A (Flexible) Synthetic Control Method for Count Data and Other Nonnegative Outcomes. Issue 5 (24th June 2021) - Bonander, Carl
Abstract : Supplemental Digital Content is available in the text. Abstract : The synthetic control method is a covariate balancing method that exploits data from untreated regions to construct a synthetic control that approximates a single, aggregate treatment unit on a time series of preintervention outcomes and covariates. The method is increasingly being used to evaluate population-level interventions in epidemiology. Although the original version can be used with bounded outcomes, it imposes strong constraints on the balancing weights to ensure that the counterfactuals are based solely on interpolation. This feature, while attractive from a causal inference perspective, is sometimes too conservative and can lead to unnecessary bias due to poor covariate balance. Alternatives exist that allow for extrapolation to improve balance but existing procedures may produce negative estimates of the counterfactual outcomes and are therefore inappropriate for count data. We propose an alternative way to allow for extrapolation, although ensuring that the estimated counterfactuals remain nonnegative. Following a related proposal, we add a penalty to the balancing procedure that favors interpolation over extrapolation whenever possible. As we demonstrate theoretically and using empirical examples, our proposal can serve as a useful alternative when existing approaches yield demonstrably poor or unrealistic counterfactuals. Finally, we provide functions to implement the method in R.