This research develops a mathematical 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 if the age-related fecundity decline is controlled. The natural fertility schedule employed in the Coale-Trussell fertility model was incorporated to adjust age effects externally. The model is able to provide good fits to fertility for the Hutterites and for rural Chinese women in the 1950s. Moreover, it is found that for the Hutterites, whose marital dissolution rate is extremely low, the estimated model's parity level indicators at each birth order are all close to one. The same result is obtained from fitting the model to fertility in rural China when adjustments for marital dissolution and the grandmother effect are introduced. These findings theoretically and empirically confirm Henry's proposition of natural fertility, i.e. fertility in the absence of parity-specific birth control.
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