Estimating Dynamic Treatment Effects in Event Studies with Heterogeneous Treatment Effects

Event studies are frequently used to estimate average treatment effects on the treated (ATT). In estimating the ATT, researchers commonly use fixed effects models that implicitly assume constant treatment effects across cohorts. We show that this is not an innocuous assumption. In fixed effect models where the sole regressor is treatment status, the OLS coefficient is a non-convex average of the heterogeneous cohort-specific ATTs. When regressors containing lags and leads of treatment are added, the OLS coefficient corresponding to a given lead or lag picks up spurious terms consisting of treatment effects from other periods. Therefore, estimates from these commonly used models are not causally interpretable. We propose alternative estimators that identify certain convex averages of the cohort-specific ATTs, hence allowing for causal interpretation even under heterogeneous treatment effects. To illustrate the empirical content of our results, we show that the fixed effects estimators and our proposed estimators differ substantially in an application to the economic consequences of hospitalization.