Title: On proximal causal inference with synthetic controls
Authors: Xu Shi - University of Michigan (United States) [presenting]
Abstract: The focus is on 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. A synthetic control (SC) method was previously proposed as an approach to relax the parallel trend assumption in difference-in-differences methods. The term SC refers to a weighted average of control units built to match the treated unit's pre-treatment outcome trajectory, such that the SC's post-treatment outcome predicts the treated unit's unobserved potential outcome under no treatment. The treatment effect is then estimated as the difference in post-treatment outcomes between the treated unit and the SC. A 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. However, it has been established that these estimators can fail to be consistent. We introduce a proximal causal inference framework for the SC approach and formalize identification and inference for both the SC weights and the treatment effect on the treated unit. We further extend the traditional linear model to nonlinear models allowing for binary and count outcomes which are currently under-studied in SC literature. We illustrate our proposed methods with simulation studies and an application to evaluate the 1990 German Reunification.