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PARTIAL IDENTIFICATION OF NONSEPARABLE MODELS USING BINARY INSTRUMENTS

Published online by Cambridge University Press:  30 October 2020

Takuya Ishihara
Takuya Ishihara*
Affiliation:
Waseda University
*
Address correspondence to Takuya Ishihara, Faculty of Social Sciences, Waseda University, Tokyo, Japan; e-mail: takuya319ti@gmail.com.
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Abstract

In this study, we explore the partial identification of nonseparable models with continuous endogenous and binary instrumental variables. We show that the structural function is partially identified when it is monotone or concave in the explanatory variable. D’Haultfœuille and Février (2015, Econometrica 83(3), 1199–1210) and Torgovitsky (2015, Econometrica 83(3), 1185–1197) prove the point identification of the structural function under a key assumption that the conditional distribution functions of the endogenous variable for different values of the instrumental variables have intersections. We demonstrate that, even if this assumption does not hold, monotonicity and concavity provide identification power. Point identification is achieved when the structural function is flat or linear with respect to the explanatory variable over a given interval. We compute the bounds using real data and show that our bounds are informative.

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Type
ARTICLES
Information
Econometric Theory , Volume 37 , Issue 4 , August 2021 , pp. 817 - 848
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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Footnotes

I would like to express my appreciation to the co-editor and anonymous referees for their careful reading and comments on the paper. I also would like to thank Katsumi Shimotsu, Hidehiko Ichimura, and the seminar participants at the University of Tokyo, Otaru University of Commerce, Kanazawa University, Hiroshima University, and Shanghai Jiao Tong University. This work was supported by the Grant-in-Aid for JSPS Fellows (20J00900) from the JSPS.

References

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