Projection properties of constrained nonparametric instrumental variable estimators

Petyo Bonev

Applied Economics Letters, 2024, vol. 31, issue 1, 1-4

Abstract: I show that a broad class of constrained nonparametric instrumental variable estimators are projections of the corresponding unconstrained estimators on the constrained set with respect to some norm. In addition, for estimators based on Tikhonov regularization, constrained estimation can be viewed as two-step projection: first project the data on the unconstrained set, and then project this projection on the constrained set. As an application, I use the projection property to establish sufficient conditions for the consistency of a sieve-based and a kernel-based constrained estimator.

Date: 2024
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DOI: 10.1080/13504851.2020.1722791

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