Selection and Parallel Trends
This paper addresses how treatment-group selection threatens the parallel trends assumption in Difference-in-Differences (DiD) estimation—a critical yet under-characterized identification challenge. Method: We formally characterize the empirical content of this threat and derive necessary and sufficient conditions for parallel trends to hold under general selection mechanisms. We propose a “selection-driven bias decomposition framework” that systematically partitions DiD estimation bias into selection effects and time-varying heterogeneity effects, and develop operational benchmarking strategies—both with and without covariates—grounded in causal inference theory, selection modeling, and sensitivity analysis. Contribution/Results: Applied to the National Supported Work (NSW) experiment reanalysis, our approach quantifies and corrects selection bias, substantially improving the credibility of DiD estimates and the robustness of causal conclusions.