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Instrumental Variable Treatment of Nonclassical Measurement Error Models

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  • Yingyao Hu
  • Susanne M. Schennach

Abstract

While the literature on nonclassical measurement error traditionally relies on the availability of an auxiliary data set containing correctly measured observations, we establish that the availability of instruments enables the identification of a large class of nonclassical nonlinear errors-in-variables models with continuously distributed variables. Our main identifying assumption is that, conditional on the value of the true regressors, some "measure of location" of the distribution of the measurement error (e.g., its mean, mode, or median) is equal to zero. The proposed approach relies on the eigenvalue-eigenfunction decomposition of an integral operator associated with specific joint probability densities. The main identifying assumption is used to "index" the eigenfunctions so that the decomposition is unique. We propose a convenient sieve-based estimator, derive its asymptotic properties, and investigate its finite-sample behavior through Monte Carlo simulations. Copyright The Econometric Society 2008.

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Bibliographic Info

Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 76 (2008)
Issue (Month): 1 (01)
Pages: 195-216

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Handle: RePEc:ecm:emetrp:v:76:y:2008:i:1:p:195-216

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  1. Whitney K. Newey, 2001. "Flexible Simulated Moment Estimation Of Nonlinear Errors-In-Variables Models," The Review of Economics and Statistics, MIT Press, vol. 83(4), pages 616-627, November.
  2. Li, Tong, 2002. "Robust and consistent estimation of nonlinear errors-in-variables models," Journal of Econometrics, Elsevier, vol. 110(1), pages 1-26, September.
  3. John Bound & Alan B. Krueger, 1989. "The Extent of Measurement Error In Longitudinal Earnings Data: Do Two Wrongs Make A Right?," NBER Working Papers 2885, National Bureau of Economic Research, Inc.
  4. Arthur Lewbel, 2003. "Estimation of Average Treatment Effects With Misclassification," Boston College Working Papers in Economics 556, Boston College Department of Economics, revised 04 Sep 2006.
  5. Xiaohong Chen & Xiaotong Shen, 1998. "Sieve Extremum Estimates for Weakly Dependent Data," Econometrica, Econometric Society, vol. 66(2), pages 289-314, March.
  6. Chernozhukov, Victor & Imbens, Guido W. & Newey, Whitney K., 2007. "Instrumental variable estimation of nonseparable models," Journal of Econometrics, Elsevier, vol. 139(1), pages 4-14, July.
  7. Susanne M Schennach, 2007. "Instrumental Variable Estimation of Nonlinear Errors-in-Variables Models," Econometrica, Econometric Society, vol. 75(1), pages 201-239, 01.
  8. 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.
  9. 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.
  10. Susanne M. Schennach, 2004. "Estimation of Nonlinear Models with Measurement Error," Econometrica, Econometric Society, vol. 72(1), pages 33-75, 01.
  11. Xiaohong Chen & Han Hong & Elie Tamer, 2005. "Measurement Error Models with Auxiliary Data," Review of Economic Studies, Oxford University Press, vol. 72(2), pages 343-366.
  12. Stefan Hoderlein & Enno Mammen, 2007. "Identification of Marginal Effects in Nonseparable Models Without Monotonicity," Econometrica, Econometric Society, vol. 75(5), pages 1513-1518, 09.
  13. Bollinger, Christopher R, 1998. "Measurement Error in the Current Population Survey: A Nonparametric Look," Journal of Labor Economics, University of Chicago Press, vol. 16(3), pages 576-94, July.
  14. Schennach, Susanne M., 2004. "Nonparametric Regression In The Presence Of Measurement Error," Econometric Theory, Cambridge University Press, vol. 20(06), pages 1046-1093, December.
  15. Andrew Chesher, 2001. "Parameter approximations for quantile regressions with measurement error," CeMMAP working papers CWP02/01, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  16. Karim Chalak & Halbert White, 2007. "An Extended Class of Instrumental Variables for the Estimation of Causal Effects," Boston College Working Papers in Economics 692, Boston College Department of Economics, revised 30 Nov 2009.
  17. Arthur Lewbel, 1998. "Semiparametric Latent Variable Model Estimation with Endogenous or Mismeasured Regressors," Econometrica, Econometric Society, vol. 66(1), pages 105-122, January.
  18. Chesher, Andrew & Dumangane, Montezuma & Smith, Richard J., 2002. "Duration response measurement error," Journal of Econometrics, Elsevier, vol. 111(2), pages 169-194, December.
  19. Aprajit Mahajan, 2006. "Identification and Estimation of Regression Models with Misclassification," Econometrica, Econometric Society, vol. 74(3), pages 631-665, 05.
  20. Joel L. Horowitz, 2006. "Testing a Parametric Model Against a Nonparametric Alternative with Identification Through Instrumental Variables," Econometrica, Econometric Society, vol. 74(2), pages 521-538, 03.
  21. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, 09.
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