State space description of national economies: the V4 countries

Abstract

We present a new approach to description of national economies. For this we use the state space viewpoint, which is used mostly in the theory of dynamical systems and in the control theory. Gross domestic product, inflation, and unemployment rates are taken as state variables. We demonstrate that for the considered period of time the phase trajectory of each of the V4 countries (Slovak Republic, Czech Republic, Hungary, and Poland) lies approximately in one plane, so that the economic development of each country can be assocated with a corresponding plane in the state space. The suggested approach opens a way to a new set of economic indicators (for example, normal vectors of national economies, various plane slopes, 2D angles between the planes corresponding to different economies, etc.). The tool used for computations is orthogonal regression (alias orthogonal distance regression, alias total least squares method), and we also give general arguments for using orthogonal regression instead of the classical regression based on the least squares method. A MATLAB routine for fitting 3D data to lines and planes in 3D is provided.