Re: Response to Gonzalo

[GONZALO FONSECA <FONSECA@xxxxxxxxxxxxx>]

	Paul Davidson correctly defines an axiom as "a universal truth
that need not be explained" implying then, if we cannot agree upon
"believing" it, then there is no point in continuing a discussion based upon
it. (Finally, here is one definition we can agree upon!)  Then he goes on
to ask:

	"Do you agree that your axiomatic structure does not require
	the classical axioms of (a) gross substitution, (b) long-run
	(and/or short-run) neutral money, and (c) a nonergodic system,
	i.e. a system where the future reality is ontologically
	uncertain?"

I am going to lay off (3) for the moment for, again, we are in a semantic
whirlwind.  But on (1) and (2), I need to ask: how on earth can one
consider these axioms?
	Now, Paul D, as I understand, dismisses all three classical
"axioms".  I too consider them absolutely erroneous (at least (1) and (2)).
 But my dismissal is not based on a BELIEF of whether these so-called
"axioms" are fulfilled or not in "reality" but rather on the knowledge that
(i) they are not axioms; (ii) they cannot be derived from axioms.  Thus I
conclude they are unjustified assumptions.
	This is not to say, a priori, that (1) and (2) cannot be true in the
sense of being met in reality - they may very well be - but they are not
axioms in any proper sense of the term.  However, I must note Paul D's
rather clever use of the word "classical" rather than "Neoclassical" or,
what is truly more appropriate, "Neo-Walrasian".  Neo-Walrasians start
from a set of well-known "axioms" on individual behavior which, as
Debreu-Sonnenschein-Mantel has shown, do NOT yield (1).  Similarly,
there is no Neo-Walrasian theory of money, therefore (2) cannot really
be a result either.
	I presume Paul D uses the word "classical" to refer to the
Pigou-Cassel type of "intuitive" (not rigorous) macroeconomics
reincarnated today in the form of RA or OLG models  (also, in my
judgement, intuitive and not rigorous - despite all appearances to the
contrary).  Thus, the "classical axioms" are only "axioms" in the sense
that they are BELIEVED to be undeniably true by some Neoclassical
theorists - although we know that there is absolutely no foundation for
them in Neo-Walrasian theory.

	So let me restate my answer to Paul's question: my axiomatic
structure does NOT require the classical "axioms" (1) and (2).  I believe
my reason for this is the same as Paul's: they are not axioms.  But my
disbelief does not lie in the fact that they are simply not true - which,
loosely interpreting, is Paul's objection to them (and, I would not dispute
that).  The source of my disbelief lies in their NOT being "fundamental"
enough and NOT deducible from more fundamental axioms.
	This returns me then to the issue of complexity and precision.
Paul claims I "make a fetish over precision - and being
 able by complex
nonlinear models to be able to pinpoint where you went wrong".  Exactly.
Precision in a complex environment enables you to show that the
so-called classical "axioms" are not plausible.
	But I do not stop simply at the Pigou-Cassel macroeconomic
"axioms".  I am also willing to take on the "fundamental" Neo-Walrasian
axioms as not being precise enough.  For instance:

Axiom (A) "There are n commodities/markets..." - a typical assumption
with no explanation.  Commodities are defined a la Debreu (i.e. located in
quality/space/time/state).  We know, therefore, that there are implicitly an
infinity of commodities (and an infinity of markets) and we can proceed
via some Bewley-type method to define equilibrium here.  My dispute:
markets are not defined separately from each other solely via these
Debreuvian criteria.  Commodities are not defined independently of the
observer (cf. composite commodity principle).  The set of commodities
and markets which is relevant is an OUTCOME and not the DATA into the
economic process.

Axiom (B) "Agents maximize utility subject to a budget constraint (defined
by given endowments and prices)."  My dispute: price-taking behavior is
not explained.  Following the Paretian argument, this can be the result
only if our economy is complex enough (a lot more edible than magical
continuum stories).  Again, it should be a RESULT to be proved and not
an assumption.

Axiom (C) "Price movements follow from market excess demands".
Implies the existence of a "warehouse" where all individual excess
demands are added up by an auctioneer and all exchanges
reapportioned from them.  Exchange is bilateral not multilateral.  If
multilateralism is a result, it must be proved.

We could go on.  But the point I am trying to get across is that much of
what we assume are "axioms" are really assumptions.   These
assumptions are "axioms" only in that we are willing to organize our
discussion around them - which, of course, should be different for
different schools.  For a Classical/Sraffian economist, a uniform rate of
profit (price-cost equality) is virtually axiomatic.  For a Neo-Walrasian this
is simply not acceptable.
	Once again, all our assumptions can only be considered "axioms"
IF they can be proved to arise from a model which is sufficiently realistic
in its foundations (i.e. sufficiently COMPLEX).  If we can prove that
exchange and production, as it actually happens with all its complex
paraphenelia, can (and does) give rise to specific sets of markets,
price-taking behavior, uniform rates of profit, etc. (you fill the rest here),
THEN we can proceed to consider these assumptions as "true" and
hence treat them "axiomatically".   To take Hicks's analogy,  the issue
comes down to discovering how the rabbits got into the hat.  This is a
fundamental part of my argument for the relevance of Santa Fe.

Paul Davidson then writes: "My claim is that it doesn't matter whether
relations are linear or nonlinear, monopolistic or perfectly competitive, the
existence of liquidity in a money-using
 contractual society can explain
the absence of endogenous forces that automatically restore
full-employment."

The implication, if I interpret this correctly, is that Paul Davidson's theory
requires less restrictions (i.e. less axioms) than approaches which
depend on non-linearities or monopolistic competition.
	I appreciate your point, but I would be careful.  Firstly, you have
"assumptions" underlying your theory which are not "axioms" and hence
may be disputed: e.g. the existence of "uncertainty", the existence of
"money", the existence of "exchange contracts" and thus existence of
some form of "property" system and so on (to say nothing, of course, of
greater disputables such as stability and substitution which many Post
Keynesian models still rely on).  Are these LESS than what a complex
theory could have?   Suppose I could "explain" uncertainty, money,
exchange contracts, a property rights system, etc. on the basis of more
indisputable axioms?  Would my theory then be more general than yours?
	You may say a complex system requires a lot more axioms than a
system such as yours.  But counting axioms does not make a system by
itself more GENERAL than another if the "axioms" are really not "axioms"
but assumptions which hide a lot more axioms.  You claim axioms are not
disputable - but the ones you employ ARE even by people (like me) who
agree with the gist of your theory.  Why?  Because I do not consider
them "fundamental" enough.  I require (and here comes the precision
fetish again) that you PROVE that uncertainty, money, etc. DOES arise.  I
believe that the world IS full of non-linear complexities and, modelling it
with an eye to capturing as much of that complexity as we can, we can
come to prove, as neatly and precisely as possibly, that the assumptions
you make are ENTIRELY valid and thus the conclusions you derive are
ENTIRELY justified.
	Your claim that "it doesn't matter" is reminiscent of Cassel's
argument that deriving downward-sloping market demand curves from
individual choice theory also "doesn't matter":

	"This purely formal theory [utility theory], which in no way
	extends our knowledge of actual processes, is in any case
	superfluous for the theory of prices.
		It should be further noted that this deduction of
	the nature of demand from a single principle, in which so much
	childish pleasure has been taken, was only made possible by
	artificial constructions and a considerable distortion of reality."

	(G. Cassel, "Theory of Social Economy", 1918, p.81)

(Menger must have being going nuts at this point!)  We know what
modern Neo-Walrasians did about all this.  Precision ain't everything, but I
think the conclusion has been sobering.

	Finally, I will try to respond to your question on the "non-linear
nine-turning point curve".  From the outset, I could give you an answer I
believe Herb Gintis gave a while ago in a slightly different context:
decimal points of accuracy make your theory closer to the "Truth".
However, I don't believe that, so I will not claim it.  Instead, I will try to
defend it as follows:  namely, if a non-linear function arises from a
complex model which is sufficiently axiomatic (i.e. sufficiently
fundamental) - which, of course, it should - then it is, a priori, better than
a linear model EVEN if our non-linear function is poorer than a linear
function in terms of standard statistical criteria (as Bill Mitchell claims it
probably will be given the loss of dfs).   The jury is still out on this last
one.  Of course, all this returns us to the deductive/inductive debate we
had a while ago, so I shall keep the peace and say no more.


Gonzalo Fonseca
New School for Social Research