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Identification and estimation of nonparametric panel data regressions with measurement error

Listed author(s):
  • Daniel Wilhelm

    ()

    (Institute for Fiscal Studies and cemmap and UCL)

This paper provides a constructive argument for identification of nonparametric panel data models with measurement error in a continuous explanatory variable. The approach point identifies all structural elements of the model using only observations of the outcome and the mismeasured explanatory variable; no further external variables such as instruments are required. In the case of two time periods, restricting either the structural or the measurement error to be independent over time allows past explanatory variables or outcomes to serve as instruments. Time periods have to be linked through serial dependence in the latent explanatory variable, but the transition process is left nonparametric. The paper discusses the general identification result in the context of a nonlinear panel data regression model with additively separable fixed effects. It provides a nonparametric plug-in estimator, derives its uniform rate of convergence, and presents simulation evidence for good performance in finite samples.

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File URL: http://www.ifs.org.uk/uploads/cemmap/wps/cwp341515.pdf
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Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP34/15.

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Date of creation: 02 Jul 2015
Handle: RePEc:ifs:cemmap:34/15
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  1. Wansbeek, Tom, 2001. "GMM estimation in panel data models with measurement error," Journal of Econometrics, Elsevier, vol. 104(2), pages 259-268, September.
  2. S. M. Schennach & Yingyao Hu, 2013. "Nonparametric Identification and Semiparametric Estimation of Classical Measurement Error Models Without Side Information," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(501), pages 177-186, March.
  3. S. Darolles & Y. Fan & J. P. Florens & E. Renault, 2011. "Nonparametric Instrumental Regression," Econometrica, Econometric Society, vol. 79(5), pages 1541-1565, 09.
  4. Yingyao Hu & Ji-Liang Shiu, 2011. "Nonparametric identification using instrumental variables: sufficient conditions for completeness," CeMMAP working papers CWP25/11, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  5. Khan, Shakeeb & Ponomareva, Maria & Tamer, Elie, 2016. "Identification of panel data models with endogenous censoring," Journal of Econometrics, Elsevier, vol. 194(1), pages 57-75.
  6. Andrews, Donald W.K., 1995. "Nonparametric Kernel Estimation for Semiparametric Models," Econometric Theory, Cambridge University Press, vol. 11(03), pages 560-586, June.
  7. Denis Chetverikov & Daniel Wilhelm, 2015. "Nonparametric instrumental variable estimation under monotonicity," Papers 1507.05270, arXiv.org.
  8. Qian, Junhui & Wang, Le, 2012. "Estimating semiparametric panel data models by marginal integration," Journal of Econometrics, Elsevier, vol. 167(2), pages 483-493.
  9. Johannes, Jan & Van Bellegem, Sébastien & Vanhems, Anne, 2011. "Convergence Rates For Ill-Posed Inverse Problems With An Unknown Operator," Econometric Theory, Cambridge University Press, vol. 27(03), pages 522-545, June.
  10. Carrasco, Marine & Florens, Jean-Pierre, 2011. "A Spectral Method For Deconvolving A Density," Econometric Theory, Cambridge University Press, vol. 27(03), pages 546-581, June.
  11. Galvao Jr, A. F. & Montes-Rojas, G., 2009. "Instrumental variables quantile regression for panel data with measurement errors," Working Papers 09/06, Department of Economics, City University London.
  12. Barnett, Steven A. & Sakellaris, Plutarchos, 1998. "Nonlinear response of firm investment to Q:: Testing a model of convex and non-convex adjustment costs1," Journal of Monetary Economics, Elsevier, vol. 42(2), pages 261-288, July.
  13. Aasness, Jorgen & Biorn, Erik & Skjerpen, Terje, 1993. "Engel Functions, Panel Data, and Latent Variables," Econometrica, Econometric Society, vol. 61(6), pages 1395-1422, November.
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