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.     

Lifespan Dispersion in Times of Life Expectancy Fluctuation: The Case of Central and Eastern Europe

Central and Eastern Europe (CEE) have experienced considerable instability in mortality since the 1960s. Long periods of stagnating life expectancy were followed by rapid increases in life expectancy and, in some cases, even more rapid declines, before more recent periods of improvement. These trends have been well documented, but to date, no study has comprehensively explored trends in lifespan variation. We improved such analyses by incorporating life disparity as a health indicator alongside life expectancy, examining trends since the 1960s for 12 countries from the region. Generally, life disparity was high and fluctuated strongly over the period. For nearly 30 of these years, life expectancy and life disparity varied independently of each other, largely because mortality trends ran in opposite directions over different ages. Furthermore, we quantified the impact of large classes of diseases on life disparity trends since 1994 using a newly harmonized cause-of-death time series for eight countries in the region. Mortality patterns in CEE countries were heterogeneous and ran counter to the common patterns observed in most developed countries. They contribute to the discussion about life expectancy disparity by showing that expansion/compression levels do not necessarily mean lower/higher life expectancy or mortality deterioration/improvements.     

Latin American convergence and divergence towards the mortality profiles of developed countries

It is uncertain whether Latin America and Caribbean (LAC) countries are approaching a single mortality regime. Over the last three decades, LAC has experienced major public health interventions and the highest number of homicides in the world. However, these interventions and homicide rates are not evenly shared across countries. This study documents trends in life expectancy and lifespan variability for 20 LAC countries, 2000–14. By extending a previous method, we decompose differences in lifespan variability between LAC and a developed world benchmark into cause-specific effects. For both sexes, dispersion of amenable diseases through the age span makes the largest contribution to the gap between LAC and the benchmark. Additionally, for males, the concentration of homicides, accidents, and suicides in mid-life further impedes mortality convergence. Great disparity exists in the region: while some countries are rapidly approaching the developed regime, others remain far behind and suffer a clear disadvantage in population health.     

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.     

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.     

Lifespan Variation by Occupational Class: Compression or Stagnation Over Time?

Cross-sectional analyses of adult lifespan variation have found an inverse association between socioeconomic position and lifespan variation, but the trends by social class are unknown. We investigated trends in lifespan variation over four decades (1971–2010) by occupational social class (manual, lower nonmanual, upper nonmanual, other) using Finnish register data. We performed age and cause-of-death decompositions of lifespan variation for each sex (a) by occupational class over time and (b) between occupational classes at a shared level of life expectancy. Although life expectancy increased in all classes, lifespan variation was stable among manual workers and decreased only among nonmanual classes. These differences were caused by early-adult mortality: older-age lifespan variation declined for all the classes, but variation in early-adult mortality increased for all classes except the highest. The manual class’s high and stagnant lifespan variation was driven by declines in circulatory diseases that were equally spread over early mortality-compressing and older mortality-expanding ages, as well as by high early-adult mortality from external causes. Results were similar for men and women. The results of this study, which is the first to document trends in lifespan variation by social class, suggest that mortality compression is compatible with increasing life expectancy but currently achieved only by higher occupational classes.     

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.     

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.     

Divergence in Age Patterns of Mortality Change Drives International Divergence in Lifespan Inequality

In the past six decades, lifespan inequality has varied greatly within and among countries even while life expectancy has continued to increase. How and why does mortality change generate this diversity? We derive a precise link between changes in age-specific mortality and lifespan inequality, measured as the variance of age at death. Key to this relationship is a young–old threshold age, below and above which mortality decline respectively decreases and increases lifespan inequality. First, we show for Sweden that shifts in the threshold’s location have modified the correlation between changes in life expectancy and lifespan inequality over the last two centuries. Second, we analyze the post–World War II (WWII) trajectories of lifespan inequality in a set of developed countries—Japan, Canada, and the United States—where thresholds centered on retirement age. Our method reveals how divergence in the age pattern of mortality change drives international divergence in lifespan inequality. Most strikingly, early in the 1980s, mortality increases in young U.S. males led to a continuation of high lifespan inequality in the United States; in Canada, however, the decline of inequality continued. In general, our wider international comparisons show that mortality change varied most at young working ages after WWII, particularly for males. We conclude that if mortality continues to stagnate at young ages yet declines steadily at old ages, increases in lifespan inequality will become a common feature of future demographic change.     

Are mortality projections always more pessimistic when disaggregated by cause of death?

"It is often observed that mortality projections are more pessimistic when disaggregated by cause of death. This article explores the generality and strength of this relationship under a variety of forecasting models. First, a simple measure of the pessimism inherent in cause-based mortality forecasts is derived. Second, it is shown that the pessimism of cause-based forecasts can be approximated using only data on the distribution of deaths by cause in two pervious time periods. Third, using Japanese mortality data during 1951-1990, the analysis demonstrates that the pessimism of cause-based forecasts can be attributed mainly to observed trends in mortality due to cancer and heart disease, with smaller contribution due to trends in stroke (women only), pneumonia/bronchitis, accidents, and suicide. The last point requires the important qualification, however, that observed trends in cancer and heart disease may be severely biased due to changes in diagnostic practice." (SUMMARY IN FRE)     

Coherent mortality forecasts for a group of populations: An extension of the lee-carter method

Mortality patterns and trajectories in closely related populations are likely to be similar in some respects, and differences are unlikely to increase in the long run. It should therefore be possible to improve the mortality forecasts for individual countries by taking into account the patterns in a larger group. Using the Human Mortality Database, we apply the Lee-Carter model to a group of populations, allowing each its own age pattern and level of mortality but imposing shared rates of, change by age. Our forecasts also allow divergent patterns to continue for a while before tapering off. We forecast greater longevity gains for the United States and lesser ones for Japan relative to separate forecasts.     

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.     

Disaggregation in population forecasting: do we need it? And how to do it simply

"We have described a method for reducing the dimensionality of the forecasting problem by parsimoniously modeling the evolution over time of the age schedules of vital rates. This method steers a middle course between forecasting aggregates and forecasting individual age specific rates: we reduce the problem to forecasting a single parameter for fertility and another one for mortality. We have described a number of refinements and extensions of those basic methods, which preserve their underlying structure and simplicity. In particular, we show how one can fit the model more simply, incorporate lower bounds to the forecasts of rates, disaggregate by sex or race, and prepare integrated forecasts of rates for a collection of regions. We also discuss alternate approaches to forecasting the estimated indices of fertility and mortality, including state-space methods. These many versions of the basic method have yielded remarkably similar results." (SUMMARY IN FRE)     

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.     

The role of population size in the determination and prediction of population forecast errors: An evaluation using conifidence intervals for subcounty areas

Producers of population forecasts acknowledge the uncertainty inherent in trying to predict the future and should warn about the likely error of their forecasts. Confidence intervals represent one way of quantifying population forecast error. Most of the work in this area relates to national forecasts; although, confidence intervals have been developed for state and county forecasts. A few studies have examined subcounty forecast error, however, they only measured point estimates of error. This paper describes a technique for making subcounty population forecasts and for generating confidence intervals around their forecast error. It also develops statistical equations for calculating point estimates and confidence intervals for areas with different population sizes. A non-linear, inverse relationship between population size and forecast accuracy was found and we demonstrate the ability to accurately predict average forecast error and confidence intervals based on this relationship.     

Modeling and Forecasting Mortality With Economic Growth: A Multipopulation Approach

Research on mortality modeling of multiple populations focuses mainly on extrapolating past mortality trends and summarizing these trends by one or more common latent factors. This article proposes a multipopulation stochastic mortality model that uses the explanatory power of economic growth. In particular, we extend the Li and Lee model (Li and Lee 2005) by including economic growth, represented by the real gross domestic product (GDP) per capita, to capture the common mortality trend for a group of populations with similar socioeconomic conditions. We find that our proposed model provides a better in-sample fit and an out-of-sample forecast performance. Moreover, it generates lower (higher) forecasted period life expectancy for countries with high (low) GDP per capita than the Li and Lee model.     

The Predictive Validity of Subjective Mortality Expectations: Evidence From the Health and Retirement Study

Several recent studies suggest that individual subjective survival forecasts are powerful predictors of both mortality and behavior. Using 15 years of longitudinal data from the Health and Retirement Study, I present an alternative view. Across a wide range of ages, predictions of in-sample mortality rates based on subjective forecasts are substantially less accurate than predictions based on population life tables. Subjective forecasts also fail to capture fundamental properties of senescence, including increases in yearly mortality rates with age. To shed light on the mechanisms underlying these biases, I develop and estimate a latent-factor model of how individuals form subjective forecasts. The estimates of this model’s parameters imply that these forecasts incorporate several important sources of measurement error that arguably swamp the useful information they convey.     

Effect of aggregation on the estimation of trend in mortality

There are three approaches to analyzing and forecasting age‐specific mortality: (1) analyze age‐specific data directly, (2) analyze each cause‐specific mortality series separately and add the results, (3) analyze cause‐specific mortality series jointly and add the results. We show that if linear models are used for cause‐specific mortality, then the three approaches often give close results even when cause‐specific series are correlated. This result holds for cross‐correlations arising from random misclassification of deaths by cause, and also for certain patterns of systematic misclassification. It need not hold, if one or more causes serve as “leading indicators”; for the remaining causes, or if outside information is incorporated into forecasting either through expert judgment or formal statistical modeling. Under highly nonlinear models or in the presence of modeling error the result may also fail. The results are illustrated with U.S. age‐specific mortality data from 1968–1985. In some cases the aggregate forecasts appear to be the more credible ones.     

Coherent Mortality Forecasting: The Product-Ratio Method With Functional Time Series Models

When independence is assumed, forecasts of mortality for subpopulations are almost always divergent in the long term. We propose a method for coherent forecasting of mortality rates for two or more subpopulations, based on functional principal components models of simple and interpretable functions of rates. The product-ratio functional forecasting method models and forecasts the geometric mean of subpopulation rates and the ratio of subpopulation rates to product rates. Coherence is imposed by constraining the forecast ratio function through stationary time series models. The method is applied to sex-specific data for Sweden and state-specific data for Australia. Based on out-of-sample forecasts, the coherent forecasts are at least as accurate in overall terms as comparable independent forecasts, and forecast accuracy is homogenized across subpopulations.