Tactics for Design and Inference in Synthetic Control Studies: An Applied Example Using High-Dimensional Data

Abstract

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.

Keywords: Synthetic Controls, Machine Learning, Marijuana Legalization, High-Dimensional Data

JEL Classification: C01, C55, C81, I18