Determining the birth function for an age structured population

This paper deals with an inverse problem in age-structured population dynamics, namely the recovery of the unknown birth function from the additional or overposed data consisting of the total population over a time interval equal to the maximum life span of the species. Conditions on the data are given to guarantee the existence and uniqueness of a solution, and the question of continuous dependence of the birth function on the data is addressed. Some numerical simulations are presented to indicate that one can, in fact, use the methods of the paper to reconstruct the birth function.     

Determining the birth function for an age structured population

This paper deals with an inverse problem in age‐structured population dynamics, namely the recovery of the unknown birth function from the additional or overposed data consisting of the total population over a time interval equal to the maximum life span of the species. Conditions on the data are given to guarantee the existence and uniqueness of a solution, and the question of continuous dependence of the birth function on the data is addressed. Some numerical simulations are presented to indicate that one can in fact use the methods of the paper to reconstruct the birth function.     

Summary indices of the age distribution of a population

In this paper a method for characterizing the age distribution of a population by means of an ‘index word’ is outlined. It is shown that the method can be applied to yield approximations to population forecasts.     

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.     

On age distribution of population,government expenditure and fiscal federalism

In this paper I build a simple model to analyze the consequences that population growth imposes on the relative needs of expenditure of governments in a fiscal federalism setup. I assume, first, that some government expenditure items can be classified according to the age of their recipient individuals and, second, that different levels of government are usually assigned different expenditure programs. The implication is that, for an initially given level of effective public good provision, changes in the size of population as well as in its age structure will influence the composition of public expenditure for different layers of administration in a different manner.I would like to thank Jordi Caballé, Ángel de la Fuente, Javier Gardeazabal, Federico Grafe, Juan Urrutia and Jesús Vázquez for their valuable comments and suggestions. Two anonymous referees helped improve the initial version. Remaining errors and shortcomings are my own responsibility. Financial support from UPV 035.321-HA090/92 and UPV 035.321-HA130/93 is gratefully acknowledged.     

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.     

The age distribution of an industrial group (Scottish Railwaymen)

The age structure of the workers in an old-established industry, and the problems which might arise from it, formed the subject of the investigation. It was found that the group was atypical in that, in addition to having a higher average age than that of the total working population of Scotland, the age distribution was bimodal, with a marked excess in the S o + and a marked deficiency in the 3 5-44 age group. The bimodality was due to high recruitment after the first world war, followed by a low one a few years later. The bimodality was especially marked among footplatemen.

On the basis of age structure it is very difficult to identify grades to which older workers might be transferred. Certain receiving grades which " accommodate " the less healthy (and potentially also the older workers) were found to be relatively small in size compared with the operating grades, footplatemen or signalmen.

Projections were made to explore some of the repercussions of converting the age structure of a bimodal distribution to a standard, the working population of Scotland. There were three assumptions on total size : maintaining the size, a slow fall to 70% and a rapid fall to 70%. Within each of these there were three assumptions on sickness absence, drawn from experience of Scottish railwaymen and particularly footplatemen. These effects are described in the paper. They are not policy recommendations of what should happen ; they are indications of what might happen in certain circumstances. In a bimodal distribution it is easy to effect a reduction in total numbers by a reduction in recruitment, but the consequential longer term fluctuations in numbers are substantial and in sickness absence more so.

Those concerned with problems arising from recruitment, redundancy and age structures of working populations could get useful information by using appropriately realistic assumptions.     

Consumption and population age structure

In this paper, the effects on aggregate consumption of changes in the age distribution of the population are analysed empirically. Economic theories predict that age influences individuals’ saving and consumption behaviour. Despite this, age structure effects are rarely controlled for in empirical consumption functions. Our findings suggest that they should. By analysing Norwegian quarterly time series data, we find that changes in the age distribution of the population have significant and life-cycle-consistent effects on aggregate consumption. Furthermore, controlling for age structure effects stabilises the other parameters of the consumption function and reveals significant real interest rate effects.      

Rethinking population distribution policies

Developed and developing nations are generally dissatisfied with the spatial distributions of their populations. Dissatisfaction is particularly acute on the part of developing nations which view their problems of population distribution as more serious than those of natural increase. The overwhelming majority of governments have already adopted policies to affect rates and patterns of internal migration or the configuration of their rural and urban populations. However, recent reviews of these policies suggest they have been only partially successful. Apparent policy deficiencies are reviewed and possible remedies suggested in regard to the need for intervention, the scope of policies, their objectives, instruments, and evaluation.     

Elementary models for population growth and distribution analysis

A version of the Lotka-Volterra interaction model is adapted to describe population growth and migration processes in a two-region system. The regions are identified as a metropolis and its non-metropolitan hinterland. Several conditions on growth and migration regimes are imposed. The time behavior of the systems are analyzed, noting especially situations where total depopulation or population explosion eventually occur in one or both populations. Neither growth control nor migration control alone results in a condition of long-run stability in both regions. If at least a momentary condition of zero growth is achieved in both regions, it is possible to maintain finite populations if each population follows a logistic natural growth process and migration flow is proportional to the volume of interaction. It is necessary also that the natural increase limitation is strong relative to migration rates. This result holds even if one population has a net migration advantage over the other.     

Symposium on population distribution

The Development and Population Redistribution in South Asia symposium, held in Pakistan during January 1980, was organized around 4 major themes: 1) national, regional and local policies of population redistribution; 2) population redistribution aspects of national development plans; 3) development projects and population redistribution; and 4) settlement of refugees. A principal concern was the ecological impact of programs of resettlement, particularly in the tarai zone of India and Nepal and in the dry zone of Sri Lanka. A 2nd major concern fo the symposium was the spatial pattern of urbanization in each country. The final symposium under the term of office of the present International Geographical Union Population Commission will deal with migration and population redistribution in the Asia and Pacific region.     

Computer display of population age structure

The standard human population pyramid contains only current information; it is often inadequate when making comparisons of different countries or years. A graphic computer program superimposes current population, life table survivor ships, stable population, and past population projected up to the present. Fertility, health conditions, migration, and demographic transition stage are better revealed by this expanded graph form. A time series of the modified pyramids reveals detailed age-specific trends for a country or region. With 'minor modifications the computer program is applicable to all machines with a Fortran IV compiler.     

The impact of taxation on the distribution of wealth in an economy with changing population

The paper investigates into the determinants of the personal distribution of income and wealth. In an overlapping generations model all individuals are assumed to be identical except for their inherited wealth. Since life time is random the bequest of an individual and thus the inherited stock of capital of its children are stochastic variables. Taxation and social security contributions affect life cycle savings, bequests, and, eventually, the distribution of income and wealth in the society. It is shown that, in general, higher tax rates reduce distributive inequality as long as the rate of interest is exogenously given. In steady state, however, where the rate of interest is determined endogenously, increasing taxation and higher social security payments both diminish the capital labor ratio so that the rate of interest rises. If this interest effect is strong enough then it may outbalance the tendency toward more equality because higher interest rates enhance initial differences in the distribution of both income and wealth and, eventually, the inequality in the distribution of income and wealth in the society.     

Residential preferences and population distribution

Public opinion research has revealed decided preferences for living in rural areas and small towns, and proponents of population deconcentration have interpreted this as support for their policies. This study, based on a national sample, yielded similar results, but when we introduced the additional possibility of a preference for proximity to a larger city, then the rural areas preferred were found, for most respondents, to be those within the commuting range of a metropolitan central city. Although persons wishing to live near large cities were found to be looking for the same qualities of living sought by those who prefer a more remote location, these findings are not, in general, consistent with the argument that public preferences support strategies of population dispersal into nonmetropolitan areas. Instead they indicate that most of those who wish to live in a different location favor the peripheral metropolitan ring areas that have, in fact, been growing rapidly by in-migration.     

非洲的人口动态与分布

非洲的人口动态长期以来具有高出生率、高死亡率的特点,20世纪90年代以后,非洲的人口动态由高出生高死亡模式向高出生中死亡模式转变．死亡率的持续下降在很大程度上是由于数种过去危害最严重的急性传染病基本上得到有效控制的结果。正是死亡率的下降和持续的高出生率导致非洲人口迅速增长。在非洲人口增长的过程中．人口分布是极不平衡的。非洲人口分布的变化与经济因素的人口定期迁移是密切相关的,大致可分为三种情况．这种独特的迁移模式均与经济活动和生产方式直接相关。     

On the rational distribution of Chinese population]

In 1949, the population distribution in China was characterized by the following distinct features. First, it was unbalanced, with high density in the eastern regions, in the plains, and in areas adjacent to railroads, river navigation routes and other transportation axes. Low population density was found in the western regions, mountainous regions, and areas far from transportation routes. Second, Hans were largest in number and distributed throughout the country, with major concentration in the eastern regions, while the minorities constituted about 10% of the total population and were distributed mainly in the far southwestern and northwestern areas. Third, over 89% of the 540 million of the population was distributed in rural areas while only about 10% in towns and cities, with high densities in some coastal cities. During the past 3 decades, the unbalanced nature of China's population has remained basically unchanged. This can be attributed to factors relating to natural conditions and resources, productivities, socioeconomic conditions, and technological development in different regions. In order to achieve a rational distribution of the Chinese population the following measures should be taken: 1) controlling the birth rate of the Hans and increasing the population of minorities; 2) moving the population of the dense areas to the border provinces in the western regions to develop their natural resources and to elevate the living standards; 3) modernizing the rural areas; 4) strictly controlling the industrial developments of large cities and their population growth; and 5) strictly restricting the unplanned migration of population to and from cities.     

An evaluation of population projections by age

A number of studies have evaluated the accuracy of projections of the size of the total population, but few have considered the accuracy of projections by age group. For many purposes, however, the relevant variable is the population of a particular age group, rather than the population as a whole. We investigated the precision and bias of a variety of age-group projections at the national and state levels in the United States and for counties in Florida. We also compared the accuracy of state and county projections that were derived from full-blown applications of the cohort-component method with the accuracy of projections that were derived from a simpler, less data-intensive version of the method. We found that age-group error patterns are different for national projections than for subnational projections; that errors are substantially larger for some age groups than for others; that differences in errors among age groups decline as the projection horizon becomes longer; and that differences in methodological complexity have no consistent impact on the precision and bias of age-group projections.     

Optimal age of retirement and population growth

The purpose of this paper is to study intergenerational optimal resources sharing when the social planer can choose the retirement age in addition to consumptions and investment. We use the extension of the Diamond analysis by Hu [1979] that incorporates endogenous retirement age. We found that the optimal retirement age is an increasing function of the population growth rate if the elasticity of substitution of old agents' labor for young agents' labor is lower than one. In the millian case, when the size of a population does not matter, and when the elasticity of substitution of old agents' labor for young agents' labor is strictly higher than one, the optimal retirement age is a decreasing function of the population growth rate. In the benthamite case, the change in the optimal retirement age is indeterminate. Received: 19 February 1999/Accepted: 27 February 2001 All correspondence to Bertrand Crettez. We would like to thank Jean-Pierre Vidal for very helpful comments on an earlier draft. An anonymous referee provided insightful comments on a previous version of this paper. Responsible editor: Alessandro Cigno.