Response to Gonzalo

[pdavidso@xxxxxxxxxxxxxxxxxx]

Dear Gonzalo: To respond to your criticisms is frustrating because you
are a moving target always changing your packaging but never your message.
Whatever Chu said or did not say -- does not make it so about lampposts or
otherwise.
you hit bingo! by (deliberately?) misinterpreting what I say. I indicated
that ALL stochastic models, i.e., with stochastic terms (in responding to
Basil) had nothing to do with uncertainty but only probabilistic risk. My
comment was for linear as well as nonlinear models that include
stochastic terms. That does NOT imply that non linear methods are
better merely because I  suggested that linear
stochastic models are (in my view) not an approximation to reality.

You make a fetish over precision -- and being able by complex nonlinear
models be able to pinpoint where you went wrong. You could also pinpoint
where you went wrong with [precise linear models. The trouble with
non-linear models is, as I have said several times but you simply ignore,
is that in any time series of points of observations, a nonlinear line
can always be found that will "fit" the observations better than a linear
line.  In other words if I have a scatter diagram, of ten points which,
for the sake of discussion, are randomly distributed around a straight
line, I can always find some line with nine turning points that will
"fit" the data better than the straight line. That nonlinear nine-turning
point curve is more precise in describing the position of the
observations -- So what?

Finally, after tossing much semantic dust in the readers' eyes you come
down to the nub of the question when you write:
"The question bears down on the axiomatic structure of each."
My god, Gonzalo, what have I been saying for 1-1/2 years on the net now.
A general theory involves less axioms to explain more. The more specific
cases requires more axioms -- including in your case that unemployment is
"explainable" only if the equational structure includes some (all?)
nonlinear relationships.
On the other hand, I have continually stated that Keynes's GENERAL theory of
employment, money and interest did not require an axiom specifying any
degree of competition, or any specific form of logical relationships,
i.e., the x = f(y) general relationship could stand for any linear or
nonlinear structure.

Hence, if nothing else, even if you agree with me (as you sometimes claim
you do -- but your attempt to change the definition of uncertainty
suggest otherwise)and accept all the fundamental axioms of Keynes and
reject the neoclassical axioms of gross substitution, neutral money, and
ergodicity, the Keynes-Davidson general theory of why there can exist
unemployment equilibrium requires one less assumption (i.e., Keynes and
Davidson do not require the logical relationships to be either entirely
linear or to encompass one or more nonlinear equational relationships to
provide a general theory of employment. If you really believe that "the
question bears down" fundamentally to the axiomatic structure (solely?),
then please explain:
 1. 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?

2. If you disagree on 1, which of these classical axioms do you
incorporate into your mathematical model? If you agree with 1, is the
only other axiom that you require that is absent from Keynes's GT and my
writing is that ONE OR MORE of the logical relationships in your
equational system MUST be nonlinear?


3 If you disagreed on 1, then your model must be closer to a special case
classical model then Keynes's GT. If you require ONE OR MORE nonlinear
equations (as an axiomatic foundation) for your vision of "scientific"
basis (which you clearly indicate is different than Keynes's vision
of "scientific" basis, then Keynes- and I have the GENERAL theory and
your requirement of a nonlinear axiom makes yours A SPECIAL CASE
THEORY.

Finally, you apparently identify nonlinear models as providing a "logical
precision" that neither linear models or general form models do.   But
logical precision merely means that you have not made any mistakes in
your syllogisms, etc. Can you explain why one loses "logical precision"
if one uses  a general form of the equations
model, if the latter is based on the same axiomatic foundation (except for
the "Chu" axiom that ALL measured things must be nonlinear)?

Finally, you implicitly accept the Austrian view of uncertainty, namely
that the future is deterministic but so complex that human computing
power (the agent's estimate) is so limited, that the number of Christians
in Damascus in 2400 AD is "unknown" except to God! (and to a Turing
machine that the Austrians call the market!) If you truly believe this,
then the system is ergodic (if not in the levels,i.e., with given
parameters) but in the rates (or ways) that the parameters are "destined"
to change according to God's grand ergodic (deterministic) scheme of things.
And when you question why I insist on an ontological transmutable (by
human action) reality as compared to your preprogrammed God-given
parameters or rate of change in parameters, you have crossed the Rubicon.
In your God-given preprogrammed complex reality, there is always a
possible deus ex machina ("the market") that can transcend the
individual's (or bureaucrat's) lack of computing power and display for
the chosen people the God's software preprogrammed package for the future
economy.

At this point we are separated by a different view of what are the
essential axiomatic of the system dear Gonzalo. And since an axiom is a
universal truth that need not be explained, no amount of further
discourse between us will provide any meeting of the minds.

I prefer a general theory which permits an explanation that there is no
endogenous logical forces (no matter whether associated with linear or
nonlinear relationships) that will return a money-using system
automatically to full employment if the system departs from full
employment. You apparently prefer the additional assumption that only in
nonlinear systems will such endogenous forces be missing, while classical
economists prefer a different special case that says as long as prices are
less than perfectly flexible, there will be no endogenous forces that
will restore full employment. Your claim to superiority over the
classical system is that reality is nonlinear. Their claim (at least as
the short-run New Keynesians are concerned) is that reality is not
perfectly competitive.  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.

Paul D.