This paper addresses the limitations of two-way fixed effects regressions in estimating dynamic treatment effects in event studies, particularly when treatment effects are heterogeneous across units. The authors show that coefficients on treatment leads and lags in such regressions can be contaminated by effects from other periods, leading to misleading conclusions about pretrends. They propose an alternative estimator that is free of contamination and more robust to treatment effect heterogeneity.
The paper begins by introducing the event study design, where units receive treatment at different times, and discusses the challenges of estimating dynamic treatment effects in this setting. It defines the cohort-specific average treatment effect on the treated (CATT) as a key building block for interpreting treatment effects. The authors then present three identifying assumptions: parallel trends in baseline outcomes, no anticipatory behavior prior to treatment, and treatment effect homogeneity.
The paper demonstrates that under the parallel trends assumption, the population regression coefficient on a relative period bin is a linear combination of CATTs from its own period and other periods. However, without strong assumptions, these coefficients can be contaminated by treatment effects from other periods. The authors show that the weights underlying these coefficients are non-linear functions of the distribution of cohorts and can be estimated using an auxiliary regression.
The paper also discusses the implications of treatment effect heterogeneity for pretrends tests. It shows that pre-period coefficients used to test for pretrends can be contaminated by treatment effects from other periods, making such tests unreliable. The authors propose an alternative estimation method that uses cohort shares as weights, leading to more interpretable estimates of dynamic treatment effects.
The paper concludes by emphasizing the importance of considering treatment effect heterogeneity when estimating dynamic treatment effects in event studies and highlights the limitations of two-way fixed effects regressions in this context. The authors provide an empirical application using hospitalization data to illustrate their findings and demonstrate the advantages of their alternative estimator.This paper addresses the limitations of two-way fixed effects regressions in estimating dynamic treatment effects in event studies, particularly when treatment effects are heterogeneous across units. The authors show that coefficients on treatment leads and lags in such regressions can be contaminated by effects from other periods, leading to misleading conclusions about pretrends. They propose an alternative estimator that is free of contamination and more robust to treatment effect heterogeneity.
The paper begins by introducing the event study design, where units receive treatment at different times, and discusses the challenges of estimating dynamic treatment effects in this setting. It defines the cohort-specific average treatment effect on the treated (CATT) as a key building block for interpreting treatment effects. The authors then present three identifying assumptions: parallel trends in baseline outcomes, no anticipatory behavior prior to treatment, and treatment effect homogeneity.
The paper demonstrates that under the parallel trends assumption, the population regression coefficient on a relative period bin is a linear combination of CATTs from its own period and other periods. However, without strong assumptions, these coefficients can be contaminated by treatment effects from other periods. The authors show that the weights underlying these coefficients are non-linear functions of the distribution of cohorts and can be estimated using an auxiliary regression.
The paper also discusses the implications of treatment effect heterogeneity for pretrends tests. It shows that pre-period coefficients used to test for pretrends can be contaminated by treatment effects from other periods, making such tests unreliable. The authors propose an alternative estimation method that uses cohort shares as weights, leading to more interpretable estimates of dynamic treatment effects.
The paper concludes by emphasizing the importance of considering treatment effect heterogeneity when estimating dynamic treatment effects in event studies and highlights the limitations of two-way fixed effects regressions in this context. The authors provide an empirical application using hospitalization data to illustrate their findings and demonstrate the advantages of their alternative estimator.