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.     

New Cohort Fertility Forecasts for the Developed World: Rises,Falls, and Reversals

With period fertility having risen in many low‐fertility countries, an important emerging question is whether cohort fertility trends are also reversing. We produce new estimates of cohort fertility for 37 developed countries using a new, simple method that avoids the underestimation typical of previous approaches. Consistent with the idea that timing changes were largely responsible for the last decades' low period fertility, we find that family size has remained considerably higher than the period rates of 1.5 in many “low‐fertility” countries, averaging about 1.8 children. Our forecasts suggest that the long‐term decline in cohort fertility is flattening or reversing in many world regions previously characterized by low fertility. We document the marked increase of cohort fertility in the English‐speaking world and in Scandinavia; signs of an upward reversal in many low‐fertility countries, including Japan and Germany; and continued declines in countries such as Taiwan and Portugal. We include in our forecasts estimates of statistical uncertainty and the possible effects of the recent economic recession.     

Long‐Term Population Projections and the US Social Security System

According to a report recently issued by the Technical Panel for the US Social Security Administration, the long‐term financial outlook for the system is worse than previously thought. The worsening projected by the panel in the long‐run funding imbalance of the Social Security System is mostly due to the recommendation by the panel to add an extra four years to the currently projected increase in life expectancy by 2075: from 81.8 years to 85.9 years. The panel recommended no change in the current intermediate projected long‐run TFR of 1.9 and net immigration of 900,000 persons per year. The recommendation to increase the projected gains in life expectancy was based on international trends as well as on historical trends in the United States and the absence of biological evidence ruling out such gains. Industrial countries have a history of under‐predicting the growth of their elderly population, and it is expected that large mortality adjustments may be needed in the projections for public pension programs also in industrial countries other than the United States.     

香港人口死亡率演变及其未来发展

与其它发展地区类似 ,二战以后香港人口死亡率已经经历了显著的下降 ,达到了一个非常低的水平。在这种极低水平的现状下 ,香港人口死亡率进一步下降的空间还有多大呢 ?本文基于香港人口死亡率历史数据 ,探讨了其演变趋势 ,同时利用Lee -Carter模型对香港未来 5 0年分性别的人口死亡率进行了预测。如果我们将预测结果与最近的官方预测数据进行比较 ,可以发现 ,本文Lee -Carter模型预测的未来香港人口死亡率下降趋势比官方预测结果要乐观     

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.     

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.     

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." The geographical focus is on the United States. (SUMMARY IN FRE)     

The expected length of male retirement in the United States, 1850–1990

This paper estimates the expected length of retirement for each labor market cohort between 1850 and 1990. Since 1850, the expected length of retirement has increased by more than six-fold and now represents up to 30% of male length of life after entry into the labor force. The rise of the duration of retirement during the twentieth century is analyzed according to the effects of mortality decline and of decreased age of retirement. Implications of the result for a number of economic issues, including the relative importance of life-cycle savings and the potential saving effect of Social Security, are discussed. Received: 22 September 1999/Accepted: 11 July 2000     

Long‐Term Trends in Life Expectancy and Active Life Expectancy in the United States

Changes in life expectancy and in active life expectancy may have effects on the fiscal integrity of both the Social Security and Medicare programs. Analysis of the fiscal stability of these programs shows that the most serious problem may be the growth of Medicare expenditures projected to surpass, in about 2024, Social Security costs. This is aggravated by the associated rapid growth of the Medicaid program. To understand how the growth of Medicare, Medicaid, and Social Security might be correlated we present estimates of changes in life expectancy and active life expectancy from 1935 to 1999 and then project those values to 2080. How the correlation of life expectancy and active life expectancy changes over time, and by age, may provide insights into how increased health care expenditures, if effective in changing health in the elderly, could modify the age structure of the labor force and the availability of human capital.     

Increasing longevity and medicare expenditures

Official Medicare projections forecast that the elderly population will be less healthy and more costly over the next century. This prediction stems from the use of age as an indicator of health status: increases in longevity are assumed to increase demand for health care as individuals survive to older and higher-use ages. In this paper I suggest an alternative approach, in which time until death replaces age as the demographic indicator of health status. Increases in longevity are assumed to postpone the higher Medicare use and costs associated with the final decade of life. I contrast the two approaches, using mortality forecasts consistent with recent projections from the U.S. Census Bureau and the Social Security Administration. The time-until-death method yields significantly lower-cost forecasts. The hypothetical cost savings from improved health care small, however, relative to the size of the Medicare solvency problem caused by population aging.     

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.     

Empirical Prediction Intervals for County Population Forecasts

Population forecasts entail a significant amount of uncertainty, especially for long-range horizons and for places with small or rapidly changing populations. This uncertainty can be dealt with by presenting a range of projections or by developing statistical prediction intervals. The latter can be based on models that incorporate the stochastic nature of the forecasting process, on empirical analyses of past forecast errors, or on a combination of the two. In this article, we develop and test prediction intervals based on empirical analyses of past forecast errors for counties in the United States. Using decennial census data from 1900 to 2000, we apply trend extrapolation techniques to develop a set of county population forecasts; calculate forecast errors by comparing forecasts to subsequent census counts; and use the distribution of errors to construct empirical prediction intervals. We find that empirically-based prediction intervals provide reasonably accurate predictions of the precision of population forecasts, but provide little guidance regarding their tendency to be too high or too low. We believe the construction of empirically-based prediction intervals will help users of small-area population forecasts measure and evaluate the uncertainty inherent in population forecasts and plan more effectively for the future.     

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.     

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.     

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.     

Evaluating the performance of the lee-carter method for forecasting mortality

Lee and Carter (LC) published a new statistical method for forecasting mortality in 1992. This paper examines its actual and hypothetical forecast errors, and compares them with Social Security forecast errors. Hypothetical historical projections suggest that LC tended to underproject gains, but by less than did Social Security. True e0 was within the ex ante 95% probability interval 97% of the time overall, but intervals were too broad up to 40 years and too narrow after 50 years. Projections to 1998 made after 1945 always contain errors of less than two years. Hypothetical projections for France, Sweden, Japan, and Canada would have done well. Changing age patterns of mortality decline over the century pose problems for the method.     

Population Variation in Cause of Death: Level,Gender, and Period Effects

The trends in 13 cause of death categories are examined with respect to expectation of life, sex differences, and period effects while misclassification of cause of death is controlled. The results suggest that as mortality declines, 1) the increasingly U-shaped age pattern of mortality is a period effect associated with the infectious diseases, 2) the risks of both overall infectious and degenerative causes of death decline, and 3) infectious disease mortality declines more in males, while degenerative disease mortality declines more in females. Finally, the model shows that some contemporary populations are approaching the .limits of reduction in mortality during infancy, childhood, and young adulthood. Past declines in the degenerative diseases, however, suggest that mortality may continue to decline.     

Differences in life expectancy by education and occupation in Italy, 1980-94: indirect estimates from maternal and paternal orphanhood

In the present study, we use the modified orphanhood method to analyse mortality differences by socio-economic status in Italy. This technique permits the indirect estimation of adult mortality from survey-based information on parents' survival in developed populations and helps to overcome several limitations of conventional studies on mortality differences by social class. We estimate a time series of life tables by education and occupation and analyse the differences in life expectancy by socio-economic status along with their changes between 1980-84, 1985-89, and 1990-94. Whereas mortality differences between the highest social class and the other socio-economic status groups increased among men, they decreased among women. We speculate about the reasons for these sex-specific trends and evaluate the application of indirect estimation techniques to the populations of developed countries.     

Beyond Material Explanations: Family Solidarity and Mortality,a Small Area‐level Analysis

Social solidarity, being embedded in a network of binding social relationships, tends to extend human longevity. Yet while average incomes in the Western world, and with them, life expectancies, have risen dramatically, the second demographic transition has occasioned a breakdown in traditional family forms. This article considers whether these trends in family life may have slowed the rise in life expectancy. I present a cross‐sectional analysis of Israeli statistical areas (SAs), for which I construct indexes of Standard of Living (SOL), Traditional Family Structure (TFS), and Religiosity (R). I show that (1) increases in all three of these indexes are associated with lower levels of mortality, (2) male mortality is more sensitive to differences in SOL and TFS than is female mortality, and (3) net of differences in SOL and TFS, there is no difference in the mortality levels of Arab and Jewish populations.     

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.