Cagan model of inflation with power-law memory effects

Abstract

This paper considers a generalization of the model that has been proposed by Phillip D. Cagan to describe the dynamics of the actual inflation. In this generalization, the memory effects and memory fading are taken into account. In the standard Cagan model, the indicator of nervousness of economic agents, which characterizes the speed of revising the expectations, is represented as a constant parameter. In general, the speed of revising the expectations of inflation can depend on the history of changes in the difference between the real inflation rate and the rate expected by economic agents. We assume that the nervousness of economic agents can be caused not only by the current state of the process, but also by the history of its changes. The use of the memory function instead of the indicator of nervousness allows us to take into account the memory effects in the Cagan model. We consider the fractional dynamics of the inflation that takes into account memory with power-law fading. The fractional differential equation, which describes the proposed economic model with memory, and the expression of its exact solution are suggested.