Synthetic Controls and Weighted Event Studies with Staggered Adoption

• Activity Number: 563 - Statistical Methods for State Health Policy Evaluation
• Type: Invited
• Date/Time: Thursday, August 6, 2020 : 3:00 PM to 4:50 PM
• Sponsor: Health Policy Statistics Section
• Author(s): Avi Feller and Eli Ben-Michael* and Jesse Rothstein
• Companies: UC Berkeley and UC Berkeley and UC Berkeley
• Keywords: Panel data; Causal inference

Abstract

Staggered adoption of policies by different units at different times creates promising opportunities for observational causal inference. The synthetic control method (SCM) is a recent addition to the evaluation toolkit but is designed to study a single treated unit and does not easily accommodate staggered adoption. In this paper, we generalize SCM to the staggered adoption setting. Current practice involves fitting SCM separately for each treated unit and then averaging. We show that the average of separate SCM fits does not necessarily achieve good balance for the average of the treated units, leading to possible bias in the estimated effect. We propose "partially pooled" SCM weights that instead minimize both average and state-specific imbalance, and show that the resulting estimator controls bias under a linear factor model. We also combine our partially pooled SCM weights with traditional fixed effects methods to obtain an augmented estimator that improves over both SCM weighting and fixed effects estimation alone. We assess the performance of the proposed method via extensive simulations and in several applications. We implement the proposed method in the augsynth R package.