The widely employed regression discontinuity (RD) causal inference method is intended for scenarios where there is a known cutoff of a running variable such that the probability of receiving treatment changes abruptly at this cutoff. Examples of such settings are countless. The key assumption underlying these analyses is that outcomes of the untreated units just left to the cutoff are good representatives of the counterfactual outcomes of the treated units just right to the cutoff had they been untreated.

However, this assumption is often implausible when changes other than the intervention of interest occur at the cutoff (for example, other treatments or policies are implemented at the same cutoff). In these scenarios, researchers retreat to ad-hoc analyses that are not justified by any theory and yield results with unclear interpretations. These analyses seek to exploit additional data for which no intervention was applied for all units (regardless of their running variable value). This could be the case when data from multiple time periods and/or multiple comparison groups are available.

In this project, we (1) Develop formal theory and statistical methods for studying causal effects with generalized RD designs utilizing multiple time periods or comparison groups data and (2) Implement the proposed methods to real data and provide practical guidance on how to conduct RD analysis with multiple time points and/or multiple comparison groups.