The economic crisis, the calculation debate, and stability theory

by on December 18, 2008 at 5:42 am in Economics | Permalink

Is the financial crisis — which is rapidly becoming the "real economy" crisis — somehow the "dual" of the socialist calculation problem? 

A’la Hayek, say the price of copper goes up.  Markets will make many adjustments and the proper adjustments usually cannot be foreseen by a central planner.  Nonetheless there is some iterative process by which those adjustments get made and, I am sad to say, our understanding of that process involves a good deal of hand waving.  It’s fine to talk about entrepreneurship but the net effect need not be equilibrating.  The relationship between local adjustment, where we have decent Marshallian theories, and global adjustment, about which we know little, remains tricky.

General equilibrium stability theory used to assume gross substitutability to derive the convergence to a new equilibrium but in fact convergence did not usually come easily in the models.  (I take gross substitutability as meaning that a decline in the price
of one good will, on the whole, lead to increased expenditures on other
goods, but here are some alternate specifications.)  Most of the time we hope that the proper local adjustments get made and the whole pinwheel turns and mutates in the proper directions over time. 

Are there conditions, however rare, under which market adjustment and convergence does not occur?  If a few of the vertices get stuck, can it become impossible for the economy to fulfill its mutating pinwheel program of change and adaptation?

Today, banking, finance, and construction all need to shrink and indeed they are shrinking.  Given the centrality of lending and project evaluation, is a sufficiently healthy banking sector needed for the pinwheel to properly turn?  Must investors abandon their quest for liquidity to bring their information to bear on market prices?

Paul Davidson, the Post Keynesian, used to stress that gross substitutability should not be taken for granted.  Was he on to something?

The kind of equilibrium stability theory that obsessed Franklin Fisher was written off as irrelevant some time ago.  Maybe people will start looking at it again.

Current December 18, 2008 at 7:51 am

This looks like one for Matthew Mueller….

I think there is lots of interesting work to be done in this area.

Alex December 18, 2008 at 9:11 am

“Maybe people will start looking at it again.”

Absolutely!

It is really embarrassing for the economic profession, that while the main pillar around which it is organized is the coordinating role of the invisible hand, economists not only know very little about it –which might be excusable– but have done very little work about it. (With the honorable exception of Franklin Fisher)

There are two main assumptions in the Fisher process: 1. The markets are sufficiently organized that if the aggregate excess demand is, say, positive for a good, then the excess demand of each individual is positive for that good.
2. The “No Favorable Surprise” assumption — basically that while market actors can be wrong by being overoptimistic they can’t be wrong by being overoptimistic (in terms of their target utility).

There are other assumptions –the main one being that we still have complete markets– but Fisher proves that this process leads to coordinated action.(Which may not be Pareto optimal)

Clearly the work has limitations, but it is ahead by leaps and bounds over the work on t√Ętonnement process. Making noises about gross substitutability is only appropriate if you believe one must use t√Ętonnement processes for stability, which is obviously not the case.

But intellectual effort is wasted on irrelevant overly-aggregated models, while the foundations of economics are simply overlooked.

Rich December 18, 2008 at 9:22 am

“Nonetheless there is some iterative process by which those adjustments get made and, I am sad to say, our understanding of that process involves a good deal of hand waving.”

Agent-based modeling allows us to create models that capture this iterative process. If you would like to collaborate on such a model please let me know.

Bob Murphy December 18, 2008 at 9:33 am

Are there conditions, however rare, under which market adjustment and convergence does not occur? If a few of the vertices get stuck, can it become impossible for the economy to fulfill its mutating pinwheel program of change and adaptation?

Today, banking, finance, and construction all need to shrink and indeed they are shrinking. Given the centrality of lending and project evaluation, is a sufficiently healthy banking sector needed for the pinwheel to properly turn? Must investors abandon their quest for liquidity to bring their information to bear on market prices?

If people want to argue about whether the boom years were examples of deregulation versus Fed/Fannie/Freddie-mortgage-pushing, that’s fine. But now we’re saying that we still have an example of a “market” that is inexplicably not fixing itself? How much ownership of the financial sector does Paulson need to take, before people start admitting that this is not a big test of how well markets work?

Even in Tyler’s quote above, we see the contradiction. On the one hand, he says the banking sector needs to shrink. Yet on the other, he is worried about the need to maintain a “healthy” banking system, and his thoughts about liquidity are rather odd, since he was in favor of the bailout and has been arguing with Alex that there is a credit crunch.

If Tyler has recently changed his mind (and some of his posts seem to indicate so), I think it would be great if he would be clear about it in a post. It’s very refreshing when you screw up just to say so.

tomrus December 18, 2008 at 9:43 am

I seem to recall my old supervisor Frank Hahn saying that the absence of the conditions for stability in general equilibrium “drove a golden nail into the coffin of capitalism”. Such a phrase maker.

liberty December 18, 2008 at 11:00 am

I third the call to agent based modeling for this. I’ve done work on labor markets using agent based models, and hope to do some work on entrepreneurship using them this year. There has been some work already of agent models in which a “shock” such as technology triggers some “creative destructive,” a ripple through the market, but re-stabilizes as firms adjust. My own work has allowed for some of this, though it wasn’t the central focus.

Most agent models show business cycles, and using them we can investigate what makes them more unstable, dramatic, or lead into recession, and what tempers them or allows them to dissipate most quickly. In general disequilibrium and the market process can be studied well with agent models. Prices can be studied, inflation, monetary policy, and so on as well.

If anyone wants to contact me about this you can contact liberty @ the website address linked.

Valter December 18, 2008 at 12:10 pm

People interested in agent-based models may like the following paper:

Herbert Gintis, The Dynamics of General Equilibrium, The Economic Journal, vol. 117 (October 2007), pp. 1280-1309.

Abstract

The Walrasian general equilibrium model is the centrepiece of modern economic theory, but progress in understanding its dynamical properties has been meagre. This article shows that the instability of Walras’ t^atonnement process is due to the public nature of prices, which leads to excessive correlation in the behaviour of economic agents. When prices are private information, a dynamic with a globally stable stationary state obtains in economies that are unstable in the t^atonnment process. We provide an agent-based model of a multi-sector Walrasian economy with production and exchange, in which prices are private information. This economy is dynamically well behaved.

TGGP December 18, 2008 at 9:28 pm

Paul Davidson has made some appearances at Matthew Mueller’s blog. If you don’t mind typos, they make for an interesting read.

Tom Grey - Liberty Dad December 23, 2008 at 1:12 pm

The whole idea of ‘equilibrium’ is only an academic concept. There has never been an economic day of equilibrium such that there were no price changes from the prior day.

Of course, what ‘else’ is equilibrium? A change in price that is smaller than some out-of-equilibrium delta?

It’s fine to talk about entrepreneurship but the net effect need not be equilibrating.
The whole point is that when prices change up, those demanding it demand less, and those supplying it supply more — when prices change down, the reverse.

The housing bubble pop crisis had prices continuing to go up (was there ever a day, week, month, or year of equilibrium?), until they stopped going up and immediately began to go down.

The most important thing from equilibrium theory is the fairly reliable prediction of the direction of changes. The specific magnitudes of any changes are up to the various micro- agents making decisions.
Some of whom are wrong.

The huge new thing of this crisis is the enormous derivative exposures of the Big Banks, with increased counter-party failure risks.

When 500 000 or so construction workers starting losing their jobs in 2007, it was not such a big deal. As 500 000 or so finance/ banking workers lose their jobs, it will also be not such a big deal EXCEPT that nobody knows where the new jobs come from.

Either entreprenuers or gov’t.

In 10 years there will be far far fewer bankers — perhaps the construction workers will be building something, again.

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