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.     

Chartering strategies for shipping companies

This paper describes a model which may be used in the evaluation of the relative effectiveness of policies used in the areas of ship chartering and the switching of combined carriers between the dry cargo market and the tanker market. The policies for chartering and market switching are expressed in the form of ‘desired proportions’ of the fleet operating in a particular charter-mode or a particular market. Graphical illustration of this form of expression of policies can be easily understood, so that alternative policies can be designed with relative ease. The effectiveness of a particular form of policy under various freight market conditions can be determined from the model, the use of which is illustrated by its application to the deployment of the fleet of an hypothetical shipping company. It is assumed that the feedback connection between the company's actions and the marketplace is negligible.     

On the Survival of Centenarians and the Span of Life

It has been argued in the literature that the observed mortality crossover among older black Americans relative to the white population is a result of ‘differential early mortality which selects the least robust persons from the disadvantaged population at relatively earlier ages so that, at advanced ages, the disadvantaged population has proportionately more robust persons’ (Kenneth G. Manton). The authors examine the plausibility of the observed black mortality crossover and the heterogeneity argument supporting its existence. In addition to citing evidence from the literature, they use life tables from various countries known to have good mortality data to explore the relation between mortality in childhood and at younger adult ages and mortality in old age for cohorts and periods. Analysis suggests that the association between childhood and old-age mortality for cohorts is positive, implying that observed mortality crossovers are produced by deficient data rather than population heterogeneity.     

Life table construction on the basis of two enumerations of a closed population

The author demonstrates that an accurate detailed life table that represents average mortality experience between two censuses can be constructed if the censuses provide accurate records of the single-year age distribution of a closed population. This life table can begin at age zero if accurate data on the annual number of births during the inter-censal period are available; otherwise the first age in the life table must equal the duration of time between the censuses. "The estimation technique involves the calculation of the number of persons attaining each age during the period between the censuses and the determination of the average rate of increase in the number at each individual age. The success of the technique comes from the use of interpolation to calculate how many in each cohort attain each exact age the cohort passes through between the censuses." The estimation technique is tested using two alternative methods of interpolation. Some illustrations based on data for Sweden and China are included.     

A reassessment of the demography of traditional rural China

An analysis of the composition, characteristics, and vital processes of the population of rural mainland China was undertaken using data collected as part of a study of land utilization carried out by Naking University in 1929-1931. These data have been reappraised using techniques for demographic analysis of faulty data which shows a consistent picture of the Chinese farmer of high morta moderate fertility, and early and universal marriage. Estimates of the singulate mean age at marriage was 17.5 for females and 21.3 for males. Fewer than 1 in 1000 women and 3 in 1000 men never married. The reported parity of older women was only slightly above 5, which disputes the very large historical family size that has been imputed to the chinese. There was a life expectancy of less than 25 years for each sex, and very high infant mortality. These characteristics were of sufficient persistence to have generated a stable age distribution.     

The use of fourier analysis to express the relation between time variations in fertility and the time sequence of births in a closed human population

A fundamental theorem of mathematical demography states that two closed populations sharing the same extended history of net fertility, no matter how variable, have the same age composition. In consequence, when in any population net fertility has long followed a purely repetitive cycle, age composition must also be repetitive with the same cycle length. Under these conditions annual births follow a path that is an exponential multiplied by a periodic time-function. If the time variation of fertility is a small amplitude sinusoidal oscillation, the periodic component of the birth sequence is also sinusoidal. The relative amplitude and timing of fertility oscillations and the consequent birth fluctuations are functions of the duration (or frequency) of the fertility cycle; the nature of the functions is determined by the age structure of net fertility.Any time sequence of fertility variation over an extended period of time can be treated as if part of a repetitious cycle of very long duration. By Fourier analysis the fertility sequence can be expressed as the sum of a series of sinusoidal terms; and finally the sinusoidal components of the resultant birth sequence can be derived. The calculated birth sequence closely approximates the actual.     

Age patterns of mortality for older women: an analysis using the age-specific rate of mortality change with age

"In this paper we propose a mortality measure that seems useful in analyzing age patterns of death rates. The measure, which will be denoted by k(x), indicates the proportional increase or decrease with age in the risk of death at a given age x, and is called the age-specific rate of mortality change with age." Estimations are presented for women in 10 countries. "Eight of the selected sets of data are for developed nations in the 1960s and 1970s, and the other two sets of data, for Taiwan, 1931-35, and for Germany, 1910-11, represent relatively high mortality. For France and West Germany, three different periods are included for an investigation of cohort effects on the observed age patterns." Other mathematical models of age-specific mortality rates are discussed and compared. (SUMMARY IN FRE)     

Revised regional model life tables at very low levels of mortality

This paper presents and discusses new model life tables at very low mortality, which make use of age-specific death rates from the 1960s, 1970s, and 1980s. These life tables fit recorded death rates in very low mortality populations better than do the existing ones at expectations of life of 77.5 and 80 years. The old tables incorporate too-high mortality at the higher ages and in infancy and they incorporate regional differences that no longer exist. The new tables "close out" the mortality schedules above age 80 more realistically. The convergence of age patterns of mortality at very high life expectancies in populations that used to conform to different families is in itself of demographic interest. Some convergence may perhaps be expected. Sullivan (1973) found that, in Taiwan, the comparison of mortality at ages 1-5 to mortality at 5-35 in the late 1950s showed higher mortality at the younger ages relative to the ensuing 30-year age interval than was found in any of the models, including the South model, which has the highest relative mortality from ages 1-5 among the 4 regional patterns. Then, in the late 1960s, the relation of mortality at 1-5 to mortality at 5-35 in Taiwan fell to a position intermediate between the West and South tables. Sullivan found in data on mortality by cause of death a large reduction in mortality from diarrhea and enteritis, no doubt as a result of environmental sanitation. Mortality from these causes is concentrated among young children, and reduction in deaths from these causes would naturally diminish the excess mortality in this age interval. The East pattern, characterized by very high mortality in infancy (but not from 1-5), may be the result of the prevalence of early weaning or avoidance of breast feeding altogether in the populations characterized by this pattern. As health conditions have improved, evidenced by the overall design of mortality, these special factors are diminished or erased. Model life tables at these very low mortality levels have different uses from most applications of model life tables at higher mortality. The use of model tables to estimate accurate schedules of mortality when the basic data are incomplete or inaccurate is less relevant in this range of mortality levels.     

Model fertility schedules: variations in the age structure of childbearing in human populations

The nature of the roots for a set of fertility functions were explored in this study, resulting in tables from creation of a family of model fertility schedules. These model fertility schedules accurately represent the full range of age structures of fertility in large populations; they have close fit to various accurately recorded fertility schedules of very different form. The text for the tables includes discussions of: 1)the basis for the fertility schedules, 2)the age structure of the proportion ever married (G(a) specified by 2 parameters, 3)single parameter specified age structure of marital fertility, 4)the similarity of model schedules of age specific fertility to the age pattern of fertility in actual populations, 5)model fertility schedules' suitability during changing nuptuality. Possible uses of the schedules and their application to different countries (England, Wales, Peru) are also described.