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)     

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     

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.     

Modeling and Forecasting Health Expectancy: Theoretical Framework and Application

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

Modeling and forecasting populations by time series: The Swedish case

Time series analysis techniques are used to model and to forecast populations. An autoregressive (AR) and a moving average (MA) model, which seem to fit the population of Sweden very well, are found. Forecasts are calculated using both models and are compared with the forecasts obtained by other methods. This comparison is very favorable for the time series models. Although our study is confined to the mid-year population of Sweden, there are good reasons to expect that the technique can be successfully applied to other population parameters.     

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.     

Far eastern patterns of Mortality

Summary In this paper a mortality pattern is identified which has not previously been described by model mortality schedules and seems to have occurred only in populations in the Far East. Mortality schedules in Taiwan, Hong Kong, Singapore, and Korea during the past several decades have been characterized by excessively high death rates of men at the older ages. This excess mortality has progressively diminished and most recent death rates for men show only slight deviations from West model life tables. An examination of statistics on causes of death suggests that tuberculosis is at least partly responsible for the excess mortality of men.     

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.     

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)     

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.     

Precision,bias, and uncertainty for state population forecasts: an exploratory analysis of time series models

Many researchers have used time series models to construct population forecasts and prediction intervals at the national level, but few have evaluated the accuracy of their forecasts or the out-of-sample validity of their prediction intervals. Fewer still have developed models for subnational areas. In this study, we develop and evaluate six ARIMA time series models for states in the United States. Using annual population estimates from 1900 to 2000 and a variety of launch years, base periods, and forecast horizons, we construct population forecasts for four states chosen to reflect a range of population size and growth rate characteristics. We compare these forecasts with population counts for the corresponding years and find precision, bias, and the width of prediction intervals to vary by state, launch year, model specification, base period, and forecast horizon. Furthermore, we find that prediction intervals based on some ARIMA models provide relatively accurate forecasts of the distribution of future population counts but prediction intervals based on other models do not. We conclude that there is some basis for optimism regarding the possibility that ARIMA models might be able to produce realistic prediction intervals to accompany population forecasts, but a great deal of work remains to be done before we can draw any firm conclusions.     

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.     

Parameterizing age patterns of demographic rates with the multiexponential model schedule

"For nearly 200 years actuaries, statisticians, and demographers have sought to summarize the age pattern of mortality rates by means of a limited number of parameters. Such 'model schedules' have also been useful in representing schedules of rates other than mortality....This paper illustrates a particular general functional form for such model schedules: the multiexponential function. It discusses the changing behavior of this function as its parameters take on different values and examines the quality of the fits of this function to observed data on mortality, fertility, and migration." This is a revised version of a paper originally presented at the 1993 Annual Meeting of the Population Association of America. (SUMMARY IN FRE)     

Empirical bayes estimation of demographic schedules for small areas

In this article, we analyze empirical Bayes (EB) methods for estimating small-area rate schedules. We develop EB methods that treat schedules as vectors and use adaptive neighborhoods to keep estimates appropriately local. This method estimates demographic rates for local subpopulations by borrowing strength not only from similar individuals elsewhere but also from other groups in the same area and from regularities in schedules across locations. EB is substantially better than standard methods when rates have strong spatial and age patterns. We illustrate this method with estimates of age-specific fertility schedules for over 3,800 Brazilian municipalities.     

The development and use of demographic models

In this review, we first examine two classical demographic models - conventional life tables and stable populations - and a modern generalization of stable population theory; we then discuss mathematical models of conception and birth. These models involve purely mathematical relations in formal demography as opposed to empirical regularities. Next we consider model age schedules of mortality, nuptialitiy, marital fertility, fertility, and migration that are explicitly based on such empirical patterns. We close this empirical section with a discussion of model stable populations, which are based on model life tables. We next examine the use of demographic models in forecasting future mortality, nuptiality, and fertility and in population projection. Following a discussion of microsimulation models, which gives us the opportunity to mention model age schedules of post partum amenorrhoea and of sterility, we close with observations about the purposes and uses of demographic models.     

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.     

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.     

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.     

Evaluation of Alternative Cohort-Component Models for Local Area Population Forecasts

It is generally accepted by demographers that cohort-component projection models which incorporate directional migration are conceptually preferable to those using net migration. Yet net migration cohort-component models, and other simplified variations, remain in common use by both academics and practitioners because of their simplicity and low data requirements. While many arguments have been presented in favour of using one or other type of model, surprisingly little analysis has been undertaken to assess which tend to give the most accurate forecasts. This paper evaluates five cohort-component models which differ in the way they handle migration, four of which are well known, with one—a composite net migration model—being proposed here for the first time. The paper evaluates the performance of these five models in their unconstrained form, and then in a constrained form in which age–sex-specific forecasts are constrained to independent total populations from an extrapolative model shown to produce accurate forecasts in earlier research. Retrospective forecasts for 67 local government areas of New South Wales were produced for the period 1991–2011 and then compared to population estimates. Assessments of both total and age-specific population forecasts were made. The results demonstrate the superior performance of the forecasts constrained to total populations from the extrapolative model, with the constrained bi-regional model giving the lowest errors. The findings should be of use to practitioners in selecting appropriate models for local area population forecasts.