Stable Growth in the Nonlinear Components-of-Change Model of Interregional Population Growth and Distribution

Ledent, J. (1978). Stable Growth in the Nonlinear Components-of-Change Model of Interregional Population Growth and Distribution. IIASA Research Memorandum. IIASA, Laxenburg, Austria: RM-78-028

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Abstract

In this paper, a general components-of-change model for a multi-regional demographic system is proposed. Characterized by independently derived retention probabilities, it subsumes two of the previously proposed models of population growth and distribution: the linear model studied by Rogers and the nonlinear model put forward by McGinnis and Henry. These two special cases are shown to be symmetrical variants of the proposed general model for a similar consideration of the independently derived retention probabilities.

The long-term behavior of the nonlinear model, partially looked at by McGinnis and Henry, is further examined here and then contrasted with the long-term behavior of the linear model. Unfortunately, the existence of a long-term equilibrium could not be formally proved. However, the derivation of various properties concerning the stable state of the system made possible the development of a methodology permitting the a priori determination of all acceptable equilibrium distributions. The ZPG (zero population growth) and non-ZPG specifications are separately examined, because the non-ZPG case is not as straight forward an extension of the ZPG case as in the linear model.

The long-term properties of the linear and nonlinear models are contrasted by applying these properties to the analysis of migration between the four U.S. Census regions over the period 1965-1970.

Because of its peculiar properties, we conclude that the nonlinear model cannot be a useful substitute for the linear model in the study of the dynamics of multiregional population systems.

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