When Covariates Mask Pre-Trends

Abstract

Honest difference-in-differences methods judge how far parallel trends may fail after treatment by how far it failed before treatment, as shown by placebo estimates. When the design adjusts for covariates, the placebo estimates are adjusted too. We show that this benchmark is valid only if the covariates are measured before the earliest placebo window. A covariate measured later already reflects shocks to the outcome during the placebo period, so adjusting for it hides part of the pre-trend. The placebos then look flatter than the true trend and the resulting confidence sets are too narrow. When the covariate is also observed at an early date, the distortion can be estimated and tested. Of 90 recent published studies that adjust for time-varying covariates, 77 measure at least one covariate too late.