Wild Bootstrap Inference for Linear Regressions with Many Covariates

TL;DR

This paper introduces a modified wild bootstrap method for linear regressions with many covariates and heteroskedastic errors, demonstrating its validity and superior finite sample performance over traditional methods.

Contribution

It proposes a simple modification to the wild bootstrap procedure and proves its asymptotic validity in high-dimensional linear regression models.

Findings

Modified wild bootstrap performs well with small samples.

Outperforms standard methods based on normal critical values.

Effective when the number of covariates is large.

Abstract

We propose a simple modification to the wild bootstrap procedure and establish its asymptotic validity for linear regression models with many covariates and heteroskedastic errors. Monte Carlo simulations show that the modified wild bootstrap has excellent finite sample performance compared with alternative methods that are based on standard normal critical values, especially when the sample size is small and/or the number of controls is of the same order of magnitude as the sample size.