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.     

Point and interval forecasts of age-specific fertility rates: a comparison of functional principal component methods

Accurate forecasts of age-specific fertility rates are critical for government policy, planning and decision making. With the availability of the Human Fertility Database (2011), the paper compares the empirical accuracy of the point and interval forecasts, obtained by the approach of Hyndman and Ullah (Comput Stat Data Anal 51(10), 4942?C4956, 2007) and its variants for forecasting age-specific fertility rates. The analyses are carried out using the age-specific fertility data of 15 mostly developed countries. Based on the one-step-ahead to 20-step-ahead forecast error measures, the weighted Hyndman-Ullah method provides the most accurate point and interval forecasts for forecasting age-specific fertility rates, among all the methods we investigated.     

Short-term, population-based forecasting in the public sector

There has recently been a tremendous expansion of the range of problems to which the demographic perspective is applied. Development of a new population-based method to solve the problem of forecasting income assistance caseloads for the state of Washington represents yet another effort in which the demographic perspective helps solve two major public-policy problems: (1) providing accurate and useful forecasts of caseloads, and (2) creating a dynamic model with which to analyze alternative policy proposals. When forecasting or examining the caseload history, it is also common to look at these caseload levels as a time-series. A caseload grows and shrinks as time passes because new members enter the caseload from a population of potential clients while other members exit the caseload. Population-based forecasting, as reported here, is really quite a novel approach to forecasting public assistance caseloads. In most situations, simple extrapolations of past trends or econometric time-series models are used. Characteristics associated with entries and exits can be used to develop dynamic models of current and future caseload changes. For budgeting purposes, these models can be readily translated into average annual caseload levels and can be directly used to examine policy alternatives and programmatic options. Entry and exit rates and volumes can be related to historical, current, and anticipated changes in economic, social, and programmatic conditions to develop models of caseload behavior, and ultimately, forecasts of caseload levels that are used for budget development.     

Labour market forecasting in Australia: The science of the art

Since 1987 nearly 50 labour market forecasts have been undertaken in Australia to assist decisions relating to government policy and budget, investment and career planning. More than 20 of these forecasts have been disaggregated by age, occupation, industry or regional labour markets. One of the chief aims of disaggregated forecasts is to help policy makers avoid future shortages or surpluses of skilled labour. A survey encompassing government departments, private research institutes and banks was undertaken to overview recent labour market forecasting exercises in Australia. This paper, which attempts to summarize these efforts, also discusses the main advantages and disadvantages of each major type of forecasting technique. Methods employed have ranged from anticipatory surveys to data-intensive input-output models. Formal evaluation of labour market forecasts requires considerable resources and no known assessments have been conducted in Australia to date. It is unclear how significant disaggregated labour market forecasts have been in guiding the allocation of funds between competing education and training courses. Nevertheless, governments eager to avoid future shortages and surpluses of skilled labour, but less enthusiastic about forecasting, could aim to make the labour market more flexible and responsive instead. Like forecasting, however, the effectiveness of this approach has yet to be scrutinized.     

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)     

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.     

A time series approach to forecasting Australian total live-births

The relationship between classical demographic deterministic forecasting models, stochastic structural econometric models and time series models is discussed. Final equation autoregressive moving average (ARMA) models for Australian total live-births are constructed. Particular attention is given to the problem of transforming the time series to stationarity (and Gaussianity) and the properties of the forecasts are analyzed. Final form transfer function models linking births to females in the reproductive age groups are also constructed and a comparison of actual forecast performance using the various models is made. Long-run future forecasts are generated and compared with available projections based on the deterministic cohort model after which some policy implications of the analysis are considered.     

Using social indicators to forecast partisan alignments in congressional election years

This paper presents five forecasting equations for political party alignments in the United States during the post-World War II period. Time series data published by various public and survey organizations are utilized to estimate for the years 1948–1974 for party identifications and results of elections for the House of Representatives. The observed equations explain from 86–93% of the variance for the years 1948–1974 and usually allow acceptance of the null hypothesis of no autocorrelation of disturbances. These equations are then employed to make forecasts of the 1976 election year alignments which are compared to observed values. The forecasting equations for 1976 are generally successful, for example, missing the congressional alignments by nine House seats. Some contingent forecasts are made for 1978 election year alignments, based upon certain alternative assumptions about economic and political climates. The equations do not intend to test new theories but rather to apply fairly simple ideas to forecasting trends in public opinion. The authors argue that forecasting equations are useful for anticipating future trends, for planning future research and for assessing whether an unusual event is manifesting itself or alternatively whether a certain trend in public opinion is to be expected from normal processes.     

Population forecasts and confidence intervals for sweden: a comparison of model-based and empirical approaches

This paper compares several methods of generating confidence intervals for forecasts of population size. Two rest on a demographic model for age-structured populations with stochastic fluctuations in vital rates. Two rest on empirical analyses of past forecasts of population sizes of Sweden at five-year intervals from 1780 to 1980 inclusive. Confidence intervals produced by the different methods vary substantially. The relative sizes differ in the various historical periods. The narrowest intervals offer a lower bound on uncertainty about the future. Procedures for estimating a range of confidence intervals are tentatively recommended. A major lesson is that finitely many observations of the past and incomplete theoretical understanding of the present and future can justify at best a range of confidence intervals for population projections. Uncertainty attaches not only to the point forecasts of future population, but also to the estimates of those forecasts' uncertainty.     

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.     

The role of population size in the determination and prediction of population forecast errors: An evaluation using conifidence intervals for subcounty areas

Producers of population forecasts acknowledge the uncertainty inherent in trying to predict the future and should warn about the likely error of their forecasts. Confidence intervals represent one way of quantifying population forecast error. Most of the work in this area relates to national forecasts; although, confidence intervals have been developed for state and county forecasts. A few studies have examined subcounty forecast error, however, they only measured point estimates of error. This paper describes a technique for making subcounty population forecasts and for generating confidence intervals around their forecast error. It also develops statistical equations for calculating point estimates and confidence intervals for areas with different population sizes. A non-linear, inverse relationship between population size and forecast accuracy was found and we demonstrate the ability to accurately predict average forecast error and confidence intervals based on this relationship.     

MAPE-R: a rescaled measure of accuracy for cross-sectional subnational population forecasts

Accurately measuring a population and its attributes at past, present, and future points in time has been of great interest to demographers. Within discussions of forecast accuracy, demographers have often been criticized for their inaccurate prognostications of the future. Discussions of methods and data are usually at the centre of these criticisms, along with suggestions for providing an idea of forecast uncertainty. The measures used to evaluate the accuracy of forecasts also have received attention and while accuracy is not the only criterion advocated for evaluating demographic forecasts, it is generally acknowledged to be the most important. In this paper, we continue the discussion of measures of forecast accuracy by concentrating on a rescaled version of a measure that is arguably the one used most often in evaluating cross-sectional, subnational forecasts, Mean Absolute Percent Error (MAPE). The rescaled version, MAPE-R, has not had the benefit of a major empirical test, which is the central focus of this paper. We do this by comparing 10-year population forecasts for U.S. counties to 2000 census counts. We find that the MAPE-R offers a significantly more meaningful representation of average error than MAPE in the presence of substantial outlying errors, and we provide guidelines for its implementation.     

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.     

The European Commission on Factors Influencing Labor Migration

A controversial issue in discussions on enlargement of the European Union beyond its existing membership of 15 countries is the migration flows that admission of new members could generate. Given major differences in income and wage levels between the EU states and the candidates for membership, casual theorizing suggests that the potential for massive international migration is very high. The fact that such migration has thus far been of modest size by most plausible criteria is attributed to the restrictive policies of the potential destination countries, policies that reflect national interests, in particular protection of labor markets, as perceived by voting majorities. With accession to membership in the EU this factor is removed: a cardinal principle of the Union, established by treaty, is the free movement of persons, including persons seeking gainful employment. The factors governing migratory movements between member states then come to resemble those that shape internal migration. This should facilitate analysis and forecasting. A clear sorting‐out of the relevant forces affecting such “internal” migration remains of course an essential precondition for success in that task. An “Information note,” entitled The Free Movement of Workers in the Context of Enlargement, issued by the European Commission, the EU's Executive Body, on 6 March 2001, presents extensive discussion of relevant information, opinion, and policy options concerning its topic. (The document is available at « http://europa.eu.int/comm/enlarge‐ment/docs/pdf/migration_enl.pdf ».) An Annex to the document. Factors Influencing Labour Movement, is a lucid enumeration of the factors migration theory considers operative in determining the migration of workers and, by extension, of people at large, that is likely to ensue upon EU enlargement. This annex is reproduced below. As is evident from the catalog of factors and their likely complex interactions, making quantitative forecasts of future migration flows, envisaged primarily as originating from countries to be newly admitted to the EU and destined for the countries of the current EU15, is exceedingly difficult. This is reflected in disparities among the existing studies that have made such forecasts. Yet there appears to be a fair degree of agreement that major increases in migration are unlikely, suggesting that the overall effect on the EU15 labor market should be limited. Typical forecasts (detailed in the Information note cited above) anticipate that in the initial year after admission, taken to be 2003, total migration from the eight prime candidate countries (the Czech Republic, Hungary, Poland, Slovakia, Slovenia, Estonia, Latvia, and Lithuania: the “CC8”) might amount to around 200,000 persons, roughly one‐third of which would be labor migration. According to these forecasts, the annual flow will gradually diminish in subsequent years. After 10 to 15 years the stock of CC8 migrants in the EU15 might be on the order of 1.8 to 2.7 million. The longer‐run migration potential from the candidate countries would be on the order of 1 percent of the present EU population, currently some 375 million. (The combined current population of the CC8 is 74 million.) Such predictions are in line with the relatively minor migratory movements that followed earlier admissions to the EU of countries with then markedly lower per capita incomes, such as Spain and Portugal. The geographic impact of migration ensuing from enlargement would, however, be highly uneven, with Germany and Austria absorbing a disproportionately large share. Accordingly, and reflecting a prevailing expectation in these two countries that enlargement would have some short‐run disruptive effects on labor markets, some of the policy options discussed envisage a period of transition following enlargement—perhaps five to seven years—during which migration would remain subject to agreed‐upon restrictions.     

A Happy Nation? Opportunities and Challenges of Using Subjective Indicators in Policymaking

This article seeks to combine decades of academic research with emerging policy demands by systematically assessing the state of the knowledge on using subjective indicators in public policy. In particular, it outlines opportunities that arise from a new focus on subjective information as a basis for policy decisions and challenges that ought to be overcome. The paper presents pros and cons of using subjective (versus objective) indicators, and it discusses six ways in which information on citizens’ subjective well-being (SWB) can advance the policymaking process: Monitoring progress, informing policy design, policy appraisal, examining the divergence of objective and subjective quality of life, ranking public institutions and allocating resources, as well as informing development strategies and goals. In doing so, best practice examples are presented and put in context. Finally, subjective measures “beyond SWB” are discussed and a new measure for the overall satisfaction with society is suggested. The next frontier for research and practice will be to build on the potential outlined here and to address the deficits in order make the most out of subjective indicators and the unique value they can add to the policymaking process.     

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.     

Statistically tested comparisons of the accuracy of forecasting methods for age-specific and sex-specific mortality and life expectancy

Although there are continuing developments in the methods for forecasting mortality, there are few comparisons of the accuracy of the forecasts. The subject of the statistical validity of these comparisons, which is essential to demographic forecasting, has all but been ignored. We introduce Friedman's test statistics to examine whether the differences in point and interval forecast accuracies are statistically significant between methods. We introduce the Nemenyi test statistic to identify which methods give results that are statistically significantly different from others. Using sex-specific and age-specific data from 20 countries, we apply these two test statistics to examine the forecast accuracy obtained from several principal component methods, which can be categorized into coherent and non-coherent forecasting methods.     

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.     

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.     

Voodoo forecasting: Technical,political and ethical issues regarding the projection of local population growth

The case of an energy production community in Colorado is used to illustrate a) the great need for reliable subnational population forecasts, especially in communities expecting rapid population growth, and b) why such projections, as currently performed, cannot be reliable. Explanations for failure in forecasting are found in the methods themselves, the unavailability and unreliability of key data, politics, and the intrusion of the designers' and users' values into the forecasting models. As one solution it is proposed that forecasting be reconceptualized from a technical to an ethical issue and that it be based upon an active rather than a passive planning/forecasting philosophy. As such, the community and industry would set a desired, realistic goal, and forecasting models would be run backwards to determine the economic-demographic paths by which this goal could be achieved.