Published on Fri Dec 06 2019
Synthetic Controls and Weighted Event Studies with Staggered Adoption
Staggered adoption of policies by different units at different times creates
promising opportunities for observational causal inference. Estimation remains
challenging, however, and common regression methods can give misleading
results. A promising alternative is the synthetic control method (SCM), which
finds a weighted average of control units that closely balances the treated
unit's pre-treatment outcomes. In this paper, we generalize SCM, originally
designed to study a single treated unit, to the staggered adoption setting. We
first bound the error for the average effect and show that it depends on both
the imbalance for each treated unit separately and the imbalance for the
average of the treated units. We then propose "partially pooled" SCM weights to
minimize a weighted combination of these measures; approaches that focus only
on balancing one of the two components can lead to bias. We extend this
approach to incorporate unit-level intercept shifts and auxiliary covariates.
We assess the performance of the proposed method via extensive simulations and
apply our results to the question of whether teacher collective bargaining
leads to higher school spending, finding minimal impacts. We implement the
proposed method in the augsynth R package.