A study recently published in MIT’s Review of Economics and Statistics suggests the answer is, “Yes.” From the abstract:

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. [Emphasis added.]

Is anybody on the left paying attention? Does anybody on the left care?