Developing strategies for deriving small population fertility rates

Many agencies require population estimates and projections by ethnic group. These projections need ethnic-specific, age-specific fertility rates (ASFRs) but their inclusion is challenging since ethnicity is not recorded at birth registration. In this paper maternity data are used in a case study of electoral wards in Bradford, West Yorkshire, to develop fertility rates for small populations for a 1991 based projection. The challenge is to capture local variations in fertility by ethnic group when data are sparse. Small areas were grouped together using cluster analysis to define combinations with similar sociodemographic and fertility experiences so that sparse data could be aggregated to estimate reliable ethnic-specific fertility rates. For comparison, the data were aggregated into the 1991 Office for National Statistics area type classification. Fertility rates by single year of age for all area types were smoothed using the Hadwiger function. For the White ethnic group there were sufficient births to create ethnic-specific, ward-level ASFRs. For other ethnicities grouping of areas was necessary. The accuracy of the ASFRs in predicting births was assessed using mean absolute percentage error. Results show that for some minority groups district-level ethnic-specific fertility rates produced the most accurate birth estimates even though they were based on a larger area. This implies that rates created may be informative about the local area for White ethnic type but not in the same way for smaller ethnic groups. In terms of grouping strategies we recommend that existing classifications are assessed to determine how well variations in rates are stratified before embarking on a custom scheme. Where population sub-groups are small in some areas, it may be more reliable to use rates derived for larger areas and apply these to local populations. Inevitably, the rates used in a projection are a compromise but hopefully will still capture important dimensions of population change.     

Understanding population projections

This is a general introduction to how population projections are made and used for the consumers of this information. Population projections are computations of what future trends in fertility, mortality and migration of a population might be given set assumptions. They are not actual forecasts. Projections are used by planners in government and business for a clearer understanding of social changes. How to prepare projections, obtain base data, select starting and future levels of rates, variant series, and the mathematics involved are discussed. Assumptions must be carefully checked and chosen, since reliability of the projections depends on assumptions. There are 3 rules of thumb for reliability: 1) the shorter the projection period, the more reliable the projection; 2) the larger the geographic area being projected the more reliable the projection; 3) the lower the current fertility and the higher the current life expectancy, the lower the projection's margin of error. Major sources of data and projections on world, regional, national, subnational, and local areas and difficulties with data for developing countries are discussed. Available microcomputer programs for IBM PC compatible machines are listed and described briefly.     

Empirical bayes estimation of demographic schedules for small areas

In this article, we analyze empirical Bayes (EB) methods for estimating small-area rate schedules. We develop EB methods that treat schedules as vectors and use adaptive neighborhoods to keep estimates appropriately local. This method estimates demographic rates for local subpopulations by borrowing strength not only from similar individuals elsewhere but also from other groups in the same area and from regularities in schedules across locations. EB is substantially better than standard methods when rates have strong spatial and age patterns. We illustrate this method with estimates of age-specific fertility schedules for over 3,800 Brazilian municipalities.     

Prospects for fertility reduction and projections for future population growth in Kenya

In 1979 Kenya's annual rate of natural population growth was 3.8%. Data from the1989 Kenya Demographic and Health Survey indicate that significant decreases in fertility levels were experienced during the 1980s. Factors associated with conditions supportive of high fertility in Kenya are discussed, and progress toward attaining significant fertility reduction thresholds during the 1980s is assessed. Findings from recent fertility surveys are presented, and 1969–1989 national level family planning data are evaluated. Four population projections for 1985–2025 are presented and analyzed. One projection is based on official government growth targets; two are based on estimates provided by the United Nations and the Population Reference Bureau, and a fourth projection is based on the assumption that Kenya will attain an annual natural population growth rate of less than 1% by the year 2025. Each projection assumes that fertility declines will be experienced. Kenya's prospects for reducing the annual population growth rate to 1% within the next sixty years and a cost-sharing development policy are addressed briefly in the concluding section. Recent data suggest that Kenya will probably not complete the demographic transition before the year 2050, but Kenya should continue to move through the transition stage.     

Estimation of vital rates by means of monte carlo simulation

Monte Carlo simulation has been used to estimate age-specific fertility and mortality rates for a small population,the French-derived isolate of Northside on St. Thomas, U. S. Virgin Islands. Estimates were based on data collected in a household census and genealogical survey and on birth, death, and marriage records for the years 1916to 1966. During this 50-year period (in which the population size increased from 202 to 657), the numbers of births and deaths were too, small to estimate age-specific rates directly, and in addition, death registration was incomplete. Mortality rates were estimated using a simulation program in which mortality was the only stochastic variable. A model mortality schedule was chosen which most accurately reproduced the growth pattern of the population over the 50-year period. To estimate fertility rates, a more complex simulation model was used in which fertility, nuptiality, and mortality were random variables with probability distributions. Preliminary estimates of fertility were made from the birth records and used as input to this simulation program. Birth probabilities were adjusted empirically from one set of simulation runs to the next, until population growth rates, as well as other demographic characteristics, were similar in the real and simulated populations. The birth rates which produced the best fit to the real population data were taken as the estimated age-specific fertility schedule. To reproduce the real population age structure more closely, secular changes in birth probabilities were applied.     

Population projections: states, 1995 - 2025

All states will have more people in the future, especially in the south and west, while population aging occurs as the baby boomers age. This report identifies population changes projected to affect the US's 50 states and District of Columbia during 1995-2015. Basic assumptions for state population projections are presented with regard to population, births, deaths, net international migration, and net internal migration. The methodology used to produce the report is also described. Total population and net change is presented in tabular format for each state over the period. These data are used as the basic input to many federal, state, and local projection models which produce detailed statistics on education, economic factors, labor force, health care, voting, and other subjects. State differentials in fertility and mortality are also projected to widen, reflecting the concentration of race and ethnic groups with high fertility in some states and differential migration patterns.     

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 development and use of demographic models

In this review, we first examine two classical demographic models - conventional life tables and stable populations - and a modern generalization of stable population theory; we then discuss mathematical models of conception and birth. These models involve purely mathematical relations in formal demography as opposed to empirical regularities. Next we consider model age schedules of mortality, nuptialitiy, marital fertility, fertility, and migration that are explicitly based on such empirical patterns. We close this empirical section with a discussion of model stable populations, which are based on model life tables. We next examine the use of demographic models in forecasting future mortality, nuptiality, and fertility and in population projection. Following a discussion of microsimulation models, which gives us the opportunity to mention model age schedules of post partum amenorrhoea and of sterility, we close with observations about the purposes and uses of demographic models.     

Calculation of age-specific fertility schedules from tabulations of parity in two censuses

The mathematics of stable populations recently has been generalized to cover populations with time-varying fertility and mortality by a modification incorporating the sum of age-varying growth rates in place of the fixed growth rate of a stable population. Equations that characterize nonstable populations apply to any cohort-like phenomenon with a measurable property that cumulates gains or losses through time. In particular, the equations fit the relation between a population's average parity at a given age and age-specific fertility rates previously experienced at lower ages. Techniques devised to derive an intercensal life table from single-year age distributions in two censuses are adapted to estimate accurate intercensal fertility schedules from distributions of parity by age of woman in two censuses. Birth-order specific fertility schedules are also estimated.     

The World's Changing Human Capital Stock: Multi‐State Population Projections by Educational Attainment

This research note presents the first global population projections by educational attainment using methods of multi‐state population projection. The educational composition of the population by age and sex and educational fertility differentials are estimated for 13 world regions, and alternative scenarios are presented to the year 2030. One of these scenarios assumes constant educational transition rates and the other assumes that all regions reach Northern American levels of enrollment rates by 2030. The strong momentum or, as the case may be, inertia in the transformation of the educational composition of a population, seen in the results, arises because education is mostly acquired at a young age. The sex bias in the educational composition, especially evident in some developing countries, is unlikely to disappear soon. China has made remarkable progress in improving educational enrollment and as a consequence by 2030 is expected to have more educated people of working age than Europe and Northern America together.     

Data quality and accuracy of United Nations population projections, 1950-95

Between 1951 and 1998, the United Nations (UN) published 16 sets of population projections for the world, its major regions, and countries. This paper reports the accuracy of the projection results. I analyse the quality of the historical data used for the base populations of the projections, and for extrapolating fertility and mortality. I study also the impact this quality has had on the accuracy of the projection results. Results and assumptions for the sets of projections are compared with corresponding estimates from the UN 1998 Revision for total fertility and life expectancy at birth, total population, and the projected age structures. The report covers seven major regions (Africa, Asia, the former USSR, Europe, Northern America, Latin America, and Oceania) and the largest ten countries of the world as of 1998 (China, India, the USA, Indonesia, Brazil, Pakistan, Russia, Japan, Bangladesh, and Nigeria).     

Constructing fertility tables for Soviet populations

Because the 1970 Soviet Union census does not provide information on the age structure of men and women separately by sex and according to their ethnic affiliation, the 1959 USSR census data serve as the basis to infer knowledge about ethnic fertility. The model takes into account (1) the total number of births in 1960, estimated from the child-woman ratio in 1959, (2) the age structure of women in 1959, and (3) the assumed pattern of age-specific birth rates structured in terms of the modal age at childbearing and the length of the fertility age span. The results show that Ukrainians among the Slav populations ranked as the lowest with 2.07 children born per woman. Their total fertility contrasts with that of Kazakhs native to Central Asia, who reportedly according to Soviet sources had 7.46 children per woman in 1958-1959, and whose estimated rate is around 8.59 children. Extreme variations appear in the estimates of fertility among nationalities of the Caucasus region, Volga Basin, and to a lesser degree in Siberia. Official Soviet calculations of crude birth rates and age-specific rates for 15 Union Republics in 1967-1968 are transcribed and compared with the estimates for nationalities in 1959-1960. The same theoretical model used to generate the Soviet rates may be adapted under different assumptions to non-Soviet populations in other situations where the data are scanty or incomplete.     

Projecting future utilization of medically assisted fertility treatments

This study estimates the future utilization of medically assisted fertility treatments in Australia, focusing on assisted reproductive technologies (ARTs), intrauterine insemination (IUI), and ovulation induction. A multistate cohort component population projection model is used to determine future fertility rates from 2016 to 2026 by age and education level. These are combined with information on recent trends in use and success rates to indirectly estimate future age-specific probabilities of fertility treatment utilization. The number of ART cycles is expected to increase by 61 per cent between 2016 and 2026 if treatment success rates remain at 2015 levels, or by 34 per cent if recent improvements in ART success rates continue. The model also predicts that numbers of IUI cycles and ovulation induction cycles will decrease by 17 and 3 per cent, respectively. This research confirms the importance of including both technological improvements and socio-demographic changes when predicting future fertility treatment utilization.     

Some fundamental problems in population projection]

When family planning work in China developed, during the 1970's, the work of population projection also expanded. Population projections were done for China and its regions beginning in 1974 and remains a relatively new activity. Some question its validity, while others speculate about its methods and beleive only higher mathematics can be used, but this is all due to a lack of understanding of the nature of population forecasting. It is possible to predict population because if a current population situation and its changes are known, population of a particular future period can be projected e.g. for each year that is lived, a person will be 1 year older. And, population changes are primarily based on changes in births and deaths. These changes in turn are influenced by social and economic factors. Population projection is basically a forecasting of a certain period's total population, age and sex structure, the number of births and deaths, and migration. Different methods and formulas can be used to measure different population indicators, but all methods utilize comparisons. There are basically 2 methods for projecting total population: 1) the "direct method" regards total population as a quantity that itself changes and 2) the "separate factor method" breaks down total population into births, deaths, and migration. In the past, population projection has focused on the natural development of population which can be called "uncontrolled" because it makes "passive measurements" of possible population developments. In China, however, population projection is "controlled." Although it too measures future population developments, China's projections are not based on natural developments, but on definite population policies and estimates of results of family planning efforts.     

Estimating the regional migration patterns of the foreign-born population in the United States: 1950-1990

"In this paper, we apply model schedules to graduate data on the internal and external regional [U.S.] migration patterns of the foreign-born population for the 1950-1990 period.... To find estimates of the unrecorded migration flows in-between for four census-defined periods in our study (that is, for 1950-1955, 1960-1965, 1970-1975, and 1980-1985) we interpolate between the data of adjacent census time periods. Finally, we combine the estimated migration data with the corresponding mortality data to calculate and analyze the multiregional life tables and projections associated with each five-year time interval." (EXCERPT)     

Probabilistic Projections of the Total Fertility Rate for All Countries

We describe a Bayesian projection model to produce country-specific projections of the total fertility rate (TFR) for all countries. The model decomposes the evolution of TFR into three phases: pre-transition high fertility, the fertility transition, and post-transition low fertility. The model for the fertility decline builds on the United Nations Population Division’s current deterministic projection methodology, which assumes that fertility will eventually fall below replacement level. It models the decline in TFR as the sum of two logistic functions that depend on the current TFR level, and a random term. A Bayesian hierarchical model is used to project future TFR based on both the country’s TFR history and the pattern of all countries. It is estimated from United Nations estimates of past TFR in all countries using a Markov chain Monte Carlo algorithm. The post-transition low fertility phase is modeled using an autoregressive model, in which long-term TFR projections converge toward and oscillate around replacement level. The method is evaluated using out-of-sample projections for the period since 1980 and the period since 1995, and is found to be well calibrated.     

Population statistics] as of July 1, 1998

This article presents estimates of relevant population numbers and vital rates in Thailand as of July 1, 1998. Utilizing the standard demographic techniques of analysis, the estimates provided are assured to be the most accurate demographic estimates possible. Total population was estimated at 61,143,000. Estimates by sex, locales, region, and by age group are included. In addition, the crude birth rate per 1000 population was estimated at 18.7; the crude death rate per 1000 population was 6.5. For the natural growth rate the estimate was at 1.2%, and the infant mortality rate was 25.0 per 1000 live births. In terms of life expectancy at birth, the estimate for males was 69.9 years, while for females it was 74.9 years. Additional years in life expectancy at age 60 were 20.3 years for males and 23.9 years for females. The total fertility rate per woman is 1.98, and contraceptive prevalence is 72.2%. The demographic data will be disseminated to Thai and international population researchers and planners.     

New techniques in small area population estimates by demographic characteristics

The increasing demand for small area population estimates calls for both innovative ways of using existing data and new techniques suitable for small area estimates. This paper explores the methods for population estimates by age, sex, race, and Hispanic origin at the census tract level for Multnomah County, Oregon. New techniques include employing building permits to indirectly estimate migration and examining the changes in age/sex structure using the American Community Survey (ACS). A practical method for bridging the race categories is also developed. Finally, the paper discusses some reflections on small area estimates and the potentials of using ACS to track the changes of the demographic characteristics for the sub-county level.     

Temporal and spatial variation in age-specific net migration in the United States

As fertility differences in the United States diminish, population redistribution trends are increasingly dependent on migration. This research used newly developed county-level age-specific net migration estimates for the 1990s, supplemented with longitudinal age-specific migration data spanning the prior 40 years, to ascertain whether there are clear longitudinal trends in age-specific net migration and to determine if there is spatial clustering in the migration patterns. The analysis confirmed the continuation into the 1990s of distinct net migration "signature patterns" for most types of counties, although there was temporal variation in the overall volume of migration across the five decades. A spatial autocorrelation analysis revealed large, geographically contiguous regions of net in-migration (in particular, Florida and the Southwest) and geographically contiguous regions of net out-migration (the Great Plains, in particular) that persisted over time. Yet the patterns of spatial concentration and fragmentation over time in these migration data demonstrate the relevance of this "neighborhood" approach to understanding spatiotemporal change in migration.     

含迁移要素的区域人口随机预测方法及其应用--以浙江省宁波市为例

以宁波市为例,基于宁波市“六普”与“五普”数据,首先利用年龄别死亡率对同批次队列人口进行年龄移算,即人口留存分析,对比2010年的实际人口数和无迁移模式下的封闭人口数之差,进一步测算两次普查期间分性别、年龄别人口的净迁移量和净迁移率。然后,将迁移率与出生率和死亡率整合,构建多要素随机人口预测模型,预测宁波市未来人口变化趋势,并评估迁移、死亡、出生三要素对人口变动的弹性影响效果。结果表明：人口净迁入对宁波市人口总量变化影响最大,而低死亡率和低出生率是未来50年加剧宁波市人口老龄化的主要原因。未来50年内,劳动力人口净迁入对降低宁波市人口老年负担系数的作用有限。鼓励夫妇生育二孩,优化人才引进与落户机制,尽快建立起应对高龄社会的公共服务体系尤其是长期照护体系,应是宁波市人口政策改革的当务之急。