PAPP103 - s03: Demographic models: fertility

Brass's relational Gompertz model of fertility

Brass’ relational Gompertz model of fertility is directly analogous to the Brass relational logit model of mortality. As with the mortality model, the relational fertility model makes use of a standard fertility schedule that is linearised (that is, converted into an (almost) straight line) by means of a mathematical function. This straight line can then be transformed into any other straight line by changing its slope and intercept, and then converted back into a fertility schedule by applying the anti-function used to linearise the standard schedule.

Brass identified the Gompertz function as describing well the pattern of cumulated fertility, F(x), in a population. This function is sigmoidal (s-shaped) and slightly right-skewed, thereby capturing neatly the presumed shape of a fertility curve, f(x), in most populations.

With a standard fertility schedule with a TFR of 1, f_s(x), F_s(x) is the proportion of TFR achieved by age x in the standard fertility schedule. The original standard fertility schedule was constructed by Heather Booth (1984), a student of Brass’.