| Abstract |
We consider evaluating the impact of an intervention when time series data on a single treated unit and multiple untreated units are observed, in pre- and post- treatment periods. In seminal work of Abadie & Gardeazabal (2003) and Abadie et al. (2010), they proposed a synthetic control (SC) method as an approach to relax the parallel trend assumption on which difference-in-differences methods typically rely upon. The term “synthetic control” refers to a weighted average of control units that is built to match the treated unit’s pre-treatment outcomes, such that the post- treatment trajectory of the SC outcome predicts the unobserved potential outcome of the treated unit. The treatment effect is then estimated as the difference in post- treatment outcomes between the treated unit and the SC. Common practice to estimate the weights is to regress the pre-treatment outcomes of the treated unit on that of the control units using ordinary or weighted least squares (OLS or WLS). However, it has been shown that these estimators can be inconsistent. In addition, inference is mostly conducted by placebo tests which lacks formal theory. In this talk, we introduce a proximal causal inference framework for the synthetic control approach, and formalize identification and inference for the average treatment effect for the treated unit. We further extend the traditional linear interactive effect model to more general cases such as nonlinear models allowing for binary and count outcomes rarely studied in the SC literature. We illustrate our proposed method in simulation studies and an application to evaluation of California’s tobacco control program. |
