Modelling gamma coefficient in the Gompertz curve to determine the variability of vehicle ownership saturation

Abstract

Vehicle ownership forecasting models based on the Gompertz curve generally employ per capita Gross Domestic Product as the primary explanatory variable. The γ coefficients in the curves specify the ultimate vehicle saturation level and α, β the profile of the S-curve shape. The γ coefficient is assumed to be the single universal value that all countries will eventually reach. The present research hypothesised that countries could have variable saturation levels and, as such, the γ coefficient would not be a universal constant. On that premise, it attempted modelling the γ coefficient as a function of several other extraneous factors that significantly influence a country’s vehicle ownership and ultimately its saturation level, thus resulting in a country-specific γ; the application of the Gompertz model and the relationship of vehicle ownership would then be influenced by the country-specific characteristics. It was found that, while vehicle ownership is influenced by the GDP as in the case of Gompertz model, the country-specific γ would also be influenced by other identifiable variables such as household size, population density, share of public transport, and percentage of female drivers in each country. The results confirm the globally observable phenomenon that high-income countries do not converge to a universal vehicle ownership saturation level. Singapore and Hong Kong are examples, usually excluded from the Gompertz model, which can now be explained by the new model.