Journal Article

Identification and shape restrictions in nonparametric instrumental variables estimation


Joachim Freyberger, Joel L. Horowitz

Published Date

30 November 2015


Journal Article

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.

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