Estimation and Inference of Treatment Effects with $L_2$-Boosting in High-Dimensional Settings

TL;DR

This paper develops methods for valid inference on treatment effects using $L_2$-Boosting in high-dimensional data, extending to instrumental variables and providing theoretical convergence results and empirical validation.

Contribution

It introduces new convergence rate results for post- and orthogonal $L_2$-Boosting in high-dimensional settings, enabling valid treatment effect inference without beta-min assumptions.

Findings

Proposed methods outperform Lasso in simulations.

Validated inference procedures for treatment effects with high-dimensional controls.

Empirical application estimates effects of bank branch overlap on stock returns.

Abstract

Empirical researchers are increasingly faced with rich data sets containing many controls or instrumental variables, making it essential to choose an appropriate approach to variable selection. In this paper, we provide results for valid inference after post- or orthogonal $L_2$-Boosting is used for variable selection. We consider treatment effects after selecting among many control variables and instrumental variable models with potentially many instruments. To achieve this, we establish new results for the rate of convergence of iterated post-$L_2$-Boosting and orthogonal $L_2$-Boosting in a high-dimensional setting similar to Lasso, i.e., under approximate sparsity without assuming the beta-min condition. These results are extended to the 2SLS framework and valid inference is provided for treatment effect analysis. We give extensive simulation results for the proposed methods and compare them with Lasso. In an empirical application, we construct efficient IVs with our proposed methods to estimate the effect of pre-merger overlap of bank branch networks in the US on the post-merger stock returns of the acquirer bank.