Monday, April 01, 2013

What is an economic equilibrium?




I get asked about this one a lot. And it's also a source of controversy...on one hand you have some econ critics who say "Econ models wrongly assume that the economy is always in equilibrium," and on the other hand you have economists responding that "No, economics models are defined to always be in equilibrium." So I thought I'd try to clear things up...hopefully I don't just end up muddling them further. But anyway:

"Equilibrium" can mean many different things.

There are many different types of equilibria in economics. This may sound intellectually dishonest, but it's not;  the same is true in biology, physics, or any other science. "Equilibrium" just means "balance", and there are lots of different kind of things that can balance. In fact, any equation you write down that isn't true by definition can be interpreted as an "equilibrium" relationship, or "equilibrium condition" - the equation is simply a statement that whatever's on the left-hand side of the equation is balanced with whatever's on the right-hand side.

Different economic models have different kinds of equilibria, so it's not like there's one kind of "equilibrium" that is all-important to modern economics. But, as my macro teacher Rudi Bachmann drilled into me, it's good to always be specific about what kind of equilibrium your model actually models.

Example 1: Walrasian Equilibrium

Walrasian equilibrium, also called "competitive equilibrium" or sometimes "general equilibrium", is basically when prices adjust so that all markets clear. In other words, supply and demand are in equilibrium for all goods in the economy. Walrasian equilibrium also contains the subtler idea that people's plans are in equilibrium; my plan takes your plan into account, and your plan takes my plan into account, etc.

Example 2: Nash Equilibrium

A Nash equilibrium is when people's strategies are best responses to each other - in other words, when no one would choose to change their plans if everyone else's plans stayed fixed. Note that Walrasian equilibrium is a type of Nash equilibrium (since in a Walrasian equilibrium, neither suppliers and demanders would choose to change their plans), but there are many types of Nash equilibria that are non-Walrasian (for example, in an adverse selection model, where markets don't clear).

Example 3: Rational Expectations Equilibrium

A Rational Expectations Equilibrium (REE) is a kind of Walrasian equilibrium with uncertainty about the future. In addition to the condition that prices adjust to clear markets, a REE includes the condition that people's subjective beliefs about the probability of future events are equal to the actual probabilities of those future events. In other words, in REE, beliefs and probabilities are also in balance; this is in contrast to, say, models in which people learn about the probabilities as they go. A REE is a kind of Radner Equilibrium.

Example 4: Constrained General Equilibrium

What if prices can't adjust to clear markets? This could happen if, for example, there were menu costs or other kinds of costs to changing prices. (It could also happen if there were a magical fairy who decided when you could and couldn't change your prices. And it could also happen with search frictions.) In that case, markets might not clear, so you wouldn't have a Walrasian equilibrium. BUT, you'd still have people's plans being consistent with each other. In this case, you'd have the kind of equilibrium in a sticky-price New Keynesian macro model, in which labor markets don't always clear.

Note: I don't think "constrained general equilibrium" is the right name for this sort of equilibrium, but I don't actually know a general name for it.

Example 5: Steady States

In most dynamic models (for example, DSGE models), the economy tends toward some "steady state", in which either nothing in the economy is changing, or in which things are only changing at constant long-term trend rates. The economy may or may not ever get to the steady state. But regardless, a steady state is technically a kind of equilibrium as well.

So how can the economy be "in equilibrium" before it reaches the steady state, if the steady state is also a kind of equilibrium? Well, that brings me to this point:

There are different equilibria for different "terms" or "runs".

In a Ramsey growth model, the economy is always in Walrasian equilibrium, but not always in the steady state. Eventually, the economy reaches the steady state, at which point it is in (at least) two kinds of equilibrium. This demonstrates the principle that dynamic econ models - models that change in time - often have short-run and long-run equilibria. The difference is how fast the economy tends toward the equilibrium. And those speeds are basically assumptions of the model. For example, in the Ramsay model, prices and plans adjust very fast, but capital adjusts slowly. Thus, Walrasian equilibrium is assumed to hold at any given time, while the steady state equilibrium only holds sometime in the future.

In New Keynesian DSGE type models, there are even more levels. There is a "short run" equilibrium, in which prices can't adjust, but plans are in equilibrium. Then there's the "long run" equilibrium in which prices have had time to adjust and supply and demand are in equilibrium, but capital has not necessarily reached its steady state. And then there's the steady state, which is an even longer-run equilibrium.

And if you modeled the adjustment of plans, you'd have another level - a "very short run". So it's clear that the economy can be in short-run equilibrium at the same time it's in long-run disequilibrium. It all hinges on those assumptions about which things happen faster and which things happen slower.

Every equilibrium has a disequilibrium.

In economics at least, everything takes some amount of time. So for every equilibrium, there's some sufficiently short time horizon at which the economy may not be close to the equilibrium yet (depending on initial conditions). This is obvious once you realize the difference between short- and long-run equilibria. It's possible (in a New Keynesian model) for plans to be in equilibrium even while supply and demand are in disequilibrium.

This means that one model's equilibrium is always another model's disequilibrium dynamics. The question of "Should we model the disequilibrium dynamics?" is therefore not well-posed.

Stability matters, but at some level you just have to assume it.

As anyone remembers from first-year differential equations class (or before), some equilibria are stable and some are unstable. As my another of my teachers, the great Yusufcan Masatlioglu, famously said, stability means "I kick you, you come back."

Any model deals with a certain "term" or "run" of equilibria, and leaves the shorter-term stuff un-modeled. This is unavoidable (unless you think you can model economics based on the interactions of its constituent particles, in which case you are both wrong and a doofus). You have to just make an assumption about the stability of the stuff that happens quicker than the stuff in your model - you have to either assume it's stable or  assume it's unstable (in which case you are still assuming that the stochastic process that governs it is, on some level, stable).

As for the stuff that is in your model, you do need to check the stability of that stuff.

For example, suppose you're making a growth model. You decide to assume that demand and supply are in equilibrium; you justify this assumption because you think that growth happens on a much longer time-scale than price adjustment. If you do this, it will make your life a lot easier to assume that supply and demand don't suddenly, unpredictably go haywire, thus throwing off your model - in other words, it's convenient to assume that the supply-demand equilibrium is stable. (Alternatively, you could assume instability of the shorter-run equilibrium; in this case you would model excess demand as a stochastic process.) Then, you have to check whether your model yields a stable long-run equilibrium (in this case, a "balanced growth path").

But if you're making a model of how supply and demand work, you can't just assume stability; you have to show it. This will generally depend on the price adjustment mechanism; getting stable supply-demand relationships is possible, but not trivial.

(Side question: Do real economies have stable prices? Some do, for sure - for example, a continuous double auction. That's an empirical fact, not a theoretical one! But there are lots of very general, plausible theoretical cases in which supply-demand equilibria are unstable.)

Also, I haven't talked about uniqueness, but that's important for similar reasons. Also, in discussing "stability" I've ignored the different kinds of stability, such as cyclic stability, in which you cycle around and around an equilibrium without ever hitting it. But anyone who has worked with those kind of things can understand pretty intuitively how those would be important.

So what about the criticism that economists "assume the economy is always in equilibrium?"

This criticism sometimes has merit, but is usually not well-phrased. It's not well-phrased because economists inevitably have to assume that some type of shorter-run equilibrium always holds in their models. That's unavoidable. But the criticism sometimes has merit, because in some cases this assumption doesn't make a lot of sense.

For example, suppose we do a lot of work analyzing the way people form their beliefs and plans, and we find that it's possible for their beliefs to change very rapidly - in other words, it seems that equilibria of plans are not usually stable (maybe due to some quirk of how people learn). But suppose all our models of slower, longer-term things - price adjustment and supply-demand balance, capital adjustment and business cycles, etc. - assume that beliefs and plans form stable very-short-term equilibria. Well, our longer-term models are going to make some mistakes! Because they're going to ignore the effects of those sudden shifts in beliefs and plans. In this case, a better thing for the long-term modeler to do would be to assume that beliefs and plans can change randomly, and assume that they change according to some sort of stochastic process.

In conclusion: "Equilibrium" is not a single, unified, principle of economics.

It's just a term for "equations describing economic relationships that are not true by definition." Some equilibrium assumptions are right; some are wrong.

That doesn't mean that arguments about specific equilibrium assumptions are pointless - far from it! For example, in his famous 1976 "Lucas Critique" paper, Robert Lucas argues that we can just assume that price adjustment happens quickly and that supply-demand equilibria are stable:
On the theoretical level, one hears talk of a "disequilibrium dynamics" which will somehow make money illusion respectable while going beyond the sterility of dp/dt = k(p-p_e)...[but this] will fail...
But then along came Greg Mankiw, Mike Woodford, Guillermo Calvo, and others, and came up with sticky-price theory, which led to New Keynesian models, which are entirely based on the idea that prices don't adjust as smoothly as Lucas assumes. And those New Keynesian models ended up basically winning the battle of hearts and minds among a majority (though not an overwhelming majority) of macroeconomists, pushing out the RBC models that made the kind of equilibrium assumption that Lucas prefers.

In other words, sometimes modeling the disequilibrium dynamics of one kind of "equilibrium" is really important. But to make that model, you assume an "equilibrium" of another kind.

48 comments:

  1. Great post. Just a minor comment - IIRC, markets do clear in New-Keynesian models even when prices are sticky. Basically producers are assumed to be monopolists, so they set their price, but even when they can't set price to their desired level (due to adjustment costs, or visit from Calvo fairy), they'll still supply whatever quantity is demanded.

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    1. I don't believe that's true, since you have involuntary unemployment - people off of their labor supply curves.

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    2. Actually in basic NK model (as presented e.g. in Gali's book), labor market is competitive and wages are flexible, so there's no unemployment. You can make wages sticky using the same modelling trick (workers as suppliers of labor are monopolists but cannot always adjust their price/wage), but that's probably not what one would call unemployment. Better way is to incorporate search/matching frictions, like in Blanchard & Gali (2010) [1]. Which is yet another kind of equilibrium :)

      [1] http://www.crei.cat/people/gali/mac_2_2_1_lowlink_pdf_v03.pdf

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    3. Actually in basic NK model (as presented e.g. in Gali's book), labor market is competitive and wages are flexible, so there's no unemployment.

      I think that's why they modified it...

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    4. search/matching frictions, like in Blanchard & Gali (2010) [1]. Which is yet another kind of equilibrium :)

      That's true! But I tend to think of those equilibria as also in the class of "constrained general equilibria"...basically, plans match up but markets don't clear because of a transaction cost.

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  2. Equilibrium in complex systems is non-existent. Complex systems are characterised by disequilibrium. If you start from the assumption that a complex system with reach any kind of equilibrium then you are not in the real world.

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    1. Anonymous6:44 PM

      2nd.

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    2. No. equilibrium is a relative concept. You are thinking of equilibrium as something that happens in a simple system which becomes extremely stable. But that is not the right way to think about. Complex system have their own level of complexity and instability. And hence there can be temporary phases and stages with relatively less instability and predictability. That can be considered equilibrium in such a system.

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    3. It is however an interesting question as to what will tend to happen if the complex system is disrupted in a particular way. That information can be useful to have an idea of, even if the complex system in question is being so frequently disrupted by shocks from different directions that it never actually reaches any equilibrium it starts heading for.

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  3. At the ultimate micro level, everything is always in equilibrium, but that's just stating that the conservation laws are instantaneously obeyed. (Yes, quantum mechanics allows short term violations, but economics deals with the classical world.) At the higher level, equilibrium seems a matter of convergence. That's the problem that held calculus in thrall from its inception until the late 19th century. It's easy to talk about equilibrium and solutions and asymptotes, but much harder to prove that they exist, especially since complex systems like those studied in economics rarely do have any simple convergences. They are much more likely to show cyclical or chaotic behavior which is better studied using the mathematics of attractors.

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  4. Anonymous8:21 PM

    When did NK models take over from RBC as the preferable model of reality by a majority of macro-economists? Was this in response to the great depression? Or did it gradually take place over many years? I ask because I was under the impression (possibly attained from reading this very blog) that RBC was the dominant paradigm of macroeconomic thought that held all the keys and opened all the doors to the elite academic journals that allowed one to depart from the terrible Swamps of Sadness Swamps of Sadness.

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    1. When did NK models take over from RBC as the preferable model of reality by a majority of macro-economists? Was this in response to the great depression? Or did it gradually take place over many years?

      It was gradual, mostly in the early 2000s.

      I ask because I was under the impression (possibly attained from reading this very blog) that RBC was the dominant paradigm of macroeconomic thought that held all the keys and opened all the doors to the elite academic journals that allowed one to depart from the terrible Swamps of Sadness

      Well, RBC models have successfully colonized other areas of econ, including A) international finance and trade, B) asset pricing, and C) labor econ. But in the core of macro, NK has mostly muscled them out, probably due to the influence of the Fed.

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  5. The economy moves with dynamics, which at times constrain it and at times don't constrain it. Equilibrium is like the water in a river. It flows but only because the landscape goes downhill. The water is in equilibrium because it flows naturally.
    The economy flows upon the landscape of the institutions we make by culture, government and business.
    I have developed the new equations for Effective demand. The dynamics are not ones of equilibrium but of flowing within the constraints.
    Here is the link to my blog...
    http://effectivedemand.typepad.com

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  6. Anonymous12:43 AM

    If we postulate that the epicycles of the epicycles of the epicycles have epicycles, then we can explain the present motions of the planets almost exactly.

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    1. Predict, or just explain?

      The Smets-Wouters DSGE model does an excellent job of fitting the curve of past U.S. GDP, but has essentially no out-of-sample forecasting power.

      If we had a macroeconomic model that was even 10% as good as epicycle-based astronomy models at making out-of-sample predictions, I'd jump for joy.

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    2. Anonymous4:32 PM

      Exactly. Why I said "explain."

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  7. This just seems like more evidence that economics is still unable to encompass concepts in mathematics that were discovered 50-80 years ago or more. Why is it so important to be in equilibrium? If life itself takes place in a thermodynamic regime that is "far from equilibrium", why should we expect that an economic system composed of many living individuals have any equilibrium properties whatsoever?

    You could try to argue, for example, that waterfalls, flames, and the famously chaotic Lorenz equations that model the weather are somehow in "equilibrium" in some way or other, but this really misses the essence of these phenomena.

    All this economics focus on equilibrium states of markets seems to be missing the point in the same sort of way. A functioning market is *always* away from equilibrium. A cleared market that has actually attained equilibrium means that no transactions are occurring, and everyone might as well pack up and go home. Any model that fully clears and attains equilibrium in any reasonable time is prima facie wrong. Studies of the equilibrium behavior of models that take infinite time to clear are way off in "who cares?" territory.

    Now, if you wanted to talk about stability parameters and Lyapounov exponents, that would be interesting, but probably still oversimplified, especially in financial markets with hedging.

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    1. George,

      You remind me of the guy on Nick Rowe's blog who started a post saying, "an economy that is efficient is an economy in which inputs match outputs." When someone pointed out that this was trivially wrong, he exclaimed "well that is how efficiency is defined in all the sciences!"

      What you call equilibrium is not what economists call equilibrium. This is most evident when you wrote "A cleared market that has actually attained equilibrium means that no transactions are occurring," which is another example of something that is trivially not true.

      You're begging the question - of course a market that cleared in equilibrium has no transactions if that's what you define equilibrium to be. But the point is that economists don't define equilibrium to mean this, so you've missed the point entirely.

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    2. It's the concept of equilibrium that is important, not being in equilibrium per se. The question is what would happen, if the current situation continues. For example, we know that physically demand cannot exceed supply (taking into account recycling, existing stocks, etc). So what will tend to happen to the economy if there's a sudden cut in supply of some commodity?

      To take the physical sciences, what happens to water in a waterfall? It keeps falling until it hits something that interrupts that motion, such as the bottom. What happens to a fire? It keeps burning until it runs out of fuel, or oxygen. These are not very exciting concepts perhaps, but useful if you are trying to stop a fire in your kitchen. Of course, putting out a kitchen fire may miss the essence of the phenomenon of fire, but that doesn't mean it's totally useless information.

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  8. Anonymous4:12 AM

    In my humble opinion, the only reason why the equilibrium issue is of any interest for ordinary laypeople and the reason why the professional debates among economists reach the world outside, is the way the issue has been manipulated. It is somehow inferred implicitly that you may have an economy free of crisis. Moreover, it is a natural state of the economy which can only be undermined and upset by unwise, indelictae and unenlightened intervention by the Government. Now, you won't be able to quote directly any at least thinly reputed expert to say such nonsense. But somehow this perception about an "economy in equilibrium" in colloquial sense persists in the world beyond the academia. This is the crux of the problem. So, basically, Noah, you are right with your post but it misses the whole point of why "economic equilibrium" has gained the notoriety and become such a titillating subject for non-economists.

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  9. Christian4:58 AM

    Nice post, but I have to object to the following muddling ;)

    Walrasian Equilibria are not Nash Equilibria. Rather than taking the individual demand and supply by others as given, walrasian equilibrium assumes that each agents takes prices as given and neglects any market power that she may have.

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  10. Anders K5:04 AM

    Great post. But surely Post-Keynesians are exempt from the statement "economists inevitably have to assume that some type of shorter-run equilibrium always holds in their models", no?

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  11. I still don't really think any of these equilibria (or disequilibria) are necessarily good ways to frame a model. Plans equilibria is a difficult assumption to work with, because it's seemingly untestable. Same for Nash equilibria. Walrasian equilibria (i.e. clearing) is testable, but is falsified in a lot of contexts, and it's arguable Walras didn't even mean clearing. He described market equilibrium (in translation from French, obviously) as: "the market is like a lake, agitated by the wind, where the water is incessantly seeking its level without ever reaching it".

    If we have to use an "equilibrium" metaphor, I'd frame it in terms of a deterministic equilibrium assumption — all actions have consequences. Obviously, this is a very loose definition and doesn't leave us with an easily-accessible mathematical framework as other equilibria assumptions like clearing do. But I'm more interested in describing the underlying reality accurately and getting my epistemology straight than I am in creating a tractable mathematical framework from which I can make predictions.

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  12. I think you can go a bit more than "all actions have consequences". For example "You can't consume more than you have produced" strikes me as one, or to put it more concretely, say the supply of X suddenly drops drastically, say there's only two factories making it and one burns down. Then either the consumption of X is going to have to drop or stocks of X are going to get drawn down, or some combination of the two, until the lost capacity is rebuilt.

    Another one is that "you can't produce more than is demanded and can be stored (allowing for losses in storage)".

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    1. Another one is that "you can't produce more than is demanded and can be stored (allowing for losses in storage)".

      Why would you say such a thing?

      Similarly, your remarkable claim above that demand cannot exceed supply. Isn't that a major reason prices move? And if it were true for commodities wouldn't it also be true for money and jobs? You sound like Dr. Pangloss to me.

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    2. Sorry, my earlier comment here was meant to be a reply to Aziz! I hope this explains the conclusion.

      Yes, demand can't exceed supply, taking into account stocks of supply. That's why, in a free market, prices move, to try to bring the two back into equilibrium (see, that concept!) The higher prices induce some combination of less demand and more supply. If prices are stopped from moving, then there's shortages.

      Equally, if an economy keeps producing stuff beyond what can be consumed, then the storage system starts overflowing and at some point this has to stop.

      I am puzzled that you think that the idea that there are some limits on economies, at least in the short-term, as being like Dr Pangloss. I thought that Dr Pangloss was famous for his excessive optimisim, am I wrong about this?

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    3. When you say that "demand cannot exceed supply" you are making an oversimplification that, in my view, serves to sweep unsightly facts under the rug. So, yes I think that is dubious optimism.

      Of course demand can exceed supply, and vice versa! Have you ever heard of famine?? Do you think the unemployment rate in the US is a reflection of unusually low demand for jobs? How do you account for low business investment in today's slack economy?

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    4. Mattski, you're the one who said "demand cannot exceed supply". I initially said "consumption cannot exceed what has already been produced." You then responded, changing my words from "consumption" to "demand."

      I was happy to go along with your change in wording at first, because it seems petty to me to argue over the meaning of words. But, given that you are now criticising me for your own restatement of my claims, I see that I was wrong to let your restatement slide. I withdraw my claim that demand cannot exceed supply, and revert to my earlier claim, "You can't consume more than you have produced". My apologies for failing to be pedantic on this point.

      Do you agree that a famine can result because a shortage of the supply of food means that consumption of food must fall to match, even if demand for food remains high?

      (Although, given even your changing definition of "demand", I don't understand the relevance of two of your examples. Isn't the case of unemployment being a case of demand for labour being lower than the supply of labour? And I don't understand how you are relating business investment to consumption-supply balances at all).

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  13. "Lotka (1925) resembled Marshall in that he recognized many different kinds and definitions of equilibria. Thus he distinguished stationary states from moving equilibria. Furthermore, he noted a 'kinematic' concept in which 'velocities vanish," a 'dynamic' concept in which 'forces are balanced in which the rsultant force vanishes,' and an 'energetic' concept in which 'virtual work done in an any small displacement compatible with the constraint vanishes,' in short minimization of potential energy. It must be further noted that Lotka defined evolution as an irreversible process driven by the operation of the Second Law of Thermodynamics and labeled as 'quasi-equilibria' those maintained by a 'dissipation or degradation of available energy.' Furthermore, he frequently used human-animal examples and argued explicitly that he was analyzing 'the biological basis of economics.' " (me, 1991, From Catastrophe to Chaos, p. 223)

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  14. Anonymous5:20 PM

    Before commenting further I would like to thank you for taking the time to put this piece together. It was a really interesting and stimulating read.

    It seems that your narrative is focused around a trichotomy of concepts relevant to equilibrium. This triple seems to be 'market clearing'-'consistency'-'stability'.

    The first of the three-'market clearing'-is related to the walrasian concept of supply and demand equality (with no reference to 'time' or dynamics of any kind).

    The second part-'consistency'-seems to encompass a bit more than the first part. In this part one finds the game theoretic notion of the Nash equilibrium along with the Keynesian pair of 'planned' vs 'actual' (expenditure?) and the REE concept. To a large extent they all deal with 'beliefs', how they 'equilibrate' and how that affect the equilibrium or 'steady state'.

    The last part of the trichotomy-the 'stability' part- seems to tackle the aspect of 'time'.

    Having said that, I think that the conclusion is unwarranted. The concept of equilibrium is an all-encompassing theme in the discipline and when 'people' 'complain' about 'equilibrium' they are not just being critical of the wrong modelling assumptions that 'some economist' made.

    Perhaps some portion of the 'complaint' has to do with the fact that despite the abundance of concepts of equilibrium-and all the connotations that come attached to it-it does not offer much help in giving a clear cut answer in what is happening in the 'real world', especially in times where there is *a lot* going on.

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    1. Having said that, I think that the conclusion is unwarranted. The concept of equilibrium is an all-encompassing theme in the discipline and when 'people' 'complain' about 'equilibrium' they are not just being critical of the wrong modelling assumptions that 'some economist' made.

      Can you explain why you think this?

      Perhaps some portion of the 'complaint' has to do with the fact that despite the abundance of concepts of equilibrium-and all the connotations that come attached to it-it does not offer much help in giving a clear cut answer in what is happening in the 'real world', especially in times where there is *a lot* going on.

      This is a valid complaint. But I think the reason is fairly innocuous - economists didn't think the concept of "equilibrium" was important enough to always warrant being precise about it.

      Why do I embrace this innocuous explanation, when I so often criticize the econ profession? Because physicists do the exact same thing. Physicists talk about equilibrium, but there are many kinds, and they never bother to say which kind they're modeling, since it becomes 100% apparent from the math itself. My bet is that economists, who tried to copy physicists since time immemorial, just picked up the same bad habit.

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    2. In the long run everything is in equilibrium. (Heh.)

      This is a layman/hacker perspective, but I get the feeling the value of equilibrium is highly psychological. It's a soothing word that helps us swallow chaotic and unpredictable events. Sure, there are patterns in the world, and reasonable people look for them. But the "balance" we long for is often simply the crisis and its aftermath.

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    3. This is a layman/hacker perspective, but I get the feeling the value of equilibrium is highly psychological. It's a soothing word that helps us swallow chaotic and unpredictable events.

      I think it ends up just being a fancy word for "system of equations".

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    4. Anonymous1:12 PM

      I think that a short answer on why I believe that 'equilibrium' is pivotal would have to do with the fact that my understanding is that economics is about 'telling a story'. All stories, be they good ones or bad ones, require a plot. The function of 'equilibrium' is to provide the structure for the plot. Equilibrium sets the main stage and winds the actors accordingly. The particular assumptions matter-they may make the difference between a 'good storyline' and a 'great storyline'-but they undoubtedly function in accordance to some equilibrium.
      Which particular equilibrium concept matters enough to make 'people' furious obviously depends on the particular pressing issues of every epoch and the stance of the profession against those issues. (I think I have stumbled upon a story somewhere about how the Queen of England was preoccupied about the inefficiency of Her economic advisers to 'foresee' the '07-'08 event. Be that as it may, even if this expressed disappointment of the sovereign never did *actually* get voiced, the story sets the tone for the scale of events and the multitude of people from where questions are raised).
      I disagree with the thesis of the 'distracted economic theorist' that was preoccupied with more pressing matters and just didn't have time to spare in defining what you describe as nothing more than a supplementary/secondary notion. On the other hand I partially agree with the 'fuzziness' of the topic but I think that it is more of a 'tactical' manoeuvre on the part of the profession which is to a large extent dictated by the nature of the subject.

      I'm not sure I see the relevance of the argument about the different types of equilibria physicists use to the centrality (or irrelevance) of the equilibrium concept in economics. I think that physics (mainly classical mechanics) is 'responsible' for the concept of 'reductionism' of the macro into the micro more than it is accountable for the fuzziness of the equilibrium concept.

      Please allow this-mostly rhetorical-question: If 'equilibrium' was not pivotal, then it would be possible to substitute it by another concept/system of concepts and still maintain the results of the economic method. Do you believe that any econ prof would be able to stand in front of a class and teach [pick a subject] without any implicit or explicit reference to an equilibrium concept? I do not.

      Again, thank you for making this really informative post and thank you for taking the time to respond to comments.

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  15. How about partial equilibrium?

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    1. Partial equilibrium is like a "less good" version of general equilibrium, which is the best kind since it applies to the most people.

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  16. John S1:13 AM

    Off topic: can you give us your take on Bitcoin? C'mon, if you did a post on brain augmentation, surely you've got to address a new $1.2 billion dollar cryptocurrency, right? :)

    JP Koning has been doing an interesting series of articles like this one:
    http://jpkoning.blogspot.kr/2013/03/selling-out-of-bitcoin-ledger.html

    Also, he did a great one on Ripple (*highly recommended*), another cryptocurrency:
    http://jpkoning.blogspot.kr/2013/02/ripple-or-bills-of-exchange-20.html

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  17. Noah says "In this case, a better thing for the long-term modeler to do would be to assume that beliefs and plans can change randomly, and assume that they change according to some sort of stochastic process."

    But beliefs and plans do not simply change according to some stochastic process but also with the outcome of the economic activity itself. And at a rate much faster than the system can accommodate to them. A system in which inputs depend on outputs in this way is never stable or predictable. And while Noah may be right the equilibrium is just whatever the equations say it is, he really is missing the essential point that from the critic/ lay person's perspective, equilibrium means predictable and stable at some known time scale, rather than chaotic and essentially unpredictable from its initial state. And if there are multiple (infinite?) equilibria, as in last post about DSGE models, that is to the lay public same as no equilibria. We want one handed economists.

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  18. Given that growing disequilibria are unsustainable in the long-run, in economic systems as in biologic and physical systems, what we need to understand urgently is how to correct the divergences in the most effective and with lowest costs and greatest equity.

    With German trade surpluses setting records, the fragile economies of the Eurozone real-life economic laboratory suffering a "combination downside", would be grateful for any movement towards a fouth or fifth best equilibrium and away from testing the limits of divergence.
    See http://ppplusofonia.blogspot.pt/2011/12/eurozone-crisis-tests-limits-of.html

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  19. I find this post silly. Herbert Scarf, Frank Hahn, and Franklin Fisher are not laypeople. I suppose you could say Donald Saari is a layperson. And, I suppose, you could say that Doyne Farmer's work on game theory is that of a layperson.

    There are good reasons, not dependent on confusion about the concept of economic equilibrium, to say mainstream economists focus too much on equilibrium. This post fails to engage those reasons at all.

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  20. Thanks for this post, Noah. You shouldn’t be spending so much time on this. Quick reactions:

    1. The lay fascination with the economist’s use of equilibrium comes from a confusion, sometimes abetted by economists, that equilibrium mean “desirable”. The word has that connotation in the vernacular. Economics, of course, is to a large extent built around the question, when is the equilibrium desirable? This confusion calls for less sloppiness (and in some cases less guile) in the way economists communicate their work to the public.

    2. Noah has described only two kinds of equilibrium, consistency of plans and attainment of a steady state. One is essentially static, the other dynamic, yes?

    3. Stability of equilibrium is huge and it borders on a sin that economists often elide it. This is an 800 pound gorilla in general equilibrium theory, for instance. Stability is related to uniqueness as well.

    4. My critique of equilibrium is that it forces economists to make too many empirically unwarranted assumptions in order to get a model, when simply positing mechanisms (usually as individual differential equations) would be enough. Even a simple model like supply and demand in an individual market, where the point is to identify an equilibrium price and quantity, can readily misrepresent the real world, as we know from lots of specialized disciplines like labor, finance, industrial organization, urban, etc. On the other hand, an adjustment process, like one that specifies a rate of change in prices over time that is anticipated from observable excess supply, depends on fewer assumptions and is empirically testable. (The equation for this can have lots of variables, of course.) An economics of processes would look quite different from the economics of equilibrium conditions we currently have.

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    Replies
    1. The lay fascination with the economist’s use of equilibrium comes from a confusion, sometimes abetted by economists, that equilibrium mean “desirable”.

      Only abetted by economists because in some models, equilibrium is desirable, and in none is it not.

      This confusion calls for less sloppiness (and in some cases less guile) in the way economists communicate their work to the public.

      Actually I disagree, because I don't think economists often use the word "equilibrium" when talking to the public.

      Noah has described only two kinds of equilibrium, consistency of plans and attainment of a steady state. One is essentially static, the other dynamic, yes?

      No, I described other kinds too! Walrasian equilibrium is the balancing of supply and demand. That's something other than the two you mention.

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    2. Economists communicating: Economists use "equilibrium" all the time in introductory textbooks, for whom the audience is the lay public, or the tuition-paying part of it. The word also crops up from time to time in op-eds and similar venues. My perception is that care is not always taken.

      You should explain why you think Walrasian equilibrium is different. In the case of S and D, the S curve represents a set of plans conditional on the price, the D curve represents this as well, and market clearing (in the simple case) reflects the simultaneous realization of these plans. Or are you using the word "plan" in a different sense?

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    3. Economists communicating: Economists use "equilibrium" all the time in introductory textbooks, for whom the audience is the lay public, or the tuition-paying part of it.

      Yes. Though I don't think of econ students as the "lay public", I agree that intro textbooks would be well-served by being more careful about the multiple definitions of equilibrium, and about stability assumptions. Krugman might listen to us if we complained to him, but Mankiw is a bigger culprit here.

      Keep in mind though, that only a very few economists write intro textbooks.

      You should explain why you think Walrasian equilibrium is different. In the case of S and D, the S curve represents a set of plans conditional on the price, the D curve represents this as well, and market clearing (in the simple case) reflects the simultaneous realization of these plans. Or are you using the word "plan" in a different sense?

      No, Walrasian equilibrium is a strict subset of equilibrium in which plans coincide. To see this, observe that in Nash equilibria, plans coincide, but not all Nash equilibria are Walrasian. An example of a non-Walrasian Nash equilibrium is a classic Akerlof lemons model.

      Remember not to commit the fallacy of the converse!

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  21. I don't think I'm committing that fallacy. My point is that "plans-coinciding" is a superset of various static equilibrium concepts in economics.

    My motivation here is similar to yours. It comes from trying to provide students with a concept of equilibrium that is flexible enough to encompass the range of typical micro and macro contexts. I think it would be a virtue to have a single definition (the superset version) that they could learn once and use over and over.

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  22. Anonymous9:55 AM

    George Soros believes that there is no equilibrium and the system is always tending to disequilibrium until acted on by external forces/intervention. However, to remain in a state of disequilibrium must imply some form of equilibrium to sustain itself. It is simply not possible to sustain a state of disequilibrium without being in a state of equilibrium in a shorter timeframe concurrent with the state of disequilibrium.

    It is a logical impossibility that there can be a state of disequilibrium and no state of equilibrium. You have to accept both can exist or completely ignore the idea of equilibria.

    I think of the concept in this fashion: any cyclical system can be moving towards a state of equilibrium at any time. Like a planet is moving to apogee to the sun and away from its former state of apogee at the same time because its on a cycle.

    For the economy, it is always moving towards equilibrium and disequilibrium because it is cyclical and obtaining a perfect state of each is impossible because it is cycling. Or you can continue to debate that one or the other doesn't exist when neither can exist without the other.

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  23. Do you know of any macro models that were reasonably good about predicting/ expecting both the dot.com bubble pop in 2000-2001, as well as the house bubble price pop of 2006-2008?

    A key output of good macro models should be future prices.
    (Just like a key output of a climate model would be future temperatures -- most of which are looking less high over the last 10 years than alarmist models predicted, despite the continued increase in CO2).

    The failure of economic models to predict the booms and busts indicates there is something missing from the modeling methodology.
    Perhaps the whole paradigm?

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