Forecasting Mortality Change

Abstract

This paper enumerates questions about the assumptions, methods, and interpretation of mortality projections that are made for policy applications. These questions are of practical concern to people who make and use projections, and cover a much narrower scope than the review by Tuljapurkar and Boe (pp. 13–47). The objective in circulating this paper was to provide an initial focus for participants at the SOA meeting.     

Mortality Change and Forecasting

Abstract

Prospects of longer life are viewed as a positive change for individuals and as a substantial social achievement but have led to concern over their implications for public spending on old-age support. This paper makes a critical assessment of knowledge about mortality change. It is oriented toward the problem of forecasting the course of mortality change and the potential of existing work to contribute to the development of useful forecasts in Canada, Mexico, and the U.S.

We first examine broad patterns in the historical decline in death rates in the three countries, the effect of these on trends in life expectancy, and the epidemiological transition. Next we review theories of the age pattern and evolution of mortality, including graduations, evolutionary theory, reliability models, dynamic models, and relational models.

The analysis and forecasting of mortality change have been shaped largely by some key historical lessons, which we summarize next. We emphasize issues that have been or are likely to be significant in mortality analysis, especially the questions of the age pattern and time trend in mortality at old ages; we distinguish patterns and facts that are established from those that remain uncertain. Next, we consider mortality differentials in characteristics such as sex, marital status, education, and socioeconomic variables; we summarize their key features and also point to the substantial gaps in our understanding of their determinants.

Finally, we review methods of forecasting, including the scenario method used by the U.S. Social Security Administration and the time series method of Lee and Carter. We set out some important recommendations for forecasters: forecasting assumptions should be made more formal and explicit; there should be retrospective evaluations of forecast performance; and greater attention should be paid to the assessment and consequences of forecast uncertainty.     

2009年中国物价走势分析与判断

2008年对中国来说,是极不寻常的一年。经济形势特别是价格形势发生了显著的变化,针对复杂多变的经济和价格形势,国家对宏观调控政策进行了迅速而重大的调整,从年初的"双防(防止经济增长     

The Lee-Carter Method for Forecasting Mortality,with Various Extensions and Applications

Abstract

In 1992, Lee and Carter published a new method for long-run forecasts of the level and age pattern of mortality, based on a combination of statistical time series methods and a simple approach to dealing with the age distribution of mortality. The method describes the log of a time series of age-specific death rates as the sum of an age-specific component that is independent of time and another component that is the product of a time-varying parameter reflecting the general level of mortality, and an age-specific component that represents how rapidly or slowly mortality at each age varies when the general level of mortality changes. This model is fit to historical data. The resulting estimate of the time-varying parameter is then modeled and forecast as a stochastic time series using standard methods. From this forecast of the general level of mortality, the actual age-specific rates are derived using the estimated age effects. The forecasts of the various life table functions have probability distributions, so probability intervals can be calculated for each variable and for summary measures such as life expectancy. The projected gain in life expectancy from 1989 to 1997 matches the actual gain very closely and is nearly twice the gain projected by the Social Security Administration’s Office of the Actuary. This paper describes the basic Lee-Carter method and discusses the forecasts to which it has led. It then discusses extensions, applications, and methodological improvements that have been made in recent years; considers shortcomings of the method; and briefly describes how it has been used as a component of more general stochastic population projections and stochastic forecasts of the finances of the U.S. Social Security system.     

Systematic Mortality Improvement Trends and Mortality Heterogeneity: Insights from Individual-Level HRS Data

Providers of life annuities and pensions need to consider both systematic mortality improvement trends and mortality heterogeneity. Although how mortality improvement varies with age and gender at the population level is well studied, how trends vary with risk factors remains relatively unexplored. This article assesses how systematic mortality improvement trends vary with individual risk characteristics using individual-level longitudinal data from the U.S. Health and Retirement Study between 1994 and 2009. Initially a Lee-Carter model is used to assess mortality improvement trends by grouping individuals with similar risk characteristics of gender, education, and race. We then fit a longitudinal mortality model to individual-level data allowing for heterogeneity and time trends in individual-level risk factors. Our results show how survey data can provide valuable insights into both mortality heterogeneity and improvement trends more effectively than commonly used aggregate models. We show how mortality improvement differs across individuals with different risk factors. Significantly, at an individual level, mortality improvement trends have been driven by changes in health history such as high blood pressure, cancer, and heart problems rather than risk factors such as education, marital status, body mass index, and smoker status.     

On the Modeling and Forecasting of Socioeconomic Mortality Differentials: An Application to Deprivation and Mortality in England

In any country, mortality rates and indices such as life expectancy usually differ across subpopulations, for example, defined by gender, geographic area, or socioeconomic variables (e.g., occupation, level of education, or income). These differentials, and in particular those related to socioeconomic circumstances, pose important challenges for the design of public policies for tackling social inequalities, as well as for the design of pension systems and the management of longevity risk in pension funds and annuity portfolios. We discuss the suitability for the modeling and forecasting of socioeconomic differences in mortality of several multiple population extensions of the Lee-Carter model, including a newly introduced relative model based on the modeling of the mortality in socioeconomic subpopulations alongside the mortality of a reference population. Using England mortality data for socioeconomic subpopulations defined using a deprivation index, we show that this new relative model exhibits the best results in terms of goodness of fit and ex post forecasting performance. We then use this model to derive projections of deprivation specific mortality rates and life expectancies at pensioner ages and analyze the impact of socioeconomic differences in mortality on the valuation of annuities.     

Diverging Mortality Inequality Trends among Young and Old in the Netherlands*

We analyse the trends in inequality in mortality across poverty groups at different ages over the period 1996–2016 in the Netherlands. In addition, we examine whether these trends are related to unequal changes in avoidable mortality, separated by preventable and treatable causes of death. We find that while inequalities in mortality have decreased at ages up to 65, inequalities increased for the oldest age groups. The decline in inequality at the younger ages can, to a large extent, be explained by a strong decrease of mortality from preventable and cardiovascular causes among the poor. The link between inequality and avoidable mortality at the oldest ages is less straightforward. The increasing inequality at old age might be the result of the inequalities shifting from the young to the older age groups, or of the rich benefiting more from the recent health (care) improvements than the poor.     

Are Professional Macroeconomic Forecasters Able To Do Better Than Forecasting Trends?

This paper investigates whether survey forecasters are able to make more accurate forecasts than simply supposing that the future values of the variable will move monotonically to the long‐run expectation. We consider the forecasts individually, and the consensus forecasts. Consensus survey forecasts are able to do so to varying degrees depending on the variable, but this ability is largely limited to forecasts of the current quarter.     

Forecasting for rulers

The trend towards presidential-style rule in contemporary democratic governments continues. Although rulers' positions are increasing in power and importance, the infrastructure and policy-making resources upon which they rely to govern have remained remarkably inadequate. The author argues that the contribution made by forecasting has been scant and often predicated upon the wrong aims. Forecasters and forecasting need a new approach.     

Coherent Modeling and Forecasting of Mortality Patterns for Subpopulations Using Multiway Analysis of Compositions: An Application to Canadian Provinces and Territories

Mortality levels for subpopulations, such as countries in a region or provinces within a country, generally change in a similar fashion over time, as a result of common historical experiences in terms of health, culture, and economics. Forecasting mortality for such populations should consider the correlation between their mortality levels. In this perspective, we suggest using multilinear component techniques to identify a common time trend and then use it to forecast coherently the mortality of subpopulations. Moreover, this multiway approach is performed on life table deaths by referring to Compositional Data Analysis (CoDa) methodology. Compositional data are strictly positive values summing to a constant and represent part of a whole. Life table deaths are compositional by definition because they provide the age composition of deaths per year and sum to the life table radix. In bilinear models the use of life table deaths treated as compositions generally leads to less biased forecasts than other commonly used models by not assuming a constant rate of mortality improvement. As a consequence, an extension of this approach to multiway data is here presented. Specifically, a CoDa adaptation of the Tucker3 model is implemented for life table deaths arranged in three-dimensional arrays indexed by time, age, and population. The proposed procedure is used to forecast the mortality of Canadian provinces in a comparative study. The results show that the proposed model leads to coherent forecasts.     

Nonparametric Tests for Positive Quadrant Dependence

We consider distributional free inference to test for positivequadrant dependence, that is, for the probability that two variablesare simultaneously small (or large) being at least as greatas it would be were they dependent. Tests for its generalizationto higher dimensions, namely positive orthant dependence, arealso analyzed. We propose two types of testing procedures. Thefirst procedure is based on the specification of the dependenceconcepts in terms of distribution functions, while the secondprocedure exploits the copula representation. For each specification,a distance test and an intersection-union test for inequalityconstraints are developed for time-dependent data. An empiricalillustration is given for U.S. insurance claim data, where wediscuss practical implications for the design of reinsurancetreaties. Another application concerns detection of positivequadrant dependence between the HFR and CSFB/Tremont marketneutral hedge fund indices and the S&P 500 index.     

First-Order Mortality Basis for Life Annuities

Mortality improvements pose a challenge for the life annuity business. For the management of such portfolios, it is important to forecast future mortality rates. Standard models for mortality forecasting assume that the force of mortality at age x in calendar year t is of the form exp, where the dynamics of the time index is described by a random walk with drift. Starting from such a best estimate of future mortality (called second-order mortality basis in actuarial science), the paper explains how to determine a conservative life table serving as first-order mortality basis. The idea is to replace the stochastic projected life table with a deterministic conservative one, and to assume mutual independence for the remaining life times. The paper then studies the distribution of the present value of the payments made to a closed group of annuitants. It turns out that De Pril–Panjer algorithm can be used for that purpose under first-order mortality basis. The connection with ruin probabilities is briefly discussed. An inequality between the distribution of the present value of future annuity payments under first-order and second-order mortality basis is provided, which allows to link value-at-risk computed under these two sets of assumptions. A numerical example performed on Belgian mortality statistics illustrates how the approach proposed in this paper can be implemented in practice.     

Revenue Forecasting Practices: Differences across Countries and Consequences for Forecasting Performance*

This paper reviews the practice and performance of revenue forecasting in selected OECD countries. It turns out that the cross‐country differences in the performance of revenue forecasting are first of all associated with uncertainty about the macroeconomic fundamentals. To some extent, they are also driven by country characteristics such as the importance of corporate and (personal) income taxes. Also, differences in the timing of the forecasts prove important. However, controlling for these differences, we find that the independence of revenue forecasting from possible government manipulation exerts a robust, significantly positive effect on the accuracy of revenue forecasts.     

A General Procedure for Constructing Mortality Models

Recently a large number of new mortality models have been proposed to analyze historic mortality rates and project them into the future. Many of these suffer from being over-parametrized or have terms added in an ad hoc manner that cannot be justified in terms of demographic significance. In addition, poor specification of a model can lead to period effects in the data being wrongly attributed to cohort effects, which results in the model making implausible projections. We present a general procedure for constructing mortality models using a combination of a toolkit of functions and expert judgment. By following the general procedure, it is possible to identify sequentially every significant demographic feature in the data and give it a parametric structural form. We demonstrate using U.K. mortality data that the general procedure produces a relatively parsimonious model that nevertheless has a good fit to the data.     

Logistic Regression for Insured Mortality Experience Studies

Properly adapted statistical modeling methodology can be a powerful tool for coping with a broad range of challenges related to life and annuity insurance industries' experience studies. In this article, we present a logistic regression model based on U.S. insured mortality experience study with a focus on gaining study efficiency and effectiveness by addressing multiple analytical predicaments within one statistical modeling framework. These predicaments include but are not limited to (a) testing statistical significances or credibility of potential mortality drivers, (b) estimation of normalized mortality, slopes, and differentials, (c) quantification of study reliability, and (d) extrapolation for under-experienced mortality, smoothing between select and ultimate estimations, and development of basic experience tables.     

Decomposing Inequality Changes: Allowing for Leisure in the Evaluation of Tax and Transfer Policy Effects

In this paper, we present two alternative methods of accounting for changes in leisure time in decomposing the inequality effects of tax and transfer policy changes. Three components are identified: tax policy, labour supply responses to tax policy changes and other population effects. The methods are used to decompose inequality changes in Australia between 2001 and 2006. Inequality is first defined in non‐welfarist terms as a function of disposable income: the independent judge places no value on leisure. Then, this is modified to allow for evaluations using a weighted geometric mean of disposable income and leisure. This is seen to modify the evaluation of changes in important ways. The results are found to differ from those obtained using a ‘welfarist’ evaluation in terms of money metric utility, where separate labour supply effects cannot be isolated.     

A Forecasting Model for Stock Market Diversity

We apply the recently introduced generalized tree-structured (GTS) model to the analysis and forecast of stock market diversity. Diversity is a measure of capital concentration across a market that plays a central role in the search for arbitrage. The GTS model allows for different conditional mean and volatility regimes that are directly related to the behavior of macroeconomic fundamentals through a binary threshold construction. Testing on US market data, we collect empirical evidence of the model’s strong potential in estimating and forecasting diversity accurately in comparison with other standard approaches. In addition, the GTS model allows for the construction of very simple portfolio strategies that systematically beat the standard cap-weighted S&P500 index. Financial support by the Foundation for Research and Development of the University of Lugano and by the National Centre of Competence in Research “Financial Valuation and Risk Management” (NCCR FINRISK) is gratefully acknowledged. The authors thank four anonymous referees for helpful comments.