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Nonparametric Instrumental Variable Estimation of Binary Response Models

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  • Samuele Centorrino
  • Jean-Pierre Florens

Abstract

We present an instrumental variable approach to the nonparametric estimation of binary response models with endogenous independent variables. We achieve nonparametric identification up to a scale via the reduced form model constructed from the decomposition of the unobserved dependent variable into the space of the instruments and we suppose the disturbances in this model to be stochastically independent of the instrumental variables. For estimation purposes, we approximate the fully nonparametric model by a sequence of locally weighted parametric ones. This approach simplifies the estimation procedure and it is robust to local model misspecification. We prove consistency of this estimator and run a simulation study to corroborate its small sample properties. We also show how to construct interesting policy parameters. We conclude the paper with an empirical illustration of female labor force participation in the US, where we showcase the implementation of our approach and we compare it with existing semiparametric estimators.

Suggested Citation

  • Samuele Centorrino & Jean-Pierre Florens, 2014. "Nonparametric Instrumental Variable Estimation of Binary Response Models," Department of Economics Working Papers 14-07, Stony Brook University, Department of Economics.
  • Handle: RePEc:nys:sunysb:14-07
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    References listed on IDEAS

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    1. 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.
    2. 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.
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    4. Chen, Xiaohong & Reiss, Markus, 2011. "On Rate Optimality For Ill-Posed Inverse Problems In Econometrics," Econometric Theory, Cambridge University Press, vol. 27(03), pages 497-521, June.
    5. 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, June.
    6. Kleibergen, Frank & Paap, Richard, 2006. "Generalized reduced rank tests using the singular value decomposition," Journal of Econometrics, Elsevier, vol. 133(1), pages 97-126, July.
    7. Hengartner, Nicolas W. & Sperlich, Stefan, 2005. "Rate optimal estimation with the integration method in the presence of many covariates," Journal of Multivariate Analysis, Elsevier, vol. 95(2), pages 246-272, August.
    8. Matzkin, Rosa L, 1991. "Semiparametric Estimation of Monotone and Concave Utility Functions for Polychotomous Choice Models," Econometrica, Econometric Society, vol. 59(5), pages 1315-1327, September.
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    11. JOHANNES, Jan & VAN BELLEGEM, Sébastien & VANHEMS, Anne, 2010. "Iterative regularization in nonparametric instrumental regression," CORE Discussion Papers 2010055, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    12. Klein, Roger W & Spady, Richard H, 1993. "An Efficient Semiparametric Estimator for Binary Response Models," Econometrica, Econometric Society, vol. 61(2), pages 387-421, March.
    13. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-531, May.
    14. Carrasco, Marine & Florens, Jean-Pierre & Renault, Eric, 2007. "Linear Inverse Problems in Structural Econometrics Estimation Based on Spectral Decomposition and Regularization," Handbook of Econometrics,in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 77 Elsevier.
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    16. Joel L. Horowitz, 2011. "Applied Nonparametric Instrumental Variables Estimation," Econometrica, Econometric Society, vol. 79(2), pages 347-394, March.
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