Saturday, December 3, 2016

Saving the scissors


Noah Smith has a great new post up about "Econ 101-ism" and the labor market. As they say, read the whole thing (including the comments). He has a great discussion of falsification right off the bat. I only have one quibble with this line:
So since people have different expectations for a theory ... whether a theory has been falsified will often be a matter of opinion.
I'd rather say that "falsified" is not a useful term for any theory except one that should never be used (e.g. aether). It's whether a theory is "good enough" (sign/direction, relative magnitude, order of magnitude, 10% error, 1% error, etc) for a problem at hand that will always be a matter of opinion.

But really, just read Noah. Towards the end he says we should stop using Econ 101 for the labor market:
If econ pundits, policy advisors, and other public-facing econ folks were scientifically minded, we'd stop using this model in our discussions of labor markets.
But he then laments that the simple framework probably won't be abandoned:
The fact that this theory is such a simple, clear, well-understood tool - so good for "organizing our thinking", even if it doesn't match reality - will keep it in use long after its sell-by date
Stephen Williamson comments:
Partial equilibrium supply/demand is a simple tool that we can teach to someone with little technical expertise, which can help them think about the basics of economic processes. But for the questions in [Noah's post], it's not even a matter of the theory being "false" - it's just the wrong tool for the job.
David Andolfatto comments as well:
As I (and others) have argued before, Marshall's scissors do not seem like the best organizing framework for the labor market. The scissors assume anonymous spot markets. In contrast, most labor markets involve relationships.
I am 100% behind everything being said. The problem is that abandoning "Econ 101" leaves economics with a dearth of easy-to-communicate tools for understanding what happens in reality. Good, you might say, Econ 101 is wrong about this stuff. And that's true. However, if we have to resort to heterogeneous agents or matching theory ‒ or worse, macro models ‒ then for most people they're going to replace supply and demand with zero sum heuristics. To a large extent, that has already happened. "Immigrants take our jobs," is the common refrain.

What we need is something that's as easy to understand as Marshall's scissors and hasn't been falsified. To that end, let me present the information equilibrium approach to the problem ... which can hopefully save the scissors by clearly defining the scope of the partial equilibrium approach.

I will just look at the labor supply shock below as I've looked at the minimum wage a few times before (notably, here and here).

*  *  *

Let's start by saying the nominal output of jobs (the aggregate demand for jobs) is $N$ and the labor supply is $L$. These derive from distributions over the possible states of the economy (jobs available in Seattle during the summer versus jobs available in Albuquerque in the winter, and workers available in Chicago in the spring), and we have equilibrium when the two distributions are the same. Everyone who wants a job at a specific time in a specific place has found one. The picture we have looks something like this:


where the blue density is the distribution of workers and the white density (with level curves) is the distribution of jobs. Think of something like this picture of population:



These represent distributions over possible states in the economy, and as such are inherently heterogeneous (e.g. just add dimensions for different kinds of jobs). What we want to know is what happens to the information entropy of the distributions when we change either distribution by a little bit (e.g. $N \rightarrow N + d N$). The simplest case would be for uniform distributions and keeping the relative information entropy constant. This results in the information equilibrium condition

$$
W \equiv \frac{dN}{dL} = k \; \frac{N}{L}
$$

where we've defined the "wage" $W$ as the "exchange rate" [1] between aggregate demand for labor and labor supply. The parameter $k$ is called the information transfer index. We can write a shorthand for this relationship using the following notation: $W : N \rightleftarrows L$. This differential equation has the solution [2]

$$
\frac{N}{N_{0}} = \left( \frac{L}{L_{0}}\right)^{k}
$$

where $N_{0}$ and  $L_{0}$ are parameters that we use to define the equilibrium (the state where the distributions pictured above match). We can also solve for the wage $W$:

$$
W = k \; \frac{N_{0}}{L_{0}} \; \left( \frac{L}{L_{0}}\right)^{k - 1}
$$

Note that we've already changed how we're approaching "Econ 101". This is the "usual" (i.e. general equilibrium) case of adding to the labor supply and we've left open the possibility that this increases wages (if $k > 1$). Let's rewrite this in terms of a difference from equilibrium $\Delta X \equiv X - X_{0}$

$$
\begin{align}
1+ \frac{\Delta N}{N_{0}} = \left( 1+ \frac{\Delta L}{L_{0}}\right)^{k}\\
\frac{W}{W_{0}} = \left(1+ \frac{\Delta L}{L_{0}} \right)^{k - 1}
\end{align}
$$

where $W_{0} \equiv k N_{0}/L_{0}$ [3]. This defines a family of relationships that depend critically on $k$


If we go back to our original relationship and ask what happens if $N$ changes slowly [4] with a change in $L$ (i.e. supply changes quickly). In this case we find that [3]

$$
W = W_{0} \; \exp \left( k\;\frac{\Delta L}{L_{0}}\right)
$$

this traces out a supply curve. Compared to the general equilibrium solution above, this is partial equilibrium. Changes in $L$ is movement along the labor supply curve. Shifts of the labor supply curve shift the parameter $L_{0}$ which defines equilibrium (note that shifting $L_{0}$ also changes $W_{0} \equiv k N_{0}/L_{0}$, so a positive/rightward shift of the supply curve represents a fall in price).

Likewise, we can ask what happens if $L$ changes slowly with respect to $N$; in this case, we get a demand curve defined by [3]:

$$
W = W_{0} \; \exp \left( - \frac{\Delta N}{k N_{0}}\right)
$$

We can show these with the traditional Marshallian scissors graphs [5] with the supply curve in red, and the demand curve in blue:


The second graph shows the rightward shift of the supply curve (movement along the demand curve) from a sudden shock of additional labor supply resulting in lower wages. We've finally gotten to the Econ 101 result, but we've had to make some additional assumptions to get here. Namely, that the supply shock is fast or large (or fast and large) relative to the change in demand.

This is where David Andolfatto's comment above comes in (along with Noah's talk of general equilibrium and matching). Under what circumstances can we ever say that a labor shock is fast relative to demand? It takes time to find jobs, and people need stuff to live while they are looking. In a sense, a big influx in migration would probably first be a positive demand shift.

This is not to say there's never a scenario where Econ 101 might occur in a labor market. It does seem to be true that a tight labor market raises wages exactly how Econ 101 says. It's possible that closing a major employer in one town might put downward pressure on wages, but that also might be tied up with a demand shock. Basically, we should probably look at the general equilibrium solutions in the labor market.

Where do the partial equilibrium solutions matter? When demand and supply can be separated and we can definitely make the assumption that supply changes faster than demand. A good example would be dumping a bunch of blueberries or Magic, the Gathering cards on the market. You can usually change the supply of either much faster than the demand for either. In this case you might briefly fall into the "partial equilibrium" regime like the simulations at this link (same as the Magic cards link):


However, the "usual case" is that an increase in labor supply either increases wages or leaves them the same, and you have to bend over backward with the assumptions to get the Econ 101 result. But lab experiments have shown supply and demand to be a useful description sometimes (see here and here), so sometimes we are in the Econ 101 domain of validity.

Can we save the scissors by clearly defining the scope?

PS Commenter Unknown makes a great point at Noah's post:
People don't oppose increasing minimum wage because of econ 101. They deploy econ 101 because they oppose increasing the minimum wage, and the opposition to it does not have a prior justification that has anything whatsoever to do with economics.

*  *  *

Footnotes:

[1] You can think of an exchange rate as the ratio of a tiny amount of dollars ($dD$) for a tiny amount of Euros ($dE$), or $dD/dE$. This is also how Irving Fisher thought about exchange in his 1892 thesis.

[2] If we're presenting this without calculus, we can just start here, just like in introductory physics without calculus you start with 

$$
S = \frac{1}{2} a t^{2}
$$

which is the result of an integral (integrating the constant $a$ twice with zero constants of integration). In fact, you solve the information equilibrium differential equation by integration.

[3] We can write these in even more compact form by defining $x \equiv X/X_{0}$ and $\Delta x \equiv \Delta X/X_{0}$

$$
\begin{align}
1+ \Delta n & = \left( 1+ \Delta \ell \right)^{k}\\
w & = \left(1+ \Delta \ell  \right)^{k - 1}
\end{align}
$$

along with the supply and demand curves

$$
\begin{align}
w & = e^{k \Delta \ell}\\
w & = e^{-\Delta n/k}
\end{align}
$$

[4] Technically, we ask

$$
\frac{dN}{dt} \ll \frac{dL}{dt}
$$

This defines the scope (domain of validity) of the partial equilibrium solutions.

[5] The angle brackets are unnecessary to the main thrust of this post, but are explained here.

4 comments:

  1. Jason: "Immigrants take our jobs," is the common refrain

    The counter to this is to point out that immigrants don’t just alter the supply of workers (“stealing out jobs”). They also act as consumers so they create new demand and increase the number of workers required to meet that demand (“creating new jobs”).

    We don’t need either Econ 101 or ITE for that. Both hide a very simple message behind complex jargon that almost no-one understands. People like Noah Smith don’t appear to understand that their failure to communicate this type of simple message to a general audience is part of the problem that leads to Trump. Smith & Co are part of the problem – not the solution.

    Jason: “Towards the end he says we should stop using Econ 101 for the labor market”

    “For the labour market” is superfluous in this sentence IMHO.

    ReplyDelete
    Replies
    1. Arg. Accidentally clicked sign out instead of publish, so lost my original reply. Here's the second take:

      Sorry, I've been on a work trip this past week so I haven't had a block of time to reply to your comments.

      I agree with your first point about immigration increasing demand; in fact that's what I meant when I said "In a sense, a big influx in migration would probably first be a positive demand shift."

      Regarding Trump, I don't think econ 101 is really to blame here. It's obvious in the "immigrants take our jobs" frame -- it's tellingly not "immigrants lower our wages" (what naive econ 101 actually says).

      The issue there is that people weren't using econ 101 reasoning at all. "Econ 101" says there are gains from trade -- so simultaneously being against free trade and immigration is inconsistent in terms of econ 101.

      The key to understanding Trump (and the right-wing push internationally) I think of it as an outbreak of zero sum thinking. If there are jobs for immigrants (so they say), then there are fewer jobs for Americans. If the US trades with Mexico (so they say), one will win and one will lose.

      This makes sense of the racism frame in the US -- non-white people getting benefits (so they say) means white people are losing out.

      That references to econ 101 are made by people in the media are essentially incidental due to confirmation bias. It's not because econ 101 is hard to understand, it's because it's easy to agree with things you already think ... especially if your paycheck depends on it.

      Delete
  2. I have to disagree here (not about Trump).

    The most important thing to understand about the economy is the division of labour. It divides us into suppliers (who are typically experts in a specific product, service, argument or idea) and customers (who are not experts).

    In a free society, we then allow the non-expert customers to pass judgement on the expert suppliers. This happens in commerce but also in other areas such as trial by jury and democratic elections.

    That is not a flaw in the design of the system (as believed by economists and academics, particularly after Brexit and Trump). That IS the design of the system.

    Economists either don’t understand this (in which case they are dumb) or they do understand it but think that, for some reason, it doesn’t apply to them (in which case they are deluded).

    It applies to scientists as well. Galileo looked out at the moons of Jupiter and saw that they were orbiting Jupiter, and he realised that the earth was not the centre of the universe. In scientific terms, that wasn’t particularly difficult. However, in social terms, it set in motion changes that are still being progressed today i.e. persuading people that their beliefs are wrong. Explaining things to non-experts, and getting them to change their world-view, is much more difficult than designing a lens. That's why social science is harder than natural science.

    You often compare economists to physicists but you don’t mention the most important differences of all.

    Physicists explain their useful ideas to the rest of society in simple terms, and they have packaged many of the simpler (and most useful for everyday life) ideas in ways that can be taught to schoolchildren. Einstein might have used mathematics to derive his ideas, but he explained them with analogies about people on trains, and people on platforms, watching each other.

    Academic economists don’t understand this. They think that they should be heard by the rest of society as they are “experts” and the rest of the population are not, even if they don’t explain their ideas in ways that the rest of society can understand. And even if they accuse half the population of being stupid and corrupt! However, that’s not how our society works. Allowing non-experts to pass judgement on experts forces the experts to raise their game; use imagination; create innovative ideas AND mechanisms for marketing / explaining those ideas; adopt effective quality controls; and show respect to the non-expert “customers”.

    Academic economists understand that competition is mostly a force for good in society and monopolies are mostly bad. However, they prefer lifetime tenure for themselves, and their journals print only those papers that conform to semi-religious prejudices.

    They have no quality control on their product. I recall a couple of economists who wrote a paper saying that 90% public sector debt was a tipping point, and who advised governments not to go past this point. It turned out that they hadn’t checked their own spreadsheets! Imagine if Apple or Pfizer or your local supermarket had quality controls like that. There would be uproar. A medical doctor or a lawyer might be struck off for that level of negligence. In the cess-pit of economics, we all just carry on as if it didn’t happen.

    When was the last time a physicist advised the government on a course of action based on the unchecked figures in a faulty spreadsheet? When was the last time a physicist said that, as physicists are experts in energy and governments are not, we should set up an independent agency of unelected physicists to make decisions on energy policy on behalf of the rest of us?

    ReplyDelete
  3. Blogspot is still eating my comments. It's not your fault and don't worry about delays in repying to my comments.

    ReplyDelete

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