  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.
