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Semiparametric Estimation of a Binary Choice Model with Sample Selection

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  • Schwiebert, Jörg

Abstract

In this paper we provide semiparametric estimation strategies for a sample selection model with a binary dependent variable. To the best of our knowledge, this has not been done before. We propose a control function approach based on two di erent identifying assumptions. This gives rise to semiparametric estimators which are extensions of the Klein and Spady (1993), maximum score (Manski, 1975) and smoothed maximum score (Horowitz, 1992) estimators. We provide Monte Carlo evidence and an empirical example to study the nite sample properties of our estimators. Finally, we outline an extension of these estimators to the case of endogenous covariates.

Suggested Citation

  • Schwiebert, Jörg, 2012. "Semiparametric Estimation of a Binary Choice Model with Sample Selection," Hannover Economic Papers (HEP) dp-505, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    • Handle: RePEc:han:dpaper:dp-505
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    References listed on IDEAS

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    1. Richard W. Blundell & James L. Powell, 2004. "Endogeneity in Semiparametric Binary Response Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 71(3), pages 655-679.
    2. Xiaohong Chen & Oliver Linton & Ingrid Van Keilegom, 2003. "Estimation of Semiparametric Models when the Criterion Function Is Not Smooth," Econometrica, Econometric Society, vol. 71(5), pages 1591-1608, September.
    3. Manski, Charles F, 1987. "Semiparametric Analysis of Random Effects Linear Models from Binary Panel Data," Econometrica, Econometric Society, vol. 55(2), pages 357-362, March.
    4. Ekaterini Kyriazidou, 1997. "Estimation of a Panel Data Sample Selection Model," Econometrica, Econometric Society, vol. 65(6), pages 1335-1364, November.
    5. Manski, Charles F. & Thompson, T. Scott, 1986. "Operational characteristics of maximum score estimation," Journal of Econometrics, Elsevier, vol. 32(1), pages 85-108, June.
    6. Manski, Charles F., 1975. "Maximum score estimation of the stochastic utility model of choice," Journal of Econometrics, Elsevier, vol. 3(3), pages 205-228, August.
    7. Meng, Chun-Lo & Schmidt, Peter, 1985. "On the Cost of Partial Observability in the Bivariate Probit Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(1), pages 71-85, February.
    8. Xiaohong Chen & Oliver Linton & Ingred van Keilegom, 2002. "Estimation of semiparametric models when the criterion function is not smooth," CeMMAP working papers 02/02, Institute for Fiscal Studies.
    9. Rothe, Christoph, 2009. "Semiparametric estimation of binary response models with endogenous regressors," Journal of Econometrics, Elsevier, vol. 153(1), pages 51-64, November.
    10. Whitney K. Newey, 2009. "Two-step series estimation of sample selection models," Econometrics Journal, Royal Economic Society, vol. 12(s1), pages 217-229, January.
    11. Manski, Charles F., 1985. "Semiparametric analysis of discrete response : Asymptotic properties of the maximum score estimator," Journal of Econometrics, Elsevier, vol. 27(3), pages 313-333, March.
    12. Van de Ven, Wynand P. M. M. & Van Praag, Bernard M. S., 1981. "The demand for deductibles in private health insurance : A probit model with sample selection," Journal of Econometrics, Elsevier, vol. 17(2), pages 229-252, November.
    13. Ahn, Hyungtaik & Powell, James L., 1993. "Semiparametric estimation of censored selection models with a nonparametric selection mechanism," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 3-29, July.
    14. William H. Greene, 1992. "A Statistical Model for Credit Scoring," Working Papers 92-29, New York University, Leonard N. Stern School of Business, Department of Economics.
    15. Boyes, William J. & Hoffman, Dennis L. & Low, Stuart A., 1989. "An econometric analysis of the bank credit scoring problem," Journal of Econometrics, Elsevier, vol. 40(1), pages 3-14, January.
    16. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-531, May.
    17. Madhu Mohanty, 2002. "A bivariate probit approach to the determination of employment: a study of teen employment differentials in Los Angeles County," Applied Economics, Taylor & Francis Journals, vol. 34(2), pages 143-156.
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    Cited by:

    1. Hans Fricke & Markus Frölich & Martin Huber & Michael Lechner, 2020. "Endogeneity and non‐response bias in treatment evaluation – nonparametric identification of causal effects by instruments," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(5), pages 481-504, August.

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    More about this item

    Keywords

    Sample selection model; binary dependent variable; semiparametric estimation; control function approach; endogenous covariates;
    All these keywords.

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation

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