Musical chairs with heterogeneity

There are two problems with musical chairs:

1. The obvious problem: there aren't enough chairs for the kids that want to sit on them.
2. The less obvious problem: chairs and kids are heterogeneous, so if kids grab any chair they can get, some tall kids will be sitting on short chairs and some short kids will be sitting on tall chairs. The tall kid sitting on a short chair won't swap seats with a short kid sitting on a tall chair, because they fear some kid without a chair will grab their seats if they try to change places.

There are two problems with a binding price floor (or binding price ceiling) on apples:

1. The obvious triangular problem: there's an excess supply of apples, so Marginal Benefit = Price > Marginal Cost, so MB > MC.
2. The less obvious fuzzy (or striped) trapezoidal problem: the apples that do get produced and sold aren't always going to be the apples with the lowest Marginal Cost. It all depends which apple orchards are lucky enough to have a customer nearby when the music stops.

There are two problems with a recession caused by an excess demand for the medium of exchange:

1. The obvious problem: there's a fall in the volume of monetary exchange, so some potentially mutually beneficial exchanges do not get made, because barter is difficult, and buyers are stuck in a Prisoners' Dilemma where it is collectively rational but individually irrational for each to hand over money to the others to trade more goods.
2. The less obvious problem: the limited number of potentially mutually beneficial exchanges that do in fact get made are not necessarily the most potentially mutually beneficial. It's not just that the dollar value of exchanges is too low; but the subjective value of the exchanges is lower than it could be even given that constraint on the total dollar value. It all depends on which seller is lucky enough to be in the right place at the right time to find a buyer.

There are two problems with the fall in employment during a recession caused by an excess demand for the medium of exchange:

1. The obvious problem: the fall in employment and rise in unemployment mean that some workers won't have jobs and won't be producing output.
2. The less obvious problem: even taking as given the total number of jobs being too low, the wrong workers will be doing the wrong jobs. Some tall workers will be sitting in short jobs, and some short workers will be sitting in tall jobs. The monetary disequilibrium prevents sorting by comparative advantage, which reduces total output for a given level of resources employed. Productivity is reduced.

This is actually good news. Because it means that output (and more importantly welfare) can actually be increased by more than the obvious amount by better monetary policy. We don't just gain a Harberger triangle; we gain a fuzzy Okun trapezoid as well.

I stole the musical chairs metaphor from Scott Sumner. A Twitter exchange between Miles Kimball and Narayana Kocherlakota prompted this post. Narayana was optimistic about the prospects for increasing output by loosening monetary policy despite the near recovery in unemployment.

A model is a parable told with math. A parable is a metaphor told as a story. I'm not quite there yet.

Comments

[Majromax]

The suggestion of this argument is straightforward: an increase in structural/cyclical unemployment also causes an increase in frictional underunemployment.

Could we find some way to infer this from available statistics? The US did see the quit rate fall significantly during the 2008 recession, and the quit rate could be seen as a proxy for chair-swaps.

Looking at this a bit more rigorously might require statistics not readily available. I'd be interested in seeing whether there was a change in wage premium among workers who both quit one job and obtained another, by year through and after the recession.

[Nick Rowe]

Majro: good question. The quit rate is one good piece of supporting evidence, but I would like to see something stronger, because we can't rule out the possibility that quits and the switches they lead to are just workers swapping jobs to get jobs (say) nearer to home. Now it is a good thing if 2 workers swap jobs because each prefers doing the other's job. But it would be an even better thing if the swap also increased each job's productivity, so their employers preferred the swap too. (Of course, 2 person exchanges are easy, and can be done with barter, but in the real world it's normally an n person exchange that's needed, because of a Wicksellian circle.)

[jonathan]

"even taking as given the total number of jobs being too low, the wrong workers will be doing the wrong jobs. Some tall workers will be sitting in short jobs, and some short workers will be sitting in tall jobs. The monetary disequilibrium prevents sorting by comparative advantage, which reduces total output for a given level of resources employed. Productivity is reduced."

Isn't the main problem that you have the wrong people sitting on the floor, not people sitting in the wrong chairs? (i.e. the workers laid off aren't necessarily the least productive workers.)

[jonathan]

(though you're probably right that there's an inefficient reduction in between-job flows in a recession. I just think this is second-order compared to productive workers not working.)

[Nick Rowe]

jonathan: "Isn't the main problem that you have the wrong people sitting on the floor, not people sitting in the wrong chairs? (i.e. the workers laid off aren't necessarily the least productive workers.)"

Hmm. That's definitely going to be part of it too.

I'm not sure about the relative magnitudes, but there's always a lot more people employed than unemployed, so even a small percentage amount of mismatch among the employed could have a big effect. Of course, if there were never any real/relative shocks, and no new entrants and retirements, it might not matter much.

[Prakash]

Valid point, but I think there might be a deeper reason as well to support good monetary policy.

If we believe the dignity hypothesis of Deirdre Mc Closkey, then the longer and more uninterrupted the march of liberal political economy in the world, in both time and space, the more the world gets prosperous. Every long recession is an opportunity for particularism/fascism on the right (take from those who don't look/behave like you)and communism on the left (take from those who are richer than you) to raise their heads. A great moderation lasting 60 years might actually be able to completely discredit, if not eliminate, their rhetoric from everywhere in the world.

It might be possible to model this with an expectations model of net worth over a lifetime (whenever it dips beyond a certain level, support for structurally bad policy increases leading to lowering of real growth rate) but that is way beyond anything I can construct. Others reading this blog, please go ahead and build on it if you feel this has some merit.

[Tel]

There are two problems with a recession caused by an excess demand for the medium of exchange:

That's all very interesting, except that I don't believe it relates to our present day problems. We have rottenness in the common mediums of exchange, and a growing demand for a better, less rotten medium. We also have deeper rottenness in other institutions, such as governments figuring that law doesn't apply to them, but fixing the exchange would be a good start.

Some tall workers will be sitting in short jobs, and some short workers will be sitting in tall jobs.

You are saying people stick with a job they don't want, because they expect that any job is hard to find right now so the search for a better job will be much more painful? OK, but officially the US unemployment rate is remarkably low right now. The low point back in 2006/2007 was 4.4% and right now it's 5.0% so that number looks pretty sweet. If this isn't a good time to look for a job, then when would be?

Wait! Surely you don't think those stats have been cooked do you? Not you of all people going down the conspiracy rabbit hole... I'm deeply shocked.

Of course, we could look at this chart right here... https://research.stlouisfed.org/fred2/graph/?g=3muG

Maybe average duration of unemployment is more relevant, maybe unemployment rate... I dunno, they used to cluster nicely, but in recent years they have kind of wandered off into a world of their own. Can't explain it, just happens now and then with economic statistics.

Getting back to the question at hand, there's no property rights in "owning" a job (despite what the unions might think) so there's no way to barter one job for another job as an exchange because the employee doesn't own the job in the first place. However, it is quite easy to apply for one job while working another job... people do that all the time. I would argue it's getting easier, with all the search engines around the place.

[Tel]

I always forget that the links don't auto activate around here... same link with the href if that's any easier.
Average (Mean) Duration of Unemployment (left), Civilian Unemployment Rate (bottom), 1948-01

[Brent Buckner]

Perhaps you could flag this post to Jared Bernstein.
c.f. https://www.washingtonpost.com/posteverything/wp/2016/02/04/the-full-employment-productivity-multiplier/
[Hat Tip: http://economistsview.typepad.com/economistsview/ ]

[Nick Rowe]

Brent: thanks. Greg Ip read both pieces, and tweeted this to Jared.

[Alex B]

"just workers swapping jobs to get jobs (say) nearer to home"

That's actually an economic gain too, you know.

[Nick Rowe]

Alex: agreed. But it won't show up in GDP and productivity numbers. ("So much the worse for GDP and productivity numbers" you say, OK. But I did want to think about the GDP and productivity numbers, as data.)