How much monopsony power is there?

Via Tyler Cowen.

"This is from Adam Ozimek:

…if big firms are bargaining down wages then why do labor economists consistently find a large firm wage premium? To take one example from many, one recent study on retailers found that after controlling for individual and store characteristics, firms with at least 1,000 employees pay 9% to 11% more than those employing 10 or fewer.
Third, if firms’ bargaining power over their employees is growing, then why are they increasingly contracting out for work? Lawrence Katz and Alan Krueger argue that from 2005 to 2015, the share of workers hired out through contract companies grew from 0.6% to 3.1%. A company with labor market power wouldn’t want to contract out work to another company. They’d want to hire workers directly to take advantage of that power.
Fourth, the CEA report points to the minimum wage literature as evidence of monopsony power. Leaving aside the debate over whether the minimum wage reduces employment (I say yes, the report says no) the literature clearly shows that the minimum wage increases prices. As Daniel Aaronson and Eric French have pointed out, the monopsony model implies that the minimum wage should increase employment and output, thereby decreasing prices. That prices rise is inconsistent with the monopsony model.

I say there is plenty of monopsony in the short run in individual situations, mostly because workers carve out perks for themselves in individual firms.  In other words, if firms have some short-run bargaining power, it is because they have lost the longer-run bargaining power game."