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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.

AbstractWe evaluate whether a lack of guidance on how to choose the matching variables used in the Synthetic Control (SC) estimator creates specification‐searching opportunities. We provide theoretical results showing that specification‐searching opportunities are asymptotically irrelevant if we restrict to a subset of SC specifications. However, based on Monte Carlo simulations and simulations with real datasets, we show significant room for specification searching when the number of pre‐treatment periods is in line with common SC applications, and when alternative specifications commonly used in SC applications are also considered. This suggests that such lack of guidance generates a substantial level of discretion in the choice of the comparison units in SC applications, undermining one of the advantages of the method. We provide recommendations to limit the possibilities for specification searching in the SC method. Finally, we analyze the possibilities for specification searching and provide our recommendations in a series of empirical applications.

In recent years, a widespread consensus has emerged about the necessity of establishing bridges between quantitative and qualitative approaches to empirical research in political science. In this article, we discuss the use of the synthetic control method as a way to bridge the quantitative/qualitative divide in comparative politics. The synthetic control method provides a systematic way to choose comparison units in comparative case studies. This systematization opens the door to precise quantitative inference in small-sample comparative studies, without precluding the application of qualitative approaches. Borrowing the expression from Sidney Tarrow, the synthetic control method allows researchers to put 'qualitative flesh on quantitative bones.' We illustrate the main ideas behind the synthetic control method by estimating the economic impact of the 1990 German reunification on West Germany. Adapted from the source document.