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.     

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.     

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.     

Stability over time in the distribution of population forecast errors

A number of studies in recent years have investigated empirical approaches to the production of confidence intervals for population projections. The critical assumption underlying these approaches is that the distribution of forecast errors remains stable over time. In this article, we evaluate this assumption by making population projections for states for a number of time periods during the 20th century, comparing these projections with census enumerations to determine forecast errors, and analyzing the stability of the resulting error distributions over time. These data are then used to construct and test empirical confidence limits. We find that in this sample the distribution of absolute percentage errors remained relatively stable over time and data on past forecast errors provided very useful predictions of future forecast errors.     

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.     

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.     

Age reporting among white Americans aged 85+: Results of a record linkage study

This study investigates age reporting on the death certificates of older white Americans. We link a sample of death certificates for native-born whites aged 85+ in 1985 to Social Security Administration records and to records of the U.S. censuses of 1900, 1910, and 1920. When ages in these sources are compared, inconsistencies are found to be minimal, even beyond age 95. Results show little distortion and no systematic biases in the reported age distribution of deaths. To explore the effect of age misreporting on old-age mortality, we estimate "corrected" age-specific death rates by the extinct-generation method for the U.S. white cohort born in 1885. With few exceptions, corrected and uncorrected rates in single years differ by less than 3% and are not systematically biased. When we compare corrected rates with those for the same birth cohort in France, Japan, and Sweden, we find that white American mortality at older ages is exceptionally low.     

Insights from the Evaluation of Past Local Area Population Forecasts

Local area population forecasts have a wide variety of uses in the public and private sectors. But not enough is known about the errors of such forecasts, particularly over the longer term (20 years or more). Understanding past errors is valuable for both forecast producers and users. This paper (i) evaluates the forecast accuracy of past local area population forecasts published by Australian State and Territory Governments over the last 30 years and (ii) illustrates the ways in which past error distributions can be employed to quantify the uncertainty of current forecasts. Population forecasts from the past 30 years were sourced from State and Territory Governments. Estimated resident populations to which the projections were compared were created for the geographical regions of the past projections. The key features of past forecast error patterns are described. Forecast errors mostly confirm earlier findings with regard to the relationship between error and length of projection horizon and population size. The paper then introduces the concept of a forecast ‘shelf life’, which indicates how far into the future a forecast is likely to remain reliable. It also illustrates how past error distributions can be used to create empirical prediction intervals for current forecasts. These two complementary measures provide a simple way of communicating the likely magnitude of error that can be expected with current local area population forecasts.     

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 Impact of Salmon Bias on the Hispanic Mortality Advantage: New Evidence from Social Security Data

A great deal of research has focused on factors that may contribute to the Hispanic mortality paradox in the United States. In this paper, we examine the role of the salmon bias hypothesis—the selective return of less-healthy Hispanics to their country of birth—on mortality at ages 65 and above. These analyses are based on data drawn from the Master Beneficiary Record and NUMIDENT data files of the Social Security Administration. These data provide the first direct evidence regarding the effect of salmon bias on the Hispanic mortality advantage. Although we confirm the existence of salmon bias, it is of too small a magnitude to be a primary explanation for the lower mortality of Hispanic than non-hispanic (NH)-White primary social security beneficiaries. Longitudinal surveys that follow individuals in and out of the United States are needed to further explore the role of migration in the health and mortality of foreign-born US residents and factors that contribute to the Hispanic mortality paradox.     

Household and Living Arrangement Projections at the Subnational Level: An Extended Cohort-Component Approach

This article presents the core methodological ideas and empirical assessments of an extended cohort-component approach (known as the “ProFamy model”), and applications to simultaneously project household composition, living arrangements, and population sizes–gender structures at the subnational level in the United States. Comparisons of projections from 1990 to 2000 using this approach with census counts in 2000 for each of the 50 states and Washington, DC show that 68.0 %, 17.0 %, 11.2 %, and 3.8 % of the absolute percentage errors are <3.0 %, 3.0 % to 4.99 %, 5.0 % to 9.99 %, and ≥10.0 %, respectively. Another analysis compares average forecast errors between the extended cohort-component approach and the still widely used classic headship-rate method, by projecting number-of-bedrooms–specific housing demands from 1990 to 2000 and then comparing those projections with census counts in 2000 for each of the 50 states and Washington, DC. The results demonstrate that, compared with the extended cohort-component approach, the headship-rate method produces substantially more serious forecast errors because it cannot project households by size while the extended cohort-component approach projects detailed household sizes. We also present illustrative household and living arrangement projections for the five decades from 2000 to 2050, with medium-, small-, and large-family scenarios for each of the 50 states; Washington, DC; six counties of southern California; and the Minneapolis–St. Paul metropolitan area. Among many interesting numerical outcomes of household and living arrangement projections with medium, low, and high bounds, the aging of American households over the next few decades across all states/areas is particularly striking. Finally, the limitations of the present study and potential future lines of research are discussed.     

An evaluation of population projections by age

A number of studies have evaluated the accuracy of projections of the size of the total population, but few have considered the accuracy of projections by age group. For many purposes, however, the relevant variable is the population of a particular age group, rather than the population as a whole. We investigated the precision and bias of a variety of age-group projections at the national and state levels in the United States and for counties in Florida. We also compared the accuracy of state and county projections that were derived from full-blown applications of the cohort-component method with the accuracy of projections that were derived from a simpler, less data-intensive version of the method. We found that age-group error patterns are different for national projections than for subnational projections; that errors are substantially larger for some age groups than for others; that differences in errors among age groups decline as the projection horizon becomes longer; and that differences in methodological complexity have no consistent impact on the precision and bias of age-group projections.     

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     

African-american mortality at older ages: Results of a matching study

In this paper we investigate the quality of age reporting on death certificates of elderly African-Americans. We link a sample of death certificates of persons age 65+ in 1985 to records for the same individuals in U.S. censuses of 1900, 1910, and 1920 and to records of the Social Security Administration. The ages at death reported on death certificates are too young on average. Errors are greater for women than for men. Despite systematic underreporting of age at death, too many deaths are registered at ages 95+. This excess reflects an age distribution of deaths that declines steeply with age, so that the base for upward transfers into an age category is much larger than the base for transfers downward and out. When corrected ages at death are used to estimate age-specific death rates, African-American mortality rates increase substantially above age 85 and the racial “crossover” in mortality disappears. Uncertainty about white rates at ages 95+, however, prevents a decisive racial comparison at the very oldest ages.     

A description of the extreme aged population based on improved medicare enrollment data

The mortality and size of the extreme aged population can be studied most accurately with Medicare enrollment data from the Social Security Administration's Master Beneficiary Record after certain types of questionable records are eliminated. With the improved data base we find that mortality rates at the very old ages are higher than published rates, we are more confident of the reality of the race crossover, and we can estimate the number of centenarians more accurately. Furthermore, a large matched-records study shows close agreement on age at death between the Master Beneficiary Record and the death certificate.     

The impact of minority group status on the projected retirement income of divorced women in the baby boom cohort

Using projections from the Social Security Administration's Modeling Income in the Near Term (MINT1), we examine the characteristics and retirement income of white non-Hispanic, black non-Hispanic, and Hispanic divorced women in the baby boom cohort. Although we find significant differences in retirement income for divorced women of different racial and ethnic groups, the characteristics associated with higher or lower retirement income are very similar. That is, being college educated, owning a home, and having pension and asset income, for example, correspond to increased retirement income for all racial and ethnic groups. However, because black and Hispanic women are less likely than white women to be college educated, to own their home, and to have pension and asset income, their retirement income tends to be lower than that of white women. We conclude the paper by briefly discussing policy options to address the retirement needs of divorced women.     

Measuring socioeconomic mortality differentials over time

Using 1973 Current Population Survey data matched to 1973-1978 Social Security mortality records, this study measures the relationship between the income and education of men and their subsequent mortality. The estimated relationships are compared with socioeconomic mortality differentials found by Kitagawa and Hauser in their study of 1960 census-death certificate matched data. The comparison suggests that there has been no improvement in the relative mortality experience of low socioeconomic status men. More generally, the article discusses how Social Security data could be used to monitor, on a continual basis, our progress toward eradicating significant mortality differentials in the United States.     

Applying Lee-Carter under conditions of variable mortality decline

The Lee-Carter method of mortality forecasting assumes an invariant age component and most applications have adopted a linear time component. The use of the method with Australian data is compromised by significant departures from linearity in the time component and changes over time in the age component. We modify the method to adjust the time component to reproduce the age distribution of deaths, rather than total deaths, and to determine the optimal fitting period in order to address non-linearity in the time component. In the Australian case the modification has the added advantage that the assumption of invariance is better met. For Australian data, the modifications result in higher forecast life expectancy than the original Lee-Carter method and official projections, and a 50 per cent reduction in forecast error. The model is also expanded to take account of age-time interactions by incorporating additional terms, but these are not readily incorporated into forecasts.     

Applying Lee-Carter under conditions of variable mortality decline

The Lee-Carter method of mortality forecasting assumes an invariant age component and most applications have adopted a linear time component. The use of the method with Australian data is compromised by significant departures from linearity in the time component and changes over time in the age component. We modify the method to adjust the time component to reproduce the age distribution of deaths, rather than total deaths, and to determine the optimal fitting period in order to address non-linearity in the time component. In the Australian case the modification has the added advantage that the assumption of invariance is better met. For Australian data, the modifications result in higher forecast life expectancy than the original Lee-Carter method and official projections, and a 50 per cent reduction in forecast error. The model is also expanded to take account of age-time interactions by incorporating additional terms, but these are not readily incorporated into forecasts.     

Retirement against the demographic trend: More older people living longer, working less, and saving less?

The American population is aging rapidly and individuals are living longer. Yet Americans are saving less and older workers are leaving the labor force at younger and younger ages. The accelerated drop in labor force participation corresponds roughly to the introduction of Social Security and the adaption of employer-provided pension plans. I have illustrated that Social Security and employer-provided pension plans provide substantial incentive to leave the labor force early. The quantitative effect of this inducement is illustrated by simulating the effects of changes in pension plan and Social Security provisions on the retirement decisions of employees in a large firm, who are covered by a typical defined benefit pension plan. Scheduled Social Security changes would have little effect on the retirement decisions of employees with a typical defined benefit pension plan like the one considered here. But if the pension plan provisions were changed to correspond to the Social Security changes, the effect would be very large. And, although not contemplated by current legislation, it is clear that an increase in the Social Security early retirement age would have a substantial effect on the early retirement rates of the large number of employees not covered by a pension plan.