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Identification and estimation by penalization in nonparametric instrumental regression

  • FLORENS, Jean-Pierre
  • JOHANNES, Jan
  • VAN BELLEGEM, Sébastien

    (Université catholique de Louvain (UCL). Center for Operations Research and Econometrics (CORE))

The nonparametric estimation of a regression function x from conditional moment restrictions involving instrumental variables is considered. The rate of convergence of penalized estimators is studied in the case where x is not identified from the conditional moment restriction. We also study the gain of modifying the penalty in the estimation, considering for instance a Sobolev-type of penalty. We analyze the effect of this modification on the rate of convergence of the estimator and on the identification of the regression function x.

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Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2007085.

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Date of creation: 01 Oct 2007
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Handle: RePEc:cor:louvco:2007085
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  1. Jean‐Pierre Florens & Jan Johannes & Sébastien Van Bellegem, 2012. "Instrumental regression in partially linear models," Econometrics Journal, Royal Economic Society, vol. 15(2), pages 304-324, 06.
  2. Rosa L. Matzkin, 2003. "Nonparametric Estimation of Nonadditive Random Functions," Econometrica, Econometric Society, vol. 71(5), pages 1339-1375, 09.
  3. Xiaohong Chen & Markus Reiss, 2007. "On Rate Optimality for Ill-posed Inverse Problems in Econometrics," Cowles Foundation Discussion Papers 1626, Cowles Foundation for Research in Economics, Yale University.
  4. Richard Blundell & Joel Horowitz, 2004. "A nonparametric test of exogeneity," CeMMAP working papers CWP15/04, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  5. Richard Blundell & Xiaohong Chen & Dennis Kristensen, 2007. "Semi-Nonparametric IV Estimation of Shape-Invariant Engel Curves," Econometrica, Econometric Society, vol. 75(6), pages 1613-1669, November.
  6. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, 09.
  7. Joel L. Horowitz & Sokbae Lee, 2007. "Nonparametric Instrumental Variables Estimation of a Quantile Regression Model," Econometrica, Econometric Society, vol. 75(4), pages 1191-1208, 07.
  8. Victor Chernozhukov & Christian Hansen, 2005. "An IV Model of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 73(1), pages 245-261, 01.
  9. Das, M., 2005. "Instrumental variables estimators of nonparametric models with discrete endogenous regressors," Journal of Econometrics, Elsevier, vol. 124(2), pages 335-361, February.
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