The synthetic control method, introduced in Abadie and Gardeazabal(2003), has emerged as a popular empirical methodology for estimating a causal effects with observational data, when the “gold standard” of a randomized control trial is not feasible. In a recent survey on causal inference and program evaluation methods in economics, Athey and Imbens (2015) describe the synthetic control method as “arguably the most important innovation in the evaluation literature in the last fifteen years”. While many of the most prominent application of the method, as well as its genesis, were initially circumscribed to the policy evaluation literature, synthetic controls have found their way more broadly to social sciences, biological sciences, engineering and even sports. However, only recently, synthetic controls have been introduced to the machine learning community through its natural connection to matrix and tensor estimation in Amjad, Shah and Shen (2017) as well as Amjad, Misra, Shah and Shen (2019).

In this tutorial, we will survey the rich body of literature on methodical aspects, mathematical foundations and empirical case studies of synthetic controls. We willprovide guidance for empirical practice, with special emphasis on feasibility and data requirements, and characterize the practical settings where synthetic controls may be useful and those where they may fail. We will describe empirical case studies from policy evaluation, retail, and sports. Moreover, we will discuss mathematical connections of synthetic controls to matrix and tensor estimation, high dimensional regression, and time series analysis. Finally, we will discuss how synthetic controls are likely to be instrumental in the next wave of development in reinforcement learning using observational data.