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Estimating Euler Equations with Noisy Data: Two Exact GMM Estimators

In this paper we exploit the specific structure of the Euler equation and develop two alternative GMM estimators that deal explicitly with measurement error. The first estimator assumes that the measurement error is lognormally distributed. The second estimator drops the distributional assumption and solves out for the unknown, but constant, conditional mean. Our Monte Carlo results suggest that both proposed estimators perform much better than conventional alternatives based on the exact Euler equation or its log-linear approximation, especially with short panels. The empirical application of the proposed estimators yields plausible estimates of the coefficient of relative risk aversion and discount rate.

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Paper provided by University of Oxford, Department of Economics in its series Economics Series Working Papers with number 283.

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Date of creation: 01 Oct 2006
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Handle: RePEc:oxf:wpaper:283
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  1. Attanasio, O.P. & Browning, M., 1993. "Consumption Over the Life Cycle and Over the Business Cycle," Papers 9314, Tilburg - Center for Economic Research.
  2. 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.
  3. J. A. Hausman & W. K. Newey & J. L. Powel, 1988. "Nonlinear Errors in Variables: Estimation of Some Engel Curves," Working papers 504, Massachusetts Institute of Technology (MIT), Department of Economics.
  4. Karen E. Dynan, 2000. "Habit Formation in Consumer Preferences: Evidence from Panel Data," American Economic Review, American Economic Association, vol. 90(3), pages 391-406, June.
  5. 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.
  6. Jerry Hausman, 2001. "Mismeasured Variables in Econometric Analysis: Problems from the Right and Problems from the Left," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 57-67, Fall.
  7. Hall, Robert E & Mishkin, Frederic S, 1982. "The Sensitivity of Consumption to Transitory Income: Estimates from Panel Data on Households," Econometrica, Econometric Society, vol. 50(2), pages 461-81, March.
  8. Runkle, David E., 1991. "Liquidity constraints and the permanent-income hypothesis : Evidence from panel data," Journal of Monetary Economics, Elsevier, vol. 27(1), pages 73-98, February.
  9. Deaton, Angus, 1985. "Panel data from time series of cross-sections," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 109-126.
  10. Hausman, Jerry A. & Newey, Whitney K. & Ichimura, Hidehiko & Powell, James L., 1991. "Identification and estimation of polynomial errors-in-variables models," Journal of Econometrics, Elsevier, vol. 50(3), pages 273-295, December.
  11. Orazio P. Attanasio & Hamish Low, 2000. "Estimating Euler Equations," NBER Technical Working Papers 0253, National Bureau of Economic Research, Inc.
  12. Martin Browning & Annamaria Lusardi, 1995. "Household Saving: Micro Theories and Micro Facts," Department of Economics Working Papers 1995-02, McMaster University.
  13. 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.
  14. Stock, James H & Wright, Jonathan H & Yogo, Motohiro, 2002. "A Survey of Weak Instruments and Weak Identification in Generalized Method of Moments," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(4), pages 518-29, October.
  15. Wansbeek, Tom, 2001. "GMM estimation in panel data models with measurement error," Journal of Econometrics, Elsevier, vol. 104(2), pages 259-268, September.
  16. repec:tpr:qjecon:v:102:y:1987:i:2:p:293-328 is not listed on IDEAS
  17. Amemiya, Yasuo, 1985. "Instrumental variable estimator for the nonlinear errors-in-variables model," Journal of Econometrics, Elsevier, vol. 28(3), pages 273-289, June.
  18. Joseph G. Altonji & Aloysius Siow, 1986. "Testing the Response of Consumption to Income Changes with (Noisy) PanelData," NBER Working Papers 2012, National Bureau of Economic Research, Inc.
  19. Hong, Han & Tamer, Elie, 2003. "A simple estimator for nonlinear error in variable models," Journal of Econometrics, Elsevier, vol. 117(1), pages 1-19, November.
  20. James H. Stock & Jonathan Wright, 2000. "GMM with Weak Identification," Econometrica, Econometric Society, vol. 68(5), pages 1055-1096, September.
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