Sunday, July 9, 2017

The labor demand curve

John Cochrane may have written the most concise argument that economic theory should be rejected:
Economic theory also forces logical consistency that would not otherwise be obvious. You can't argue that the labor demand curve is vertical today, for the minimum wage, and horizontal tomorrow, for immigrants. There is one labor demand curve, and it is what it is.
The conclusion should be: Therefore, we must reject the concept of a fixed labor demand curve.

Overall, Cochrane seems to get the concept of science wrong. A few days ago, I noted that Cochrane does not seem to understand what economic theory is for. Now he seems to misunderstand what empirical data is for.

See, the issue is that no one is "arguing" that the labor demand curve is vertical for the minimum wage. No novel theory is being constructed to give us a vertical labor demand curve. The studies are empirical studies. The empirical studies show if there is such a thing as a labor demand curve, it must be vertical for the minimum wage. But really, all the studies show is that raising the minimum wage does not appear to have a disemployment effect. The "Econ 101" approach pictures this as a vertical labor demand curve. And that would be fine on its own.

Likewise, no one is "arguing" that the labor demand curve is horizontal for an influx of workers. Again, no novel theory is being constructed to give us a horizontal labor demand curve. The empirical studies are only showing that an influx of workers does not lower wages. The "Econ 101" approach pictures this as a horizontal labor demand curve. And that would be fine on its own.

But those two results do not exist in a vacuum. If you try to understand both empirical results with a fixed labor demand curve, then your only choice is to reject the fixed curve. You have two experiments. One shows the labor demand curve is horizontal, the other vertical. Something has to give.

*  *  *

Now there is a way to make sense of these results using information equilibrium. Here are several posts on the minimum wage (here, here, and here). The different effects of immigration versus other supply shocks are described in this post. If you are curious, click the links. But the main point is that when we make "Econ 101" arguments, we are making lots of assumptions and therefore restricting the scope of our theory. 

In order to obtain the Econ 101 result for the minimum wage and immigration, you essentially have to make the same specific assumptions (assume the same scope): 1) demand changes slowly with time and 2) supply increases rapidly compared to demand changes. The commensurate scope is the reason why the Econ 101 diagrams are logically consistent. But they're both inconsistent with the empirical data. Therefore we should question the scope. Under different scope conditions (i.e demand and supply change), information equilibrium tells us increasing the minimum wage or increasing immigration increases output ‒ meaning that you should probably accept that demand is changing in both cases. Which is the point of higher minimum wage and pro-immigration arguments: they create economic growth. 

As an aside, I think the a lot of the right-leaning economics might stem from assuming demand changes slowly. The cases I just mentioned made me think of a case where Dierdre McCloskey seems to be assuming demand changes slowly to argue against Thomas Piketty.

In the same sense that while you can obtain an isothermal expansion curve [1] from a restricted scope of an ideal gas (that scope being that temperature is constant, hence isothermal), if your data is inconsistent with the theory you should begin to question the scope (was it really isothermal?). Unfortunately, Econ 101 ‒ and for that matter much of economic theory ‒ does not examine its scope. As Cochrane says: it's about "logic". Logic has no scope. Things are either logical or illogical. That's not now science works. Some descriptions are approximate under particular assumptions (constant temperature, speeds slower than the speed of light) and fail when those assumptions aren't met.

Given empirical data requiring contradictory interpretations of theory (different labor demand curves), a scientific approach would immediately question the scope of the theory being applied. What assumptions did I make to come up with a fixed demand curve? I definitely shouldn't assume studies that contradict the theory are wrong.



[1] Actually, in information equilibrium the Econ 101 demand curve is essentially an isodemand curve (i.e. a curve where demand is held constant/changes slowly) analogous to an isothermal process using the thermodynamic analogies. If I say the minimum wage won't decrease employment because it increases overall demand, the Econ 101 rebuttal is to come back and say "assuming demand doesn't change ...". It'd be kind of funny if it wasn't so perversely in the defense of the powerful.


  1. My own thinking is heavily influenced by ideas from the field of Hydraulics, especially flow through apertures.

    Energy provide by gravity and fluid characteristics interact to form the base case for volume of flow. Aperture shape and upstream characteristics heavily influence the actual flow. The final result is a formula based on empirical data for each aperture, all formulas having in common applied energy and fluid characteristics.

    I see the theoretical drivers for minimum wage and immigration being the same. However, the case for each represents a much different "aperture" with the result that we should expect each case to be heavily influenced by the "upstream" situation. Despite differences between empirical data, we should be able to find basic drivers common to both wage-employment models.

    I have not personally compared minimum wage and immigration unemployment empirical studies searching for common elements. Having made this comment, I will try to look for common elements in future readings on these subjects.

    1. One of the problems with applying fluid flow models to economics is that fluid flow equations essentially derive from conservation laws (and therefore the spatial, temporal, and other symmetries of the system).

      What is being conserved? What are these symmetries?

    2. Good Questions!

      In fluid flow, we would conserve energy and the fluid itself. We add the observed constraint that energy only flows in one direction, towards a more diffuse condition. I would add my observation that both energy and fluids seem to have been created by methods beyond human control..

      On the other hand, money is an entirely human invention.

      Humans invented money. Money is like the fluid used in a model. Money must be made by some human method and we must be able to destroy it. At the same time, money is carefully conserved by most users who are generally unable (by legal fiat) to make their own money.

      This duality of must-be-created and conservation is a major hurdle for macro-economics. To some of us, bank lending is the key to money creation and destruction. Conservation of money is the key to fair trade between trading partners and the key to maintaining value for newly created money.

      If money is a parallel to a fluid, what is parallel to energy? I would suggest that the value of money is a parallel to energy. Money without value will create flow about as well as a fluid in the ocean. That said, I don't draw many parallels between energy and value. The two concepts don't invite quick links in my mind.

      Labor enters this picture as supply item. Each person has a new hour of time allocated each hour. Labor is clearly a renewable resource, to be either used or allowed to pass unused, following the choice of the owner.

      We see empirically see that labor interacts with money. I always keep an interface between the two physically different concepts. By that I mean that while they might be expressed as one in terms of the other, any actual flow must follow both the rules for labor and the rules for money.

      The rule for labor is simply that each hour is used or left unused. Labor hours cannot be stored as labor hours but can be stored in traded value as money. The trick here is that labor can only be traded-for-money if someone first has money to trade.

      You can see that I think there are clear parallels between fluid flow and economics. Most important is the parallel between money and the fluid itself. Humans make money; God(?) makes fluids.

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  3. Why can't a single demand curve be both nearly vertical and nearly horizontal? The rectangular hyperbola is such a curve though there are others too. So the effect measured (whether of minimum wage changes or immigration) would depend on whether the labour supply curve cuts the labour demand curve at a point where it is horizontal or vertical. This simple fact explains the huge variety of results in empirical studies. Typically most studies fail to mention when they were carried out.

    See "The derivation of involuntary unemployment from Keynesian micro-foundations" in Real-World Economics Review June 2017 for an explanation of why the general form of both the labour demand curve and of aggregate demand (and every other demand curve) is the rectangular hyperbola.

    1. It would have to be both horizontal and vertical near the the same point since the empirical studies are both deviations from "normal" (i.e. a change in min wage, or a change in labor supply). No continuous curve can have two different values for the derivative at the same point.

      The situation you are describing would be two different systems -- one in a state on the flat part of the curve, the other in a state on the steep part of the curve. I believe that is one of the ways mainstream economics tries to square this particular circle. Or more precisely, the part of mainstream econ that wants to keep the simple econ 101 picture (e.g. Caplan, Cochrane, and Borjas) says the empirical data is from tests conducted on different parts of the curve. So congratulations, you've re-discovered right wing neoclassical economics :)

    2. No. It does not have to be at the same point. That is because changes in demand on the rectangular hyperbola are reflected in changes across curves, not changes along curves.

      You need to read the paper before jumping to sarcastic conclusions.

    3. We are exogenously setting a price floor in one case (minimum wage) and exogenously adding supply in the other (immigration). We are not exogenously changing demand therefore we are moving *along* a demand curve. Changes "across demand curves" represent e.g. population growth, income growth, or some other exogenous change in demand (shifts of the demand curve).

      As an aside, your insistence in your paper on the importance of a "rectangular hyperbola" compared to a linear function means that all changes are large compared to whatever scale you are considering. ΔU/U ~ 1, ΔNGDP/NGDP ~ 1. These are clearly false for most modern economies (even in a bad recession ΔU/U ~ 0.1, ΔNGDP/NGDP ~ 0.1). If you zoom in on a "rectangular hyperbola" you get a line. So your arguments dependent on the rectangular hyperbola would fail for small shifts such as Seattle's change in minimum wage from ~ 11 to 13 dollars (Δp/p ~ 0.1). It doesn't make basic mathematical sense.

      I'm sorry about the sarcasm, but I think you should potentially consider you might be suffering from the Dunning-Kruger effect. You've made an undergraduate level error about how supply and demand curves work; do you really think you've come up with something that will change how economists look at their field? Are you sure?

    4. I think you are being too quick to criticize Philip. Two points:

      1. If you zoom in on a "rectangular hyperbola", you never get a line. You get a curve that approaches a line, with the deviation tending towards "too small to matter". How small that must be is a matter for judgement.

      2. Philip uses an example of increased availability of fish at lower price. He is correct to say that both fish supplier and fish customer tend to handle near the same TOTAL VALUE of fish in that circumstance (although it will not be a constant gross value).

      However, more fish would displace some other product(s) which, in turn, would decrease consumption and total valuation for that(those) products. We would therefore expect to see that a shift along one demand curve can cause as shift in location for other demand curves. I think that considering all the shifts in aggregate, we would trend towards your more conventional linear demand curve, which in turn, would make your argument also make sense.

      You can see that I think both Philips argument and yours can be brought to logical congruence.

    5. You get a curve that approaches a line, with the deviation tending towards "too small to matter". How small that must be is a matter for judgement.

      If only there was a way to put this mathematically ...

      We can't really be brought into logical congruence because Philip thinks that the decision to empirically measure the effect of a minimum wage retroactively moves your equilibrium to a different demand curve. If I decide to measure the effect of an increase of immigration, my equilibrium moves to yet another demand curve.

      It's a quantum economy. If I measure its wave nature (min wage), it's a wave (vertical demand curve). If I measure its particle nature (immigration), it's a particle (horizontal demand curve).

      How does the economy know in advance which empirical test I'm about to conduct?

      Or are all minimum wage rises happening in an economy with a vertical labor demand curve and all immigration happens when we have horizontal curves?

      That's at least a defensible argument -- politics and economic forces might well make minimum wage rises more likely in some scenarios than others. But this isn't what Philip is saying.


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