David R. Henderson  

Krugman's Baby-Sitting Analogy

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This is another in an open-ended series on strengths and weaknesses in Paul Krugman's writing.

In a 1999 review of Krugman's The Return of Depression Economics, I wrote:

One of Krugman's strengths is his talent for analogies that help readers understand economic reasoning. He starts with an analogy, developed by Joan and Richard Sweeney in the February 1977 Journal of Money, Credit, and Banking, between a baby-sitting co-op in Washington, D.C., and a large, complex economy.
In the co-op, people earned one half-hour coupon by providing one half-hour of baby-sitting services. At one point there was too little scrip in circulation. Couples would try to earn more scrip by offering to baby-sit. But there weren't enough other couples wanting to go out, because they didn't want to run down their inventory of coupons, and so there was an excess supply of baby-sitting services. This baby-sitting economy with about 150 couples was in a recession.
As Krugman points out, this situation is analogous to an excess supply of goods in a real economy, and thus, he concludes, it shouldn't be hard for people to accept that a much more complex economy in which millions of good and services are exchanged can suffer from lack of demand. The solution that the baby-sitting co-op finally accepted was to print more coupons, and it worked. This is like printing money to get an economy out of a recession, which also usually works.
But nowhere does Krugman mention that another way to solve a problem of excess supply is to let prices fall. This missing piece is interesting, given that it was explicitly discussed in the article from which Krugman draws the analogy. The Sweeneys pointed out that because the founders of the co-op economy imposed price controls, decreeing that one unit of scrip must always exchange for a half-hour of baby-sitting services, there would be shortages when demand was too high and surpluses when it was too low. It's not surprising that Krugman left this out: He seems to be biased in favor of having government step in rather than letting markets work things out.

In other words, the problem came about because prices were not allowed to adjust. Interestingly, Krugman seems to alternate between saying that prices (wages) don't adjust quickly and saying that prices (wages) shouldn't adjust quickly. This is the same ambiguity that many scholars have noted in Keynes's General Theory.

Interestingly also, after my review appeared, I noticed that the frequency with which Krugman used his day-care analogy declined substantially. I was disappointed, therefore, but not surprised, that he kept it in his latest edition of the book.

Also, one thing that rereading my review showed me, something I had forgotten in light of Krugman's over 800 New York Times columns, is that the same weaknesses that are on display so regularly in his columns were presaged in the 1990s. See the second paragraph of my review.


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COMMENTS (19 to date)
Andang Kustamsi writes:

Paul Krugman used the baby-sitting co-op analogy in his Peddling Prosperity book (in The Attack on Keynes chapter).

david writes:

But, real employees and employers alike do shy away from wage cuts during a recession, even in the absence of wage controls. This isn't a point about whether they should do this; this is what in fact does happen.

It is tempting to conclude from the babysitting co-op experience that the problem with recessions is wage rigidity. To be sure, the 'babysitting recession' would probably have vanished had the 'babysitting wage' been allowed to float. But having permitted this we have lost sight of the point of citing the model: that is, to model an economy in which wage rigidity is real. To seize on removing the interesting constraint as the solution is rather like modeling flight by assuming away gravity.

This provides a rather more charitable explanation of why Krugman has avoided mentioning the model: if a fellow economist can walk away with the impression that the model implies that the problem is wage controls, then the model is clearly misleading even to educated readers.

Mattyoung writes:

Reading Scott Sumner's blog, The Money Illusion has been partially illuminating to me. I come away with the conclusion that liquidity (script) adapts fairly quickly to changing circumstances. But liquidity changes are paced by other constraints which are slowly adapting.

In this case, there is a constraint. Couples cannot change their lifestyle and baby-sitters cannot adapt their consumption model at the same rate that liquidity can. Worker idleness is paced by other constraints in distribution, not by liquidity constraints.

Econobrowser referenced this paper:
http://www.columbia.edu/%7Err2572/papers/RWpure.pdf

In which the authors measured measured constraints caused by slow adapting liquidity to be about 10-15% in typical times. The other 85-90% is a result of others goods having slower adaption times.

macquechoux writes:

"But, real employees and employers alike do shy away from wage cuts during a recession,.."

Some years ago during an oil patch recession I had an uncle who worked for a large international oil field service company. In his division management gave the employees a choice: They were going to layoff 15% (I forget the actual %) of the employees across the board or take a corresponding cut in wages and everyone keeps their job.

Everyone kept their job.

gnat writes:

How would this work? Each supply of baby-sitting would exchange for (e.g.) two baby sits? How about the coupon hoarders, do they get a windfall? I would guess that this coop would quickly go to barter. The exce4ss demand would simply buy outside the coop.

The alternative is increasing the supply of coupons.

Kevin Donoghue writes:

But nowhere does Krugman mention that another way to solve a problem of excess supply is to let prices fall.

Evidently PK is selling abridged versions of his work in the US, so that Chapter 9 of the 1999 Penguin edition is reserved for Europeans only. What a cunning devil. But here is some of what PK wrote for his readers on this side of the pond:

"In the story of the depressed baby-sitting co-op, one way the situation could have resolved itself would have been for the price of an hour of baby-sitting in terms of coupons to fall, so that the purchasing power of the existing supply of coupons would have risen, and the co-op would have returned to 'full employment' without any action by its management."

There is more. But never mind that. Let's get to the heart of the problem - PK's dastardly policy of short-changing his US readers, so many of whom are obviously reading inferior versions? Perhaps we should arrange for bootleg copies of the UK edition to be sold in the US?

El Presidente writes:

I second david's remark, wholeheartedly.

I would also add that there is nothing ambiguous or contradictory about syaing that wages are observed to usually be downwardly rigid in the short run (positive statement) and that wages should be downwardly rigid in the short run (normative statement). The circumstance upon which wages fall is one in which the marginal value of real output declines and more labor must be expended to obtain the same wage. Why should anybody want that to occur to themselves or anyone else? Do we have a shortage of industrial character that needs to be remedied for the betterment of mankind? Are you saying we're lazy? Is that the normative principle driving your argument? This technical solution fails to address the human side of the problem and is partly to blame for the seemingly substantiated view that libertarian economists have little regard for the short-run consequences of their long-run preferences on people.

Focusing more directly on Krugman's analogy, why should a half-hour of babysitting services provided garner less than a half-hour of babysitting services in return? There are several possible answers, but I want to know which one(s) you're relying on to justify your argument. There are normative principles underlying your preferences and it would be good for the discussion if you would disclose them to your audience.

gnat writes:

If price changes were the answer, why didn't prices fall?

Daniel Kuehn writes:

You have a SERIES on the quality of Krugman's writing? Wow... that's pretty lame.

By the way - Krugman is giving the Lionel Robbins lecture at LSE, apparently. I bet that smarts!

Peter writes:

It is said that people did not go out because they wanted to save the opportunity to go out in the future, but this seems to be missing something, which is that obviously the people holding these coupons did not want to earn more. They were consumers only and not producers. There was not a lack of demand but a lack of production.

The other silly thing in the parable is the idea that an economy should keep producing-baby sitting despite a reduced demand for it. The analogy cannot be extended to the economy as a whole because the structure of production adapts to changes in demand when producers find that their products are not wanted as much as before.

Bill Woolsey writes:

Peter:

The people holding the coupons were produers--they had already provided baby sitting services. They were saving for some later time.

Your notion that it is foolish to produce baby sitting services that people do not want, is correct, but only because of scarcity. There are other goods that the time used for baby sitting services could be used to produce. Providing baby sitting services at the expense of more valuable products is a waste.

But that issue must be ignored (baby sitting is the only good in the analogy.) The reason to ignore it is that it doesn't apply to the economy as a whole. If there is a surplus of all other goods matched by a shortage of money, opportunity cost in production is irrelevant.

"The structure of production will adjust?" Really...

You need to always keep concepts like scarcity and opportunity cost in mind when thinking about recession.

We should produce fewer consumer goods because people don't demand them _only_ makes sense if people _want_ to enjoy more leisure. People don't want to work, because they would rather thave the time off than than the goods and service they could buy with the income they could earn.

That is not very well connected with a scenario where people want to work, but cannot because firms don't want to hire them, because the firms can't sell the products, because people don't want to buy them. Such a scenario follows from a shortage of money. It can be clear up by an icnrease in the nominal quantity of money (more dollars) Or an increase in the real quantity of money (lower prices for the goods and services.)

gnat writes:

"It can be clear up by an increase in the nominal quantity of money (more dollars) Or an increase in the real quantity of money (lower prices for the goods and services.)"

How does the "price" of baby-sitting service fall?

Boonton writes:

How would this work? Each supply of baby-sitting would exchange for (e.g.) two baby sits? How about the coupon hoarders, do they get a windfall? I would guess that this coop would quickly go to barter. The exce4ss demand would simply buy outside the coop.

Well in the recession case I imagine the problem is too many people who want to babysit and too few people wanting to go out. So a price response would be for people wanting to go out to offer a lower return to babysitters. Maybe something like "for every two hours you babysit for me I'll pay you only one coupon'. Coupon hoarders would get a nice windfall as do money holders in a deflationary environment.

This would all imply then that deflation is more or less harmless...maybe even a bit positive since it rewards the thrifty saver and punishes the deadbeat debtor. Missing from this model, though, is any account of investment. Savings here simply shifts consumption from one time period to another but babysitting is essentially the same. IRL, though, deflation could choke investment (the additional product you can produce tomorrow from your investment will sell at a lower price....maybe you can't pay back the debt you incurred because of that) and demand (if prices are falling why spend now? Maybe next week you can get away with paying one coupon for four hours of sitting?).

Letting prices vary also complicates the model. Here savings is in a 'real form'. If you do an hour of sitting or decide not to go out, you have an hour of sitting you can get in the future. With varying prices you introduce an element of speculation. Maybe the 4 coupons you saved in the winter will yield 4 hours of sitting in the summer....or maybe not in which case you could have had 4 hours in the winter but now only get 1! I can even imagine financial bubbles in this case. Imagine the FDIC is expected to hire a hundred new young workers. The DC co-opt imagines soon there will be a mass of new baby sitters joining making it easy to both earn new coupons and hire sitters. As a result people empty their savings and start spending their coupons now. Going out reaches a peak but then the FDIC says the new workers will be located in NYC. The bubble collapses. Coupon borrowers can't pay back their debts, lenders take losses. The price of going out bottoms out.....but people don't respond by going out more but less. they don't want to part with what little coupons they have left no matter how much sitting time they will buy.

gnat writes:

Coop members both pay baby sits and earn baby sits. A decrease in price decreases income. Price does not operate as a negative feedback, as in a market under cet. par. conditions. This is the Keynesian problem: price and income are endogenous and the outcome depends upon expectations.

Boonton writes:

Is this a problem or a feature? In the real economy lower prices are both a boon to those doing the buying and a bust to those doing the selling. The only difference here is that we assume a person can just as easily be a seller as a buyer in the coop economy.

Peter writes:

Bill, when I said that the people holding coupons were consumers only, I meant that they had ceased to produce, at least temporarily (the story does not say).

As for changes in production, the story seems to me to be intended to provide a simply explanation for the idea that there can be a failure of demand arising on its own and over time, as compared to a sudden shock. To bring the story into current context you'd have to have half the kids in the building die in a school bus crash or something.

gnat writes:

Boonton: your model rocks.Let me take another try.
DH is right that if a change in M works then flexible prices also work. But if D and S are inelastic then neither works since markets do not clear.

The coop story was that to earn a coop dollar you had to supply baby sitting hour(s). In a two-period coop economy, assume that HHa is willing to supply x hours in period 1 and demands 0 hours, and in period 2 HHa demands x hours and supplies 0 hours. HHb is willing and able to demand and supply x hours in both periods. In period 2 both HHs demand x (so demand is 2x) and HHb is willing to supply x.

If x dollars are distributed—one half to each HH, and prices are fixed, HHb can buy only 1/2x in period 1. With 2x dollars (e.g., doubling dollars), HHb can buy x in period 1. Flexible prices achieves the same result. But demand is 2x in period 2 while supply is x. If demand and supply are inelastic, neither flexible prices nor changes in dollars will clear the market.

Jeff Reisberg writes:

Look at all the discussion Krugman's analogy has stimulated. If nothing else he has stimulated our minds. I like that the co-op story is in there because the reason it went into a recession, and the depth of the recession all had its root in human psychology. The economy still had the same actors as it did when it functioned, but the actors became aware the velocity had slowed so script became more rare, causing them to hoard it. When will economists realize that their dark arts are a subfield of psychology?

As for your disappointment that not allowing prices to fall was not an option you have to look at why it wasn't a possibility. Each coupon was worth 1/2 hour of babysitting time. That exchange rate was fixed. That money guaranteed the couples that if they put in 1/2 hour of babysitting, they would get 1/2 hour back. It was about fairness. But money is a curious thing. It's value wasn't just about the purchasing power of that money, it was availability.

Letting prices fall, or devaluing the currency could have changed the ratios between past babysitting for current babysitting, but it doesn't prevent the currency from repeating all of its past problems again, and people who worked 1/2 hr in the past will have gotten only less then that in return. If it were me I'd give up on the system.

Lastly I like his part in the new version of the book, what if couples in general like to save up coupons in the winter and spend their savings in the summer? All couples spending at once in the summer makes availability of couples to babysit limited. All saving in the winter makes availability of children to sit limited. Krugman did discuss changing the value of money in this case as a solution to the social problem. Winter babysitting should be worth less then summer babysitting! But this is a question of justice, not economics. :)

So common guys, don't knock an economist who likes to play with model economies.

Tom A. writes:

Another paradox, and a reason to not let wages fall from Krugman:

An individual company or worker can preserve a business or a job by accepting a lower price; but when everyone does it, we get debt deflation — a rising real burden of debt, which weighs on the economy — and also start to have deflationary expectations built into lending and investment decisions, which further depresses the economy. And once you’re in a deflationary trap, it’s very hard to get out.

http://krugman.blogs.nytimes.com/2009/01/30/damnification/

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