A model of the age patterns of births by parity in natural fertility populations

This research develops a convolution model to express the age patterns of fertility at each birth order in natural fertility populations in terms of six parameters, directly representing the proximate determinants of fertility, and a series of parity level indicators. The parity level indicators at each birth order are simply the proportions of women in a cohort who will eventually have births at each birth order it the age‐related fecundity decline is controlled. The Coale‐McNeil nuptiality model is adopted to represent the age pattern of first marriage rates and the natural fertility schedule employed in the Coale‐Trussell fertility model is incorporated to adjust age effects. The fast Fourier transform is used in solving the model numerically. It proves that the model is able to provide excellent fits to fertility for rural Chinese women in the 1950s.