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

Most applied synthetic control studies do not explain the identifying assumptions supporting causal inference. We describe these assumptions, illustrate how they can fail, and examine the consequences of such failures. We offer recommendations for discretionary implementation decisions, connecting each to a core identifying assumption. We also show how to implement a Synthetic Control Using Lasso, which allows a high-dimensional donor pool, automates model selection, allows donors from multiple variable types, and permits extrapolation and negative weights. In an application, we estimate how recreational marijuana legalization affects sales of alcohol and over-the-counter painkillers, finding reductions in alcohol sales.