneth J, 1983. "Stochastic Consumption, Risk Aversion, and the Temporal Behavior of Asset Returns," Journal of Political Economy, University of Chicago Press, vol. 91(2), pages 249-65, April.
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  22. Keane, Michael P & Runkle, David E, 1992. "On the Estimation of Panel-Data Models with Serial Correlation When Instruments Are Not Strictly Exogenous," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(1), pages 1-9, January.
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