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Root-N Consistent Semiparametric Estimators of a Dynamic Panel Sample Selection Model

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  • George-Levi Gayle
  • Christelle Viauroux
Abstract
This paper considers the problem of identification and estimation in panel-data sample-selection models with a binary selection rule when the latent equations contain possibly predetermined variables, lags of the dependent variables, and unobserved individual effects. The selection equation contains lags of the dependent variables from both the latent and the selection equations as well as other possibly predetermined variables relative to the latent equations. We derive a set of conditional moment restrictions that are then exploited to construct a three-step sieve estimator for the parameters of the main equation including a nonparametric estimator of the sample-selection term. In the second step the unknown parameters of the selection equation are consistently estimated using a transformation approach in the spirit of Berkson's minimum chi-square sieve method and a first-step kernel estimator for the selection probability. This second-step estimator is of interest in its own right. It can be used to semiparametrically estimate a panel-data binary response model with correlated random effects without making any distributional assumptions. We show that both estimators (second and third stage) are √n-consistent and asymptotically normal.This paper considers the problem of identification and estimation in panel-data sample-selection models with a binary selection rule when the latent equations contain possibly predetermined variables, lags of the dependent variables, and unobserved individual effects. The selection equation contains lags of the dependent variables from both the latent and the selection equations as well as other possibly predetermined variables relative to the latent equations. We derive a set of conditional moment restrictions that are then exploited to construct a three-step sieve estimator for the parameters of the main equation including a nonparametric estimator of the sample-selection term. In the second step the unknown parameters of the selection equation are consistently estimated using a transformation approach in the spirit of Berkson's minimum chi-square sieve method and a first-step kernel estimator for the selection probability. This second-step estimator is of interest in its own right. It can be used to semiparametrically estimate a panel-data binary response model with a nonparametric individual specific effect without making any other distributional assumptions. We show that both estimators (second and third stage) are √n-consistent and asymptotically normal.

Suggested Citation

  • George-Levi Gayle & Christelle Viauroux, "undated". "Root-N Consistent Semiparametric Estimators of a Dynamic Panel Sample Selection Model," GSIA Working Papers 2004-E62, Carnegie Mellon University, Tepper School of Business.
    • Handle: RePEc:cmu:gsiawp:1095622259
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    3. Ai, Chunrong & Chen, Xiaohong, 2007. "Estimation of possibly misspecified semiparametric conditional moment restriction models with different conditioning variables," Journal of Econometrics, Elsevier, vol. 141(1), pages 5-43, November.
    4. Victor Chernozhukov & Iv·n Fern·ndez-Val & Alfred Galichon, 2010. "Quantile and Probability Curves Without Crossing," Econometrica, Econometric Society, vol. 78(3), pages 1093-1125, May.
    5. Wladimir Raymond & Pierre Mohnen & Franz Palm & Sybrand Schim van der Loeff, 2007. "The Behavior of the Maximum Likelihood Estimator of Dynamic Panel Data Sample Selection Models," CESifo Working Paper Series 1992, CESifo.
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    8. Mehmet Soytas & Limor Golan & George-Levi Gayle, 2014. "What Accounts for the Racial Gap in Time Allocation and Intergenerational Transmission of Human Capital?," 2014 Meeting Papers 83, Society for Economic Dynamics.
    9. Giulia Bettin & Riccardo Lucchetti & Claudia Pigini, 2016. "State dependence and unobserved heterogeneity in a double hurdle model for remittances: evidence from immigrants to Germany," Mo.Fi.R. Working Papers 127, Money and Finance Research group (Mo.Fi.R.) - Univ. Politecnica Marche - Dept. Economic and Social Sciences.
    10. George‐Levi Gayle & Limor Golan & Mehmet A. Soytas, 2018. "Estimation of dynastic life‐cycle discrete choice models," Quantitative Economics, Econometric Society, vol. 9(3), pages 1195-1241, November.
    11. Giulia Bettin & Riccardo Lucchetti, 2016. "Steady streams and sudden bursts: persistence patterns in remittance decisions," Journal of Population Economics, Springer;European Society for Population Economics, vol. 29(1), pages 263-292, January.
    12. Sergi Jiménez-Martín & José María Labeaga, 2016. "Monte Carlo evidence on the estimation of AR(1) panel data sample selection models," Working Papers 2016-01, FEDEA.
    13. Giulia BETTIN & Riccardo LUCCHETTI, 2012. "Intertemporal remittance behaviour by immigrants in Germany," Working Papers 385, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    14. Costa-Campi, M.T. & Duch-Brown, N. & García-Quevedo, J., 2014. "R&D drivers and obstacles to innovation in the energy industry," Energy Economics, Elsevier, vol. 46(C), pages 20-30.
    15. Viauroux, Christelle, 2011. "Pricing urban congestion: A structural random utility model with traffic anticipation," European Economic Review, Elsevier, vol. 55(7), pages 877-902.
    16. Bester, C. Alan & Hansen, Christian B., 2016. "Grouped effects estimators in fixed effects models," Journal of Econometrics, Elsevier, vol. 190(1), pages 197-208.
    17. Soiliou Namoro & Wayne-Roy Gayle, 2006. "Estimation of a Nonlinear Panel Data Model with Predetermined Variables and Semiparametric Individual Effects," Working Paper 251, Department of Economics, University of Pittsburgh, revised Sep 2008.
    18. Majid M. Al-Sadoon & Sergi Jiménez-Martín & José M Labeaga, 2019. "Simple Methods for Consistent Estimation of Dynamic Panel Data Sample Selection Models," Working Papers 1069, Barcelona School of Economics.
    19. Emir Malikov & Diego A. Restrepo-Tobón & Subal C. Kumbhakar, 2018. "Heterogeneous credit union production technologies with endogenous switching and correlated effects," Econometric Reviews, Taylor & Francis Journals, vol. 37(10), pages 1095-1119, November.
    20. Gayle, Wayne-Roy & Namoro, Soiliou Daw, 2013. "Estimation of a nonlinear panel data model with semiparametric individual effects," Journal of Econometrics, Elsevier, vol. 175(1), pages 46-59.
    21. Nestor Duch-Brown & Andrea de Panizza & Ibrahim Kholilul Rohman, 2016. "Innovation and productivity in a S&T intensive sector: the case of Information industries in Spain," JRC Research Reports JRC101847, Joint Research Centre.
    22. Spiess, Martin & Kroh, Martin, 2010. "A Selection Model for Panel Data: The Prospects of Green Party Support," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 18(2), pages 172-188.
    23. Georg-Levi Gayle & Limor Golan & Mehmet A. Soytas, "undated". "Estimating the Returns to Parental Time Investment in Children Using a Life Cycle Dynastic Model," GSIA Working Papers 2011-E18, Carnegie Mellon University, Tepper School of Business.
    24. Cizek, Pavel & Sadikoglu, Serhan, 2022. "Nonseparable Panel Models with Index Structure and Correlated Random Effects," Other publications TiSEM 7899deb9-0eda-47e6-a3b8-2, Tilburg University, School of Economics and Management.
    25. Bettin, Giulia & Lucchetti, Riccardo & Pigini, Claudia, 2018. "A dynamic double hurdle model for remittances: evidence from Germany," Economic Modelling, Elsevier, vol. 73(C), pages 365-377.

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