Using Event Studies as an Outcome in Causal Analysis

Music City Center 

We propose a causal framework for applications where the outcome of interest is a unit-specific response to events, which first needs to be measured from the data. We suggest a two-step procedure: first, estimate unit-level event studies (ULES) by comparing pre- and post-event outcomes of each unit to a suitable control group; second, use the ULES in causal analysis. We outline the theoretical conditions under which this two-step procedure produces interpretable results, highlighting the underlying statistical challenges. Our method overcomes the limitations of regression-based approaches prevalent in the empirical literature, allowing for a deeper examination of heterogeneity and dynamic effects. We apply this framework to analyze the impact of childcare provision reform on the magnitude of child penalties in the Netherlands, illustrating its ability to reveal nuanced positive relationships between childcare provision and parental labor supply. In contrast, traditional regression-based analysis delivers negative effects, thereby emphasizing the benefits of our two-step approach.