Nonlinear growth model with long memory: generalization of Haavelmo model

Abstract

The Haavelmo economic growth model is one of the most famous nonlinear macroeconomic models proposed by Trygve Haavelmo, who received the Alfred Nobel Memorial Prize in Economic Sciences in 1989. In this paper, we proposed a generalization of the Haavelmo growth model, in which we take into account the fading memory and variable parameters. Equation of the proposed model is described by nonlinear fractional differential equation, in which the Caputo fractional derivative of non-integer order are used to take into account long memory with power-law fading. The paper proposes an exact solution for the nonlinear equation of the suggested model with memory. The conditions of the existence of the suggested exact solution for this nonlinear fractional differential equation are described. These conditions impose restrictions on the nonlinear economic dynamics with memory. For proposed model, expressions for the warranted rate of growth with power-law memory are derived.