The case for statistical equilibrium in economics
The text below is an excerpt from my forthcoming book Finitary Probabilistic Methods in Econophysics, written with Ubaldo Garibaldi for CUP. It is a partial answer to the post of Jean-Phillippe Bouchaud (less poetic, however).
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In Economics, distributional problems appear at least in the following frameworks
1. economic growth (and its dependence on firms’ sizes);
2. allocation of resources (in particular the distribution of wealth).
Our presentation emphasizes the positive (rather than the normative) aspect of distributional problems. However, there is a general policy problem worth mentioning which was highlighted by Federico Caffe’ in his lectures [1]. When introducing the 1938 paper by A. Bergson [2], Caffe’ wrote “… when, in economic reasoning, the social wealth distribution is assumed “given”, this means that the existing distribution is accepted, without evaluating whether it is good or bad, acceptable or unacceptable … this must be explicitly done further clarifying that the conclusions are conditioned on the acceptabiliy of the distributional set-up”.
Two main probabilistic methods were used to derive/justify observed/empirical distributions:
1. the statistical equilibrium method (discussed in this book). According to this approach, the time evolution of an economic system is represented by an aperiodic, irreducible Markov chain and the distribution of relevant quantities is given by the invariant distribution of the Markov chain.
2. The diffusive (possibly non-equilibrium) method. According to this approach, the time evolution of an economic system is represented by a random walk (see also Sections 9.8 and 10.8).
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The statistical equilibrium method was challenged from at least two points of view. Some scholars do not believe that economic systems can achieve any sort of equilibrium, including statistical equilibrium and, on the contrary, they claim that such systems are strongly out-of-equilibrium. Other scholars, and in particular, post-Keynesian economists, do not believe that the behaviour of macroeconomic systems can be explained in terms of the behaviour of interacting individuals. In other words, they challenge the microfoundation of macroeconomics, possibly including a probabilistic microfoundation in terms of statistical equilibrium. Our provisional reply to these objections is that the concept of statistical equilibrium may prove useful even in economics and may be helpful to describe/justify empirical distributional properties. In other words, before rejecting the usefulness of this concept, it is worth studying its implications and understand what happens even in simple models. As argued by John Angle (personal communication), it may well be the case that the economic dynamics is fast enough to let relevant variables reach statistical equilibrium even in the presence of shocks moving the economic system out of this equilibrium.
Another common objection is that in economics, at odds with physics, there is no conservation of wealth or of the number of workers or of any other relevant quantity. This is true, but the example discussed in Section 7.6 shows how to study a market where the number of participant is not fixed, but yet statistical equilibrium is reached. In other words, the absence of conserved quantities in itself is not a major obstacle.
The last objection we consider does not deny the usefulness of statistical equilibrium, but of a probabilistic dynamical description. When considering large macroeconomic aggregates or a long time evolution, fluctuations may become irrelevant and only the deterministic dynamics of expected values is important. In other words, stochastic processes may be replaced by difference equations or even by differential equations for empirical averages. To answer this objection, in many parts of this book we have pointed the attention of the reader to the phenomenon of lack of self averaging, which is often there in the presence of correlations (see Section 5.2.1). In other words, when correlations are there, it is not always possible to neglect fluctuations and the description of economic systems in terms of random variables and stochastic processes becomes necessary.
[1] F. Caffe’, Lezioni di politica economica, Bollati-Boringhieri, (1978).
[2] A. Bergson, A reformulation of certain aspects of welfare economics, Quarterly
Journal of Economics 52, 310-334, (1938).
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For a more quantitative discussion on what I mean by “statistical equilibrium” and further references, you can consult the relevant page of the Reykjavik manifesto:
http://reykjavikmanifesto.wikidot.com/statistical-equilibrium-in-economics
8 Comments
Apr 15, 201010:30 am
Hi ycz, thanks for your comment.
The style of an argument has nothing to do with its validity and its truth value. Otherwise, here we have a paralogism.
My point should be sufficiently clear. In a nutshell, the argument is as follows: if the “driving” dynamics is slower than the economic dynamics, then an economy has the time to reach statistical equilibrium, and the distributions we observe (wealth, etc.) are invariant and equilibrium distributions.
How to defend this position? Think of the rate of economic transactions compared to the rate of the possible driving phenomena. My educated guess is that the rate of economic transactions is much higher than the rate of demographic changes, than the rate of institutional changes and than the rate of cultural changes (including also innovations, etc.). Therefore, an economy might reach statistical equilibrium.
However, and this is correct, my point is not a very strong one because I am not so sure of the relevance of statistical equilibrium. I just think it is worth and fun exploring this possibility.
Studying statistical equilibrium in economics is not pseudoscience, as it can be falsified (for instance, by a careful measurement of the above rates). Finally, note that Joe McCauley has already several arguments against the relevance of statistical equilibrium in economics (in his papers and in his book Dynamics of Markets).
Cheers
Enrico
Apr 16, 20104:12 am
Hi Enrico
I think it’s pretty clear that the concept of statistical equilibrium is essential to the proper understanding of macroeconomic phenomena.
One objection that is sometimes raised, which you repeat here, and with which I disagree, is that there are no quantities that are conserved in economics. Neoclassical economics and Post Keynesian economics do not have a theory of objective value or “costs of production”, in contrast to some Classical authors prior to the marginal revolution and the introduction of subjective utility theory. Also, there is a great deal of confusion over what “money” is and its relation to endogenous bank money (credit), which leads to the belief that value can be created ex nihilo. For both these reasons an essential conservation principle — the conservation of value in exchange — is alien to many economists. The Classical authors (e.g., Ricardo and Marx), however, maintained this principle, and introduced the idea of conservation-breaking processes in production that generate a `surplus’, which is then contested and distributed as forms of income (wages, rents and profits). I think this original conception ultimately needs to be combined with statistical equilibrium approaches.
Best wishes,
-Ian.
Apr 16, 20108:53 am
Dear Enrico, let’s take a simpler analog (see also JP’s Spring in Norway to the same effect).
Erosion of earth surfaces has been going on since the genesis, and yet our planet is not flat, even winds, waves, rains trying to flatten these daily and hours.
You count only what’s visible, as a good accountant would do, but what’s invisible is written off by statisticians by definition.
In the earth surface case, what is ignored is the under the surfaces, slow and hard to quantify, yet it’s
these forces that make tectonic movements over long run, volcanoes and earthquakes over short run, that shape our landscapes.
19th century physicists like Pareto, Walrus misled a generation of economics on the mechanics-imitating wrong path, and now you’re trying to inject new life &
mislead them for another one?
Based on only statistics, without looking into underlying complexities, apply scientific tools—precisely what is wrong with the mainstream economics, or Feynman called it as “Cargo Cult” science.
Apr 19, 201012:55 pm
Dear Ian,
Thank you for your comment. You write:
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Indeed, the statement that there are no conserved quantities in economics is quite strong as there are rather trivial balance sheet equalities leading to conservations.
However, what you write on value is much more interesting and related to Sraffa’s 1960 book “Production of commodities by means of commodities”
as well as to the Cambridge capital controversy. I do agree that these ideas should be incorporated in statistical equilibrium approaches.
Best regards
Enrico
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12:42 pm
Dear Enrico, what an enlightening article, since when you learned the economic-speak, lengthy discussion without making a clear point? Not one example to defend your position (if any)?
General Equilibrium and neoclassical economics would be saved by tending out an extra straw.
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