On event studies and distributed-lags in two-way fixed effects models: Identification, equivalence, and generalization

We discuss properties and pitfalls of panel-data event study designs. We derive three main results. First, assuming constant treatment effects before and/or after some event time, also known as binning, is a natural restriction imposed on theoretically infinite effect windows. Binning identifies dynamic treatment effects in the absence of never-treated units and is particularly suitable in case of multiple events. Second, event study designs with binned endpoints and distributed-lag models are numerically identical leading to the same parameter estimates after correct reparametrization. Third, classic dummy variable event study designs can be generalized to models that account for multiple events of different sign and intensity of the treatment, which are common in public and labor economics. We demonstrate the practical relevance of our methodological points in an application studying the effects of unemployment benefit duration on job search effort.