On the statistical dynamics of economics

Abstract

Statistical properties are explored for typical ergodic processes in economics. A paradox has been observed – although the long-run average of a variable may converge to a constant, its average growth rate in the long-run is always non-negative so as to induce an illusion of growth. The same characteristic exists even if a dynamic process is reversed. For the chaotic and ergodic processes involving a limited growth rate mechanism, it is demonstrated that chaos may be preferred to a equilibrium in the sense that the long-run average return may be higher than the equilibrium return.