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Identification and estimation of semiparametric two‐step models


  • Juan Carlos Escanciano
  • David Jacho‐Chávez
  • Arthur Lewbel


Let H 0 (X) be a function that can be nonparametrically estimated. Suppose E [Y&7CX]=F 0 [X⊤β 0 , H 0 (X)]. Many models fit this framework, including latent index models with an endogenous regressor and nonlinear models with sample selection. We show that the vector β 0 and unknown function F 0 are generally point identified without exclusion restrictions or instruments, in contrast to the usual assumption that identification without instruments requires fully specified functional forms. We propose an estimator with asymptotic properties allowing for data dependent bandwidths and random trimming. A Monte Carlo experiment and an empirical application to migration decisions are also included.

Suggested Citation

  • Juan Carlos Escanciano & David Jacho‐Chávez & Arthur Lewbel, 2016. "Identification and estimation of semiparametric two‐step models," Quantitative Economics, Econometric Society, vol. 7(2), pages 561-589, July.
  • Handle: RePEc:wly:quante:v:7:y:2016:i:2:p:561-589

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    Cited by:

    1. Le-Yu Chen & Sokbae (Simon) Lee & Myung Jae Sung, 2013. "Maximum score estimation of preference parameters for a binary choice model under uncertainty," CeMMAP working papers CWP14/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. Lewbel, Arthur, 2018. "Identification and estimation using heteroscedasticity without instruments: The binary endogenous regressor case," Economics Letters, Elsevier, vol. 165(C), pages 10-12.
    3. Yingying Dong & Arthur Lewbel, 2015. "A Simple Estimator for Binary Choice Models with Endogenous Regressors," Econometric Reviews, Taylor & Francis Journals, vol. 34(1-2), pages 82-105, February.
    4. Klein, Roger & Shen, Chan & Vella, Francis, 2015. "Estimation of marginal effects in semiparametric selection models with binary outcomes," Journal of Econometrics, Elsevier, vol. 185(1), pages 82-94.
    5. Mammen, Enno & Rothe, Christoph & Schienle, Melanie, 2016. "Semiparametric Estimation With Generated Covariates," Econometric Theory, Cambridge University Press, vol. 32(5), pages 1140-1177, October.
    6. Bo E. Honoré & Luojia Hu, 2020. "Selection Without Exclusion," Econometrica, Econometric Society, vol. 88(3), pages 1007-1029, May.
    7. Francesco Bravo & Ba M. Chu & David T. Jacho-Chávez, 2017. "Semiparametric estimation of moment condition models with weakly dependent data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(1), pages 108-136, January.
    8. 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.
    9. Patricia Moreno-Mencía & Juan M. Rodríguez-Poo & David Cantarero-Prieto, 2021. "A Multi-step Process Approach for Estimating Public Sector Wages. The Spanish Expe¬rience," Hacienda Pública Española / Review of Public Economics, IEF, vol. 237(2), pages 33-56, June.
    10. Songnian Chen & Shakeeb Khan & Xun Tang, 2020. "Dummy Endogenous Variables in Weakly Separable Multiple Index Models without Monotonicity," Boston College Working Papers in Economics 996, Boston College Department of Economics.
    11. Victor Chernozhukov & Juan Carlos Escanciano & Hidehiko Ichimura & Whitney K. Newey, 2016. "Locally robust semiparametric estimation," CeMMAP working papers CWP31/16, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    12. Songnian Chen & Shakeeb Khan & Xun Tang, 2020. "Identification and Estimation of Weakly Separable Models Without Monotonicity," Papers 2003.04337,, revised Apr 2020.
    13. Arthur Lewbel, 2019. "The Identification Zoo: Meanings of Identification in Econometrics," Journal of Economic Literature, American Economic Association, vol. 57(4), pages 835-903, December.
    14. Sadikoglu, Serhan, 2019. "Essays in econometric theory," Other publications TiSEM 99d83644-f9dc-49e3-a4e1-5, Tilburg University, School of Economics and Management.
    15. Bravo, Francesco & Chu, Ba M. & Jacho-Chávez, David T., 2017. "Generalized empirical likelihood M testing for semiparametric models with time series data," Econometrics and Statistics, Elsevier, vol. 4(C), pages 18-30.
    16. Geneviève Vallée, 2018. "How Long Does It Take You to Pay? A Duration Study of Canadian Retail Transaction Payment Times," Staff Working Papers 18-46, Bank of Canada.
    17. Juan Carlos Escanciano & Lin Zhu, 2013. "Set inferences and sensitivity analysis in semiparametric conditionally identified models," CeMMAP working papers CWP55/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    18. Laurent Delsol & Ingrid Van Keilegom, 2020. "Semiparametric M-estimation with non-smooth criterion functions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(2), pages 577-605, April.

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