Disequilibrium in the Canadian Regional System: Preliminary Evidence, 1961–1983

Abstract

Disequilibrium seems to be a natural concept for dynamical systems. To fix ideas, consider the following situation (Kanaroglou, et. al., 1985, pp. 26–27):

Suppose that you hold in your hands an invisible spherical bowl with a visible ball in it. As you walk, the ball moves inside the bowl. At any moment, given the characteristics of your walk, there is a point around the bottom of the bowl on which the ball would rest. This is the steady-state of the moment for the system ball-bowl. As it changes during your walk, the ball ‘tries’ to follow it, never catching it except by chance, and then for a fleeting moment. You could, of course, describe in three dimensions the trajectory of the ball during your walk without any reference to the bowl: after all, the only thing you see is the ball. Yet a study of the relationships between the ball, the bowl and the characteristics of your walk help you to understand the object of your concern. In particular, suppose that you could model this system and represent the characteristics of your walk by a set of parameters. At any moment, you can monitor the position of the ball and estimate the set of parameters associated with that moment. Since the bowl is spherical you know that, for any particular feasible set of parameters, there is a single position of the ball which represents a steady- state. Introducing the estimated set of parameters in your mode 1, you can compute the steady-state of the moment. Comparing the difference between the observed and the steady-state positions of the ball, you could derive a measure of disequilibrium for the system, which corresponds to that particular moment. For example, the distance between the observed and steady-state positions of the ball could serve as a simple measure of disequilibrium. You may repeat the same procedure several times to learn something about the evolution of disequilibrium in your system, i.e about the evolution of the difference between the observable trajectory of the ball and the unobservable trajectory of the corresponding steady-state.