Estimating Increment-Decrement Life Tables with Multiple Covariates from Panel Data: The Case of Active Life Expectancy*

A fundamental limitation of current multistate life table methodology-evident in recent estimates of active life expectancy for the elderly-is the inability to estimate tables from data on small longitudinal panels in the presence of multiple covariates (such as sex, race, and socioeconomic status). This paper presents an approach to such an estimation based on an isomorphism between the structure of the stochastic model underlying a conventional specification of the increment-decrement life table and that of Markov panel regression models for simple state spaces. We argue that Markov panel regression procedures can be used to provide smoothed or graduated group-specific estimates of transition probabilities that are more stable across short age intervals than those computed directly from sample data. We then join these estimates with increment-decrement life table methods to compute group-specific total, active, and dependent life expectancy estimates. To illustrate the methods, we describe an empirical application to the estimation of such life expectancies specific to sex, race, and education (years of school completed) for a longitudinal panel of elderly persons. We find that education extends both total life expectancy and active life expectancy. Education thus may serve as a powerful social protective mechanism delaying the onset of health problems at older ages.     

Expectancy of life at birth in 36 nationalities of the Soviet Union: 1958-60

In the 36 nationalities of the Soviet Union the estimated expectancy of life at birth ranged from 50·0 years for Chechens to 71·1 years for Latvians with a median of about 67·5 years for Russians.

In essence, the life table function e₀ was generated from the child-woman ratios with the use of intricate equations based on empirical data obtained from official Soviet publications. A modified version of Bourgeois-Pichat's model was used to estimate life expectancies at birth among the 36 nationalities on the basis of their crude death rates and the percentage of population aged 65 years and over. The 1959 U.S.S.R. Census of Population provided information pertaining to the older age groups. The crude death rates were estimated separately with the aid of second-degree polynomials fitted to the crude demographic measures for 109 administrative areas of the Soviet Union for 1960.

Information about recent improvements in public health, as well as conjectural evaluations of economic advancement in recent years were examined and related to the past and present level of mortality among the Russian people and the remaining population of minorities.     

Expectancy of life at birth in 36 nationalities of the Soviet Union: 1958-60

Abstract In the 36 nationalities of the Soviet Union the estimated expectancy of life at birth ranged from 50·0 years for Chechens to 71·1 years for Latvians with a median of about 67·5 years for Russians. In essence, the life table function e(0) was generated from the child-woman ratios with the use of intricate equations based on empirical data obtained from official Soviet publications. A modified version of Bourgeois-Pichat's model was used to estimate life expectancies at birth among the 36 nationalities on the basis of their crude death rates and the percentage of population aged 65 years and over. The 1959 U.S.S.R. Census of Population provided information pertaining to the older age groups. The crude death rates were estimated separately with the aid of second-degree polynomials fitted to the crude demographic measures for 109 administrative areas of the Soviet Union for 1960. Information about recent improvements in public health, as well as conjectural evaluations of economic advancement in recent years were examined and related to the past and present level of mortality among the Russian people and the remaining population of minorities.     

Fertility change in rural China, 1949–1982

In the present study, the technique of life table analysis is used to examine fertility change by birth order in rural China, particularly in the rural portion of Anhui province. The study mainly focuses on the relationship between fertility change by birth order and planned socioeconomic changes. Change in fertility by birth order in the last few decades in rural China and Anhui is used as an indicator of the effects of planned socioeconomic changes on the process of family building. Some light is shed on the extent to which fertility changes affected women at different stages of their reproductive career. The data are from the 1/1000 Fertility Survey of China, conducted by the Family Planning Commission in 1982.     

A new look at entropy and the life table

The mathematical derivations described in this paper offer a new look at the entropy of the life table, denoted by H. Contrary to previous claims, it is theoretically possible, and has been observed empirically, for life tables to have entropy values greater than unity. A re-expression of H as a weighted average of life expectancy at different ages relative to life expectancy at birth demonstrates clearly the conditions under which reductions in mortality by a fixed amount at all ages can result in even greater gains in life expectancy.     

Modeling and Forecasting Health Expectancy: Theoretical Framework and Application

Life expectancy continues to grow in most Western countries; however, a major remaining question is whether longer life expectancy will be associated with more or fewer life years spent with poor health. Therefore, complementing forecasts of life expectancy with forecasts of health expectancies is useful. To forecast health expectancy, an extension of the stochastic extrapolative models developed for forecasting total life expectancy could be applied, but instead of projecting total mortality and using regular life tables, one could project transition probabilities between health states simultaneously and use multistate life table methods. In this article, we present a theoretical framework for a multistate life table model in which the transition probabilities depend on age and calendar time. The goal of our study is to describe a model that projects transition probabilities by the Lee-Carter method, and to illustrate how it can be used to forecast future health expectancy with prediction intervals around the estimates. We applied the method to data on the Dutch population aged 55 and older, and projected transition probabilities until 2030 to obtain forecasts of life expectancy, disability-free life expectancy, and probability of compression of disability.     

How Long Do We Live?

Period life expectancy is calculated from age‐specific death rates using life table methods that are among the oldest and most widely employed tools of demography. These methods are rarely questioned, much less criticized. Yet changing age patterns of adult mortality in countries with high life expectancy provide a basis for questioning the conventional use of life tables. This article argues that when the mean age at death is rising, period life expectancy at birth as conventionally calculated overestimates life expectancy. Estimates of this upward bias, ranging from 1.6 years for the United States and Sweden to 3.3 years for Japan for 1980–95, are presented. A similar bias in the opposite direction occurs when mean age at death is falling. These biases can also distort trends in life expectancy as conventionally calculated and may affect projected future trends in period life expectation, particularly in the short run.     

Black-White Disparities in Life Expectancy: How Much Can the Standard SES Variables Explain?

This article quantifies the extent to which socioeconomic and demographic characteristics can account for black-white disparities in life expectancy in the United States. Although many studies have investigated the linkages between race, socioeconomic status, and mortality, this article is the first to measure how much of the life expectancy gap remains after differences in mortality are purged of the compositional differences in socioeconomic characteristics between blacks and whites. The decomposition is facilitated by a reweighting technique that creates counterfactual estimation samples in which the distribution of income, education, employment and occupation, marital status, and other theoretically relevant variables among blacks is made to match the distribution of these variables among whites. For males, 80% of the black-white gap in life expectancy at age 1 can be accounted for by differences in socioeconomic and demographic characteristics. For females, 70% percent of the gap is accounted for. Labor force participation, occupation, and (among women only) marital status have almost no additional power to explain the black-white disparity in life expectancy after precise measures for income and education are controlled for.     

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.     

The effect of World War I and the 1918 influenza pandemic on cohort life expectancy of South Australian males born in 1881–1900

Cohort lifetime distribution functions have been estimated for the twenty separate calendar year cohorts of South Australian males born in 1881–1900. A cohort life expectancy at birth was calculated from each of these distribution functions, and a composite assessment made of the reduction in cohort life expectancy at birth due to both World War I 1914–1918 and the 1918 Influenza Pandemic. By partitioning each cohort, the cohort life expectancy at birth of the subgroup that had overseas military service is estimated to be 85 to 90 per cent of the cohort life expectancy at birth of the subgroup that remained in South Australia.     

A state-based regression model for estimating substate life expectancy

Life expectancy is an important indicator of the level of mortality in a population. However, the conventional way of calculating life expectancy--constructing a life table--has rigorous data requirements. As a consequence, life expectancy data are not usually available for substate areas. In this article, a regression model for estimating life expectancy is constructed, using state-level data, and is tested against two sets of 1980 life expectancy data: (1) a nationwide sample of metropolitan areas and (2) selected cities, their suburbs, and rural counties in Ohio. An additional test shows the sensitivity of the model's accuracy to errors in one of its input data elements. The results suggest that the model should be given serious consideration for generating life expectancy estimates for substate areas.     

Measuring and explaining the change in life expectancies

A set of new indices for interpreting change in life expectancies, as well as a technique for explaining change in life expectancies by change in mortality at each age group are presented in the paper. The indices, as well as the new technique for explaining the differences in life expectancies, have been tested and examples using United States life tables are presented. The technique for explaining life expectancy differentials can be used for analyzing change in mortality or mortality differentials by sex, ethnicity, region, or any other subpopulations. The technique can be applied to life expectancies at birth or temporary life expectancies between any desirable ages.     

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.     

Life Expectancy during the Great Depression in Eleven European Countries

The recent global economic recession has renewed interest in knowing whether a declining economy affects population health. Understanding the extreme case of the Great Depression may inform the current debate as well as theory regarding biological and behavioral adaptations to unwanted economic change. We test the hypothesis, recently suggested in the literature, that period life expectancy at birth improved during the Great Depression. We applied time‐series methods to annual period life expectancy data of the civilian population from eleven European countries. Methods control for trends and other forms of autocorrelation in life expectancy that could induce spurious associations. We cannot reject the null hypothesis that period life expectancy at birth during the Great Depression remained within the interval forecasted from historical values. Additional analyses using an automated, rule‐based methodology also cannot reject the null hypothesis. During the most severe phase of the Great Depression, period life expectancy in eleven European countries generally did not rise above expected levels.     

The length of working life

The rapid growth of the aged population in recent years has underscored the economic problems of dependency in old age and has focused attention on the length of working life as compared to the total life span. In addition to interest in the average work-life span, students of labour-force dynamics have found a need for related measures of withdrawals from the labour force at different ages. In this paper, the author adopts the technique of the life table to a measurement of the work-life span by the construction of a table of working life.

Significant contrast is shown between total life expectancy and working life expectancy. In the United States, the average male worker at 20, for example, could expect to live for an additional 46.8 years and to remain in the labour force for an additional 41.1 years. He would therefore have to provide for almost 6 years of retirement. Significant differences are also indicated in comparisons by colour and residence. Further areas of study in applying the concept of working life are suggested.     

The Association Between Individual Income and Remaining Life Expectancy at the Age of 65 in the Netherlands

This article quantifies the association between individual income and remaining life expectancy at the statutory retirement age (65) in the Netherlands. For this purpose, we estimate a mortality risk model using a large administrative data set that covers the 1996–2007 period. Besides age and marital status, the model includes as covariates individual and spouse’s income as well as a random individual specific effect. It thus allows for dynamic selection based on both observed and unobserved characteristics. We find that conditional on marital status, individual income is about equally strong and negatively associated with mortality risk for men and women and that spouse’s income is only weakly associated with mortality risk for women. For both men and women, we quantify remaining life expectancy at age 65 for low-income individuals as approximately 2.5 years less than that for high-income individuals.     

Recent Perspectives on Active Life Expectancy for Older Women

SUMMARY

This article provides a critical review of recent active life expectancy literature, describing trends of special interest to women. We review findings from leading perspectives used to study life expectancy and active life expectancy, including gender, racial and socioeconomic differences, disease-specific effects, and biodemography. We examine three competing theories of population health that frame active life expectancy research—compression of morbidity, expansion of morbidity, and dynamic equilibrium—concluding there is support for both the compression of morbidity and dynamic equilibrium theories. Policy implications for women include a greater understanding of the role of education and racial and ethnic diversity in active life trends, and an increased public policy emphasis on prevention and treatment of chronic disease, together with adoption of more healthy lifestyles.     

Demographic and Economic Correlates of Development as Measured by Energy Consumption

Per capita consumption of energy in 112 world areas was related to a series of economic and demographic variables. Linear associations were found for four economic variables, and a curvilinear association in the form of a J curve for four demographic variables. It was found that the exponential distribution y = e(-X) for the curves for the demographic variables (crude birth rate, infant mortality rate, percent of deaths from contagious and infectious diseases, and life expectancy). By using a table of exponential functions, one can determine values for the distribution of these variables and the crude death rate for any desired level of energy consumption.     

Active life expectancy estimates for the U.S. elderly population: A multidimensional continuous-mixture model of functional change applied to completed Cohorts, 1982–1996

An increment-decrement stochastic-process life table model that continuously mixes measures of functional change is developed to represent age transitions among highly refined disability states interacting simultaneously with mortality. The model is applied to data from the National Long Term Care Surveys of elderly persons in the years 1982 to 1996 to produce active life expectancy estimates based on completed-cohort life tables. At ages 65 and 85, comparisons with extant period estimates for 1990 show that our active life expectancy estimates are larger for both males and females than are extant period estimates based on coarse disability states.     

Inequality in Life Spans and a New Perspective on Mortality Convergence Across Industrialized Countries

The second half of the twentieth century witnessed substantial convergence in life expectancy around the world. We examine differences in the age pattern of mortality in industrialized countries over time to show that inequality in adult life spans, which we measure with the standard deviation of life table ages at death above age 10 years, S₁₀, is increasingly responsible for the remaining divergence in mortality. We report striking differences in level and trend of S₁₀ across industrialized countries since 1960, which cannot be explained by aggregate socioeconomic inequality or differential external‐cause mortality. Rather, S₁₀ reflects both within‐ and between‐group inequalities in life spans and conveys new information about their combined magnitudes and trends. These findings suggest that the challenge for health policies in this century is to reduce inequality, not just lengthen life.