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.

(Sourced from Uneasy Money)

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