The momentum of mortality change

Mortality change is not usually assigned much importance as a source of population growth when future population trends are discussed. Yet it can make a significant contribution to population momentum. In populations that have experienced mortality change, cohort survivorship will continue varying for some time even if period mortality rates become constant. This continuing change in cohort survivorship can create a significant degree of mortality-induced population change, a process we call the 'momentum of mortality change'. The momentum of mortality change can be estimated by taking the ratio of e0 (the period life expectancy at birth) to CAL (the cross-sectional average length of life) for a given year. In industrialized nations, the momentum of mortality change can attenuate the negative effect on population growth of declining fertility or sustained below-replacement fertility. In India, where population momentum has a value of 1.436, the momentum of mortality change is the greatest contributor to its value.     

Empirical analysis of the contribution of age composition to population growth

The method of decomposition is applied to rates of natural increase in order to elucidate the role played by age composition in the growth of populations. A population’s age distribution and fertility schedule are contrasted to those in a "stationary" population having the same mortality rates and having a fertility schedule equal to that of the observed population divided by its net reproduction rate. In this manner it is shown that about one-quarter to one-third of the growth of most current high-growth populations can be attributed to non-stationarity of their age distributions. This fraction will rise, as it has in most industrialized countries, if fertility is reduced and age distributions become middle-heavy. In projections of the 1963 Venezuelan female population with fertility rates declining by 20/0 and 1% annually, more than half of the growth (in numbers) that occurs prior to zero-growth attainment is contributed by non-stationarity of its intervening age distributions.

     

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.     

The momentum of mortality change

Mortality change is not usually assigned much importance as a source of population growth when future population trends are discussed. Yet it can make a significant contribution to population momentum. In populations that have experienced mortality change, cohort survivorship will continue varying for some time even if period mortality rates become constant. This continuing change in cohort survivorship can create a significant degree of mortality-induced population change, a process we call the ‘momentum of mortality change’. The momentum of mortality change can be estimated by taking the ratio of e ₀ (the period life expectancy at birth) to CAL (the cross-sectional average length of life) for a given year. In industrialized nations, the momentum of mortality change can attenuate the negative effect on population growth of declining fertility or sustained below-replacement fertility. In India, where population momentum has a value of 1.436, the momentum of mortality change is the greatest contributor to its value.     

Crossovers that link populations with the same vital rates

"In this paper, we consider crossovers of demographic density distributions from...populations that have the same fertility and mortality rates. We focus on observed populations and their associated stationary and stable models, and on proportional distributions of persons, births, deaths and reproductive values....Three different populations were selected to represent a range of demographic behavior. Those populations are Japan 1963, a low mortality, low fertility population; Togo 1961, a high mortality, high fertility population; and the United States 1919-1921, a population whose fertility and mortality are intermediate."     

A close look at the demography of Afghanistan

The first survey designed to allow estimates of the demographic characteristics of Afghanistan's sedentary population was conducted during the period 1972-1974. Our analysis of these data, based on recently developed techniques for handling imcomplete or inaccurate data, suggests that this population lives under conditions that are extreme when judged by modern standards. Marriage is early, especially for females, and universal. Marital fertility conforms to a pattern of natural fertility and total fertility is high. The birth rate is among the highest in the world today, and the expectation of life at birth is among the very lowest. Mortality is lower in urban areas than in rural areas, whereas total fertility is approximately the same in both. Our estimates of fertility and mortality imply stable populations which match closely the observed age distributions for both the rural and urban areas.     

Fertility of the american negro in 1830 and 1850

Abstract A comparison of the proportionate age distributions for negroes enumerated in the decennial censuses of the United States in the first half of the rorh century indicates that by 1850, negro fertility apparently had been declining for at least 20 years. This paper develops the relationship of the age distribution of a declining fertility population, where the decline has persisted for less than 25 years, to the stable population with the same current schedules of fertility and mortality. This relationship is used to estimate the negro birth rate and total fertility as of 1850. In turn, these estimates and the relationship of the age distributions of two stable populations with different fertility are used to estimate the negro birth rate and total fertility as of 1830.     

Stable, semi-stable populations and growth potential

Abstract Starting from the definition of a Malthusian population given by Alfred J. Lotka, the author recalls how the concept of stable population is introduced in demography, first as a particular case of stable populations, and secondly as a limit of a demographic evolutionary process in which female age-specific fertility rates and age-specific mortality rates remain constant. Then he defines a new concept: the semi-stable population which is a population with a constant age distribution. He shows that such a population coincides at any point of time with the stable population corresponding to the mortality and the fertility at this point of time. In the remaining part of the paper it is shown how the concept of a stable population can be used for defining a coefficient of inertia which measures the resistance of a population to modification of its course as a consequence of changing fertility and mortality. Some formulae are established to calculate this coefficient first for an arbitrary population, and secondly for a semistable population. In this second case the formula is particularly simple. It appears as a product of three terms: the expectation of life at birth in years, the crude birth rate, and a coefficient depending on the rate of growth and for which a numerical table is easy to establish.     

Estimation of vital rates for Ghana

Abstract A complete and efficient registration system, of the type which would provide good data on births and deaths, does not exist in Ghana. However, registration of vital events is supposed to be compulsory in 39 towns in the country but the data collected in these areas are too inadequate and defective to provide a sound basis for the analysis of the dynamics of population growth. The results of the censuses conducted by the colonial governments are so defective and unreliable that they do not allow scientific research in the field of population analysis. Before 1960, therefore, when the national census and the post-enumeration survey (based on a 5% sample of the population) were carried out, estimates of fertility and mortality levels were little more than guesses. In this study an attempt has been made to utilize the information on the age-sex composition provided by the 1960 census and post-enumeration survey data on births and deaths to determine, as far as possible, the levels of fertility and mortality and the rates of population growth in Ghana. The fertility estimates-i.e. a crude birth rate of 50, total fertility rate of 6.9 and a gross reproduction rate of 3.4-show that Ghana's fertility is one of the highest in the world. An expectation of life at birth of 40 years, an infant mortality of 160 and a crude death rate of 23 appear to be the most plausible estimates. These estimates yield a rate of natural increase of 2.7% and a growth rate of 3.0% per annum.     

The longevity of Jews in Canada, 1940–1942

A life table for the Jewish population of Canada, based upon their mortality experience during 1940–2, yielded an average length of life (expectation of life at birth) of 67–53 years for males and 69·89 years for females. These figures are greater than those for the general population of Canada by 4·58 years for males and 3·60 years for females. These margins decrease with advance in age; the expectations of life for Jews and for the total Canadian population are equal at age 25 in the case of females, and at age 35 in the case of males.

Jewish infants in Canada start life with a mortality rate, in the first year, only two-fifths of that for the general population. This advantage for Jews is observed through childhood, adolescence, and early maturity. However, the margin between the Jewish and total populations decreased with advance in age until, shortly after age 50, the Jews begin to show the higher mortality rates.

The Jewish populations of the United States and of Canada have great similarities in their social and economic structures. They also share, very largely, in their European origins, and they have come to North America during the same period. It is, therefore, a fair assumption that the longevity and mortality characteristics of the relatively small Jewish population of Canada may be indicative of what might be found for the millions of Jews in the United States, for whom such information is not available.     

Akinetic model of population dynamics

The relations between fertility, mortality, growth rate and age distribution in closed populations have been derived by means of a set of differential equations based on the well known theory of chemical kinetics. The classical relations for stable populations are easily obtained in this model by simple algebraic manipulations. A rough but useful further simplification is to divide the population into three groups—pre-reproductive, reproductive, and post-reproductive. For this three-group model simple algebraic expressions connect fertility, mortality, growth rate and the fractions of the population in each group. Although the relations obtained are not precise, they serve to illustrate simply and directly the interactions among the basic population variables.     

The demographic evolution of human populations: The role of selection and environmental factors

Selection (genetic and cultural) and environmental variation are the principal mechanisms determining patterns of demographic change in human populations. Conditions exist under which the nature and intensity of these forces can be inferred from temporal trends in the demographic variables. These conditions, which can be expressed in terms of relations between the Malthusian parameter and population entropy, provide a means for evaluating the effect of selective and nonselective factors on demographic trends in human populations. The distinction between the roles of selection and environmental factors is illustrated by a study of the demographic transition in Sweden (1778-1965). This study shows that demographic changes during the pre- and posttransitional phases are determined mainly by environmental factors, whereas the changes during the transitional phase are mainly due to cultural selection. This analysis provides, for all three phases of the demographic transition, quantitative measures of the intensity of the forces (selective and nonselective) acting on both mortality and fecundity distributions.     

Mortality,marriage, and growth in pre-industrial populations

It has been widely assumed that in pre-industrial European populations postponement of marriage was a major check on fertility, and that marriage was contingent upon access to a livelihood in the form of a homestead or a craft. Death made room for new families, and the age at inheritance might therefore be an index of the age at marriage. High mortality should then mean early marriage and high fertility. When the effect of a uniform increase in the force of mortality on the “natural rate of growth” is estimated quantitatively, it is found that fertility response is of the same magnitude as the change in mortality so that within a wide range mortality differentials alone would not suffice to account for persistent differentials in growth rates. The assumption of a reasonably effective control through the prudential check is thus strengthened.     

Effect of mortality change on stable population parameters

The stable population model is used to establish formulas expressing the effects of mortality change on population growth rates, birth rates, and age composition. The change in the intrinsic growth rate is shown to be quite accurately approximated by the average decline in age-specific death rates between age zero and the mean age at childbearing in the stable population. This change is essentially independent of the initial level of fertility in the population. Changes in birth rates and age composition are shown to be simple functions of the age pattern of cumulative changes in mortality rates relative to an appropriately defined “neutral” standard.     

The relations between male and female nuptiality in a stable population

Both male and female nuptiality conditions can be calculated from any given population. Generally these conditions will be inconsistent in the sense that if applied continuously with given mortality and fertility conditions they would produce different sets of marriages, both in total numbers and in age distribution of bridegrooms and brides. It is shown that, given, say, male nuptiality, female nuptiality conditions consistent in the sense that both male and female conditions could hold in a stable population can be deduced. These consistent conditions depend on the ultimately stable rate of growth of the population. The mathematical formulae for the relations connecting various characteristics of the two consistent sets of nuptiality conditions are worked out (e.g. net probability of marrying, mean ages at marriage, marriage-rates at particular ages, etc.), the magnitudes of the parameters in the relations estimated and the relations are translated into numerical terms, showing the effects of changes in the level of the stable rate of growth on the. consistent nuptiality conditions.     

Populations with constant immigration

"We consider a Leslie-type model of a one-sex (female) population of natives with constant immigration. The fertility and mortality schedule of the natives may be below or above replacement level. Immigrants retain their fertility and mortality, their children adopt the fertility and mortality of the natives. It is shown how this model may be written in a homogeneous form (without additive term) with a Leslie-type matrix. Reproductive values of individuals in each age group are discussed in terms of a left eigenvector of this matrix. The homogeneous form of our projection model permits the transformation into a Markov chain with transient and recurrent states. The Markov chain is the basis for the definition of genealogies, which incorporate immigration. It is shown that genealogies describe the life histories of individuals in a population with immigration. We calculate absorption times of the Markov chain and relate them to genealogies. This extends the theory originally designed for closed populations to populations with immigration." (SUMMARY IN FRE)     

On the momentum of population growth

If age-specific birth rates drop immediately to the level of bare replacement the ultimate stationary number of a population will be given by (9): $$\left( {{\textstyle{{b\mathop e\limits^ \bullet {}_0} \over {r\mu }}}} \right)\left( {\frac{{R_0 - 1}}{{R_0 }}} \right)$$ multiplied by the present number, where b is the birth rate, r the rate of increase, \(\mathop e\limits^ \bullet _0 \) the expectation of life, and R ₀ the Net Reproduction Rate, all before the drop in fertility, and μ the mean age of childbearing afterwards. This expression is derived in the first place for females on the stable assumption; extension to both sexes is provided, and comparison with real populations shows the numerical error to be small where fertility has not yet started to drop. The result (9) tells how the lower limit of the ultimate population depends on parameters of the existing population, and for values typical of underdeveloped countries works out to about 1. 6. If a delay of 15 years occurs before the drop of the birth rate to replacement the population will multiply by over 2. 5 before attaining stationarity. The ultimate population actually reached will be higher insofar as death rates continue to improve. If stability cannot be assumed the ultimate stationary population is provided by the more general expression (7), which is still easier to calculate than a detailed projection.     

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.     

Demographic transition and economic growth: Empirical evidence from Greece

Over the past decades, due to a combination of declining fertility rates and rising life expectancies, most industrialized countries have experienced aging populations and low numbers of young populations that may pose economic problems in the future. This paper investigates the relationship first between fertility rate and infant mortality rate and second among demographic changes, real wages and real output in Greece over the period 1960–96. When we control for fluctuations in overall economic activity and the labor market on the bivariate relationship between fertility and mortality rates, the evidence suggests that Granger-causation must exist in at least one direction. The results show that in the long run a decrease in infant mortality rates, taking into consideration economic performance and the labor market, causes a reduction in fertility rates. Also, employing the vector error-correction models, the variance decomposition analysis and the impulse response functions, the empirical results support the endogeneity of fertility choice to infant mortality, the labor market and the growth process. Received: 16 May 1999/Accepted: 18 September 2000     

Populations with constant immigration

We consider a Leslie‐type model of a one‐sex (female) population of natives with constant immigration. The fertility and mortality schedule of the natives may be below or above replacement level. Immigrants retain their fertility and mortality, their children adopt the fertility and mortality of the natives. It is shown how this model may be written in a homogeneous form (without additive term) with a Leslie‐type matrix. Reproductive values of individuals in each age group are discussed in terms of a left eigenvector of this matrix. The homogeneous form of our projection model permits the transformation into a Markov chain with transient and recurrent states. The Markov chain is the basis for the definition of genealogies, which incorporate immigration. It is shown that genealogies describe the life histories of individuals in a population with immigration. We calculate absorption times of the Markov chain and relate them to genealogies. This extends the theory originally designed for closed populations to populations with immigratioa