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Identification region of the potential outcome distributions under instrument independence

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  • Toru Kitagawa

    () (Institute for Fiscal Studies and cemmap and University College London)

Abstract

This paper examines identification power of the instrument exogeneity assumption in the treatment effect model. We derive the identification region: The set of potential outcome distributions that are compatible with data and the model restriction. The model restrictions whose identifying power is investigated are (i)instrument independence of each of the potential outcome (marginal independence), (ii) instrument joint independence of the potential outcomes and the selection heterogeneity, and (iii) instrument monotonicity in addition to (ii) (the LATE restriction of Imbens and Angrist (1994)), where these restrictions become stronger in the order of listing. By comparing the size of the identification region under each restriction, we show that the joint independence restriction can provide further identifying information for the potential outcome distributions than marginal independence, but the LATE restriction never does since it solely constrains the distribution of data. We also derive the tightest possible bounds for the average treatment effects under each restriction. Our analysis covers both the discrete and continuous outcome case, and extends the treatment effect bounds of Balke and Pearl(1997) that are available only for the binary outcome case to a wider range of settings including the continuous outcome case.

Suggested Citation

  • Toru Kitagawa, 2009. "Identification region of the potential outcome distributions under instrument independence," CeMMAP working papers CWP30/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:30/09
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    File URL: http://cemmap.ifs.org.uk/wps/cwp3009.pdf
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    Cited by:

    1. Huber, Martin & Mellace, Giovanni, 2012. "Relaxing monotonicity in the identification of local average treatment effects," Economics Working Paper Series 1212, University of St. Gallen, School of Economics and Political Science.
    2. Hahn, Jinyong, 2010. "Bounds on ATE with discrete outcomes," Economics Letters, Elsevier, vol. 109(1), pages 24-27, October.
    3. Lewbel, Arthur & Yang, Thomas Tao, 2016. "Identifying the average treatment effect in ordered treatment models without unconfoundedness," Journal of Econometrics, Elsevier, vol. 195(1), pages 1-22.
    4. Beresteanu, Arie & Molchanov, Ilya & Molinari, Francesca, 2012. "Partial identification using random set theory," Journal of Econometrics, Elsevier, vol. 166(1), pages 17-32.
    5. Chen, Xuan & Flores, Carlos A. & Flores-Lagunes, Alfonso, 2015. "Going Beyond LATE: Bounding Average Treatment Effects of Job Corps Training," IZA Discussion Papers 9511, Institute for the Study of Labor (IZA).
    6. Martin Huber, 2015. "Testing the Validity of the Sibling Sex Ratio Instrument," LABOUR, CEIS, vol. 29(1), pages 1-14, March.
    7. Guido Imbens, 2014. "Instrumental Variables: An Econometrician's Perspective," NBER Working Papers 19983, National Bureau of Economic Research, Inc.
    8. Dahl, Christian M. & Huber, Martin & Mellace, Giovanni, 2017. "It's never too LATE: A new look at local average treatment effects with or without defiers," Discussion Papers of Business and Economics 2/2017, University of Southern Denmark, Department of Business and Economics.
    9. Gautier, Eric & Hoderlein, Stefan, 2011. "A triangular treatment effect model with random coefficients in the selection equation," TSE Working Papers 15-598, Toulouse School of Economics (TSE), revised 25 Aug 2015.
    10. Lee, Jinhyun, 2013. "Sharp Bounds on Heterogeneous Individual Treatment Responses," SIRE Discussion Papers 2013-89, Scottish Institute for Research in Economics (SIRE).
    11. Huber, Martin & W├╝thrich, Kaspar, 2017. "Evaluating local average and quantile treatment effects under endogeneity based on instruments: a review," FSES Working Papers 479, Faculty of Economics and Social Sciences, University of Freiburg/Fribourg Switzerland.
    12. Steinmayr, Andreas, 2014. "When a random sample is not random: Bounds on the effect of migration on household members left behind," Kiel Working Papers 1975, Kiel Institute for the World Economy (IfW).
    13. Zahra Siddique, 2014. "Randomized control trials in an imperfect world," IZA World of Labor, Institute for the Study of Labor (IZA), pages 110-110, December.
    14. Raffaella Giacomini & Toru Kitagawa & Alessio Volpicella, 2017. "Uncertain identification," CeMMAP working papers CWP18/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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