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The economic crisis, the calculation debate, and stability theory
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.
Posted by Tyler Cowen on December 18, 2008 at 05:42 AM in Economics | Permalink
Comments
This looks like one for Matthew Mueller....
I think there is lots of interesting work to be done in this area.
Posted by: Current at Dec 18, 2008 7:51:15 AM
A disequilibrium that was either ignored or missed was the unsustainable increase in the (maybe call it) affordability index: median house price to median income, or vice versa if you like. Housing prices (in some markets - see Case Shiller) rose at double digit rates while incomes rose at single digit rates or declined ($5 a gallon gasoline and commuting from Stockton to the Bay Area or Silicon Valley) in real terms.
"Central planner": I like that. I've been calling him "that genius at HUD" that decided everyone has the basic human right to own a house (3Q2008: 67.9% 0f US households). I think subprime/Alt-A/Option ARM sounds so much nicer than predatory lending. Don't you?
The lib dems Dodd, Frank, Raines, Johnson, Obama) were intent on advancing their favored constituencies while the Reps kept it going because their favored constituencies were making money hand over fist.
Now, we all "pay."
Posted by: T. Shaw at Dec 18, 2008 9:08:35 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 tâtonnement process. Making noises about gross substitutability is only appropriate if you believe one must use tâtonnement 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.
Posted by: Alex at Dec 18, 2008 9:11:17 AM
"being overoptimistic they can't be wrong by being overoptimistic"
The last word should be over-pessimist.
Posted by: Alex at Dec 18, 2008 9:17:20 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.
Posted by: Rich at Dec 18, 2008 9:22:38 AM
Tyler wrote:
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?
I would think yes. A series of disruptive events could prevent order from re-emerging. A realistic example of that would be an initial shock, followed by others or, more likely, a series of responses that prevent a new equilibrium from forming.
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?
You need to first define what a healthy banking sector looks like and does. What we know today is that a healthy banking sector doesn't look like what it did in the last decade, nor should it do what the banking sector did in the last decade. Instead, we should look at those financial institutions that escaped the carnage and make it possible for more of those kinds of institutions to rise to the forefront.
The biggest problem out there is that far too many people are consumed by trying to put things back the way they were. In a way, it's almost like they're trying to re-assemble a cow from a truckload of hamburger - what they're doing ain't pretty, nor is it likely to be successful.
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.
Well, yes, now that you mention it, some are, although I think that an econometric approach is the wrong way to go.
The problem is that a lot of econometrics tries to shoehorn real world data around a Gaussian normal distribution, which ultimately requires one to assume the underlying datapoints are statistically independent of each other. That's not how the world really works.
That approach can be useful and periodically holds, once you adopt Paretian assumptions (where power-law distributions and interdependencies hold), how prices change become lot easier to explain. Even in our current situation.
Posted by: Ironman at Dec 18, 2008 9:24:43 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.
Posted by: Bob Murphy at Dec 18, 2008 9:33:50 AM
Tyler, are you kidding?
It has been well known for ages that the equilibria in general equilibrium models are guaranteed to be stable (even in a tatonnement sense) only under unrealistically restrictive conditions (just look at Arrow-Hahn, 1971 for a survey). Fisher's excellent work on non-tatonnement stability (or lack thereof) points out even more serious problems with those models.
I doubt that stability issues were ever "written off as irrelevant".
Simply the economics profession has decided to keep focusing on the equilibria of our models while praying that, for some reason, the disequilibrium dynamics would not make the equilibrium analysis irrelevant.
Since we have so little clue about disequilibrium dynamics, that is not an entirely irresponsible strategy, though it should inspire much more modesty than we typically observe.
Posted by: Valter at Dec 18, 2008 9:35:29 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.
Posted by: tomrus at Dec 18, 2008 9:43:56 AM
Rich,
I was thinking the same thing. I've written an agent based model in R for financial markets, but was thinking that the model could be extended to other areas, and in particular this style of problem is well suited to agent models.
contact me through email and would love to chat more about this.
Posted by: mickslam at Dec 18, 2008 9:51:14 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.
Posted by: liberty at Dec 18, 2008 11:00:31 AM
It is an interesting theoretical exercize to imagine a world in which a change in one market leads to a never ending serious of adustments in all other markets--never settling down again, even if there were no futher changes in tastes or real production possiblities. Isn't this what GE stability theory amounts to? Since there is plenty of reason to believe that there are changes going on all the time, how would we know whether we live in a "stable" or an "unstable" system?
How does this relate to problems of now one wants to buy, but everyone still wants to sell. And they cannot? What must be happening to the supply and demand for money?
Posted by: Bill Woolsey at Dec 18, 2008 11:09:55 AM
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.
Posted by: Valter at Dec 18, 2008 12:10:23 PM
Thanks very much for the link, Valter. Interesting to read about agent-based approaches. Sounds like a pretty good way to go. Certainly better than the nonsensical aggregation of unrelated economic activity into a single number.
It will be challenging to come up with realistic enough models of our situation. We may learn "interesting patterns" from simple models such as Gintis', but Macro 101 tells us lots of "interesting patterns" too. What we want are predictive patterns, which may require high-fidelity, extremely complex models, situated to our precise initial conditions.
Has anyone done work, or is anyone doing work, to translate vast quantities of actual price/purchase/construction/etc. data, into a model of the actual economy?
It's a huge undertaking, but with so many nonlinear effects at work, I don't know how much we can learn from low-dimensional model spaces. Well, one thing we can learn is "humility," and that's actually very important.
Posted by: mk at Dec 18, 2008 12:53:40 PM
Paul Davidson has made some appearances at Matthew Mueller's blog. If you don't mind typos, they make for an interesting read.
Posted by: TGGP at Dec 18, 2008 9:28:23 PM
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.
Indeed, economists' understanding of this process involves a lot of hand waving. Take heart though, because a lot of other disciplines describe their own attractors and fitness landscapes with plenty of rigor, thankyouverymuch, so it's definitely something that can be done. I think the first step is to accept that if you have to violate some general case principle of information theory in order to describe your special case process, then it's probably your description that's wrong, not information theory.
I suppose there's just not as much money to be made telling people things they don't want to hear though. Like "there's no free lunch" and "inability to measure places fundamental limits on ability to predict" and "even with the best imaginable measurements predictions will occasionally but unpredictably go spectacularly wrong?" Certainly chemists and biologists and physicists have had trouble in the past tryng to tell people things they didn't want to hear. ;-)
Posted by: radish at Dec 19, 2008 7:35:05 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.
Posted by: Tom Grey - Liberty Dad at Dec 23, 2008 1:12:07 PM
