"Synthetic Difference in Differences"
Stanford GSB

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 the proposed ``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.
Joint with Dmitry Arkhangelsky, David A. Hirshberg, Guido W. Imbens, Stefan Wager