Scaling laws in a stochastic growth process and its application to macroeconomics
Economies are complex systems and exhibit scaling in several quantities, as well as in fluctuations. However, mainstream economic theory does not address these phenomena, although they are generated from a succession of production cycles. In this talk I introduce a simple macroeconomic agent-based model, which is in essence a stochastic firm growth process. It generates several interrelated scaling laws for quantities like firm size and firm growth rate. Stochasticity comes from competition of firms in markets for a finite resource. I use entropy maximization to obtain analytical results.
In a second step, heterogeneity is introduced, which leads to additional relative growth following replicator equations. Its effect on the scaling laws is analyzed numerically and theoretically. This extended model is economically more plausible, and its more comprehensive results are compared to empirical data. Its aggregate fluctuations can also be interpreted as simple business cycles. The model is an example of using complexity theory to describe a problem where several dynamics are relevant