A flexible, heterogeneous treatment-effects difference-in-differences estimator for repeated cross-sections

The difference-in-differences (DID) study design is an important tool for causal inference. A commonly observed special case involves a staggered entry into treatment. In this context, the observation that the standard two-way fixed-effects estimator that assumes a constant treatment effect across cohorts and time can produce a biased estimate of the overall treatment effect has led to several new approaches for dealing with both staggered timing and heterogeneous treatment effects (for example, Callaway and Sant’Anna 2021). In Deb et al. (https://www.nber.org/papers/w33026, 2025), we show that an appropriate regression specification using a pooled repeated cross-sectional sample can provide consistent treatment effects in a DID design with staggered entry under the usual DID assumptions. Our flexible linear model estimated by ordinary least squares with covariates (X)—FLEX—allows the covariates to enter the model in a flexible way. To be precise, we prove that FLEX is equivalent to an imputation estimator derived in Borusyak et al. (2024). In this presentation, we will describe FLEX and the associated Stata command, flexdid. We will illustrate the use of FLEX with an empirical example and provide comparisons with some benchmark estimators.