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Semiparametric estimation of binary response models with endogenous regressors

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  • Rothe, Christoph

Abstract

In this paper, we propose a two-step semiparametric maximum likelihood (SML) estimator for the coefficients of a single index binary choice model with endogenous regressors when identification is achieved via a control function approach. The first step consists of estimating a reduced form equation for the endogenous regressors and extracting the corresponding residuals. In the second step, the latter are added as control variates to the outcome equation, which is in turn estimated by SML. We establish the estimator's -consistency and asymptotic normality. In a simulation study, we compare the properties of our estimator with those of existing alternatives, highlighting the advantages of our approach.

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  • Rothe, Christoph, 2009. "Semiparametric estimation of binary response models with endogenous regressors," Journal of Econometrics, Elsevier, vol. 153(1), pages 51-64, November.
  • Handle: RePEc:eee:econom:v:153:y:2009:i:1:p:51-64
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    Cited by:

    1. Chernozhukov, Victor & Fernández-Val, Iván & Kowalski, Amanda E., 2015. "Quantile regression with censoring and endogeneity," Journal of Econometrics, Elsevier, vol. 186(1), pages 201-221.
    2. Klein, Roger & Shen, Chan & Vella, Francis, 2015. "Estimation of marginal effects in semiparametric selection models with binary outcomes," Journal of Econometrics, Elsevier, vol. 185(1), pages 82-94.
    3. Zhang, Zhengyu & He, Xiaobo, 2012. "Estimation of a heteroscedastic binary choice model with an endogenous dummy regressor," Economics Letters, Elsevier, vol. 117(3), pages 753-757.
    4. Dong, Yingying, 2010. "Endogenous regressor binary choice models without instruments, with an application to migration," Economics Letters, Elsevier, vol. 107(1), pages 33-35, April.
    5. Schwiebert, Jörg, 2012. "Semiparametric Estimation of a Sample Selection Model in the Presence of Endogeneity," Hannover Economic Papers (HEP) dp-504, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    6. Kinge, Jonas Minet, 2016. "Waist circumference, body mass index and employment outcomes," HERO On line Working Paper Series 2016:4, Oslo University, Health Economics Research Programme.
    7. Xiaofeng Lv & Rui Li, 2013. "Smoothed empirical likelihood analysis of partially linear quantile regression models with missing response variables," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 97(4), pages 317-347, October.
    8. Zhang, Xibin & King, Maxwell L. & Shang, Han Lin, 2014. "A sampling algorithm for bandwidth estimation in a nonparametric regression model with a flexible error density," Computational Statistics & Data Analysis, Elsevier, vol. 78(C), pages 218-234.
    9. Mammen, Enno & Rothe, Christoph & Schienle, Melanie, 2016. "Semiparametric Estimation With Generated Covariates," Econometric Theory, Cambridge University Press, vol. 32(05), pages 1140-1177, October.
    10. Schwiebert, Jörg, 2012. "Semiparametric Estimation of a Binary Choice Model with Sample Selection," Hannover Economic Papers (HEP) dp-505, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    11. Caetano, Carolina & Rothe, Christoph & Yıldız, Neşe, 2016. "A discontinuity test for identification in triangular nonseparable models," Journal of Econometrics, Elsevier, vol. 193(1), pages 113-122.
    12. Xibin Zhang & Maxwell L. King & Han Lin Shang, 2011. "Bayesian estimation of bandwidths for a nonparametric regression model with a flexible error density," Monash Econometrics and Business Statistics Working Papers 10/11, Monash University, Department of Econometrics and Business Statistics.
    13. Matzkin, Rosa L., 2016. "On independence conditions in nonseparable models: Observable and unobservable instruments," Journal of Econometrics, Elsevier, vol. 191(2), pages 302-311.
    14. Gutknecht, Daniel, 2016. "Testing for monotonicity under endogeneity," Journal of Econometrics, Elsevier, vol. 190(1), pages 100-114.
    15. Escanciano, Juan Carlos & Jacho-Chávez, David T. & Lewbel, Arthur, 2014. "Uniform convergence of weighted sums of non and semiparametric residuals for estimation and testing," Journal of Econometrics, Elsevier, vol. 178(P3), pages 426-443.
    16. Kinge, Jonas Minet & Morris, Stephan, 2015. "The impact of childhood obesity on health and health service use: an instrumental variable approach," HERO On line Working Paper Series 2015:2, Oslo University, Health Economics Research Programme.
    17. Fernihough, Alan, 2017. "Less is More? The child quantity-quality trade-off in early 20th century England and Wales," QUCEH Working Paper Series 2017-07, Queen's University Belfast, Queen's University Centre for Economic History.
    18. Bontemps, Christophe & Nauges, Céline, 2017. "Endogenous Variables in Binary Choice Models: Some Insights for Practitioners," TSE Working Papers 17-855, Toulouse School of Economics (TSE).
    19. Halkos, George, 2012. "The use of contingent valuation in assessing marine and coastal ecosystems’ water quality: A review," MPRA Paper 42183, University Library of Munich, Germany.
    20. Roger Klein & Chan Shen & Francis Vella, 2014. "Semiiparametric Selection Models with Binary Outcomes," Departmental Working Papers 201403, Rutgers University, Department of Economics.
    21. Jerome M. Krief, 2011. "Kernel Weighted Smoothed Maximum Score Estimation for Applied Work," Departmental Working Papers 2011-07, Department of Economics, Louisiana State University.
    22. Joakim Westerlund & Per Hjertstrand, 2014. "Indirect Estimation of Semiparametric Binary Choice Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 76(2), pages 298-314, April.

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