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

This paper asks whether regional wage differences can identify the effects of a national minimum wage. I study two common exposure-based approaches: effective-minimum-wage designs, which compare the minimum wage to contemporaneous local wages, and fraction-affected/gap designs, which measure pre-reform exposure to the new minimum. Using theory, simulations, and evidence from Brazil, I show when these approaches can mislead and how their performance depends on specification choices. The results lead to practical recommendations for applied researchers, including when to avoid these designs, how to test their assumptions, which specifications are more reliable, and how similar concerns may apply to other settings.