This is actually about the minimum wage debate. And I'm more asking you a question than giving you my answer. Bear with me for a minute.
You are a seller. You sell a good for money. You have some degree of monopoly power over the good you sell. You face a downward-sloping demand curve, you set a price somewhere along that demand curve, and the buyers decide how much you will actually sell at that price. You always want to sell more at that price, because the price you set is above your marginal cost. If you set your price, and then demand unexpectedly increases, you are pleased to sell more. The seller with monopoly power is always hungry to sell more at the posted price; buyers are not hungry to buy more.
You are a buyer. You buy a good for money. You have some degree of monopsony power over the good you buy. You face an upward-sloping supply curve, you set a price somewhere along that supply curve, and the sellers decide how much you will actually buy at that price. You always want to buy more at that price, because the price you set is below your marginal benefit. If you set your price, and then supply unexpectedly increases, you are pleased to buy more. The buyer with monposony power is always hungry to buy more at the posted price; sellers are not hungry to sell more.
I hope the symmetry in the above two paragraphs is obvious. The "good" might be an output or an input. The "good" might be labour. (And please note that I have been explicit about the good being sold or bought for money. That matters. Because in a barter economy, anyone who has monopoly power ipso facto has monopsony power. If I swap apples for bananas, the downward-sloping demand curve for my apples is the very same thing as the upward-sloping supply curve for my bananas. Sorry for this digression, but I can't help being a money/macro guy, and this whole monopoly/monopsony thing is very important for how I do macroeconomics. Monetary policy would have the exact opposite Short Run real effects if we had a supply-constrained monopsonistic economy instead of a demand-constrained monopolistic economy.)
Applied econometrics, and applied labour economics, are not my forte. So I have been leaving the recent minimum wage debate for those who have a comparative (and absolute) advantage in those things. But I would like to try to fit what they say into my macroeconomic worldview. And the easiest way for me to do this is to suppose that there sometimes tends to be monopsony power in the market for the lowest-paid workers -- those most likely to be affected by changes in the minimum wage. This would explain why the employment effects of an increase in the minimum wage would tend to be mixed. A small increase in the minimum wage (relative to the equilibrium with no minimum wage) might increase employment, and a large increase might decrease employment. The net effects will depend very much on the particular time and place.
But if the monopsony explanation is correct, we should expect to see buyers of minimum wage labour hungrier to buy more labour than sellers are to sell more labour. Does that seem plausible? (I don't know, which is why I'm asking.)
Now ideally I ought to define exactly what I mean by "hungriness" and say how it is measured. But I can't, so I won't. I can only give an example, to illustrate what I have in mind. Take the example of the market in restaurant meals. This looks like monopolistic competition to me. I find it very plausible that an individual restaurant faces a downward-sloping demand curve, and so has monopoly power in that sense. If it raises its menu prices by 10%, it will sell fewer meals, but won't lose all its customers. And most restaurants most of the time seem to want to sell more meals at the prices posted on their menus. They rarely turn extra customers away. If I want a restaurant meal, and am willing to spend the money, all I usually need to do is find a restaurant I like. It's usually not hard to persuade them to sell me a meal. It's usually harder for them to persuade me to buy a meal from them.
Restaurants are (usually) "hungry" to sell more meals; their patrons are not (usually) "hungry" to buy more meals. That's what monopoly power looks like.
OK, so what about the market for labour in restaurants (or the market for any type of labour that pays at or close to the mimimum wage)? Are the buyers of that labour hungrier to buy than the sellers are to sell? If so, that looks like monopsony. If not, it doesn't.
Anecdata welcome (because that's probably all we've got).