Friday, November 19, 2010

Foley, Sidrauski, and the Microfoundations Project

In a previous post I mentioned an autobiographical essay by Duncan Foley in which he describes in vivid detail his attempts to "alter and generalize competitive equilibrium microeconomic theory" so as to make its predictions more consonant with macroeconomic reality.  Much of this work was done in collaboration with Miguel Sidrauski while the two were members of the MIT faculty some forty years ago. Both men were troubled by the "classical scientific dilemma" facing economics at the time: the discipline had "two theories, the microeconomic general equilibrium theory, and the macroeconomic Keynesian theory, each of which seemed to have considerable explanatory power in its own domain, but which were incompatible." This led them to embark on a "search for a synthesis" that would bridge the gap.

This is how Duncan describes the basic theoretical problem they faced, the strategies they adopted in trying to solve it, the importance of the distinction between stock and flow equilibrium, and the desirability of a theory that allows for intertemporal plans to be mutually inconsistent in the aggregate (links added):
My intellectual preoccupation at M.I.T. was what has come to be called the "microeconomic foundations of macroeconomics." The general equilibrium theory forged by Walras and elaborated by Wald (1951), McKenzie (1959), and Arrow and Debreu (1954) can be used, with the assumption that markets exist for all commodities at all future moments and in all contingencies, to represent macroeconomic reality by simple aggregation. The resulting picture of macroeconomic reality, however, has several disturbing features. For one thing, competitive general equilibrium is efficient, so that it is incompatible with the unemployment of any resources productive enough to pay their costs of utilization. This is difficult to reconcile with the common observation of widely fluctuating rates of unemployment of labor and of capacity utilization of plant and equipment. General equilibrium theory reduces economic production and exchange to the pursuit of directly consumable goods and services, and as a result has no real role for money... The general equilibrium theory can accommodate fluctuations in output and consumption, but only as responses to external shocks to resource availability, technology or tastes. It is difficult to reconcile these relatively slowly moving factors with the large business-cycle fluctuations characteristic of developed capitalist economies. In assuming the clearing of markets for all contingencies in all periods, general equilibrium theory assures the consistency... of individual consumption, investment, and production plans, which is difficult to reconcile with the recurring phenomena of financial crisis and asset revaluation that play so large a role in actual capitalist economic life...

Keynes' theory, on the other hand, offers a systematic way around these problems. Keynes views money as central to the actual operation of developed capitalist economies, precisely because markets for all periods and contingencies do not exist to reconcile differences in agents' opinions about the future. Because agents cannot sell all their prospects on contingent claims markets, they are liquidity constrained. In a liquidity constrained economy there is no guarantee that all factor markets will clear without unemployed labor or unutilized productive capacity. Market prices are inevitably established in part by speculation on an uncertain future. As a result the economy is vulnerable to endogenous fluctuations as the result of herd psychology and self-fulfilling prophecy. From this point of view it is not hard to see why business cycle fluctuations are a characteristic of a productively and financially developed capitalist economy, nor why the potential for financial crisis is inherent in decentralized market allocation of investment...

But there are many loose ends in Keynes' argument. In presenting the equilibrium of short-term expectations that determines the level of output, income and employment in the short period, for example, Keynes argues that entrepreneurs hire labor and buy raw materials to undertake production because they form an expectation as to the volume of sales they will achieve when the production process runs its course... But Keynes offers no systematic alternative account of how entrepreneurs form a view of their prospects on the market to take the place of the assumption of perfect competition and market clearing. This turns out, in detail, to be a very difficult problem to solve.

Given the supply of nominal money, a fall in prices appears to be a possible endogenous source of increased liquidity. Keynes argues that the money price level is largely determined by the money wage level, but offers no systematic explanation of the dynamics governing the movements of money wages.

Though money is the fulcrum on which his theory turns, Keynes does not actually set out a theory of the economic origin or determinants of money. As a result it is difficult to relate the fluctuations in macroeconomic variables such as the velocity of money to the underlying process of the circulation of commodities.

On point after point Keynes' plausible macroeconomic concepts raise unanswered questions about the microeconomic behavior that might support them.

Thus economics in the late 1960s suffered from a classical scientific dilemma in that it had two theories, the microeconomic general equilibrium theory, and the macroeconomic Keynesian theory, each of which seemed to have considerable explanatory power in its own domain, but which were incompatible. The search for a synthesis which would bridge this gap seemed to me to be a good problem to work on. From the beginning the goal of my work in this area was to alter and generalize competitive equilibrium microeconomic theory so as to deduce Keynesian macroeconomic behavior from it.

In the succeeding years I approached this project from two angles. One was to fiddle with general equilibrium theory in the hope of introducing money into it in a convincing and unified way. The other was to rewrite as much as possible of Keynesian macroeconomics in a form compatible with competitive general equilibrium.
This latter project came to fruition first as a close collaboration with Miguel Sidrauski, and resulted in a book Monetary and Fiscal Policy in a Growing Economy (Foley and Sidrauski, 1971)... Our joint work... sought to develop a canonical model with which it would be possible to analyze the classical problems of the impact of government policy on the path of output of an economy... Following my notion that the price of capital goods are determined in asset markets, and the flow of new investment adjusts to make the marginal cost of investment equal to that price, we assumed a two-sector production system, so that there would be a rising marginal cost of investment. The asset equilibrium of the model is a generalization of Sidrauski's (and Tobin's) portfolio demand theory, which in turn is a generalization of Keynes' theory of liquidity preference. One of my chief goals was to sort out rigorously and explicitly the relation between stock and flow variables, so that we analyzed the model as a system of differential equations in continuous time, a setting in which the difference between stock and flow concepts is highlighted. At each instant asset market clearing of money, bonds, and capital markets in stocks together with labor and consumption good flow market clearing determine the price of capital, the interest rate, the price level, income, consumption and investment. Government policies determining the evolution of supplies of money and bonds together with the addition of investment flows to the capital stock move the model through time in a transparent trajectory. The book considers the comparative statics and dynamics of this model in detail...

Monetary and Fiscal Policy in a Growing Economy had a mixed reception... The fact that we did not derive the asset and consumption demands of households from explicit intertemporal expected utility maximization turned out to be an unfashionable choice for the 1970s, when the economics profession was persuaded to put an immense premium on models of "full rationality." Sidrauski and I were quite aware of the possibility of such a model, which would have been a generalization of his thesis work. At a conference at the University of Chicago in 1968, David Nissen presented a perfect foresight macroeconomic model that made clear that this path would lead directly back to the Walrasian general equilibrium results. Since I didn't believe in the relevance of that path to the understanding of real macroeconomic phenomena, I thought the main point in exploring this line of reasoning was to show how unrealistic its results were...

The project of a macroeconomic theory distinct from Walrasian general equilibrium theory rests heavily on the distinction between stock and flow equilibrium. In Keynes' vision, asset holders are forced to value existing and prospective assets speculatively without a full knowledge of the future. Our model represented this moment through the clearance of asset markets. In the Walrasian vision this distinction is dissolved through the imaginary device of clearing futures and contingency markets which establish flow prices that imply asset prices. The moral of Sidrauski's and my work is that some break with the full Walrasian system along temporary equilibrium lines is necessary as a foundation for a distinct macroeconomics. Once the implications of the stock-flow distinction in macroeconomics became clear, however, the temptation to finesse them by retreating to the Walrasian paradigm under the slogan of "rational expectations" became overwhelming to the American economics profession....

In my view, the rational expectations assumption which Lucas and Sargent put forward to "close" the Keynesian model, was only a disguised form of the assumption of the existence of complete futures and contingencies markets. When one unpacked the "expectations" language of the rational expectations literature, it turned out that these models assumed that agents formed expectations of futures and contingency prices that were consistent with the aggregate plans being made, and hence were in fact competitive general equilibrium prices in a model of complete futures and contingency markets. Arrow and Debreu had made the assumption of the existence of complete futures and contingency markets to give their version of the Walrasian model the appearance of coping with the real-world problems posed by the uncertainty of the future. To my mind, the rational expectations approach amounted to making the perfect-foresight assumptions that I had already considered and rejected on grounds of unrealism in the course of working with Sidrauski... What the profession took to be an exciting breakthrough in economic theory I saw as a boring and predictable retracing of an already discredited path.
To my mind the most appealing feature of the Foley-Sidrauski approach to microfoundations is that it allows for the possibility that individuals make mutually inconsistent plans based on heterogeneous beliefs about the future. This is what the rational expectations hypothesis rules out. Auxillary assumptions such as sticky prices must then be imposed in order to make the models more consonant with empirical observation.

In contrast, the notion of temporary equilibrium (introduced by John Hicks) allows for the clearing of asset markets despite mutually inconsistent intertemporal plans. As time elapses and these inconsistencies are revealed, dynamic adjustments are made that affect prices and production. There is no presumption that such a process must converge to anything resembling a rational expectations equilibrium, although there are circumstances under which it might. The contemporary literature closest to this vision of the economy is based on the dynamics of learning, and this dates back at least to Marcet and Sargent (1989) and Howitt (1992), with more recent contributions by Evans and Honkapohja (2001) and Eusepi and Preston (2008). I am not by any means an insider to this literature but my instincts tell me that it is a promising direction in which to proceed.


Update (11/20). Nick Rowe (in a comment) directs us to an earlier post of his in which the importance of allowing for mutually inconsistent intertemporal plans is discussed. He too argues for an explicit analysis of the dynamic adjustment process that resolves these inconsistencies as they appear through time. It's a good post, and makes the point with clarity.

Some of the comments on Nick's post reflect the view that explicit consideration of disequilibrium dynamics is unnecessary since they are known to converge to rational expectations in some models. My own view is that a lot more work needs to be done on learning before this sanguine claim can be said to have theoretical support. Furthermore, local stability of a rational expectations equilibrium in a linearized system does not tell us very much about the global properties of the original (nonlinear) system, since it leaves open the possibility of corridor stability: instability in the face of large but not small perturbations. (Tobin made a similar point in a paper that I have discussed previously here.)


Update (12/13). Mark Thoma and Leigh Caldwell have both posted interesting reactions to this. There's clearly a lot more to be said on the topic but for the moment I'll just link without further comment.


  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.

  2. "To my mind the most appealing feature of the Foley-Sidrauski approach to microfoundations is that it allows for the possibility that individuals make mutually inconsistent plans based on heterogeneous beliefs about the future."


    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.