Friday, January 17, 2014

Minimum wage theory: a commenter's question

I am not a very good theorist. To some extent I think I probably grasp macro theory better than micro theory, but the point is I'm not a theorist in any case. Day in and day out I am an empirical economist with varying degrees of sophistication depending on the project I'm working on. Out of personal interest I sometimes moonlight as a third-rate dealer in second-hand theories of first-order importance (in other words, I like to do a little history of economic thought).

I don't pretend to be a theorist, though, and in the interest of not pretending to be one I wanted to just share commenter YouNotSneaky!'s questions and thoughts about the theory behind the nil effect of the minimum wage in the data:
"Can you give a link to a paper that makes the monopsony argument? It's been awhile since I looked at it. I did look up the Burdette & Mortensen matching model recently which I gather is what this argument is based on. However, in that model (or ye basic search model, like say in Romer's Adv Macro) minimum wage still decreases employment. In B&M a minimum wage *can* increase social welfare but that's different (the increase in utility of those who retain higher paying jobs is greater than those who experience longer unemployment spells). You can use the B&M monopsony model to argue for minimum wage, but you can't use it to explain why the empirical work does not detect employment effects.

Personally I'm pretty sure something else is going on (probably the data just isn't good enough, not enough variation, close to equilibrium min wages, adjustments in hours rather than persons etc)

This is one version of the B&M"
I don't know Burdette and Mortensen specifically although it is this sort of model that Manning uses and refers to when he talks about monopsony and the minimum wage. I've read a little of him, and I've read some of Pissarides on equilibrium unemployment. I rely on much simpler expositions of fixed costs and turnover to motivate my understanding of the connection to the minimum wage - namely, the Oi paper on quasi-fixed factors. And I agree (and have stated here) that this flavor of models is not entirely reassuring on the employment effects, however that should be more apparent in the long run than in the short run I think. I don't know - let me know what you think about that argument.

I think the data is getting better and the identification strategies are getting better and the result is not going away, so I would not blame the data.

I do think the other two issues raised are relevant: that these are often "modest" increases, not departing far from the equilibrium wage, and that there are adjustments on other margins potentially. Dube, Lester, and Reich do provide an upper bound on the hours adjustment. It's not immediately obvious to me why it would make sense to make your adjustment on hours rather than employment (in the pre-Obamacare era at least!). The only reason to do that, it seems to me, is to deliberately fool economists.


  1. "It's not immediately obvious to me why it would make sense to make your adjustment on hours rather than employment "

    Training costs for one. If you anticipate that at some point in the future you might want to increase your labor input back up, then retaining your already-trained workers but giving each one fewer hours makes more sense than letting a trained worker go and then having to hire a new worker and having to train them all over again.

    Or maybe fairness and morale? You're going to cut down total labor input. If you let one person go that person bears the whole brunt of the adjustment. Makes your remaining workers skitty, because they think "that could happen to me". If you cut hours across the board you spread the pain out.

    1. But we generally find that firms DON'T want to spread the pain. They would rather concentrate cuts in employment cuts than hours or wages. I'm not sure whether that's different in these labor markets, but that's our usual assumption.

      A lot of this is part time work, so there's only so many hours you can cut in the first place and still have people interested in the job. Much easier to hire fewer.

      Training costs make sense as a response to something like cyclical fluctuations or shocks - but the minimum wage is a permanent change. I'm still not sure this is your strongest point.

    2. We find this? For salaried workers obviously, but in minimum wage sector?

      The part-time work hours here can be something like 35 hours a week so there's room. Of course if the min wage increase is big enough you'd pretty much have to let people go, but again, we're talking about fairly small increases here.

      With the training costs, a minimum wage is in a sense actually a temporary shock, not a permanent one if there are ongoing (exogenous) productivity increases. Sooner or later these will erode the value of the minimum wage so that it's not a binding floor anymore. This doesn't even have to be your own productivity increase, just economy wide, which increases demand for your product.

  2. Let me see if I can explain a bit more about why search & matching and resulting monopsony power will not get you that minimum wages increase employment.

    Start with a basic search model, for example that found in Romer's Advanced Macro. That model can be characterized by two curves in wage/employment space. The first is a "wage bargaining curve" which gives you the wage rate that results from a bargaining process, given the level of employment. More existing employment (lower unemployment) means workers have more bargaining power so wages are higher and this curve is upward sloping (it's a lot like a Philips Curve used in the old days by economists who these days might be described as "heterodox"). Then there is the "free entry curve" which is obtained by setting the (present discounted) value of a vacancy to zero (any constant will do). The value of a vacancy is decreasing in the wage that will be paid when the vacancy is filled. So if wages are higher, to keep that value of a vacancy at zero (constant) firms must be able to find workers faster (otherwise you're sitting there with an empty, costly vacancy for a long time). This means that the existing level of employment must be lower - there must be lots of unemployed workers out there looking for jobs. So this curve is downward sloping.

    You can introduce a minimum wage by replacing the "wage bargaining curve" with a horizontal line. If the minimum wage is above the wage that would obtain in search equilibrium, you still get lower employment because the "free entry" curve is downward sloping.

    If you look at Burdette and Mortensen the set up is similar, except that instead of bargaining, firms post wages (they have wage setting power) and workers, when matched, decide whether to accept or reject these offers. This results in an equilibrium wage distribution. But the key is that for the purposes of the effect of minimum wages, this doesn't matter. There is still a "free entry" curve, it's downward sloping, so a higher minimum wage will still decrease employment (in fact, a higher minimum wage *might* decrease the average wage offered in the market)

    But this result is more general. Basically, as long as you got a search model with an endogenous number of vacancies (jobs, firms, etc) you have something like a free entry condition. Any non-crazy model will have V depend negatively on wages and positively on how fast that vacancy will be filled. In other words, it will depend positively on the unemployment rate. The V=0, or V=constant condition then describes a downward sloping curve.

    As long as you got that curve, it doesn't matter how wages are determined; posting, setting, monopsony, competition, aliens. As long as the minimum wage is above the wage that would prevail without it, you'll get lower employment.

    Of course there might be some search and matching model that works differently. But I don't know of one off hand and that's why I was asking for a specific reference.


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