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Asymptotic Normality Of A Nonparametric Instrumental Variables Estimator

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  • Joel L. Horowitz

Abstract

This article gives conditions under which the nonparametric instrumental variables estimator of Hall and Horowitz ("Annals of Statistics" 33 (December 2005), 2904-2929) is asymptotically normally distributed. With sufficiently large samples, the asymptotic normality result can be used to form confidence intervals for the unknown function that is estimated by the Hall-Horowitz procedure. The article reports the results of a Monte Carlo investigation of the finite-sample coverage probabilities of the confidence intervals. Copyright 2007 by the Economics Department Of The University Of Pennsylvania And Osaka University Institute Of Social And Economic Research Association.

Suggested Citation

  • 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.
  • Handle: RePEc:ier:iecrev:v:48:y:2007:i:4:p:1329-1349
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    Citations

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    Cited by:

    1. 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 1-27, October.
    2. repec:wyi:journl:002112 is not listed on IDEAS
    3. Xiaohong Chen & Demian Pouzo, 2013. "Sieve Wald and QLR Inferences on Semi/nonparametric Conditional Moment Models," Cowles Foundation Discussion Papers 1897R, Cowles Foundation for Research in Economics, Yale University, revised Apr 2014.
    4. Xiaohong Chen & Demian Pouzo, 2013. "Sieve Quasi Likelihood Ratio Inference on Semi/nonparametric Conditional Moment Models," Cowles Foundation Discussion Papers 1897, Cowles Foundation for Research in Economics, Yale University.
    5. Fève, Frédérique & Florens, Jean-Pierre, 2014. "Non parametric analysis of panel data models with endogenous variables," Journal of Econometrics, Elsevier, vol. 181(2), pages 151-164.
    6. Horowitz, Joel L. & Lee, Sokbae, 2012. "Uniform confidence bands for functions estimated nonparametrically with instrumental variables," Journal of Econometrics, Elsevier, vol. 168(2), pages 175-188.
    7. Santos, Andres, 2011. "Instrumental variable methods for recovering continuous linear functionals," Journal of Econometrics, Elsevier, vol. 161(2), pages 129-146, April.
    8. Carolina Caetano & Juan Carlos Escaniano, 2015. "Identifying Multiple Marginal Effects with a Single Binary Instrument or by Regression Discontinuity," Caepr Working Papers 2015-009 Classification-C, Center for Applied Economics and Policy Research, Economics Department, Indiana University Bloomington.
    9. Fabian Dunker, 2015. "Convergence of the risk for nonparametric IV quantile regression and nonparametric IV regression with full independence," Papers 1511.03977, arXiv.org.
    10. Joel L. Horowitz, 2013. "Ill-posed inverse problems in economics," CeMMAP working papers CWP37/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    11. Kaspar Wüthrich, 2014. "A Comparison of two Quantile Models with Endogeneity," Diskussionsschriften dp1408, Universitaet Bern, Departement Volkswirtschaft.
    12. S. Darolles & Y. Fan & J. P. Florens & E. Renault, 2011. "Nonparametric Instrumental Regression," Econometrica, Econometric Society, vol. 79(5), pages 1541-1565, September.
    13. Liao, Yuan & Jiang, Wenxin, 2011. "Posterior consistency of nonparametric conditional moment restricted models," MPRA Paper 38700, University Library of Munich, Germany.
    14. Joel L. Horowitz, 2013. "Adaptive nonparametric instrumental variables estimation: empirical choice of the regularization parameter," CeMMAP working papers CWP30/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    15. Xiaohong Chen & Demian Pouzo, 2014. "Sieve Wald and QLR Inferences on Semi/nonparametric Conditional Moment Models," Papers 1411.1144, arXiv.org, revised Mar 2015.
    16. Gagliardini, Patrick & Scaillet, Olivier, 2012. "Tikhonov regularization for nonparametric instrumental variable estimators," Journal of Econometrics, Elsevier, vol. 167(1), pages 61-75.
    17. Victor Chernozhukov & Whitney K. Newey & Andres Santos, 2015. "Constrained conditional moment restriction models," CeMMAP working papers CWP59/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    18. Chen, Xiaohong, 2007. "Large Sample Sieve Estimation of Semi-Nonparametric Models," Handbook of Econometrics,in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 76 Elsevier.
    19. Xiaohong Chen & Demian Pouzo, 2014. "Sieve Wald and QLR Inferences on Semi/nonparametric Conditional Moment Models," CeMMAP working papers CWP38/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    20. Zongwu Cai & Qi Li, 2013. "Some Recent Develop- ments on Nonparametric Econometrics," WISE Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    21. Xiaohong Chen & Demian Pouzo, 2013. "Sieve Wald and QLR Inferences on Semi/nonparametric Conditional Moment Models," Cowles Foundation Discussion Papers 1897RR, Cowles Foundation for Research in Economics, Yale University, revised Nov 2014.
    22. Cazals, Catherine & Fève, Frédérique & Florens, Jean-Pierre & Simar, Léopold, 2016. "Nonparametric instrumental variables estimation for efficiency frontier," Journal of Econometrics, Elsevier, vol. 190(2), pages 349-359.
    23. Horowitz, Joel L., 2014. "Adaptive nonparametric instrumental variables estimation: Empirical choice of the regularization parameter," Journal of Econometrics, Elsevier, vol. 180(2), pages 158-173.

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