[OPE-L:5134] RE: Re: comparative statics

From: Mongiovi Gary (mongiovg@stjohns.edu)
Date: Fri Mar 09 2001 - 10:23:17 EST

This is an interesting line of discussion because it brings very close to 
the surface so many of the issues that separate heterodox economics from 
mainstream theory, and that cause divisiveness across heterodox traditions. 

We might begin with a point that I think every competent economist -- 
orthodox, marxian (all variants), sraffian, post keynesian, Austrian, 
whatever -- would accept: that a useful explanation of how a market economy 
functions must eventually deal with issues that fall under the heading of 
dynamics.  Acknowledging that these issues are important doesn't preclude 
the view that OTHER issues, the kind that are sorted out within a 
comparative static framework, are also important and deserving of 
attention. Rakesh argues that:

"comparative statics suffers from at least the following well known 

1. it exogenizes technology and other sources of change.
2. it neglects transitional processes.
3. it eshews a real causal theory of the developmental consequences of 
capital accumulation; in short it seems ill suited as a method to lay bare 
the laws of motion."

Well, to the extent that he's saying that there are certain kinds of 
questions -- extremely important ones, I contend -- that aren't susceptible 
of analysis within the traditional long-period comparative static 
framework, he's not saying anything that Smith, Ricardo, Sraffa, or 
Marshall and Pareto, for that matter, would deny. I've never understood the 
position that one must take an either/or stance: comparative statics on one 
side versus some version of dynamic analysis on the other.

"Horses for courses", as they say. There are different types of questions 
in economics, and they frequently call for different methodologies. 
Questions relating to the fundamental mechanisms that operate on prices and 
distribution, it seems to me, ought to be sorted out, in the first 
instance, via the traditional method.

Questions relating to dynamics are a lot more complicated, and I'm not sure 
non-linear dynamics and intertemporal models are always the best way to go. 
 I don't know enough about them to feel I can reject them out of hand.  I 
imagine that such models can shed some light on particular aspects of what 
goes on in market economies.  (I've always thought there was something 
potentially useful in traverse analysis -- Hicks and Lowe). Such models can 
of course endogenize technical change and can pay attention to transitional 
processes; and can elucidate some aspects of the accumulation process.  But 
they have their limitations too.

For a start, I don't see how technical change and transitional processes 
can be modeled without relying on suppositions that are much more ad hoc 
than what one finds in, say, Sraffa-type long-period models.  The existing 
technical conditions of production are more or less objective facts, as are 
the living standards of workers, and while they do change, they tend to 
change rather slowly over time, so that not much violence is done to 
reality by taking them as given when explaining the profit rate and 
relative prices.  I'm not so sure we can say the same thing about the 
mechanisms that drive technical change: these are much more slippery 
concepts even than the "real wage".  So dynamic models that impose some 
rather rigid assumption about how the technical conditions evolve over time 
gives results that are much more tentative than the insights derived from a 
long-period equilibrium theory of value and distriubtion.  I'm not saying 
that these dynamic models are not useful at all, but only that their 
applicability is NO LESS LIMITED, and is perhaps even MORE LIMITED, than 
the applicability of comparative static models.

The upshot is that for the anlysis of dynamic questions it might be more 
appropriate to adopt the approach of Adam Smith and Marx: look at history 
and institutions.  By all means, supplement the history and institutional 
analyisis with formal dynamic models when the latter can shed light on 
complex processes that have a systematic dimension.  But in the end, I 
think that formal modeling is less helpful to the analysis of capitalism's 
temporal trajectory than good old-fashioned in-the-trenches historical and 
institutional work.  Isn't this what Marx was doing throughout most of 
Capital, and Smith was doing throughout most of the Wealth of Nations? I 
don't think the basic approach is outmoded.


Gary Mongiovi

-----Original Message-----
From:	Steve Keen [SMTP:s.keen@uws.edu.au]
Sent:	Friday, March 09, 2001 12:49 AM
To:	ope-l@galaxy.csuchico.edu
Subject:	[OPE-L:5132] Re: Re: Re: comparative statics

I promised to answer Jerry's question some time ago, and then got caught
up. So I'll try a fast answer now.

Dynamic systems are ones in which the model is specified in terms of rates
of change, rather than as a set of simultaneous equations. These rates of
change can be either in continuous (differential) or discrete (difference)
form (mixed difference/differential versions are also feasible, but that's
real rocket science stuff). The general form is thus


where X signifies a vector of variables, and F a vector of functions. The
latter can be linear, but the really interesting stuff is where those
functions are nonlinear.

Boring dynamic models have a dependence of the form


ie, the dependence is of one variable on the values of another; interesting 
ones have the form


where the rate of change of variable x depends on itself and on other

Solutions to these models can be closed form for low dimensional models,
but the norm is for high ( >2 ) dimensions, in which case for nonlinear
models, closed form solutions do not exist. Instead, the time paths of the
models can only be found by simulation and exploration of what's known as
the phase space.

There is no presumption that dynamic models will converge to an equilibrium 
solution. In this case, comparative static models can be seen as a subset
of dynamic models in which convergence to equilibrium is assumed.

Chaotic models occur in continuous time models of dimension 3 or above;
they cannot occur for lower dimensional models. The essential feature which 
allows you to add the moniker 'chaotic' is that the overall dynamics of the 
system are such that points which are very close together initially lead to 
highly divergent time paths. A > 2 dimensional model can have this
characteristic, but it needn't necessarily.

 From what I have seen of TSS, the models there are not fully specified
dynamic models: they are rather numeric examples of what could be the
outcome of dynamic models. Dynamic modelling is much more difficult than
comparative statics, precisely because the techniques of linear algebra
can't be used to derive closed form solutions--and because continuous time
problems of dimension >2 don't have solutions.

Some rules of consistency from comparative statics carry over to dynamics.
While it is possible to generate dynamic models which have no equilibrium
for some parameter values (see my paper in "Commerce, complexity and
evolution", CUP 2000), normally dynamic models will have equilibria. It is
possible that a poorly specified model will have no equilibria, not because 
one does not exist, but because the model is either over or
underdetermined. This is my expectation of TSS, though it would take some
serious work to put the argument in a form where that expectation could be

That's a very quick and dirty pastiche. I'll try to provide something more
detailed when I have time.

At 12:17 AM 3/9/01 -0500, you wrote:
>Re [5128] and [5130]:
>Comparative statics or what?  It seems to me that
>there is a lot more talk about dynamic (and chaotic)
>theories and models than actual dynamic (and
>chaotic) models: it is easy to say that one needs
>dynamic analysis, it is harder to do it.
>I asked a related question in [OPE-L:4960]
>on "dynamic and chaotic systems": namely, I asked
>anyone to specify the *formal characteristics* of
>dynamic systems and chaotic systems.  Since
>nobody answered that question it was hard to move
>on to what would have been my next question:
>which (if any) Marxist theories and models could be
>said to be truly dynamic models and which could
>be said to be chaotic models?
>Let me be clear here. I am not asking whether a
>theory is consistent with the *possibility* of dynamic
>and chaotic modeling. I think that begs the question.
>I am asking whether a theory is actually *in a formal sense*  dynamic, 
>Until one can answer that, then
>all the talk against comparative statics is just talk, imo.
>In solidarity, Jerry

Dr. Steve Keen
Senior Lecturer
Economics & Finance
Campbelltown, Building 11 Room 30,
School of Economics and Finance
s.keen@uws.edu.au 61 2 4620-3016 Fax 61 2 4626-6683
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