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Partial Identification of the Distribution of Treatment Effects in Switching Regime Models and its Confidence Sets

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  • Yanqin Fan
  • Jisong Wu

Abstract

In this paper, we establish sharp bounds on the joint distribution of potential outcomes and the distribution of treatment effects in parametric switching regime models with normal mean-variance mixture errors and in the semi-parametric switching regime models of Heckman (1990) . Our results for parametric switching regime models with normal mean-variance mixture errors extend some existing results for the Gaussian switching regime model and our results for semi-parametric switching regime models supplement the point identification results of Heckman (1990) . Compared with the corresponding sharp bounds when selection is random, we observe that self-selection tightens the bounds on the joint distribution of the potential outcomes and the distribution of treatment effects. These bounds depend on the identified model parameters only and can be easily estimated once the identified model parameters are estimated. The important issue of inference is briefly discussed. Copyright , Wiley-Blackwell.

Suggested Citation

  • Yanqin Fan & Jisong Wu, 2010. "Partial Identification of the Distribution of Treatment Effects in Switching Regime Models and its Confidence Sets," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 77(3), pages 1002-1041.
    • Handle: RePEc:oup:restud:v:77:y:2010:i:3:p:1002-1041
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    File URL: http://hdl.handle.net/10.1111/j.1467-937X.2009.00593.x
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    Cited by:

    1. Ismaël Mourifié & Marc Henry & Romuald Méango, 2020. "Sharp Bounds and Testability of a Roy Model of STEM Major Choices," Journal of Political Economy, University of Chicago Press, vol. 128(8), pages 3220-3283.
    2. Wooyoung Kim & Koohyun Kwon & Soonwoo Kwon & Sokbae Lee, 2018. "The identification power of smoothness assumptions in models with counterfactual outcomes," Quantitative Economics, Econometric Society, vol. 9(2), pages 617-642, July.
    3. Chen, Songnian & Zhou, Yahong & Ji, Yuanyuan, 2018. "Nonparametric identification and estimation of sample selection models under symmetry," Journal of Econometrics, Elsevier, vol. 202(2), pages 148-160.
    4. Callaway, Brantly, 2021. "Bounds on distributional treatment effect parameters using panel data with an application on job displacement," Journal of Econometrics, Elsevier, vol. 222(2), pages 861-881.
    5. Giorgio Calzolari & Maria Gabriella Campolo & Antonino Pino & Laura Magazzini, 2023. "Assessing individual skill influence on housework time of Italian women: an endogenous-switching approach," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(2), pages 659-679, June.
    6. Yanqin Fan & Marc Henry, 2020. "Vector copulas," Papers 2009.06558, arXiv.org, revised Apr 2021.
    7. Rafael Lalive & Armin Schmutzler, 2011. "Auctions vs negotiations in public procurement: which works better?," ECON - Working Papers 023, Department of Economics - University of Zurich.
    8. Liu, Ruixuan & Yu, Zhengfei, 2022. "Sample selection models with monotone control functions," Journal of Econometrics, Elsevier, vol. 226(2), pages 321-342.
    9. Firpo, Sergio & Ridder, Geert, 2019. "Partial identification of the treatment effect distribution and its functionals," Journal of Econometrics, Elsevier, vol. 213(1), pages 210-234.
    10. Xiaohong Chen & Matthew Gentry & Tong Li & Jingfeng Lu, 2020. "Identification and Inference in First-Price Auctions with Risk Averse Bidders and Selective Entry," Cowles Foundation Discussion Papers 2257, Cowles Foundation for Research in Economics, Yale University.
    11. Chen, Heng & Fan, Yanqin & Liu, Ruixuan, 2016. "Inference for the correlation coefficient between potential outcomes in the Gaussian switching regime model," Journal of Econometrics, Elsevier, vol. 195(2), pages 255-270.
    12. Brigham R. Frandsen & Lars J. Lefgren, 2021. "Partial identification of the distribution of treatment effects with an application to the Knowledge is Power Program (KIPP)," Quantitative Economics, Econometric Society, vol. 12(1), pages 143-171, January.
    13. David Koch & Steve Ofili & Abel Cudjoe, 2017. "Identifications of the Distribution of Treatment Effect with Duration Outcomes," Journal of Banking and Financial Dynamics, Sophia, vol. 1(1), pages 36-41.
    14. Kevin E. Staub, 2014. "A Causal Interpretation of Extensive and Intensive Margin Effects in Generalized Tobit Models," The Review of Economics and Statistics, MIT Press, vol. 96(2), pages 371-375, May.
    15. Dunker, Fabian & Hoderlein, Stefan & Kaido, Hiroaki & Sherman, Robert, 2018. "Nonparametric identification of the distribution of random coefficients in binary response static games of complete information," Journal of Econometrics, Elsevier, vol. 206(1), pages 83-102.
    16. Firpo, Sergio & Galvao, Antonio F. & Parker, Thomas, 2023. "Uniform inference for value functions," Journal of Econometrics, Elsevier, vol. 235(2), pages 1680-1699.
    17. Fan, Yanqin & Guerre, Emmanuel & Zhu, Dongming, 2017. "Partial identification of functionals of the joint distribution of “potential outcomes”," Journal of Econometrics, Elsevier, vol. 197(1), pages 42-59.
    18. Christian Bontemps & Thierry Magnac, 2017. "Set Identification, Moment Restrictions, and Inference," Annual Review of Economics, Annual Reviews, vol. 9(1), pages 103-129, September.
    19. Wooyoung Kim & Koohyun Kwon & Soonwoo Kwon & Sokbae (Simon) Lee, 2014. "The identification power of smoothness assumptions in models with counterfactual outcomes," CeMMAP working papers 17/14, Institute for Fiscal Studies.
    20. Fan, Yanqin & Henry, Marc, 2023. "Vector copulas," Journal of Econometrics, Elsevier, vol. 234(1), pages 128-150.
    21. Han, Sukjin & Vytlacil, Edward J., 2017. "Identification in a generalization of bivariate probit models with dummy endogenous regressors," Journal of Econometrics, Elsevier, vol. 199(1), pages 63-73.

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