The synthetic control method has become a valuable and widely-used technique to estimate causal effects even when more traditional fixed effects methods are inappropriate. This paper relaxes two critical assumptions required to implement the synthetic control estimator. First, the synthetic control estimator assumes that the outcomes of the treated unit are within the "convex hull" of the outcomes of the untreated units. In this paper, I show that estimation of the policy effect is possible when the treated unit composes part of the synthetic control for any of the untreated units, permitting the treated unit to be outside the convex hull of the other units. Instead of constructing a synthetic control only for the treated unit, this paper recommends creating a synthetic control for every unit. The difference in the post-treatment outcomes for each unit compared to its synthetic control is related to the corresponding difference in the policy variable, identifying the policy effect. Second, the synthetic control estimator assumes the existence of a "perfect" synthetic control, which only occurs if the outcome variable is not subject to transitory shocks. In this paper, I suggest a straightforward two-step approach which first generates predicted values of the outcome variables for each unit and uses these predicted values instead of the actual values of the outcome variable when constructing the synthetic control units. Together, these two modifications significantly reduce the restrictions imposed by the synthetic control estimator and provide asymptotically unbiased estimates of the policy effect. Simulations show that this approach outperforms the traditional synthetic control estimator. I apply the new estimator to study the mortality effects of the 2006 Massachusetts Health Care Reform and estimate that the reform reduced the mortality rate by 3%.
Powell, David, Imperfect Synthetic Controls: Did the Massachusetts Health Care Reform Save Lives?. Santa Monica, CA: RAND Corporation, 2018. https://www.rand.org/pubs/working_papers/WR1246.html.
Powell, David, Imperfect Synthetic Controls: Did the Massachusetts Health Care Reform Save Lives?, Santa Monica, Calif.: RAND Corporation, WR-1246, 2018. As of June 22, 2022: https://www.rand.org/pubs/working_papers/WR1246.html