Statistical modeling of selected aspects of the childbearing process with application to world fertility survey countries∗

The childbearing process should be monitored in developing countries experiencing high population growth rates and high levels of maternal and infant mortality. A mathematical model for estimation of certain aspects of the childbearing process, which requires only data on age‐specific fertility rates, is developed. Synthetic maternal childbearing indices, namely, mean ages at first and last birth, length of reproductive life span, inter‐birth spacing, and proportion of childless women, in addition to the well‐known mean age at childbearing, for the WFS countries are obtained using the proposed model. The indices are free from age truncation effects, and, under certain assumptions, provide information about a cohort's completed fertility before the women stop reproducing. The effects of women's residence and education on fertility are also examined.     

Software announcement: LIPRO 2.0

We describe a method for fitting the Coale‐Trussell model to fertility rates or to counts of births and exposure by single years of age. The procedure maximizes a quasi‐likelihood function and can easily be implemented using standard software. An extension to handle covariates is discussed.     

Turbulent dynamics in a Xviith century population

A reconstruction of the population of the Pays de Caux (1589–1700) yields the time series of a fertility behavior indicator, the overall Coale index If. In spite of the noisy appearance of its evolution, the trajectory of If looks ordered, as if it were confined alternatively to two given zones, looping in each of them for a while, then suddenly jumping from the low one to the higher one, or slowly whirling down from the high to the low one.

An attempt is made to explain this general temporal structure by using a simulation model based on the autoregulation model (the so‐called European Marriage Pattern), putting into play a choice of the spouse function, a fertility function, modalities of marriage and remarriage, under the environmental forcing of the reconstructed mortality conditions.

The correspondence between reconstruction and simulation turns out to be quite good, not only for the population size or the Coale index, but also for the marriage series, quite independently of the reconstructioa

A second simulation with simulated mortality conditions shows a bifurcation point: as the mean frequency of crisis increases, the state of the system leaves the lower level and concentrates more and more in the higher level.

Thus, not only does the autoregulator model appear validated by empirical data, but its bi‐modal structure is revealed, depicting the dynamic response of a traditional community both to the environment and to the endogeneous demographic process.     

Stabilization,birth waves,and the surge in the elderly*

Substantial regularities characterize the transition to stability that follows a shift from one set of vital rates to another. The new vital, rates interact with the population's initial age composition and generate birth waves whose amplitude and attenuation depend on the ratio of ultimate to initial growth and on the new pattern of stable net maternity. A greater change in growth and a later stable net maternity pattern produce larger fluctuations in the number of births. Stabilization begins at the youngest ages and proceeds upward. Sixty years after the shift, the birth waves have largely disappeared and the proportion under age 15 approximates the stable level implied by the new rates. Those patterns are manifest in the stabilization of both observed and Coale‐Demeny model stable populations.

When fertility falls, the new stable population has a larger fraction at all ages above (approximately) 30, with greater changes characterizing the extremes of life. Fifteen years after the fall, there is a trough in the number at ages 0–14. Sixty years after the fall, when the largest pre‐decline cohort is age 60–74 and the smallest post‐decline cohort is age 45–59, there is a surge in the relative size of the elderly population. Thus after two generations, the birth waves produced by a rapid decline in fertility accentuate the effects of population aging.     

The TFR and birth control]

Total fertility rate if (TFR) is a simple an straight forward measure of women's fertility. However, it is difficult to use the TFR as a target measure in FP programs. If TFR level is set as a target for a particular year, how can women's fertility be regulated to achieve this target? The following analysis suggests a simple model to control the proportion of birth parity. First, the TFR is decomposed into a parity- specific TFR. The parity-specific TFR can be worked out using coefficients of the regression models calculated from data of previous fertility surveys. Once the TFR is given, the parity-specific total fertility can be calculated using a model with coefficients from empirical data. Then the number of births of each parity may be calculated from the parity-specific TFR using the female age structure in a particular year, the survival probability, and the standard fertility model for each parity. When the number of surviving children of each women at child-bearing age is known, the desired proportion of births of each parity can be calculated using the standard birth probability during a years. From these models, it would be possible to calculate how many women can have their first child/year, and how many can have the second. Thus, family planning organizations would be in a position to formulate a birth quota on the basis of the above information.     

Findings and implications of a correlation analysis of the closed and the open birth intervals

A correlation analysis of data on four fertility variables viz. closed birth interval, open birth interval, age and parity, collected in a survey of about 2,000 married women in the reproductive ages in rural India, is carried out in order to study the interrelationships among these variables. Two hypotheses are formulated governing the relationship of the closed and open birth intervals with the fecundability distribution of fertile women, and Parity Progression Ratios which are largely influenced by the proportion of women becoming sterile after each parity. The data lend support to the hypothesis that while the closed intervals are influenced mainly by the distribution of fecundability of women of non-zero fecundability, the open birth intervals are influenced mainly by Parity Progression Ratios or the proportion of women becoming secondarily sterile after each parity. The analysis suggests that we can use the mean open intervals of women classified by parity as indices of fertility, and such an index is comparable to the index of average age of women of given parity. In areas where it is difficult to ascertain the correct age of women this might be of practical value.     

Estimating birth stopping and spacing behavior

A decomposition of age-specific marital fertility rates into indices related to spacing and stopping is developed by using Coale and Trussell's indices and the first few parity progression ratios. This approach leads to estimates of the mean birth interval among low-parity births that can be used to address the issue of fertility control early in marriage. In this way the model addresses several of the most serious limitations of Coale and Trussell's approach. The usefulness of the proposed indices is demonstrated by applications to historical data from the United States and Europe.     

Birth spacing and fertility limitation: a behavioral analysis of a nineteenth century frontier population

Our analysis of changing birth interval distributions over the course of a fertility transition from natural to controlled fertility has examined three closely related propositions. First, within both natural fertility populations (identified at the aggregate level) and cohorts following the onset of fertility limitation, we hypothesized that substantial groups of women with long birth intervals across the individually specified childbearing careers could be identified. That is, even during periods when fertility behavior at the aggregate level is consistent with a natural fertility regime, birth intervals at all parities are inversely related to completed family size. Our tabular analysis enables us to conclude that birth spacing patterns are parity dependent; there is stability in CEB-parity specific mean and birth interval variance over the entire transition. Our evidence does not suggest that the early group of women limiting and spacing births was marked by infecundity. Secondly, the transition appears to be associated with an increasingly larger proportion of women shifting to the same spacing schedules associated with smaller families in earlier cohorts. Thirdly, variations in birth spacing by age of marriage indicate that changes in birth intervals over time are at least indirectly associated with age of marriage, indicating an additional compositional effect. The evidence we have presented on spacing behavior does not negate the argument that parity-dependent stopping behavior was a powerful factor in the fertility transition. Our data also provide evidence of attempts to truncate childbearing. Specifically, the smaller the completed family size, the longer the ultimate birth interval; and ultimate birth intervals increase across cohorts controlling CEB and parity. But spacing appears to represent an additional strategy of fertility limitation. Thus, it may be necessary to distinguish spacing and stopping behavior if one wishes to clarify behavioral patterns within a population (Edlefsen, 1981; Friedlander et al., 1980; Rodriguez and Hobcraft, 1980). Because fertility transition theories imply increased attempts to limit family sizes, it is important to examine differential behavior within subgroups achieving different family sizes. It is this level of analysis which we have attempted to achieve in utilizing parity-specific birth intervals controlled by children ever born.(ABSTRACT TRUNCATED AT 400 WORDS)     

用孩次递进比模拟“全面二孩”政策调整初期的生育行为--以湖北省为例

以2014年湖北省卫生和计划生育委员会提供的包括“单独”、“双独”方面的数据为基础,描述了生育政策调整下被压抑的生育潜能释放的规律性和用孩次递进比的方法预测“全面二孩”政策调整初期的生育行为,与意愿分析方法相互比照,丰富了当下生育政策下生育行为预测研究。从分析结果可以看出,假定2016年“全面二孩”生育政策调整,湖北省第一年内会新增二孩出生量52621人,占湖北省2014年总出生量的7?41％;三年内最低会新增139262人的二孩生育量。城乡对比发现,农村新增二孩生育占到将近六成,且由抢生而导致的堆积主要集中在农村,40岁后的高龄抢生情况不严重。     

Fertility of Australian birth cohorts: Components and differentials

The paper examines the change in the level and pattern of fertility that took place in the post-1971 period, and the downward completed fertility of successive generations of Australian women born since 1933–37. The change in cohort fertility is assessed in terms of the cohort parity progression ratios, and the four components of cohort total fertility: the proportion of women who proceeded to have a birth, mean age at first birth, mean age at last birth, and average interbirth interval for women who had at least two births. The other aspects discussed are the cohort fertility differentials and the implications of the current trends for future fertility in Australia.     

The construction of the fertility model of variable parity from family planning practice]

Understanding the changing patterns of age specific fertility under the planning system is essential for building a fertility model which reflects birth control policy implementation in China. In building a Parity Variable Fertility Model, 4 basic elements are to be considered: 1) psychosocial, and physiological variables, 2) patterns of the total fertility rate and age-specific fertility rate, 3) socioeconomic development, and 4) distribution of parity-specific fertility. THe natural fertility of women is 17, calculated from a 309-years childbearing period, with 17% of non-susceptible time. In China, about 86% of natural fertility is suppressed by various factors. In this model, the following variables are included: 1) The first marriage ratio, which is the proportion of women in each age group which enters into a first marriage. The range and spread of this ratio is closely associated with the first birth. 2) The first birth ratio, which is the proportion of a marriage cohort to have a first birth each year. 3) the birth interval, which determines the distribution of second births. 4) Regulation coefficient B, which represents birth control regulations which approximately determine the number of second-parity or higher order births. The difference between the fertility level generated from the Parity Variable Fertility Model and reality depends on the implementation of birth control program, the assumptions on regulation coefficients, and changes in social and cultural factors. The model is easy to use, especially for areas where the marriage and fertility records of women of child-bearing are well kept.     

关于中国1990年代低生育水平的再讨论

本文根据全国第五次人口普查样本计算了 1 990年代各年份的分性别平均初婚年龄 ,这一结果再次表明这一时期中初婚年龄有显著提高。本文还根据以往历次调查的各年份年龄别生育率按队列计算了累计生育率 ,结果发现 2 0 0 0年时各队列的累计生育率水平高于五普数据中各队列的平均活产子女数。本文还就队列累计生育率计算结果详细分析了 1 990年代终身生育水平的趋势。这些分析从一个新的角度说明 ,1 990年代各队列的终身生育水平也在发生显著的下降 ,正在接近现行生育政策所要求的水平     

我国实际低生育水平的影响因素分析——邦戈茨低生育率模型应用

本文使用2010年江苏省六县市"生育意愿与生育行为研究"跟踪调查数据,应用邦戈茨低生育率模型,对已基本完成生育周期且可生育二孩妇女的实际生育水平的影响因素进行了分析。在以意愿生育水平为参照的条件下,研究发现,初育年龄推迟、教育水平提高,工作压力等都对妇女的实际生育水平产生了显著的抑制作用。     

Reproductive histories of Chinese women in rural Taiwan

In the summer of 19 5 3, a 3 % sample of the households in a rural area of Taiwan was enumerated. Special attention was paid to the fertility histories of women and, among other information, dates of births of live-born children to women living at the survey date were obtained. The data were extracted from registration records, occasionally checked by personal interview.

Women aged 45–64 had borne an average of 7.1 children. The oldest cohorts (women over 65 at survey) appeared to have a lower fertility. This is in part due to the reduction in the incidence of early widowhood, caused by the improved mortality of men since the beginning of the century.

The data are further analysed by parity and age at marriage.

Tabulations of the intervals between births of successive order, show that these remain constant with increasing birth order at about 2.7 years. The age at the last confinement was about 40 years.     

Lifetime probability of additional births by age and parity for American women, 1935–1968: A new measurement of period fertility

A new fertility measurement, probability that a woman of specified parity and age will bear a given number of births in her remaining lifetime, is proposed in this article. The measurement is a summary index of a set of age-parity-specific birth probabilities and in a particular case it is conceptually analogous to the total fertility by birth order but free from the influence of the parity distribution. Fertility of American women for the period 1935-1968 was studied by use of such lifetime probabilities. It appears that the trend of fertility of high birth orders has been parallel with that of low orders. Initiation of the recent decline in fertility depends on parity and age of woman.     

Presentation and establishment of a system of total progressive fertility rates and relevant models

Demographic studies necessarily rely on adequate and accurate statistical data. To take into consideration China's present situation of population control and planned birth practice, a system of total progressive fertility rate (TPFR) different from the parity progression ratio is established and its relevant model presented in order to make indicators used in analysing women's 1st marriage and fertility level reflect as closely as possible the actual situation. Here, TFR and TPFR, both used in analyzing fertility level, are compared so as to show that TPFR is a methodology more appropriate for use in the analysis of China's fertility. The model is based on the fact that women's vital events happen progressively from being born to completing childbearing. In composing the model, both women's age structure and parity structure are considered and the regularity of their changes with different years is defined. In China, the population development program has been brought into the overall social and economic development plan. Thus it is necessary to practice planned birth in order to make the population develop in a way which is in keeping with the social and economic development. Compared with other models or theories, it is more realistic to use the model discussed above in studies on China's population policy.     

A model of numbers of births in three countries,with persistent forty‐year cycles

A non‐linear model of fertility is described, which was derived from data for more than a century from England and Wales, New Zealand, and the U.S.A. The demographic transition is modelled with a logistic function, and age‐specific fertility rates are estimated using lognormal distributions. The stepwise inclusion of a partner availability estimate in the model showed that it accounts for twenty‐nine percent of otherwise unexplained variance. Projected future births stabilise in sustained or limit cycles with periods a little longer than 40 years, and amplitudes at least 7% of the mean. The necessary conditions for cycle persistence are outlined on a graph of maximum and minimum fertility parameters.     

子女孩次性别结构与女性再生育——基于孩次性别递进生育率的分析

现有子女的孩次性别结构是影响女性再生育的重要因素。使用中国2000年人口普查数据和时期孩次性别递进生育指标对女性生育水平进行了测算。结果显示,女性普遍生育但终身只生育一个孩子的比例很大,基于孩次性别结构的生育行为体现了男孩偏好;城市和镇在生育第一孩时就存在性别选择;第一个孩子是女孩的女性生育二孩的可能性较大,且二孩是男孩的比例显著大于是女孩的比例;第一个孩子是男孩的城市和镇的女性大部分不再生育,而农村女性有很大比例会生育二孩,但几乎不存在性别选择。采用某地区2019年的数据进行补充验证,同样发现:只有一个女孩的女性相比较只有一个男孩的女性生育者生第二孩的可能性要高很多,以上研究发现对当前二孩生育行为具有一定的启示意义。     

The Correspondence Between Fertility Intentions and Behavior in the United States

Using data from the 1979 National Longitudinal Survey of Youth, we describe the correspondence between intended family size and observed fertility for US men and women in the 1957–64 birth cohorts. Mean fertility intentions calculated from reports given in the mid‐20s modestly overstate completed fertility. But discrepancies between stated intent and actual fertility are common—the stated intent at age 24 (for both women and men) is more likely to miss than to match completed fertility. We focus on factors that predict which women and men will have fewer or more children than intended. Consistent with life‐course arguments, those unmarried, childless, or (for women) still in school at approximately age 24 were most likely to underachieve their intended parity (i.e., had fewer children than intended at age 24). We discuss how such discrepancies between intentions and behavior may cumulate to produce sizable cross‐group fertility differences.     

Age patterns of chinese marital fertility, 1950–1981

Coale and Trussell’s model of marital fertility is used to analyze data from China’s National One-per-Thousand Fertility Survey. Rural China experienced a regime of natural fertility until 1970, after which levels of fertility control rose with unprecedented speed and with an age pattern starkly dissimilar from that observed in other populations. Urban marital fertility was apparently under a modest level of deliberate control in the 1950s, with a sustained rise in control beginning in 1963. Natural fertility was low relative to other populations, with the urban level exceeding the rural.