Tactics for design and inference in synthetic control studies: An applied example using high-dimensional data

We describe identification assumptions underlying synthetic control studies and offer recommendations for key---and normally ad hoc---implementation decisions, focusing on model selection; model fit; cross-validation; and decision rules for inference. We outline how to implement a Synthetic Control Using Lasso (SCUL). The method---available as an R package---allows for a high-dimensional donor pool; automates model selection; includes donors from a wide range of variable types; and permits both extrapolation and negative weights. In an application, we employ our recommendations and the SCUL strategy to estimate how recreational marijuana legalization affects sales of alcohol and over-the-counter painkillers, finding reductions in alcohol sales.