Inference for High-Dimensional Sparse Econometric Models

TL;DR

This paper develops estimation and inference methods for high-dimensional sparse econometric models, addressing imperfect regressor selection and applying these techniques to instrumental variables and partially linear models.

Contribution

It introduces novel inference methods for high-dimensional sparse models, especially in econometrics, considering imperfect regressor selection and applying to IV and partially linear models.

Findings

New inference results for IV and partially linear models

Effective methods for regressor selection with imperfect information

Applications to returns to schooling and growth regression

Abstract

This article is about estimation and inference methods for high dimensional sparse (HDS) regression models in econometrics. High dimensional sparse models arise in situations where many regressors (or series terms) are available and the regression function is well-approximated by a parsimonious, yet unknown set of regressors. The latter condition makes it possible to estimate the entire regression function effectively by searching for approximately the right set of regressors. We discuss methods for identifying this set of regressors and estimating their coefficients based on $\ell_1$-penalization and describe key theoretical results. In order to capture realistic practical situations, we expressly allow for imperfect selection of regressors and study the impact of this imperfect selection on estimation and inference results. We focus the main part of the article on the use of HDS models and methods in the instrumental variables model and the partially linear model. We present a set of novel inference results for these models and illustrate their use with applications to returns to schooling and growth regression.