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.”
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.
ReplyDeleteAnonymous: 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)
DeleteAnonymous, 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.
DeleteNick, thanks for writing. I'm a big fan of your blog. Did SW ever respond to your SOKOL post pointing out the simple mistake?
Greg: Thanks!
DeleteI 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.
Hmmm. I *think* Axel is saying sort of the same thing, about NK models.
DeleteGreg, I loved this post. See my recap with one or two further observations of my own.
ReplyDeletehttp://uneasymoney.com/2014/01/09/macroeconomic-science-and-meaningful-theorems/
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.
DeleteYes did enjoy it. As usual Axel nails it. Thanks for the link
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ReplyDeleteWhat happened to the Malaysian Malay women and their fashion trends today? Have they all forgotten about what is required in Islam? nsf online
ReplyDelete