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Optimal Linear Instrumental Variables Approximations

Juan Carlos Escanciano () and Wei Li

Papers from arXiv.org

Abstract: Ordinary least squares provides the optimal linear approximation to the true regression function. This paper investigates the Instrumental Variables (IV) version of this problem. The resulting parameter is called the Optimal Linear IV Approximation (OLIVA). The OLIVA is invariant to the distribution of the instruments. This paper shows that a necessary condition for standard inference on the OLIVA is also sufficient for the existence of an IV estimand in a linear IV model. The necessary regularity condition holds for a binary endogenous treatment, leading also to a LATE interpretation with positive weights in a fully heterogeneous model. The instrument in the IV estimand is unknown and may not be identified. A Two-Step IV (TSIV) estimator based on a Tikhonov regularized instrument is proposed, which can be implemented by standard regression routines. We establish the asymptotic normality of the TSIV estimator assuming neither completeness nor identification of the instrument. As an important application of our analysis, we robustify the classical Hausman test for exogeneity against misspecification of the linear model. Monte Carlo simulations suggest a good finite sample performance for the proposed inferences.

New Economics Papers: this item is included in nep-ecm
Date: 2018-05, Revised 2018-12
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