Journal
JOURNAL OF ECONOMETRICS
Volume 217, Issue 1, Pages 79-111Publisher
ELSEVIER SCIENCE SA
DOI: 10.1016/j.jeconom.2019.09.009
Keywords
High-dimensional inference; Instrumental variables; De-biasing
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Funding
- University of Washington Royalty Research Fund
- Cloud Credits for Research by Amazon
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This paper concerns statistical inference for the components of a high-dimensional regression parameter despite possible endogeneity of each regressor. Given a first-stage linear model for the endogenous regressors and a second-stage linear model for the dependent variable, we develop a novel adaptation of the parametric one-step update to a generic second-stage estimator. We provide conditions under which the scaled update is asymptotically normal. We then introduce a two-stage Lasso procedure and show that the second-stage Lasso estimator satisfies the aforementioned conditions. Using these results, we construct asymptotically valid confidence intervals for the components of the second-stage regression coefficients. We complement our asymptotic theory with simulation studies, which demonstrate the performance of our method in finite samples. (C) 2019 Elsevier B.V. All rights reserved.
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