Before revision:  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 .
After revision:  We show that in settings with variation in treatment timing across units, the coefficient on a given lead or lag picks up spurious terms consisting of treatment effects from other periods .