[OPE-L:967] Message from Steve Keen re Lucas & rational expectations

glevy@acnet.pratt.edu (glevy@acnet.pratt.edu)
Tue, 6 Feb 1996 12:46:16 -0800

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---------- Forwarded message ----------
Date: Wed, 07 Feb 1996 06:23:17 +1000
From: Steve.Keen@unsw.EDU.AU
To: glevy@acnet.pratt.edu
Subject: Re: PKT references?

Thanks Jerry,
I saw the message yesterday but let it pass because (a) it called for
marxist refs, and (b) I'm flat chat getting the papers ready for my
conference next week. But I should have said something.

Off the top of my head, the best references on this point are ones that
deal with chaos. The simple reason is that Lucas' "rational expectations"
alleges that, being rational beings, we all walk around with a model of
an Arrow-Debreu economy in our heads, and use that to analyse the potential
impact of any policy shift by the government. Since, according to A-D, the
best policy is no policy, we react to a policy such as an increase in
the money supply by immediately adjusting our expected prices--thus
immediately converting the government policy, which was intended perhaps
to boost output, into inflation, with no change in output.

However, this implies that knowing the function which is generating some
data lets us extrapolate that data into the indefinite future. Chaos
theory, in contrast, has established that (if the function is nonlinear)
even the smallest error in our exact knowledge of the data at time t
means that at some time t+x (where x is fairly small, say 10 quarters in
economics, or less), we will be completely wrong in our estimates of
where the economy will be.

I've used this idea in the introductory talk I'm giving at the conference.
The example I've used is "the market for lemmings". Say you are a lemming
farmer. You know exactly how large your farm is, and thus the amount of
"population pressure" exerted per lemming; you know the population rate
of reproduction in ideal circumstances; you therefore know the population
generating function, which is:

x(t) = a*x(t-1) -b*x(t-1)^2

Let's say you know the number of lemmings in your field to an accuracy of
1%: you htink you've got 100 lemmings to start with, whereas you've
actually got 101.

Then you try to estimate the equilibrium population (and hence the yield
you can expect). Easy, it's a/b.

The problem is, whether the equilibrium is stable depends on the value of
a. For a<2, it's stable, for a < 2.7 (roughly) you get cycles -- 2 cycles
(where 2 numbers repeat indefinitely), 4-cycles, all the way up to
infinity cycles -- and for a > 2.7, you get aperiodic cycles -- chaos.

With a=2.9, for example, the percentage error of your estimate in this
example is, starting at 10 breeding cycles into the future:
while by 61 cycles, for example, you're 499% wrong (and then -20 0n the next

Thus, even assuming Lucas' idea of rationality, and the ability of people to
(a) carry such a model in their heads) and (b) do the computations necessary
to solve it, if the economic system itself is sufficiently nonlinear (or of
high enough dimensionality with minor nonlinearities), there is a "wall of
uncertainty" which means that prediction, and hence rational expectations,
is impossible beyond a certain (fairly nearby) point.

Reason for writing this is that I haven't got time to check on actual
refs; but I would recommend HW Lorenz's _Nonlinear dynamical economics and
chaotic motion_, Springer Verlag 1993; Barkley Rosser's _From catastrophe
to chaos: a general theory of economic discontinuities_. Paul Davidson
also has a go at Lucas in his _Post Keynesian Macroeconomic Thought_, but
I wouldn't recommend it (he attacks it from his own perspective on Keynes
and ontological uncertainty) as representative of PK methodology in
general, despite its title.

I'll check up refs later (after next week); hope you can forward this
along in the meantime.