Benchmarking parallel trends violations in regression imputation difference-in-differences

Difference-in-differences studies increasingly use regression imputation methods as analternative to the conventional two-way fixed effects (TWFE) estimator, fitting a TWFEregression on the controls to impute treated counterfactuals. A common method for obtainingpre-trend placebo estimates uses the same model to impute outcomes for control units –the default in the popular fect R package. We decompose this “in-sample imputation”estimator into its component 2×2 differences-in-differences to show two severe biases: anattenuation bias driven by redundant differences-in-differences that are zero by constructionand a contamination bias resulting from the use of “early adopters” as controls. This leads tomisleading estimates of the magnitude and shape of the pre-treatment trends. “Leave-one-out” approaches address this, but only when done separately by treatment timing group. Ourresults suggest a trilemma: no single approach simultaneously avoids redundant comparisons,uses the same baseline periods as the treatment effects, and produces estimates for every pre-treatment period. We re-analyze a study on the political effects of the 2008 “shale shock” onRepublican vote share in U.S. coal counties (Gazmararian 2025). While the original analysisused in-sample imputation and concluded pre-trends were small, corrected approaches revealpre-trends comparable to the estimated treatment effects.