Omitted variable bias of Lasso-based inference methods: A finite sample analysis

TL;DR

This paper analyzes the finite sample biases of Lasso-based inference methods, revealing they can suffer from significant omitted variable bias even with large samples, challenging existing asymptotic inference assumptions.

Contribution

It provides a finite sample analysis of Lasso-based inference methods, highlighting their limitations and comparing them to high-dimensional OLS approaches.

Findings

Lasso-based methods can have substantial omitted variable bias in finite samples.

Bias persists even with large samples and sparse coefficients.

Comparison shows limitations of Lasso-based inference relative to OLS methods.

Abstract

We study the finite sample behavior of Lasso-based inference methods such as post double Lasso and debiased Lasso. We show that these methods can exhibit substantial omitted variable biases (OVBs) due to Lasso not selecting relevant controls. This phenomenon can occur even when the coefficients are sparse and the sample size is large and larger than the number of controls. Therefore, relying on the existing asymptotic inference theory can be problematic in empirical applications. We compare the Lasso-based inference methods to modern high-dimensional OLS-based methods and provide practical guidance.