Wednesday, January 07, 2009

The Meaning Of A Word Is Its Use In The Language

The economy is never in equilibrium, or so many heterodox economists say. Being a Joan Robinson fan, I'm likely to agree. To understand the implications of the idea, and the use and abuse of equilibrium analysis, one must understand what economists mean by "equilibrium".

Tyler Cowen and Richard Fink provide an example of abuse, that is, a confusion about the implications of the economy not being in equilibrium. In the following passage, Cowen and Fink explicitly put aside income effects, false prices, strategic behavior, etc.:
"all that the Rothbard-Mises analysis implies is that there is a tendency towards equilibrium in a world with frozen data. Of course, this implies little or nothing about whether there is a tendency towards equilibrium in a world where the data are not frozen. All that [Evenly Rotating Economy] theorists are saying is that, if we freeze the disequilibrating forces, then the equilibrating forces will prevail. But on this basis we may likewise assert a tendency towards disequilibrium. By allowing the data to change just as it does in the real world, and 'freezing' all individual learning, we can demonstrate that the economy would degenerate into a series of successively less-coordinated states of disequilibrium. However, this would clearly be an illegitimate proof of a real world tendency towards disequilibrium..." -- Tyler Cowen and Richard Fink, "Inconsistent Equilibrium Constructs: The Evenly Rotating Economy of Mises and Rothbard", m V. 75, N. 4 (Sep. 1985): 866-869
(Hat tip to Matthew Mueller.) If there were a tendency, with frozen data, towards a ERE, the time path of the ERE corresponding to the data at each moment of time would show the tendency of the economy as a function of time. This is not the only point at which Cowen and Fink are confused.

What economists mean by equilibrium is not a simple question. Economists use the word "equilibrium" in many ways. The number of such ways has proliferated with the development of game theory. In this post, I compare and contrast only two uses of the word "equilibrium". And I think I don't fully explicate even these two uses.

The economy can be said to be in equilibrium when the following two conditions are met:
  • The quantity supplied equals the quantity demanded of all commodities with positive prices
  • The quantity supplied does not fall below the quantity demanded of all goods with zero prices.
This definition is specific to a particular neoclassical theory (or model).

Another definition comes out of the mathematical abstraction of a dynamical system. A dynamical system specifies how state variables change at any momement of time as a function of the location in state space. For example, a system of differential equations can define a dynamical system:
dx(t)/dt = f(x(t))
A limit point is a location, x, in the state space such that that location does not change with respect to time as function of the system dynamics. In other words, f(x) is zero at a limit point. Certain loci, other than the set of limit points, are of interest in dynamical systems. I am thinking specifically of limit cycles, strange attractors, and non-wandering sets. Consider a model of the economy as a dynamical system. The economy is in equilibrium, by a dynamical systems definition, when it is at a limit point.

The definition of equilibrium as equating supply and demand can be read as a special case of the definition of equilibrium as a limit point in a dynamical system. The tâtonnement process is a model of a type of dynamical system. Equilibrium, in the sense of a limit point in this system, is equilibrium in the sense of no excess demand for goods.

But Keynes can be read as suggesting the dynamical system definition of equilibrium need not equate supply and demand, particularly in the labor market. That is, Keynes' view of the possibility of the existence of an equilibrium with unemployment is more general and points to a non-neoclassical theory of prices.


Anonymous said...

The big question is, if we assume that an economy is not in equilibrium then where does that leave arguments which blame, say, unemployment on wages being too high (i.e., not at their equilibrium price) or, dare I say it, interest rates not being at their "natural" rate?

Take this quote from Hayek ""cause of unemployment . . . is a deviation of prices and wages from their equilibrium position which would establish itself with a free market and stable money. But we can never know at what system of relative prices and wages such an equilibrium would establish itself." Therefore, "the deviation of existing prices from that equilibrium position . . . is the cause of the impossibility of selling part of the labour supply."

If equilibrium is a meaningless concept, where does that leave this argument? Unemployment may be unrelated to high wages and cutting them may have the opposite effect than equilibrium analysis suggests (as Keynes suggested back in 1936).

So it would be interesting to see how this pans out, but I'm not sure whether mainstream economics will be able to reject the lure of equilibrium. As can be seen, even the Austrians (who pay lip-service to opposing equilibrium analysis) appeal to it when necessary...

An Anarchist FAQ

Anonymous said...

Actually, Garegnani (1976) is a very cleaver insight on the concept of equilibrium. According to him, first-generation neoclassicals (like Walras, Marshall and Wicksell) shared the same idea that Ricardo, Smith and Marx; i.e., "natural" values as a centre of gravitation of "actual" values. The content of both theories (Classical and Neoclassical) are different, but the method is esencially the same.
Mises ideas are more or less the same.

Some difficulties with the treatment of capital as an homogenous quantity of a given magnitud but of variable form, which was the predominant idea of Marshall, Walras and Wicksell, led Hicks, Hayek and Lindhal to formulate concepts like temporal and intertemporal equilibrium. Value and Capital is the most important piece o work of this tradition, where capital is no more a amount of exchangeable value, but a vector of heterogeneous goods.

The fact that the economy is never in equilibrium wasn´t a big deal before Hicks´s book, but nowadays Arrow-Debreu disaggregated model needs perpetual equilibrium in order to "work".

Best regards (and sorry for very a poor translation),

Robert Vienneau said...

Hayek seems mistaken. Iain, where is that quote from?

Guala, one of my objections to the Cowen and Fink paper is that they do not reference that Garegnani paper. One cannot simply replace the Arrow-Debreu intertemporal equilibrium with Mises' Evenly Rotating Economy, or vice versa, without thinking more about stability arguments.

Apparently, Garegnani's most recent statement of his thesis is from last week's AEA meeting. I found Christopher Bliss's response often misdirected. The inability of most mainstream economists to competently evaluate logical criticism is irrelevant to the validity of that criticism.

Others, such as Harvey Gram, emphasize that any time to get in an Arrow-Debreu equilibrium is too much time.