Adversarially Robust Synthetic Control: Ensuring Robustness Against Highly Correlated Controls and Weight Shifts

Music City Center 

The synthetic control method estimates the causal effect by comparing the outcomes of a treated unit to a weighted average of control units that closely match the pre-treatment outcomes of the treated unit. This method presumes that the relationship between potential outcomes of treated and control units remains consistent before and after treatment. However, this estimator may become unreliable when there are shifts in these relationships or when control units are highly correlated. To address these challenges, we introduce the Adversarially Robust Synthetic Control (ARSC). This framework enhances robustness by accommodating potential shifts in relationships and addressing high correlations among control units, thereby ensuring a more reliable causal estimand. When key assumptions for the classical synthetic control method hold, the ARSC method performs comparably to traditional methods. However, under assumption violations, ARSC produces a conservative estimate of the true effect. The ARSC approach employs a distributionally robust optimization by defining the causal estimand as the solution to a worst-case optimization problem, taking into account all possible distributions of the treated unit's potential outcomes that align with observed pre-treatment data. We derive a closed-form solution for the population ARSC estimand and develop a corresponding data-dependent estimator. The consistency of this estimator is established, and its practical utility is demonstrated through various case studies, including an analysis of the economic impact of terrorism in the Basque Country.

Causal inference

Synthetic control method

Adversarial robustness

Distributional shift 

IMS