Does regional variation in wage levels identify the effects of a national minimum wage?

This paper examines the identification assumptions underlying two types of estimators of the causal effects of minimum wages based on regional variation in wage levels: the "effective minimum wage" and the "fraction affected/gap" designs. For the effective minimum wage design, I show that the identification assumptions emphasized by Lee (1999) are crucial for unbiased estimation but difficult to satisfy in empirical applications for reasons arising from economic theory. For the fraction affected design at the region level, I show that economic factors such as a common trend in the dispersion of worker productivity or regional convergence in GDP per capita may lead to violations of the "parallel trends" identifying assumption. The paper suggests ways to increase the likelihood of detecting those issues when implementing checks for parallel pre-trends. I also show that this design may be subject to biases arising from the misspecification of the treatment intensity variable, especially when the minimum wage strongly affects employment and wages.