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

Abstract

We discuss important properties and pitfalls of panel-data event study designs. We derive three main results. First, binning of effect window endpoints is a practical necessity and key for identification of dynamic treatment effects. 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 particularly interesting for research in labor economics and public finance. We show the practical relevance of our methodological points in a replication study.

Forecasts for a post‐Roe America: The effects of increased travel distance on abortions and births

“…A triple‐difference specification with state‐by‐year fixed effects to control for annual state‐level shocks yields similar results (Appendix Table A1, Panel C), demonstrating that the effects of distance are not confounded with contemporaneous state policy changes. Additionally, a model with distributed lags and leads, which is equivalent to an event study research design implemented for a continuous treatment variable (Schmidheiny & Siegloch, 2023), supports the conclusion that there are not substantial pre‐trends in abortions or births in advance of travel distance changes (Appendix Table A5 and Figure A3). This finding belies a reverse causality story in which changes in distance are driven by changes in demand.…”

Buying time: The effect of Market Facilitation Program payments on the supply of grain storage

“…Essentially, the model estimates the effect of observed treatment levels on outcomes at different points in time. To identify these dynamic effects, there must be one reference period where no dynamic effect is estimated; we omit the 2017-18 marketing year j = −1 as is typical in panel data event studies (Freyaldenhoven et al, 2019;Schmidheiny & Siegloch, 2019).…”

Covid-19 Lockdown in Ecuador: Are there Gender Differences in Unemployment?

“…We have five pre-lockdown and three post-lockdown time periods. We set the period before the policy implementation (t = −1) as the omitted category (normalized to 0) (Freyaldenhoven, Hansen, & Shapiro, 2019;Fuest, Peichl, & Siegloch, 2018;Schmidheiny & Siegloch, 2022). In addition to exploring potential pre-trends, event study designs are useful for examining dynamic effects after the onset of the policy.…”