Macroeconomic models with long dynamic memory: Fractional calculus approach

Abstract

This article discusses macroeconomic models, which take into account effects of power-law fading memory. The power-law long memory is described by using the mathematical tool of fractional calculus that includes the fractional derivatives and integrals of non-integer orders. We obtain solutions of the fractional differential equations of these macroeconomic models. Examples of dependence of macroeconomic dynamics on the memory effects are suggested. Asymptotic behaviors of the solutions, which characterize the rate of technological growth with memory, are described. We formulate principles of economic dynamics with one-parametric and multi-parametric memory. It has been shown that the effects of fading long memory can change the economic growth rate and change dominant parameters, which determine growth rates.