A Guide to Dynamic Difference-in-Differences Regressions for Political Scientists

Difference-in-differences (DiD) designs for estimating causal effects have grown in popularity throughout political science. It is common for DiD studies report their main results using a ``dynamic" or ``event study" two-way fixed effects (TWFE) regression. This regression combines estimates of average treatment effects for multiple post-treatment time periods alongside placebo tests of the main identifying assumption: parallel trends. Despite their ubiquity, there is little clear and consistent guidance in the discipline for how researchers should estimate dynamic treatment effects. This paper develops a novel decomposition of the dynamic TWFE regression coefficients in terms of their component 2x2 difference-in-differences comparisons in the style of Goodman-Bacon (2021). We use this decomposition to illustrate how bias can result from the incorrect specification of baseline time periods, the inclusion of units and time periods where all observations are treated, and heterogeneity in the dynamic treatment effects across different treatment timing groups. Our results provide additional intuition for the source of bias due to effect heterogeneity---what Sun and Abraham (2021) term ``contamination bias"---by directly characterizing the contaminated 2x2 comparisons. We then provide a common framework for connecting the many proposed ``heterogeneity-robust" estimators in the literature, noting that they vary primarily in which 2x2 comparisons they choose to include. Through a replication of three studies published in prominent political science journals, we conclude by showing how attentiveness to baseline selection and specification can alter findings.