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INSTRUMENTAL VARIABLES METHODS WITH HETEROGENEITY AND MISMEASURED INSTRUMENTS

Published online by Cambridge University Press:  15 February 2016

Karim Chalak
Karim Chalak*
Affiliation:
University of Virginia
*
*Address correspondence to Karim Calak, Department of Economics, University of Virginia, P.O. Box 400182, Charlottesville, VA 22904-4182, email: [email protected].
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Abstract

We study the consequences of substituting an error-laden proxy W for an instrument Z on the interpretation of Wald, local instrumental variable (LIV), and instrumental variable (IV) estimands in an ordered discrete choice structural system with heterogeneity. A proxy W need only satisfy an exclusion restriction and that the treatment and outcome are mean independent from W given Z. Unlike Z, W need not satisfy monotonicity and may, under particular specifications, fail exogeneity. For example, W could code Z with error, with missing observations, or coarsely. We show that Wald, LIV, and IV estimands using W identify weighted averages of local or marginal treatment effects (LATEs or MTEs). We study a necessary and sufficient condition for nonnegative weights. Further, we study a condition under which the Wald or LIV estimand using W identifies the same LATE or MTE that would have been recovered had Z been observed. For example, this holds for binary Z and therefore the Wald estimand using W identifies the same “average causal response,” or LATE for binary treatment, that would have been recovered using Z. Also, under this condition, LIV using W can be used to identify MTE and average treatment effects for e.g., the population, treated, and untreated.

Type
ARTICLES
Information
Econometric Theory , Volume 33 , Issue 1 , February 2017 , pp. 69 - 104
Copyright
Copyright © Cambridge University Press 2016 

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Footnotes

An earlier version of this paper was circulated under the title “Identification of Local Treatment Effects Using a Proxy for an Instrument.” I thank the co-editor and three referees for helpful feedback. I also thank the participants in the California Econometrics Conference 2010, the 2011 North American Winter Meeting of the Econometric Society, the Boston College labor lunch seminar, and the econometrics seminars at UCSD, Brown, UC Riverside, Ohio State University, Yale, UCL, Oxford, UBC, Northwestern, Harvard/MIT, UC Davis, Stanford, and the Federal Reserve Bank of Cleveland as well as Gary Chamberlain, Xavier d’Haultfoeuille, Scott Fulford, Peter Gottschalk, Guido Imbens, Stefan Hoderlein, Ivana Komunjer, Tobias Klein, Arthur Lewbel, Ke-Li Xu, Mathis Wagner, and Halbert White for helpful comments and suggestions. I thank Mehmet Onur Ezer for excellent research assistance. Any errors are the author’s responsibility.

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