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Tighter bounds in triangular systems

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  • Jun, Sung Jae
  • Pinkse, Joris
  • Xu, Haiqing

Abstract

We study a nonparametric triangular system with (potentially discrete) endogenous regressors and nonseparable errors. Like in other work in this area, the parameter of interest is the structural function evaluated at particular values. We impose a global exclusion and exogeneity condition, in contrast to Chesher (2005), but develop a rank condition which is weaker than Chesher's. The alternative rank condition can be satisfied for binary endogenous regressors, and it often leads to an identified interval tighter than Chesher (2005)'s minimum length interval. We illustrate the potential of the new rank condition using the Angrist and Krueger (1991) data.

Suggested Citation

  • Jun, Sung Jae & Pinkse, Joris & Xu, Haiqing, 2011. "Tighter bounds in triangular systems," Journal of Econometrics, Elsevier, vol. 161(2), pages 122-128, April.
    • Handle: RePEc:eee:econom:v:161:y:2011:i:2:p:122-128
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    References listed on IDEAS

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    1. 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.
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    6. Whitney K. Newey & James L. Powell & Francis Vella, 1999. "Nonparametric Estimation of Triangular Simultaneous Equations Models," Econometrica, Econometric Society, vol. 67(3), pages 565-604, May.
    7. Andrew Chesher, 2003. "Identification in Nonseparable Models," Econometrica, Econometric Society, vol. 71(5), pages 1405-1441, September.
    8. 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.
    9. Joshua D. Angrist & Alan B. Keueger, 1991. "Does Compulsory School Attendance Affect Schooling and Earnings?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 106(4), pages 979-1014.
    10. 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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    Cited by:

    1. Stefan Hoderlein & Yuya Sasaki, 2013. "Outcome conditioned treatment effects," CeMMAP working papers CWP39/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. Ismael Mourifié & Yuanyuan Wan, 2017. "Testing Local Average Treatment Effect Assumptions," The Review of Economics and Statistics, MIT Press, vol. 99(2), pages 305-313, May.
    3. 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.
    4. Pereda-Fernández, Santiago, 2023. "Identification and estimation of triangular models with a binary treatment," Journal of Econometrics, Elsevier, vol. 234(2), pages 585-623.
    5. Alexander Torgovitsky, 2019. "Partial identification by extending subdistributions," Quantitative Economics, Econometric Society, vol. 10(1), pages 105-144, January.
    6. Sungwon Lee, 2020. "Identification and Confidence Regions for Treatment Effect and its Distribution under Stochastic Dominance," Working Papers 2011, Nam Duck-Woo Economic Research Institute, Sogang University (Former Research Institute for Market Economy).
    7. Ma, Jun & Marmer, Vadim & Yu, Zhengfei, 2023. "Inference on individual treatment effects in nonseparable triangular models," Journal of Econometrics, Elsevier, vol. 235(2), pages 2096-2124.
    8. Kasy, Maximilian, "undated". "Instrumental variables with unrestricted heterogeneity and continuous treatment - DON'T CITE! SEE ERRATUM BELOW," Working Paper 33257, Harvard University OpenScholar.
    9. Balat, Jorge F. & Han, Sukjin, 2023. "Multiple treatments with strategic substitutes," Journal of Econometrics, Elsevier, vol. 234(2), pages 732-757.
    10. Christoph Rothe, 2012. "Partial Distributional Policy Effects," Econometrica, Econometric Society, vol. 80(5), pages 2269-2301, September.
    11. Sung Jae Jun & Joris Pinkse & Haiqing Xu & Nese Yildiz, 2012. "Identification of treatment effects in a triangular system of equations," Department of Economics Working Papers 130910, The University of Texas at Austin, Department of Economics, revised Oct 2012.
    12. Liu, Nianqing & Vuong, Quang & Xu, Haiqing, 2017. "Rationalization and identification of binary games with correlated types," Journal of Econometrics, Elsevier, vol. 201(2), pages 249-268.
    13. Andrew Chesher & Adam Rosen, 2012. "Simultaneous equations for discrete outcomes: coherence, completeness, and identification," CeMMAP working papers CWP21/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    14. 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.
    15. Andrew Chesher & Konrad Smolinski, 2010. "Sharp identified sets for discrete variable IV models," CeMMAP working papers CWP11/10, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    16. Kédagni, Désiré & Mourifié, Ismael, 2014. "Tightening bounds in triangular systems," Economics Letters, Elsevier, vol. 125(3), pages 455-458.
    17. Brendan Kline, 2016. "Identification of the Direction of a Causal Effect by Instrumental Variables," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(2), pages 176-184, April.
    18. Lee, Jinhyun, 2013. "Sharp Bounds on Heterogeneous Individual Treatment Responses," SIRE Discussion Papers 2013-89, Scottish Institute for Research in Economics (SIRE).
    19. Maximilian Kasy, 2014. "Instrumental Variables with Unrestricted Heterogeneity and Continuous Treatment," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 81(4), pages 1614-1636.
    20. Jinhyun Lee, 2013. "Sharp Bounds on Heterogeneous Individual Treatment Responses," Discussion Paper Series, School of Economics and Finance 201310, School of Economics and Finance, University of St Andrews.
    21. 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.

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