Advocates of minimum wage increases have long touted their potential to reduce poverty. This study assesses this claim. Using data spanning nearly four decades from the March Current Population Survey, and a dynamic difference-in-differences approach, we find that a 10 percent increase in the minimum wage is associated with a (statistically insignificant) 0.17 percent increase in the probability of longer-run poverty among all persons. With 95% confidence, we can rule out long-run poverty elasticities with respect to the minimum wage of less than -0.129, which includes central poverty elasticities reported by Dube (2019). Prior evidence suggesting large poverty-reducing effects of the minimum wage are (i) highly sensitive to researcher’s choice of macroeconomic controls, and (ii) driven by specifications that limit counterfactuals to geographically proximate states (“close controls”), which poorly match treatment states’ pre-treatment poverty trends. Moreover, an examination of the post-Great Recession era — which saw frequent, large increases in state minimum wages — failed to uncover poverty-reducing effects of the minimum wage across a wide set of specifications. Finally, we find that less than 10 percent of workers who would be affected by a newly proposed $15 federal minimum wage live in poor families.