The 1 vs 3 Model of Quick Recessions vs Slow Recoveries

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.


via Worthwhile Canadian Initiative

September 3, 2018 at 08:21AM

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