[OPE-L:2916] Okishio and the poverty of mathematical economics

Gerald Lev (glevy@pratt.edu)
Wed, 28 Aug 1996 17:11:39 -0700 (PDT)

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Duncan writes in #2915

> From my experience in
> having conversations with economists of various ideological persuasions, I
> would expect that they would also say something like: "Of course a fully
> dynamic theory would be better, and as soon as somebody produces one that
> has reasonable generality and produces definite results, I'll switch over
> to it as a mode of reasoning. But I don't see such a theory at present,
> and so in the interests of arriving at some kind of positive results, I'll
> work with the stationarity assumption, where at least I know where I stand
> and I can reach mathematically clear conclusions."

I think that Duncan precisely captures the "logic" of many economists. In
the reasoning above, the desire for "mathematically clear results" is
allowed to take precedence over an effort to explain social reality. What
is most dramatic in the above, in other words, is the positivist bias
towards developing "definite results" -- no matter whether those results
conform to any reasonable understanding of the social world.

> Much could be said
> against this position, but positive results in simple models tend to hold
> the field against general negative criticism in the history of thought.

This is a result of the methodologies that most economists use when
developing their "simple models", which frequently do violence towards
understanding the complexity of the real world.

> The quote Alan produces from Marx (CIII p 173) in part 3 of his notes
> shows, as do many other passages (such as the theory of simple and
> expanded reproduction), that Marx himself was acutely aware of the
> analytical advantage of equilibrium reasoning in certain circumstances and
> correctly employed.

Marx, though, was much clearer in his use of a concept of equilibrium. For
instance, in the reproduction schemes, Marx showed the "formal and
abstract" _possibility_ of crisis. Equilibrium, then, was simply a step in
a process of explaining the process of disequilibrium. Marx never claimed
(far from it!) that the capitalist economy was ever (except perhaps during
a fleeting moment en route to disequilibrium) in equilibrium.

> In fact, if there is a very different conclusion about the falling rate of
> profit to be reached from Okishio's in the context of continuous technical
> change, it will probably become influential by being put forward as a
> particular carefully specified example with as much equilibrium and
> stationarity assumed as possible (for example in a model with technical
> change continuing at a constant rate), rather than as a very general claim
> in a very general dynamic model.

"it will probably become influential" is: a) speculative, and; b) takes as
given a bias on the part of most economists against a "very general
dynamic model." In any event, the let's put the desire to arrive at a
_meaningful_ analysis before our concern about whether most economists
will accept our results.

> But this is not the usual usage of the
> word "refutation" in mathematics, at least: if a hypothesis of a theorem
> does not correspond to reality, it doesn't make the theorem wrong as a
> logical construction, it makes the theorem irrelevant to explaining the
> phenomenon at hand.

If a hypothesis that purports to explain reality is incapable of
explaining reality, then what use is it? Using the above test, I could
develop a mathematical theorem that would have no relevance for life in
this or any other potential galaxy, yet could still not be refuted (even
though it was developed as a theorem to explain life in *this* galaxy)!

In OPE-L Solidarity,