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Non Parametric Instrumental Regression

  • Darolles, Serge
  • Fan, Yanqin
  • Florens, Jean-Pierre
  • Renault, Eric

The focus of the paper is the nonparametric estimation of an instrumental regression function ϕ defined by conditional moment restrictions stemming from a structural econometric model: E [Y − ϕ (Z) | W] = 0, and involving endogenous variables Y and Z and instruments W . The function ϕ is the solution of an ill-posed inverse problem and we propose an estimation procedure based on Tikhonov regularization. The paper analyses identification and overidentification of this model and presents asymptotic properties of the estimated nonparametric instrumental regression function.

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Paper provided by Institut d'Économie Industrielle (IDEI), Toulouse in its series IDEI Working Papers with number 228.

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Date of creation: 2003
Date of revision: 2010
Publication status: Published in Econometrica, vol.�79, n°5, septembre 2011, p.�1541-1565.
Handle: RePEc:ide:wpaper:1034
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  1. Rothe, Christoph, 2010. "Nonparametric estimation of distributional policy effects," Journal of Econometrics, Elsevier, vol. 155(1), pages 56-70, March.
  2. Florens, J.P. & Mouchart, M. & Rolin, J.M., 1993. "Noncausality and Marginalization of Markov Processes," Econometric Theory, Cambridge University Press, vol. 9(02), pages 241-262, April.
  3. Xiaohong Chen & Markus Reiss, 2007. "On rate optimality for ill-posed inverse problems in econometrics," CeMMAP working papers CWP20/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  4. Florens, Jean-Pierre & Johannes, Jan & Van Bellegem, Sébastien, 2009. "Instrumental Regression in Partially Linear Models," IDEI Working Papers 613, Institut d'Économie Industrielle (IDEI), Toulouse.
  5. Richard Blundell & Joel L. Horowitz, 2007. "A Non-Parametric Test of Exogeneity," Review of Economic Studies, Oxford University Press, vol. 74(4), pages 1035-1058.
  6. JOHANNES, Jan & VAN BELLEGHEM, Sébastien & VANHEMS, Anne, 2007. "A unified approach to solve ill-posed inverse problems in econometrics," CORE Discussion Papers 2007083, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. Abadie, Alberto, 2003. "Semiparametric instrumental variable estimation of treatment response models," Journal of Econometrics, Elsevier, vol. 113(2), pages 231-263, April.
  8. Florens, Jean-Pierre & Johannes, Jan & Van Bellegem, Sébastien, 2011. "Identification And Estimation By Penalization In Nonparametric Instrumental Regression," Econometric Theory, Cambridge University Press, vol. 27(03), pages 472-496, June.
  9. 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.
  10. Hansen, Bruce E., 2008. "Uniform Convergence Rates For Kernel Estimation With Dependent Data," Econometric Theory, Cambridge University Press, vol. 24(03), pages 726-748, June.
  11. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
  12. Whitney K. Newey & Fushing Hsieh & James M. Robins, 2004. "Twicing Kernels and a Small Bias Property of Semiparametric Estimators," Econometrica, Econometric Society, vol. 72(3), pages 947-962, 05.
  13. Amemiya, Takeshi, 1974. "The nonlinear two-stage least-squares estimator," Journal of Econometrics, Elsevier, vol. 2(2), pages 105-110, July.
  14. Imbens, Guido W & Angrist, Joshua D, 1994. "Identification and Estimation of Local Average Treatment Effects," Econometrica, Econometric Society, vol. 62(2), pages 467-75, March.
  15. P. Gagliardini & O. Scaillet, 2006. "Tikhonov Regularization for Functional Minimum Distance Estimators," Swiss Finance Institute Research Paper Series 06-30, Swiss Finance Institute, revised Nov 2006.
  16. Amemiya, Takeshi, 1975. "The nonlinear limited-information maximum- likelihood estimator and the modified nonlinear two-stage least-squares estimator," Journal of Econometrics, Elsevier, vol. 3(4), pages 375-386, November.
  17. Joel L. Horowitz, 2007. "Asymptotic Normality Of A Nonparametric Instrumental Variables Estimator," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(4), pages 1329-1349, November.
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