Synthetic Difference in Differences

• Activity Number: 3 - Individualized Treatment Rules
• Type: Invited
• Date/Time: Monday, August 3, 2020 : 10:00 AM to 11:50 AM
• Sponsor: Biometrics Section
• Author(s): David Abraham Hirshberg* and Dmitry Arkhangelsky and Susan Athey and Guido Imbens and Stefan Wager
• Companies: Stanford GSB and CEMFI Madrid and Stanford University and Stanford GSB and Stanford University
• Keywords: causal inference; panel data; treatment effect; difference in differences; synthetic control; longitudinal

Abstract

We propose a new estimator for the average treatment effect on the treated in panel data with simultaneous adoption of treatment. The estimator is a weighted version of the well-known difference in differences estimator. Like the synthetic control estimator, our estimator uses unit weights to improve the validity of the comparison between treated and control units. And like time-series forecasting methods based on linear regression, our estimator compares a weighted average of pre-treatment time periods that is predictive of the post-treatment period to improve the validity of pre/post comparisons. We find that this new Synthetic Difference in Differences estimator has attractive properties compared to synthetic control, linear forecasting, and difference-in-differences estimators. We show that our estimator is asymptotically unbiased and normal under relatively weak assumptions and give a consistent estimator for its standard error.