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Guest Post: Equilibrium Analysis

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Rajiv Sethi

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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7 comments

  1. Knute Rife

    I agree with your linked position that Minsky’s financial instability hypothesis is consistent with economic rationality. A system is stable because its unstable frontiers have not been reached, but if profit is the goal and profit is found at the margin, the strongest players will go seeking that margin, which will destabilize the system. Unlike a machine that can be tested in the shop (“The engine runs, now let’s see how high it will rev.”), though, the economy is tested to destruction out on the track.

  2. Seth

    Economics uses both too little and too much math. Too few mathematical ideas, too many journal pages of repetitious and unenlightening mathematical arguments based on that limited toolkit of ideas.

    Steve Keen and Doyne Farmer are both making worthwhile efforts to extend the toolkit.

  3. Bat

    “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.”

    Marx’s three volumn Das Kapital develops several models of capitalism under best case scenarios…no fraud, workers adequately compensated, best possible direction of capital for returns, fair competition with government regulation applied to all, etc. None of Marx’s capitalist models displayed equilibrium in labor or capital.

    Of course there will be those that will say that Marx was biased…but Marx was standing on the shoulders of Smith, Ricardo, etc.

    I don’t believe that employment stability, or anything close to stability, is possible with the large wage differences in the globalized labor force.

    In addition, as I have pointed out before; human labor is becoming a smaller portion of production cost continually. We have already seen it in agriculture, where the US changed from 96% of labor involved in Ag, to today, when 4% of labor is involved in Ag. When computer controlled robotics replace a large number of workers in the ‘services’ portion of economies (services now comprise 50% of the consumer catagory, and consumer spending is ~70% of US GDP), as they have already done in manufacturing…Well, what to do with the ~ 7 Billion people that are no longer needed?

    Neither Keynes or Marx saw the coming of computer robotics that can perform any function a human can…and, the robotics do not ask for union representation or pay raises.

    I believe that economic theory and models developed prior to globalization and computer robotics need be revisited. Just as actual events, like an air attack on Pearl Harbor, caused a total revision of naval ships and strategy.

    How about an economic model that predicts long term unemployment with the current macro outlook in mind; ie, cheap labor being replaced by cheaper robotics?

    1. Toby

      That’s the song I like to sing too, Bat. You have my full support in raising the issue of the effects of ever changing technological developments as they affect economic thinking that still is rooted in centuries old dogma.

      The deepest core, as far as I can tell, of the classical and neoclassical economic world view is scarcity. Not only is technology wreaking havoc with human labour (and will get better and better at doing so), we are, as a species, slowly coming to realize that ever more consumption (aka perpetual GDP growth) delivers neither happiness nor sustainability. That realized, the next logical realization is that we are surrounded by an abundance of all we need — we are not insatiably greedy, neither by nature, nor in any other way. As economics and money are together about dealing with the distribution of scarce goods and services — scarcity being the result of infinite wants meeting finite resources — the double whammy of the end of ‘labour for a wage’ and the recognition of abundance puts orthodox economics on very thin ice indeed. Pretty much all of it needs to be revisited and rewritten.

      All of that before we even touch the absurdity of equilibrium.

  4. alex

    Rajiv Sethi: “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.”

    It’s depressing that such an obviously needed line of inquiry has been abandoned for so long.

    BTW, the Buiter link is excellent.

  5. craazyman

    “Given the potential of disequilibrium dynamic models to illuminate our understanding of the economy, why are they generally neglected in contemporary economics?”

    Could be that the wolves of the economics and finance profession profit massively from a world administered by equilibrium models . . . while the peasants pay.

    Economics is neither a science or even a self-consistent set of theories and realities. It seems more a sort of religion, or a social pyschic architecture that guides the distribution of money-spirit-energy like the totems and taboos (which our “enlightened” society finds nonsensical) that regulated the movement of life energy among the “savage tribes” of colonialist days with their witch doctors and rain dances and clans and sacrifices to the gods.

    We think we have matured from that. But the song remains the same, and only the words have changed.

  6. Bruce Johnson

    I am pleased that this analysis is finally being discussed. I am almost finished with the first book that treats far-from-equilibrium conditions in economics; Eric Beinhocker’s The Origin of Wealth, the best book on economics I have ever read. He often refers to “punctuated equilibrium” to discuss why equilibrium economics appears to occasionally work on the average but is way off base in crises. However, even Beinhocker fails to distinguish between assuming econometric fluctuations represent a stationary random process with meaningful future probabilities as opposed to admitting that extreme events really represent non-stationary processes which lack meaningful future probabilities. This is because the sequence of events leading up to a crisis is sufficiently complex as to be a never reapeating sequence. Thus hindcasting the past has little to do with future shocks. Well behaved equilibrium economics is somewhat like well behaved hurricane track predictions. If the boundary conditions are stable, the predictions have a zone of possible tracks which may indeed happen. If, however, the boundry conditions are not following familiar patterns, hurricane tracks like Mitch seem to wander around and are unpredictable as to their future directions. I can go on but will stop here.
    Cheers,
    Bruce

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