Modelling and Forecasting Human Populations using Sigmoid Models

Early this century "S-shaped" curves, sigmoids, gained popularity among demographers. However, by 1940, the approach had "fallen out of favour", being criticised for giving poor results and having no theoretical validity. It was also considered that models of total population were of little practical interest, the main forecasting procedure currently adopted being the bottom-up "cohort-component" method. In the light of poor forecasting performance from component methods, a re-assessment is given in this thesis of the use of simple trend models. A suitable means of fitting these models to census data is developed, using a non-linear least squares algorithm based on minimisation of a proportionately weighted residual sum of squares. It is demonstrated that useful models can be obtained from which, by using a top-down methodology, component populations and vi tal components can be derived. When these models are recast in a recursive parameterisation, it is shown that forecasts can be obtained which, it is argued, are superior to existing official projections. Regarding theoretical validity, it is argued that sigmoid models relate closely to Malthusian theory and give a mathematical statement of the demographic transition. In order to judge the suitability of extrapolating from sigmoid models, a framework using Catastrophe Theory is developed. It is found that such a framework allows one quali tati vely to model population changes resulting from subtle changes in influencing variables. The use of Catastrophe Theory has advantages over conventional demographic models as it allows a more holistic approach to population modelling.