Ansley J. Coale’s research while affiliated with Princeton University and other places

An elaboration of Preston's (Preston and Hill, 1980) procedure for determining the completeness with which deaths are recorded in approximately stable populations is presented. Both the procedures of Preston and that of Brass are conventionally limited to mortality beyond early childhood, to mortality above age 5 or age 10. The method considered here is based on characteristics of stable populations, i.e., populations that have been subject for a long time to little variation in age-specific mortality schedules or in overall levels of fertility. The essential features of a stable population are maintained even if fertility has changed. This is the case as long as no strong trend in fertility existed more than 15 or 20 years before the date at which the population is observed. Recent changes in fertility may affect the structure of the population at adult ages, but the effect on estimates of completeness of death records can generally be kept within tolerably narrow limits. Prior to showing how explicit estimates of the relative completeness of recording of numbers of deaths and persons can be derived from counts of deaths and persons by age, it is noted that a life table for a stable population can be constructed directly from the recorded distribution of deaths by age, or from the recorded distribution of persons. The procedures described are applied to several different populations in order to illustrate the computational steps necessary to estimate the completeness of death records at ages above childhood in populations that are approximately stable.

A mathematical formula is given for the asymptotic trajectory of the complex roots of Lotka's equation. This formula is obtained by use of a Taylor expansion of the net fertility function in the neighborhood of the age beyond which fertility is zero. The approximate trajectory is compared with an exact trajectory obtained by use of a computational algorithm for finding complex roots suggested by Turner. For two examples, the agreement is surprisingly good.

An analysis of the composition, characteristics, and vital processes of the population of rural mainland China was undertaken using data collected as part of a study of land utilization carried out by Naking University in 1929-1931. These data have been reappraised using techniques for demographic analysis of faulty data which shows a consistent picture of the Chinese farmer of high morta moderate fertility, and early and universal marriage. Estimates of the singulate mean age at marriage was 17.5 for females and 21.3 for males. Fewer than 1 in 1000 women and 3 in 1000 men never married. The reported parity of older women was only slightly above 5, which disputes the very large historical family size that has been imputed to the chinese. There was a life expectancy of less than 25 years for each sex, and very high infant mortality. These characteristics were of sufficient persistence to have generated a stable age distribution.

The nature of the roots for a set of fertility functions were explored in this study, resulting in tables from creation of a family of model fertility schedules. These model fertility schedules accurately represent the full range of age structures of fertility in large populations; they have close fit to various accurately recorded fertility schedules of very different form. The text for the tables includes discussions of: 1)the basis for the fertility schedules, 2)the age structure of the proportion ever married (G(a) specified by 2 parameters, 3)single parameter specified age structure of marital fertility, 4)the similarity of model schedules of age specific fertility to the age pattern of fertility in actual populations, 5)model fertility schedules' suitability during changing nuptuality. Possible uses of the schedules and their application to different countries (England, Wales, Peru) are also described.

The age composition of populations experiencing no mortality and various kinds of fertility is derived. It is then shown that, if successive mortality schedules can be expressed as the sum of a component that varies with age and a component that varies with time, only the former has any effect on the age structure of the population. One implication is that a population in which mortality varies with time but not with age has the same composition as a population with no mortality at all.

PIP The authors present 2 methods for the approximation of a representative schedule recording first marriage frequencies by age. Both treatments are mathematically complex. One method achieves a very close approximation with a simple closed form frequency function, which is the limiting distribution of the convolution of an infinite number of exponentially distributed components. The other method achieves an equal approximation by the convolution of a normal distribution of age of entry into a marriageable state and as few as 3 exponentially distributed delays. This latter convolution provides a feasible model of nuptiality, a model receiving surprising empirical support.