A new technique to estimate infant mortality with an application for El Salvador and Colombia

The paper presents new estimates of infant mortality for Colombia and El Salvador for the years 1950--1970. These estimates are obtained by using a technique which improves on Brass's method in that it suppresses the assumption of constant mortality and introduces instead assumptions about linear and nonlinear changes in mortality risks affecting various cohorts of individuals.     

A modification for use in destabilized populations of brass's technique for estimating completeness of death registration

Summary Brass has developed a method of estimating completeness of death registration using only data on deaths and population by age and sex. In this paper, his method is briefly outlined and the assumptions upon which it is based are discussed. In particular, the implications of the failure of the assumption of stability of the population are investigated. It is found that in populations where mortality has been declining, use of the technique leads to underestimation of completeness. A modification of the technique based on knowledge of the duration and rate of mortality change is proposed for use in such populations. Using simulated destabilized populations, the modification is tested and found to yield more accurate estimates of completeness of death registration than the unmodified technique. The usefulness of the modified technique is further illustrated by applying it to data for Costa Rican females in 1963.     

Are Cohort Mortality Rates Autocorrelated?

In this paper the author examines the proposition that heterogeneity in individual frailty leads to autocorrelation in cohort mortality rates. A simple model is used to construct analytic expressions for the covariance of cohort mortality rates at different ages under a number of alternative assumptions about the stochastic process generating shocks in mortality. The model then is used to construct a procedure that uses correlations in cohort mortality rates to estimate the extent of heterogeneity in a population without relying on strong assumptions about the distribution of frailty or the shape of the underlying hazard. The procedure then is used to show that cohort mortality data from France are consistent with a generalized random-effects model in which frailty is gamma-distributed.     

Contribution of mortality decline to longer working life: The case of indonesian males 1980–1995

The length of working life of Indonesian males has been estimated for 1980 and 1995. Data on age specific labour force participation rates are obtained from the 1980 census and the 1995 intercensal population survey. Data on agespecific mortality have been adopted from appropriate model life tables based on indirect estimates of child mortality in the absence of any direct information about mortality. The contribution of declining mortality to the lengthening of working life has been greater than the contribution of higher labour force participation rates. Reductions in mortality at ages before entry into the labour force have increased the potential for added and improved education and training needed for the work force, which is also a contribution of reduced mortality to human capital development. The findings have implications for policy and future employment plans.     

Evaluation of estimates of underenumeration in the census and the age pattern of mortality,philadelphia, 1880

The schedule of mortality by age for Philadelphia's 1880 population classified by sex and race showed aberrations from Coale and Demeny West, South, and North model life tables. Deviations from standard age patterns of mortality were especially pronounced for the black population. The question addressed in this paper is whether the alternative age patterns of mortality are produced by underenumeration in the 1880 census or by actual variations in the age-specific mortality experience. The conclusion was reached that the underenumeration of the urban population, especially the blacks, exceeds estimates for the national population. In addition, the results indicated that the black population faced risks of dying that genuinely differed from standard age patterns. An attempt to use a Brass logit model to generalize the black mortality experience met with success for females but not for males.     

Estimation of Exposure Time Distributions

In many demographic analyses, such as the assessment of environmental cancer risks, one may be interested not only in the age-by-state distribution of the population but also in the distribution of the population by time spent in a given state. States can represent geographic areas, marital statuses, labor force participation, or states of epidemiologic exposure. Recursive formulas for the calculation of the distribution of the population according to exposure time are derived under time-invariant state transition rates. Although populations can have identical growth rates and identical age-by-state distributions, they can have very different distributions by exposure time. An application to the analysis of carcinogenic exposure states is given, using data from Finland. The effect of population heterogeneity on the estimated exposure time distributions is studied.     

Constructing fertility tables for Soviet populations

Because the 1970 Soviet Union census does not provide information on the age structure of men and women separately by sex and according to their ethnic affiliation, the 1959 USSR census data serve as the basis to infer knowledge about ethnic fertility. The model takes into account (1) the total number of births in 1960, estimated from the child-woman ratio in 1959, (2) the age structure of women in 1959, and (3) the assumed pattern of age-specific birth rates structured in terms of the modal age at childbearing and the length of the fertility age span. The results show that Ukrainians among the Slav populations ranked as the lowest with 2.07 children born per woman. Their total fertility contrasts with that of Kazakhs native to Central Asia, who reportedly according to Soviet sources had 7.46 children per woman in 1958-1959, and whose estimated rate is around 8.59 children. Extreme variations appear in the estimates of fertility among nationalities of the Caucasus region, Volga Basin, and to a lesser degree in Siberia. Official Soviet calculations of crude birth rates and age-specific rates for 15 Union Republics in 1967-1968 are transcribed and compared with the estimates for nationalities in 1959-1960. The same theoretical model used to generate the Soviet rates may be adapted under different assumptions to non-Soviet populations in other situations where the data are scanty or incomplete.     

Consistent correction of data for aboriginal populations

A consistent correction procedure is used to determine improved, consistent estimates by sex of census age distributions, intercensal births, intercensal deaths and net migration by age for the Aboriginal populations of the Northern Territory, South Australia and Western Australia during the period 1986–91. Undercount estimates and life tables show the Aboriginal populations to have lower coverage in statistical collections and much higher death risks than the total Australian population. Inter-regional net migration estimates show that component of change can no longer be ignored.     

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.     

Estimating census and death registration completeness

This article presents a new method for estimating the relative completeness of 2 census enumerations and of intercensal registered deaths. The Growth Balance Equation was developed by Brass (1975) to estimate the completeness of death registration relative to the completeness of census enumeration. The method presented here can be seen either as an extension of Martin's formulation to allow explicitly for changes in census coverage or as a modification of Brass's method to use deaths by age group rather than deaths by cohort, preferable on the grounds that age group comparisons will be less distorted by age misreporting than cohort comparisons if the patterns of age misreporting are similar for 2 successive censuses. This simple method estimates simultaneously the relative coverage of the 2 censuses and the completeness of registration of intercensal deaths. The key assumptions of the method are that the population is closed to migration and that all the coverage factors involved are invariant with age, at least for the age range studied. Analysis of the sensitivity of the estimates to the assumptions and further work on extending the method to open populations would be useful.     

Mortality estimation from registered deaths in less developed countries

Age-specific population growth rates were introduced to demographic analysis in earlier work by Bennett and Horiuchi (1981) and Preston and Coale (1982). In this paper, we derive a method which uses these growth rates to transform what may be a set of incompletely recorded deaths by age into a life table that accurately reflects the true mortality experience of the population under study. The method does not rely on the assumption of stability and, for example, in contrast to intercensal cohort survival techniques, is simple to implement when presented with nontraditional intercensal interval lengths. Thus we can obtain mortality estimates for less developed countries with defective data, despite departures from stability. Further, we assess the sensitivity of the method to violations in various assumptions underlying the procedure: error in estimated growth rates, existence of non-zero net intercensal migration, age dependence in the completeness of death registration, and misreporting of age at death and age in the population. We demonstrate the use of the method in an application to data referring to Argentine females during the period 1960 to 1970.     

Stationary and stable population]

The properties of stationary and stable population models are discussed. In particular, the changes in population size and age structure that will occur under assumptions of constant fertility and mortality rates and no migration are explored.     

A close look at the demography of Afghanistan

The first survey designed to allow estimates of the demographic characteristics of Afghanistan's sedentary population was conducted during the period 1972-1974. Our analysis of these data, based on recently developed techniques for handling imcomplete or inaccurate data, suggests that this population lives under conditions that are extreme when judged by modern standards. Marriage is early, especially for females, and universal. Marital fertility conforms to a pattern of natural fertility and total fertility is high. The birth rate is among the highest in the world today, and the expectation of life at birth is among the very lowest. Mortality is lower in urban areas than in rural areas, whereas total fertility is approximately the same in both. Our estimates of fertility and mortality imply stable populations which match closely the observed age distributions for both the rural and urban areas.     

Data quality and accuracy of United Nations population projections, 1950-95

Between 1951 and 1998, the United Nations (UN) published 16 sets of population projections for the world, its major regions, and countries. This paper reports the accuracy of the projection results. I analyse the quality of the historical data used for the base populations of the projections, and for extrapolating fertility and mortality. I study also the impact this quality has had on the accuracy of the projection results. Results and assumptions for the sets of projections are compared with corresponding estimates from the UN 1998 Revision for total fertility and life expectancy at birth, total population, and the projected age structures. The report covers seven major regions (Africa, Asia, the former USSR, Europe, Northern America, Latin America, and Oceania) and the largest ten countries of the world as of 1998 (China, India, the USA, Indonesia, Brazil, Pakistan, Russia, Japan, Bangladesh, and Nigeria).     

A Turning Point in Gender Bias in Mortality? An Update on the Number of Missing Women

Amartya Sen started a debate about gender bias in mortality by estimating the number of “missing women,” which refers to the number of females of any age who have presumably died as a result of discriminatory treatment. Depending on the assumptions made, the combined estimates for countries exhibiting the presence of such gender bias varied between 60 and 107 million. As new population data have become available for these countries, this article examines whether the number of “missing women” has changed in the past decade. The combined estimate of the number of missing women has risen in absolute terms but has fallen slightly in relation to overall population. Considerable improvement is evident in West Asia, North Africa, and parts of South Asia, while only small improvements have occurred in India and a deterioration took place in China. Analyses of the underlying causes of gender bias in mortality suggest that improvements are largely related to improved female education and employment opportunities and rising overall incomes, while deterioration is mostly attributable to the rising incidence of sex‐selective abortions.     

A flexible two-dimensional mortality model for use in indirect estimation

Mortality estimates for many populations are derived using model life tables, which describe typical age patterns of human mortality. We propose a new system of model life tables as a means of improving the quality and transparency of such estimates. A flexible two-dimensional model was fitted to a collection of life tables from the Human Mortality Database. The model can be used to estimate full life tables given one or two pieces of information: child mortality only, or child and adult mortality. Using life tables from a variety of sources, we have compared the performance of new and old methods. The new model outperforms the Coale-Demeny and UN model life tables. Estimation errors are similar to those produced by the modified Brass logit procedure. The proposed model is better suited to the practical needs of mortality estimation, since both input parameters are continuous yet the second one is optional.     

Estimates of coverage of the population by sex,race, and age in the 1970 census

Several estimates of total net underenumeration and of net census errors by sex, race (white, Negro-and-other-races, Negro), and age (five-year groups) in the 1960 and 1970 Censuses, for the total population of the United States, derived by the methods of demographic analysis, are presented. The different data, procedures, and assumptions employed in developing the various estimates are described briefly, and the findings are then discussed in terms of a”preferred” set of estimates. The preferred set of estimates of corrected population for 1970 combines estimates for persons under age 35 based directly on birth, death, and migration statistics, estimates for females aged 35 to 64 based on the Coale-Zelnik estimates (white) for 1950 or the Coale-Rives estimates (Negro) for 1960, estimates for males aged 35 to 64 based on the use of expected sex ratios, and estimates for the population 65 and over based on”Medicare” enrollments and expected sex ratios. These estimates indicate an overall net underenumeration of 5.3 million persons or 2.5 percent in 1970, as compared with 5.1 million or 2.7 percent in 1960, and a net underenumeration of 1.9 percent for whites and of 7.7 percent for Negroes in 1970, as compared with 2.0 percent and 8.0 percent, respectively, in 1960. As in 1960, undercoverage in 1970 was greatest for Negro males (9.9 percent); net error rates exceeded 12 percent in each age group 20 to 49 and reached 17 to 19 percent at ages 25 to 44. All sex-race groups showed marked increases between 1960 and 1970 for children under ten and marked declines at ages ten to 24. Equally reliable estimates of population coverage cannot be prepared for states and smaller geographic units or for the population of Spanish ancestry.     

Unobserved Heterogeneity Can Confound the Effect of Education on Mortality

Two opposing hypotheses were proposed to explain the life course pattern in the effect of education on mortality: “cumulative advantage,” where the education effect becomes stronger with age, and “age-as-leveler,” where the effect becomes weaker in old age. Most empirical studies bring evidence for the latter hypothesis, but the observed convergence of mortality patterns could be an artifact of selective mortality due to unobserved heterogeneity. A simulation shows that unobserved heterogeneity can bias the estimated effect of education downward so that the cohort-average effect of education decreases in old age regardless of the shape of the underlying subject-specific trajectory.     

Significance and effect of the population census]

A summary of topics on which the Chinese government is seeking further information through the 1982 census is provided. Topics to be covered include total population; fertility, mortality, and growth rates; urban and rural population distribution; population projections, including age, sex, and marital status characteristics; labor force size; and minority population estimates.