**Next message:**Gerald_A_Levy: "[OPE-L:5133] the capital-form and the state"**Previous message:**Gerald_A_Levy: "[OPE-L:5131] Re: Re: comparative statics"**In reply to:**Gerald_A_Levy: "[OPE-L:5131] Re: Re: comparative statics"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

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 dX/dt=F(X) X[t+1]=F(X[t],[X[t-1],...) 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 dx/dt=f(y) ie, the dependence is of one variable on the values of another; interesting ones have the form dx/dt=f(x,[X]), where the rate of change of variable x depends on itself and on other variables. 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 tested. That's a very quick and dirty pastiche. I'll try to provide something more detailed when I have time. Steve 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, etc. >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 UNIVERSITY WESTERN SYDNEY LOCKED BAG 1797 PENRITH SOUTH DC NSW 1797 Australia s.keen@uws.edu.au 61 2 4620-3016 Fax 61 2 4626-6683 Home 02 9558-8018 Mobile 0409 716 088 Home Page: http://bus.macarthur.uws.edu.au/steve-keen/

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