Differentially Private Synthetic Control

Abstract

Synthetic control is a causal inference tool used to estimate the treatment effects of an intervention by creating synthetic counterfactual data. This approach combines measurements from other similar observations (i.e., donor pool) to predict a counterfactual time series of interest (i.e., target unit) by analyzing the relationship between the target and the donor pool before the intervention. As synthetic control tools are increasingly applied to sensitive or proprietary data, formal privacy protections are often required. In this work, we provide the first algorithms for differentially private synthetic control with explicit error bounds. Our approach builds upon tools from non-private synthetic control and differentially private empirical risk minimization. We provide upper and lower bounds on the sensitivity of the synthetic control query and provide explicit error bounds on the accuracy of our private synthetic control algorithms. We show that our algorithms produce accurate predictions for the target unit and that the cost of privacy is small. Finally, we empirically evaluate the performance of our algorithm, and show favorable performance in a variety of parameter regimes, as well as provide guidance to practitioners for hyperparameter tuning.