New estimates of fertility and child mortality in Africa, south of the Sahara

Summary Earlier work by Page and Coale has estimated demographic indices of fertility and mortality for parts of Africa using the Sullivan modification of Brass's technique. The present paper presents modified and more accurate estimates of fertility and child mortality, not only for the sub-national units covered by Page and Coale but also for areas not covered by them. The present analysis which employs Trussell's refinement of Brass and Sullivan's techniques also includes improvements overlooked in earlier estimates. The salient finding that emerges is that while the Brass mortality technique is very powerful, his equally ingenious fertility technique is very weak and should not be relied on for estimating fertility parameters.     

Transforming gompertz's function for fertility analysis: The development of a standard for the relational gompertz function

Summary The relational Gompertz function improves upon the Gompertz for fertility analysis by achieving a better fit in the tails of the distribution. This is obtained by a transformation of the age scale corresponding to an empirical standard. This standard is developed from Coale and Trussell's model and is appropriate for use with populations of high fertility. The model is tested on two sets of data and is shown to produce good estimates of completed fertility even for data truncated at quite early ages. Good results are also obtained for declining fertility.     

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.     

Age patterns of chinese marital fertility, 1950–1981

Coale and Trussell’s model of marital fertility is used to analyze data from China’s National One-per-Thousand Fertility Survey. Rural China experienced a regime of natural fertility until 1970, after which levels of fertility control rose with unprecedented speed and with an age pattern starkly dissimilar from that observed in other populations. Urban marital fertility was apparently under a modest level of deliberate control in the 1950s, with a sustained rise in control beginning in 1963. Natural fertility was low relative to other populations, with the urban level exceeding the rural.     

Software announcement: LIPRO 2.0

We describe a method for fitting the Coale‐Trussell model to fertility rates or to counts of births and exposure by single years of age. The procedure maximizes a quasi‐likelihood function and can easily be implemented using standard software. An extension to handle covariates is discussed.     

The index of overall headship: A simple measure of household complexity standardized for age and sex

This paper develops and tests an age-sex standardized measure of household complexity, defined broadly as the tendency of adults (other than spouses) to head their own households or to share households. The aim is a measure of household complexity which can be computed with a minimum of demographic data, namely, data on number of households and on the population by age and sex. The procedure is similar to that of Coale for fertility measurement (Coale, 1969); it is a form of indirect standardization in which the actual number of households is related to the number that would exist if maximum age-sex-specific household headship rates were to apply. Various forms of this indirectly standardized measure show a correlation of better than 0.9 with directly standardized measures for a sample of 33 nations for which requisite data are available. The new measure promises to extend considerably the geographical and temporal range of comparable empirical measures of household complexity.     

Ansley J. Coale on Increases in Expectation of Life and Population Growth

The rapid decline in mortality after the end of World War II, in combination with a much slower downward adjustment of fertility, resulted in an extraordinary acceleration of world population growth. In a contribution prepared for the 1959 Vienna conference of the International Union for the Scientific Study of Population, Ansley J. Coale présented a concise and spirited exploration of the influence of mortality and fertility on the levels and patterns of growth and on the distribution of the population by age. Using the stable population model as his tool of exploration, Coale présents a comparative analysis of the implications of movements between stable states, making imaginative illustrative assumptions on changes over time and highlighting the often surprising and counterintuitive results of such calculations. The full text of this article, omitting summaries in English and French, is reproduced below from pp. 36–41 in Union Internationale pour I?étude scientifique de la population, Internationaler Bevölkerungskongress, Wien:Im Selbstverlag, 1959. Ansley Coale was one of the most prominent figures in demography in the second half of the twentieth century. He was born in 1917 and was educated at Princeton University. He spent his entire professional career at Princeton, as a member of the economics faculty and in association with the Office of Population Research, of which he was director from 1959 to 1975. In 1967/68 he was president of the Population Association of America, and from 1977 to 1981 he was president of IUSSP. His many scientific works include Population Growth and Economic Development in Low‐Income Countries (1958), coauthored with Edgar M. Hoover, a book that was highly influential in shaping the international population policy agenda from the 1960s on—lately receiving renewed attention as a predictor of the “demographic dividend” benefiting economies as a result of the transition to low fertility. He was initiator and leader of the Princeton project exploring the causes of the decline in marital fertility in Europe, culminating in the 1986 book, coedited with Susan C. Watkins, The Decline of Fertility in Europe. His most lasting contribution to population studies, however, was in the field of formal demography, as both teacher and scholar. His research in this area is exemplified by the 1972 book The Growth and Structure of Human Populations: A Mathematical Investigation, and in the application of demographic models to the estimation and analysis of population data. Ansley Coale died on 5 November 2002, at the age of 84.     

Practical aspects on the estimation of the parameters in Coale’s model for marital fertility

This paper demonstrates the estimation of the parameters in the Coale model for marital fertility by the maximum likelihood method, under the assumption of a simple Poisson process model. The necessary calculations are easily performed in the statistical computer program package GLIM, and the necessary commands are noted. Without access to GLIM, or any equivalent, it is still possible to fit the model approximately by the use of any weighted linear regression program. In both cases, goodness of fit tests are available.     

Recent net alien immigration to the United States: Its impact on population growth and native fertility

Estimates of the size and structure of recent alien immigration to the United States are made. Substituting these revised estimates in the Series II projections of the U.S. Bureau of the Census implies a future U.S. population smaller than that implied by the Census Bureau’s estimates of immigration. The analysis of Coale (1972)—which calculates the decline in native-born fertility required to accommodate immigration and, at the same time, maintain a stationary population—is replicated, using both the Census Bureau’s estimates and the revised estimates reported here. The revised estimates indicate a smaller reduction in native fertility and a smaller ultimate size of the stationary population than are implied by the Census Bureau’s immigration estimates. The importance of age structure in all of these calculations is demonstrated.     

Fertility transition,conscious choice,and numeracy

One of the preconditions of the fertility transition, as stated by A.J. Coale, is that reproductive decisions must be within the calculus of conscious choice. It is suggested that the change in mentality which leads to family limitation includes "numeracy about children," a clear notion of what family size ought to be and the awareness of individuals of where they stand with respect to the norm. The article explores the hypothesis that numeracy about children appeared historically in various times and places, and that the conceptualization of family size was a necessary condition for adopting family limitation.     

Turbulent dynamics in a Xviith century population

A reconstruction of the population of the Pays de Caux (1589–1700) yields the time series of a fertility behavior indicator, the overall Coale index If. In spite of the noisy appearance of its evolution, the trajectory of If looks ordered, as if it were confined alternatively to two given zones, looping in each of them for a while, then suddenly jumping from the low one to the higher one, or slowly whirling down from the high to the low one.

An attempt is made to explain this general temporal structure by using a simulation model based on the autoregulation model (the so‐called European Marriage Pattern), putting into play a choice of the spouse function, a fertility function, modalities of marriage and remarriage, under the environmental forcing of the reconstructed mortality conditions.

The correspondence between reconstruction and simulation turns out to be quite good, not only for the population size or the Coale index, but also for the marriage series, quite independently of the reconstructioa

A second simulation with simulated mortality conditions shows a bifurcation point: as the mean frequency of crisis increases, the state of the system leaves the lower level and concentrates more and more in the higher level.

Thus, not only does the autoregulator model appear validated by empirical data, but its bi‐modal structure is revealed, depicting the dynamic response of a traditional community both to the environment and to the endogeneous demographic process.     

What is natural fertility? The modelling of a concept

The value and importance of the concept of natural fertility have been widely debated since Henry's work in the late 1950s. Whereas Henry regarded natural fertility largely as a useful concept for model building, Coale-Trussell demonstrated that this concept could also be used to analyze patterns of age-specific fertility. The set of age-specific marital fertility schedules assembled by Henry and then used by Coale and Trussell involved largely small populations drawn from disparate sources. Nonetheless, from this diverse and fragmentary data, Henry was able to construct a standard of natural fertility which, in the operational form developed by Coale-Trussell, has proved remarkably general in its application and utility. This in turn suggests that the physiological forces shaping fertility are exceedingly strong, especially the incidence of physiological sterility. There appears to be no single universal pattern of natural fertility. Rather, there is a set of closely related age profiles, the exact shape of which is determined by specific behavioral and social factors that influence childbearing. The increase in physiological sterility with age serves to give an upper limit to fertility at each age, while other factors determine how close a given population comes to that maximum. Although no society has ever demonstrated Henry's ideal notion of a purely physiological fertility pattern, the effect of the intervening factors is often weak. In terms of the Coale-Trussell model, maximum likelihood estimation offers the most informative method of implementation and a time series for 1 population is more readily interpretable than a cross-section comparing several populations.     

A comment on Coale's life table construction

In a recent issue of Population Index, Coale (1984) described a method of deriving a life table for an intercensal period separated by T years from 2 census single-year age distributions of a closed population. This note examines the formula used by Coale and points out that although it works well for all practical purposes, the formula with his new growth rate is an approximation, not an identity as is assumed by Coale. The Coale formula involves more steps than the usual method of estmating mortality and yields less accurate results. Coale's formula is explained. In general, in the case under consideration, if a larger cohort is followed by a smaller cohort, the survival probability calculated by the formula exceeds unity, whereas if a smaller cohort is followed by a larger cohort, the calculated survival probability becomes less than unity. The size of the relative cohorts determines the degree of error in the calculated probability. The formula does not give the survival probability of unity as it should if it were an identity. The formula in the continuous time is an identity. Feeney's alternative method presented in Coale's Computational Appendix 3 produces an exact life table without using any formula. Feeney's method is, however, less accurate than the usual method, given the same data, because it omits some information. The Coale procedure losses its usefulness in that it requires extra data manipulation, only to yield less accurate results.     

A note of correction with reference to parameters of the menstrual cycle and the efficiency of rhythm methods of contraception

It is known that further mortality reductions in industrialized countries depend heavily on trends in mortality rates at the oldest ages. In this article, a model proposed by Coale and Kisker is used to investigate mortality trends at the extreme old age of 110 years. The most important conclusions are that (1) the form of the model proposed by Coale and Kisker fits observed mortality schedules very well indeed, and (2) the trend in mortality rates at extremely high ages has apparently been flat for men, but may have declined slightly for women during this century.     

Nonreporting of births or nonreporting of pregnancies? Some evidence from four rural counties in North China

Coale and Banister argue that in China, elevated sex ratios in retrospective surveys are in part a function of collecting birth histories in a culture in which the definition of a birth may exclude mortality shortly after birth: an infant death in the West may be a stillbirth in east Asia. I present data from a recent sample survey featuring a retrospective pregnancy history. These data reveal that at least in the first pregnancy, from which the preponderance of sample births arise, there is no evidence of elevated female infant mortality or of high numbers of stillbirths, but that reported sex ratios are unusually high. The proportion of stillbirths grows for later pregnancies, but not enough to account for high sex ratios. Retrospective fertility data regarding recall over a recent interval are vexed less by a misunderstanding of what a live birth is than by a “misunderstanding” of what a (reportable) pregnancy is.     

Some problems in the use of open birth intervals as indicators of fertility change

Abstract To measure changes in fertility brought about by specific family planning programmes has been one of the problems faced by demographers as well as policy-makers. This problem is particularly difficult in developing countries where the basic data are poor. Hence, there is a need to find indices of fertility that are easy to obtain, sensitive to changes in fertility and either not grossly affected by errors in data, or alternatively amenable to correction of data errors. Among many possible indices, the open live birth interval has attracted attention of many researchers and experts.(1).     

The fertility of the asian community of East Africa

Summary Fertility indices of one sort or another can be calculated for the Asian populations of Uganda and Kenya back to 1931. These indices suggest that fertility has fallen sharply during the 1950s and 1960s. Considerable problems are experienced in trying to determine the actual level of fertility, however, since all the techniques developed to deal with defective data are so affected by the falling fertility and migratory movements of the population, as to be virtually useless. An analysis of the causes of the fertility decline suggests that both changes in marriage patterns and changes in fertility within marriage have contributed to the fall, and that these changes have come about as a result of the better education and economic opportunities available to the Asian community.     

Fertility In England: A Long-Term Perspective

This paper deals with two aspects of long-run fertility trends in England. First detailed and widely comparable fertility measures (Coale's indices) are reconstructed for England from the mid-sixteenth century to the present. Secondly the extent and nature of local and regional variation in those indices is discussed. The calculation of Coale's indices has never previously been attempted for so long a time span. Doing so requires the use of several different sources of information and a new method for combining them. The results provide significant insights into the development of the distinctive English demographic regime. The analysis of spatial patterns makes it apparent that local, rather than regional, variation was the main source of different fertility patterns in the nineteenth century. These patterns are obscured when counties or larger units are made the framework for analysis.     

Recent European fertility patterns: fitting curves to 'distorted' distributions

Recent patterns of fertility in Europe show marked differences between countries. Recent United Kingdom and Irish fertility curves show 'distortions' in terms of a 'bulge' in early age fertility, distinct from the smoother curves of other European countries. These patterns may not be adequately described by mathematical functions used by previous studies to model fertility curves. A mixture model with two component distributions may be more appropriate. The suitability of the simple and mixture Hadwiger functions is examined in relation to the fertility curves of a number of European countries. While the simple Hadwiger model fits recent period age-specific fertility distributions for some countries, others which display a 'bulge' in early age fertility distributions for some countries, others which display a 'bulg' in early age fertility require a mixture Hadwiger model. Some of the parameters of the Hadwiger models appear to be related to familiar demographic indices. The simple and mixture Hadwiger models appear useful in describing and comparing fertility patterns across European countries.