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When the future evolution of demographic processes is described in a stochastic setting, the challenge is to communicate the meaning of forecast uncertainty in an understandable way, to decision makers and public at large. For the purpose... more
When the future evolution of demographic processes is described in a stochastic setting, the challenge is to communicate the meaning of forecast uncertainty in an understandable way, to decision makers and public at large. For the purpose of risk communication, a formal setting is developed in which the roles of the demographic processes on point forecasts, and more generally, on predictive distributions, can be elucidated. The communication problem becomes central in fiscal decision making, when eventual forecast errors have differential implications on the value of the policy options being considered. Tax rate that is required to maintain financial sustainability, until a given target year, is used for illustration.
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"Errors in population forecasts arise from errors in the jump-off population and errors in the predictions of future vital rates. The propagation of these errors through the linear (Leslie) growth model is studied, and prediction... more
"Errors in population forecasts arise from errors in the jump-off population and errors in the predictions of future vital rates. The propagation of these errors through the linear (Leslie) growth model is studied, and prediction intervals for future population are developed. For U.S. national forecasts, the prediction intervals are compared with the U.S. Census Bureau's high-low intervals." In order to assess the accuracy of the predictions of vital rates, the authors "derive the predictions from a parametric statistical model and estimate the extent of model misspecification and errors in parameter estimates. Subjective, expert opinion, so important in real forecasting, is incorporated with the technique of mixed estimation. A robust regression model is used to assess the effects of model misspecification."
Research Interests: Mathematics, Demography, Econometrics, Research Design, Forecasting, and 15 moreDeveloping Countries, Research, Medicine, Parameter estimation, Methods, Population, Americas, Expert Opinion, North America, Developed Countries, Reproducibility of Results, Statistical Model, Robust Regression, Parametric Statistics, and Growth Model
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"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... more
"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)
Research Interests: Mathematics, Applied Mathematics, Demography, Econometrics, Data Analysis, and 15 moreForecasting, Population Dynamics, Mortality, Medicine, Functional Connectivity, Population, Americas, Expert Opinion, North America, Jump, Developed Countries, Age Factors, Population Characteristics, Mortality rate, and Cause of death
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Numerical procedures for calculating likelihood ratio test and score test based confidence intervals in generalized linear models are considered. Newton's method appears to have better convergence properties than the secant method in... more
Numerical procedures for calculating likelihood ratio test and score test based confidence intervals in generalized linear models are considered. Newton's method appears to have better convergence properties than the secant method in the likelihood ratio test case. However, the secant method may be easier to program for models with link functions that are not natural. Similarly, the secant method is easier to implement for the computation of score test based intervals. The practical implementation of the procedures in GLIM is illustrated.
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Small area usually refers to an administrative unit that is part of a larger unit, such as a county, province, city, or municipality within a state. In some cases one is interested in domains defined by other criteria, such as age, sex,... more
Small area usually refers to an administrative unit that is part of a larger unit, such as a county, province, city, or municipality within a state. In some cases one is interested in domains defined by other criteria, such as age, sex, educational level, etc. In the case of municipalities or city blocks, populations can be small in the sense that they vary considerably from year to year. Large cities or counties may have stable populations, but their share of a national sample may be too small for direct estimation. Both types of data may have similar administrative uses, the allocation of funds, for example. In some countries direct estimates of small area populations can be continuously available from population registers. In countries that rely on censuses, demographic book keeping, administrative records, or sampling techniques are used for intercensal small area estimation. The methods used include synthetic methods that impute large area characteristics to small areas, and composite methods (such as Empirical Bayes and Hierarchical Bayes) that combine direct estimates and synthetic estimates. Forecasts of the populations of small areas differ from those of national populations because of the larger effect of migration. The handling of migration flows separates the different techniques of forecasting. Multistate methods are promising but require a lot of data. A new development in small area estimation and forecasting is the introduction of the geographic information systems (GIS). When all housing units are given geographic coordinates, new aggregates can be defined that are independent of existing administrative boundaries.
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Female life expectancy has almost universally been higher than male life expectancy. But, both have increased rapidly during the past century. European countries differ as regards the magnitude and time trends of the female-male... more
Female life expectancy has almost universally been higher than male life expectancy. But, both have increased rapidly during the past century. European countries differ as regards the magnitude and time trends of the female-male difference. In countries that can be characterised as Egalitarian from the point of view of gender equality, the difference increased rapidly after World War II. It is thought that a major factor in this was then wider adoption of smoking on the part of males. Subsequently the gap has clearly narrowed, and it is believed that the narrowing continues. In countries that can be characterised as Traditional from the point of view of gender equality, the gap started to widen already a century ago, with acceleration after World War II. these countries show only limited evidence of subsequent narrowing. In former socialist countries the gap has been large, and shows little narrowing. These developments are described in detail by graphical displays. It is shown that...
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We propose a new view of initial nonresponse bias in longitudinal surveys. Under certain conditions, an initial bias may "fade-away" over consecutive waves. This effect is discussed in a Markovian framework. A general... more
We propose a new view of initial nonresponse bias in longitudinal surveys. Under certain conditions, an initial bias may "fade-away" over consecutive waves. This effect is discussed in a Markovian framework. A general contraction theorem for time inhomogeneous Markov chains is presented. The result is that two chains with different starting distributions will eventually converge to equal state distributions. Two conditions are required: transition probabilities must be equal for respondents and nonrespondents, and attrition in later panel waves must not depend on the state of the individuals. The theory is applied to a German survey on social benefit recipience. Minor deviations from assumptions are shown to have only a negligible impact on the strength of the fade-away effect. Results from other European surveys indicate that the fade-away effect is present in them, as well. Extensions are pointed out.
Research Interests: Psychology, German, Markov chains, Attrition, DDC, and 3 moreMarkov chain, Panel Attrition, and Panel Surveys
This series contains research reports, written by or in cooperation with staff members of the Statistical Research Division, whose content may be of interest to the general statistical research community. The views reflected in these... more
This series contains research reports, written by or in cooperation with staff members of the Statistical Research Division, whose content may be of interest to the general statistical research community. The views reflected in these reports are not necessarily those of the Census Bureau nor do they necessarily represent Census Bureau statistical policy or practice. Inquiries may be addressed to the author(s) or the SRD Report Series Coordinator, Statistical Research Division, Bureau of the Census, Washington, D.C. 20233.
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Demographic forecasts are inherently uncertain. Nevertheless, an appropriate description of this uncertainty is a key underpinning of informed decision making. In recent decades various methods have been developed to describe the... more
Demographic forecasts are inherently uncertain. Nevertheless, an appropriate description of this uncertainty is a key underpinning of informed decision making. In recent decades various methods have been developed to describe the uncertainty of future populations and their structures, but the uptake of such tools amongst the practitioners of official population statistics has been lagging behind. In this letter we revisit the arguments for the practical uses of uncertainty assessments in official population forecasts, and address their implications for decision making. We discuss essential challenges, both for the forecasters and forecast users, and make recommendations for the official statistics community.
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The practical application of likelihood ratio test based interval estimates for LD50, ED50, and related quantities is considered. Our mathematical setting is that of a generalized linear model with a known scale parameter. We extend the... more
The practical application of likelihood ratio test based interval estimates for LD50, ED50, and related quantities is considered. Our mathematical setting is that of a generalized linear model with a known scale parameter. We extend the results of Williams (1986, Biometrics 42, 641-645) by showing how Newton's method can be used to calculate the end points of the intervals. To accommodate epidemiologic applications we permit other explanatory variables besides those related to dose in our model. We illustrate the use of the methods in a case in which there are two sources of exposure, whose joint impact is of interest. We also discuss the computation of the confidence sets, when they consist of the whole real line or when they are unions of disjoint intervals. Special problems connected with the cases in which some of the maximum likelihood estimators do not exist are studied. Simulation is used to compare the adequacy of the likelihood ratio based approach to that of the classical Fieller limits. The Fieller limits frequently fail to exist in small samples. The likelihood ratio-based limits always exist, but they are sometimes slightly too narrow. The likelihood ratio-based limits appear not to be as often infinite as the Fieller limits are.
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The first official cohort-component projection of the population of Finland was prepared by Gunnar Modeen (1934a), an actuary with the Central Statistical Office of Finland at the time. Modeen’s work had elements of genuine forecasting in... more
The first official cohort-component projection of the population of Finland was prepared by Gunnar Modeen (1934a), an actuary with the Central Statistical Office of Finland at the time. Modeen’s work had elements of genuine forecasting in that he commented on past trends in fertility, mortality, and migration, and discussed their possible long-term implications (Modeen 1934b). On the other hand, the work was rather schematic in nature. In particular, age-specific mortality was assumed not to change during the projection period, although Modeen was aware of its declining trend since the late nineteenth century (Modeen 1934a, 38). Unable to pinpoint the future rate of decline exactly, Modeen rejected any alternative assumption as speculative (cf., Modeen and Fougstedt 1938).
The first official cohort-component projection of the population of Finland was prepared by Gunnar Modeen (1934a), an actuary with the Central Statistical Office of Finland at the time. Modeen’s work had elements of genuine forecasting in... more
The first official cohort-component projection of the population of Finland was prepared by Gunnar Modeen (1934a), an actuary with the Central Statistical Office of Finland at the time. Modeen’s work had elements of genuine forecasting in that he commented on past trends in fertility, mortality, and migration, and discussed their possible long-term implications (Modeen 1934b). On the other hand, the work was rather schematic in nature. In particular, age-specific mortality was assumed not to change during the projection period, although Modeen was aware of its declining trend since the late nineteenth century (Modeen 1934a, 38). Unable to pinpoint the future rate of decline exactly, Modeen rejected any alternative assumption as speculative (cf., Modeen and Fougstedt 1938).
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Methods used in drawing up mortality projections Predictive distributions of future mortality
The concept of “probability” is used as a step in life table construction to get the expected number of survivors in a cohort. However, in traditional texts on demographic methods (e.g., Shryock and Siegel 1976), variance in the number of... more
The concept of “probability” is used as a step in life table construction to get the expected number of survivors in a cohort. However, in traditional texts on demographic methods (e.g., Shryock and Siegel 1976), variance in the number of survivors plays no role. Similarly, concepts of estimation, estimation error, and bias are routinely used, but standard error and sampling distribution are not (except in connection with sample surveys). Although statistically satisfactory accounts of the life table theory have existed for a long time (e.g., Chiang 1968; Hoem 1970), a reason for neglecting population level random variability, and statistical estimation error, has been that the populations being studied are so large that random error must be so small as not to matter, in practice.
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Are population processes easy to predict? The relative inertia of population stocks suggests that this is the case. Indeed, errors in population forecasts five to ten years into the future are often smaller than the errors of economic... more
Are population processes easy to predict? The relative inertia of population stocks suggests that this is the case. Indeed, errors in population forecasts five to ten years into the future are often smaller than the errors of economic forecasts over a similar period (Ascher, 1978). However, population flows are much harder to predict (Keilman, 1990), so in the long run, population processes are much more uncertain than generally recognized. Yet, many tasks of social policy, such as planning of schools and health care require information about the likely developments of population variables for twenty or thirty years into the future. Analyses of the sustainability of pension systems require that we take an even longer view, so the US Office of the Actuary routinely prepares forecasts seventy-five years into the future (Andrews and Beekman, 1987), for example. One way the uncertainty in population variables manifests itself is through changing views, over time, of the demographic futu...
Journal of Official Statistics publishes articles on statistical methodology and theory, with an emphasis on applications. Published by Statistics Sweden.
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An increase in life expectancy can put a strain on the finances of a definedbenefit pension system. A possible way to alleviate the effect is to adjust the levels of pensions to changes in life expectancy. However, as future development... more
An increase in life expectancy can put a strain on the finances of a definedbenefit pension system. A possible way to alleviate the effect is to adjust the levels of pensions to changes in life expectancy. However, as future development of life expectancy cannot be predicted without error, we can only assess the possible risks probabilistically. A predictive distribution for adjustment factors is derived in the Finnish setting. The distribution indicates that by year 2050 we can expect an adjustment factor of 0.87. The width of an 80 % prediction interval is 20 percentage points, if past volatility of mortality is used as a guide.
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Anticipatory covariates are regressors whose values become known only after the value of the dependent variable has been ascertained. Hoem (1995) has given an informal discussion concerning the possible pitfalls in the use of such... more
Anticipatory covariates are regressors whose values become known only after the value of the dependent variable has been ascertained. Hoem (1995) has given an informal discussion concerning the possible pitfalls in the use of such covariates in event history analysis. This paper complements Hoem’s findings by using simple linear regression as the framework. It turns out that complex patterns of bias may be introduced by the use of anticipatory covariates. In all cases it may not be possible to guarantee that the magnitude of the bias remains small. Therefore, extreme care is needed in interpreting results from studies that have relied on anticipatory covariates.
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Gunnar Modeen made the first cohort-component forecast for Finland in 1934. This was a time when demographic transition was just over, but that fact could not have been known at the time. Would it have made any difference if Modeen had... more
Gunnar Modeen made the first cohort-component forecast for Finland in 1934. This was a time when demographic transition was just over, but that fact could not have been known at the time. Would it have made any difference if Modeen had had the tools of modern time-series analysis available? We find that the essential question of how to deal with changing trends would have still been difficult. However; the modern tools would have given the forecast user a realistic indicator of the uncertainty of the forecast being made. This suggests that in developing countries that are undergoing transition now, more effort should he paid to the analysis of uncertainty of forecasting.
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Vaikka muuttoliike voi tuoda maahan tyoikaisia henkiloita, yleisesti ajatellaan, ettei se voisi mer kittavasti vaikuttaa vaeston ikarakenteen vanhe nemiseen. Tata johtopaatosta tukevat esimerkik si YK:n vuonna 2000 julkaisemat... more
Vaikka muuttoliike voi tuoda maahan tyoikaisia henkiloita, yleisesti ajatellaan, ettei se voisi mer kittavasti vaikuttaa vaeston ikarakenteen vanhe nemiseen. Tata johtopaatosta tukevat esimerkik si YK:n vuonna 2000 julkaisemat laskelmat. Niis sa maariteltiin muun muassa, kuinka suuri net tomuutto tarvittaisiin, jotta tyoikaisen vaeston maara ei lahtisi laskuun tai vanhushuoltosuhde ei nousisi (Population Division 2000, 13). Laskel mat tehtiin kahdeksalle suurelle maalle ja EU:lle. Johtopaatos oli, etta tarvittavat muuttavien maa rat nayttivat liian suurilta ollakseen uskottavia. Korvaavuuslaskelmat voivat perustua monen laisiin oletuksiin. Esimerkiksi YK:n laskelmis sa korostuvat laskelmien tekohetkella vallitsevat olot. Talloin lahivuosien kehityksesta voidaan saada tarkka kuva, mutta pitkan tahtaimen naky mat saattavat hamartya. Tassa kirjoituksessa va litsen tarkastelutavan, jossa paapaino on pitkal la tahtaimella. 1 Osoittautuu, etta muuttoliikkeel la voi olla merkittavia vaikutuksia, jotka eivat pal jastu aiemmin kaytetyissa skenaarioissa. Vaikka yksistaan vaestonrakennetta koskevien tarkaste luiden perusteella ei voi tehda politiikkasuosituk sia, analyysi osoittaa, etta erityisesti Suomessa on runsaasti kayttamattomia mahdollisuuksia. Muuttoliikkeeseen liittyy monia mielikuvia kulttuurien yhteentormayksesta, rikollisuuden kasvusta, tyottomyydesta jne. Toisaalta koulu tettujen maahanmuuttoa suositaan virallisesti kin. Maahanmuuttajien hedelmallisyyden usko taan olevan korkeampi kuin kantavaeston; tama voisi vaikuttaa vaeston uusiutumiseen. Kiinnosta vuudestaan huolimatta en seuraavassa puutu nai hin aiheisiin. Tarkastelen sen sijaan ikaantymista ja muuttoliikkeen vaikutusta vaeston kasvuvauh tiin yksinkertaistavin oletuksin. Ikaantymisen komponentit