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Identification region of the potential outcome distributions under instrument independence

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  • Toru Kitagawa

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    (Institute for Fiscal Studies and UCL)

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    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.

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    File URL: http://cemmap.ifs.org.uk/wps/cwp3009.pdf
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    Bibliographic Info

    Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP30/09.

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    Date of creation: Oct 2009
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    Handle: RePEc:ifs:cemmap:30/09

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    Cited by:
    1. Hahn, Jinyong, 2010. "Bounds on ATE with discrete outcomes," Economics Letters, Elsevier, vol. 109(1), pages 24-27, October.
    2. Guido Imbens, 2014. "Instrumental Variables: An Econometrician's Perspective," NBER Working Papers 19983, National Bureau of Economic Research, Inc.
    3. Beresteanu, Arie & Molchanov, Ilya & Molinari, Francesca, 2012. "Partial identification using random set theory," Journal of Econometrics, Elsevier, vol. 166(1), pages 17-32.
    4. Imbens, Guido W., 2014. "Instrumental Variables: An Econometrician's Perspective," IZA Discussion Papers 8048, Institute for the Study of Labor (IZA).
    5. 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.

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