Does Regional Variation in Wage Levels Identify the Effects of a National Minimum Wage?

This paper uses theory and extensive simulations to study two approaches that use regional wage differences to identify the effects of a national minimum wage: effective-minimum-wage designs, which measure exposure using contemporaneous local wages, and fraction-affected/ gap designs, which measure exposure before reform. I show that these designs can be unreliable in many plausible settings. A Brazilian case study shows that employment and wage-inequality estimates vary sharply across specifications, providing a plausible explanation for conflicting findings in the existing Brazilian literature. The paper concludes with practical recommendations for applied researchers and discusses how similar concerns may arise in other settings.