IDEAS home Printed from https://ideas.repec.org/p/cmu/gsiawp/1095622259.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://student-3k.tepper.cmu.edu/gsiadoc/wp/2004-E62.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Sumru Altuğ & Robert A. Miller, 1998. "The Effect of Work Experience on Female Wages and Labour Supply," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(1), pages 45-85.
    2. Hotz, V Joseph & Kydland, Finn E & Sedlacek, Guilherme L, 1988. "Intertemporal Preferences and Labor Supply," Econometrica, Econometric Society, vol. 56(2), pages 335-360, March.
    3. James J. Heckman, 1976. "The Common Structure of Statistical Models of Truncation, Sample Selection and Limited Dependent Variables and a Simple Estimator for Such Models," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 5, number 4, pages 475-492, National Bureau of Economic Research, Inc.
    4. Arellano, Manuel & Bover, Olympia, 1995. "Another look at the instrumental variable estimation of error-components models," Journal of Econometrics, Elsevier, vol. 68(1), pages 29-51, July.
    5. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    6. 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.
    7. Bo E. Honore & Arthur Lewbel, 2002. "Semiparametric Binary Choice Panel Data Models Without Strictly Exogeneous Regressors," Econometrica, Econometric Society, vol. 70(5), pages 2053-2063, September.
    8. S. Darolles & Y. Fan & J. P. Florens & E. Renault, 2011. "Nonparametric Instrumental Regression," Econometrica, Econometric Society, vol. 79(5), pages 1541-1565, September.
    9. 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.
    10. MaCurdy, Thomas E, 1981. "An Empirical Model of Labor Supply in a Life-Cycle Setting," Journal of Political Economy, University of Chicago Press, vol. 89(6), pages 1059-1085, December.
    11. Honore, Bo E., 1993. "Orthogonality conditions for Tobit models with fixed effects and lagged dependent variables," Journal of Econometrics, Elsevier, vol. 59(1-2), pages 35-61, September.
    12. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-1370, November.
    13. Nijman, Theo & Verbeek, Marno, 1992. "Nonresponse in Panel Data: The Impact on Estimates of a Life Cycle Consumption Function," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(3), pages 243-257, July-Sept.
    14. Whitney K. Newey, 2009. "Two-step series estimation of sample selection models," Econometrics Journal, Royal Economic Society, vol. 12(s1), pages 217-229, January.
    15. Stephen Bond & Costas Meghir, 1994. "Dynamic Investment Models and the Firm's Financial Policy," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(2), pages 197-222.
    16. Newey, Whitney K., 1994. "Kernel Estimation of Partial Means and a General Variance Estimator," Econometric Theory, Cambridge University Press, vol. 10(2), pages 1-21, June.
    17. Ekaterini Kyriazidou, 1997. "Estimation of a Panel Data Sample Selection Model," Econometrica, Econometric Society, vol. 65(6), pages 1335-1364, November.
    18. Newey, Whitney K., 1994. "Series Estimation of Regression Functionals," Econometric Theory, Cambridge University Press, vol. 10(1), pages 1-28, March.
    19. Mitali Das & Whitney K. Newey & Francis Vella, 2003. "Nonparametric Estimation of Sample Selection Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 70(1), pages 33-58.
    20. Arellano, Manuel & Carrasco, Raquel, 2003. "Binary choice panel data models with predetermined variables," Journal of Econometrics, Elsevier, vol. 115(1), pages 125-157, July.
    21. Chunrong Ai & Xiaohong Chen, 2003. "Efficient Estimation of Models with Conditional Moment Restrictions Containing Unknown Functions," Econometrica, Econometric Society, vol. 71(6), pages 1795-1843, November.
    22. Xiaohong Chen & Xiaotong Shen, 1998. "Sieve Extremum Estimates for Weakly Dependent Data," Econometrica, Econometric Society, vol. 66(2), pages 289-314, March.
    23. Newey, Whitney K, 1994. "The Asymptotic Variance of Semiparametric Estimators," Econometrica, Econometric Society, vol. 62(6), pages 1349-1382, November.
    24. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
    25. Ekaterini Kyriazidou, 2001. "Estimation of Dynamic Panel Data Sample Selection Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 68(3), pages 543-572.
    26. Ahn, Seung C. & Schmidt, Peter, 1995. "Efficient estimation of models for dynamic panel data," Journal of Econometrics, Elsevier, vol. 68(1), pages 5-27, July.
    27. Arellano, Manuel, 2003. "Panel Data Econometrics," OUP Catalogue, Oxford University Press, number 9780199245291.
    28. Matzkin, Rosa L, 1992. "Nonparametric and Distribution-Free Estimation of the Binary Threshold Crossing and the Binary Choice Models," Econometrica, Econometric Society, vol. 60(2), pages 239-270, March.
    29. Chamberlain, Gary, 1986. "Asymptotic efficiency in semi-parametric models with censoring," Journal of Econometrics, Elsevier, vol. 32(2), pages 189-218, July.
    30. 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.
    31. Heckman, James, 2013. "Sample selection bias as a specification error," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 31(3), pages 129-137.
    32. Zabel, Jeffrey E., 1992. "Estimating fixed and random effects models with selectivity," Economics Letters, Elsevier, vol. 40(3), pages 269-272, November.
    33. 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.
    34. Heckman, James J, 1974. "Shadow Prices, Market Wages, and Labor Supply," Econometrica, Econometric Society, vol. 42(4), pages 679-694, July.
    35. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, September.
    36. Bo E. Honoré & Ekaterini Kyriazidou, 2000. "Panel Data Discrete Choice Models with Lagged Dependent Variables," Econometrica, Econometric Society, vol. 68(4), pages 839-874, July.
    37. Manuel Arellano & Stephen Bond, 1991. "Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(2), pages 277-297.
    38. Anderson, T. W. & Hsiao, Cheng, 1982. "Formulation and estimation of dynamic models using panel data," Journal of Econometrics, Elsevier, vol. 18(1), pages 47-82, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Sergi Jiménez-Martín & José M. Labeaga & Majid al Sadoon, 2020. "Consistent estimation of panel data sample selection models," Working Papers 2020-06, FEDEA.
    2. 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.
    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.
    6. Yamana Kazufumi, 2020. "Monte Carlo Evidence on the Estimation Method for Industry Dynamics," Journal of Econometric Methods, De Gruyter, vol. 9(1), pages 1-12, January.
    7. Fernández-Val, Iván & Vella, Francis, 2011. "Bias corrections for two-step fixed effects panel data estimators," Journal of Econometrics, Elsevier, vol. 163(2), pages 144-162, August.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    2. Chen, Xiaohong, 2007. "Large Sample Sieve Estimation of Semi-Nonparametric Models," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 76, Elsevier.
    3. Williams, Benjamin, 2020. "Nonparametric identification of discrete choice models with lagged dependent variables," Journal of Econometrics, Elsevier, vol. 215(1), pages 286-304.
    4. Shiu, Ji-Liang & Hu, Yingyao, 2013. "Identification and estimation of nonlinear dynamic panel data models with unobserved covariates," Journal of Econometrics, Elsevier, vol. 175(2), pages 116-131.
    5. Fernández-Val, Iván & Vella, Francis, 2011. "Bias corrections for two-step fixed effects panel data estimators," Journal of Econometrics, Elsevier, vol. 163(2), pages 144-162, August.
    6. Gayle, Wayne-Roy, 2013. "Identification and N-consistent estimation of a nonlinear panel data model with correlated unobserved effects," Journal of Econometrics, Elsevier, vol. 175(2), pages 71-83.
    7. Xiaohong Chen & Andres Santos, 2018. "Overidentification in Regular Models," Econometrica, Econometric Society, vol. 86(5), pages 1771-1817, September.
    8. repec:hal:wpspec:info:hdl:2441/3vl5fe4i569nbr005tctlc8ll5 is not listed on IDEAS
    9. Breunig, Christoph & Mammen, Enno & Simoni, Anna, 2018. "Nonparametric estimation in case of endogenous selection," Journal of Econometrics, Elsevier, vol. 202(2), pages 268-285.
    10. 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.
    11. repec:hal:spmain:info:hdl:2441/3vl5fe4i569nbr005tctlc8ll5 is not listed on IDEAS
    12. repec:spo:wpmain:info:hdl:2441/3vl5fe4i569nbr005tctlc8ll5 is not listed on IDEAS
    13. repec:spo:wpecon:info:hdl:2441/3vl5fe4i569nbr005tctlc8ll5 is not listed on IDEAS
    14. Liu, Ruixuan & Yu, Zhengfei, 2022. "Sample selection models with monotone control functions," Journal of Econometrics, Elsevier, vol. 226(2), pages 321-342.
    15. James J. Heckman, 2005. "Micro Data, Heterogeneity and the Evaluation of Public Policy Part 2," The American Economist, Sage Publications, vol. 49(1), pages 16-44, March.
    16. Cheng Hsiao, 2007. "Panel data analysis—advantages and challenges," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(1), pages 1-22, May.
    17. Hidehiko Ichimura & Whitney K. Newey, 2022. "The influence function of semiparametric estimators," Quantitative Economics, Econometric Society, vol. 13(1), pages 29-61, January.
    18. Hübler, Olaf, 2005. "Panel Data Econometrics: Modelling and Estimation," Hannover Economic Papers (HEP) dp-319, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    19. Jochmans, Koen, 2015. "Multiplicative-error models with sample selection," Journal of Econometrics, Elsevier, vol. 184(2), pages 315-327.
    20. Jeffrey M. Wooldridge, 2005. "Simple solutions to the initial conditions problem in dynamic, nonlinear panel data models with unobserved heterogeneity," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(1), pages 39-54, January.
    21. Xin, Kai & Zhang, ZhengYu & Zhou, YaHong & Zhu, PingFang, 2021. "Time-varying individual effects in a panel data probit model with an application to female labor force participation," Economic Modelling, Elsevier, vol. 95(C), pages 181-191.
    22. William Greene, 2001. "Fixed and Random Effects in Nonlinear Models," Working Papers 01-01, New York University, Leonard N. Stern School of Business, Department of Economics.
    23. 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.
    24. Hoderlein, Stefan & White, Halbert, 2012. "Nonparametric identification in nonseparable panel data models with generalized fixed effects," Journal of Econometrics, Elsevier, vol. 168(2), pages 300-314.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cmu:gsiawp:1095622259. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Steve Spear (email available below). General contact details of provider: https://www.cmu.edu/tepper .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.