**Next message:**Rakesh Narpat Bhandari: "[OPE-L:5135] Re: the capital-form and the state"**Previous message:**Gerald_A_Levy: "[OPE-L:5133] the capital-form and the state"**Next in thread:**Rakesh Narpat Bhandari: "[OPE-L:5141] Re: RE: Re: comparative statics"**Reply:**Rakesh Narpat Bhandari: "[OPE-L:5141] Re: RE: Re: comparative statics"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

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 defects: 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. Regards, 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 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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