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Euler Equation Estimation on Micro Data

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Author Info

  • Sule Alan

    ()
    (Koc University and University of Cambridge)

  • Kadir Atalay

    (University of Sydney)

  • Thomas F. Crossley

    (Koc University, University of Cambridge and Institute for Fiscal Studies, London)

Abstract

First order conditions from the dynamic optimization problems of consumers and firms are important tools in empirical macroeconomics. When estimated on micro-data these equations are typically linearized so standard IV or GMM methods can be employed to deal with the measurement error that is endemic to survey data. However, it has recently been argued that the approximation bias induced by linearization may be worse than the problems that linearization is intended to solve. This paper explores this issue in the context of consumption Euler equations. These equations form the basis of estimates of key macroeconomic parameters: the elasticity of inter-temporal substitution (EIS) and relative prudence. We numerically solve and simulate 6 different life-cycle models, and then use the simulated data as the basis for a series of Monte Carlo experiments in which we consider the validity and relevance of conventional instruments, the consequences of different data sampling schemes, and the effectiveness of alternative estimation strategies. The first-order Euler equation leads to biased estimates of the EIS, but that bias is perhaps not too large when there is a sufficient time dimension to the data, and sufficient variation in interest rates. A sufficient time dimension can only realistically be achieved with a synthetic cohort. Estimates are unlikely to be very precise. Bias will be worse the more impatient agents are. The second order Euler equation suffers from a weak instrument problem and offers no advantage over the first-order approximation.

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Bibliographic Info

Paper provided by Koc University-TUSIAD Economic Research Forum in its series Koç University-TUSIAD Economic Research Forum Working Papers with number 1221.

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Length: 45 pages
Date of creation: Aug 2012
Date of revision:
Handle: RePEc:koc:wpaper:1221

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Keywords: Euler Equations; Measurement Error; Instrumental Variables; GMM.;

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References

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  1. Altug, Sumru & Miller, Robert A, 1990. "Household Choices in Equilibrium," Econometrica, Econometric Society, vol. 58(3), pages 543-70, May.
  2. Jinyong Hahn & Jerry Hausman & Guido Kuersteiner, 2004. "Estimation with weak instruments: Accuracy of higher-order bias and MSE approximations," Econometrics Journal, Royal Economic Society, vol. 7(1), pages 272-306, 06.
  3. Attanasio, Orazio P & Weber, Guglielmo, 1995. "Is Consumption Growth Consistent with Intertemporal Optimization? Evidence from the Consumer Expenditure Survey," Journal of Political Economy, University of Chicago Press, vol. 103(6), pages 1121-57, December.
  4. Amemiya, Yasuo, 1985. "Instrumental variable estimator for the nonlinear errors-in-variables model," Journal of Econometrics, Elsevier, vol. 28(3), pages 273-289, June.
  5. repec:bla:restud:v:77:y:2010:i:4:p:1231-1261 is not listed on IDEAS
  6. M. Fatih Guvenen, 2002. "Reconciling Conflicting Evidence on the Elasticity of Intertemporal Substitution: A Macroeconomic Perspective," RCER Working Papers 491, University of Rochester - Center for Economic Research (RCER), revised Mar 2003.
  7. Sule Alan & Orazio Attanasio & Martin Browning, 2005. "Estimating Euler Equations with Noisy Data: Two Exact GMM Estimators," CAM Working Papers 2005-10, University of Copenhagen. Department of Economics. Centre for Applied Microeconometrics.
  8. Deaton, Angus, 1985. "Panel data from time series of cross-sections," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 109-126.
  9. Michael P. Murray, 2006. "Avoiding Invalid Instruments and Coping with Weak Instruments," Journal of Economic Perspectives, American Economic Association, vol. 20(4), pages 111-132, Fall.
  10. Thomas F. Crossley & Hamish Low & Matthew Wakefield, 2009. "The Economics of a Temporary VAT Cut," Fiscal Studies, Institute for Fiscal Studies, vol. 30(1), pages 3-16, 03.
  11. Sule Alan & Martin Browning, 2003. "Estimating Intertemporal Allocation Parameters using Simulated Residual Estimation," CAM Working Papers 2003-03, University of Copenhagen. Department of Economics. Centre for Applied Microeconometrics.
  12. Moulton, Brent R., 1986. "Random group effects and the precision of regression estimates," Journal of Econometrics, Elsevier, vol. 32(3), pages 385-397, August.
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