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Demographic aspects of ageing.

The first part of this paper examines future changes in the age structure of the population of England and Wales which are likely to occur as a result of past and future changes in fertility and mortality. These changes in fertility and mortality are examined in some detail. Different methods of projecting future changes in mortality are discussed. On the basis of conservative estimates of these changes, estimates are made of the future economic strain of dependency and there is some discussion of the way in which this might be best handled to the advantage of both the active and the elderly populations. The second part of the paper looks at different ways of examining improvements in longevity and also discusses some of the biological and environmental factors involved. Reference is made to the limited morbidity data available and the tentative conclusion is reached that improvement in longevity, so far, owes less to the reduction of disease incidence than to medical maintenance. This review paper, which relates to England and Wales, is in two main parts: (1) a general discussion of the population factors and changes which have led to a focusing of attention upon the ageing of the population and associated economic problems; and (2) a consideration of the implications of current health advances for individual survival.

Aging↗
PubMed1988

A semigroup approach to the strong ergodic theorem of the multistate stable population process.

"In this paper we first formulate the dynamics of multistate stable population processes as a partial differential equation. Next, we rewrite this equation as an abstract differential equation in a Banach space, and solve it by using the theory of strongly continuous semigroups of bounded linear operators. Subsequently, we investigate the asymptotic behavior of this semigroup to show the strong ergodic theorem which states that there exists a stable distribution independent of the initial distribution. Finally, we introduce the dual problem in order to obtain a logical definition for the reproductive value and we discuss its applications." (SUMMARY IN FRE)

Demography↗
PubMed1988

The effect of variability in the fertility schedule on numbers of kin.

"The kinship formulas developed by Goodman, Keyfitz, and Pullum (1974) are extended to encompass populations in which fertility varies among women. An expression is derived to determine the amount by which the number of sisters in a heterogeneous population exceeds that in a population with homogeneous fertility. This expression, which is a function of the variance in the gross reproduction rate of the population, can readily be applied to numbers of other kin, such as aunts and cousins. Several trial calculations indicate that calculations of average numbers of sisters based on an assumption of uniform fertility could result in a underestimate of about 13 percent." (SUMMARY IN FRE)

Demography↗
PubMed1988

Stable growth in native-dependent multistate population dynamics.

"Users of multistate life tables and projections have recognized that the Markovian assumptions underlying such models are unduly restrictive and should be relaxed whenever data permit. Efforts to include the influences of previous occupancies have included the incorporation of place-of-birth dependence. This paper addresses the stable growth properties of such generalized multistate models. It shows how place-of-birth-specific stable growth measures can be calculated without projection simply by solving the characteristic equation. An example using Canadian data illustrates the argument." (SUMMARY IN FRE)

Americas↗
PubMed1988

Comparison of microcomputer programs for making population projections: an update.

"There are many programs for making population projections now available for use with microcomputers. This article reviews six of approximately 15 microcomputer population projection programs. Each program is compared to a standard set of criteria relating to such items as hardware and software requirements, input data requirements and specification of assumptions, methodology and documentation, and summary output indicators. Numerical results from projections of six test data sets reflecting different assumptions about mortality, fertility, and migration are compared. Qualitative comments are included for describing special features and for making an overall assessment of each program." (SUMMARY IN FRE)

Computers↗
PubMed1988

Asymptotic properties of the inhomogeneous Lotka-Von Foerster system.

"In this paper, we investigate an extension of the multistate stable population model, which makes allowances for migration. The model is formulated as an inhomogeneous system of first order partial differential equations with integral boundary conditions. First, we construct its classical solution. Next, we reformulate the system as an abstract inhomogeneous Cauchy problem on a Banach space, and give its mild solution by using the population semigroup. Our main purpose is to investigate the asymptotic behavior of the mild solution." (SUMMARY IN FRE)

Demography↗
PubMed1989

Leslie matrix models.

A review of the Leslie matrix model theory and its literature 1941-1987 is presented. The point of view is that of a mathematician who focuses on the parts of the theory which are relevant to demography. Works of a decidedly applied nature are not dealt with.

Age Factors↗
PubMed1990

Capital accumulation, aspiration adjustment, and population growth: limit cycles in an Easterlin-type model.

"One of the recent interesting hypotheses of population growth is due to Easterlin who suggests the possibility of self-generating fluctuations in birth numbers. The present paper tries to answer the question whether feedback mechanisms produce persistent oscillations in population growth. A system of two nonlinear differential equations for the per capita capital stock and the aspiration level is studied by a phase portrait analysis. Using the Poincare-Bendixson theorem we derive sufficient conditions for the existence of a stable limit cycle." (SUMMARY IN FRE)

Demography↗
PubMed1990

The profile of intercohort increase.

"The paper develops a technique for identifying the cohorts that initiated what in the 1950s was designated the population explosion. A numerical example is given for Indonesia, but essentially the same picture appears for many other countries, and for the aggregate of the world. The intercohort increase can be estimated for each age using two successive censuses; the method here developed gives very nearly the same increase whatever age is used for the estimate." (SUMMARY IN FRE)

Asia↗
PubMed1990

The exponential multidimensional demographic projection model.

"This paper presents the multidimensional demographic projection on the basis of an exponential specification, which avoids the problems associated with the widely used specification on the basis of the linear integration hypothesis. It generalizes earlier work by Gill (1986) on Markov models for closed populations to include the case of open populations. A numerical illustration is also provided." (SUMMARY IN FRE)

Forecasting↗
PubMed1990

Statistical modeling of selected aspects of the childbearing process with application to World Fertility Survey countries.

"A mathematical model for estimation of certain aspects of the childbearing process, which requires only data on age-specific fertility rates, is developed. Synthetic maternal childbearing indices, namely, mean ages at first and last birth, length of reproductive life span, inter-birth spacing, and proportion of childless women, in addition to the well-known mean age at childbearing, for the WFS [World Fertility Surveys conducted in developing] countries are obtained using the proposed model. The indices are free from age truncation effects, and, under certain assumptions, provide information about a cohort's completed fertility before the women stop reproducing. The effects of women's residence and education on fertility are also examined." (SUMMARY IN FRE)

Age Factors↗
PubMed1990

Effects of targets and aggregation on the propagation of error in mortality forecasts.

"Official forecasts of mortality depend on assumptions about target values for the future rates of decline in mortality rates. Smooth functions connect the jump-off (base-year) mortality to the level implied by the targets. Three alternative sets of targets are assumed, leading to high, middle, and low forecasts. We show that this process can be closely modeled using simple linear statistical models. These explicit models allow us to analyze the error structure of the forecasts. We show that the current assumption of perfect correlation between errors in different ages, at different forecast years, and for different causes of death, is erroneous. An alternative correlation structure is suggested, and we show how its parameters can be estimated from the past data. The effect of the level of aggregation on the accuracy of mortality forecasts is considered." The geographical focus is on the United States. (SUMMARY IN FRE)

Age Factors↗
PubMed1990

Buffon's needle and the estimation of migration distances.

"A procedure is suggested for estimating migration distances from data on the proportion of migrants crossing regional boundaries. The method makes use of Buffon's needle, a problem in geometrical probability from the eighteenth century.... The procedure is described for various scenarios that differ in their assumptions about region shape, the spatial distribution of population, and the distribution of migration distances. An application to migration distances in the United States is given, and additional attention is given to the estimation of intraregional migration distances." (SUMMARY IN FRE)

Americas↗
PubMed1990

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)

Adult↗
PubMed1990

Mathematical investigations of the escape from the Malthusian trap.

"We present a simulation model that synthesizes Malthusian and Boserupian notions of the way population growth and economic development were intertwined. The non-linear stochastic model consists of a system of equations whose dynamics culminate in an industrial revolution after hundreds of iterations. The Industrial Revolution [in Europe] can thus be conceptualized as a permanent 'escape' from the Malthusian trap that occurs once the economy is capable of permanently sustaining an ever growing population. We investigate the conditions for such an escape and their sensitivity to the parameters of the model.... Our results show that the likelihood of an escape is sensitive to the savings rate and to the output elasticities of the two sectors of the economy. When not in a subsistence crisis, the chances that an escape will occur increase for larger values of the ratio of the savings rate to the growth rate of the population. The chances of an escape also increase substantially for larger values of the output elasticities of labor." (SUMMARY IN FRE)

Demography↗
PubMed1991

Effect of aggregation on the estimation of trend in mortality.

"There are three approaches to analyzing and forecasting age-specific mortality: (1) analyze age-specific data directly, (2) analyze each cause-specific mortality series separately and add the results, (3) analyze cause-specific mortality series jointly and add the results. We show that if linear models are used for cause-specific mortality, then the three approaches often give close results even when cause-specific series are correlated. This result holds for cross-correlations arising from random misclassification of deaths by cause, and also for certain patterns of systematic misclassification.... The results are illustrated with U.S. age-specific mortality: (1) analyse age-specific mortality data from 1968-1985. In some cases the aggregate forecasts appear to be the more credible ones." This is a revised version of a paper originally presented at the 1990 Annual Meeting of the Population Association of America (see Population Index, Vol. 56, No. 3, Fall 1990, p. 407).

Americas↗
PubMed1991

From birth expectations to birth forecasts: a partial-adjustment approach.

"As women's expectations about their own future fertility tend to deviate systematically from realizations, these expectations cannot be used directly for forecasting purposes. This paper discusses a partial-adjustment approach for deriving forecasts from the expectations. The sensitivity of the results to various assumptions is examined. Empirical results obtained for the Netherlands seem promising."

Birth Rate↗