2017/12/21 by Alexandre Belloni, Christian Hansen, Belloni, Alexandre +3
Mathematics · #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1712.08102
High-dimensional linear models with endogenous variables play an increasingly\nimportant role in recent econometric literature. In this work we allow for\nmodels with many endogenous variables and many instrument variables to achieve\nidentification. Because of the high-dimensionality in the second stage,\nconstructing honest confidence regions with asymptotically correct coverage is\nnon-trivial. Our main contribution is to propose estimators and confidence\nregions that would achieve that. The approach relies on moment conditions that\nhave an additional orthogonal property with respect to nuisance parameters.\nMoreover, estimation of high-dimension nuisance parameters is carried out via\nnew pivotal procedures. In order to achieve simultaneously valid confidence\nregions we use a multiplier bootstrap procedure to compute critical values and\nestablish its validity.\n