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.
Devavrat Shah is a Professor with the department of Electrical Engineering and Computer Science and Director of Statistics and Data Science at the Massachusetts Institute of Technology. His current research interests are at the interface of Statistical Inference and Social Data Processing. His work has been recognized through prize paper awards in Machine Learning, Operations Research and Computer Science, as well as career prizes 2008 ACM Sigmetrics Rising Star Award, 2010 Erlang prize from the INFORMS Applied Probability Society and 2019 ACM Sigmetrics Test of Time Paper Award. He is a distinguished young alumni of his alma mater IIT Bombay. He has authored monographs “Gossip algorithms” and “Explaining the success of nearest neighbors in prediction’’. He co-founded machine learning start-up Celect, Inc. which is part of Nike, Inc. since August 2019.
Alberto Abadie is an econometrician and empirical microeconomist, with broad disciplinary interests that span economics, political science and statistics. Professor Abadie received his Ph.D. in Economics from MIT in 1999. Upon graduating, he joined the faculty at the Harvard Kennedy School, where he was promoted to full professor in 2005. He returned to MIT in 2016, where he is Professor of Economics and Associate Director of the Institute for Data, Systems, and Society (IDSS).
His research areas are econometrics, statistics, causal inference, and program evaluation. Professor Abadie’s methodological research focuses on statistical methods to estimate causal effects and, in particular, the effects of public policies, such as labor market, education, and health policy interventions. He is Associate Editor of Econometrica and AER: Insights, and has previously served as Editor of the Review of Economics and Statistics and Associate Editor of the Journal of Business and Economic Statistics. He is a Fellow of the Econometric Society.