A model to estimate births averted due to IUCDs and sterilizations

The computation of births averted due to a specific family planning programme requires special treatment instead of application of the usual population projection technique using conventional fertility rates. The reason for this is that adopters of a family planning method are a selective group from the general population with respect to a number of demographic and biological characteristics, including the initial susceptibility status at the time of adoption. In the present paper a matrix of annual birth probabilities specific to age at adoption of a method and duration since adoption is obtained. One matrix is presented for adopters of IUCD, another for salpingectomy, and a third for vasectomy. These matrices are used to obtain estimates of births averted for India due to IUCDs and sterilizations performed during 1956–69. The results are compared with those that could have been obtained by using the usual age-specific marital fertility rates under identical conditions, except for initial susceptibility. The entire work is programmed on a high speed electronic computer.     

A method for deriving mortality estimates from incomplete vital Statistics

Summary Although they are available in many developing countries vital registration records are very little used for mortality estimation which is still mainly based on census returns. However, defective death records may yield accurate estimations of mortality. This procedure requires few data only; a sex-age distribution of the population (preferably at the middle of a period) and a sexage distribution of deaths, either derived from vital records or from census returns to questions relating to deaths during the preceding twelve months. This method is based on the observation that for a fixed age structure of the population, there is a one-one relation between the age structure of deaths (measured by the proportion of deaths at older ages) and the level of mortality (measured by the death rate above a certain minimum age). It is assumed that at ages above this minimum the rate of underregistration of deaths does not vary significantly with age. Therefore, the age distribution of registered deaths makes it possible to estimate the true proportion of deaths at older ages. This in its turn will permit the estimation of the true level of mortality, because of the relation which exists between age structure of deaths and level of mortality. The true level is then compared with the observed, to estimate the rate of underregistration, and observed age-specific death rates can be adjusted in the light of this knowledge.     

A census-based method for estimating adult mortality

Abstract A simple method is presented for converting an age distribution in any closed population into the stationary population corresponding to its current mortality conditions. The conversion only requires a set of age-specific growth rates, which will normally be available from successive censuses. From the stationary population, any life table mortality measure of interest can be computed. The index most robust to normal data errors in developing countries is life expectancy, and the paper focuses on its calculation. The sensitivity of results to various forms of data error is considered, and procedures are proposed for removing errors resulting from differential census coverage completeness and from age misstatement at older ages. Applications of the procedures are made to data from Sweden, India and South Korea. Because of the absence of a radix, estimation of life expectancy usually will begin at the fifth birthday.     

On the relationship between household composition and population age distribution

Summary Composition of households by age of head and by age of other household members has recently been presented in a convenient algebraic expression, the household composition matrix. It has been shown that this matrix operates as a linear transformation from the vector of household distribution by age of head to the vector of population age distribution. A further analysis will show that the first row of the matrix may be interpreted as representing a vector of average household fertility rates. If the linear relationship between household and population distributions is fully implemented, then a relationship between household fertility and the size of the youngest age group can be derived. If w is the population age distribution and w (1) is the number of persons in the youngest age group, then: where α is the first row of the household composition matrix with its first element eliminated, C is the household composition matrix with its first row and first column eliminated, and Ψ is the vector w with its first element, w (1) eliminated. Extension of this result will enable simultaneous projection of population and households, suitable for computer application to conventional five-year age groups.     

Estimating the completeness of reporting of adult deaths in populations that are approximately stable

An elaboration of Preston's (Preston and Hill, 1980) procedure for determining the completeness with which deaths are recorded in approximately stable populations is presented. Both the procedures of Preston and that of Brass are conventionally limited to mortality beyond early childhood, to mortality above age 5 or age 10. The method considered here is based on characteristics of stable populations, i.e., populations that have been subject for a long time to little variation in age-specific mortality schedules or in overall levels of fertility. The essential features of a stable population are maintained even if fertility has changed. This is the case as long as no strong trend in fertility existed more than 15 or 20 years before the date at which the population is observed. Recent changes in fertility may affect the structure of the population at adult ages, but the effect on estimates of completeness of death records can generally be kept within tolerably narrow limits. Prior to showing how explicit estimates of the relative completeness of recording of numbers of deaths and persons can be derived from counts of deaths and persons by age, it is noted that a life table for a stable population can be constructed directly from the recorded distribution of deaths by age, or from the recorded distribution of persons. The procedures described are applied to several different populations in order to illustrate the computational steps necessary to estimate the completeness of death records at ages above childhood in populations that are approximately stable.     

Validity of centenarian data in the 1960 Census

This paper examines the question of how many genuine centenarians there actually are in the United States as compared with those reported in the census. It is concluded that the numbers of centenarians shown in various United States censuses are definite overstatements of the number of true centenarians. It seems likely that instead of the 10,326 centenarians reported in the 1960 census there were at most only about 3,700. Overstatement of ages seems to be particularly the case among those who claim to be aged 110 or over, and it is believed that there probably are no persons who are actually this old.The analysis has been made by projecting, through the me of population life table survival factors, the populations reported cit carious advanced age groups in one census to the next census and then comparing the results with the corresponding number reported in the latter census for the same age cohort. In general, the enumerated populations at ages below 95 are reasonably close to the projected populations, especially for white persons. On the other hand, at ages 95 and over-especially for centenarians-the enumerated populations significantly exceed the projected ones.As a subsidiary part of the analysis, the paper points out the significant differences at the older ages between the "full count" age distribution in the 1960 census and the corresponding "inflated 25 per cent sample" one. This is a subject that bears further investigation and explanation.The paper also discusses centenarians on the social security benefit rolls and concludes that the present data cannot be considered of substantial accuracy with regard to genuine centenarians, particularly the oldest ones. In a number of years, however, this program will provide excellent data, became the individuals involved will have been on the benefit rolls for many years and will have had their ages proved with reasonable accuracy.     

Construction of nuptiality tables for the single population in India: 1901–1931

In this paper abridged nuptiality tables for the single population of India have been constructed for the three consecutive decades 1901–1911, 1911–1921 and 1921–1931. No significant time trend has been observed in the nuptiality rates among the single population of India. The rates are initially small, but increase rapidly until they reach a maximum at ages 25–30 for bachelors and 15–20 for spinsters, following which they gradually decline. During 1901–1931, unlike Western countries, India had not experienced any revolution in marriage habits encompassing traditional child marriages. The distinctive marks of the Indian age patterns of marriage are higher age-specific marriage rates combined with lower ages at marriage and lower proportions of people who never marry with relative stability of marriage habits during the early part of the twentieth century.     

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.     

Examination of the generalized age distribution

The formula for the age distribution and other relationships that follow from it for any (non-stable) population presented by Preston and Coale are significant contributions to demography. The formulas summarize the relationships among various demographic measures precisely, and are formally analogous to the relationships that hold for stable populations. The significance of these formulas cannot be overstated; they allow us to understand clearly the relationships among demographic measures in any arbitrary population. However, when it comes to using them for estimating demographic measures when census data are defective, the method of estimation is still affected by defective data. The reason is that the series of age-specific growth rates reflects the observed census age distributions exactly so that any defects in the census data are summarized in the growth rates. This paper begins with the formulation of the discrete version of the "new synthesis" developed by Preston and Coale. With the discrete formulation, the three kinds of errors introduced when the continuous time formulas are applied to real data can be avoided. Then it is pointed out that when two accurate census data are available, the Preston-Coale procedure of "estimating" the age distribution at the second census is equivalent to checking the identity of the age distribution formula. Also "estimating" mortality by the procedure of Preston-Coale is shown to be equivalent to obtaining mortality directly from intercensal survival rates. That the procedure which involves the age-specific growth rates is equivalent to those that involve the intercensal survival rates may have escaped notice because there are no a priori constraints for patterns of age-specific growth rates to follow. The irregularity in growth rates due to defective data are not distinguishable from true irregularity that exists in the population, contrary to the well-known regularity in the pattern of survival rates in human populations.     

Estimation of demographic measures for India, 1881-1961, based on census age distributions

Abstract India is one of the very few developing countries which have a relatively long history of population censuses. The first census was taken in 1872, the second in 1881 and since then there has been a census every ten years, the latest in 1971. Yet the registration of births and deaths in India, even at the present time, is too inadequate to be of much help in estimating fertility and mortality conditions in the country. From time to time Indian census actuaries have indirectly constructed life tables by comparing one census age distribution with the preceding one. Official life tables are available for all the decades from 1872-1881 to 1951-1961, except for 1911-1921 and 1931-1941. Kingsley Davis(1) filled in the gap by constructing life tables for the latter two decades. He also estimated the birth and death rates ofIndia for the decades from 1881-1891 to 1931-1941. Estimates of these rates for the following two decades, 1941-1951 and 1951-1961, were made by Indian census actuaries. The birth rates of Davis and the Indian actuaries were obtained basically by the reverse survival method from the age distribution and the computed life table of the population. Coale and Hoover(2), however, estimated the birth and death rates and the life table of the Indian population in 1951 by applying stable population theory. The most recent estimates of the birth rate and death rate for 1963-1964 are based on the results of the National Sample Survey. All these estimates are presented in summary form in Table 1.     

Mortality estimation from registered deaths in less developed countries

Age-specific population growth rates were introduced to demographic analysis in earlier work by Bennett and Horiuchi (1981) and Preston and Coale (1982). In this paper, we derive a method which uses these growth rates to transform what may be a set of incompletely recorded deaths by age into a life table that accurately reflects the true mortality experience of the population under study. The method does not rely on the assumption of stability and, for example, in contrast to intercensal cohort survival techniques, is simple to implement when presented with nontraditional intercensal interval lengths. Thus we can obtain mortality estimates for less developed countries with defective data, despite departures from stability. Further, we assess the sensitivity of the method to violations in various assumptions underlying the procedure: error in estimated growth rates, existence of non-zero net intercensal migration, age dependence in the completeness of death registration, and misreporting of age at death and age in the population. We demonstrate the use of the method in an application to data referring to Argentine females during the period 1960 to 1970.     

New midyear age-sex-color-specific estimates of the U.S. population for the 1940s and 1950s: including a revision of coverage estimates for the 1940 and 1950 censuses

This paper describes new midyear (July 1) estimates of the "true" population of the United States by age, sex, and color (white, nonwhite) for the 1940s and 1950s. It also presents the corresponding implied coverage estimates for the 1940 and 1950 censuses. The new population estimates are calculated by combining the most recent figures on the 1960 population with estimates of the demographic components of change for the 1950s and 1940s in an iterative reverse cohort-component projection algorithm. Among the principal findings of the new estimates are: (a) existing midyear estimates of the "true" population in the 1950s are 450,000 to 500,000 too high; (b) existing age-specific estimates for the 1950s tend to underestimate the population at the older ages (55 years and over) and overestimate the population in the young and middle adult years (15 to 54 years); (c) estimates of the "true" population in the 1940s were too low except for nonwhites at ages 65 and over; (d) existing estimates of percentage net undercount and underenumeration for the 1950 and 1940 censuses tend to be too high, substantially so for nonwhites in the 1940 Census; and (e) nonwhites were more completely enumerated in 1940 than in 1950. Thus, in addition to being methodologically and temporally consistent with post-1960 estimates, the new population estimates described here imply some substantial revisions in demographic, social, and economic statistics for the two decades prior to 1960.     

Determining the initial age distribution for an age structured population

"This paper deals with an inverse problem in age-structured population dynamics; the recovery of an unknown initial age distribution. We attempt to recover this function from overposed data which consists of either the total population over a time interval equal to the maximum life span of the species or the age structure of the population at a fixed later time. Existence, uniqueness and continuous dependence of the initial distribution function on the data are addressed. Some numerical simulations are presented to illustrate the feasibility of recovery using the methods of the paper."     

General growth balance method: A reformulation for populations open to migration

This paper proposes a reformulation of the general growth balance method for estimating census and registration completeness so as to make it applicable even to populations that are affected by migration. It also discusses a new procedure of line fitting that could be useful in countries where the input data are severely affected by age misreporting. The method is applicable to countries where data on age distribution of the population are available for two points in time from either censuses or surveys. Following closely the original proposal of Brass, it involves adjusting the 'partial' birth rates for age-specific disturbances from growth and migration rates. Beyond correcting the death rates, the method is useful in inferring the relative completeness of the censuses, and in deriving a robust estimate of birth rate under certain conditions. The application of the method is illustrated using the example of the male population of the Indian state of Uttar Pradesh for the period 1981 to 1991.     

老龄化背景下基于个人效用最大化的

我国进入老龄化社会后,又以较快的速度即将进入超老龄化社会,社会保障基金的支付压力持续加剧,从而不得不采取有效的应对措施.本文基于个人效用最大化原理,通过考虑工资回报率、劳动者区分因子等变量,建立三状态的最优退休年龄模型.在此基础上,对比脑力劳动者与体力劳动者的不同退休倾向,并依据中国人口平均预期寿命的变化,从各省市的角度对1990年、2000年、2010年的最优退休年龄分布特点进行比较分析.结果表明:脑力劳动者的最优退休年龄应以高于体力劳动者1-2年为宜;北京、上海等经济强省可率先推行延迟退休年龄的政策,贵州、云南等地可较小幅度延迟或滞后延迟.     

General growth balance method: A reformulation for populations open to migration

This paper proposes a reformulation of the general growth balance method for estimating census and registration completeness so as to make it applicable even to populations that are affected by migration. It also discusses a new procedure of line fitting that could be useful in countries where the input data are severely affected by age misreporting. The method is applicable to countries where data on age distribution of the population are available for two points in time from either censuses or surveys. Following closely the original proposal of Brass, it involves adjusting the ‘partial’ birth rates for age-specific disturbances from growth and migration rates. Beyond correcting the death rates, the method is useful in inferring the relative completeness of the censuses, and in deriving a robust estimate of birth rate under certain conditions. The application of the method is illustrated using the example of the male population of the Indian state of Uttar Pradesh for the period 1981 to 1991.     

Surplus Chinese Men: Demographic Determinants of the Sex Ratio at Marriageable Ages in China

We explore the demographic factors contributing to China's unbalanced sex ratio at marriagable ages. We develop a stable population model of the sex ratio at marriagable ages, and compare a series of population projections with alternative underlying assumptions about the key demographic inputs. The stable population model demonstrates that several demographic factors interact to influence the sex ratio at marriagable ages, including the sex ratio at birth, population growth, the age gap of marriage partners, and the sex ratio of survival from birth to marriageable age. The population projections further demonstrate that policies that seek to reduce the sex ratio at birth and the age gap at marriage and, to a lesser extent, increase fertility would be most effective at alleviating the problem. But no demographic changes are likely to occur quickly enough to balance the sex ratio at marriagable ages in the near future.     

Bombay migration study: A pilot analysis of migration to an Asian metropolis

This paper reports on a pilot study of migration to Greater Bombay, initiated on the recommendation of the Population Commission of United Nations, and utilizes both published tables from the 1961 Census of India and a set of specially prepared tables from the same census. Migrants were defined by birthplace and cross-classified by age and duration of residence in Bombay.Data (1901-61) on net migration (obtained from successive age-sex distributions) are analyzed in terms of underlying trends to give historical perspective to the analysis of recent data with special emphasis on changes in industrial and occupotiona structure.For the 1951-61 decade, the extensiveness of out-migration of former in-migrants, its age-sex selectivity, and its high incidence among recent migrants are demonstrated. As is true elsewhere, migration to Bombay is shown to be highly selective for ages of maximum economic activity. Migration streams to Bombay were preponderantly male, and, among males, the married segment predominated. The propensity to migrate was unusually high among minority religious groups. As to educational level, migrants were superior to the general population at origin but inferior to nonmigrants residing in Bombay. The work participation rates of migrants were higher for every age group than for resident nonmigrants; the proportion of employees was higher; and there was evidence of migrant concentration in industries and occupations requiring less skill, less education, and less capital than was true of nonmigrants. There were significant tendencies toward "division of labor" among various migration streams on the basis of skills and abilities acquired not only by formal education but also through tradition and precept. From the standpoint of the promotion of social change, the large volume (and selectivity) of reverse or return migration is especially note-worthy.The paper concludes with a methodological evaluation of the reliability and validity of duration-of-residence data and indicates that the relatively simple techniques of enumeration and tabulation utilized in this pilot study may have wide applicability in other developing countries.     

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.     

Understanding Mortality Rate Deceleration and Heterogeneity

ABSTRACT

Generic relationships between heterogeneity in population frailty and flattening of aggregate population hazard functions at extreme ages are drawn from classical mathematical results on the limiting behavior of Laplace transforms. In particular, it shows that the population hazard function converges to a constant precisely when the distribution of unobserved heterogeneity in initial mortalities behaves asymptotically as a polynomial near zero.