A simple equation for estimating the expectation of life at old ages

Abstract There is much direct and indirect evidence that in a number of populations the ages of older persons tend to be exaggerated, both when reported in censuses and in records of deaths. This results in overestimated expectations of life at old ages. The bias may be corrected by estimating the expectation of life at age a, e(a), from the mortality rate and growth rate at age a and above, M(a+) and r(a+), using the equation developed in this paper: 1/ê(a) = M(a+) exp (β . r(a+). M(a+)(-α)). For a ?, 65, α = 1.4 and β = 0.0951 have been chosen. The value of the equation rests on the following: since ages of older persons tend to be exaggerated, there may be an age a such that most age transfer occurs above that age, and age transfer across the age is small or cancels, so that reasonably accurate values of M(a+) and r(a +) can be obtained, even though ages are badly reported above a. The analysis of artificial data on Gompertzian stable popultions aged over 50 and actual statistics for some selected populations has suggested that the equation provides quite accurate estimates of e(a). The equation also seems useful in closing life tables, since it provides a value of e(a) for the highest age group.     

Three dimensions of the survival curve: horizontalization,verticalization, and longevity extension

Three dimensions of the survival curve have been developed: (1) "horizontalization," which corresponds to how long a cohort and how many survivors can live before aging-related deaths significantly decrease the proportion of survivors; (2) "verticalization," which corresponds to how concentrated aging-related ("normal") deaths are around the modal age at death (M); and (3) "longevity extension," which corresponds to how far the highest normal life durations can exceed M. Our study shows that the degree of horizontalization increased relatively less than the degree of verticalization in Hong Kong from 1976 to 2001. After age normalization, the highest normal life durations moved closer to M, implying that the increase in human longevity is meeting some resistance.     

United States population estimates and components of change: 1970 to 1987

This report analyzes year-to-year change in the US population from 1970 to 1987, including natural increase and net civilian immigration. Data are drawn from Current Population Reports. 1) The January 1, 1988 total population including Armed Forces overseas was over 245 million. This reflects a .9% increase over January 1, 1987, and an increase of 18 million since the April 1, 1980 census. 2) In the beginning of 1988, Whites numbered 206,979 million, Blacks 30,083, and Blacks and other races 38,130. 3) The crude birth rate dipped from 15.9 in 1980 to 15.6 in 1987; there is no evidence of a consistent trend since 1980. 4) The 3.8 million births in 1987 reflect a continuation of the gradual increase births that has been occurring since the mid-1970s, an increase attributed to Baby Boomers. 5) There was an 8.7/1000 death rate in 1987. This rate has fluctuated in the 8.5-8.7/1000 range since 1977 after declining from 9.4/1000 in 1972. The 2.1 million deaths in 1987 continue the gradual increase that has occurred since the end of the 1940s. This increase is attributed to the growth in population and to the population's continued aging. 6) Net immigrants/1000 population dropped slightly to 2.5 in 1987, down from 2.7 in 1986 and 3.7 in 1980. 7) Rates of growth for both Blacks and Whites have declined substantially since 1960; Blacks declined by about 1/3 (from 2.2%) and Whites by more than 1/2 (from 1.5%). The population of other races increased by 4.5% in 1987. The Black population grew by 1.5% in 1987, compared with a growth of .7% for the White population.     

Examining cross-state variation in the increase in father-only families

Each state has the power to establish its own policy and laws relating to child custody determination. The number of single-parent families with children that are headed by fathers has been growing in the United States. This paper explores the extent of cross-state variation in the prevalence in father-only families in 1990, and the extent to which there was cross-state variation in the increase in father-only families in the 1980s. The 1980 and 1990 Public Use Microdata Samples (PUMS) drawn from the US decennial censuses are used. Decomposition analyses of growth indicate that increases in the number of father-only families occurred across all states during this period, but at varying rates. The primary reason for the increase in most states is an increase in the proportion of ever-married single-parent families that are headed by a father. It is for these families that are headed by divorced or separated parents that state policy relating to child custody determination is most relevant.     

A survey on the sex ratio at birth in Beijing]

A survey was conducted on the sex ratio at birth in Beijing for the period between 1964 and 1982. In the 1960s, birth control ideas and plans were first introduced. In the 1970s, birth control measures were gradually taken to curb the population growth. In the 1980s, the policy of 1 child for each married couple was adopted and put into practice. Although the birthrate is being maintained at a low level, the number of childbearing age women has increased, and the birthrate has shown some increase. Statistics show almost equality in the sex at birth, but the number of newborn boys is slightly higher than that of newborn girls. Under the influence of Chinese tradition, a great many people in the countryside still prefer to have boys rather than girls, and they might have reported fewer newborn girls than the actual number. The average sex ratio for the past 3 years has still been close to a balance. With the practice of 1 child for each family, the sex ratio has been maintained close to a balance. This overall situation is made possible because of the development in the quality of birth and eugenics and the improvement in health care.     

Demographic crisis: The impact of the Bangladesh civil war (1971) on births and deaths in a rural area of Bangladesh

Summary In Matlab Bazaar Thana the Cholera Research Laboratory has registered the births, deaths and migrations in a population of approximately 125,000 since 1966. Although this rural area was not the scene of any significant armed encounters, striking changes in birth and death rates were registered during and after the conflict. Birth rates did not change during the relatively brief period of the civil war, but a small decline was registered for one year after the war. Fertility rates which had been declining slightly and irregularly in the pre-war baseline period may have increased slightly during the war and fell substantially in all age groups in the year following the war. The crude death rate, which rose by 37 per cent during the war, was a very sensitive reflection of the administrative and economic problems. Overall infant mortality rose by only 15 per cent over pre-war levels because all of the increase was observed in the post-neo-natal component, which traditionally accounts for less than one-third of the total infant mortality in Bangladesh. Children and older adults accounted for the majority of excess deaths which were largely attributed to acute diarrhoeas and other gastro-intestinal causes. The death rate at ages 1-4 rose by 43 per cent and at ages 5-9 soared to 208 per cent above pre-war baseline rates. All increases in age-specific mortality rates fell to baseline levels during the year following the war, except the 5-9-year age group, in which rates continued to be high largely because of deaths due to dysentery.     

The influence of cohort effects on mortality trends in India

The inferences drawn from this study are as follows: The stagnation/ increase in mortality rates of adult ages in the recent years in India as well as for the major states may be attributed to food shortages and price hikes experienced in the country during 1960–74. In other words, all those who were adults during 1980s had experienced the crisis of hunger due to nonavailability of food as well as entitlement failure during their childhood. These persons would have had higher risk of dying in their life time and that may be one of the main reasons for the stagnation or increase in adult mortality in India and in most of the states. The findings of the study suggest that, the economic crisis experienced in India during the late eighties, may decrease the survival chances of those born during this period in their future life time. However, successful containment of increase in food prices during the period of crisis would be helpful in protecting the entitlement of vulnerable groups. The policy implication of the study is that it is essential to control the prices of food during the time of food shortages and or economic crisis and even in the period when food is available, measures should be undertaken to evolve efficient distribution system ensuring the supply of food to those vulnerable groups, who were unlucky to be born or were in infancy during the period of economic crisis. Thus, essentially this is a study in interaction of economic factors and demographic trends in an economy where large segments of the population are periodically subject to heightened food insecurities, compression of real wages and entitlement failures.     

Fertility decline in Taiwan: A study using parity progression ratios

Taiwan's decline in fertility is studied by using period parity progression ratios. Levels of marriage and motherhood are found to have been high and essentially constant though the late 1980s, suggesting that the decline has been due almost entirely to declines in second and higher order-births. Families with three or more children play an important role in maintaining the current level of fertility. The level of fertility would be even lower without these families. They contributed more than one-half child per woman to the total fertility rate during most of the 1980s. Total fertility rates computed from the period parity progression ratios indicate a substantially higher level of fertility than the conventional total fertility rate; they remained above or at replacement level through 1988. A formal demographic analysis suggests that the conventional total fertility rate has been depressed by shifts in age at childbearing.     

Africa's expanding population: old problems,new policies

Sub-Saharan Africa faces an historic challenge: to achieve economic and social progress while experiencing extraordinary population growth. With an estimated 1989 population of 512 million, the 42 countries of sub-Saharan Africa have the highest birth and death rates of any major world region. While death rates have fallen since the 1960s, persistently high birth rates yield annual growth rates above 3% in many countries. The United Nations projects that the region's population will increase 2.7 times by 2025--to 1.4 billion. Throughout the region, population has outstripped economic growth since the mid-1970s. In addition, many African countries are experiencing an epidemic of AIDS (Acquired Immunodeficiency Syndrome). The extent and demographic impact of the epidemic still are unknown, but disturbing social and political effects are already being felt. The region's population growth will slow only when African couples begin to have fewer children. The average number of children per woman ranges from 6 to 8 for most countries. The Africans' preference for large families is deeply rooted in the culture and fed by the perceived economic benefits they receive from their children. Economic stagnation during the 1980s prompted many national governments to recognize that rapid population growth was hindering their socioeconomic development. The political climate has shifted away from pronatalist or laissez-faire attitudes toward official policies to slow population growth. The policy formation process--detailed here for 4 countries (Zambia, Nigeria, Zaire, and Liberia)--is ponderous and beset with political and bureaucratic pitfalls, However, policy shifts in more and more countries combined with evidence of increased contraceptive use and fertility downturns in a few countries give some hope that the region's extraordinary population growth may have peaked and will start a descent. Whatever the case, the decade of the 1990s will be crucial for the future of sub-Saharan Africa.     

Fertility and replacement: Some alternative stochastic models and results for Brazil

The observed joint distribution of births and child deaths for a cohort of women at a given point in time depends on the number of children that would have been born had the family experienced no deaths, the number of child deaths experienced, and the proportion of these deaths that are replaced by a subsequent birth. In this paper we estimate the parameters of the assumed distributions of these three events using a minimum distance estimation model and data from the 1970 Brazilian census. The parameter estimates are shown to be similar to those obtained previously using a maximum likelihood estimation model. When the data are subdivided according to women's years of schooling, estimates of probability of a child death and mean and variance of children born if no deaths decrease while estimates of probability of replacement of a dead child increase as years of schooling increase.     

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.     

Long-term trends in the longevity of scientific elites: evidence from the British and the Russian academies of science

National science academies represent intellectual elites and vanguard groups in the achievement of longevity. We estimated life expectancy (LE) at age 50 of members of the British Royal Society (RS) for the years 1670-2007 and of members of the Russian Academy of Sciences (RAS) for the years 1750-2006. The longevity of academicians was higher than that of their corresponding national populations, with the gap widening from the 1950s. Since the 1980s, LE in the RS has been higher than the maximum LE among all high-income countries. In each period, LE in the RS was greater than in the RAS, although since the 1950s it has risen in parallel in the two academies. This steep increase shared by academicians in Britain and Russia suggests that general populations have the potential for a substantial increase in survival to high ages.     

Russian Mortality Crisis and the Quality of Vital Statistics

Mortality from ill-defined conditions in Russia has the fastest rate of increase compared to all other major causes of death. High proportion of deaths in this category is indicative for low quality of mortality statistics. This article examines the trends and possible causes of mortality from ill-defined conditions in Russia. During 1991–2005, mortality from ill-defined conditions in Russia increased in all age groups. The pace of increase was particularly high at working ages and the mean expected age at death from ill-defined conditions has shifted to younger ages, particularly for men. The analysis of individual medical death certificates issued in Kirov and Smolensk regions of Russia demonstrate that 89–100% of working-age deaths from ill-defined conditions correspond to human bodies found in a state of decomposition. Data from Smolensk region shows that over 60% of these decedents were unemployed. Temporal trends of mortality from ill-defined conditions and injuries of undetermined intent in Moscow city suggest that deaths from the latter cause were probably misclassified as ill-defined conditions. This practice can lead to underestimation of mortality from external causes. Growing number of socially isolated marginalized people in Russia and insufficient investigation of the circumstances of their death contribute to the observed trends in mortality from ill-defined conditions.     

Trends in Numbers and Mortality at High Ages in England and Wales

In the paper new estimates of the numbers of deaths and death rates at ages 80 and over in England and Wales are derived for the period 1911–90. These estimates were made by applying the methods of extinct generations and reverse survival to data on deaths in 1911–90, and pensioners in 1990. Estimates are given for individual years of age. It is found that death rates at these high ages have been falling, slowly, for the last 50 years. The paper also gives information on the highest ages at death which have been recorded and verified.     

The growth of families headed by women: 1950–1980

In recent decades, the number of families headed by women has increased dramatically. In this article, we use U.S. census data from 1950 to 1980 to consider the extent to which population growth, fertility change, decreased marriage, increased divorce, and increased household headship have contributed to the growth of female-headed families. For white women, the major source of growth during the 1960s and 1970s was an increase in the number of formerly married mothers due to increased divorce and decreased remarriage. There is a similar pattern for black women for the 1960-1970 period. During the 1970-1980 decade, however, the major source of growth for black women was an increase in the number of never-married mothers due to decreased marriage and increased fertility among nonmarried women.     

On the Far Eastern pattern of mortality

Since the early 1980s, it has been accepted widely that there is a Far Eastern pattern of mortality, a pattern characterized by excessively high death rates among older men relative to death rates among younger men and among women. It has been regarded as a unique regional mortality pattern, applying primarily to Far Eastern populations. A re-examination of the mortality data of some Far Eastern populations reveals that changes in both age patterns of and sex differentials in mortality have been widely observed. Further, mortality patterns similar to the so-called Far Eastern mortality model have been found in many other populations.     

On the Far Eastern pattern of mortality

Since the early 1980s, it has been accepted widely that there is a Far Eastern pattern of mortality, a pattern characterized by excessively high death rates among older men relative to death rates among younger men and among women. It has been regarded as a unique regional mortality pattern, applying primarily to Far Eastern populations. A re-examination of the mortality data of some Far Eastern populations reveals that changes in both age patterns of and sex differentials in mortality have been widely observed. Further, mortality patterns similar to the so-called Far Eastern mortality model have been found in many other populations.     

Natural Increase: A New Source of Population Growth in Emerging Hispanic Destinations in the United States

Updated US Census Bureau estimates and race/ethnic‐specific birth and death data for the post‐2000 period are used to highlight the increasing role of natural increase as an engine of population growth in emerging Hispanic destinations. Newly emerging Hispanic growth areas are distinguished from established and high‐growth areas from the 1990s. The findings document that recent Hispanic population gains have been generated increasingly by natural increase—the excess of Hispanic births over deaths. Hispanics accounted for 46 percent of the population gain and 53 percent of the natural increase in nonmetro America in 2000–2005. Yet, Hispanics represented only 5.4 percent of the nonmetro population in 2000. In metro areas, they accounted for 50 percent of the population gain and 47 percent of the natural increase, although they comprised only 14 percent of the metro population. Current trends suggest that the ascendancy of the US Hispanic population is likely to continue unabated, whether restrictive immigration legislation is enacted or not. The growth of the Hispanic population, caused increasingly by natural increase, has taken on a demographic momentum of its own.     

Rising Mortality in Hungary

Although Hungary is not alone in Eastern Europe in experiencing a rising death rate during recent years, this adverse development would seem to have progressed further there than in neighbouring socialist countries, with the possible exception of the Soviet Union. The Hungarian death rate has been rising since the mid-1960s in part because the population was ageing but, more significantly from the health point of view, because of a real increase in mortality among certain sections of the population. The age-specific death rates of males aged 15 and over were all higher in 1980 than in the mid-1960s, the increase being particularly marked for the age group 30–59; moreover, women aged 30–59 are also now beginning to display the same characteristic. In the paper the individual contributions of the various causes of death to these trends are examined and some of the factors that are thought to have enhanced the risk of dying are outlined.     

Continued Reductions in Mortality at Advanced Ages

Mortality data for 30 mostly developed countries available in the Kannisto–Thatcher Database on Old‐Age Mortality (KTDB) are drawn on to assess the pace of decline in death rates at ages 80 years and above. As of 2004 this database recorded 37 million persons at these ages, including 130,000 centenarians (more than double the number in 1990). For men, the probability of surviving from age 80 to age 90 has risen from 12 percent in 1950 to 26 percent in 2002; for women, the increase has been from 16 percent to 38 percent. In the lowest‐mortality country, Japan, life expectancy at age 80 in 2006 is estimated to be 6.5 years for men and 11.3 years for women. For selected countries, average annual percent declines in age‐specific death rates over the preceding ten years are calculated for single‐year age groups 80 to 99 and the years 1970 to 2004. The results are presented in Lexis maps showing the patterns of change in old‐age mortality by cohort and period, and separately for men and women. The trends are not favorable in all countries: for example, old‐age mortality in the United States has stagnated since 1980. But countries with exceptionally low mortality, like Japan and France, do not show a deceleration in death rate declines. It is argued that life expectancy at advanced ages may continue to increase at the same pace as in the past.