We structurally estimate an equilibrium search model using German administrative data and use this for counterfactual analyses of a uniform minimum wage. The model with worker and firm heterogeneity does not restrict the sign of employment effects a priori and allows for different job offer arrival rates for the employed and the unemployed. We find that unemployment is a non-monotonic function of the minimum wage level. Effects differ strongly by labour market segment. Cross-segment variation of the estimated effects is mostly driven by firm productivity levels rather than by search frictions or the opportunity cost of employment.