Patterns underlying fertility schedules: A decomposition by both age and marriage duration

Summary Model fertility schedules based on the proportions married and the age pattern of marital fertility are unsatisfactory to the extent that marital fertility does not depend on age alone but also on other factors. Most notably, models based just on age fail to allow for differences between populations in their composition by marriage duration. Examination of the major series of fertility rates specific by both age and duration of marriage (Sweden 1911-70, England and Wales, 1941-70) reveals striking underlying regularities. The marital fertility rates observed at any given point in time can be factored into three independent components - an overall level, a vector of age effects common to all marriage durations and a vector of duration effects common to all age groups. A simple product of these three components is shown to approximate the data very closely over the entire series, despite major changes in the aggregate levels of fertility and nuptiality during the periods concerned. Not only are the data tightly structured, conforming very closely to this simple multiplicative model, but the vectors of age and duration effects themselves are shown to exhibit clear and meaningful regularities.     

Demographic responses and demographic transitions: A case study of sweden

An important study by Friedlander investigated some of the effects of different demographic responses on national demographic transitions. England and Sweden were advanced as cases that approximated the suggested hypothetical models of transitions. His argument implied that the rural population of a country (in this case Sweden) experiencing mortality decline but little industrialization would reduce its fertility rates if out-migration from agricultural areas were not possible. This present study, using more complete data and better measures, concludes that this did not occur in Sweden—it did not conform to Friedlander’s hypothesized model. Because the potential implications of these findings could be profound and wide-ranging, there is a need for more studies of individual countries using better data and giving more careful attention to Davis’s theory on which the Friedlander hypothesis is based.     

Precision,bias, and uncertainty for state population forecasts: an exploratory analysis of time series models

Many researchers have used time series models to construct population forecasts and prediction intervals at the national level, but few have evaluated the accuracy of their forecasts or the out-of-sample validity of their prediction intervals. Fewer still have developed models for subnational areas. In this study, we develop and evaluate six ARIMA time series models for states in the United States. Using annual population estimates from 1900 to 2000 and a variety of launch years, base periods, and forecast horizons, we construct population forecasts for four states chosen to reflect a range of population size and growth rate characteristics. We compare these forecasts with population counts for the corresponding years and find precision, bias, and the width of prediction intervals to vary by state, launch year, model specification, base period, and forecast horizon. Furthermore, we find that prediction intervals based on some ARIMA models provide relatively accurate forecasts of the distribution of future population counts but prediction intervals based on other models do not. We conclude that there is some basis for optimism regarding the possibility that ARIMA models might be able to produce realistic prediction intervals to accompany population forecasts, but a great deal of work remains to be done before we can draw any firm conclusions.     

中国人口时间序列预测模型的探讨

以 1 95 2～ 2 0 0 2年人口序列数据为基础 ,构建了中国人口时间序列预测模型 ,采用一般回归法、后退法和逐步回归法三种方法对所设计的模型进行估计 ,得到 72个模型。然后 ,从中筛选出估计标准误较小 ,自相关影响基本消除的预测模型。作为中国人口总量的预测模型 ,我们提出的预测模型有估计精度高 ,误差低的特点 ,是目前用自回归方法估计得出的较好的中国人口预测模型。     

‘A perfect fit’ – Swedish midwives’ interest in continuity models of midwifery care

BackgroundMidwifery continuity models of care are highly recommended yet rare in Sweden, although approximately 50% of pregnant women request them. Before introducing and scaling up continuity models in Sweden, midwives’ attitudes about working in continuity models must be investigated.Objectiveto investigate Swedish midwives’ interests in working in midwifery continuity models of care and factors influencing the midwifery workforce’s readiness for such models.MethodsA cross-sectional online survey was utilised and information collected from a national sample of midwives recruited from two unions regarding background and work-related variables. Crude and adjusted odds ratios and logistic regression analysis were used in the analysis.ResultsA total of 2084 midwives responded and 56.1% reported an interest. The logistic regression model showed that respondents’ ages 24–35 years (OR 1.73) or 35–45 years (OR 1.46); years of work experience 0–3 years (OR 5.81) and 3–10 years (OR 2.04); rotating between wards or between tasks (OR 2.02) and working temporary (OR 1.99) were related to interest in continuity models. In addition, working daytime only (OR 1.59) or on a two-shift schedule (OR 1.93) was associated with such interest.ConclusionA sufficient number of midwives in Sweden appear to be interested in working in continuity models of midwifery care to align with women’s interest in having a known midwife throughout pregnancy, birth and postpartum period. Developing strategies and continuity models that will address the preferences of women in various areas of Sweden is important for offering evidence-based maternity services.     

The third birth in Sweden

This paper considers the formulation, estimation and interpretation of microdynamic models of fertility. Our model explains parity choices, sterility, childlessness, interbirth intervals and initiation of pregnancy within a unified framework. We develop a general methodology for estimating the determinants of transition times to births of different orders. Our procedure incorporates time-varying explanatory variables and unobservables. We present conditions that justify conventional formulae relating hazards to survivor functions when time-varying variables enter hazards. We also consider the validity of widely-used piecemeal estimation strategies that focus on one birth at a time. We consider methods for selecting a best model among a class of non-nested models. Two criteria are set forth and used to evaluate the detminants of third births in Sweden.We find that two models fit Swedish microdata equally well. One model is consistent with neoclassical economic theory. It assigns a central role to the wages of men and women in explaining the timing and spacing of births. The other model is purely demographic and excludes wages. Purely statistical criteria cannot distinguish these models although in other work we show that the economic models are more parsimonious in terms of the number of parameters that must be estimated and are better able to forecast aggregate time series.We demonstrate how to interpret the output of multistate fertility models. Wage effects on third births are decomposed into two components: (a) an in direct effect that determines whether a woman is at risk to have a third birth, and (b) a direct effect on the transition rate to the third birth given that a woman has had two births. We find that female wages play an important role in postponing first births but play only a minor role in explaining childlessness. Female wages substantially affect third births. Male wage effects are weaker. We find that female wage effects weaken for more recent cohorts of women. This evidence is consistent with the introduction of progressively more pronatal Swedish policies.This research was supported by NIH Grant No. HD-19226 to NORC. We have benefited from the comments of Elja Arjas and Ricardo Barros. This paper was presented at an IUSSP Conference in Paris, France, in March 1988, and as an invited lecture at the Fourth ESPE Meetings in Istanbul, Turkey, June, 1990. This paper is one part of a trilogy. Heckman and Walker (1990a) presents a succinct summary of the main economic results. Heckman and Walker (1990b) presents a more complete discussion of the empirical results. This paper presents a more purely demographic discussion.     

Childbearing Across Partnerships in Australia,the United States,Norway, and Sweden

This article compares mothers’ experience of having children with more than one partner in two liberal welfare regimes (the United States and Australia) and two social democratic regimes (Sweden and Norway). We use survey-based union and birth histories in Australia and the United States and data from national population registers in Norway and Sweden to estimate the likelihood of experiencing childbearing across partnerships at any point in the childbearing career. We find that births with new partners constitute a substantial proportion of all births in each country we study. Despite quite different arrangements for social welfare, the determinants of childbearing across partnerships are very similar. Women who had their first birth at a very young age or who are less well-educated are most likely to have children with different partners. The educational gradient in childbearing across partnerships is also consistently negative across countries, particularly in contrast to educational gradients in childbearing with the same partner. The risk of childbearing across partnerships increased dramatically in all countries from the 1980s to the 2000s, and educational differences also increased, again, in both liberal and social democratic welfare regimes.     

区域研究中的常用人口预测模型

人口是一国和地区发展的重要因素。准确的人口预测是制定国民经济计划、区域发展规划的基础。文章以甘肃省为例,介绍了线性回归模型、马尔萨斯模型、Logistic模型和GM（1,1）模型在人口预测中的应用,包括模型的建立、参数的求解以及精度检验。并分别用这几种模型对甘肃省2006—2020年的总人口进行预测。结果表明几种模型的拟合精度都比较高,预测值比较接近。取几种模型的预测平均值作为甘肃省总人口规模的预测结果。几种模型的平均预测结果为：2010年甘肃省总人口将达到2745．84万人,2015年将达到2840．91万人。2020年将达到2934．23万人．     

Age structure,growth, attrition and accession: A new synthesis

This paper shows that each equation describing relationships among demographic parameters in a stable population is a special case of a similar and equally simple equation that applies to any closed population and demonstrates some implications of these new equations for demographic theory and practice. Much of formal demography deals with functions that pertain to individuals passing through life, or to a stationary population in which births of individuals are evenly distributed over time. These functions include life expectancy, probabilities of survival, net and gross reproduction rates, expected years spent in various states and the probability that certain events will occur in the course of life. The stable population model permits the translation of population structure or processes in a more general type of population, with constant growth rates, back into equivalent populations for a stationary population. The method for translation developed in this paper, requiring only a set of age-specific growth rates is even more general, applying to any population. Age specific growth rates may also be useful for performing reverse translations, between a population's life table and its birth rate or its age distribution. Tables of numbers of females by single years of age in Sweden are used to illustrate applications. Tables summarize the basic relations among certain functions in a stationary population, a stable population and any population. Applications of new equations, particularly to demographic estimation of mortality, fertility and migration, from incomplete data, are described. Some other applications include; the 2 sex problem, increment decrement tables, convergence of population to its stable form, and cyclical changes in vital rates. Stable population models will continue to demonstrate long term implications of changes in mortality and fertility. However, in demographic estimation and measurement, new procedures will support most of those based on stable assumptions.     

Sweden faces zero population growth

In this discussion of Sweden as it approaches zero population growth, focus is on the following: population growth in perspective, fertility trends (childbearing concentrated and cohort versus period fertility), marital status (non-marital cohabitation, out-of-wedlock births, and divorce), women's changing status (increasing education and increasing employment), constraints and supports for women's dual role (family allowances and housing), birth control (contraceptive methods and practice and abortion), mortality trends, changing age structure and the elderly (average population age and proportion of elderly and cost of elderly support), international migration (from emigration to immigration and demographic impact of immigration), immigration policy, recent population debate (immigration issues and facing zero population growth). Since 1900 the primary features of Sweden's demographic history are a continuing decline in the birth rate to very low levels -- relieved by some upward movement in the 1940s and 1960s -- and a marked shift in the migration balance from emigration to immigration. It is almost entirely because of immigration that Sweden's population growth rate has not yet turned negative. If Swedish women were to continue to bear children at the rate that all women in the reproductive ages actually did in 1978, each women would end up with an average well below the level necessary to exactly replace each adult in the population leaving migration out, an annual total fertility rate of 2.1 children per woman would have to be sustained for births and deaths to be in balance under the low mortality conditions prevaling in Sweden.     

Coherent Mortality Forecasting: The Product-Ratio Method With Functional Time Series Models

When independence is assumed, forecasts of mortality for subpopulations are almost always divergent in the long term. We propose a method for coherent forecasting of mortality rates for two or more subpopulations, based on functional principal components models of simple and interpretable functions of rates. The product-ratio functional forecasting method models and forecasts the geometric mean of subpopulation rates and the ratio of subpopulation rates to product rates. Coherence is imposed by constraining the forecast ratio function through stationary time series models. The method is applied to sex-specific data for Sweden and state-specific data for Australia. Based on out-of-sample forecasts, the coherent forecasts are at least as accurate in overall terms as comparable independent forecasts, and forecast accuracy is homogenized across subpopulations.     

The interaction of migration,income, and employment in Sweden

A common approach in migration studies is to explain interregional migration by single-equation models. Such models are likely to suffer from simultaneous-equation bias when used in studies attempting to analyze migration over a long period of time. In this study, a simultaneous-equation approach is applied, which takes account of the interdependence between migration and income and employment changes. The four-equation model is estimated for 70 labor market areas in Sweden.     

The harmonic mean as the basis of a realistic two-sex marriage model

The “two-sex problem” is one of attempting to preserve the essential character of male and female rates of marriage (or birth), since the expression of those rates is influenced both by the age-sex composition of the population and the underlying age-sex schedule of preferences. The present paper focuses on marriage and advances a theoretically based, realistic, and conceptually simple solution. In the continuous case, where exact male and female ages are used, equation (11) provides a mathematical relationship which equates the sum of the male and female marriage propensities of the observed population with that of the model. When discrete age intervals are used, the two-sex consistency condition is given by equation (14) which equates observed and model population rates calculated using the harmonic means of the number of persons in the relevant male and female age groups. The harmonic mean consistency condition is shown to be fully sensitive to the competitive nature of the “marriage market.” When compared with alternative approaches to the two-sex problem in the context of data for Sweden, 1961–64, the simple harmonic mean method yields results fairly similar to those of the other methods. None of the two-sex methods do particularly well at predicting the actual distribution of marriages, however. The likely reason is that the underlying marriage preferences changed, a circumstance which emphasizes the importance of carefully conceptualizing how observed behavior can be decomposed into the effects produced by age-sex composition and those produced by the underlying preferences.     

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.     

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.     

A two-sex nuptiality-mortality life table

The “problem of the sexes” has been one of trying to reconcile inconsistent male and female demographic rates. The present paper deals with that question in the context of a two-sex nuptiality-mortality life table. A “rectangular” population, with equal numbers of persons in each age-sex group, is introduced as a standard, and a standardization relationship expressed in equation (9) relates changes in rectangular population rates to changes in age-sex composition. The standardization relationship is shown to satisfy a number of desirable properties and produce a realistic two-sex model. The standardization approach is then applied to data from Sweden for 1973, and the results and their implications are discussed. In particular, it is seen that the total number of marriages in a two-sex population neither is nor should be bounded by the total numbers of marriages in the associated male and female one-sex nuptiality-mortality tables.     

Interpolation and forecasting of population census data

Since population censuses are not annually implemented, population estimates are needed for the intercensal period. This paper describes simultaneous implementations of the temporal interpolation and forecasting of the population census data, aggregated by age and period. Since age equals period minus cohort, age-period-cohort decomposition suffers from the identification problem. In order to overcome this problem, the Bayesian cohort (BC) model is applied. The efficacy of the BC model for temporal interpolation is examined in comparison with official Japanese population estimates. Empirical results suggest that the BC model is expected to work well in temporal interpolation. Regarding the age-period-cohort decomposition of the Japanese census data, it is shown that the cohort effect is the largest while the other two effects are very small but not negligible. With regard to the forecasting of the Japanese population, the official population forecast considerably outperforms the BC forecast in most forecast horizons. However, the pace of increase in root mean square error for longer-term forecasting is larger in the official population forecast than in the BC forecasts. As a result, a variant of the BC forecast is best for 10-year forecast.     

Population forecasting: do simple models outperform complex models?

"This paper reviews the growing literature on population forecasting to examine a curious paradox: despite continuing refinements in the specification of models used to represent population dynamics, simple exponential growth models, it is claimed, continue to outperform such more complex models in forecasting exercises. Shrinking a large complex model in order to simplify it typically involves two processes: aggregation and decomposition. Both processes are known to introduce biases into the resulting representations of population dynamics. Thus it is difficult to accept the conclusion that simple models outperform complex models. Moreover, assessments of forecasting performance are notoriously difficult to carry out, because they inevitably depend not only on the models used but also on the particular historical periods selected for examination....This paper reviews some of the recent debate on the simple versus complex modeling issue and links it to the questions of model bias and distributional momentum impacts." (SUMMARY IN FRE)