On the basis of a structural labor demand model employment effects of a minimum wage are estimated from a single cross-sectional wage distribution. The main contribution of the paper is to relax restrictive functional form assumptions of earlier papers by introducing more flexible semi-parametric censored quantile regressions to this framework. We apply the model to the sectoral minimum wage in the German construction sector. It can be shown that the semi-parametric estimates are within a plausible range: employment levels would be 4-5% higher without the minimum wage in the East where the minimum was binding. The effect for West Germany is markedly smaller, since the minimum wage level was lower in relation to the wage distribution. This semi-parametrically estimated structural approach can be a useful alternative to more popular panel data or difference-in-difference models when the necessary institutional variation or data base is either not available, or the necessary assumptions are problematic.