A (Flexible) Synthetic Control Method for Count Data and Other Non-Negative Outcomes.

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 pre-intervention outcomes and covariates. The method is increasingly being used to evaluate population-level interventions in epidemiology. While 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 while ensuring that the estimated counterfactuals remain non-negative. 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.