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Multiple Discrete Endogenous Variables in Weakly-Separable Triangular Models

Author

Listed:
  • Sung Jae Jun

    (CAPCP and Department of Economics, Pennsylvania State University, 608 Kern Graduate Building, University Park, PA 16802, USA)

  • Joris Pinkse

    (CAPCP and Department of Economics, Pennsylvania State University, 608 Kern Graduate Building, University Park, PA 16802, USA)

  • Haiqing Xu

    (Department of Economics, University of Texas at Austin, 78712 Austin, TX, USA)

  • Neşe Yıldız

    (Department of Economics, University of Rochester, 222 Harkness Hall, Rochester, NY 14627, USA)

Abstract

We consider a model in which an outcome depends on two discrete treatment variables, where one treatment is given before the other. We formulate a three-equation triangular system with weak separability conditions. Without assuming assignment is random, we establish the identification of an average structural function using two-step matching. We also consider decomposing the effect of the first treatment into direct and indirect effects, which are shown to be identified by the proposed methodology. We allow for both of the treatment variables to be non-binary and do not appeal to an identification-at-infinity argument.

Suggested Citation

  • Sung Jae Jun & Joris Pinkse & Haiqing Xu & Neşe Yıldız, 2016. "Multiple Discrete Endogenous Variables in Weakly-Separable Triangular Models," Econometrics, MDPI, vol. 4(1), pages 1-21, February.
  • Handle: RePEc:gam:jecnmx:v:4:y:2016:i:1:p:7-:d:63449
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    References listed on IDEAS

    as
    1. James J. Heckman & Edward Vytlacil, 2005. "Structural Equations, Treatment Effects, and Econometric Policy Evaluation," Econometrica, Econometric Society, vol. 73(3), pages 669-738, May.
    2. Brian Jacob & Lars Lefgren & Enrico Moretti, 2007. "The Dynamics of Criminal Behavior: Evidence from Weather Shocks," Journal of Human Resources, University of Wisconsin Press, vol. 42(3).
    3. Richard W. Blundell & James L. Powell, 2004. "Endogeneity in Semiparametric Binary Response Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 71(3), pages 655-679.
    4. Michael Gerfin & Michael Lechner, 2002. "A Microeconometric Evaluation of the Active Labour Market Policy in Switzerland," Economic Journal, Royal Economic Society, vol. 112(482), pages 854-893, October.
    5. David Card, 1995. "The Wage Curve: A Review," Working Papers 722, Princeton University, Department of Economics, Industrial Relations Section..
    6. Jun, Sung Jae & Pinkse, Joris & Xu, Haiqing, 2011. "Tighter bounds in triangular systems," Journal of Econometrics, Elsevier, vol. 161(2), pages 122-128, April.
    7. Chiburis, Richard C., 2010. "Semiparametric bounds on treatment effects," Journal of Econometrics, Elsevier, vol. 159(2), pages 267-275, December.
    8. Lewbel, Arthur, 2007. "Endogenous selection or treatment model estimation," Journal of Econometrics, Elsevier, vol. 141(2), pages 777-806, December.
    9. Markus Frölich & Martin Huber, 2017. "Direct and indirect treatment effects–causal chains and mediation analysis with instrumental variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(5), pages 1645-1666, November.
    10. Sung Jae Jun & Joris Pinkse & Haiqing Xu, 2012. "Discrete endogenous variables in weakly separable models," Econometrics Journal, Royal Economic Society, vol. 15(2), pages 288-303, June.
    11. Kane, Thomas J & Rouse, Cecilia Elena, 1995. "Labor-Market Returns to Two- and Four-Year College," American Economic Review, American Economic Association, vol. 85(3), pages 600-614, June.
    12. repec:fth:prinin:343 is not listed on IDEAS
    13. Lorraine Dearden & Javier Ferri & Costas Meghir, 2002. "The Effect Of School Quality On Educational Attainment And Wages," The Review of Economics and Statistics, MIT Press, vol. 84(1), pages 1-20, February.
    14. Guido W. Imbens & Jeffrey M. Wooldridge, 2009. "Recent Developments in the Econometrics of Program Evaluation," Journal of Economic Literature, American Economic Association, vol. 47(1), pages 5-86, March.
    15. Guido W. Imbens & Whitney K. Newey, 2009. "Identification and Estimation of Triangular Simultaneous Equations Models Without Additivity," Econometrica, Econometric Society, vol. 77(5), pages 1481-1512, September.
    16. Flores, Carlos A. & Flores-Lagunes, Alfonso, 2009. "Identification and Estimation of Causal Mechanisms and Net Effects of a Treatment under Unconfoundedness," IZA Discussion Papers 4237, Institute of Labor Economics (IZA).
    17. Black, Dan A. & Smith, J.A.Jeffrey A., 2004. "How robust is the evidence on the effects of college quality? Evidence from matching," Journal of Econometrics, Elsevier, vol. 121(1-2), pages 99-124.
    18. Azeem M. Shaikh & Edward J. Vytlacil, 2011. "Partial Identification in Triangular Systems of Equations With Binary Dependent Variables," Econometrica, Econometric Society, vol. 79(3), pages 949-955, May.
    19. Shakeeb Khan & Elie Tamer, 2010. "Irregular Identification, Support Conditions, and Inverse Weight Estimation," Econometrica, Econometric Society, vol. 78(6), pages 2021-2042, November.
    20. Cragg, John G, 1971. "Some Statistical Models for Limited Dependent Variables with Application to the Demand for Durable Goods," Econometrica, Econometric Society, vol. 39(5), pages 829-844, September.
    21. David Card, 1995. "The Wage Curve: A Review," Journal of Economic Literature, American Economic Association, vol. 33(2), pages 285-299, June.
    22. Andrew Chesher, 2003. "Identification in Nonseparable Models," Econometrica, Econometric Society, vol. 71(5), pages 1405-1441, September.
    23. Kosuke Imai & David A. van Dyk, 2004. "Causal Inference With General Treatment Regimes: Generalizing the Propensity Score," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 854-866, January.
    24. Anja Lambrecht & Katja Seim & Catherine Tucker, 2011. "Stuck in the Adoption Funnel: The Effect of Interruptions in the Adoption Process on Usage," Marketing Science, INFORMS, vol. 30(2), pages 355-367, 03-04.
    25. Victor Chernozhukov & Christian Hansen, 2005. "An IV Model of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 73(1), pages 245-261, January.
    26. Edward Vytlacil & Nese Yildiz, 2007. "Dummy Endogenous Variables in Weakly Separable Models," Econometrica, Econometric Society, vol. 75(3), pages 757-779, May.
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