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Nonparametric Instrumental Regression

Author Info

  • DAROLLES, Serge
  • FLORENS, Jean-Pierre
  • RENAULT, Éric

Abstract

The focus of the paper is the nonparametric estimation of an instrumental regression function P defined by conditional moment restrictions stemming from a structural econometric model : E[Y-P(Z)|W]=0 and involving endogenous variables Y and Z and instruments W. The function P 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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File URL: http://hdl.handle.net/1866/373
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Paper provided by Universite de Montreal, Departement de sciences economiques in its series Cahiers de recherche with number 2002-05.

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Length: 39 pages
Date of creation: 2002
Date of revision:
Handle: RePEc:mtl:montde:2002-05
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Keywords: instrumental variables; integral equation; ill-sed oblem; Tikhonov regularization; Kernel smoothing;

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Find related papers by JEL classification:
  • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
  • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General

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  1. 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.
  2. 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.
  3. Frédérique Fève & Jean-Pierre Florens, 2010. "The practice of non-parametric estimation by solving inverse problems: the example of transformation models," Econometrics Journal, Royal Economic Society, vol. 13(3), pages S1-S27, October.
  4. 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.
  5. 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).
  6. FLORENS, Jean-Pierre & JOHANNES, Jan & VAN BELLEGEM, Sébastien, 2007. "Identification and estimation by penalization in nonparametric instrumental regression," CORE Discussion Papers 2007085, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. FLORENS, Jean-Pierre & JOHANNES, Jan & VAN BELLEGEM, Sébastien, 2006. "Instrumental regression in partially linear models," CORE Discussion Papers 2006025, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  8. Joshua D. Angrist & Guido W. Imbens, 1995. "Identification and Estimation of Local Average Treatment Effects," NBER Technical Working Papers 0118, National Bureau of Economic Research, Inc.
  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. 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.
  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. Abadie, Alberto, 2003. "Semiparametric instrumental variable estimation of treatment response models," Journal of Econometrics, Elsevier, vol. 113(2), pages 231-263, April.
  13. 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.
  14. 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.
  15. Amemiya, Takeshi, 1974. "The nonlinear two-stage least-squares estimator," Journal of Econometrics, Elsevier, vol. 2(2), pages 105-110, July.
  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. 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.
  18. Rothe, Christoph, 2010. "Nonparametric estimation of distributional policy effects," Journal of Econometrics, Elsevier, vol. 155(1), pages 56-70, March.
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