Macroeconomic Science and Meaningful Theorems

Greg Hill has a terrific post on his blog, providing the coup de grace to Stephen Williamson’s attempt to show that the way to increase inflation is for the Fed to raise its Federal Funds rate target. Williamson’s problem, Hill points out is that he attempts to derive his results from relationships that exist in equilibrium. But equilibrium relationships in and of themselves are sterile. What we care about is how a system responds to some change that disturbs a pre-existing equilibrium.

Williamson acknowledged that “the stories about convergence to competitive equilibrium – the Walrasian auctioneer, learning – are indeed just stories . . . [they] come from outside the model” (here).  And, finally, this: “Telling stories outside of the model we have written down opens up the possibility for cheating. If everything is up front – written down in terms of explicit mathematics – then we have to be honest. We’re not doing critical theory here – we’re doing economics, and we want to be treated seriously by other scientists.”

This self-conscious scientism on Williamson’s part is not just annoyingly self-congratulatory. “Hey, look at me! I can write down mathematical models, so I’m a scientist, just like Richard Feynman.” It’s wildly inaccurate, because the mere statement of equilibrium conditions is theoretically vacuous. Back to Greg:

The most disconcerting thing about Professor Williamson’s justification of “scientific economics” isn’t its uncritical “scientism,” nor is it his defense of mathematical modeling. On the contrary, the most troubling thing is Williamson’s acknowledgement-cum-proclamation that his models, like many others, assume that markets are always in equilibrium.

Why is this assumption a problem?  Because, as Arrow, Debreu, and others demonstrated a half-century ago, the conditions required for general equilibrium are unimaginably stringent.  And no one who’s not already ensconced within Williamson’s camp is likely to characterize real-world economies as always being in equilibrium or quickly converging upon it.  Thus, when Williamson responds to a question about this point with, “Much of economics is competitive equilibrium, so if this is a problem for me, it’s a problem for most of the profession,” I’m inclined to reply, “Yes, Professor, that’s precisely the point!”

Greg proceeds to explain that the Walrasian general equilibrium model involves the critical assumption (implemented by the convenient fiction of an auctioneer who announces prices and computes supply and demand at that prices before allowing trade to take place) that no trading takes place except at the equilibrium price vector (where the number of elements in the vector equals the number of prices in the economy). Without an auctioneer there is no way to ensure that the equilibrium price vector, even if it exists, will ever be found.

Franklin Fisher has shown that decisions made out of equilibrium will only converge to equilibrium under highly restrictive conditions (in particular, “no favorable surprises,” i.e., all “sudden changes in expectations are disappointing”).  And since Fisher has, in fact, written down “the explicit mathematics” leading to this conclusion, mustn’t we conclude that the economists who assume that markets are always in equilibrium are really the ones who are “cheating”?

An alternative general equilibrium story is that learning takes place allowing the economy to converge on a general equilibrium time path over time, but Greg easily disposes of that story as well.

[T]he learning narrative also harbors massive problems, which come out clearly when viewed against the background of the Arrow-Debreu idealized general equilibrium construction, which includes a complete set of intertemporal markets in contingent claims.  In the world of Arrow-Debreu, every price in every possible state of nature is known at the moment when everyone’s once-and-for-all commitments are made.  Nature then unfolds – her succession of states is revealed – and resources are exchanged in accordance with the (contractual) commitments undertaken “at the beginning.”

In real-world economies, these intertemporal markets are woefully incomplete, so there’s trading at every date, and a “sequence economy” takes the place of Arrow and Debreu’s timeless general equilibrium.  In a sequence economy, buyers and sellers must act on their expectations of future events and the prices that will prevail in light of these outcomes.  In the limiting case of rational expectations, all agents correctly forecast the equilibrium prices associated with every possible state of nature, and no one’s expectations are disappointed. 

Unfortunately, the notion that rational expectations about future prices can replace the complete menu of Arrow-Debreu prices is hard to swallow.  Frank Hahn, who co-authored “General Competitive Analysis” with Kenneth Arrow (1972), could not begin to swallow it, and, in his disgorgement, proceeded to describe in excruciating detail why the assumption of rational expectations isn’t up to the job (here).  And incomplete markets are, of course, but one departure from Arrow-Debreu.  In fact, there are so many more that Hahn came to ridicule the approach of sweeping them all aside, and “simply supposing the economy to be in equilibrium at every moment of time.”

Just to pile on, I would also point out that any general equilibrium model assumes that there is a given state of knowledge that is available to all traders collectively, but not necessarily to each trader. In this context, learning means that traders gradually learn what the pre-existing facts are. But in the real world, knowledge increases and evolves through time. As knowledge changes, capital — both human and physical — embodying that knowledge becomes obsolete and has to be replaced or upgraded, at unpredictable moments of time, because it is the nature of new knowledge that it cannot be predicted. The concept of learning incorporated in these sorts of general equilibrium constructs is a travesty of the kind of learning that characterizes the growth of knowledge in the real world. The implications for the existence of a general equilibrium model in a world in which knowledge grows in an unpredictable way are devastating.

Greg aptly sums up the absurdity of using general equilibrium theory (the description of a decentralized economy in which the component parts are in a state of perfect coordination) as the microfoundation for macroeconomics (the study of decentralized economies that are less than perfectly coordinated) as follows:

What’s the use of “general competitive equilibrium” if it can’t furnish a sturdy, albeit “external,” foundation for the kind of modeling done by Professor Williamson, et al?  Well, there are lots of other uses, but in the context of this discussion, perhaps the most important insight to be gleaned is this: Every aspect of a real economy that Keynes thought important is missing from Arrow and Debreu’s marvelous construction.  Perhaps this is why Axel Leijonhufvud, in reviewing a state-of-the-art New Keynesian DSGE model here, wrote, “It makes me feel transported into a Wonderland of long ago – to a time before macroeconomics was invented.”

To which I would just add that nearly 70 years ago, Paul Samuelson published his magnificent Foundations of Economic Analysis, a work undoubtedly read and mastered by Williamson. But the central contribution of the Foundations was the distinction between equilibrium conditions and what Samuelson (owing to the influence of the still fashionable philosophical school called logical positivism) mislabeled meaningful theorems. A mere equilibrium condition is not the same as a meaningful theorem, but Samuelson showed how a meaningful theorem can be mathematically derived from an equilibrium condition. The link between equilibrium conditions and meaningful theorems was the foundation of economic analysis. Without a mathematical connection between equilibrium conditions and meaningful theorems analogous to the one provided by Samuelson in the Foundations, claims to have provided microfoundations for macroeconomics are, at best, premature.


13 Responses to “Macroeconomic Science and Meaningful Theorems”

  1. 1 (Luis) Miguel Navascués January 10, 2014 at 11:59 am

    I always learn so many new things reading you!


  2. 2 Tom January 10, 2014 at 1:26 pm

    All good points, but I think overthinking it. Williamson’s theory might work if consumer price inflation and interest rates were the only variables. But there’s also asset price inflation. And gee, that’s what’s been happening.


  3. 3 Mike Sax January 11, 2014 at 12:34 pm

    Great post David. I particularly think Greg Hill is apt in describing SW’s smug scientism-he and his friends are pure scientists everyone else is just grunting or the like.


  4. 4 Greg Hill January 11, 2014 at 9:58 pm

    David, thanks for your encouragement. A couple of thoughts. I can’t get too upset with Stephen’s unreflective scientism precisely because his mind has yet to make contact with the critics of this pretension, and I don’t mean post-modernist critiques, but rather critiques like those put forward by philosophers like Hilary Putnam (who solved one of Hilbert’s long-standing math problems with Martin Davis).

    You make an interesting point about the distinction between collective, or total, knowledge, and its dispersion across market participants. My first thought was of Hayek and his stress on the decentralized nature of economic knowledge. For rational expectations, I think everyone must know everything and, insofar as there are game theoretic aspects of their interaction, they must know that everyone else knows what they know, which seems a ridiculously tall order.

    As you point out, knowledge itself becomes a deep conceptual problem. G.L.S. Shackle was fond of saying that, if human beings aren’t cogs in a causal machine, then we can originate by imagination something entirely new, something that can’t predicted from what has happened in the past. This claim, if true, has lots of implications, but, in particular, probabilistic knowledge must give ground to a more recalcitrant uncertainty, and, because of all the unanticipated ideas, discoveries, inventions, etc., there will be lots of discontinuities in the structure of economic life, making econometric estimations very difficult to say the least.

    Finally, what we learn depends on what we do and on how the economy develops, which means that expectations, rational or otherwise, will be path dependent, and this poses tough problems for general equilibrium theories.


  5. 5 Tom January 12, 2014 at 6:12 am

    I’m sorry, my previous attempt to post came through with no paragraph separators and thus very hard to read. I’ll try again and hope you do all a favor by deleting the previous attempt.

    At the risk of beating a dead horse, I’d like to explain my previous comment a bit better.

    The flaw in Williamson’s argument is not that he doesn’t explain how his model gets to equilibrium. The problem is at a much simpler level.

    To recap, his argument is: “To induce people to hold more currency, its return must rise, so the inflation rate must fall.” Hence, QE is disinflationary.

    This sounds deceptively attractive. Currency, after as all, is just another financial asset. So, he suggests that it follows, if currency is to be made more attractive, the real interest rate must rise.
    But wait. That’s not true of currency.

    With bonds, any drop in value is equivalent to a rise in rates. But that’s true in part because bonds are valued in terms of currency. Currency however is valued relative to the goods, services and assets that it buys. The relative value of currency can drop *without* implying any change in the real interest rate on currency.

    Moreover, changes in the relative value of currency are often unevenly reflected in the prices of goods, services and assets. One can have low consumer inflation and sharp increases in the prices of domestic assets and foreign currency, as in Japan. Or one can have low consumer price inflation, relatively stable prices of foreign currency and steady increases in prices of domestic assets, as in the US.

    The most common perceived impact of US QE is a rise in the price of financial assets (in some cases, eg long bonds or EM assets, coming off since last year as markets priced in taper). And indeed that’s what QE was meant to do: chase people into riskier assets and bring down term and risk premiums.
    Besides that, it’s very easy to show how central bank monetary emission can cause higher, not lower inflation. There’s a very simple reason why so many people expected QE to cause inflation – because QE is a kind of central bank monetary emission, and emissions have a long record of causing inflation. However, as a rule, countries with chronically high inflation or hyperinflation have governments that rely on emission to rapidly increase nominal public spending. In that situation, the relative devaluation of currency necessary to induce people to hold more currency is accomplished mainly through consumer price inflation: the currency devalues relative to goods and services.

    And what’s more there’s a third way real rates on currency can rise: nominal rates can rise! Developing countries that lean on monetary emission and suffer from chronic high inflation tend to also have high real interest rates.

    It’s stunning that Williamson missed these other ways that currency can relatively devalue. I’m surprised also that his critics so far as I’ve seen haven’t brought them up, and have instead looked for flaws in his model mechanics or scientism or lack of a narrative story or some such. The other ways that currency can relatively devalue are after all pretty gosh darn obvious.

    To be fair to Williamson, he appears to have one point: if a country undertook QE or any other kind of central bank monetary emission, and for whatever reason there was no desire to spend the extra currency created – not on consumer goods or services, not on any kind of domestic or foreign assets, not on anything at all – then indeed the only way left to incentivize people to hold that cash would be for inflation to fall (or deflation to accelerate). I don’t believe there has ever been any real life example, and I have trouble imagining how such a depressed yet resolutely unpanicked situation could come about.


  6. 6 David Glasner January 12, 2014 at 12:33 pm

    Luis, Thanks, so nice of you to say so.

    Mike, I agree.

    Greg, You are a tolerant soul. Please tell me more about the critique by Hillary Putnam that you are referring to and to the Hilbert problem that he and Martin Davis solved.

    Yes, my point certainly starts with Hayek’s work, but one could also add two of Hayek’s students, Shackle (whom you are obviously knowledgeable about) and Lachmann, who also contributed importantly to the understanding of the open-ended, undetermined nature of real world economics. It’s not just that knowledge is decentralized, so that no agent one possesses all available knowledge, it’s also that knowledge unfolds over time in a way that is inherently unpredictable. You can’t predict what is unknown today, but will become known in the future.

    Is it really the case that rational expectations requires that everyone knows everything, or is it possible that only some sufficiently large subset of agents know everything? My intuition is that only a proper subset would be necessary, but I haven’t thought about it, and don’t think I could figure it out if I did, so I am wondering whether you have or know if anyone else has. But either way, I agree that it’s a ridiculously tall order.

    Tom, Thanks for sharing you take on Willaimson’s model. I think that there are (or at least may be) multiple flaws in Williamson’s attempt to show that QE tends to reduce inflation. I wrote a couple of posts in December discussing potential problems with what he was doing. My more recent criticisms are not directed specifically at his argument that QE is deflationary, but at the idea that some sort of DSGE model provides microfoundations for macroeconomic analysis.

    You said:

    “So, he suggests that it follows, if currency is to be made more attractive, the real interest rate must rise.”

    Actually, I don’t think that this was his argument. His point was that QE was increasing the amount of currency and thereby satisfying an excess demand for assets that could be used as collateral, thereby reducing the liquidity premium on money. It was the high liquidity premium on money that, at the zero lower bound, required expected inflation to be positive, as the liquidity premium falls, expected inflation also falls. The argument makes the implicit assumption that at the zero lower bound, a change in the liquidity premium implies a change in expected inflation, but, using only his equilibrium conditions, one could just as easily conclude that a reduced liquidity premium is reflected in a reduced real interest rate rather than in a reduced expected rate of inflation. See my post (“Stephen Williamson Gets Stuck at the Zero Lower Bound.”)


  7. 7 greghill1000 January 12, 2014 at 6:51 pm

    David, first of all, I’m still a net debtor in our exchange of ideas.

    In 1900, David Hilbert listed twenty-three unsolved problems in math, and Hilary Putnam played a role in demonstrating the unsolvability of Hilbert’s tenth problem (which was to find a method for deciding whether a Diophantine equation has an integral solution). I mentioned this because Williamson drew a dichotomy between science and “critical theory” (perhaps a derogatory reference to the post-modernism taught in English departments), and I wanted to introduce Putnam as someone whose views on science can’t be easily ignored by “scientific economists.”

    Putnam once shared W.V.O. Quine’s view that philosophy was in no position to question science (“the best metaphysics is physics”), but later rejected this view. Here’s a citation from his book, “Reality with a Human Face,” to give you the flavor of his critique: “What I am saying, then, is that the elements of what we call ‘language’ or ‘mind’ penetrate so deeply into what we call reality that the very project of representing ourselves as ‘mappers’ of something ‘language-independent’ is fatally compromised from the very start.” This is not to say that we, or our language, “make the world,” but that “the world” cannot be factored into language or mind, on one side, and raw facts or “the given,” on the other. The world is not the “product” of anything; it’s just there.” You can Google Putnam to find out more, or email me.

    I’m in complete agreement regarding the contributions of Hayek, Shackle, and Lachmann, and would only add that Lachmann chided his fellow Austrians for not paying more attention to disequilibrium, leaving the field to Shackle, whom, interestingly even drew the attention of Arrow. And, you’re right, is not just the decentralization of knowledge, it’s lack of knowledge in anything outside a causal web. The presence of other minds, with imaginations, destroys the possibility of demonstrably optimal choice (as Shackle might have put it).


  8. 8 Mike Sax January 13, 2014 at 5:30 pm

    If you have any doubt who”s got ir right here see SW’s sniffy rejoinder when I offered him the opportunity to reply:

    “Well, apparently some people don’t know much economics.”


  9. 9 Tom January 14, 2014 at 2:41 am

    Thanks for the reply. You do a fine job of explaining the mechanism by which Williamson proposes that QE lowers the inflation rate. I didn’t get into that much detail. That is the means by which Williamson suggests inflation falls. It’s an elaboration of, not an alternative or opponent of his broader explanation, which is that real interest rates must rise to make currency enough more attractive to accommodate the emission.

    Here’s how he worded it on page 4 of the paper: “Inflation falls because one of the effects of QE is to increase the real stock of currency held by the private sector, and agents require an increase in currency’s rate of return (a fall in the inflation rate) to induce them to hold more currency.”
    The quote in my previous post – “To induce people to hold more currency, its return must rise, so the inflation rate must fall.” – are also his words, from page 16.

    Getting back to the issue of modeling, imagine Williamson had made a different argument: that a rise in the public deficit will increase the interest rate on sovereign bonds. Instead of the sentence above, he could have written, “To induce people to hold more sovereign bonds, the nominal return must rise.” His model could have been much simpler and based merely on liquidity premia being inverse to bond supply. He’d have a very simple but plausible model leading to a non-controversial conclusion.

    Somebody might criticize such a line of argument for incompleteness – eg what about the effects on inflation?. Somebody might point out that it could have done better and more simply with a Tobin portfolio balance model. But nobody would say he was wrong.

    Cheers and thanks for the food for thought.


  10. 10 Shahid January 17, 2014 at 2:24 am


    its always a pleasure to read your posts. Aside from your interest in monetary economics, your insights and explanation of matters concerning economic history are very educating for a person like me. This post is no exception, and thanks again for such an educating post.

    Just wanted to add my two bits’ worth. This fallacy of getting the ‘right’ prices from Walrasian equations were the basis of modern ‘Planning’. This fallacy had been soundly disproved by two great Austrian economists (Mises and Hayek) during what later became known as the ‘Socialist Calculation Debate’. And the dismemberment of the USSR, which ran its economy on long term ‘plans’ should have buried this concept for good. Yet it continues to be practiced, especially in developing nations like my country of residence (Pakistan). The question that i often get asked by my friends (who studied Econ with me in US) is that why persist with ‘Planning’, given the historically futile attempts at this particular methodology of running an economy?

    The answer, in short, is lack of economic education (and economic history in particular), and the hold of bureaucracy. The economics teaching in this part of the world is still stuck in pre 1950’s,and the best that is taught here is basic level micro and macro. As a subject, its not just attractive for universities. The only economist who’s famous here is Keynes,and others like Fischer, Friedman, Ricardo, Smith, etc, are unheard of. Quiet interestingly(and laughingly) planning and bigger governments are somehow tagged to Keynes’ thoughts. Try arguing people (especially part of bureaucracy) out of it, and they would tell you that you know nothing about economics.

    The second reason that planning persists in developing nations is that its a dumping ground for bureaucracy, one more useless institution/department where bureaucrats can find a place and dictate how an economy should be run! No wonder our economy usually finds itself in dire straits.

    This all can easily be linked to your point that its fallacious to think that education in a society is stationary or stagnant. Using the wrong information to make policies is likely to hurt more than help. And surely the policy will be a disaster if its not just based on outdated information, but ‘false information’. The level of education, institutions, expertise and techniques of economic management evolve over time. Unfortunately, the only thing resistant to this evolution seems to be individuals themselves.


  11. 11 David Glasner January 17, 2014 at 9:48 am

    Greg, Thanks, but I’m not keeping track of our exchanges, except that they seem to be mutually beneficial. Do you have a reference for where Arrow discusses Shackle?

    Mike, That’s just the way he is. What can you do?

    Tom, Thanks for your comment. I think the reason that Williamson did it the way he did is that he assumed that the preferred strategy of increasing the supply of bonds was politically impossible because of pressure to reduce the deficit.

    Shahid, Thanks. Your description of the mindset in Pakistan is pretty depressing, but it does seem that in other countries sensible ideas have made some inroads, so don’t despair.


  12. 12 greghill1000 January 17, 2014 at 10:40 am

    Here you go: Arrow, K. and Hurwicz, L. (1972), “Decision making under ignorance,” in C. F. Carter and J. L. Ford (eds.), Uncertainty and Expectations in Economics. Essays in Honour of G. L. S. Shackle. Oxford: Basil Blackwell.


  1. 1 G. L. S. Shackle and the Indeterminacy of Economics | Uneasy Money Trackback on January 22, 2014 at 6:17 pm

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About Me

David Glasner
Washington, DC

I am an economist in the Washington DC area. My research and writing has been mostly on monetary economics and policy and the history of economics. In my book Free Banking and Monetary Reform, I argued for a non-Monetarist non-Keynesian approach to monetary policy, based on a theory of a competitive supply of money. Over the years, I have become increasingly impressed by the similarities between my approach and that of R. G. Hawtrey and hope to bring Hawtrey’s unduly neglected contributions to the attention of a wider audience.

My new book Studies in the History of Monetary Theory: Controversies and Clarifications has been published by Palgrave Macmillan

Follow me on Twitter @david_glasner


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