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Xie, Yu. 1990. "What is Natural Fertility? The Remodeling of a Concept." Population Index, 56(4): 656-63.
The concept of natural fertility has proved useful in demographic research, although the dispute over its applicability to real populations still persists. One of the most important extensions of Henry's original conceptualization of natural fertility was made by Coale (1971) and Coale and Trussell (1974, 1975) in the framework of model fertility schedules. Coale and Trussell characterized age-specific fertility rates of any population by two parameters as deviations from a set of standard natural fertility rates. One parameter, M, measures the departure of the population concerned in the level of fertility; another parameter, m, measures the degree of fertility control, which has a built-in increasing function with age. Wilson et al. (1988) use Coale and Trussell's method to model natural fertility because natural fertility can always be seen as a special case of regular fertility.
Successful as it appears, this last project completes a questionable cycle. The Coale-Trussell model presumes perfect knowledge of a set of standard fertility rates. The use of the Coale-Trussell formulation to model natural fertility challenges this assumption. Furthermore, Wilson et al. (1988) apply the Coale-Trussell model to the same data from which Coale and Trussell (1974) obtained the standard natural fertility schedule; from the viewpoint of statistical estimation, there is less information in the data than imposed by this procedure. Finally, Wilson et al. (1988) forcefully and convincingly demonstrate the importance of treating the data as samples rather than as populations. If the data are treated as samples, as they should be, the natural fertility standard should also be statistically estimated as are m and M parameters.
Henry (1961) as well as Coale and Trussell (1974) identified natura fertiity as a peculiar age pattern. For physiological and social factors, different populations not exercising fertility control may have different levels of fertility. But their age patterns should be the same. This idea was evident in Henry's work and was formalized into the Coale-Trussell method. For the data initially reported by Henry (1961) and later used by Coale and Trussell (1974), differing levels of fertility with a common age pattern were assumed but, unfortunately, untested. Coale and Trussell (1974) obtained their natural fertility standard by averaging the ten natural fertility schedules reported by Henry that are believed to be reliable. In its later use, this standard is always treated as exactly known.
This paper applies log-linear models to Henry's data on natural fertility. It tests various assumptions leading to ways of obtaining a standard natural fertility schedule through explicit modeling. The models specify that births follow an independent Poisson distribution for each age interval of each population. All parameters are estimated through an iterative maximum-likelihood procedure.