Inference in Nonparametric Instrumental Variables With Partial Identification


  • Andres Santos

    1. Dept. of Economics, University of California–San Diego, 9500 Gilman Drive 0508, La Jolla, CA 92093-0508, U.S.A.;
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    • I thank Whitney Newey and three anonymous referees for comments that helped greatly improve the paper. Parts of this paper derive from my doctoral dissertation, completed under the guidance and encouragement of Frank Wolak. I also thank Brendan Beare, Xiaohong Chen, Peter Hansen, Joel Horowitz, Aprajit Mahajan, Sriniketh Nagavarapu, Azeem Shaikh, and seminar participants where this paper was presented. The financial support of the Stanford Institute for Economic and Policy Research is gratefully acknowledged.


This paper develops methods for hypothesis testing in a nonparametric instrumental variables setting within a partial identification framework. We construct and derive the asymptotic distribution of a test statistic for the hypothesis that at least one element of the identified set satisfies a conjectured restriction. The same test statistic can be employed under identification, in which case the hypothesis is whether the true model satisfies the posited property. An almost sure consistent bootstrap procedure is provided for obtaining critical values. Possible applications include testing for semiparametric specifications as well as building confidence regions for certain functionals on the identified set. As an illustration we obtain confidence intervals for the level and slope of Brazilian fuel Engel curves. A Monte Carlo study examines finite sample performance.