Estimating Causal Effects in the Presence of Partial Interference Using Multivariate Bayesian Structural Time Series Models

Researchers regularly use synthetic control methods for estimating causal effects when a sub-set of units receive a single persistent treatment, and the rest are unaffected by the change. In many applications, however, units not assigned to treatment are nevertheless impacted by the intervention because of cross-unit interactions. This paper extends the synthetic control methods to accommodate partial interference, allowing interactions within predefined groups, but not between them. Focusing on a class of causal estimands that capture the effect both on the treated and control units, we develop a multivariate Bayesian structural time series model for generating synthetic controls that would have occurred in the absence of an intervention enabling us to estimate our novel effects. In a simulation study, we explore our Bayesian procedure’s empirical properties and show that it achieves good frequentists coverage even when the model is misspecified. Our work is motivated by an analysis of a marketing campaign’s effectiveness by an Italian supermarket chain that permanently reduced the price of hundreds of store-brand products. We use our new methodology to make causal statements about the impact on sales of the affected store-brands and their direct competitors. Our proposed approach is implemented in the CausalMBSTS R package.