Why cite economists doing literature reviews on the minimum wage when you can cite a report by Republican politicians? This seems to be Don Boudreaux's perspective.
There are literature reviews compiled by economists on this. My understanding of these literature reviews is that there are a lot of studies with small positive effects, a lot of studies with small negative effects, none with particularly big effects, and it kinda centers on a zero effect. This suggests to me that a simple competitive supply and demand model of the minimum wage is missing something because there should not be an average zero effect (much less the presence of some clear positives in some cases) if that model were true. That's why I think the monopsony model makes a fair deal of sense. With a monopsony model you're not guaranteed to get a positive effect of course. If the minimum wage increase is sufficiently large given the production technology and market conditions of an individual firm, some firms may indeed reduce their employment as a result. But it explains why we'd see these mixed and weak findings.
I said as much in my response to the question Don posed to me the other day on the minimum wage. I'm still curious what his response is (I emailed it to him and he responded, so I know he saw it).