This paper resolves issues in the minimum wage-employment debate by using factor model econometric methods to address concerns related to unobserved heterogeneity. Recent work has shown that the negative effects of minimum wages on employment found using traditional methods are sensitive to the inclusion of controls for regional heterogeneity and selection of states that experience minimum wage hikes, leaving the two sides of the debate in disagreement about the appropriate approach. Factor model methods are an ideal solution for this disagreement, as they allow for the presence of multiple unobserved common factors, which can be correlated with the regressors. These methods provide a more flexible way of addressing concerns related to unobserved heterogeneity and are robust to critiques from either side of the debate. The factor model estimators produce minimum wage-employment elasticities that are much smaller than the traditional OLS results and are not statistically different from zero. These results hold for many specifications and two data sets that have been used in the minimum wage-employment literature. A simulation shows that unobserved common factors can explain the different estimates seen across methodologies in the literature.