Equilibrium Analysis

In a recent post on his (consistently interesting) blog, David Murphy questions the value of equilibrium analysis in economics and finance, and points to two earlier posts of his in which the same point is made. Here he is in July 2007:

An interesting post on the Street Light Blog, on currency misalignments, suggests an interesting question: is economics an equilibrium discipline? The very idea of a misaligned FX rate suggests that the natural state is an aligned one: perhaps the fundamentals move faster than the markets adjust, so FX is never in equilibrium. Perhaps (in the language of statistical mechanics) the relaxation time is much longer than the average time between forcings.

And here, in August 2008:

My own view is that finance is not an equilibrium discipline, mostly, so while classical economics might work well in explaining the price of coffee... it does rather less well in asset allocation or explaining the return distribution of financial assets. Rather new news arrives faster than the market can restore equilibrium after the last perturbation, meaning that most of the time equilibrium is not a useful concept.

In a 1975 paper that remains worth reading to this day, James Tobin was explicit about the limitations of equilibrium analysis in understanding large scale economic fluctuations:

Keynes's General Theory attempted to prove the existence of equilibrium with involuntary unemployment, and this pretension touched off a long theoretical controversy. A. C. Pigou, in particular, argued effectively that there could not be a long-run equilibrium with excess supply of labor. The predominant verdict of history is that, as a matter of pure theory, Keynes failed to prove his case.

Very likely Keynes chose the wrong battleground. Equilibrium analysis and comparative statics were the tools to which he naturally turned to express his ideas, but they were probably not the best tools for his purpose... The real issue is not the existence of a long-run static equilibrium with unemployment, but the possibility of protracted unemployment which the natural adjustments of a market economy remedy very slowly if at all. So what if, within the recherché rules of the contest, Keynes failed to establish an "underemployment equilibrium"? The phenomena he described are better regarded as disequilibrium dynamics.

Tobin then goes on to develop a dynamic disequilibrium model of the macroeconomy (discussed at length here) which has a unique equilibrium characterized by full employment, steady inflation, and correct expectations. He shows that even if this equilibrium is locally stable, so that small perturbations are self-correcting, it need not be globally stable: sufficiently large shocks to the economy can result in cumulative divergence away from equilibrium unless arrested by a significant policy response. This seems to describe what we have experienced over the past couple of years better than any equilibrium model of which I am aware.

Note that Tobin's model is deterministic. The problem here is not that the economy is being buffeted by frequent shocks that arrive before a transition to equilibrium can occur, it is that the internal dynamics of adjustment simply do not approach the equilibrium from certain (large) sets of initial states even in the absence of shocks. The idea that the instability of steady growth with respect to disequilibrium dynamics is an important feature of modern market economies, and cannot be neglected in a comprehensive theory of economic fluctuations was forcefully advanced by Richard Goodwin as far back as 1951, and Paul Samuelson had explored the possibility even earlier. As Willem Buiter has recently lamented, this line of research in macroeconomics simply dried up about a generation ago.

Another area in which equilibrium analysis is likely to be inadequate is in the study of asset markets with significant speculative activity. Price and volume dynamics in such markets depend not just on changes in fundamentals but also on the distribution of trading strategies, and this in turn adjusts under pressure of differential performance. The idea of an equilibrium composition of trading strategies is a contradiction in terms: if there were any such thing there would be a new strategy that could enter to exploit the resulting regularity. It is the complexity of this disequilibrium process that allows information arbitrage efficiency to be approximately satisfied, while allowing for significant departures from fundamental valuation efficiency (the distinction, naturally, is also due to Tobin.)

Finally consider Hyman Minsky's financial instability hypothesis, built on the paradoxical idea that stability itself can be destabilizing. In Minsky's framework stable expansions give rise to increasingly aggressive financial practices as those firms having the greatest maturity mismatch between assets and liabilities profit relative to their closest competitors. The resulting erosion in margins of safety increases financial fragility, interpreted as the likelihood that a major default will trigger a crisis of liquidity. Such a crisis eventually materializes, devastating precisely those firms whose actions gave rise to greater fragility. The balance of financial practices is then shifted in favor of increased prudence, and the stage is set for another period of stability. Trying to give this analysis an equilibrium interpretation is a futile exercise; expectations of financial market tranquility are self-falsifying, and no fixed distribution of financial practices can be stable.

Given the potential of disequilibrium dynamic models to illuminate our understanding of the economy, why are they generally neglected in contemporary economics? In part it is because the quality of a disequilibrium model is hard to evaluate and the dynamics are necessarily arbitrary to a degree. There is a professional consensus on how equilibrium analysis should be done, but none (so far) when it comes to disequilibrium analysis. Furthermore, equilibrium models can be enormously insightful, even in applications to macroeconomics and finance. The work of John Geanakoplos on the leverage cycle is a case in point, and Abreu and Brunnermeier's paper on bubbles and crashes is another. I have used equilibrium methods frequently and will continue to do so. But it seems that there ought to be greater space in the profession for serious work on the dynamics of disequilibrium.

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Update (7/31). In an email (posted with permission) David Murphy adds:

One of the main reasons people study equilibrium models is that they are an order of magnitude easier, mathematically, than non-equilibrium. If you consider a simple problem like cooling, for instance, the equilibrium version is high school physics, and the non-equilibrium version is still a research problem (with useful application to the improvement of annealing methods). Economists in my experience are very comfortable with the maths they know (a bit - stress a bit - of stochastic calculus), but they are not willing to venture much further because it gets really, really hard quite quickly. Hence the 'we have a hammer, everything looks like a nail' problem.

I think this is correct as far as analytical results are concerned; proving theorems (aside from convergence-to-equilibrium results) with the standard toolbox is not easy in disequilibrium models. But if one adopts a computational approach the reverse may be true. I, for one, find it easier to write an algorithm to simulate a recursive system than one that requires the computation of fixed points in high dimensional spaces. But (as noted above) there does not exist anything close to a professional consensus on how the quality of such models should be evaluated, and so they are usually rejected out of hand at most mainstream journals.