A re-estimation of the multiplying factors for the Brass technique for determining childhood survivorship rates

Summary One of the truly significant contributions to practical demography is the procedure developed by William Brass for estimating life-table values from minimal data obtained in fertility surveys. Specifically, Brass designed a set of factors dependent on the shape of the fertility schedule, which convert proportions of children dead of women in standard age intervals into life table q(x)-values. Jeremiah Sullivan recently presented in this journal a method for simplifying the calculations involved in obtaining the multiplying factor in the Brass procedure. Both Brass and Sullivan employed restrictive fertility schedules to obtain their multiplying factors, and a rigorous test of either model has been hampered by the lack of numerous adequately recorded fertility schedules, especially those which begin early. Recently, a set of model fertility schedules which adequately duplicates empirical fertility schedules has been developed. These schedules were used to test the Brass and Sullivan procedures and to obtain new estimates of multiplying factors. Although the Brass and Sullivan procedures are shown to produce good estimators, new estimators, which prove superior to either, are developed and analysed.     

Age,biological factors,and socioeconomic determinants of fertility: A new measure of cumulative fertility for use in the empirical analysis of family size

To influence the number of children ever born to a woman, socioeconomic variables must operate through behavioral and biological mechanisms such as the age at marriage, the level of fertility in the absence of deliberate fertility control, and the level of control exerted to reduce fertility within marriage. In this paper, we propose a new measure of cumulative fertility which is standardized for the age-fecundity relationship and for exposure to the risk of conception associated with duration of marriage. A simple model of fertility behavior which incorporates some of the mechanisms through which socioeconomic factors may affect fertility is developed and applied to data from the United States to demonstrate the properties of alternative measures of family size. The results indicate that use of the new measure allows more precise estimates of socioeconomic fertility relationships than would be obtained with children ever born or by sample stratification.     

Cohort parity analysis: Statistical estimates of the extent of fertility control

Cohort parity analysis (CPA) is a method for indirect measurement of the extent and timing of the adoption of fertility control within marriage. It uses information on the parity distribution of a cohort of women of specified marriage ages and durations. A multinomial model of parity provides a convenient framework for the computation of distributional parameters describing the extent to which marital fertility control has been accepted and characterizing the way control has been used within specific durations of marriage. This leads to a pair of easily implemented formulas for upper- and lower-bound estimates of the expected proportion of the population ever controlling and the distribution of controllers by parity. The power of CPA is illustrated, using census data for currently married couples in Dublin, Belfast, and other county boroughs of Ireland in 1911.     

Cohort estimates of nonmarital fertility for U.S. Women

Historical trends in U.S. nonmarital fertility have been compiled almost exclusively from vital statistics on births. This paper complements this historical record by providing cohort estimates of nonmarital fertility for cohorts of U.S. women spanning approximately 50 years of cohort experience. Life table estimates using retrospective marital and fertility histories in the June 1980, 1985, 1990, and 1995 Current Population Surveys reveal nonnegligible levels of nonmarital fertility historically. For women born between 1925 and 1929, nearly 1 in 10 had at least one nonmarital birth by age 30. For women born between 1965 and 1969, more than 1 of 4 had one or more nonmarital births by age 30, with roughly 1 of5 white, 3 of 5 black, and 1 in 3 Hispanic women having at least one nonmarital birth by age 30. Life table estimates reveal a twofold increase between ages 20 and 30 in the percentage of women with at least one child outside of formal marriage for all cohorts of white and Hispanic women, and an increase of roughly two-thirds for all cohorts of black women. I also document qualitative differences in nonmarital fertility by race/ethnicity, with the percentage of nonmarital births following a divorce or marital separation for white women approximately twice that for black or Hispanic women. Finally, I introduce a new measure, the cohort nonmarital fertility ratio (CNMFR), which provides a cohort complement to the standard period nonmarital fertility ratio. Conservative estimates reveal a roughly threefold increase in the CNMFR for women born from 1925-1929 to 1950-1954 for both whites and blacks, despite substantially higher levels of nonmarital fertility among black women. Overall, these findings reveal surprisingly high levels of nonmarital fertility for women born since the 1920s and confirm that nonmarital fertility has become an increasingly substantial component of overall U.S. fertility.     

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.     

Cohort nuptiality in England and Wales

Summary A computerized nuptiality system, called GENMAR, has been developed to investigate trends in cohort nuptiality in England and Wales. This system has five main programmes dealing with first marriage, the effects of changes in mortality on nuptiality measures, divorce, re-marriage, and marital status distribution. This paper summarizes the results of the application of the first programme to England and Wales data on first marriages of persons who were born in every single year since 1900. GENMAR-1 generated for each of these cohorts a 'complete' gross nuptiality table. The analysis shows that there have been substantial increases in the intensity of first marriage at young ages, a downward shift in the modal age at marriage, and a significant rise in the proportion ever married among women. The cohort nuptiality tables also show that the change in the nuptiality of women was due to changes in both the tempo and level of nuptiality, whereas the change for men was mainly the effect of shifts in the temporal pattern of nuptiality. There are, however, signs of a slow down of marriage among the cohorts born since the early 1950's.     

Regional trends in fertility and mortality in Brazil

Abstract Questions asked in the 1970 Brazilian census allow the application of fertility and childhood mortality techniques developed by W. Brass. Using some propositions based on fertility estimates from the 1970 census data it was possible to extend the analysis to the 1940, 1950 and 1960 censuses. Estimates are also provided for ten Brazilian regions, for 1940, 1950 and 1970. These estimates show a slight decrease in the fertility level for the country as a whole, but two different trends at regional levels. Between 1940-50 and 1960-70 the poorer regions experienced constant or increasing fertility levels while developed regions experienced declining ones, with only one exception. The mortality estimates indicate a consistent decline in the mortality level of all regions, but also a divergent trend between poor and developed regions, in life expectancies at birth. This work is a summarized version of Chapters II, III and IV of my Ph.D. thesis written under the supervision of Professor D. V. Glass and Mr J. Hobcraft at the University of London. I am most grateful to my supervisors as well as to Professor W. Brass for valuable comments on several aspects of the thesis. While carrying out this study, the author was supported by grants from the Federal University of Minas Gerais, Brazil, and the Ford Foundation.     

Child survivorship estimation: methods and data analysis

"The past 20 years have seen extensive elaboration, refinement, and application of the original Brass method for estimating infant and child mortality from child survivorship data. This experience has confirmed the overall usefulness of the methods beyond question, but it has also shown that...estimates must be analyzed in relation to other relevant information before useful conclusions about the level and trend of mortality can be drawn.... This article aims to illustrate the importance of data analysis through a series of examples, including data for the Eastern Malaysian state of Sarawak, Mexico, Thailand, and Indonesia. Specific maneuvers include plotting completed parity distributions and 'time-plotting' mean numbers of children ever born from successive censuses. A substantive conclusion of general interest is that data for older women are not so widely defective as generally supposed."     

Parental survival data: Some results of the application of Ledermann's model life tables

Summary Ledermann's one- and two-parameter model life tables are used in order to summarize and compare adult mortality estimates derived from parental survival data, and also to link parental survival with child survival data. The Ledermann models provide an alternative to the logit model used by Brass and Hill. Examination of life tables derived from actual child and adult mortality estimates reveals that although the two types of models yield similar overall levels of mortality, they show marked differences in the estimated patterns by sex and age. It has not been possible to disentangle completely how much of this divergence is due to the models themselves and how much to inadequacies in the data available. Finally, we question whether it is always wise to establish a full life table from child and adult mortality estimates when these are based on data which refer to different periods of exposure to the risk of dying, without allowance for possible distortions resulting from mortality change.     

Multidimensional Life Table Estimation of the Total Fertility Rate and Its Components

Using discrete-time survival models of parity progression and illustrative data from the Philippines, this article develops a multivariate multidimensional life table of nuptiality and fertility, the dimensions of which are age, parity, and duration in parity. The measures calculated from this life table include total fertility rate (TRF), total marital fertility rate (TMFR), parity progression ratios (PPR), age-specific fertility rates, mean and median ages at first marriage, mean and median closed birth intervals, and mean and median ages at childbearing by child’s birth order and for all birth orders combined. These measures are referred to collectively as “TFR and its components.” Because the multidimensional life table is multivariate, all measures derived from it are also multivariate in the sense that they can be tabulated by categories or selected values of one socioeconomic variable while controlling for other socioeconomic variables. The methodology is applied to birth history data, in the form of actual birth histories from a fertility survey or reconstructed birth histories derived from a census or household survey. The methodology yields period estimates as well as cohort estimates of the aforementioned measures.     

Mortality in Ghana: Evidence from the cape coast project data

Abstract This paper deals with the estimation of mortality for a rural community of about 20,000 persons in the rain-forest area of south-west Ghana. Specifically, infant, child and adult mortality estimates have been obtained by the application of a wide range of direct and indirect methods of measuring mortality from the different statistics collected by a longitudinal mortality and fertility project conducted during 1974-7. It was noted that infant and childhood mortality rates obtained from death registrations were consistent with those rates yielded by pregnancy histories and child survival statistics. However, the adult mortality estimates derived from orphanhood statistics tended to be lower than those suggested by death registrations. The analysis revealed an infant mortality rate of 100 for boys and 84 for girls, equal childhood mortality rates for boys and girls (85-6), a lower expectation of life at birth for men (45.8 years) than for women (52.8), and a much more severe incidence of mortality among men aged over 40 than for women at the corresponding ages.     

Marriage and divorce in twentieth century American cohorts

Marital status life tables have provided a basis for describing the marriage, divorce, and mortality experience of U.S. cohorts born 1888-1950. In brief, marriage occurred earlier and became more universal from the earliest cohorts to those of the late 1930s. More recent cohorts show declines in the proportion ever marrying and increases in the mean age at marriage. Period data for 1980 and cumulative cohort data by age suggest the likelihood of a continuing retreat from first marriage. Divorce has been rising steadily, with the latest cohorts indicating that 46 percent of male marriages and 42 percent of female marriages will end in divorce. Period data for males in 1980 raise the possibility that levels of divorce may have reached a peak, but cumulative cohort data by age show no such pattern. The present results are consistent with the view that a fundamental change in the traditional concept of marriage is underway. Traditional marriage involved the husband providing the wife with economic support and protection in return for her companionship and maternal services. Strong social pressures urged men and women to marry, and made the coveted services married persons provided each other difficult to obtain elsewhere. Recent economic changes have undermined the social and economic forces that maintained the institution of marriage. The U.S. economy has grown to include a large service sector in its labor force, and that growth has produced a dramatic increase in female labor force opportunities (Oppenheimer, 1970). The resultant large scale participation of women in economic activity blurs the traditional division of labor by sex, and goes to the very heart of the traditional marriage "bargain." At the same time, economic changes have weakened family ties by encouraging lower fertility, stressing achieved as opposed to ascribed characteristics, and fostering geographical mobility (Goode, 1970). The "marital union" of the past may be giving way to the "marital partnership" of the future, which will accommodate informal as well as formal marriages, less dependence between spouses, greater egalitarianism, lower fertility, and higher levels of divorce.     

Estimating the completeness of reporting of adult deaths in populations that are approximately stable

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.     

Marriage markets and nonmarital fertility in the United States

We merge census microdata with vital statistics data to examine the effect of women's marriage opportunities on nonmarital fertility rates and ratios across 75 U.S. metropolitan areas. Measures of the quantity and "quality" of marriageable men simultaneously specific for women's age, race, education, and place of residence reveal especially poor marriage prospects for highly educated black women. The effect of mate availability on nonmarital fertility is generally modest. Among white women, marriage opportunities are associated inversely with the nonmarital fertility rate, perhaps reflecting an increased likelihood that a premarital conception will be legitimated. Marriage opportunities also reduce nonmarital fertility ratios for young black and white women. The nonmarital fertility rate is lower among women whose marriage pool includes a large percentage of nonemployed males. Only a small proportion of the racial difference in nonmarital fertility appears attributable to differences in the marriage markets of black and of white women.     

The sources of error in Brass's method for estimating child survival: the case of Bangladesh

Abstract Brass's method for estimating child mortality is based on an ingeniously simplified model. However, it frequently leads to values of q(x) that are not consistent with each other. This is most obvious for estimates of q(1). This paper examines the extent to which such inconsistencies are caused by simplifications in the model. Three assumptions are relaxed by adjusting for differences in infant mortality by birth order, taking account of annual fluctuations in mortality, and using a different age pattern of fertility for each cohort. These adjustments are applied to data from the 1974 Bangladesh Retrospective Survey of Fertility and Mortality and the 1975 Bangladesh Fertility Survey in which additional data from the Cholera Research Laboratory are used. The resulting estimates are more consistent both internally and with estimates from other surveys and by other procedures.     

Census-derived estimates of fertility by duration since first marriage in the Republic of Korea

This paper estimates ever-married birth rates by age and duration since first marriage and ever-married total fertility rates for the Republic of Korea, derived by applying an extension of the own-children method of fertility estimation to the 1975 and 1980 censuses. Since each census provides annual estimates for the 15-year period previous to enumeration, there is a ten-year period of overlapping estimates that facilitates checks for consistency and accuracy. Comparisons are also made with estimates derived from the 1974 Korea National Fertility Survey, which was part of the World Fertility Survey. The method works well, except in its application to the 1975 Census where the evidence suggests considerable misreporting of age at first marriage because of the way the question was asked and coded. Results confirm that ever-married fertility fell substantially in Korea between 1961 and 1980, with a temporary resurgence in the late 1960s and early 1970s. Ever-married fertility rose at younger ages and shorter durations and fell at older ages and longer durations. Ever-married fertility differentials by urban-rural residence and by education were usually in the expected direction, with urban fertility generally lower than rural fertility and the fertility of those with more education usually lower than the fertility of those with less education. Differential ever-married fertility by urban-rural residence and education declined over the estimation period.     

关于中国1990年代低生育水平的再讨论

本文根据全国第五次人口普查样本计算了 1 990年代各年份的分性别平均初婚年龄 ,这一结果再次表明这一时期中初婚年龄有显著提高。本文还根据以往历次调查的各年份年龄别生育率按队列计算了累计生育率 ,结果发现 2 0 0 0年时各队列的累计生育率水平高于五普数据中各队列的平均活产子女数。本文还就队列累计生育率计算结果详细分析了 1 990年代终身生育水平的趋势。这些分析从一个新的角度说明 ,1 990年代各队列的终身生育水平也在发生显著的下降 ,正在接近现行生育政策所要求的水平     

Demographic aspects of fertility in Thailand

Abstract Data from a national rural and urban sample survey are analysed in order to examine various demographic aspects of fertility in Thailand. Marital fertility rates found for Thailand are among the highest in Asia. Particularly noteworthy is the persistence of high fertility at older ages of childbearing for rural women. Cumulative fertility shows a pronounced relationship with age at marriage and current marital status. Women who marry at an older age or who experience disruption of their marriages are clearly more likely to have fewer children ever born. Differences in both current and cumulative fertility are strongly associated with residence. Rural women who constitute the vast majority of Thai women, experience the highest fertility, Bangkok-Thonburi women experience the lowest fertility and provincial urban women are characterized by an intermediate fertility level which is closer, however, to the experience of their counterparts in the capital than in the countryside. Rural-urban fertility differences are mitigated but by no means eliminated by differences in infant mortality. In both rural and urban areas a positive association between cumulative fertility and infant morality is evident. Breast-feeding, commonly practised for extended periods-among both rural and urban Thai women, undoubtedly serves to some extent as an intervening variable in this relationship. A comparison of current fertility with cumulative fertility strongly suggests that a decline in marital fertility has been under way recently among urban women, especially those residing in the capital, but not at all among rural women. Although it seems safe to assume that the urban fertility decline results in large part from an increasing use of contraception among urban women, those still in the reproductive ages who were using or had previously used birth control were characterized by higher cumulative fertility than women who had never practised contraception. Evidently couples resort to family planning only late in the family building process after they have already achieved or exceeded the number of children they wish to have.     

Mortality in Ghana: Evidence from the cape coast project data

This paper deals with the estimation of mortality for a rural community of about 20,000 persons in the rain-forest area of south-west Ghana. Specifically, infant, child and adult mortality estimates have been obtained by the application of a wide range of direct and indirect methods of measuring mortality from the different statistics collected by a longitudinal mortality and fertility project conducted during 1974–7. It was noted that infant and childhood mortality rates obtained from death registrations were consistent with those rates yielded by pregnancy histories and child survival statistics. However, the adult mortality estimates derived from orphanhood statistics tended to be lower than those suggested by death registrations. The analysis revealed an infant mortality rate of 100 for boys and 84 for girls, equal childhood mortality rates for boys and girls (85–6), a lower expectation of life at birth for men (45.8 years) than for women (52.8), and a much more severe incidence of mortality among men aged over 40 than for women at the corresponding ages.