The 1 vs 3 Model of Quick Recessions vs Slow Recoveries

Business cycles are not symmetric; if you flipped the time-series data upside-down the fluctuations would look different. Recessions are usually quick; recoveries are usually slow. And Milton Friedman's "Plucking Model" seems to fit the data: big falls in economic activity are usually followed by big increases; but big increases are not usually followed by big falls. It's as if there were some "normal" level of economic activity, and the economy sometimes falls below "normal" temporarily, by greater or lesser amounts, but rarely rises much above "normal". Recessions are bigger than booms. Big news is usually bad news: it's an illness, and not a burst of super-normal health. So on average it's less than "normal" (which is why I put "normal" in "scare quotes"). And it suggests (but does not prove) that if you could reduce the fluctuations, you could maybe increase the average level of economic activity towards "normal".

Why? Here's a story (I think it makes sense):

A simple model of a monetary exchange economy is the Wicksellian Triangle. The apple producer wants to consume bananas; the banana producer wants to consume cherries; the cherry producer wants to consume apples. But it's hard to coordinate 3 people meeting in the same place at the same time so they can do a 3-way swap in the central Walrasian market. They can only meet pairwise, so they have to use money. And let's suppose they use some 4th good as money (because my story is simpler that way). So we have a circular flow of money clockwise around the Wicksellian triangle; and a flow of fruit counterclockwise.

It only takes 1 person to reduce the circular flow of money. If the apple producer decides he wants to hold more money, he can unilaterally decide to slow down or stop spending his money. He does not need anyone else's consent to do this; because exchange requires mutual consent. Quantity traded is whichever is less: quantity demanded; or quantity supplied. The change in his stock of money equals the flow in minus the flow out; he needs the cherry producer's consent to increase his flow in, but can reduce his flow out to the banana producer unilaterally. And if the apple producer decides to slow down or stop his spending, the whole circular flow of money and fruit slows down or stops too.

The circular flow of money is like an "O-ring" model; a chain is only as strong as it's weakest link.

It takes all 3 people to increase the circular flow of money. The apple producer needs to spend more quickly, the banana producer needs to spend more quickly, the cherry producer needs to spend more quickly. (And each of those 3 decisions requires the mutual consent of both parties to the trade of money for fruit, because the apple producer cannot buy more bananas unless the banana producer agrees to sell more bananas. And only if all 3 have an excess supply of fruit matched by an excess demand for money will that consent be readily forthcoming. [Update: But I put that bit in brackets because I'm thinking of a demand-side model here, and the supply-side will usually not be a constraint in a recession, or if the economy is monopolistically competitive, which it mostly is.])

The circular flow of money is like 3 cars circling a one-lane roundabout, they all need to go faster for any one of them to go faster.

So far I've been talking about the velocity of the circular flow of money; but the same thing applies if we take the derivative with respect to time and talk about the rate of acceleration. It's the rate of deceleration that represents how quickly the economy goes into recession; it's the rate of acceleration that represents how quickly the economy recovers.

The rate of deceleration of cars on the Wicksellian roundabout is determined by the rate of deceleration of the car whose driver wants to decelerate the most; the rate of acceleration of cars on the Wicksellian roundabout is determined by the rate of acceleration of the car whose driver wants to accelerate the least. (That's not exactly true of course, because drivers leave an adjustable buffer zone of space between themselves and the car in front; just like they hold an adjustable buffer stock inventory of money so their flows in and out don't have to match exactly. But it's good enough for this post.) If we take two sets of 3 random numbers, the biggest number in the first set will usually be bigger than the smallest number in the second set. So recessions are usually quicker than recoveries.

And you get Friedman's "Plucking Model" because something going wrong and performing worse than normal has bigger effects than something going right (unless it's the same thing that had previously gone wrong, which it probably won't be).

The Wicksellian triangle is really a many-sided Wicksellian polygon, in any modern highly interdependent economy. So it will be 1 vs n rather than 1 vs 3. But there is usually more than one person producing apples, or bananas, or cherries, so each corner of the Wicksellian triangle is an average of several people, not just one person. And there's usually some degree of substitutability between different goods when relative prices change. And maybe those modifications to the model would roughly cancel out, or maybe not. And we aren't just talking about trade in newly-produced final goods and services (GDP); because (almost) everything gets traded for money, including labour, intermediate goods, real assets, financial assets, etc.

Sure, it's just a story, and not a real "model" with math. But I think you get the drift.

Comments

[Majromax]

I'm not entirely sure I buy this. This nominal-terms story suggests that we could raise real spending infinitely quickly, if only the central bank printed an arbitrarily large quantity of money and handed it out equally. Even if the desired nominal savings rate differed, the level of nominal spending could be made arbitrarily large.

This is true enough in a recession, but it's clearly false when we are at capacity and real-terms constraints (like the time to research and deploy technology) become binding.

We still get a "plucking model," however, because while the economy is below capacity, we do in fact lose out on potential gains. If we take a few years off from building new factories, we can't build the next new one at lighting speed. Similarly, out-of-work people have decaying human capital, both in objective and subjective terms.

[Majromax]

(In the true spirit of the pressed 'post' button, I have a pithy summary of my point above to add):

In short, I think the best outcome we can hope for from a monetary economy is for money to "get out of the way," such that we can all act like only real-terms constraints are binding.

[Jussi]

'for money to "get out of the way,"'

Close enough for me but I like 'for credit (frictions) to "get out of the way"' :)

All the agents will have "money" when they have access to credit. IMO saying that money is "4th good as money" doesn't create an useful model. (Credit) Money can always be created if agent has inventories or future production to be pledged as collateral.

[Majromax]

@Jussi:

> Close enough for me but I like 'for credit (frictions) to "get out of the way"' :)

I think that's something slightly different.

If money gets out of the way, we can pretend we have a barter economy with no problem of coincidence of wants. For practical purposes, prices and wages would be flexible, and the demand to hold money would be negligible compared to total AD. In the real world for an individual person, this is more or less accomplished by anybody who holds little in the way of cash savings -- for them every transaction is in real terms.

If credit gets out of the way, then agents must also have the ability to completely time-smooth their consumption. That less resembles the real world to me. In particular, to assume away credit markets we need to impose something like a no-default condition. In the real world, however, we do see counterparty risk when agents are leveraged, and small changes in a 'fundamental' variable can cause large swings in the NPV of a debt portfolio (cf Rowe's Law).

[Jussi]

Okay, I meant it slightly differently :)

I agree the money part, being out of the way means the economy enjoys only real constraints, as you said.

Yet, I would say that the credit is exactly the thing that pushes money "out of the way". In the real world every transaction is completed with three agents: credit (money) provider (bank) and two agents conducting the trade. There is no circular flow of money at all. It is always the credit conditions, which collapsed during the crises, not the amount of money (monetary base / reserves).

So while Nick's model is neat and logically correct it (IMO) hasn't much to do with the real world.

[Majromax]

> In the real world every transaction is completed with three agents: credit (money) provider (bank) and two agents conducting the trade

That's true for a fiat money, but it's not obviously true with commodity money. With a bitcoin transaction, for example, there is no credit provider.

Even with fiat money, provided we restrict ourselves to the use of base money the credit provider isn't usually relevant. A bill in my pocket is a notional liability of the Bank of Canada, but since the central bank has credibility wrt its inflation target I don't have to care about their credit practices.

I think on the balance you're right, but to really explore it we need to be very careful about the difference between base money, circulating money, and "safe collateral" that can conventionally be turned into money at will. (The asset-backed commercial paper freeze-up in the 2007-8 crisis is an example of the failure of the latter.)

[PaulS]

In the real world, the figure would no longer be a triangle, but nor would it become a many-sided polygon. It would be more like a mesh made of a huge number of polygons, with most nodes highly interconected.

That would make the question of why the whole thing should ever slow down much more "interesting". After all there's no a priori reason why slowing down (or even stopping) one polygon or node within a huge mesh should slow the whole works down significantly. Thus the model appears, at least on its face, to break down.

[Nick Rowe]

Paul: Imagine an economy with 3 million people, instead of 3.
Yes, if we represent that by a polygon with 3 million points, so any 1 of those 3 million people can make the whole thing grind to a halt, that is obviously too extreme.
Or we could represent it by a triangle with 1 million people at each point. In which case it would only grind to a halt if all 1 million people at one point do the same thing. Which they might do, if they are all the same, and get hit by the same shock, but it's still probably too extreme in the other direction. The roundabout doesn't have an infinite number of lanes, and we prefer driving on some lanes than others, so may slow down if the car in front slows, rather than switching lanes.

It's some sort of mixture. But since it's very early days for this theory, I'm starting out with the extreme version, even if it does exaggerate the effect I'm talking about, just to try to understand that effect better in the simplest model. Then we can relax it, so the effect should be weaker, but still present. What's the best picture for that relaxed model? Dunno yet. Some sort of interlocking circles, but not a wide open mesh.

[dilbert dogbert]

Seems like a way to talk about Say's Law with money as a commodity and also talk about how folks in general fear loses more than they enjoy gains. It is easy to hold money therefore bad news cascades into a "stop" and good news cascades more slowly therefore a slower grind uphill out of a recession.

[Nick Rowe]

dilbert: yes, but the money in my story doesn't have to be a commodity money. It could be bits of paper. What I meant was that my story is simpler if they don't use apples (or bananas, or cherries) as money, but use some 4th thing.

[Pete Bias]

Hi Nick,

Once again you're thinking in a non-paradigmatic way. I love it.

A traffic jam analogy is perceptive. A few cars slowing down to observe something off to the side will slow down the whole interstate. And the recovery is painfully slow until the cars have passed the 'show' and accelerate back to normal speed. The slowdown happens fast, the creeping along to try to recover is long and painful and gains speed until back to normal. Much like an economic slowdown and recovery.

Maybe we're using the wrong models for macroeconomics and should instead be studying traffic congestion models for a better perspective. Our macro-model paradigm might be a completely wrong way to view a dynamic, congested trade-fest.

Keep at it Nick!

Pete