Synthetic Control Estimation Beyond Case Studies: Does the Minimum Wage Reduce Employment?

Abstract

Panel data are often used in empirical work to account for additive fixed time and unit effects. More recently, the synthetic control estimator relaxes the assumption of additive fixed effects for case studies, using pre-treatment outcomes to create a weighted average of other units which best approximate the treated unit. The synthetic control estimator is currently limited to case studies in which the treatment variable can be represented by a single indicator variable. Applying this estimator more generally, such as applications with multiple treatment variables or a continuous treatment variable, is problematic. This paper generalizes the case study synthetic control estimator to permit estimation of the effect of multiple treatment variables, which can be discrete or continuous. The estimator jointly estimates the impact of the treatment variables and creates a synthetic control for each unit. Additive fixed effect models are a special case of this estimator. Because the number of units in panel data and synthetic control applications is often small, I discuss an inference procedure for fixed N. The estimation technique generates correlations across clusters so the inference procedure will also account for this dependence. Simulations show that the estimator works well even when additive fixed effect models do not. I estimate the impact of the minimum wage on the employment rate of teenagers. I estimate an elasticity of -0.44, substantially larger than estimates generated using additive fixed effect models, and reject the null hypothesis that there is no effect.