Abstract
Chaos and complexity theory have entered the old debate between Classicals and Keynesians regarding the nature of macroeconomic fluctuations and the ability and desirability of government efforts to stabilize them. In its recent incarnation between New Classicals and New Keynesian both sides have used the assumption of rational expectations to varying degrees. For the New Classicals (Lucas, 1972, 1975; Barro, 1974; Kydland and Prescott, 1982; and Long and Plosser, 1983) real business cycles arise from exogenous supply-side shocks to a basically stable economy which lead to fluctuations due to sectoral or labor market misperceptions or “time-tobuild” lags in capital investment. Government stabilization policies will be ineffective if systematic and non-optimal if effective. This view of the economy as a basically stable (and linear) system whose fluctuations derive from random exogenous shocks is due to Frisch (1933) and Slutzky (1937).
“A. A violent order is disorder; and B. A great disorder is an order. These Two things are one. (Pages of illustrations.) The pensive man…. He sees that eagle float For which the intricate Alps are a single nest.”
Wallace Stevens, 1947
“Connoisseur of Chaos”
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Notes
Strong” New Keynesians fully adopt rational expectations assumptions whereas “weak” New Keynesians emphasize asymmetric information and adopt “near rationality” (Akerlof and Yellen, 1985a,b) to show fixity of nominal wages due to menu cost arguments or other fixities or market “imperfections” and hence downward-sloping short-run Phillips Curves. See Rosser (1990, 1998a) for a more detailed discussion of the implications of chaos theory for the varieties of Keynesianism.
Good reviews of such endogenous chaotic macroeconomic models can be found in Grandmont (1988), Baumol and Benhabib (1989), Brock and Malliaris (1989), Boldrin and Woodford (1990), Rosser (1990, 1996b), Scheinkman (1990), Benhabib (1992), Guesnerie and Woodford (1992), Bullard and Butler (1993), Day and Chen (1993), Lorenz (1993a), Medio with Gallo (1993), Semmler (1994), Dechert (1996), and Puu (1997).
Major early efforts along these lines include Kalecki (1935, 1937, 1939), Harrod (1936), Samuelson (1939a), Kaldor (1940), Metzler (1941), Hicks (1950), and Goodwin (1951). Sawyer (1996) provides a good discussion of the evolution of Kalecki’s seminal approach.
The use of the term “sunspots” here obviously refers to Jevons’ (1884, Chap. 7) sunspot theory of business cycles. But his is more a real business cycle theory with sunspots directly influencing agricultural production through climate, including an impact on nineteenth century British industrial activity because of the impact of the Indian monsoon on cotton production. Alternatively it has been hypothesized that sunspots can directly influence people’s moods, their “animal spirits.” However the real spirit of Shell’s view is that people believe that sunspots affect other people’s beliefs and actions. Thus a mutually self-fulfilling prophecy occurs and equilibrium results.
Clearly the term “extrinsic uncertainty” suggests the possibility that these are also “exogenous shock” cycles. The distinction may be that it is endowments or technology that are shocked in real business cycles, but that it is expectations that are shocked in sunspot equilibria cycles.
Farmer (1986) and Reichlin (1986) both present OLG models with production and capital as well as labor that generate endogenous cycles. In contrast with the Grandmont model these assume a positive relationship between the rate of interest and the level of savings. Farmer assumes an inelastic labor supply with a neoclassical production function. Cycles arise when the government fixes the value of the deficit rather that of the debt. Reichlin assumes an elastic labor supply. If the elasticity of substitution between capital and labor is sufficiently low then cycles can arise due to the opposing effects on savings of wage income and intertemporal substitution as factor prices change, although neither of these models generates chaotic fluctuations.
The Grandmont model has been criticized because of the intergenerational length of the resulting cycles. Woodford (1986a) has shown that quite short cycles can arise in a model with infinitely lived agents if there are constraints on borrowing for reasonable model parameter values. Government can stabilize the economy through stabilizing aggregate money expenditure, an optimistically New Keynesian outcome, although not necessarily a Pareto optimal one (Woodford, 1989). Aiyagari (1989) has shown that endogenous cycles can exist in an OLG model with individuals living many periods and financial market imperfections. As number of periods approaches infinity the cycles tend to disappear. Nevertheless the existence of two-period cycles with multi-period living individuals gives us more realistic cycle lengths.
Much of this literature uses the concept of the discount factor rather than the discount rate. These are inversely related in the following way. If ß is the discount factor and 5 is the discount rate, then 3 = 1/(1+5). Thus the discount factor varies from zero to one, with zero indicating an infinite discount rate, that is total myopia, whereas a discount factor of one indicates a discount rate of zero, that is total farsightedness.
In contrast to the models presented in the previous section, Dechert (1984) has shown that this model cannot be derived from an infinite-horizon, representative agent, optimizing framework.
An alternative approach incorporating neoclassical technologies, “time to build” investment (interpreted as an OLG assumption), and adaptive expectations that can generate chaotic dynamics has been developed by Lin, Tse, and Day (1989).
Goodwin’s model (1967) represents one of the first applications to economics of the Lotka-Volterra predator-prey model of ecology.
An excellent summary can be found in Lorenz (1993a).
Although much studied (Lasota and Mackey, 1985; Domowitz and EI-Gamal, 1993; ElGamal, 1991) it must be noted that no fully general conditions regarding ergodicity of chaotic dynamics have not yet been developed. It is well known that tent map systems can generate ergodic chaos.
The term “chaotic hysteresis” was originally coined by Abraham and Shaw (1987).
Ramsey, Sayers, and Rothman (1988) re-examined the results of Barnett and Chen (1988), Sayers (1988), and Scheinkman and LeBaron (1989) using methods due to Ramsey and Yuan (1989) for correcting for small sample size in dimension estimates. They found these not to remain constant thus making a hypothesis of deterministic chaos unlikely, except possibly for Sayers’ work stoppages data. However all series still exhibit nonlinear dependence.
More generally, Brock and Dechert (1991) argue that estimated chaotic dynamics should be reconstructed by other means. One method proposed by Mayfield and Mizrach (1992) is to alter the time unit of observation. By moving to 20 second interval observations for stock return data, they found dimension estimates went up very dramatically.
Many of the papers presenting the debates regarding the empirical existence or nonexistence of chaos in economic systems can be found in Day and Chen (1993), Semmler (1994), Trippi (1995), Dechert (1996), and Barnett, Kirman, and Salmon (1996).
Kurz and Salvadori (1999) provide a critical historical perspective on endogenous growth theory.
Coordination failure can occur even without nonlinear dynamics, as emphasized by Clower (1965), Leijonhufvud (1973), and Howitt (1985). Colander (1998) and Colander and van Ees (1996) emphasize coordination failure as a central problem for Post Walrasian macroeconomics.
Both rational bubbles and sunspot equilibria involve self-fulfilling prophesies. The crucial difference between them is that the former involves prices whereas the latter involve real investment or output. Of course price bubbles can affect real output as discussed in Chapter 5, thus eliding this distinction somewhat.
Despite the “optimistic” convergence results of Hommes and Sorger (1998) and Hommes and Rosser (1999), Kurz (1992) shows that if a price process is sufficiently complex it cannot be learned. The conditions involved somewhat resemble the problem raised by Diaconis and Freedman (1986) that Bayesian learning may not converge on a true value in an infinite dimensional space. Kurz (1992, p. 312) argues that “economic environments may be characterized by complex, nonstationary, stochastic structures for which a finite parameter space is not sufficient.” Koppl and Rosser (1998) further consider this problem in a game theoretic context.
The Lucas Critique was recognized earlier by Marschak (1953) who noted that policymakers must pay attention to structural changes that their policies engender. I thank Donald Hester for this point.
thank Prigogine’s student, Peter Allen and also Hermann Haken for making me aware of their interactions with Hayek and of his interest in and awareness of their work. Although he is frequently identified with such a position, Hayek was not necessarily a supporter of full laissez-faire.
This can be viewed as a lineal descendent of Leijonhufvud’s (1981) earlier “corridor of stability” argument that economies can harmlessly oscillate within certain bounds, even in complex patterns, but will behave severely dysfunctionally if they go outside those bounds. This can be argued to be a variation of the “stability versus resiliency” argument of ecology (Holling, 1973), that there might be a conflict between local and global stability. Too great an effort to create local stability may lead to the undermining of the institutions that support global stability (resilience), with the collapse of the apparently stable formerly socialist economies being a possible example (Rosser and Rosser, 1997).
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Rosser, J.B. (2000). Chaos Theory and Complex Macroeconomic Dynamics. In: From Catastrophe to Chaos: A General Theory of Economic Discontinuities. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1613-0_7
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