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Approximation bias in linearized Euler equations

  • Sydney Ludvigson
  • Christina H. Paxson

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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  1. 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.
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  12. 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.
  13. Merrigan, Philip & Normandin, Michel, 1996. "Precautionary Saving Motives: An Assessment from UK Time Series of Cross-Sections," Economic Journal, Royal Economic Society, vol. 106(438), pages 1193-1208, September.
  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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  26. repec:fth:harver:1435 is not listed on IDEAS
  27. Campbell, John, 1993. "Intertemporal Asset Pricing Without Consumption Data," Scholarly Articles 3221491, Harvard University Department of Economics.
  28. 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.
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  30. 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.
  31. 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.
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