Inference for high-dimensional instrumental variables regression
arXiv:1708.05499
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.
arXiv comment53 pages
References in corpus (9)
- Nearly unbiased variable selection under minimax concave penalty
- Simultaneous analysis of Lasso and Dantzig selector
- On the conditions used to prove oracle results for the Lasso
- Least squares after model selection in high-dimensional sparse models
- Regularization Methods for High-Dimensional Instrumental Variables Regression With an Application to Genetical Genomics
- Inference for High-Dimensional Sparse Econometric Models
- A Practical Scheme and Fast Algorithm to Tune the Lasso With Optimality Guarantees
- Reconstruction from anisotropic random measurements
- On the Distribution of Penalized Maximum Likelihood Estimators: The LASSO, SCAD, and Thresholding