IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v199y2017i1p63-73.html
   My bibliography  Save this article

Identification in a generalization of bivariate probit models with dummy endogenous regressors

Author

Listed:
  • Han, Sukjin
  • Vytlacil, Edward J.

Abstract

This paper provides identification results for a class of models specified by a triangular system of two equations with binary endogenous variables. The joint distribution of the latent error terms is specified through a parametric copula structure that satisfies a particular dependence ordering, while the marginal distributions are allowed to be arbitrary but known. This class of models is broad and includes bivariate probit models as a special case. The paper demonstrates that having an exclusion restriction is necessary and sufficient for global identification in a model without common exogenous covariates, where the excluded variable is allowed to be binary. Having an exclusion restriction is sufficient in models with common exogenous covariates that are present in both equations. The paper then extends the identification analyses to a model where the marginal distributions of the error terms are unknown.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:econom:v:199:y:2017:i:1:p:63-73
    DOI: 10.1016/j.jeconom.2017.04.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407617300465
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jeconom.2017.04.001?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Mourifié, Ismael & Méango, Romuald, 2014. "A note on the identification in two equations probit model with dummy endogenous regressor," Economics Letters, Elsevier, vol. 125(3), pages 360-363.
    3. Isaiah Andrews & Anna Mikusheva, 2016. "Conditional Inference With a Functional Nuisance Parameter," Econometrica, Econometric Society, vol. 84(4), pages 1571-1612, July.
    4. 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.
    5. Rainer Winkelmann, 2012. "Copula Bivariate Probit Models: With An Application To Medical Expenditures," Health Economics, John Wiley & Sons, Ltd., vol. 21(12), pages 1444-1455, December.
    6. Chen, Xiaohong & Fan, Yanqin & Tsyrennikov, Viktor, 2006. "Efficient Estimation of Semiparametric Multivariate Copula Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1228-1240, September.
    7. Joseph G. Altonji & Todd E. Elder & Christopher R. Taber, 2005. "An Evaluation of Instrumental Variable Strategies for Estimating the Effects of Catholic Schooling," Journal of Human Resources, University of Wisconsin Press, vol. 40(4), pages 791-821.
    8. Neal, Derek, 1997. "The Effects of Catholic Secondary Schooling on Educational Achievement," Journal of Labor Economics, University of Chicago Press, vol. 15(1), pages 98-123, January.
    9. Lee, Lung-Fei, 1983. "Generalized Econometric Models with Selectivity," Econometrica, Econometric Society, vol. 51(2), pages 507-512, March.
    10. 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.
    11. Trivedi, Pravin K. & Zimmer, David M., 2007. "Copula Modeling: An Introduction for Practitioners," Foundations and Trends(R) in Econometrics, now publishers, vol. 1(1), pages 1-111, April.
    12. Wilde, Joachim, 2000. "Identification of multiple equation probit models with endogenous dummy regressors," Economics Letters, Elsevier, vol. 69(3), pages 309-312, December.
    13. Victor Chernozhukov & Christian Hansen, 2005. "An IV Model of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 73(1), pages 245-261, January.
    14. Isaiah Andrews & Anna Mikusheva, 2016. "Conditional Inference With a Functional Nuisance Parameter," Econometrica, Econometric Society, vol. 84, pages 1571-1612, July.
    15. Goldman D. P. & Bhattacharya J. & McCaffrey D. F. & Duan N. & Leibowitz A. A. & Joyce G. F. & Morton S. C., 2001. "Effect of Insurance on Mortality in an HIV-Positive Population in Care," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 883-894, September.
    16. Heckman, James J, 1978. "Dummy Endogenous Variables in a Simultaneous Equation System," Econometrica, Econometric Society, vol. 46(4), pages 931-959, July.
    17. Rothenberg, Thomas J, 1971. "Identification in Parametric Models," Econometrica, Econometric Society, vol. 39(3), pages 577-591, May.
    18. Frank Kleibergen, 2005. "Testing Parameters in GMM Without Assuming that They Are Identified," Econometrica, Econometric Society, vol. 73(4), pages 1103-1123, July.
    19. William N. Evans & Robert M. Schwab, 1995. "Finishing High School and Starting College: Do Catholic Schools Make a Difference?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 110(4), pages 941-974.
    20. Isaiah Andrews & Anna Mikusheva, 2016. "A Geometric Approach to Nonlinear Econometric Models," Econometrica, Econometric Society, vol. 84, pages 1249-1264, May.
    21. Fan, Yanqin & Park, Sang Soo, 2010. "Sharp Bounds On The Distribution Of Treatment Effects And Their Statistical Inference," Econometric Theory, Cambridge University Press, vol. 26(3), pages 931-951, June.
    22. James H. Stock & Jonathan Wright, 2000. "GMM with Weak Identification," Econometrica, Econometric Society, vol. 68(5), pages 1055-1096, September.
    23. Freedman, David A. & Sekhon, Jasjeet S., 2010. "Endogeneity in Probit Response Models," Political Analysis, Cambridge University Press, vol. 18(2), pages 138-150, April.
    24. Chiburis, Richard C., 2010. "Semiparametric bounds on treatment effects," Journal of Econometrics, Elsevier, vol. 159(2), pages 267-275, December.
    25. Sherrie L. W. Rhine & William H. Greene & Maude Toussaint-Comeau, 2006. "The Importance of Check-Cashing Businesses to the Unbanked: Racial/Ethnic Differences," The Review of Economics and Statistics, MIT Press, vol. 88(1), pages 146-157, February.
    Full references (including those not matched with items on IDEAS)

    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. Sukjin Han & Sungwon Lee, 2019. "Estimation in a generalization of bivariate probit models with dummy endogenous regressors," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(6), pages 994-1015, September.
    2. Santiago Acerenza & Otávio Bartalotti & Désiré Kédagni, 2023. "Testing identifying assumptions in bivariate probit models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(3), pages 407-422, April.
    3. Lina Zhang & David T. Frazier & D. S. Poskitt & Xueyan Zhao, 2020. "Decomposing Identification Gains and Evaluating Instrument Identification Power for Partially Identified Average Treatment Effects," Papers 2009.02642, arXiv.org, revised Sep 2022.
    4. Antoine, Bertille & Lavergne, Pascal, 2023. "Identification-robust nonparametric inference in a linear IV model," Journal of Econometrics, Elsevier, vol. 235(1), pages 1-24.
    5. Giampiero Marra & Rosalba Radice & Silvia Missiroli, 2014. "Testing the hypothesis of absence of unobserved confounding in semiparametric bivariate probit models," Computational Statistics, Springer, vol. 29(3), pages 715-741, June.
    6. Frank Kleibergen & Zhaoguo Zhan, 2021. "Double robust inference for continuous updating GMM," Papers 2105.08345, arXiv.org.
    7. Steve Bradley & Rob Crouchley, 2020. "The effects of test scores and truancy on youth unemployment and inactivity: a simultaneous equations approach," Empirical Economics, Springer, vol. 59(4), pages 1799-1831, October.
    8. Gregory Cox, 2022. "Weak Identification in Low-Dimensional Factor Models with One or Two Factors," Papers 2211.00329, arXiv.org, revised Mar 2024.
    9. Jean-Jacques Forneron, 2019. "Detecting Identification Failure in Moment Condition Models," Papers 1907.13093, arXiv.org, revised Oct 2023.
    10. Forneron, Jean-Jacques, 2024. "Detecting identification failure in moment condition models," Journal of Econometrics, Elsevier, vol. 238(1).
    11. Alexander Torgovitsky, 2019. "Partial identification by extending subdistributions," Quantitative Economics, Econometric Society, vol. 10(1), pages 105-144, January.
    12. Jörg Schwiebert, 2016. "Multinomial choice models based on Archimedean copulas," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 100(3), pages 333-354, July.
    13. Brandts, Jordi & El Baroudi, Sabrine & Huber, Stefanie J. & Rott, Christina, 2021. "Gender differences in private and public goal setting," Journal of Economic Behavior & Organization, Elsevier, vol. 192(C), pages 222-247.
    14. Hiroaki Kaido & Kaspar Wüthrich, 2021. "Decentralization estimators for instrumental variable quantile regression models," Quantitative Economics, Econometric Society, vol. 12(2), pages 443-475, May.
    15. Craig E. Landry & Dylan Turner & Daniel Petrolia, 2021. "Flood Insurance Market Penetration and Expectations of Disaster Assistance," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 79(2), pages 357-386, June.
    16. Patrick McEwan, 2001. "The Effectiveness of Public, Catholic, and Non-Religious Private Schools in Chile's Voucher System," Education Economics, Taylor & Francis Journals, vol. 9(2), pages 103-128.
    17. Victor Chernozhukov & Christian Hansen & Kaspar Wuthrich, 2020. "Instrumental Variable Quantile Regression," Papers 2009.00436, arXiv.org.
    18. Wang, Wenjie & Zhang, Yichong, 2024. "Wild bootstrap inference for instrumental variables regressions with weak and few clusters," Journal of Econometrics, Elsevier, vol. 241(1).
    19. J. E. Prieger & A. Choi, 2024. "E-cigarettes and Smoking: Correlation, Causation, and Selection Bias," Journal of Consumer Policy, Springer, vol. 47(4), pages 471-498, December.
    20. Dennis Lim & Wenjie Wang & Yichong Zhang, 2022. "A Conditional Linear Combination Test with Many Weak Instruments," Papers 2207.11137, arXiv.org, revised Apr 2023.

    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:eee:econom:v:199:y:2017:i:1:p:63-73. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jeconom .

    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.