Tuesday, September 13, 2011

Are Recessions All About Money: Quasi-Monetarists and Babysitting Co-ops

Today Paul Krugman takes up the question of the post below, are recessions all about (excess demand for) money? The post is in response to an interesting criticism by Henry Kaspar of what Kaspar calls "quasi-monetarists," a useful term. Let me rephrase Kaspar's summary of the quasi-monetarist position [1]:

1. Logically, insufficient demand for goods implies excess demand for money, and vice versa.
2. Causally, excess demand for money (i.e. an increase in liquidity preference or a fall in the money supply) is what leads to insufficient demand for goods.
3. The solution is for the monetary authority to increase the supply of money.

Quasi-monetarists say that 2 is true and 3 follows from it. Kaspar says that 2 doesn't imply 3, and anyway both are false. And Krugman says that 3 is false because of the zero lower bound, and it doesn't matter if 2 is true, since asking for "the" cause of the crisis is a fool's errand. But everyone agrees on 1.

Me, though, I have doubts.

An overall shortfall of demand, in which people just don’t want to buy enough goods to maintain full employment, can only happen in a monetary economy; it’s correct to say that what’s happening in such a situation is that people are trying to hoard money instead (which is the moral of the story of the baby-sitting coop). And this problem can ordinarily be solved by simply providing more money.
For those who don't know it, Krugman's baby-sitting co-op story is about a group that let members "sell" baby-sitting services to each other in return for tokens, which they could redeem later when they needed baby-sitting themselves. The problem was, too many people wanted to save up tokens, meaning nobody would use them to buy baby-sitting and the system was falling apart. Then someone realizes the answer is to increase the number of tokens, and the whole system runs smoothly again. It's a great story, one of the rare cases where Keynesian conclusions can be drawn by analogizing the macroeconomy to everyday experience. But I'm not convinced that the fact that demand constraints can arise from money-hoarding, means that they always necessarily do.

Let's think of the baby-sitting co-op again, but now as a barter economy. Every baby-sitting contract involves two households [2] committing to baby-sit for each other (on different nights, obviously). Unlike in Krugman's case, there's no scrip; the only way to consume baby-sitting services is to simultaneously agree to produce them at a given date. Can there be a problem of aggregate demand in this barter economy. Krugman says no; there are plenty of passages where Keynes seems to say no too. But I say, sure, why not?

Let's assume that participants in the co-op decide each period whether or not to submit an offer, consisting of the nights they'd like to go out and the nights they're available to baby-sit. Whether or not a transaction takes place depends, of course, on whether some other participant has submitted an offer with corresponding nights to baby-sit and go out. Let's call the expected probability of an offer succeeding p. However, there's a cost to submitting an offer: because it takes time, because it's inconvenient, or just because, as Janet Malcolm says, it isn't pleasant for a grown man or woman to ask for something when there's a possibility of being refused. Call the cost c. And, the net benefit from fulfilling a contract -- that is, the enjoyment of going out baby-free less the annoyance of a night babysitting -- we'll call U.

So someone will make an offer only when U > c/p. (If say, there is a fifty-fifty chance that an offer will result in a deal, then the benefit from a contract must be at least twice the cost of an offer, since on average you will make two offers for eve contract.) But the problem is, p depends on the behavior of other participants. The more people who are making offers, the greater the chance that any given offer will encounter a matching one and a deal will take place.

It's easy to show that this system can have multiple, demand-determined equilibria, even though it is a pure barter economy. Let's call p* the true probability of an offer succeeding; p* isn't known to the participants, who instead form p by some kind of backward-looking expectations looking at the proportion of their own offers that have succeeded or failed recently. Let's assume for simplicity that p* is simply equal to the proportion of participants who make offers in any given week. Let's set c = 2. And let's say that every week, participants are interested in a sitter one night. In half those weeks, they really want it (U = 6) and in the other half, they'd kind of like it (U = 3). If everybody makes offers only when they really need a sitter, then p = 0.5, meaning half the contracts are fulfilled, giving an expected utility per offer of 2. Since the expected utility from making an offer on a night you only kind of want a sitter is - 1, nobody tries to make offers for those nights, and the equilibrium is stable. On the other hand, if people make offers on both the must-go-out and could-go-out nights, then p = 1, so all the offers have positive expected utility. That equilibrium is stable too. In the first equilibrium, total output is 1 util per participant per week, in the second it's 2.5.

Now suppose you are stuck in the low equilibrium. How can you get to the high one? Not by increasing the supply of money -- there's no money in the system. And not by changing prices -- the price of a night of baby-sitting, in units of nights of baby-sitting, can't be anything but one. But suppose half the population decided they really wanted to go out every week. Now p* rises to 3/4, and over time, as people observe more of their offers succeeding, p rises toward 3/4 as well. And once p crosses 2/3, offers on the kind-of-want-to-go-out nights have positive expected utility, so people start making offers for those nights as well, so p* rises further, toward one. At that point, even if the underlying demand functions go back to their original form, with a must-go-out night only every other week, the new high-output equilibrium will be stable.

As with any model, of course, the formal properties are less interesting in themselves than for what they illuminate in the real world. Is the Krugman token-shortage model or my pure coordination failure model a better heuristic for understanding recessions in the real world? That's a hard question!

Hopefully I'll offer some arguments on that question soon. But I do want to make one logical point first, the same as in the last post but perhaps clearer now. The statement "if there is insufficient demand for currently produced goods, there must excess be demand for money" may look quite similar to the statement "if current output is limited by demand, there must be excess demand for money." But they're really quite different; and while the first must be true in some sense, the second, as my hypothetical babysitting co-op shows, is not true at all. As Bruce Wilder suggests in comments, the first version is relevant to acute crises, while the second may be more relevant to prolonged periods of depressed output. But I don't think either Krugman, Kaspar or the quasi-monetarists make the distinction clearly.

EDIT: Thanks to anonymous commenter for a couple typo corrections, one of them important. Crowd-sourced editing is the best.

Also, you could think of my babysitting example as similar to a Keynesian Cross, which we normally think of as the accounting identity that expenditure equals output, Z = Y, plus the behavioral equation for expenditure, Z = A + cY, except here with A = 0 and c = 1. In that case any level of output is an equilibrium. This is quasi-monetarist Nick Rowe's idea, but he seems to be OK with my interpretation of it.

FURTHER EDIT: Nick Rowe has a very thoughtful response here. And my new favorite econ blogger, the mysterious rsj, has a very good discussion of these same questions here. Hopefully there'll be some responses here to both, soonish.

[1] Something about typing this sentence reminds me unavoidably of Lucky Jim. This what neglected topic? This strangely what topic? Summary of the quasi-what?

[2] Can't help being bugged a little by the way Krugman always refers to the participants as "couples," even if they mostly were. There are all kinds of families!


  1. This is pretty close to the Diamond general equilibrium search model of unemployment.

  2. You know, I was going to add a line at the end saying, "A real economist would probably talk about this in terms of a search model," but for whatever reason I didn't.

    But we don't want to think of the coordination failure being (primarily) in the labor market, do we? at least not if we want to tell a story about aggregate demand. In the real world, the coordination failure is among firms setting output levels, not between firms and workers looking for the right employment match.

  3. Very good post. A couple of random thoughts.

    1. It's like a disco, where the boys only go if they expect the girls to go, and the girls only go if they expect the boys to go. Multiple equilibria for for number of dance partners. Barter model. Like Diamond, as walt says.

    2. But it misses what to me is a crucial empirical feature of recessions. In your model, it's hard to both buy and sell in a recession. Buying *is* selling in your model, so both must be equally hard (or easy). But in real world recessions (it seems to me) buying is easier than normal, and selling is harder than normal (for most goods). (In other words, in a recession, selling *money* is easier than normal, and buying *money* is harder than normal.)

    Theoretically I have no problem with your model. Empirically it doesn't work as well as a model with monetary exchange.

    3. I find it easier to think of self-employed worker-firms, rather than a separate labour and output market. Everything, both labour and output, gets harder to sell and easier to buy in a recession.

    4. I think of excess supply/excess demand as just the limiting case of harder to sell/harder to buy in a search model.

  4. Why Lucky Jim? I read that book ages ago.

  5. Thanks, Nick.

    You may be right that in practice, recessions look more like money-hoarding models than pure coordination problem models. I'm agnostic about this as a general point the money-hoarding dynamic certainly is the main story in some cases at least. The main thing I want to establish is just that the notion of demand constraints, in the sense that over some horizon changes in output are driven by changes in desired expenditure, is not logically equivalent to the existence of excess demand for money. In principle we can talk about the former without the latter.

    in real world recessions (it seems to me) buying is easier than normal, and selling is harder than normal (for most goods). (In other words, in a recession, selling *money* is easier than normal, and buying *money* is harder than normal.)

    This is what I'm not sure about. Yes, it's definitely true in a crisis, or in the transition from a higher to a lower equilibrium. But is it necessarily true once expectations have stabilized at a new, lower level?

    What do we expect to see, if money, or liquidity, is harder to buy? Well, higher interest rates to begin with, since the interest rate is just the price of liquidity. Credit ration; less market liquidity, i.e. assets that could formerly be easily converted to money via sale or hypothecation, no longer can be. That all happens in financial crises, including the one in 2008; it's almost constitutive of them. But three years on, it seems to me that it's actually pretty hard to find indicators of the ease of converting command over goods into money, that look significantly worse than pre-recession. And yet the output gap remains much larger.

    Of course it's true that if firms wanted to produce more, they would have trouble converting the incremental output into money. But that's (almost) always true, no?

    You're right, at this level of abstraction we could just as well talk about worker-firms; that's what we have in the babysitting co-op. I just didn't want the parallel with the labor-market search model to suggest that there was some specific failure of matching between workers and prospective employers, like you get with these skill-switching stories.

    Why Lucky Jim? It's from a passage where he mocks himself savagely for the obscurity of the academic article he's writing. (Tho in fact, the article sounds kind of interesting.) Here it signals a momentary awareness that one is writing a blog post about someone else's blogpost responding to another person's post on "quasi-monetarism," which seems to be getting a bit far away from the central problems of life.

  6. JW: "Of course it's true that if firms wanted to produce more, they would have trouble converting the incremental output into money. But that's (almost) always true, no?"

    It's almost always harder selling (most) goods than buying goods. More people work in sales than work in purchasing. I think that's because of monopolistic competition. (I'm very much a New Keynesian in that regard).

    But it gets harder still in a recession, and a little less hard in a boom.

    And then there's labour, which is always a bit hard to convert into money, but gets very hard in a recession.

    We can't just look at the bond market to tell us money is tight or easy. That was the point I was trying to make in my "Peanut theory of recessions post". If the price of peanuts was perfectly flexible, you would always be able to convert peanuts into money. But the peanut market wouldn't be able to tell you if money was tight or loose. (The price of peanuts might even rise in a recession, if peanuts were an inferior good).

  7. Two random questions:

    1.) Can you really do the Keynesian Cross without money? How does the behavioral equation have a positive intercept? Without money, wouldn't positive consumption without output require an offsetting disinvestment?

    2.) Wouldn't durable goods imply cycles of demand? Think autos. Once there's a sufficient stock of used cars, demand for new cars be a function of the age and condition of the stock, in a way that will make new car demand cycle. If production capacity is dedicated, those cycles will ensure that output varies in relation to capacity. (maybe rsj is making a more general point along these lines)