As in so many issues, the short run is not the same as the long run for the minimum wage

Important points here.

In the long run, of course, the real value of the minimum wage is pretty stable (right now its a little below what it was in the late 60s - in other words, not even growing with productivity), which is what you'd like to see if we think the long-run impacts of the minimum wage are more substantial than the short-run impacts.