On the Testability of Identification in Some Nonparametric Models With Endogeneity

Authors

  • Ivan A. Canay,

    1. Dept. of Economics, Northwestern University, 2001 Sheridan Road, Evanston, IL 60208, U.S.A.; iacanay@northwestern.edu
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  • Andres Santos,

    1. Dept. of Economics, University of California—San Diego, 9500 Gilman Drive #0508, La Jolla, CA 92093, U.S.A.; a2santos@ucsd.edu
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  • Azeem M. Shaikh

    1. Dept. of Economics, University of Chicago, 1126 E. 58th Street, Chicago, IL 60657, U.S.A.; amshaikh@uchicago.edu
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    • We thank James Stock, Victor Chernozhukov, and four anonymous referees whose valuable suggestions helped greatly improve the paper. We are also indebted to Xiaohong Chen, Joel Horowitz, Patrick Kline, Whitney Newey, Elie Tamer, Daniel Wilhelm, and numerous seminar participants for valuable comments. The research of the first author has been supported by National Science Foundation Grant SES-1123586. The research of the third author has been supported by National Science Foundation Grants DMS-0820310 and SES-1227091, and the Alfred P. Sloan Foundation.


Abstract

This paper examines three distinct hypothesis testing problems that arise in the context of identification of some nonparametric models with endogeneity. The first hypothesis testing problem we study concerns testing necessary conditions for identification in some nonparametric models with endogeneity involving mean independence restrictions. These conditions are typically referred to as completeness conditions. The second and third hypothesis testing problems we examine concern testing for identification directly in some nonparametric models with endogeneity involving quantile independence restrictions. For each of these hypothesis testing problems, we provide conditions under which any test will have power no greater than size against any alternative. In this sense, we conclude that no nontrivial tests for these hypothesis testing problems exist.

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