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High-dimensional linear models with many endogenous variables
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DOI：10.1016/j.jeconom.2021.06.011.png)
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Abstract
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High-dimensional linear models with endogenous variables play an increasingly important role in the recent econometric literature. In this work, we allow for models with many endogenous variables and make use of many instrumental variables to achieve identification. Because of the high-dimensionality in the structural equation, constructing honest confidence regions with asymptotically correct coverage is nontrivial.Our main contribution is to propose estimators and confidence regions that achieve this goal. Our approach relies on moment conditions that satisfy the usual instrument orthogonality condition but also have an additional orthogonality property with respect to specific linear combinations of the endogenous variables which are treated as nuisance parameters. We propose new pivotal procedures for estimating the high-dimensional nuisance parameters which appear in our formulation. We use a multiplier bootstrap procedure to compute critical values and establish its validity for achieving simultaneously valid confidence regions for a potentially high-dimensional set of endogenous variable coefficients. (c) 2021 Published by Elsevier B.V.
Keywords:
Honest confidence regions
Instrumental variables
High dimensional models
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