Testing Common Causality of Covariates: Evidence from Private-Sector Ban-the-Box Policies

Abstract

When including covariates in Difference-in-Differences, researchers must consider not only which covariates to include, but also how to model them. The Common Causality of Covariates (CCC) assumption requires that covariate coefficients in the untreated potential-outcome model remain constant across regions and periods. Violations can bias DID estimators even when the relevant covariates are correctly included. I develop a CCC test based on Wald tests from an additive model that uses untreated observations in pre-treatment periods to assess whether covariate coefficients vary across regions, periods, or both. Motivated by this specification problem, I show theoretically that well-specified Integrated DID estimators are consistent, whereas overly restrictive models can introduce bias and, under conditional homoskedasticity, unnecessarily flexible models can reduce efficiency. Monte Carlo simulations show that the CCC test has good size and power. An application to private-sector Ban-the-Box policies finds variation across both regions and periods, with positive estimated effects on wages and occupational quality among employed private-sector workers.