This paper analyzes the effects of the minimum wage on wage inequality, relative employment and over-education. Using an effciency wage model we show that over-education can be generated endogenously and that an increase in the minimum wage can raise both total and low-skill employment, and produce a fall in inequality. Evidence from the US suggests that these theoretical results are empirically relevant. The over-education rate has been increasing and our regression analysis suggests that the decrease in the minimum wage may have led to a deterioration of the employment and relative wage of low-skill workers.