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Approximation bias in linearized Euler equations

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  • Sydney Ludvigson
  • Christina H. Paxson

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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Bibliographic Info

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. Dynan, Karen E, 1993. "How Prudent Are Consumers?," Journal of Political Economy, University of Chicago Press, vol. 101(6), pages 1104-13, December.
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  3. Carroll Christopher Dixon, 2001. "Death to the Log-Linearized Consumption Euler Equation! (And Very Poor Health to the Second-Order Approximation)," The B.E. Journal of Macroeconomics, De Gruyter, vol. 1(1), pages 1-38, April.
  4. John Y. Campbell, 1992. "Intertemporal Asset Pricing Without Consumption Data," NBER Working Papers 3989, National Bureau of Economic Research, Inc.
  5. Phillippe Weil, 1997. "The Equity Premium Puzzle and the Risk-Free Rate Puzzle," Levine's Working Paper Archive 1833, David K. Levine.
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  7. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
  8. Jonathan S. Skinner, 1987. "Risky Income, Life Cycle Consumption, and Precautionary Savings," NBER Working Papers 2336, National Bureau of Economic Research, Inc.
  9. Pischke, Jorn-Steffen, 1995. "Individual Income, Incomplete Information, and Aggregate Consumption," Econometrica, Econometric Society, vol. 63(4), pages 805-40, July.
  10. Giucca, P. & Jappelli, T. & Terlizzese, D., 1992. "Earning Uncertainty and Precautionary Saving," Papers 161, Banca Italia - Servizio di Studi.
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  12. Orazio Attanasio & James Banks & Costas Meghir & Guglielmo Weber, 1995. "Humps and bumps in lifetime consumption," IFS Working Papers W95/14, Institute for Fiscal Studies.
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  21. 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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  23. Stephen Zeldes, . "Consumption and Liquidity Constraints: An Empirical Investigation," Rodney L. White Center for Financial Research Working Papers 24-85, Wharton School Rodney L. White Center for Financial Research.
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  26. 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.
  27. Kuehlwein, Michael, 1991. "A test for the presence of precautionary saving," Economics Letters, Elsevier, vol. 37(4), pages 471-475, December.
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  29. Attanasio, Orazio P & Weber, Guglielmo, 1993. "Consumption Growth, the Interest Rate and Aggregation," Review of Economic Studies, Wiley Blackwell, vol. 60(3), pages 631-49, July.
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  32. repec:fth:harver:1435 is not listed on IDEAS
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