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Estimating Euler equations

  • Orazio Attanasio

    ()

    (Institute for Fiscal Studies and University College London)

  • Hamish Low

    ()

    (Institute for Fiscal Studies and Trinity College, Cambridge)

In this paper we consider conditions under which the estimation of a log-linearized Euler equation for consumption yields consistent estimates of 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 despite the absence of measurement error. 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.

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Paper provided by Institute for Fiscal Studies in its series IFS Working Papers with number W02/06.

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Length: 82 pp
Date of creation: Mar 2002
Date of revision:
Handle: RePEc:ifs:ifsewp:02/06
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  1. Orazio P. Attanasio & James Banks & Sarah Tanner, 2002. "Asset Holding and Consumption Volatility," Journal of Political Economy, University of Chicago Press, vol. 110(4), pages 771-792, August.
  2. 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.
  3. Hansen, Lars Peter & Singleton, Kenneth J, 1996. "Efficient Estimation of Linear Asset-Pricing Models with Moving Average Errors," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(1), pages 53-68, January.
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  6. Deaton, A., 1989. "Saving And Liquidity Constraints," Papers 153, Princeton, Woodrow Wilson School - Public and International Affairs.
  7. Pierre-Olivier Gourinchas & Jonathan A. Parker, 2002. "Consumption Over the Life Cycle," Econometrica, Econometric Society, vol. 70(1), pages 47-89, January.
  8. Richard Blundell & Martin Browning & Costas Meghir, 1993. "Consumer demand and the life-cycle allocation of household expenditures," IFS Working Papers W93/11, Institute for Fiscal Studies.
  9. 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.
  10. 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.
  11. 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.
  12. Tauchen, George & Hussey, Robert, 1991. "Quadrature-Based Methods for Obtaining Approximate Solutions to Nonlinear Asset Pricing Models," Econometrica, Econometric Society, vol. 59(2), pages 371-96, March.
  13. Attanasio, Orazio P & Browning, Martin, 1995. "Consumption over the Life Cycle and over the Business Cycle," American Economic Review, American Economic Association, vol. 85(5), pages 1118-37, December.
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  15. Orazio P. Attanasio, 1998. "Consumption Demand," NBER Working Papers 6466, National Bureau of Economic Research, Inc.
  16. Sumru Altug & Robert A. Miller, 1987. "Household choices in equilibrium," Working Papers 341, Federal Reserve Bank of Minneapolis.
  17. Den Haan, Wouter J & Marcet, Albert, 1994. "Accuracy in Simulations," Review of Economic Studies, Wiley Blackwell, vol. 61(1), pages 3-17, January.
  18. Hansen, Lars Peter & Heaton, John & Yaron, Amir, 1996. "Finite-Sample Properties of Some Alternative GMM Estimators," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 262-80, July.
  19. Browning, Martin & Deaton, Angus & Irish, Margaret, 1985. "A Profitable Approach to Labor Supply and Commodity Demands over the Life-Cycle," Econometrica, Econometric Society, vol. 53(3), pages 503-43, May.
  20. Orazio Attanasio & James Banks & Costas Meghir & Guglielmo Weber, 1995. "Humps and bumps in lifetime consumption," IFS Working Papers W95/14, Institute for Fiscal Studies.
  21. Costas Meghir & Luigi Pistaferri, 2001. "Income variance dynamics and heterogenity," IFS Working Papers W01/07, Institute for Fiscal Studies.
  22. 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.).
  23. Fumio Hayashi, 1985. "Tests for Liquidity Constraints: A Critical Survey," NBER Working Papers 1720, National Bureau of Economic Research, Inc.
  24. Martin Browning & Mette Ejrnæs, 2009. "Consumption and Children," The Review of Economics and Statistics, MIT Press, vol. 91(1), pages 93-111, February.
  25. Chamberlain, Gary, 1984. "Panel data," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 22, pages 1247-1318 Elsevier.
  26. Dynan, Karen E, 1993. "How Prudent Are Consumers?," Journal of Political Economy, University of Chicago Press, vol. 101(6), pages 1104-13, December.
  27. 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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