Thursday, January 9, 2014

The Emperor’s New Clothes: Economists’ Models and Stories


There’s been a spirited debate on the Econ Blogosphere over the merits of models and stories in understanding economic phenomena. It began with Stephen Williamson’s post, “Liquidity Premia and Monetary Policy,” in which Williamson wrote down some equations and derived a counterintuitive result.

There were several objections to the post (Nick Rowe), (Brad Delong), and (Paul Krugman), but the most interesting was the criticism that Williamson’s model lacked a narrative about the decisions “real people” would actually make and how these decisions would interact to produce the equilibrium outcome derived in the model.  In reply, Williamson offered the following defense, “Equilibrium is often a very convenient way to think through all of that, and all of us sometimes use wording about what the economy ‘needs’ or ‘requires’ [to reach equilibrium] as shorthand.”

When pressed further, 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.”

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!” 

Let’s take a closer look.  Stephen identifies “the Walrasian auctioneer” as one of the “the stories about convergence to competitive equilibrium,” but this characterization is, I think, mistaken and revealingly so.  In Walras’s version of GE, market participants submit their conditional intentions to an “auctioneer,” who searches for a set of prices that will bring everything into balance.  But the really crucial constraint with respect to the point at issue is that no trading is allowed until all of these conditional intentions to buy and sell are pre-reconciled in a mutually consistent set of plans. 

This idealized process of tâtonnement is very far removed from “the convergence to competitive equilibrium” Williamson envisions.  The difficulty, in brief, is that no one has shown how real-world decisions taken “before” all plans have been harmonized will result in a general equilibrium.  Quite the contrary, 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”?
The other “story” from “outside the models” that props up the GE premise on Stephen’s list is “learning.”  But the 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.”
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.”

10 comments:

  1. I agree with most of what you say in this post, but I still sympathize with Williamson's argument: critics of his model should put up their own, or stop pretending to solve mathematical equations to express economic relationships. I would argue the latter is the best course; Williamson would say the former. Either way, his point is valid.

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    1. Anonymous: I put up my own "mathematical" model here: http://worthwhile.typepad.com/worthwhile_canadian_initi/2013/12/nominal-interest-rates-and-inflation.html (OK, I didn't actually solve for the equilibrium, but that's only because I am bad at math; any good grad student could solve it in a couple of hours or days)

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    2. Anonymous, Thanks for taking the time to reply. There are many competing models, like Nick's, so it's not as if SW's critics haven't come forward with anything. I'm fine with mathematical models provided we all know what the symbols mean and what the, often unstated, assumptions are.

      Nick, thanks for writing. I'm a big fan of your blog. Did SW ever respond to your SOKOL post pointing out the simple mistake?

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    3. Greg: Thanks!

      I don't think SW responded, though we did argue in comments on his blog. Brad DeLong responded to my Sokol post. (Brad also did an earlier post about Franklin Fisher et al.)

      BTW, standard New Keynesian DSGE models aren't really in anything like Walrasian competitive equilibrium, ever. But NK models have their own problems about coordination. And the biggest problem is that they *just assume* that people expect an eventual convergence to the natural rate of employment, with absolutely nothing in the model that says why people will expect that. But that is less a lack of a *stability* story, than a lack of *any* sort of story whatsoever.

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    4. Hmmm. I *think* Axel is saying sort of the same thing, about NK models.

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  2. Greg, I loved this post. See my recap with one or two further observations of my own.

    http://uneasymoney.com/2014/01/09/macroeconomic-science-and-meaningful-theorems/

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    1. David, thank you very much. I look forward to reading your post! If you haven't read "Axel in Wonderland," cited in my post, I think you'd enjoy it.

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    2. Yes did enjoy it. As usual Axel nails it. Thanks for the link

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    3. The Hat of the Three-Toed Man-BabyJanuary 12, 2014 at 8:42 PM

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  3. The Hat of the Three-Toed Man-BabyJanuary 12, 2014 at 8:44 PM

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