Prof. Brian Fath, Towson University, USA

Complex economic dynamics

Both economic and ecological dynamics have been understood as a complex system cycle of growth and development along the following four phase trajectory: growth - conservation - dissolution - reorganization. This cycle was identified by Schumpeter (1942) in economics and Holling (1986) in ecosystems. Research into the economic and ecological complex system cycle takes many facets. Much of standard economic growth theory only focuses on the first stage of this dynamic as was the case with the early literature on ecological succession, yet to truly understand the economic dynamic it is necessary to see the growth phase in the context of the larger cycle (Rosser 1999, Holling 2001).

The objective in these lectures is to introduce the students to the complex system cycle and how economic dynamics are similar to ecological dynamics making a case for similar modelling approaches in assessment of integrated socio-ecological systems. Complexity methods include agent based modelling, spatial and hierarchical modelling, self-organized criticality, and evolutionary game theory, to name a few. Economic applications include simulating artificial stock markets and other phenomena in which bounded rationality replaces rational expectations.

The growth stage is when the system experiences strong positive feedback controls as the centripetal force pulls more and more resources into the burgeoning structure. The first phase is commonly modeled using standard exponential growth models or more recently using positive feedbacks characteristic of increasing returns (Arthur 1988). The growth and development dynamic can also be modeled using the optimization of goal functions (Fath et al. 2004, Ayres and Ware 2005) The growth phase however, is ultimately constrained by the resource space in which the system resides and therefore is followed by a period of conservation, when resources are brought to bear to maintain the existing structure but without capacity for additional growth.

The transition from growth to conservation is modeled using logistic function in which the negative feedbacks from environmental constraints are dominant. Over the long term, the conservation phase is marked by the dissolution of the system organization, either due to internal (e.g., as new innovation or collapse) or external (e.g., invaders or disasters) perturbations. Anticipating the transition from conservation into dissolution is most challenging. The phase transition can be modeled using discrete choice theory. For example, Brock (1993) developed the "mean field" approach for the two choice case with n individuals choosing from a discrete choice set, with parameters for the average number of agents' choices, strength of interaction between the agents, intensity of choice, a utility gain from switching, and an exogenous stochastic process. Early warning signals or critical thresholds have also been applied for anticipating and modelling the phase transition.

The release of the previous rigid structure (e.g., as would be the case after a monopoly break-up) allows for a reorganization of the constituencies which will re-ignite the growth process perhaps following the previous travelled trajectory or finding new avenues that surpass it in overall complexity. Much anthropological work has been done to investigate why economies and civilizations collapse (Tainter 1988, Diamond 2005), but formal methodological approaches are still alluding.

References:
Arthur WB. 1988. Self-reinforcing mechanisms in economics. In: Anderson PW, Arrow K, Pines D. (eds.). The Economy as an Evolving Complex System. Westview Press.
Ayres RU, Warr B. 2005. Accounting for growth: the role of physical work. Structural Change and Economic Dynamics. 16, 181-209.
Brock WA. 1993. Pathways to Randomness in the Economy: Emergent Nonlinearity in Economics and Finance. Estudios Económicos, 8, 1, 3 55.
Diamond, J. 2005. Collapse: How Societies Choose to Fail or Succeed. Viking Press.
Fath BD, Jørgensen SE, Patten BC, Straskraba M. 2004. Ecosystem growth and development. Biosystems 77, 213–228.
Holling CS. 1986. The resilience of terrestrial ecosystems: local surprise and global change. In: Clark WC, Munn RE (Eds.), Sustainable Development of the Biosphere. Cambridge University Press, Cambridge, pp. 292–317.
Holling CS. 2001. Understanding the Complexity of Economic, Ecological, and Social Systems. Ecosystems 4, 390-405.
Jørgensen SE, Nielsen , SN. 1998. Thermodynamic orientors: Exergy as a goal function in ecological modeling and as an ecological indicator for the description of ecosystem development. In: F. Müller and M. Leupelt, Editors, Eco Targets, Goal Functions, and Orientors, Springer, Berlin, pp. 63–86.
Rosser JB. 1999. On the Complexities of Complex Economic Dynamics. Journal of Economic Perspectives. 13(4), 169-192.
Schumpeter JA. 1942. Capitalism, Socialism and Democracy. New York: Harper.
Tainter J. 1988. The Collapse of Complex Societies. Cambridge University Press.