Recreational Marijuana Legalization and Substitution of Recreational Psychoactive Substances: An Application of Synthetic Control Using Lasso

We use retail scanner and DEA monitoring data to study the effects of marijuana legalization on sales of several types of alcohol and tobacco products, and opioid prescriptions. The scanner data allows us to investigate the possibility that marijuana affects markets for different product types in different ways. Previous work has examined only broad categories of psychoactive goods and our analysis shows that these aggregate estimates mask underlying heterogeneity. We find that sales of hard liquor and malt liquor decrease following legalization, but that sales of cases (30 cans) of light beer increase following legalization. We use a novel estimator that is an extension of synthetic controls, the Synthetic Control Using Lasso (SCUL), which allows us to combine data from a large set of control states and control goods. This estimation strategy allows for a comparison interrupted time series research design. This estimator should be broadly applicable to research designs where there are either a small number of treated units or where there are a larger number of candidate controls than observations.