“Synthetic Difference-in-Differences” (2021), by Dmitry Arkhangelsky et al. Mathematics research paper. Original abstract below, unchanged. A free PDF is available.

Synthetic Difference-in-Differences

Dmitry Arkhangelsky, Susan Carleton Athey, David A. Hirshberg et al. · November 30, 2021 · Mathematics

Abstract

We present a new estimator for causal effects with panel data that builds on insights behind the widely used difference-in-differences and synthetic control methods. Relative to these methods we find, both theoretically and empirically, that this “synthetic difference-in-differences” estimator has desirable robustness properties, and that it performs well in settings where the conventional estimators are commonly used in practice. We study the asymptotic behavior of the estimator when the systematic part of the outcome model includes latent unit factors interacted with latent time factors, and we present conditions for consistency and asymptotic normality. (JEL C23, H25, H71, I18, L66)

Free PDF DOI: 10.1257/aer.20190159