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Identification and shape restrictions in nonparametric instrumental variables estimation

Authors: Joachim Freyberger and Joel L. Horowitz
Date: 30 November 2015
Type: Journal Article, Journal of Econometrics, Vol. 189, No. 1, pp. 41--53
DOI: 10.1016/j.jeconom.2015.06.020

Abstract

This paper is concerned with inference about an unidentified linear functional, L(g), where g satisfies Y=g(X)+U; E(U|W)=0. In much applied research, X and W are discrete, and W has fewer points of support than X. Consequently, L(g) is not identified nonparametrically and can have any value in (−∞,∞). This paper uses shape restrictions, such as monotonicity or convexity, to achieve interval identification of L(g). The paper shows that under shape restrictions, L(g) is contained in an interval whose bounds can be obtained by solving linear programming problems. Inference about L(g)can be carried out by using the bootstrap. An empirical application illustrates the usefulness of the method.

Previous version:
Joachim Freyberger and Joel L. Horowitz July 2013, Identification and shape restrictions in nonparametric instrumental variables estimation, cemmap Working Paper, CWP31/13

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