Saturday, July 11, 2009

Labor Demand Curves Slope Down?

Consider the consequences of capital-reversing. I like to say that one is that explaining wages and employment by well-behaved supply and demand functions for labor is of doubtful logic. Here's what some others have had to say:
"the pattern of activities adopted in the face of long-run factor-price changes can be complicated and counterintuitive. Consequently, the long-run demand for factors can be badly behaved functions of factor prices." -- Michael Mandler (1999) Dilemmas in Economic Theory: Persisting Foundational Problems of Microeconomics, Oxford University Press.

"However, as was argued in Section 3 with regard to 'perversely' shaped, that is, upward sloping, factor-demand functions, this possibility would question the validity of the entire economic analysis in terms of demand and supply." -- H. D. Kurz and N. Salvadori (1995) Theory of Production: A Long Period Analysis, Cambridge University Press

"The essential point of the criticism concerns the factor demand curves. The discovery that factor demand curves may be positively sloped in the relevant range, not negatively..." -- Bertram Schefold (1990) "Joint Production, Intertemporal Preferences, and Long-Period Equilibirum," Political Economy: Studies in the Surplus Approach, V. 6, 1990, pp. 162-163.

"there is not necessarily an inverse monotonic relation between the cost-minimizing quantity of an input and its price... Figures 6.17a-6.17c can be interpreted as demand curves for labour... in Figure 6.17b, ...the sectoral demand curve is upward-sloping... I have shown in Figure 6.17c that the aggregate demand curve is not downward-sloping in the presence of reswitching: indeed, like the sectoral demand curve, it is not even monotonic. Reswitching is sufficient, not necessary, for the aggregate demand curve for labour not to be downward-sloping: to see this, consider Figure 6.18..." -- J. E. Woods (1990) The Production of Commodities: An Introduction to Sraffa, Humanities Press
It is a theme of this blog that mainstream economists have yet to integrate this challenge into their theories and teaching.


Gabriel said...

Of course people are aware of this [ ] but there's nothing to integrate as such.

On some ranges, the demand curve can be sloped whichever way, but this either a) doesn't matter for the question at hand; or b) can be assumed away with a choice of functional forms. Also, this doesn't seem to be the answer to any major empirical puzzle out there, so if you can progress without including that extra layer of flexibility, people will choose to do that.

As you yourself point out plenty of times, the general non-existence of comparative statics results in competitive economies can be attributed ot the Mantel-Debreu theorem. But there are comparative statics results for particular functional forms and under other assumptions re: market structure.

chrismealy said...

Robert, do you have any favorite empirical studies of factor price dynamics? I'm thinking of stuff along the lines of Blinder's "Asking About Prices"

BruceMcF said...

"On some ranges, the demand curve can be sloped whichever way, but this either a) doesn't matter for the question at hand; or b) can be assumed away with a choice of functional forms."

This is a key difference between science and math ... in science, assuming a functional form in order to "solve" the problem that the real world relationship may (1) not be functional and (2) may not have a form compatible with a given analytical toolkit even if it is functional ...

... is not something that counts as "solving" the problem at hand.

Anonymous said...

"this either a) doesn't matter for the question at hand; or b) can be assumed away with a choice of functional forms"

true science at work... If the facts get in the way, then assume that they don't and then "solve" the problem.

I'm surprised that the Catholic Church did not take that approach with Galileo -- they could just have announced that the earth-centric view of the world was correct as the evidence against doesn't matter for the question at hand or can be assumed away...

An Anarchist FAQ

Robert Vienneau said...

Chris, I don't know about favorites, but I'm currently reading Nitzan and Bichler's Capital as Power, and I was impressed with Hall and Hitch's 1939 paper when I recently skimmed it.

I'm of course more with Bruce than Gabriel.

YouNotSneaky! said...

Ugh. I hate it when people think that expressing an opinion unequivocally, with enough "snark" qualifies as intelligent argument. Particularly when they're really heavy handed and not too creative on the "snark" part (hey, aesthetics counts for something). Here, let me show you how to do it.

So what Gabriel means is that any model of human behavior that is general enough is going to admit ... general phenomenon. In other words, once you relax enough assumptions you arrive at a description of human behavior where "anything can happen". In economics, this is true on the demand side with the SMD Theorem (Robert's favorite "heterodox" approaches circumvent this problem by constructing their models so that demand doesn't even play a role - so it's sort of "cheating" of them to even quote SMD) and with the whole "reswitching business" (et al) it's also true on the production side. As it's been shown the Sraffian approach basically means that anything can happen. Wages could shoot up to crazy levels if a hamster farts somewhere and plummet when Joan Robinson turns in her grave. In fact, that approach, with its production-side generality, has no predictive power what so ever and so in fact shouldn't even be called a model (warning: snark ahead) but rather a CCEGA. That is a "contrived counter example generating algorithm". That's all it's good for. It doesn't shed any insight on any human phenomenon. It doesn't explain anything. It doesn't predict anything. All it says is that "if I pick my parameters reallly, realllllly, carefully, I can get a different result" - because it is a general approach.

So what Gabriel means, I think, is that to get away from this "anything can happen, therefore what my ideology tells me is right will happen" approach you got to make stronger assumptions. I.e. You got to assume some functional forms. And then you go to the data and see if the date contradict the strong assumptions you've made. Yes? Ok, then we have a candidate. No, then we make different assumptions on the functional forms. But we just can't work in a model that can always change the answer on us.

And yes, that is how "real science", or at least about as real as you can get in social science, works.