Methodological Foundations of the Synthetic Control Group Design: Formalizing Model Construction for Case Study Applications in the Social Sciences
To estimate the effect of an exogenous intervention on a treated unit, a control unit is necessary. Control time-series are chosen to render threats to internal validity implausible. While a literature review can often reveal the most plausible threats to the internal validity for a particular research design or substantive outcome, literature reviews rarely suggest an appropriate control time-series. Sometimes, appropriate control time series simply do not exist. When an appropriate control time-series is not available, it may be possible to construct a close approximation of an ideal control series from a set of control units that are less than appropriate individually. I describe the statistical theory underlying the synthetic control group design, outline the modeling procedure to construct a synthetic control group, and identify aspects of the model construction process that are in need of formalization. The importance of choosing an appropriate scaling method for the outcome of interest, and the inclusion of pre-intervention observations versus covariates as predictors are discussed at length in Chapters 4 and 5. Beyond those prescriptive conclusions, the early chapters trace the development of causal reasoning, contextualize synthetic control methods within the econometric wave, and serve as an algebraic reference. The dissertation concludes with a discussion of some of some remaining unknowns regarding synthetic control applications, including predictor “trimming”, fuzzy onset treatments, and restricting the analysis timeframe. Guidelines for social science applications of the synthetic control method are outlined, and readers are cautioned to avoid applying the method in a few specific circumstances.