Increment–Decrement Life Table Estimates of Happy Life Expectancy for the U.S. Population

Using large nationally representative longitudinal data on changes in happiness and mortality and multivariate increment–decrement life tables, we assess length of quality life through cohort estimates of happy life expectancies. We examine population-based and status-based life expectancies in absolute term of years and relative term of proportions. We find that happy life expectancies exceed unhappy life expectancies in both absolute and relative terms for the overall population and population in each state of happiness at any given age. Being happy (as opposed to unhappy) at any age brings a longer life and more of the future life spent in happiness. We also examine social differentials in the estimates of happy life expectancy at each age by sex, race, and education. The educational gap in happy life expectancies is larger than the sex and race gaps. For the better educated, longer life consists of a longer happy life and shorter unhappy life in both years and proportions and regardless of happy or unhappy status at any given age.     

Relating Changes in Life Expectancy to Changes in Mortality

I address the problem of what can be said of changes in mortality rates, if one knows how life expectancies change. I note a general formula relating life expectancies in different ages to mortality and prove that if mortality changes over time following a proportional-hazard model, then there is a one-to-one correspondence between life expectancy at birth and mortality rates. Extensions and an application of these results to the analysis of mortality change are presented.     

On the decomposition of changes in expectation of life and differentials in life expectancy

The projection of mortality rates requires inter alia close examination of the mortality experience of a population over a long period of time and will usually also involve the analysis of mortality trends by cause of death. In two of the more important recent contributions, techniques were devised for explaining change in life expectancy in terms of mortality changes in particular age groups and by different causes of death. The approaches adopted by the authors differ, and the purpose of this article is to reconcile the two and tie the results in with those obtained by earlier writers. A new method for explaining the change in a life expectancy differential in terms of the observed changes in the mortality differentials and the observed change in overall mortality level is also described.     

A generalization of life expectancy which incorporates the age distribution of the population and its use in the measurement of the impact of mortality reduction

Two new families of indices measuring the gain in life expectancy resulting from reduction in mortality are introduced: the first looks at the impact of cause of death reduction from the perspective of the entire population; the second, at that segment of the population due to die of the cause. Special cases include both well-established measures and extensions that incorporate the age distribution of the population. A further generalization is introduced with the consideration of life expectancies that only give weight to years of life up to age 70. A number of inequalities are derived that relate cause-deleted life expectancies to their cause-reduced counterparts.     

European perspectives on healthy aging in women

Using data from the 1994 European Community Household Panel, we compare active life expectancy differentials at age 65 years between women and men in 12 European countries. We seek to explain the extent to which differences are a reflection of gender differentials in life expectancy at 65 years or reflect differences in active life expectancy earlier in life. Considerable variation in the gender differentials in both total and active life expectancies at age 65 years exist within Europe, with some countries experiencing 20% lower life expectancy at age 65 years for men compared to women. Some evidence was found to suggest that gender differentials in active life expectancy may continue from younger ages through to later life.     

Mortality in Poland in the period 1950-1990

"In this paper, crude, specific [mortality] rates as well as nonstandardized and standardized indices of regional mortality differentials are analysed [for Poland] for the period 1950-1990, in order to show mortality differentiation, its increase by age, sex, and place of residence. Taking into account cause specific death rates, the pattern of causes of deaths was found to be similar to that existing in the western countries, although the level of standardized mortality is higher in Poland. Values of calculated indices of regional mortality differentials point to significant differences in mortality by voivodship."     

Mortality in Quebec during the nineteenth century: from the state to the cities

The aim of this paper is to explore mortality in Quebec during the nineteenth century from a demographic perspective. During the nineteenth century, there was excess urban mortality in various countries; in order to identify such mortality differentials, we compared mortality indicators for the province of Quebec and then for the urban areas of Montreal and Quebec City. Using data from various studies, we produced life tables and compared life expectancies. We show that at different times during the nineteenth century, spatial variations in mortality levels across the province of Quebec and its urban areas were significant. According to the data we analyzed, mortality is undoubtedly higher in urban areas even though a convergence in trends took place towards the end of the century, resulting in an overall reduction in mortality. Also, exploring life expectancies within a cohort approach at times of fast-changing mortality patterns has proved to be instructive. Life expectancy estimates based on a cross-sectional approach were systematically lower than those resulting from a cohort-specific one. Trends diverged to a greater extent beginning with the 1870 cohort, reflecting the improvements made from that point on to World War II. Since current mortality levels are substantially determined by the cumulative effects of past behaviour specific to each generation, it is quite obvious that mortality analysis will reveal its true meaning only with the help of cohort life tables.     

European Perspectives on Healthy Aging in Women

SUMMARY

Using data from the 1994 European Community Household Panel, we compare active life expectancy differentials at age 65 years between women and men in 12 European countries. We seek to explain the extent to which differences are a reflection of gender differentials in life expectancy at 65 years or reflect differences in active life expectancy earlier in life. Considerable variation in the gender differentials in both total and active life expectancies at age 65 years exist within Europe, with some countries experiencing 20% lower life expectancy at age 65 years for men compared to women. Some evidence was found to suggest that gender differentials in active life expectancy may continue from younger ages through to later life.     

Future life expectancy in Australia,Europe, Japan and North America

Human life expectancy has risen in most developed countries over the last century, causing the observed demographic shifts. Babel, Bomsdorf and Schmidt (forthcoming) introduce a stochastic mortality model using panel data procedures which distinguishes between a common time effect and a common age effect of mortality evolvement. Using this mortality model, the present paper provides forecasts of future life expectancy for 17 countries divided into 12 regions: Australia, Alps, Bene, Canada, England and Wales, France, Germany, Italy, Japan, Spain, Scandinavia and the United States of America. We consider (traditional) period life expectancies as well as cohort life expectancies, the latter being a more realistic approach but less common. It turns out that a continuing increase of life expectancy is expected in all considered countries. Further, we show that the probabilistic uncertainty of forecast life expectancies is different if either period life expectancies or cohort life expectancies are considered and, moreover, the uncertainty increases substantially if the error of parameter estimation is included.     

Socioeconomic Determinants of White and Black Males’ Life Expectancy Differentials, 1980

Epidemiological transition theory suggests that two population existing under disparate socioeconomic conditions would have different life expectancies as the result of cause-of-death differences. The effect of racial socioeconomic differentials on the total racial life expectancy differential are examined as they act through specific cause-of-death differentials. Results suggest that residential isolation of blacks has a strong effect on the total life expectancy differential as it acts through the racial homicide differential. The racial unemployment difference also has a strong effect on the total differential as it acts through the racial heart disease differential. Implications of the findings for reducing life expectancy differentials are discussed.     

Time series analysis and stochastic forecasting: An econometric study of mortality and life expectancy

Methods for time series modeling of mortality and stochastic forecasting of life expectancies are explored, using Canadian data. Consideration is given first to alternative indexes of aggregate mortality. Age-sex group system models are then estimated. Issues in the forecasting of life expectancies are discussed and their quantitative implications investigated. Experimental stochastic forecasts are presented and discussed, based on nonparametric, partially parametric, and fully parametric methods, representing alternatives to the well known Lee-Carter method. Some thoughts are offered on the interpretation of historical data in generating future probability distributions, and on the treatment of demographic uncertainty in long-run policy planning. All correspondence to Frank T. Denton. This paper is a revised version of one presented at the Annual Congress of the European Society for Population Economics, Athens, Greece, June 2001. The underlying work was carried out as part of the SEDAP (Social and Economic Dimensions of an Aging Population) Research Program supported by the Social Sciences and Humanities Research Council of Canada, Statistics Canada and the Canadian Institute for Health Information. Ronald Lee provided comments that were very helpful in revising an earlier version of the paper. We thank him and participants at the ESPE session at which that version was presented. We thank also the Journal's anonymous referees. Responsible editor: Junsen Zhang.     

Using Subjective Expectations to Forecast Longevity: Do Survey Respondents Know Something We Don’t Know?

Old-age mortality is notoriously difficult to predict because it requires not only an understanding of the process of senescence-which is influenced by genetic, environmental, and behavioral factors-but also a prediction of how these factors will evolve. In this paper I argue that individuals are uniquely qualified to predict their own mortality based on their own genetic background, as well as environmental and behavioral risk factors that are often known only to the individual. Given this private information, individuals form expectations about survival probabilities that may provide additional information to demographers and policymakers in their challenge to predict mortality. From expectations data from the 1992 Health and Retirement Study (HRS), I construct subjective, cohort life tables that are shown to predict the unusual direction of revisions to U.S. life expectancy by gender between 1992 and 2004: that is, for these cohorts, the Social Security Actuary (SSA) raised male life expectancy in 2004 and at the same lowered female life expectancy, narrowing the gender gap in longevity by 25% over this period. Further, although the subjective life expectancies for men appear to be roughly in line with the 2004 life tables, the subjective expectations of women suggest that female life expectancies estimated by the SSA might still be on the high side.     

Revised regional model life tables at very low levels of mortality

This paper presents and discusses new model life tables at very low mortality, which make use of age-specific death rates from the 1960s, 1970s, and 1980s. These life tables fit recorded death rates in very low mortality populations better than do the existing ones at expectations of life of 77.5 and 80 years. The old tables incorporate too-high mortality at the higher ages and in infancy and they incorporate regional differences that no longer exist. The new tables "close out" the mortality schedules above age 80 more realistically. The convergence of age patterns of mortality at very high life expectancies in populations that used to conform to different families is in itself of demographic interest. Some convergence may perhaps be expected. Sullivan (1973) found that, in Taiwan, the comparison of mortality at ages 1-5 to mortality at 5-35 in the late 1950s showed higher mortality at the younger ages relative to the ensuing 30-year age interval than was found in any of the models, including the South model, which has the highest relative mortality from ages 1-5 among the 4 regional patterns. Then, in the late 1960s, the relation of mortality at 1-5 to mortality at 5-35 in Taiwan fell to a position intermediate between the West and South tables. Sullivan found in data on mortality by cause of death a large reduction in mortality from diarrhea and enteritis, no doubt as a result of environmental sanitation. Mortality from these causes is concentrated among young children, and reduction in deaths from these causes would naturally diminish the excess mortality in this age interval. The East pattern, characterized by very high mortality in infancy (but not from 1-5), may be the result of the prevalence of early weaning or avoidance of breast feeding altogether in the populations characterized by this pattern. As health conditions have improved, evidenced by the overall design of mortality, these special factors are diminished or erased. Model life tables at these very low mortality levels have different uses from most applications of model life tables at higher mortality. The use of model tables to estimate accurate schedules of mortality when the basic data are incomplete or inaccurate is less relevant in this range of mortality levels.     

A reconsideration of negro-white mortality differentials in the united states

This paper summarizes the results of an investigation of the validity of Negro-white mortality differentials as reflected in the series of official United States life tables since the turn of the century. Pertinent excerpts from these often-quoted tables are reproduced in Appendix Table A-1 for convenient reference. The paper divides into two main parts.First, mortality levels and differentials beyond early childhood are derived, without use of the existing vital records, by interpreting the series of ten-year cumulative survival rates implicit in the census records for native whites and for Negroes. The results are in general agreement with the official figures, particularly for males.Second, mortality levels and differentials in early childhood are estimated by extrapolating the official 1)5 values via model life tables; that is, by the analytical procedure that would be followed in the absence of direct information on early childhood mortality. Unless it is assumed that age patterns of death for United States Negroes were extremely deviant from those found in populations with reliable census and vital statistics, one must conclude that the official figures grossly underestimate early childhood mortality for Negroes, at least for the period, 1910-40. It follows that, during those decades, Negro-white mortality differentials in terms of expectation of life at birth were also substantially higher than is suggested by the official estimates.     

Mortality,marriage, and growth in pre-industrial populations

It has been widely assumed that in pre-industrial European populations postponement of marriage was a major check on fertility, and that marriage was contingent upon access to a livelihood in the form of a homestead or a craft. Death made room for new families, and the age at inheritance might therefore be an index of the age at marriage. High mortality should then mean early marriage and high fertility. When the effect of a uniform increase in the force of mortality on the “natural rate of growth” is estimated quantitatively, it is found that fertility response is of the same magnitude as the change in mortality so that within a wide range mortality differentials alone would not suffice to account for persistent differentials in growth rates. The assumption of a reasonably effective control through the prudential check is thus strengthened.     

A simple model for linking life tables by survival mortality ratios

Patterns of variation in mortality can be studied by measuring changes in selected life table functions. A model is proposed in which the rate of change over time in the life table survivorship probability at any age has been assumed as proportional to the product of its own value and its complementary probability or the probability of dying by that age, where the proportion is the same for all ages and depends only on the time duration between successive life tables. The end result is that the logit functions of the survivorship probabilities at two points in time are linearly related with a slope of one. The projecting power of the model has been tested by using U.S. life tables for the years 1950 and 1970 as well as Coale and Demeny's regional model life tables. In the latter case, the model produced surprisingly close matches even when the expectations of life differed by as much as 20 years.     

The Segmented Trend Line of Highest Life Expectancies

The well‐known Oeppen–Vaupel straight line of maximum female life expectancies showed that the highest life expectancy observed in a given year increased linearly from 1840 to 2000. Their analysis fueled major controversy, especially when used to extrapolate future improvements in life expectancy at the same pace. We improve on the empirical analysis by enriching the dataset, expanding the period to 1750–2005, and considering both maximum life expectancy at birth and lowest age‐specific survival rates. It clearly appears that the original Oeppen–Vaupel straight line must be divided into several segments characterized by different slopes and that each segment corresponds to a major advance in the health transition. There is room to push life expectancy higher, but unless some new breakthrough increases the human life span, progress will very likely decelerate as mortality reduction affects individuals at older and older ages. The main key to the future lies not in knowing whether the observed straight line can be extrapolated but in anticipating the next major health improvement that will lead to an additional increase in life expectancy.     

Perturbation Analysis of Indices of Lifespan Variability

A number of indices exist to calculate lifespan variation, each with different underlying properties. Here, we present new formulae for the response of seven of these indices to changes in the underlying mortality schedule (life disparity, Gini coefficient, standard deviation, variance, Theil’s index, mean logarithmic deviation, and interquartile range). We derive each of these indices from an absorbing Markov chain formulation of the life table, and use matrix calculus to obtain the sensitivity and the elasticity (i.e., the proportional sensitivity) to changes in age-specific mortality. Using empirical French and Russian male data, we compare the underlying sensitivities to mortality change under different mortality regimes to determine the conditions under which the indices might differ in their conclusions about the magnitude of lifespan variation. Finally, we demonstrate how the sensitivities can be used to decompose temporal changes in the indices into contributions of age-specific mortality changes. The result is an easily computable method for calculating the properties of this important class of longevity indices.     

Changing Life Expectancy and Health Expectancy Among Russian Adults: Results from the Past 20 Years

The decade following the collapse of the Soviet Union was characterized by wide fluctuations in Russian mortality rates, but since the early 2000s, life expectancy has improved progressively. Recent upturns in longevity have promoted policy debates over extending the retirement age in the country. However, whether observed gains in life expectancy are accompanied by improving health remains to be addressed. Using data from the 1994–2014 Russian Longitudinal Monitoring Survey of the Higher School of Economics, this study investigates trends over 20 years in healthy life expectancy (HLE) and illness-free life expectancy (IFLE) for men and women at adult ages. Analyses using the Sullivan method show that men and women at adult ages have experienced large increases in health expectancies during the post-Soviet period. Increases in HLE exceeded increases in total life expectancy for both genders. Further, health expectancies have evolved over time through cycles of increases and decreases, just like life expectancy. These results suggest increases in good-quality years among men and women at working ages, offering support for changing the official retirement age. The extent of the change in the retirement age, however, needs to be carefully considered, given that, despite recent improvements, the health expectancy of the Russian population still remains low.