  We study the role of selection into treatment in difference-in-differences
(DiD) designs. We derive necessary and sufficient conditions for parallel
trends assumptions under general classes of selection mechanisms. These
conditions characterize the empirical content of parallel trends. For settings
where the necessary conditions are questionable, we propose tools for
selection-based sensitivity analysis. We also provide templates for justifying
DiD in applications with and without covariates. A reanalysis of the causal
effect of NSW training programs demonstrates the usefulness of our
selection-based approach to sensitivity analysis.
