Friday, November 19, 2010

Foley, Sidrauski, and the Microfoundations Project




















  1. If we take the temporary equilibrium approach we assume the firm can make fine tuned adjustments to internal inventory to cover a mismatch between available input and flow solutions. The firm is limited to a specific transaction rate and size n input and another set on output. This is the Hicks formulation of the Keynes problem of a limited iiquidity system.

    Because of the mismatch in input and pout flow we have introduced a cyclic component. Call this quantization error, and in the stochastic model appeas as gaussian noise.

    So far so good with the hick's formulation, and they almost got it with the "uncertainty constant", which is the tolerable quantization error. Had they understood this to be a constant level of acceptable inventory variance, then they would have been automatically led to a Shannon Channel being formed out of a sequence of temporary markets.

    They missed that last connection.
    To get learning, I would use duality. Since the yield curve is a computational derivative of a sequences of transactions, one can set up the conditions of duality and treat the economy as computing the yield curve. From there you are led to the exact physical network, a directed graph of real goods with agents at each node trying to adjust inventories to get them all within bounds, and thus unknowingly creating the optimum Shannon information. The information units being actual products moving through the system under the duality concept and adaptive learning. channel.

    The number of temporary equilibrium (the rank in the distribution graph) determines the precision of the computer. But you see, the assumption of fixed uncertainty fixes the quantization error which fixes the median length of the inventory chain.

    In short, Shannon information theory gives you all the math tools to cover monopolies and economies of scale.



    But, as far as I can see, even if they have exactly the same *beliefs* about the future, their *plans* for the future could still be mutually inconsistent. For example, everybody believes that everybody else will spend $100 next year, and so each believes he will have an income of $100, but each plans to spend $90.

    This is exactly what I was trying to argue in this old post:

    New Keynesian macro models assume that individuals' plans for future consumption are mutually consistent with absolutely zero explanation or story about what would make them consistent.

    (Nobody understood what I was yammering on about, sniff!)

    And yes, I think that Howitt Evans approach is a promising way to go.

    I didn't know about Foley and Sidrauski. (I knew of Sidrauski's super-neutrality paper, but that was all.)

  3. It's Foley's work with statistical equilibrium you need to read.

    Walras et al is maths for two body systems, and static ones to boot, and is completely inappropriate.

    For multi-body systems you need statistical mechanics.

    Foley is the only economist to have understood this fully. One day, probably quite soon, his contribution will be recognised.

  4. Nick, thanks for telling my about your post, I have appended a paragraph that discusses and links to it. It's a great post and I agree completely. I also agree with your point about mutual inconsistency of intertemporal plans in the face of belief homogeneity - after all, doesn't that describe the adaptive expectations hypothesis?

    Matt, I wish I could understand your comment better but some of the jargon is unfamiliar to me. Perhaps you can post a couple of helpful links?

    Geoff, I read Duncan's statistical equilibrium paper even before it was published in JET. It has some interesting ideas and I may even blog about it at some point. But I think that the temporary equilibrium approach with adaptive learning (perhaps in an agent-based framework) is more promising.

  5. The theory of rational beliefs equilibria, developed by Mordecai Kurz, allows for agents to make decisions based on mutually inconsistent beliefs provided that these beliefs are consistent with the economy's empirical distribution.

  6. Rajiv,

    As one of the commenters on Nick's post I'd like to point out that I thought I did understand his point and that it was just wrong.

    I think we should try to make something of a distinction between the "model" and the equilibrium concept that we try to solve it for. That is, I want to agree to terminology where if we take a New-Keynesian set-up and solve first for the rational expectations equilibrium and then for equilibrium under adaptive learning it is not two different models, it is one model solved for two different types of equilibrium.

    With that terminology, in an NK model when we ask about Nick's example where everyone plans to spend 90 out of income of 100 there are two questions. One, can the model handle that situation? The answer is yes. Two, can that situation happen in equilibrium? Here the answer is yes for adaptive expectations and no for REE.

    The point is that the model has no problem here, and under adaptive learning the condition can happen and nothing goes wrong. Under REE the condition doesn't happen in the first place but their is a mechanism to rule it out.

    So, before specifying an equilibrium what happens in an NK model if everyone plans next period to spend 90 out of their income of 100? Well, in the basic model there is no capital and so there is no savings so next period something will have to adjust. When tomorrow arrives either income will fall to 90 or the real interest rate will fall making people choose to spend their whole income. The model has no inconsistency. The only question is what will happen in a particular equilibrium.

    First take adaptive expectations. In that case it's perfectly possible for people to make such plans, when tomorrow arrives the real rate is lowered to clear the savings market and everyone ends up spending all their income. Where's the problem? Of course, if this happens repeatedly then people learn to anticipate the change in the real rate leading to...

    In REE everyone anticipates that they won't want to save because the real rate will change to whatever value makes them not want to save. So they don't plan to save in the first place. So in a rational expectations equilibrium Nick's example never happens, but their is a mechanism to rule it out. Agents anticipate the real rate adjustment.

    Now, we can argue about the plausability of various equilibrium concepts but if you read Nick's post he was saying that NK modles were internally inconsistent ("New Keynesian macroeconomists are much more sloppy...), that's just not true. What was going on was that Nick was failing to understand the model, and instead concluding that the problem lay not with his understanding but with everyone elses.

  7. Rajiv,

    Just a follow up to clarify. I'm actually disagreeing with Nick but not you.

    You're point that convergence to an REE is perhaps more delicate then sometimes presumed is something that I agree with. I think on this point Nick, you and I agree.

    Nick however, to my reading, was saying that in an NK model you *can't* study these things because of missing parts. Failing to distinguish planned aggregate expenditure and income or whatever.

    It's on that point that I thought he was just wrong, all that stuff is there but has been solved out by the time you linearize and write down the 3 equations that characterize the REE. Nick appeared to be looking at the already solved model and concluding that a bunch of stuff was missing. Of course, if you open up Woodford or Gali you see that all that stuff is there in the derivation, just not in the solution.

  8. Adam, here's what I understood Nick to be saying: (i) we live in a world with millions of people making plans regarding current and future economic activities in a decentralized, uncoordinated manner, (ii) as far as current activities are concerned these plans are made consistent by the operation of markets, (iii) no such mechanisms exist to bring plans for future activity into consistency with each other since we do not have a complete set of futures markets for all contingent claims, (iv) the RE hypothesis is based on the assumption that the economy operates as if such complete markets existed, and (v) there is no justification for such a claim.

    This is very close to what Foley discovered forty years ago, as described in his essay.

    I cringe a bit when I see expressions like "equilibrium under adaptive expectations" because this use of the equilibrium concept strips it of all meaning and usefulness. An equilibrium is a profile of plans such that no individual has a profitable deviation conditional on their beliefs (including beliefs about the beliefs of others, etc.), and these beliefs are consistent with each other in some manner. If the beliefs are arbitrary, we are talking about rationalizability, not equilibrium. There is no sense in which adaptive expectations is an equilibrium hypothesis, it quite clearly describes a process of expectation revision in the face of disequilibrium.

    Regarding internal consistency, I'm with you - there's nothing inconsistent about an RE model, NK or otherwise. But internal consistency is a truly minimal requirement for a theory.

  9. Adam, I posted my last reply before I saw your latest comment... yes, I agree with you on the internal consistency point. I just didn't think this was Nick's main concern in this particular post.

  10. Ok, I agree with everything you just said how you read Nick's post. If he actually said what you just did then I'd have been with him 100%.

    However, if he wanted to critique the ratex assumption he should have said that. Why even mention the NK framework then? Ratex is in all the basic models that I learned in grad school, RBC, NK, whatever.

    And then why all the statements about sloppiness? (And this was the argument, his examples of perceived sloppiness were the things I thought were wrong.)

    I guess this is entirely irrelevant to the point you wanted to make, I just took a bit of exception to Nick saying nobody understood his point.

  11. Agreed - the focus should have been on RE not NK. Based on some of his other posts I do think that Nick believes the NK model to be inconsistent in some way, but I've never been able to figure out exactly why.

  12. The NK model must stationary but the equilibrium outcome where 'the real interest rate will fall making people choose to spend their whole income.' fails the stationary test, no?

  13. My comment above. We are a positive definite economy, rates do not go negative. The obvious reason is that we cannot really disassemble a new car and put the parts back into inventory.

    If we are so asymmetric, then the NK derivation will work only for very short run observations.

    We operate as a series of Hicks temporary equilibriums in time and space, and these equilibrium processors are generally one way.

    The Hicks equilibriator will select the best market choice from limited market options, then adjust internal inventories. That process is a different norm, it is a maximum entropy norm.

    So consider the case where the yield curve gets the negative shock and contracts. The Hicks equilibriators can only make a positive choice, choosing to buy over longer intervals in greater sizes; and they do more inventory management inside the firm. Excess assets get taken off the market, internalized and bundled, and rereleased over larger intervals, the yield curve remains positive definite.

    The problem of quantization and economies of scale force us into a positive definite norm.

  14. nice post as usual

    i think df had the wrong project i thought it back in 78
    a case of too much sunk cost in the old GET paradigm
    open self evolving market systems
    basically cashiers all this
    but DF's personal look at agent based systems came too late
    for him to do the kind of big work he was capable of

    a casuality of time and place

  15. Paine, welcome back, always good to hear from you. Not sure I agree though - I think Duncan may have given up on the project too soon. I just emailed him to say this:

    "I think that the temporary equilibrium approach combined with heterogeneous beliefs and adaptive learning (perhaps in an agent based framework) could be very promising. The key to finding a general theory of economic fluctuations lies in the stability analysis of the learning process. I suspect that there must be conditions under which learning is locally unstable, or characterized by corridor stability in the Leijonhufvud sense. Tobin's 1975 AER paper lays out the basic mechanisms but is not microfounded."

    I've been asked to write a chapter for a volume in honor of Duncan, which is why I've started thinking about these things again after many years. Macro should be the most interesting subject in the world, instead it has become a minor branch of decision theory. Macro courses should really be called applied stochastic dynamic programming.

  16. Foley's work is indeed a breath of fresh air.

    One point that is puzzling, however, is the unduly intense focus as monetary policy and money transactions as point upon which there is disagreement about future beliefs and plans, and as the mechanism through which macroeconomic instability emerges.

    Surely long term financial transactions have intertemporal implications, but the assumption that they are the primary driver of instability in the macro economy seems to be merely assumed by much of economic theory, rather than empirically established.

    Yet, given the fact that the financial sector has a much better developed futures market than almost any other part of the economy, and the various methods like selling bonds at premiums and disscounts that allow mistaken future expectations to be rapidly resolved, is that assumption really well founded.

    The current financial crisis and the burst bubble that set off Japan's lost decade, both had their roots in sustained and extreme overvaluaton of real estate. The problem in the real economy in each case could be stated as devoting lots of resources to building buildings that the economy didn't actually need, which caused the entire construction industry to collapse when this was realized.

    Likewise the tech bubble and its collapse can be understood as an episode where lots of people followed the business model summed up as:

    1. Come up with cool tech.
    2. ?????
    3. Profit

    In other words, the tech bubble collapse recession was a result of people devoting lots of economic resources to develop tech that the economy didn't need.

    The notion of calling a recession of "correction" captures this idea. A "real economy" perspective attributes most economic downturns to the fact that the economy got carried away by devoting too many resources to productive activities that produced goods and services that the economy didn't need.

    Thus, a capitalist recession is to some extent just a subtle version of the same problem that the Soviet's used to have with their five year plans. The economy produced a lot, but it produced the wrong things.

    From this perspective, the big questions about the business cycle are: (1) "why do businesses produce the wrong things?," and (2) "why do they realize this all at once rather than gradually?" There are lots of answers to the first question, but you only create business cycles when the second question is an issue as well.

    The financial sector plays a role in both stories, but it isn't at all obvious that either money per se, or the financial sector generally is at the core of either story. It seems like a case of trying to understand the message by carefully studying the postman.

    One of the virtues of trying to look at bad decisions in the real economy as a source of instability (quite possibly due to poor coordination of future plans), is that this captures and emphasizes the path dependency and secular trends of economic development, while a monetary narrative sees only repeating cycles without devoting much attention to what is different in the economy before and after an economic cycle runs its course.

    Since excruciating attention to the financial side of business cycles has proven basically futile at taming them, perhaps more attention to their role in restructuring the real economy might be more fruitful. For example, if one can see recessions as often having roots in making things that no one needs, then futile stimulus programs like the home buyer's tax credit and cash for clunkers, which tried to restore the economy to a pre-recession equilibrium that was clearly a false one, would seem instinctively wrong, despite their appeal if one seems business cycles a cyclical returns from one equilbrium to the next without regard to how the equilibriums differ from each other.

  17. Like Mark Thoma, I've had this post open for ages planning a response. His link yesterday prompted me to write the following:

    Foley's questions are really powerful and I hope they stimulate lots of ideas on how to come up with answers. He's on the board of advisers of George Soros's INET, but who knows whether that will end up being an influential body or just a well-funded one.

  18. Leigh, I've appended an update that links to your post (and Mark's). Thanks for your comments. The comparison with interfluidity is flattering - Steve's blog is brilliant and wise. You should also look at Macroeconomic Resilience, which is full of interesting research ideas presented at a high level of analytical rigor.

    Andrew, thanks as always for your detailed and thoughtful comments. I did not respond because there is so much to respond to and time has been scarce recently. But I always read and appreciate your remarks.

  19. Thanks, Rajiv. I do read Macroeconomic Resilience (perhaps I got it originally from a link of yours?) and agree with you that the ideas there are really good - and many of them devastatingly practical in their application. Like me, the author is based in London, and I must finally get around to contacting him to see if we can meet up.