A simple method for projecting or estimating alpha and beta: 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, f irst marriage, divorce, remarriage, and leaving the parental home. The meth od has been successfully tested by fittings to 180 reliable observed demogr aphic schedules in various countries and periods, and to nearly 10,000 simu lated 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 pop ulation and family household projections. It releases the traditional unrea listic 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 delaye d or advanced, while the curve becomes more spread or more concentrated, or , more specifically, assume that young people delay the events more than th e older persons do, or vice versa. Our proposed method is also useful to fo rmulate assumptions on future demographic trends for purposes of policy ana lysis and planning. It can be used to indirectly estimate demographic sched ules when the detailed age-specific data are not currently available, which is useful for developing countries and sub-region studies in developed cou ntries. A crucial point for a successful application of the method is that the standard schedule chosen can capture the general pattern of the demogra phic process in the population under study.