Subjective mortality hazard shocks and the adjustment of consumption expenditures

I estimate the effect of shocks to subjective mortality hazards on consumption expenditures of retired individuals using the Survey of Health, Ageing and Retirement in Europe. I measure mortality expectations with survey responses on survival probabilities. To create plausibly exogenous variation in mortality hazard, I use the death of a sibling as an instrument. My results show that survey responses contain economically relevant information about longevity expectations and confirm the predictions of life-cycle theories about the effect of these expectations on intertemporal choice.     

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.     

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.     

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.     

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)     

Using Subjective Expectations to Forecast Longevity: Do Survey Respondents Know Something We Don’t Know?

Old-age mortality is notoriously difficult to predict because it requires not only an understanding of the process of senescence-which is influenced by genetic, environmental, and behavioral factors-but also a prediction of how these factors will evolve. In this paper I argue that individuals are uniquely qualified to predict their own mortality based on their own genetic background, as well as environmental and behavioral risk factors that are often known only to the individual. Given this private information, individuals form expectations about survival probabilities that may provide additional information to demographers and policymakers in their challenge to predict mortality. From expectations data from the 1992 Health and Retirement Study (HRS), I construct subjective, cohort life tables that are shown to predict the unusual direction of revisions to U.S. life expectancy by gender between 1992 and 2004: that is, for these cohorts, the Social Security Actuary (SSA) raised male life expectancy in 2004 and at the same lowered female life expectancy, narrowing the gender gap in longevity by 25% over this period. Further, although the subjective life expectancies for men appear to be roughly in line with the 2004 life tables, the subjective expectations of women suggest that female life expectancies estimated by the SSA might still be on the high side.     

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.     

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.     

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     

Child mortality and fertility decline: Does the Barro-Becker model fit the facts?

I compare the predictions of three variants of the altruistic parent model of Barro and Becker for the relationship between child mortality and fertility. In the baseline model fertility choice is continuous, and there is no uncertainty over the number of surviving children. The baseline model is contrasted to an extension with discrete fertility choice and stochastic mortality and a setup with sequential fertility choice. The quantitative predictions of the models are remarkably similar. While in each model the total fertility rate falls as child mortality declines, the number of surviving children increases. The results suggest that factors other than declining infant and child mortality are responsible for the large decline in net reproduction rates observed in industrialized countries over the last century. Financial support by the National Science Foundation (grant SES-0217051) and the UCLA Academic Senate is gratefully acknowledged. I thank Sebnem Kalemli-Oczan, Rodrigo Soares, and two anonymous referees for comments that helped to substantially improve the paper. Olesya Baker and Ilya Berger provided excellent research assistance. Responsible editor: Junsen Zhang.     

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.     

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.     

An Ecological Regional Analysis of South Carolina

This study of the counties of South Carolina introduces a limited purpose, modifiable technology that is designed to reproduce the rapid discovery strategy of the natural sciences. It uses factor analysis to identify types of communities and the threats they face, and evaluates their success in dealing with these by comparisons based on age-adjusted mortality rates. The factor analysis of mostly census indicators generated an Urbanization factor along with two measures of the interaction with the environment, Growth and Poverty. Growth was expected to predict mortality negatively while Poverty should predict positively. Regression analysis confirms both predictions but only for each race. That is, Growth predicted lower mortality, but only for African-Americans. Poverty predicted higher mortality, but only for whites. These and other puzzling findings are explored, illustrating the “rapid discovery” technology that is the central feature of this paper.     

Relating Changes in Life Expectancy to Changes in Mortality

I address the problem of what can be said of changes in mortality rates, if one knows how life expectancies change. I note a general formula relating life expectancies in different ages to mortality and prove that if mortality changes over time following a proportional-hazard model, then there is a one-to-one correspondence between life expectancy at birth and mortality rates. Extensions and an application of these results to the analysis of mortality change are presented.     

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.     

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.     

Accounting for migration in cohort-component projections of state and local populations

Migration is the most difficult component of state and local population growth to forecast accurately because it is more volatile than either births or deaths, and subject to much larger fluctuations within a short period of time. In addition, migration rates can be based on several different measures of migration and the base population. The choice of the appropriate base population has received little attention from demographic researchers, but can have a tremendous impact on population projections. In this article, I develop three different models for projecting migration, each using a different denominator for migration rates. Population projections for ten states are made, using identical data and cohort component techniques, except for the different formulations of migration rates. Differences among the three sets of projections are noted, and conclusions are drawn regarding their usefulness as forecasts of population growth.     

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.