Re: [OPE] Models and Marx

Hi Paul

> But it seems to me that the relationship between Ian's model and Marx's theory is
> somewhat different from that between Newtons theory and the mathematical models
> Laplace's celestial mechanics. In the case of Ian, the condition of that the model aims
> at is being able to reproduce what Marx says should happen. In the case of Laplace,
> the condition of validity was the ability to reproduce ex ante the positions in which the
> planets would later be observed. Also, Newtons equations, directly guided, after
> suitable elaboration and transformation, Laplace's own ones.

What you are saying is that my model cannot be directly confronted
with empirical data. I agree.

To take another example, there has been some work on confronting
Goodwin's Lokta-Volterra model with the empirical data. Desai, for
example, concludes that the original formulation of the model makes
simplifications that prevent it replicating empirical time series.

There are two things to say here. First, as you know, model
development is a work-in-progress. The route from empirical study to
theory development to empirical explanation and prediction can be a
long one. During that process science can be in a "creative modelling
phase" (to use Bhaskar's term). That phase may or may not bear
fruition in terms of finally confronting empirical data. But it's a
necessary phase that needs to be evaluated and judged by different
criteria (certainly not Popperian criteria).

Second, what's the purpose of the model? My purpose (in this paper) is
primarily a philosophical one. I develop the formal model as a tool to
help understand conceptual issues surrounding the classical *theory*
of competition. So the object of inquiry, as you say, is already at
one level of indirection from reality.

However, I also believe that the model is simultaneously a stepping
stone to the development of a more complete model that can be
confronted with empirical data, although this is not my focus in the
paper. For example, although the model makes many counterfactual
assumptions it is arguably much richer and enjoys greater realism
compared to standard neoclassical economic models (particularly
because there is an attempt to focus on out-of-equilibrium dynamics).
But to really hit the data would, I think, require a complete
recasting in terms of random, rather than deterministic, variables.

As it happens, it's quite difficult to develop stochastic differential
equation models.

> In he had to invent
> equations that would reproduce Marx's final result -- much more had to be filled
> in as Marx did not provide precisely formulated 'laws to which Ian's micro dynamic
> equations had to be subject. Beyond that, it can not count as a model of the capitalist
> economy as it generates counter factual conclusions. It is a model for Marx's theory,
> not a model for a capitalist economy. Its function is to reproduce in numerical terms
> what Marx's theory describes in general qualitative terms.

Yes ... But if one's aim were to model a capitalist economy, and given
that an economy is a complex adaptive system, which is multiply
determined by many different kinds of causal mechanisms operating at
different time-scales (i.e., it's complicated!), then the kind of
counterfactual assumptions that Marx makes are necessary.

> If I understand it correctly, its utility lies in showing that given certain simplifying
> assumptions and given certain mathematical form for various dynamical processes,
> then the general result described by Marx's theory in vol 3 of capital can be
> reproduced.

Yes. The specific mathematical forms for out-of-equilibrium adjustment
aren't sufficiently general (yet) to make definitive claims about the
homeostatic properties of classical competition (i.e., supply/demand
dynamics, and allocation of resources driven by profit-seeking
behavior). But they are very suggestive. I feel that it may be
possible to develop some very general stability proof of cross-dual
dynamics that make very few assumptions about the precise functional
forms.

But -- again -- this would not directly imply that "capitalism is
stable". Since a lot more happens in reality than cross-dual dynamics.

> The counter factual nature of the predictions though, shows that the model is not yet
> a good description of real capitalist economies.

Agreed.

> But this shortfall is not something that is limited to Ian's model, it is a shortfall of the
> less formal account given by Marx as well.

Yes. Although "shortfall" isn't quite the right term, in my view,
given that counterfactual abstractions are necessary moments toward
the development of comprehensive theory.

-Ian.
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Received on Mon Feb 14 14:48:21 2011