Difference-in-differences with "bad controls"

2026-08-04

AI Summary

This study addresses the identification bias in difference-in-differences (DiD) estimation arising from the use of covariates affected by treatment—commonly termed “bad controls.” When the parallel trends assumption holds only after conditioning on such variables, the paper proposes two novel approaches: first, conditioning exclusively on their pre-treatment values; second, under an unconfoundedness condition for the covariates, combining imputation with double/debiased machine learning to estimate treatment effects. The work provides the first systematic characterization of the identification conditions under which “bad controls” can serve as valid control variables and extends the framework to staggered treatment settings, offering corresponding pre-tests. Empirical application to the effect of unemployment on income demonstrates the validity and robustness of the proposed methods.

Abstract

This paper considers difference-in-differences identification strategies when the parallel trends assumption holds after conditioning on covariates that may themselves be affected by the treatment (often referred to as "bad controls"). We show that common approaches such as simply dropping bad controls are often ill-advised and develop two alternative approaches that allow bad controls to function as genuine controls despite being affected by treatment. First, we derive explicit conditions that rationalize conditioning only on pre-treatment values of the bad control, leading naturally to the Callaway and Sant'Anna (2021) estimator with pre-treatment values as covariates. Second, under a covariate unconfoundedness condition, we develop imputation and double/debiased machine learning estimators that recover the average treatment effect on the treated. We extend these results to staggered treatment adoption, provide pre-tests for the identifying assumptions, and apply the methods to study the effects of job displacement on earnings.

Problem

• difference-in-differences
• bad controls
• parallel trends
• treatment effect
• covariate adjustment

Innovation

• bad controls
• difference-in-differences
• double machine learning
• pre-treatment covariates
• staggered treatment