Modeling of the national economies in state-space: A fractional calculus approach

Abstract

A new approach to macroeconomic modeling is presented and illustrated by an application to modeling the behavior of national economies of the three Commonwealth countries. The developed approach is based on three essential modern tools.The first is state-space modeling adopted from the classical control theory, and as state variables describing the behavior of a system the gross domestic product (GDP), inflation, and unemployment rate (UE) were chosen. The history of development of the modeled economy in time, which is represented by triples of the values of GDP, inflation, and UE, is then considered as a trajectory in state-space.The second tool is fractional-order differential equations; solutions of a system of three fractional-order differential equations are used for fitting the available economic data.The third tool is the orthogonal distance fitting method, which is used for identification of the parameters of the system of fractional differential equations that is used as a general model.The obtained models of the state-space trajectories of the economics of the United Kingdom, Canada, and Australia have similar shape (which can be explained, for example, by similarities in their political and economical systems) but look like stretched compared to each other (which can be explained, for example, by different size of population and its social structure).