Complex dynamics and post keynesian economics

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  1. Barkley Rosser, Jr.

Program in Economics

James Madison University

Harrisonburg, VA 22807 USA


[forthcoming in Complexity, Endogenous Money and Macroeconomics: Essays in Honour of Basil J. Moore, edited by Mark Setterfield, London: Routledge, 2005]

February, 2005

Acknowledgement: The author wishes to thank Geoff Harcourt and Mark Setterfield for useful and thoughtful remarks. The usual caveat holds.


The nature of the relationship between complex dynamics and Post Keynesian economics1 (PKE) has been a controversial matter for some time. Some argue that it is a distraction that leads innocent Post Keynesians into “classical sin.” Davidson (1994, 1996) argues that core Post Keynesian (PK) ideas such as that insufficient aggregate demand arise from fundamental uncertainty in a monetary economy do not depend on nonlinearity or complexity, that these core concepts are axiomatically and ontologically true, and that the inability of agents to forecast well in dynamically complex situations reflects mere epistemological problems of insufficient computational abilities. Thus complex dynamics is merely a classical stalking horse.

This writer (Rosser, 1990, 1998, 2001) disagrees with the argument presented above and its relatives (Mirowski, 1990; Carrier, 1993). Dynamic complexity provides a foundation for fundamental uncertainty in Keynesian and PK models, and this applies to most of the various sub-branches of PKE besides Davidson’s “fundamentalist” or “Keynes-Post Keynesian”2 approach.

The argument will be considered regarding three subdivisions of Post Keynesianism as identified by Hamouda and Harcourt (1988): the aforementioned fundamentalist Keynesianism, Sraffian (or neo-Ricardian), and Kaleckian (or Kaleckian-Robinsonian).3 Following King (2002, chap. 10), I admit to being more in sympathy with those he describes as “synthesizers” than with the more partisan sectarians of these approaches.4 I shall describe how each sub-branch has been analyzed using ideas of complex dynamics, and I suggest that this common element should be kept in mind by those who do hold to any of the more sharply held positions in this debate. I shall also discuss PK approaches that are not so easily labeled, notably the hysteresis and evolutionary approaches. I shall discuss the question of equilibrium versus disequilibrium and methodological issues relating to open versus closed systems.

Of the schools of PKE, Basil J. Moore has been identified with the fundamentalist Keynesian school, based on his role as perhaps the most influential developer and advocate of the idea of endogenous money (Moore, 1988). Along with the idea of fundamental uncertainty, the fundamentalist Keynesian school is also often viewed as stressing the role of money in the economy more than the Sraffian or Kaleckian schools. However, Moore has increasingly stressed the role of complexity in various forms as intrinsically linked with the process of endogenous money formation and the uncertainties of economic dynamics, openly disagreeing with Davidson on this issue on the PKT internet list5 and elsewhere. He argues that all this implies the need for non-equilibrium and open-system approaches in his forthcoming book, Shaking the Invisible Hand: Complexity, Endogenous Money and Exogenous Interest Rates.

Defining Complex Dynamics

Elsewhere (Rosser, 1999a) I have discussed defining complex dynamics for applications in economics. Richard Day (1994) argues that a system is dynamically complex if due to endogenous reasons it fails to converge to a point, a limit cycle,6 or a smooth explosion or implosion. Such systems can generate endogenous discontinuities in system variables. Nonlinearity7 somewhere in the system is a necessary but not sufficient condition for such endogenous dynamics in an economy, with simple exponential growth models showing how nonlinear dynamics may not be complex as defined above.

For Post Keynesians the endogenous nature of fluctuations is important, as the new classical school explains macroeconomic fluctuations as due to exogenous stochastic shocks describable by a probability function implicitly known by agents with rational expectations. Such fluctuations may be both equilibrium and Pareto optimal, thus abrogating any argument for sustained policy intervention. The reality of complex dynamics undermines this view on two grounds, first that the presence of complex endogenous dynamics means that the economy is not necessarily self-stabilizing or optimal, and second that such dynamics undermine the assumption of rational expectations. Chaotic dynamics imply sensitive dependence on initial conditions (Rosser, 1996), or “butterfly effect,” the idea that a butterfly flapping its wings in Brazil could set off hurricanes in the United States (Lorenz, 1993). Recognition of this led one prominent new classical economist to modify his views (Sargent, 1993).

While the physicist Seth Lloyd has accumulated about 45 different definitions of “complex system” from many different disciplines (Horgan, 1997, p. 303, footnote 11), most of these have not been used in economics. Some emphasize difficulty for computability or length of algorithms, used occasionally in economics (Albin, 1982; Albin with Foley, 1998; Leijonhufvud, 1993; Stodder, 1997). Another definition with some resonance with standard Sraffian models is “structural” and focuses on the “complicatedness” of patterns of intersectoral connections and institutional relations in the economy (Pryor, 1995; Stodder, 1995). Some argue that complexity implies a new philosophical perspective on how humanity relates to nature and the world, indeed on how each individual does so, replacing formal deduction with inductive or abductive methods as analysts seek to understand an ever-changing and evolving complex reality.

In Rosser (1999a) I identified the first definition above as “broad tent complexity,” seen as consisting of four sub-types, the “four C’s,” cybernetics, catastrophe theory, chaos theory, and “narrow tent complexity.” The first was developed by Norbert Wiener (1961) and has had relatively limited application in economics, with Forrester (1977) being an important example.8 Catastrophe theory was developed by René Thom (1972), with Christopher Zeeman’s (1974) model of stock market crashes and Hal Varian’s (1979) model of endogenous business cycles based on an arguably Post Keynesian model of Kaldor (1940) providing economic applications. Chaos theory had numerous developers in mathematics and physics, with Robert May 1976) first suggesting applications in economics, and David Rand (1978) the first to take him up on it.9 “Small tent complexity” emphasizes models of heterogeneous interacting agents, often using computer simulations, with Thomas Schelling’s (1971) model of urban racial segregation and Hans Föllmer’s (1974) statistical mechanics model being early examples. Horgan argues that these were all fads that have risen and deservedly fallen, but I argue that they represent a cumulative intellectual development that is now reaching fruition10 and that allows PK ideas to broadly enter mainstream economics, which is undergoing profound changes that are leading it into uncharted areas (Colander, Holt, and Rosser, 2004).

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