A multi-population evaluation of the Poisson common factor model for projecting mortality jointly for both sexes

Mortality forecasts are critically important inputs to the consideration of a range of demographically-related policy challenges facing governments in more developed countries. While methods for jointly forecasting mortality for sub-populations offer the advantage of avoiding undesirable divergence in the forecasts of related populations, little is known about whether they improve forecast accuracy. Using mortality data from ten populations, we evaluate the data fitting and forecast performance of the Poisson common factor model (PCFM) for projecting both sexes’ mortality jointly against the Poisson Lee–Carter model applied separately to each sex. We find that overall the PCFM generates the more desirable results. Firstly, the PCFM ensures that the projected male-to-female ratio of death rates at each age converges to a constant in the long run. Secondly, using out-of-sample analysis, we find that the PCFM provides more accurate projection of the sex ratios of death rates, with the advantage being greater for longer-term forecasts. Thus the PCFM offers a viable and sensible means for coherently forecasting the mortality of both sexes. There are also significant financial implications in allowing for the co-movement of mortality of females and males properly.     

A combined Brass-random walk approach to probabilistic household forecasting: Denmark,Finland, and the Netherlands, 2011–2041

Probabilistic household forecasts to 2041 are presented for Denmark, Finland, and the Netherlands. Future trends in fertility, mortality and international migration are taken from official population forecasts. Time series of shares of the population in six different household positions are modelled as random walks with drift. Brass’ relational model preserves the age patterns of the household shares. Probabilistic forecasts for households are computed by combining predictive distributions for the household shares with predictive distributions of the populations, specific for age and sex. If current trends in the three countries continue, we will witness a development towards more and smaller households, often driven by increasing numbers of persons who live alone. We can be quite certain that by 2041, there will be between two and four times as many persons aged 80 and over who live alone when compared with the situation in 2011.     

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.     

Uncrossing the U.S. Black-White Mortality Crossover: The Role of Cohort Forces in Life Course Mortality Risk

In this article, I examine the black-white crossover in U.S. adult all-cause mortality, emphasizing how cohort effects condition age-specific estimates of mortality risk. I employ hierarchical age-period-cohort methods on the National Health Interview Survey-Linked Mortality Files between 1986 and 2006 to show that the black-white mortality crossover can be uncrossed by factoring out period and cohort effects of mortality risk. That is, when controlling for variations in cohort and period patterns of U.S. adult mortality, the estimated age effects of non-Hispanic black and non-Hispanic white U.S. adult mortality risk do not cross at any age. This is the case for both men and women. Further, results show that nearly all the recent temporal change in U.S. adult mortality risk was cohort driven. The findings support the contention that the non-Hispanic black and non-Hispanic white U.S. adult populations experienced disparate cohort patterns of mortality risk and that these different experiences are driving the convergence and crossover of mortality risk at older ages.     

Lifespan Disparity as an Additional Indicator for Evaluating Mortality Forecasts

Evaluating the predictive ability of mortality forecasts is important yet difficult. Death rates and mean lifespan are basic life table functions typically used to analyze to what extent the forecasts deviate from their realized values. Although these parameters are useful for specifying precisely how mortality has been forecasted, they cannot be used to assess whether the underlying mortality developments are plausible. We therefore propose that in addition to looking at average lifespan, we should examine whether the forecasted variability of the age at death is a plausible continuation of past trends. The validation of mortality forecasts for Italy, Japan, and Denmark demonstrates that their predictive performance can be evaluated more comprehensively by analyzing both the average lifespan and lifespan disparity—that is, by jointly analyzing the mean and the dispersion of mortality. Approaches that account for dynamic age shifts in survival improvements appear to perform better than others that enforce relatively invariant patterns. However, because forecasting approaches are designed to capture trends in average mortality, we argue that studying lifespan disparity may also help to improve the methodology and thus the predictive ability of mortality forecasts.     

Reconciling Forecasts of Infant Mortality Rates at National and Sub-National Levels: Grouped Time-Series Methods

Mortality rates are often disaggregated by different attributes, such as sex, state, education, religion, or ethnicity. Forecasting mortality rates at the national and sub-national levels plays an important role in making social policies associated with the national and sub-national levels. However, base forecasts at the sub-national levels may not add up to the forecasts at the national level. To address this issue, we consider the problem of reconciling mortality rate forecasts from the viewpoint of grouped time-series forecasting methods (Hyndman et al. in, Comput Stat Data Anal 55(9):2579–2589, 2011). A bottom-up method and an optimal combination method are applied to produce point forecasts of infant mortality rates that are aggregated appropriately across the different levels of a hierarchy. We extend these two methods by considering the reconciliation of interval forecasts through a bootstrap procedure. Using the regional infant mortality rates in Australia, we investigate the one-step-ahead to 20-step-ahead point and interval forecast accuracies among the independent and these two grouped time-series forecasting methods. The proposed methods are shown to be useful for reconciling point and interval forecasts of demographic rates at the national and sub-national levels, and would be beneficial for government policy decisions regarding the allocations of current and future resources at both the national and sub-national levels.     

Forecasting Mortality: A Parameterized Time Series Approach

This article links parameterized model mortality schedules with time series methods to develop forecasts of U.S. mortality to the year 2000. The use of model mortality schedules permits a relatively concise representation of the history of mortality by age and sex from 1900 to 1985, and the use of modern time series methods to extend this history forward to the end of this century allows for a flexible modeling of trend and the accommodation of changes in long-run mortality patterns. This pilot study demonstrates that the proposed procedure produces medium-range forecasts of mortality that meet the standard tests of accuracy in forecast evaluation and that are sensible when evaluated against the comparable forecasts produced by the Social Security Administration.     

Death and Taxes: Longer life, consumption, and social security

We analyze in three steps the influence of the projected mortality decline on the long run finances of the Social Security System. First, on a theoretical level, mortality decline adds person years of life which are distributed across the life cycle. The interaction of this distribution with the age distribution of labor earnings minus consumption, or of taxes minus benefits, partially determines the corresponding steady state financial consequences of mortality decline. The effect of mortality decline on population growth rates also matters, but is negligible in low mortality populations. Second, examination of past mortality trends in the United States and of international trends in low mortality populations, suggests that mortality will decline faster than foreseen by the Social Security Administration s forecasts. Third, we combine the work of the first two parts in dynamic simulations to examine the implications of mortality decline and of alternative forecasts of mortality for the finances of the social security system. Also, we use stochastic population forecasts to assess the influence of uncertainty about mortality decline on uncertainty about finances; we find that uncertainty about fertility still has more important implications than uncertainty about mortality, contrary to sensitivity tests in the official forecasts.     

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.     

Mortality Deceleration and Mortality Selection: Three Unexpected Implications of a Simple Model

Unobserved heterogeneity in mortality risk is pervasive and consequential. Mortality deceleration—the slowing of mortality’s rise with age—has been considered an important window into heterogeneity that otherwise might be impossible to explore. In this article, I argue that deceleration patterns may reveal surprisingly little about the heterogeneity that putatively produces them. I show that even in a very simple model—one that is composed of just two subpopulations with Gompertz mortality—(1) aggregate mortality can decelerate even while a majority of the cohort is frail; (2) multiple decelerations are possible; and (3) mortality selection can produce acceleration as well as deceleration. Simulations show that these patterns are plausible in model cohorts that in the aggregate resemble cohorts in the Human Mortality Database. I argue that these results challenge some conventional heuristics for understanding the relationship between selection and deceleration; undermine certain inferences from deceleration timing to patterns of social inequality; and imply that standard parametric models, assumed to plateau at most once, may sometimes badly misestimate deceleration timing—even by decades.     

Structure and change in causes of death: An international summary

Abstract Model patterns of the cause structure of mortality at different levels were established for males and females, based on data for 165 national populations. These patterns suggest that the cause of death most responsible for mortality variation is influenza/bronchitis, followed by 'other infectious and parasitic diseases', respiratory tuberculosis, and diarrhoeal disease. Together, these causes typically account for about 60 per cent of the change in level of mortality from all causes combined. Their respective contributions have not depended in an important way on the initial level of mortality. These results - especially tbe importance of the respiratory and diarrhoeal diseases - imply that past accounts may have over-emphasized the role in mortality decline of specific and well-defined infectious diseases and their corresponding methods of control. There is strong statistical support for the suggestion that most of the remainder of mortality variation should be ascribed to changes in cardio-vascular diseases, but that methods of cause-of-death assignment in high-mortality populations have often obscured the importance of these diseases. When death rates from 'other and unknown' causes are held constant, changes in cardio-vascular disease account for about one-quarter of the decline in mortality from 'all causes'.Although the causal factors are poorly established, corroborative results have been demonstrated cross-sectionally in the United States. The composition of the group of populations most deviant from the structural norms is apparently dominated by differentials in the mode of assigning deaths to cardio-vascular disease. However, when broad groups of regions or periods are distinguished, more subtle differences emerge. Controlling mortality level for all causes combined, diarrhoeal diseases are significantly higher in non-Western populations and southern/eastern Europe than in overseas Europe or northern/western Europe. These differences are probably related to standards of nutrition and personal hygiene, but may also reflect climatic factors. Much higher cardio-vascular mortality in overseas European populations than in non-Western populations at similar overall levels probably reflects variation in habits of life. Regional differences in death rates from violence, maternal mortality, respiratory tuberculosis and influenza/pneumonia/bronchitis are briefly noted and commented upon. Cause-of-death structures at a particular level of mortality display some important changes over time. Respiratory tuberculosis and 'other infectious and parasitic diseases' have tended to contribute less and less to a certain level of mortality. They have in part been 'replaced' by diarrhoeal disease, specifically in non-Western populations. These developments reflect an accelerating rate of medical and public health progress against the specific infectious diseases, and a disappointing rate of progress against diarrhoeal disease. Western and non-western populations have shared to approximately the same extent in the accelerating progress against infectious diseases, and developments during the post-war period are more appropriately viewed as an extension of prior trends rather than as radical departures therefrom. For males, cardio-vascular disease and cancer have significantly increased their contribution to a particular level of mortality, while no such tendency is apparent for females. These developments may be related to changes in personal behaviour and in environmental influences whose differential impact on the sexes has been demonstrated in epidemiological studies. Although we have avoided an explicit treatment of age by having recourse at the outset to standardization, certain of the results are apparently reflected in studies of age patterns of mortality. The joint occurrence in non-Western populations and Southern/Eastern populations of exceptionally high death rates from diarrhoeal disease may explain why the 'South' age-pattern, with it high death rates between ages one and five, is often the most accurate referent for use in Latin America and Asia. The fact that the list of populations with the least deviation cause structure is almost exclusively confined to members of the 'West' group of Coale and Demeny may account for the lack of persistent deviation in this group's age patterns. Finally, tbe increasing importance of cardio-vascular disease and neoplasms in cause-of-death structures for males but not females is probably associated with the changing age patterns of male mortality noted by Coale and Demeny.     

Statistical Security for Social Security

The financial viability of Social Security, the single largest U.S. government program, depends on accurate forecasts of the solvency of its intergenerational trust fund. We begin by detailing information necessary for replicating the Social Security Administration's (SSA's) forecasting procedures, which until now has been unavailable in the public domain. We then offer a way to improve the quality of these procedures via age- and sex-specific mortality forecasts. The most recent SSA mortality forecasts were based on the best available technology at the time, which was a combination of linear extrapolation and qualitative judgments. Unfortunately, linear extrapolation excludes known risk factors and is inconsistent with long-standing demographic patterns, such as the smoothness of age profiles. Modern statistical methods typically outperform even the best qualitative judgments in these contexts. We show how to use such methods, enabling researchers to forecast using far more information, such as the known risk factors of smoking and obesity and known demographic patterns. Including this extra information makes a substantial difference. For example, by improving only mortality forecasting methods, we predict three fewer years of net surplus, $730 billion less in Social Security Trust Funds, and program costs that are 0.66% greater for projected taxable payroll by 2031 compared with SSA projections. More important than specific numerical estimates are the advantages of transparency, replicability, reduction of uncertainty, and what may be the resulting lower vulnerability to the politicization of program forecasts. In addition, by offering with this article software and detailed replication information, we hope to marshal the efforts of the research community to include ever more informative inputs and to continue to reduce uncertainties in Social Security forecasts.     

Reexamining the Dominance of Birth Cohort Effects on Mortality

The association between birth cohort and subsequent mortality has been of interest especially following publication of studies around 1930 of cohorts born up to the latter part of the nineteenth century, particularly for England and Wales. Updated results are presented for this population, together with those for two other cohorts, twentieth‐century Japanese and British populations born about 1930, which have been identified as having particularly clear‐cut birth cohort patterns, and which are used to underpin incorporation of cohort effects in both British official and actuarial mortality forecasts. Graphical methods used to identify cohort patterns are discussed. A number of limitations and difficulties are identified that mean that the conclusions about the predominance of cohort effects are less robust than often assumed. It is argued that alternative explanations should be considered and that the concentration on birth cohorts with particularly advantaged patterns may distort research priorities.     

Optimizing the Lee-Carter Approach in the Presence of Structural Changes in Time and Age Patterns of Mortality Improvements

Researchers using the Lee-Carter approach have often assumed that the time-varying index evolves linearly and that the parameters describing the age pattern of mortality decline are time-invariant. However, as several empirical studies suggest, the two assumptions do not seem to hold when the calibration window begins too early. This problem gives rise to the question of identifying the longest calibration window for which the two assumptions hold true. To address this question, we contribute a likelihood ratio–based sequential test to jointly test whether the two assumptions are satisfied. Consistent with the mortality structural changes observed in previous studies, our testing procedure indicates that the starting points of the optimal calibration windows for most populations fall between 1960 and 1990. Using an out-of-sample analysis, we demonstrate that in most cases, models that are estimated to the optimized calibration windows result in more accurate forecasts than models that are fitted to all available data or data beyond 1950. We further apply the proposed testing procedure to data over different age ranges. We find that the optimal calibration windows for age group 0–49 are generally shorter than those for age group 50–89, indicating that mortality at younger ages might have undergone (another) structural change in recent years.     

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.     

The Effect of Age Misreporting in China on the Calculation of Mortality Rates at Very High Ages

When mortality rates by age are calculated from recorded deaths and enumerated populations, rates at higher ages are typically in error because of misstated ages. Mortality rates for China in 1981 have been calculated from the number of deaths in 1981 in each household recorded in the 1982 census, and from the census population back-projected one year. Because age was determined from date of birth, and because persons of the Chinese culture have very precise knowledge of date of birth, the mortality rates even at high ages should be unusually accurate. This expectation is fulfilled for most of China, but severe misreporting of age is found in a province that contains a large minority of a non-Han nationality, which lacks precise knowledge of date of birth. Although the province contains only 1.3% of China's population, male death rates above age 90 for all of China are distorted seriously by the erroneous data from this location.     

The peculiar pattern of mortality of Jews in Moscow, 1993-95

Russian Jews, particularly men, have a large mortality advantage compared with the general Russian population. We consider possible explanations for this advantage using data on 445,000 deaths in Moscow, 1993-95. Log-linear analysis of the distribution of deaths by sex, age, ethnic group, and cause of death reveals a relatively high concentration of endogenous causes and a relatively low concentration of exogenous and behaviourally induced causes among Jews. There is also a significant concentration of deaths from breast cancer among Jewish women. Mortality estimates using the 1994 micro-census population as the denominator reveal an 11-year Russian-Jewish gap in the life expectancy of males at age 20, but only a 2-year life-expectancy gap for women. Only 40 per cent of the Russian-Jewish difference for men, but the entire difference for women, can be eliminated by adjustment for educational differences between the two ethnic groups. Similarities with other Jewish populations and possible explanations are discussed.     

Adult mortality differentials associated with cigarette smoking in the USA

Although cigarette smoking has been extensively researched, surprising little knowledge has been produced by demographers using demographic perspectives and techniques. Thus, this paper contributes to the literature by extending a demographic framework to an important behavior for mortality research: cigarette smoking. In earlier works, the authors used nationally-representative data to show that cause of death patterns varied by smoking status and that multiple causes of death characterized smokers moreso than non-smokers. The present work extends previous analysis by estimating smoking status mortality differentials by underlying and multiple causes of death and by age and sex. Data from the 1986 National Mortality Followback Survey are related to data from the 1985 and 1987 National Health Interview Survey supplements to assess the smoking-related mortality differentials. We find that cigarette smoking is associated with higher mortality for all population categories studied, that the smoking mortality differentials vary across the different smoking status categories and by demographic group, and that the mortality differentials vary according to whether underlying cause or multiple cause patterns of death are examined. Moreover, the multiple cause analysis highlights otherwise obscured smoking-mortality relations and points to the importance of respiratory diseases and cancers other than lung cancer for cigarette smoking research.     

Effects of targets and aggregation on the propagation of error in mortality forecasts

Official forecasts of mortality depend on assumptions about target values for the future rates of decline in mortality rates. Smooth functions connect the jump‐off (base‐year) mortality to the level implied by the targets. Three alternative sets of targets are assumed, leading to high, middle, and low forecasts. We show that this process can be closely modeled using simple linear statistical models. These explicit models allow us to analyze the error structure of the forecasts. We show that the current assumption of perfect correlation between errors in different ages, at different forecast years, and for different causes of death, is erroneous. An alternative correlation structure is suggested, and we show how its parameters can be estimated from the past data.

The effect of the level of aggregation on the accuracy of mortality forecasts is considered. It is not clear whether or not age‐ and cause‐specific analyses have been more accurate in the past than analyses based on age‐specific mortality alone would have been. The major contribution of forecasting mortality by cause appears to have been in allowing for easier incorporation of expert opinion rather than in making the. data analysis more accurate or the statistical models less biased.     

Age patterns of mortality and cause-of-death structures in Sweden,Japan, and the United States

This paper uses a new standard model of adult mortality to compare the mortality patterns of Swedes, Japanese, and U.S. whites between 1950 and 1985. It examines changes in the age patterns of mortality and the cause-of-death structures within the populations. and the relationships between those two factors. As Japan has reached a level of mortality similar to that in Sweden, the age patterns of mortality in the two populations have become more similar despite distinct differences in causes of death. The United States has a cause-of-death structure similar to that of Sweden, but the age pattern of mortality is very different. High mortality in the middle age range in the United States results in approximately a one-year loss of life expectancy at age 45 in comparison with Sweden.