Synthetic Difference in Differences

70 Pages Posted: 12 Feb 2019 Last revised: 7 Oct 2021

See all articles by Dmitry Arkhangelsky

Dmitry Arkhangelsky

Centre for Monetary and Financial Studies (CEMFI)

Susan Athey

Stanford Graduate School of Business

David Hirshberg

Stanford University

Guido W. Imbens

Stanford Graduate School of Business

Stefan Wager

Stanford University - Department of Statistics

Date Written: February 2019

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.

Suggested Citation

Arkhangelsky, Dmitry and Carleton Athey, Susan and Hirshberg, David and Imbens, Guido W. and Wager, Stefan, Synthetic Difference in Differences (February 2019). Available at SSRN: https://ssrn.com/abstract=3332279

Dmitry Arkhangelsky (Contact Author)

Centre for Monetary and Financial Studies (CEMFI) ( email )

Casado del Alisal 5
28014 Madrid
Spain

Susan Carleton Athey

Stanford Graduate School of Business ( email )

655 Knight Way
Stanford, CA 94305-5015
United States

David Hirshberg

Stanford University

Stanford, CA 94305
United States

Guido W. Imbens

Stanford Graduate School of Business ( email )

655 Knight Way
Stanford, CA 94305-5015
United States

Stefan Wager

Stanford University - Department of Statistics ( email )

Stanford, CA 94305
United States

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