A simple method for projecting or estimating α and β: An extension of the Brass Relational Gompertz Fertility Model

This paper proposes a simple method that analytically links the parameters alpha and beta, which are not demographically interpretable and measurable in the Brass Relational Gompertz Fertility Model, with demographic measures of median age and interquartile range. We also extend the Brass model that deals only with age-specific fertility to age-parity-specific fertility, first marriage, divorce, remarriage, and leaving the parental home. The method has been successfully tested by fittings to 180 reliable observed demographic schedules in various countries and periods, and to nearly 10,000 simulated schedules with various combinations of possible values (including the extremes) of alpha and beta. Our proposed method that uses median age and interquartile range instead of alpha and beta as input is useful in the population and family household projections. It releases the traditional unrealistic assumption in population projections that the curve of the fertility schedule moves to the right or left in a parallel way. Instead, using our proposed method, one can assume that the demographic events would be delayed or advanced, while the curve becomes more spread or more concentrated, or, more specifically, assume that young people delay the events more than the older persons do, or vice versa. Our proposed method is also useful to formulate assumptions on future demographic trends for purposes of policy analysis and planning. It can be used to indirectly estimate demographic schedules when the detailed age-specific data are not currently available, which is useful for developing countries and sub-region studies in developed countries. A crucial point for a successful application of the method is that the standard schedule chosen can capture the general pattern of the demographic process in the population under study