Inference for high-dimensional instrumental variables regression

David Gold, Johannes Lederer and Jing Tao

Journal of Econometrics, 2020, vol. 217, issue 1, 79-111

Abstract: 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.

Keywords: High-dimensional inference; Instrumental variables; De-biasing (search for similar items in EconPapers)
JEL-codes: C14 C31 C36 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (14)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:217:y:2020:i:1:p:79-111

DOI: 10.1016/j.jeconom.2019.09.009

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