Multivariate time series projections of parameterized age-specific fertility rates

1 solution to the dimensionality problem raised by projection of individual age-specific fertility rates is the use of parametric curves to approximate the annual age-specific rates and a multivariate time series model to forecast the curve parameters. Such a method reduces the number of time series to be modeled for women 14-45 years of age from 32 to 40 (the number of curve parameters). In addition, the curves force even longterm fertility projections to exhibit the same smooth distribution across age as historical data. The data base used to illustrate this approach was age-specific fertility rates for US white women in 1921-84. An important advantage of this model is that it permits investigation of the interactions among the total fertility rate, the mean age of childbearing, and the standard deviation of age at childbearing. In the analysis of this particular data base, the contemporaneous relationship between the mean and standard deviation of age at childbearing was the only significant relationship. The addition of bias forecasts to the forecast gamma curve improves forecast accuracy, especially 1-2 years ahead. The most recent US Census Bureau projections have combined a time series model with longterm projections based on demographic judgment. These official projections yielded a slightly higher ultimate mean age and slightly lower standard deviation than those resulting from the model described in this paper.     

Forecasting births in post-transition population: stochastic renewal with serially correlated fertility

Time series analysis of fertility can improve demographic forecasts. The optimal forecast and its variance for births to an age-structured population subject to serially correlated random fertility are developed. The general case in which the fertility process had arbitrary autoregressive structure is dealt with and then the 4 special cases of white noise, 1st-order autoregressive, 2nd-order autoregressive, and random walk are considered. Consequently, it is determined that the predictions and their variances are highly sensitive to the autoregressive structure of fertility and, therefore, if stochastic models are to be used for prediction, they must emphasize this aspect of the problem. Preliminary empirical efforts to model the time series of U.S. fertility from 1917 to 1972 proved unsuccessful, but it is obvious that at least a 2nd-order autoregressive scheme is require d. The analysis proveded should be helpful in: 1) any application of the procedures requires a successful parameterization of the fertility process; 2) fertility variations could be decomposed into the effects of nuptiality and marital fertility and then births and marriages could be jointly predicted; and 3) the simplifying approximations should be dropped and each age-specific rate could be analyzed and predicted.     

Seasonal patterns of fertility measures: theory and data

The distribution of births by month exhibits a seasonal pattern in most populations. The monthly marital fertility rate for an area of Bangladesh provides a good example of the seasonal periodicity. Seasonal patterns of measures of reproduction in a population of married women are considered. Equations are developed that predict the seasonal patterns of these alternative measures under the assumption that the fertility rate (R) follows a trigonometric curve. This is followed by an empirical analysis of the measures in a Bangladesh population that has a pronounced seasonal fertility. The investigation is intended both to validate the theoretical framework developed in the 1st part of the paper as well as to determine whether seasonal variation in actual populations is sufficiently large to affect the alternative measures significantly. 4 measures are considered: pregnancy prevalence (PP)--the proportion of married women who are pregnant at the survey date; mean open birth interval (MOI)--the time from the last live birth to the date of the survey for parous women and from the time of marriage to the date of the survey for nulliparous women; mean closed interval-birth (MCIB)--the mean interval between the last 2 live births for married women who have a birth in the period immediately preceding the survey date; and mean closed interval-woman (MCIW)--the mean interval between the last 2 live births for women who have had at least 2 children by the time of the survey. It is assumed that the seasonal pattern of the fertility rate of a population follows a cosine curve and that there is no trend in annual fertility from year to year. The lag and relative variability of the other measures are considered in comparison with the fertility rate curve. The predictions from this theoretical effort, when compared with observed patterns and trigonometric regression results for each measure in data from Bangladesh, are shown to be quite accurate. The figure and regression results show that R, PP, and MOI have definite seasonal periodicity, but MCIB and MCIW do not display any seasonal patterns. If there is a secular trend in fertility in addition to seasonality, these relationships between the seasonal patterns of the measures may no longer hold. There is a disadvantage to using closed interval measures, for they are unable to detect effects of limiting of childbearing in a population since they are based only on information from women who have births.     

The importance of intentions in the mechanism of reproductive behaviour formation

In a situation of low fertility like that operating nowadays, studying the determinants of reproductive behaviour is very important. In a context such as Western industrialized one, in which birth control induces a feature of consciousness into fertility conduct, reproductive intentions have a fundamental role. This paper examines the mechanism which leads to the formation of reproductive behaviour starting from intentions, with reference to a large city in Italy, where fertility is very low, Milan. In addition, the hypothesis that women have innate and unobservable propensities toward family formation is verified through a simultaneous equations model. It allows to control for the potential endogeneity of reproductive intentions in determining subsequent behaviour. Results partially confirm this hypothesis: no significant correlation is found between unobservable components influencing intentions and behaviour. The relevance of reproductive intentions for subsequent fertility behaviour is, however, pointed out.     

The dynamics and differentials of fertility in the USSR (survey results)

The results of a fertility survey carried out in the USSR in 1978 are presented. The survey included 33,076 women aged 18 to 59. Data are included on fertility rates by region and Union Republic and by urban or rural area, and on expected fertility of women aged 18 to 44. Changes in actual and desired fertility over time are compared for five-year periods from 1945 to 1978. Differences in fertility are analyzed by type of settlement, educational status, and nationality.     

Women in the USSR

This is a selection of statistical data on women in the USSR; it covers the period 1970-1989. Tabular data are provided on the number of women by Union republic; the number of women and men by age group and rural or urban area; women's educational levels, sources of income, and occupations; family size for the whole country and for rural and urban areas; women's marital status by age; marriages and divorces; divorce by women's education, age, and number of children; birth rate by Union republic and by nationality; abortion and childbirth for selected years and by Union republic; maternal deaths by Union republic; infant deaths; and female life expectancy.     

Intergenerational fertility changes

Intergenerational changes in fertility in Poland are analyzed using data from a 1977 sample survey of 38,600 women. The author notes that total fertility declined from 4.4 to 2.5 within the space of two generations. An analysis of fertility is presented by various characteristics of females, including age group, education, duration of marriage, and economic status.     

Ethnic differentials in fertility in the USSR

Ethnic differentials in fertility in the USSR are analyzed using data from official sources. Age-specific and total fertility rates for women of various nationalities are presented by Union republic for selected years from 1945 to 1984.     

Differentiation of female fertility by educational attainment

The author examines fertility differentials by educational attainment for Polish women using official vital statistics on births as modified in 1974. Comparisons are made with fertility recorded in previous studies based on census or sample survey data     

Do divorcing couples become happier by breaking up?

Summary.  Divorce is a leap in the dark. The paper investigates whether people who split up actually become happier. Using the British Household Panel Survey, we can observe an individual's level of psychological well-being in the years before and after divorce. Our results show that divorcing couples reap psychological gains from the dissolution of their marriages. Men and women benefit equally. The paper also studies the effects of bereavement, of having dependant children and of remarriage. We measure well-being by using general health questionnaire and life satisfaction scores.     

Assessing the use of sample selection models in the estimation of fertility postponement effects

Several studies have shown that at the individual level there exists a negative relationship between age at first birth and completed fertility. Using twin data in order to control for unobserved heterogeneity as possible source of bias, Kohler et al. (2001) showed the significant presence of such "postponement effect" at the micro level. In this paper, we apply sample selection models, where selection is based on having or not having had a first birth at all, to estimate the impact of postponing first births on subsequent fertility for four European nations, three of which have now lowest-low fertility levels. We use data from a set of comparative surveys (Fertility and Family Surveys), and we apply sample selection models on the logarithm of total fertility and on the progression to the second birth. Our results show that postponement effects are only very slightly affected by sample selection biases, so that sample selection models do not improve significantly the results of standard regression techniques on selected samples. Our results confirm that the postponement effect is higher in countries with lowest-low fertility levels.     

Models of procreative behavior based on the concept of the life cycle

This is the first in a planned series of papers applying path analysis methods to the study of reproductive behavior in rural areas in Poland. Factors considered include total number of births, birth intervals, birth control and abortion, and future fertility intentions. The objective is to examine how the fertility of rural women is affected by various social and economic factors. (SUMMARY IN ENG)     

A new behavioural model for fertility schedules

Modelling age-specific fertility rates is of great importance in demography because of their influence on population growth. Although we have a variety of fertility models in the demographic literature, most of them do not have any demographic interpretation for their parameters. It is generally expected that models with behavioural interpretation are more universal than those without any interpretation. Even though the famous Gompertz model has some behavioural interpretation it suffers from other drawbacks. In the present work, we propose a new fertility model, which has its genesis in the generalization of logistic law. The proposed model has good behavioural interpretation, alongside having nice parameter interpretations.     

Appraisal of the factors influencing changes in the total number and composition of births by mother's age

The causes of the temporary and unexpected increase in fertility in Poland that occurred at the beginning of the 1980s are reviewed. Among the possible causes considered are a change in the number of women of reproductive age, changes in the size of the female population in selected areas due to migration, and actual changes in age-specific fertility.     

Fertility in Poland during the 1980s: analysis of a maternity questionnaire

Recent fertility trends in Poland are analyzed using data from a mail survey conducted in 1984. The demographic, social, and economic characteristics of women who gave birth in 1984, their husbands, and their parents are examined. The results show an increase in fertility in the early 1980s, particularly in urban areas.     

The relative orientation of addresses of spouses before their marriage:an analysis of circular data

The addresses of marriage partners just before their marriage were extracted from the marriage entries of a representative sample of marriages solemnised in England and Wales during 1979. The relative orientation of each marriage was calculated, and for marriages which ranged over 10 kilometres, the angles were found to follow a von Mises distribution with a ‘Preferred direction’ along an axis which was approximately North West/South East. Further investigation, using a combinatorial method, strongly suggests that the phenomenon is largely due to the geographical distribution of persons eligible to marry.     

Duration of marriages in Poland

Some estimates of future marriage duration in Poland are presented. The estimates are based on the assumption that marriages will end at the death of either spouse, and these deaths are projected using 1980-1981 official life tables by sex. The tables showing the probability of marriages ending in this way are provided for various five-year age groups and take into account differences in age between husband and wife.     

Statistical materials. Results of the 1985 socio-demographic sample survey of the population

Results from the five percent socio-demographic sample survey of the USSR conducted in 1985 are presented. Data are provided on the educational status of the population and the labor force by nationality, republic, sex, and rural or urban area; income; marital status; marriage duration; divorce and separation; intervals between marriages; family size; family characteristics; families with children under 18; internal migration; and distribution of women by number of children ever born, republic, nationality, educational status, and expected family size     

The accuracy of the migration sample in the national population census of 1978

The author assesses the accuracy of migration data collected by sample in the 1978 census of Poland. He discusses the possibility of studying fertility trends using 1988 census data for a one-percent sample of married women aged 15-70.     

Socio-demographic interests of the population during the transition to a market economy

These are the results of a 1971 survey on reproductive behavior in the former Soviet Union. The survey covered 3,152 women aged 16 or over living in rural or urban areas. Questions were included on ideal, desired, and expected number of children. The results indicate that low fertility expectations characterize the majority of the population and that current political and economic problems are likely to push expected fertility even lower. Significant differences between rural and urban populations and among regions are identified.