Mortality in Vietnam, 1979–1989

Little is known about past and present mortality in Vietnam, as the first official data on mortality have only recently become available from censuses taken in 1979 and 1989. Using these data, I estimate Vietnamese mortality during the intercensal period using two techniques that rely on age-specific growth rates from two successive age distributions. Intercensal emigration and differential completeness of census enumeration associated with massive outflows of refugees in the wake of the Vietnam War; population-redistribution policies, and a highly mobile population represent important sources of bias for the estimation of intercensal mortality. I incorporate several strategies to minimize bias from these sources and to select the method that is least sensitive to errors associated with them. Life expectancy at birth estimated for the 1979–1989 intercensal period is 61.4 years for males and 63.2 for females. These results suggest a trend of declining mortality between the 1970s and the 1980s and add solid empirical evidence to the debate over whether mortality in Vietnam has been deteriorating or improving.     

Estimating African-American mortality from inaccurate data

This paper evaluates the quality of vital statistics and census data for estimating African-American mortality over a period of six decades. The authors employ intercensal cohort comparisons and extinct generation estimates to demonstrate that conventionally constructed African-American death rates may be seriously flawed as early as age 50. Using the crude death rate at ages 50+ for 1978-1982 in conjunction with estimated growth rates and two model life table systems, the authors estimate black age-specific death rates in 1978–1982. These results suggest that if a racial crossover in death rates occurs, the age pattern of mortality among African-Americans must be far outside the range observed in populations with more accurate data.     

Examination of the generalized age distribution

The formula for the age distribution and other relationships that follow from it for any (non-stable) population presented by Preston and Coale are significant contributions to demography. The formulas summarize the relationships among various demographic measures precisely, and are formally analogous to the relationships that hold for stable populations. The significance of these formulas cannot be overstated; they allow us to understand clearly the relationships among demographic measures in any arbitrary population. However, when it comes to using them for estimating demographic measures when census data are defective, the method of estimation is still affected by defective data. The reason is that the series of age-specific growth rates reflects the observed census age distributions exactly so that any defects in the census data are summarized in the growth rates. This paper begins with the formulation of the discrete version of the "new synthesis" developed by Preston and Coale. With the discrete formulation, the three kinds of errors introduced when the continuous time formulas are applied to real data can be avoided. Then it is pointed out that when two accurate census data are available, the Preston-Coale procedure of "estimating" the age distribution at the second census is equivalent to checking the identity of the age distribution formula. Also "estimating" mortality by the procedure of Preston-Coale is shown to be equivalent to obtaining mortality directly from intercensal survival rates. That the procedure which involves the age-specific growth rates is equivalent to those that involve the intercensal survival rates may have escaped notice because there are no a priori constraints for patterns of age-specific growth rates to follow. The irregularity in growth rates due to defective data are not distinguishable from true irregularity that exists in the population, contrary to the well-known regularity in the pattern of survival rates in human populations.     

Calculation of age-specific fertility schedules from tabulations of parity in two censuses

The mathematics of stable populations recently has been generalized to cover populations with time-varying fertility and mortality by a modification incorporating the sum of age-varying growth rates in place of the fixed growth rate of a stable population. Equations that characterize nonstable populations apply to any cohort-like phenomenon with a measurable property that cumulates gains or losses through time. In particular, the equations fit the relation between a population's average parity at a given age and age-specific fertility rates previously experienced at lower ages. Techniques devised to derive an intercensal life table from single-year age distributions in two censuses are adapted to estimate accurate intercensal fertility schedules from distributions of parity by age of woman in two censuses. Birth-order specific fertility schedules are also estimated.     

Estimating the completeness of death registration

Summary Death registration statistics, even when incomplete, can provide valuable information about mortality. In particular, the age structure of deaths can be used to estimate the completeness of registration, provided that this completeness does not vary substantially with age. Two methods of estimating the completeness of death registration from the distribution of deaths by age are described. The first is derived from stable population theory and requires an estimate of the rate of natural increase of the population, as well as assuming stability. However, the technique can also be used to generate simultaneously estimates of the rate of natural increase and of death registration completeness. The second method which requires two census age distributions and intercensal deaths by age, estimates the relative enumeration completeness of the two censuses as well as the completeness of death registration and requires only that the population be closed. Results are sensitive to overstatement of age. The methods are illustrated by being applied to figures from Thailand for the period 1960-70 and are found to work satisfactorily.     

A reply to Kim's comment

This reply criticizes Kim's note as incorrectly characterizing the essential feature of the method proposed for life table construction. The method suggested for estimating N(a), the number attaining age 2 during the intercensal period, is to make a separate estimate of the contribution to N (a) made by each single-year cohort that attains 'a' during the period between censuses. Each cohort estimate is constructed by interpolation, utilizing as data the recorded number in the relevant single-year cohorts in the 2 censuses. 2 methods of interpolation were proposed. 1 is an iterative procedure that constructs a preliminary life table by linear interpolation for each cohort and then derives more refined interpolation factors from this preliminary life table. The other procedure derives interpolation factors on the assumption that the proportionate distribution of deaths by age as each cohort moves from the earlier to the later census date is the same as the proportionate distribution of deaths by age over the same age range in a model life table. The advantage of the proposed procedure is that it supplies better estimates of N (a) than do alternative methods. The author concedes that a life table calculated from accurately recorded deaths and an accurately enumerated population would ordinarily be superior. However, he also notes that in the absence of registered deaths data, there is no precise enough conventional method to yield accurate values of average intercensal single-year age-specific mortality rates from nothing more than 2 accurate censuses 11 years apart. A common procedure for calculating life expectation at a very advanced age is to calculate the reciprocal of the death rate among persons over the age in question.     

Methods of adjusting the stable estimates of fertility for the effects of mortality decline

Summary The paper shows how stable population methods, based on the age structure and the rate of increase, may be used to estimate the demographic measures of a quasi-stable population. After a discussion of known methods for adjusting the stable estimates to allow for the effects of mortality decline two new methods are presented, the application of which requires less information. The first method does not need any supplementary information, and the second method requires an estimate of the difference between the last two five-year intercensal rates of increase, i.e. five times the annual change of the rate of increase during the last ten years. For these new methods we do not need to know the onset year of mortality decline as in the Coale-Demeny method, or a long series of rates of increase as in Zachariah's method.     

Estimating intercensal age schedules by intracohort interpolation

"This paper describes a procedure for estimating intercensal age schedules of rates of occurrence of demographic events (birth, death, marriage) from tabulations at two points in time of a status of the population (average children ever born, persons surviving, proportion ever married) classified by age." The procedure is called iterative intracohort interpolation. The paper describes a more general version than that originally developed by Ansley J. Coale and provides a probabilistic interpretation of the age-specific rates estimated by the procedure.     

Estimation of interregional migration streams from place-of-birth-by-residence data

Place-of-birth-by-residence data, tabulated by age and sex for the same areal units in two successive censuses, have been used to estimate intercensal net migration flows. However, a fuller use of the same data permits the estimation of place-to-place flows. This paper describes a method for estimating intercensal migration streams from place-of-birth-by-residence data and illustrates its application with data on the white female native population of the United States.     

New estimates of the vital rates of the United States black population during the nineteenth century

The difficulties of obtaining credible estimates of vital rates for the black population throughout the entire nineteenth century are overcome in this study. The methodology employed the notion of deviating networks of mortality rates for each general mortality level, which was taken from the United Nations studyThe Concept of a Stable Population. Period life tables and vital rates for intercensal periods were generated from the new estimates of the black population at each census date. The results of this study are highly compatible both with the life tables for the death-registration states in the twentieth century and the recent Coale and Rives reconstruction for the period from 1880 to 1970 and with several estimates of vital rates previously made for the mid-nineteenth century. This study places the mean life expectancy at birth for the black population during the nineteenth century at about 33.7 years for both sexes. The infant death rate (1000m (0)) is shown to have varied between 222 and 237 for females and between 266 and 278 for males. The intrinsic crude death rate centered on 30.4 per thousand during the century, while the birth rate declined from 53.2 early in the century to about 43.8 at the end.     

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.     

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.     

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.     

Effect of mortality change on stable population parameters

The stable population model is used to establish formulas expressing the effects of mortality change on population growth rates, birth rates, and age composition. The change in the intrinsic growth rate is shown to be quite accurately approximated by the average decline in age-specific death rates between age zero and the mean age at childbearing in the stable population. This change is essentially independent of the initial level of fertility in the population. Changes in birth rates and age composition are shown to be simple functions of the age pattern of cumulative changes in mortality rates relative to an appropriately defined “neutral” standard.     

Migration between India and Pakistan, 1951–61

A critical evaluation of the available data on migration between India and Pakistan in the 1951-61 decade leads to the conclusion that there was a substantial net migration of Pakistan-born persons into India, but only a negligible net migration of India-born persons into Pakistan. Annual administrative statistics published by the Indian Government suggest an immigration from Pakistan of the order of 1.16 to 1.32 million. More importantly, birthplace data from the Indian censuses indicate a net intercensal immigration of Pakistan-born persons amounting to 1.19 to 1.34 million, depending on the assumed level of mortality. The Pakistani census data on the India-born show no net influx from India during 1951-61. Intercensal growth rates for the populations of different religious faiths in Pakistan are consistent with the estimates of net immigration into India. The migrants and the survivors of their progeny are estimated to represent a net gain of about 1.68 million by India and to account for no more than 2.2 per cent of the total population growth in India during 1951-61.     

A description of the extreme aged population based on improved medicare enrollment data

The mortality and size of the extreme aged population can be studied most accurately with Medicare enrollment data from the Social Security Administration's Master Beneficiary Record after certain types of questionable records are eliminated. With the improved data base we find that mortality rates at the very old ages are higher than published rates, we are more confident of the reality of the race crossover, and we can estimate the number of centenarians more accurately. Furthermore, a large matched-records study shows close agreement on age at death between the Master Beneficiary Record and the death certificate.     

Differences in mortality by marital status in Finland from 1976 to 2000: analyses of changes in marital-status distributions, socio-demographic and household composition, and cause of death

Being currently not married is more common today than 25 years ago. Over this period relative differences in mortality by marital status have increased in several countries, mainly as a result of a sharp decline in mortality among the married. Using Finnish census data linked with death certificates, we show that these increases are not explained by the non-married population becoming more marginalized in socio-economic status or household composition. However, the increases in marital-status differences in mortality from accidental, violent, and alcohol-related causes of death in the 30-64 age group indicate that changes in the health-related behaviour of the non-married population may play a role. The public-health burden associated with not being married has also grown. At the end of the 1990s about 15 per cent of all deaths above the age of 30 would not have occurred if the non-married population had had the same age-specific mortality rates as the married population.     

An integrated system for demographic estimation from two age distributions

This paper presents a simple method for estimating a birth rate and a level of mortality for an intercensal period. The birth rate is estimated from the intercept of a line fitted to data and the level of mortality from the slope of that line. The formula that is developed is based upon a recent generalization of stable population relations. An estimate of childhood mortality level is an optional but significant piece of additional input. An important by-product of the procedure is an estimate of the true age distribution.     

Separating the Signal From the Noise: Evidence for Deceleration in Old-Age Death Rates

Widespread population aging has made it critical to understand death rates at old ages. However, studying mortality at old ages is challenging because the data are sparse: numbers of survivors and deaths get smaller and smaller with age. I show how to address this challenge by using principled model selection techniques to empirically evaluate theoretical mortality models. I test nine models of old-age death rates by fitting them to 360 high-quality data sets on cohort mortality after age 80. Models that allow for the possibility of decelerating death rates tend to fit better than models that assume exponentially increasing death rates. No single model is capable of universally explaining observed old-age mortality patterns, but the log-quadratic model most consistently predicts well. Patterns of model fit differ by country and sex. I discuss possible mechanisms, including sample size, period effects, and regional or cultural factors that may be important keys to understanding patterns of old-age mortality. I introduce mortfit, a freely available R package that enables researchers to extend the analysis to other models, age ranges, and data sources.     

A method for deriving mortality estimates from incomplete vital Statistics

Summary Although they are available in many developing countries vital registration records are very little used for mortality estimation which is still mainly based on census returns. However, defective death records may yield accurate estimations of mortality. This procedure requires few data only; a sex-age distribution of the population (preferably at the middle of a period) and a sexage distribution of deaths, either derived from vital records or from census returns to questions relating to deaths during the preceding twelve months. This method is based on the observation that for a fixed age structure of the population, there is a one-one relation between the age structure of deaths (measured by the proportion of deaths at older ages) and the level of mortality (measured by the death rate above a certain minimum age). It is assumed that at ages above this minimum the rate of underregistration of deaths does not vary significantly with age. Therefore, the age distribution of registered deaths makes it possible to estimate the true proportion of deaths at older ages. This in its turn will permit the estimation of the true level of mortality, because of the relation which exists between age structure of deaths and level of mortality. The true level is then compared with the observed, to estimate the rate of underregistration, and observed age-specific death rates can be adjusted in the light of this knowledge.