Fertility levels and patterns (cont.)
Desired properties of fertility models
We can distil from the above the essential properties that a model of fertility should demonstrate:
- The model should be flexible enough to produce the variety of shapes and levels of fertility depicted on the previous pages.
- The rates should be smooth with respect to age.
- The rates should be concave with respect to age – in other words, the rates should increase monotonically up to some age where fertility rates reach a maximum, and then decrease monotonically
- The age distribution of fertility should not be symmetrical – typically rates increase from zero at menarche to a maximum between ages 25 and 30 – about 10-15 years after menarche, before declining for about 20-25 years until the age of menopause. Thus, fertility rate distributions will tend to be slightly skewed to the right.
- The rates produced by a model should be zero before menarche and after menopause.
- Desirable but not essential, the rates described by the model should be analytically tractable – in other words, other associated properties of the fertility schedule (the mean age at child bearing; cumulated fertility to a given age, for example) should be able to be computed with ease, either analytically or directly
The suitability of any model of fertility should be judged against these properties. The next section introduces parametric models of fertility.