Applying Lee-Carter under conditions of variable mortality decline

The Lee-Carter method of mortality forecasting assumes an invariant age component and most applications have adopted a linear time component. The use of the method with Australian data is compromised by significant departures from linearity in the time component and changes over time in the age component. We modify the method to adjust the time component to reproduce the age distribution of deaths, rather than total deaths, and to determine the optimal fitting period in order to address non-linearity in the time component. In the Australian case the modification has the added advantage that the assumption of invariance is better met. For Australian data, the modifications result in higher forecast life expectancy than the original Lee-Carter method and official projections, and a 50 per cent reduction in forecast error. The model is also expanded to take account of age-time interactions by incorporating additional terms, but these are not readily incorporated into forecasts.     

Modeling and Forecasting Health Expectancy: Theoretical Framework and Application

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

Consistent correction of data for aboriginal populations

A consistent correction procedure is used to determine improved, consistent estimates by sex of census age distributions, intercensal births, intercensal deaths and net migration by age for the Aboriginal populations of the Northern Territory, South Australia and Western Australia during the period 1986–91. Undercount estimates and life tables show the Aboriginal populations to have lower coverage in statistical collections and much higher death risks than the total Australian population. Inter-regional net migration estimates show that component of change can no longer be ignored.     

Extending the Lee-Carter Method to Model the Rotation of Age Patterns of Mortality Decline for Long-Term Projections

In developed countries, mortality decline is decelerating at younger ages and accelerating at old ages, a phenomenon we call “rotation.” We expect that this rotation will also occur in developing countries as they attain high life expectancies. But the rotation is subtle and has proved difficult to handle in mortality models that include all age groups. Without taking it into account, however, long-term mortality projections will produce questionable results. We simplify the problem by focusing on the relative magnitude of death rates at two ages (0 and 15–19) while making assumptions about changes in rates of decline at other ages. We extend the Lee-Carter method to incorporate this subtle rotation in projection. We suggest that the extended Lee-Carter method could provide plausible projections of the age pattern of mortality for populations, including those that currently have very high life expectancies. Detailed examples are given using data from Japan and the United States.     

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.     

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.     

The forecast accuracy of Australian Bureau of Statistics national population projections

This paper examines the forecast accuracy of Australian Bureau of Statistics national population projections produced from the 1960s to the early 2000s. As well as total populations, the accuracy of the following is assessed: age-sex-specific populations, the Total Fertility Rate, life expectancy at birth and net international migration. It is shown that forecasts of the 1960s and 70s were the most inaccurate; forecasts of the 1980s and later proved to be much more reliable. The paper goes on to take an alternative perspective on population forecast error through the use of an adapted percentage error measure which accounts for offsetting errors in births, deaths, net migration and the jump-off population. This measure also permits an assessment of the relative contributions of the components of demographic change to overall inaccuracy. It is shown that errors in forecasting net international migration have generally contributed most to inaccuracy followed by births and then deaths and jump-off error. ABS projections of total population are also compared to those produced using a simple naïve model. The paper concludes by arguing that the new error measure could prove valuable in other studies of population forecast accuracy.     

A modified Lee-Carter model for analysing short-base-period data

This paper introduces a new modified Lee-Carter model for analysing short-base-period mortality data, for which the original Lee-Carter model produces severely fluctuating predicted age-specific mortality. Approximating the unknown parameters in the modified model by linearized cubic splines and other additive functions, the model can be simplified into a logistic regression when fitted to binomial data. The expected death rate estimated from the modified model is smooth, not only over ages but also over years. The analysis of mortality data in China (2000-08) demonstrates the advantages of the new model over existing models.     

A reply to Kim's comment

This reply criticizes Kim's note as incorrectly characterizing the essential feature of the method proposed for life table construction. The method suggested for estimating N(a), the number attaining age 2 during the intercensal period, is to make a separate estimate of the contribution to N (a) made by each single-year cohort that attains 'a' during the period between censuses. Each cohort estimate is constructed by interpolation, utilizing as data the recorded number in the relevant single-year cohorts in the 2 censuses. 2 methods of interpolation were proposed. 1 is an iterative procedure that constructs a preliminary life table by linear interpolation for each cohort and then derives more refined interpolation factors from this preliminary life table. The other procedure derives interpolation factors on the assumption that the proportionate distribution of deaths by age as each cohort moves from the earlier to the later census date is the same as the proportionate distribution of deaths by age over the same age range in a model life table. The advantage of the proposed procedure is that it supplies better estimates of N (a) than do alternative methods. The author concedes that a life table calculated from accurately recorded deaths and an accurately enumerated population would ordinarily be superior. However, he also notes that in the absence of registered deaths data, there is no precise enough conventional method to yield accurate values of average intercensal single-year age-specific mortality rates from nothing more than 2 accurate censuses 11 years apart. A common procedure for calculating life expectation at a very advanced age is to calculate the reciprocal of the death rate among persons over the age in question.     

Lee-Carter估计模式推算中国农村老年人口死亡率的研究

死亡率的估算与人口老龄化密切相关,中国60岁及以上老年人口主要集中在农村地区,本文运用Lee-Carter模型对农村分性别单岁组的死亡率数据进行建模,预测出农村人口死亡率与期望寿命的发展趋势。     

Long-range trends in adult mortality: Models and projection methods

In the study reported here, I had two objectives: (1) to test a new version of the logistic model for the pattern of change over time in age-specific adult mortality rates and (2) to develop a new method for projecting future trends in adult mortality. A test of the goodness of fit of the logistic model for the force of mortality indicated that its slope parameter is nearly constant over time. This finding suggests a variant of the model that is called the shifting logistic model. A new projection method, based on the shifting mortality model, is proposed and compared with the widely used Lee-Carter procedure.     

Recent trends in mortality in Australia—an analysis of the causes of death through the application of life table techniques

The paper examines the post-1971 reduction in Australian mortality in light of data on causes of death. Multiple-decrement life tables for eleven leading causes of death by sex are calculated and the incidence of each cause of death is presented in terms of the values of the life table functions. The study found that in the overall decline in mortality over the last 20 years significant changes occurred in the contribution of the various causes to total mortality. Among the three leading causes of death, heart disease, malignant neoplasms (cancer), and cerebrovascular disease (stroke), mortality rates due to neoplasms increased and those of the other two causes decreased. The sex-age-cause-specific incidence of mortality changed and the median age at death increased for all causes except for deaths due to motor-vehicle accidents for both sexes and suicide for males. The paper also deciphers the gains in the expectation of life at birth over various time periods and the sex-differentials in the expectation of life at birth at a point in time in terms of the contributions made by the various sex-age-cause-specific mortality rates.     

Estimating census and death registration completeness

This article presents a new method for estimating the relative completeness of 2 census enumerations and of intercensal registered deaths. The Growth Balance Equation was developed by Brass (1975) to estimate the completeness of death registration relative to the completeness of census enumeration. The method presented here can be seen either as an extension of Martin's formulation to allow explicitly for changes in census coverage or as a modification of Brass's method to use deaths by age group rather than deaths by cohort, preferable on the grounds that age group comparisons will be less distorted by age misreporting than cohort comparisons if the patterns of age misreporting are similar for 2 successive censuses. This simple method estimates simultaneously the relative coverage of the 2 censuses and the completeness of registration of intercensal deaths. The key assumptions of the method are that the population is closed to migration and that all the coverage factors involved are invariant with age, at least for the age range studied. Analysis of the sensitivity of the estimates to the assumptions and further work on extending the method to open populations would be useful.     

Optimizing the Lee-Carter Approach in the Presence of Structural Changes in Time and Age Patterns of Mortality Improvements

Researchers using the Lee-Carter approach have often assumed that the time-varying index evolves linearly and that the parameters describing the age pattern of mortality decline are time-invariant. However, as several empirical studies suggest, the two assumptions do not seem to hold when the calibration window begins too early. This problem gives rise to the question of identifying the longest calibration window for which the two assumptions hold true. To address this question, we contribute a likelihood ratio–based sequential test to jointly test whether the two assumptions are satisfied. Consistent with the mortality structural changes observed in previous studies, our testing procedure indicates that the starting points of the optimal calibration windows for most populations fall between 1960 and 1990. Using an out-of-sample analysis, we demonstrate that in most cases, models that are estimated to the optimized calibration windows result in more accurate forecasts than models that are fitted to all available data or data beyond 1950. We further apply the proposed testing procedure to data over different age ranges. We find that the optimal calibration windows for age group 0–49 are generally shorter than those for age group 50–89, indicating that mortality at younger ages might have undergone (another) structural change in recent years.     

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     

WOrkers for Australia: a profile of british and Irish migrants assisted to New South Wales in 1841

Convict transportation to New South Wales was terminated in 1841. It was swiftly replaced by a new population stock in the form of the greatest Australian immigration before the gold rushes. This profile of 20,000 British and Irish assisted migrants, based on individual-level data, establishes their age, sex, religious, educational and occupational characteristics. Their composition differed markedly from the existing colonial population and other migrant flows at the time. They reflected the recruiting methods of the time as well as the changing migration propensities in the British Isles. The migrants were better human capital than was acknowledged at the time. They constituted a new start in Australian demographic development. This reconstruction of the socio-economic characteristics of the 1841 migrants provides a new mid-century benchmark for systematic comparisons with other migrant populations, within and beyond Australia, and in other periods. It is a contribution to the quantitative study of colonial society.     

Estimating Indigenous life expectancy: pitfalls with consequences

The methods used by the Australian Bureau of Statistics (ABS) to estimate life expectancies of Aboriginal and Torres Strait Islander peoples in 2009 have been controversial and require critical and sensitive analysis. The introduction by ABS of the direct method for estimating Indigenous life expectancies, based on estimated deaths and populations, has been generally welcomed. But the way this method has been applied and, in particular, death estimates used by the ABS, warrant scrutiny. These estimates were based on a first ever linkage between Indigenous deaths and census records following the 2006 census. Census-based identification was used in place of identification in the death registrations, rather than as a supplementary data source. The various national, state and regional life expectancy estimates published may have been biased upwards by this process. Because the impact of the methodology varies across Australia, regional differentials reported appear substantial but are not soundly based. The questionable ABS results are highlighted and discussed. Analysis based on more comprehensive linkage of death records in New South Wales over 5?years suggests that the ABS methods have understated Indigenous deaths and so overstated life expectancy. The effect of an alternative ABS approach is also discussed. ABS estimates published in 2009 are not necessarily definitive and may well overestimate Aboriginal and Torres Strait Islander life expectancy and underestimate the life expectancy gap. Estimates should be based on accurate estimates of deaths and population. Consultation and a thorough review are essential before the next round of estimates following the findings of the 2011 population census. Closing the Gap commitments focus on eliminating the life expectancy gap between Aboriginal and Torres Strait Islander peoples and other Australians. Life expectancy estimates need to be based on methods and data that are well understood and broadly supported. The alternative is unproductive debate about statistics rather than the range of policies and resourcing issues needed to improve Indigenous health.     

Forecasting cohort incomplete fertility: A method and an application

Drawing on insights from previous work on fertility forecasts, we develop a method for forecasting incomplete cohort fertility. Our approach involves two basic steps. First, we use a singular-value-decomposition (SVD) model to establish a relationship between the level and the age pattern of fertility for completed cohorts. This relationship is then applied to incomplete cohorts to obtain forecast fertility. We propose techniques to evaluate model assumptions and illustrate our method using cohort data from Canada, the USA, Norway, and Japan. With the exception of Japan, our results show that the model fits the data well, and that the youngest cohort whose total fertility can be reliably forecast is age 25 for Canada, the USA, and Norway. Our method is less applicable to Japan, where the youngest cohort whose total fertility could be forecast was age 35 or older. We discuss the limitations of our method in the context of model assumptions.     

A method for deriving mortality estimates from incomplete vital Statistics

Summary Although they are available in many developing countries vital registration records are very little used for mortality estimation which is still mainly based on census returns. However, defective death records may yield accurate estimations of mortality. This procedure requires few data only; a sex-age distribution of the population (preferably at the middle of a period) and a sexage distribution of deaths, either derived from vital records or from census returns to questions relating to deaths during the preceding twelve months. This method is based on the observation that for a fixed age structure of the population, there is a one-one relation between the age structure of deaths (measured by the proportion of deaths at older ages) and the level of mortality (measured by the death rate above a certain minimum age). It is assumed that at ages above this minimum the rate of underregistration of deaths does not vary significantly with age. Therefore, the age distribution of registered deaths makes it possible to estimate the true proportion of deaths at older ages. This in its turn will permit the estimation of the true level of mortality, because of the relation which exists between age structure of deaths and level of mortality. The true level is then compared with the observed, to estimate the rate of underregistration, and observed age-specific death rates can be adjusted in the light of this knowledge.     

Aboriginal fertility: Trends and prospects

Estimates of Aboriginal fertility compiled from an analysis of 1981 and 1986 Census data on children ever borne by Aboriginal women reveal age-specific fertility rates slightly higher than those of other Australian women at ages above 25, but very much higher rates for younger women. The result is a total fertility ratio more than 50 per cent higher than in the total Australian population, with no more than slight variation between States and Territories. A differential analysis using standardized indices shows considerable differences in levels of fertility of categories of young Aboriginal women classified by education, labour force status and income, and also differences between urban and rural areas. Analysis of prospects for Aboriginal fertility levels confirms the likelihood of continuation in the downward drift in levels of fertility that has been established during the past decade. Comparison of the estimates with another recent set of estimates obtained using the own-children method shows broad conformity in levels of total fertility ratios over time, except in the most recent period, the mid-1980s. Nevertheless, the own-children estimates distort the recent trend and also the age distribution of Aboriginal fertility.