Sequential Synthetic Difference in Differences

TL;DR

The paper introduces Sequential SDiD, a new estimator for event studies with staggered treatments that remains reliable even when traditional assumptions fail, supported by theoretical guarantees and iterative imputation.

Contribution

It develops a novel iterative imputation estimator for staggered adoption event studies, with proven asymptotic equivalence to an oracle estimator and formal inference properties.

Findings

Estimator is asymptotically equivalent to oracle OLS

Provides robust inference with asymptotic normality

Effective when parallel trends assumption fails

Abstract

We propose the Sequential Synthetic Difference-in-Differences (Sequential SDiD) estimator for event studies with staggered treatment adoption, particularly when the parallel trends assumption fails. The method uses an iterative imputation procedure on aggregated data, where estimates for early-adopting cohorts are used to construct counterfactuals for later ones. We prove the estimator is asymptotically equivalent to an infeasible oracle OLS estimator within a linear model with interactive fixed effects. This key theoretical result provides a foundation for standard inference by establishing asymptotic normality and clarifying the estimator's efficiency. By offering a robust and transparent method with formal statistical guarantees, Sequential SDiD is a powerful alternative to conventional difference-in-differences strategies.