Difference-in-Differences Subset Scan

Difference-in-differences (DiD) has been extensively applied in the literature to elicit the average causal effect of an intervention or policy. Though researchers explore heterogeneity in the treatment effect with respect to time or some observed covariate (usually driven by domain knowledge), there is limited work on a principled, algorithmic approach to discovering the subgroups that exhibit heterogeneity in the treatment effect in DiD settings. In this research, we propose the Difference-in-Differences Subset Scan (DiD-Scan), which finds subregions of the observed covariate space corresponding to anomalous patterns in the conditional mean treatment effect. We mold our method to the DiD setting by also enabling a scan for dynamic effects over time and across multiple outcome variables. This supports the discovery of patterns where a subset of outcomes are highly impacted for a limited time window. We develop a generalized likelihood ratio-based scoring function to quantify the treatment effect of a given subgroup and propose a computationally efficient method to discover the subgroups with the largest treatment effect. We extend the method to consider correlations across time, a common condition in difference-in-difference settings that increases the difficulty of subset identification. Lastly, we demonstrate the efficacy and interpretability of the method with both simulations and applications to real datasets, replicating and extending two published studies.