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Semiparametric Estimation Of A Heteroskedastic Sample Selection Model

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  • Chen, Songnian
  • Khan, Shakeeb

Abstract

This paper considers estimation of a sample selection model subject to conditional heteroskedasticity in both the selection and outcome equations. The form of heteroskedasticity allowed for in each equation is multiplicative, and each of the two scale functions is left unspecified. A three-step estimator for the parameters of interest in the outcome equation is proposed. The first two stages involve nonparametric estimation of the “propensity score” and the conditional interquartile range of the outcome equation, respectively. The third stage reweights the data so that the conditional expectation of the reweighted dependent variable is of a partially linear form, and the parameters of interest are estimated by an approach analogous to that adopted in Ahn and Powell (1993, Journal of Econometrics 58, 3–29). Under standard regularity conditions the proposed estimator is shown to be -consistent and asymptotically normal, and the form of its limiting covariance matrix is derived.We are grateful to B. Honoré, R. Klein, E. Kyriazidou, L.-F. Lee, J. Powell, two anonymous referees, and the co-editor D. Andrews and also to seminar participants at Princeton, Queens, UCLA, and the University of Toronto for helpful comments. Chen's research was supported by RGC grant HKUST 6070/01H from the Research Grants Council of Hong Kong.

Suggested Citation

  • Chen, Songnian & Khan, Shakeeb, 2003. "Semiparametric Estimation Of A Heteroskedastic Sample Selection Model," Econometric Theory, Cambridge University Press, vol. 19(6), pages 1040-1064, December.
    • Handle: RePEc:cup:etheor:v:19:y:2003:i:06:p:1040-1064_19
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    Cited by:

    1. Xavier D’Haultfoeuille & Arnaud Maurel & Xiaoyun Qiu & Yichong Zhang, 2020. "Estimating selection models without an instrument with Stata," Stata Journal, StataCorp LP, vol. 20(2), pages 297-308, June.
    2. Huber, Martin & Melly, Blaise, 2011. "Quantile Regression in the Presence of Sample Selection," Economics Working Paper Series 1109, University of St. Gallen, School of Economics and Political Science.
    3. J. M. C. Santos Silva & Silvana Tenreyro, 2015. "Trading Partners and Trading Volumes: Implementing the Helpman–Melitz–Rubinstein Model Empirically," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 77(1), pages 93-105, February.
    4. Marc-Andreas Muendler & Sascha O. Becker, 2010. "Margins of Multinational Labor Substitution," American Economic Review, American Economic Association, vol. 100(5), pages 1999-2030, December.
    5. Chen, Songnian & Zhou, Yahong, 2010. "Semiparametric and nonparametric estimation of sample selection models under symmetry," Journal of Econometrics, Elsevier, vol. 157(1), pages 143-150, July.
    6. Bo E. Honore & Luojia Hu, 2021. "Sample Selection Models Without Exclusion Restrictions: Parameter Heterogeneity and Partial Identification," Working Paper Series WP 2022-33, Federal Reserve Bank of Chicago.
    7. Manuel Arellano & Stéphane Bonhomme, 2017. "Quantile Selection Models With an Application to Understanding Changes in Wage Inequality," Econometrica, Econometric Society, vol. 85, pages 1-28, January.
    8. Manuel Arellano & Stéphane Bonhomme, 2017. "Sample Selection in Quantile Regression: A Survey," Working Papers wp2017_1702, CEMFI.
    9. Kamhon Kan & Chihwa Kao, 2005. "Simulation-Based Two-Step Estimation with Endogenous Regressors," Center for Policy Research Working Papers 76, Center for Policy Research, Maxwell School, Syracuse University.
    10. Biewen, Martin & Fitzenberger, Bernd & Seckler, Matthias, 2020. "Counterfactual quantile decompositions with selection correction taking into account Huber/Melly (2015): An application to the German gender wage gap," Labour Economics, Elsevier, vol. 67(C).
    11. Giuseppe De Luca & Valeria Perotti, 2011. "Estimation of ordered response models with sample selection," Stata Journal, StataCorp LP, vol. 11(2), pages 213-239, June.
    12. D’Haultfœuille, Xavier & Maurel, Arnaud & Zhang, Yichong, 2018. "Extremal quantile regressions for selection models and the black–white wage gap," Journal of Econometrics, Elsevier, vol. 203(1), pages 129-142.
    13. Kyungchul Song, 2009. "Two-Step Extremum Estimation with Estimated Single-Indices," PIER Working Paper Archive 09-012, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    14. Bernd Fitzenberger & Jakob Lazzer, 2022. "Changing selection into full-time work and its effect on wage inequality in Germany," Empirical Economics, Springer, vol. 62(1), pages 247-277, January.
    15. Martin Huber & Blaise Melly, 2012. "A test of the conditional independence assumption in sample selection models," Working Papers 2012-11, Brown University, Department of Economics.
    16. Garbay, Sergio & Barrera, Raquel, 2021. "¿Mujeres en suelos pegajosos? Un análisis de la evolución de las distribuciones de ingresos laborales en Bolivia en el periodo 2011-2019," Revista Latinoamericana de Desarrollo Economico, Carrera de Economía de la Universidad Católica Boliviana (UCB) "San Pablo", issue 36, pages 123-168, Noviembre.
    17. Manuel Arellano & Stéphane Bonhomme, 2017. "Sample Selection in Quantile Regression: A Survey," Working Papers wp2018_1702, CEMFI.
    18. Guo, Jing & Wang, Lei & Zhang, Zhengyu, 2022. "Identification and estimation of a heteroskedastic censored regression model with random coefficient dummy endogenous regressors," Economic Modelling, Elsevier, vol. 110(C).
    19. Song, Kyungchul, 2014. "Semiparametric models with single-index nuisance parameters," Journal of Econometrics, Elsevier, vol. 178(P3), pages 471-483.
    20. Chandra Kiran B. Krishnamurthy & Bengt Kriström, 2016. "Determinants of the Price-Premium for Green Energy: Evidence from an OECD Cross-Section," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 64(2), pages 173-204, June.

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