We estimate the impact of youth minimum wages on youth employment by exploiting a large discontinuity in Danish minimum wage rules at age 18, using monthly payroll records for the Danish population. The hourly wage jumps up by 40 percent at the discontinuity. Employment falls by 33 percent and total input of hours decreases by 45 percent, leaving the aggregate wage payment almost unchanged. We show theoretically how the discontinuity may be exploited to evaluate policy changes. The relevant elasticity for evaluating the effect on youth employment of changes in their minimum wage is in the range 0.6-1.1.