PD and the JPKE

[bjm@xxxxxxxxxxxxxxxx]

Paul
We cannot make a nonergodic model of the real (nonergodic) world. The world
is much too complex. We can only formally develop models that are comprised
of either linear or nonlinear equations. (This is intended as
exclusive. There are no other kinds of models.)***(Correct me here if I am
wrong, since this is my key point.)***

If the nonlinear equations do not yield closed-form solutions, we can only
 simulate their behavior. This gets us into computer simulations a la Brian
Arthur and the Santa Fe Institute, which may eventually be the only way to go
 forward, but on which many of us remain unconvinced.

 We can of course add stochastic terms to our linear equations. But these
terms are simply a very crude way to represent randomness, and unfortunately
do not add anything fundamental about the structure of what we are modelling.
(They are like saying that we should use bands rather than lines in
 our  models.) This merely ensures that we cannot get deterministic outcomes,
 but does not help our understanding of what we are attempting to model.

    If these equations systems do have a unique solution, they are by
definition "deterministic".  Even quite simple nonlinear equations do not in
general have unique solutions.  In that way they are more like our real
 (nonergodic) world. They enable us to explain uncertainty without simply
putting in exogenously a stochastic term, and getting a stochastic result.

 Do you really wish to argue that one cannot use nonlinear equations to
 model reality, because the real world is nonergodic and not deterministic?
You surely cannot wish to argue that one can only use linear models,
on the grounds that nonlinear  models are deterministic???  Surely linear
models are even more deterministic?

Finally if  you are arguing against both linear and nonlinear models, isn't
this an argument against any sort of formal theorizing whatsoever? Surely
everything you say against nonlinear modelling is applicable in spades
against linear modelling?

        And isn't this exactly what many mainstream economists
object to about Post Keynesian economics (ie. its nihilism)?  Do you really
wish to argue against any sort of formal modelling? That is even more extreme
 than my argument against using general equilibrium, and I am having a very
 tough time trying to get that past even most Post Keynesians.

Our challenge is to devise models to capture aspects of the nonergodic world
 we observe. I think nonlinear models do just that. And I think we can use
 nonlinear models without having to believe that the world is deterministic.
Aren't all formal models with equilibrium solutions deterministic? Basil