A method for calculating rates of induced abortion

Accurate measurement of induced abortion is necessary for understanding the fertility dynamics of a population and for making projections about the future. Changes in abortion rates can amplify or dampen the impact of changes in contraception. This paper presents a methodology for calculating marital induced abortion rates from observed marital fertility and contraceptive prevalence and for modeling the impact of substituting contraception for abortion on future fertility. The methodology is validated against observed abortion complications in three populations, and the impact of substituting contraception for abortion on expected fertility is demonstrated.     

A Simple method for estimating age-specific rates from sequential cross sections

I develop and demonstrate a simple formula for estimating age-specific event rates for a period from "before" and "after" cross sections. The general approach applies to a wide range of estimation problems in demography, the social sciences, and epidemiology. The method arises from the formal mathematics of unstable populations and is similar in spirit to "variable-r" methods. Unlike those methods, however, the new technique does not require specialized computer programming or iterative calculations, and event rates can be calculated directly from cross-sectional data in simple spreadsheets. The article includes a formal mathematical exposition of the method, simulation tests, and several examples.     

Point and interval forecasts of age-specific fertility rates: a comparison of functional principal component methods

Accurate forecasts of age-specific fertility rates are critical for government policy, planning and decision making. With the availability of the Human Fertility Database (2011), the paper compares the empirical accuracy of the point and interval forecasts, obtained by the approach of Hyndman and Ullah (Comput Stat Data Anal 51(10), 4942?C4956, 2007) and its variants for forecasting age-specific fertility rates. The analyses are carried out using the age-specific fertility data of 15 mostly developed countries. Based on the one-step-ahead to 20-step-ahead forecast error measures, the weighted Hyndman-Ullah method provides the most accurate point and interval forecasts for forecasting age-specific fertility rates, among all the methods we investigated.     

Forecasting Australian subnational age-specific mortality rates

Journal of Population Research - When modeling sub-national mortality rates, it is important to incorporate any possible correlation among sub-populations to improve forecast accuracy. Moreover,...     

Cohort size and age-specific suicide rates: A contingent relationship

Trends in age-specific suicide rates relate to debates about the consequences of population aging and changes in cohort size for social well-being. Easterlin argues that large cohort size increases suicide rates by reducing relative income; Preston claims that suicide rates fall in large cohorts with high levels of political and social power. To integrate these competing arguments, this paper uses aggregate data on 18 high-income nations from 1953 to 1986 to demonstrate that the direction and strength of the relationship between cohort size and suicide depend on (1) age of the cohort, (2) gender, (3) national context, and (4) time period. The results show that large cohort size raises suicide for the young and middle-aged, but reduces it for the elderly. Also, the effects of cohort size prove stronger for men than for women, for nations with less collectivist institutions than for nations with more collectivist institutions, and for the 1950s and 1960s than for the 1970s and 1980s.     

[Classification of age-specific fertility and regional differences].]

Differentials in age-specific fertility in China according to economic conditions, culture, and geographic regions are examined using 1982 census data.     

Intermediate fertility variables and marital fertility rates

Summary Using relatively simple mathematical techniques, an analysis is made of a comprehensive reproductive model that describes the relationships between a set of intermediate fertility variables and the marital fertility rate. Two types of intermediate fertility variables are distinguished: (1) biological parameters and (2) control variables. A homogeneous model is outlined first. Next, this version is extended to include heterogeneity with respect to fecundability and coital rates. Tests of the model with data from two historical populations (i.e. Crulai, 1674-1742, and Tourouvre au Perche, 1665-1765) demonstrate that the model is, indeed, consistent with observed reproductive behaviour in actual populations.     

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.     

A sensitivity analysis of the bongaarts-feeney method for adjusting bias in observed period total fertility rates

Our sensitivity analysis shows that the adjusted TFR'(t) using the formula of Bongaarts and Feeney (1998), which assumes an invariant shape for the fertility schedule, usually does not differ significantly from an adjusted TFR"(t) that allows the shape of the fertility schedule to change at a constant annual rate. Because annual changes in the shape of the fertility schedules often are approximately constant except in abnormal conditions, the Bongaarts-Feeney (B-F) method is generally robust for producing reasonable estimates of the adjusted TFR'(t). The adjusted TFR'(t) neither represents any real cohort experiences from the past nor forecasts any future trend. It merely provides an improved reading of the period fertility measure, which reduces the tempo distortion.     

A comment on total fertility]

Total fertility rate (TFR) cannot be interpreted as the average number of children a couple will have, as the TFR is influenced by a number of factors. The most important factor is the fertility rate of each individual age group. A decline in these rates brings about a decline in the TFR, but other elements also play a part. Another important factor is the age at which women are getting married. The natural childbearing years run for 35 years, from age 15 through 49, but if women are not permitted to marry before age 23, this period will be reduced to 27 years, which would in turn lower the TFR. The number of children each couple is permitted to bear also has an influence on the TFR; the lower the number of children permitted, the lower the TFR. Another factor which affects the TFR is the number of women who, by law, cannot bear any more children. On a long-term basis, it does not appear that the TFR will drop to 1 by the end of this century; it will fall somewhere between 1 and 2. If it is maintained below 1.5-1.6 after 1985, and continues to gradually decline, China's population will be approximately 12 billion at the end of the 20th/Century, and the aging of the population will not become a serious problem.     

The method of measuring probability of the annual fertility]

At the present time, under the guidance of national planning, population control is the most important theme of China's population policy. In order to realize the national goal of controlling population growth, family planning should be worked out at local levels. How to achieve a reasonable population planning norm at a local level is a very crucial problem in family planning work. Up to the present time, various methods have been used to measure the probability of the annual fertility. In his report, the author provides a new formula to calculate the probability of the annual fertility. Based upon this formula, we may calculate the number of planned birth for a certain year and its fertility. From the figure we may set a reasonable goal according to population policy and actual population components. This formula is suitable for use in annual planning, as well as short-term or long-term population planning.     

Variety expansion and fertility rates

To investigate how fertility rates interrelate with the modern economy, we construct a simple model in which variety expansion of consumption goods reduces fertility rates. In our model, variety expansion reduces the relative price of a composite of differentiated goods compared to child-rearing costs. Thus, parents raise the expenditure share for differentiated goods and lower the number of children. We show that this model can be applied to a growth model in which economic growth progresses with variety expansion of consumption goods and fertility rates decrease with economic growth. Thus, we show a new mechanism for fertility decline, and this mechanism can be applied to a growth model.     

The Pattern of Age-Specific fertility rates

A study of the pattern of age-specific fertility rates by five-year age-groups has revealed the possibility of using the Pearsonian type I curve as a graduating equation. Such distinctions have been examined for fifty countries having high, medium, and low fertility rates. Results have been found to be quite satisfactory, even when, for purposes of simplicity, the parameters have been restricted to depend on the first two moments, instead of the first four. The number of independent parameters has thus been reduced to only three, and method shave been suggested for their estimates, using ancillary information which is usually provided in the census reports. The findings seem to be particularly useful for countries lacking effective registration systems of vital events such as births related, as they are, to the age of the mother.In short, the determination of a series of age-specific fertility rates depends primarily on the modal fertile age (a1) and on one of the two exponents (m, or m2) of the type I distribution. It has been shown that the proportions of women married in the age groups 20-24 years and 25-29 years can be used for approximate evaluations of both of these parameters. While estimates of a, and m, are sufficient to generate a relative distribution of age-specific fertility rates, actual values can be obtained if, in addition, the annual number of births is either known or can be estimated from census age distributions of children.Modal distributions of relative values of age-specific fertility rates (such that the sum of these rates adds up to 100.0) have also been obtained for different combinations of al and m1, but are not shown here for lack of space. Once the estimates of al and m, have been made, the modal tables can always be referred to for the corresponding distributions of age-specific fertility rates.     

A socio-psychological analysis of attitudes toward fertility]

This is an introduction to the study of attitudes toward fertility and the psychosocial factors that influence them. Both individual and group attitudes are included. The author also examines how such attitudes change over time.     

A method for comparative analysis of fertility dynamics represented by sequences of fertility schedules

A method to compare fertility sequences, each of which represents a cyclical fluctuation around an underlying trend, is presented. Each fertility sequence is viewed as composed of a time trend in childspacing pattern and a corresponding trend in terminal fertility rate. The procedure involved in comparing each component of one fertility sequence with the corresponding component of another is described and illustrated. Using hypothetical data it is shown, among other things, that ifA andB are two cyclical fluctuations in fertility such that (i) the cycles in both are of the same length, (ii) the terminal fertility components of the two are identical, and (iii) the trend in the mean age at childbirth associated withA is higher than the corresponding trend associated withB, then, replacingB withA need not necessarily result in lowering the long-run rates of increase in the birth sequence.     

The geometric mean of the age-specific death rates as a summary index of mortality

Even though a single summary index of mortality can never replace the set of age-specific death rates, it has been found to be extremely useful for a wide variety of purposes. Such indexes are generally one of two types: aggregative indexes, such as directly standardized rates which reflect absolute differences between corresponding age-specific mortality rates; and average of relatives indexes which reflect proportional differences between those rates. The choice of index depends upon the purposes for which it is to be used, and is important as different indexes can produce very different results. While directly standardized rates are widely used, they depend upon the selection of an appropriate standard population and give disproportionately heavy weight to the high ages. Average of relatives indexes give equal weight to all ages, but are infrequently used as no index of that type has gained wide acceptability. This paper recommends the use of the geometric mean of the age-specific mortality rates as such an index, and shows that this index is readily calculable, unbiased, needs no standard population, is directly comparable to all other indexes so calculated, and accurately reflects exponential mortality patterns.     

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.     

A review of the studies on fertility transition in China]

This article is a summary of papers and analysis in recent years on fertility transition and the association between fertility decline and socioeconomic development in China. These papers discuss the causes of fertility decline and the role of family planning programs in demographic transition. The major points are: 1. The demographic transition in China has the same characteristics as in the countries that have completed the transition. The transition had already started in the more developed areas or completed in a few large cities before family planning programs were implemented. 2. The role of family planning programs is to lead and to accelerate the demographic transition, which is the key idea of the "induced fertility transition". 3. The socioeconomic development and family planning programs worked together to affect the fertility decline, however socioeconomic development is the fundamental factor. Without the existence of the socioeconomic development, which included the changes in the function of family, traditional ideas on fertility, increased level of education, the status of women and social security system; the family planning program is not likely to make an impact.