Relations between demographic parameters

The mean life-expectancy e describes the average prospective life-time of an individual aged zero. This parameter can be explicitly described in terms of the survivorship distribution of the population. The Malthusian parameter r represents the asymptotic growth rate of a population. This parameter can be implicitly expressed in terms of the net-maternity distribution. The parameters e and r incompletely incorporate the age-specific fertility and mortality pattern of a population; distinct populations may have the same growth rate but different net-maternity functions; distinct populations may be characterized by the same mean life expectation but may have different survivorship distributions. This article analyzes a class of parameters called the entropy of a population (Demetrius, 1974a) which distinguishes between net-maternity functions with the same growth rate and also mortality distributions with the same mean life expectation. This class of parameters measures the convexity of the fertility and mortality distributions. This paper analyzes the relations between the entropy parameter and the standard demographic parameters.     

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.     

The development and use of demographic models

In this review, we first examine two classical demographic models - conventional life tables and stable populations - and a modern generalization of stable population theory; we then discuss mathematical models of conception and birth. These models involve purely mathematical relations in formal demography as opposed to empirical regularities. Next we consider model age schedules of mortality, nuptialitiy, marital fertility, fertility, and migration that are explicitly based on such empirical patterns. We close this empirical section with a discussion of model stable populations, which are based on model life tables. We next examine the use of demographic models in forecasting future mortality, nuptiality, and fertility and in population projection. Following a discussion of microsimulation models, which gives us the opportunity to mention model age schedules of post partum amenorrhoea and of sterility, we close with observations about the purposes and uses of demographic models.     

Diverging Demography: Hispanic and Non-Hispanic Contributions to U.S. Population Redistribution and Diversity

The substantial growth and geographic dispersion of Hispanics is among the most important demographic trends in recent U.S. demographic history. Our county-level study examines how widespread Hispanic natural increase and net migration has combined with the demographic change among non-Hispanics to produce an increasingly diverse population. This paper uses U.S. Census Bureau data and special tabulations of race/ethnic specific births and deaths from NCHS to highlight the demographic role of Hispanics as an engine of new county population growth and ethnoracial diversity across the U.S. landscape. It highlights key demographic processes—natural increase and net migration—that accounted for 1990–2010 changes in the absolute and relative sizes of the Hispanic and non-Hispanic populations. Hispanics accounted for the majority of all U.S. population growth between 2000 and 2010. Yet, Hispanics represented only 16 % of the U.S. population in 2010. Most previous research has focused on Hispanic immigration; here, we examine how natural increase and net migration among both the Hispanic and non-Hispanic population contribute to the nation’s growing diversity. Indeed, the demographic impact of rapid Hispanic growth has been reinforced by minimal white population growth due to low fertility, fewer women of reproductive age and growing mortality among the aging white population America’s burgeoning Hispanic population has left a large demographic footprint that is magnified by low and declining fertility and increasing mortality among America’s aging non-Hispanic population.     

Bridewealth and Birth Control: Low Fertility in the Indonesian Archipelago, 1500–1900

Before the onset of the present demographic transition, population growth in Indonesia had reached unprecedentedly high levels. This article demonstrates that such high levels were a recent phenomenon. Prior to 1900 rates of natural population increase were low to very low in most areas in Indonesia. This runs counter to expectations based on Hajnal's “Eastern marriage pattern,” which could imply high growth levels in extended family areas, such as most Indonesian regions outside Java in the past. Usually, the low population growth rates in Southeast Asia are attributed to high mortality owing to high levels of violent conflict. It is argued that other factors contributing to such high levels of mortality should receive more attention. In this article it is also argued that low fertility rates, too, played a role in generating low rates of natural increase. The article discusses the influence of marriage patterns, household structure, methods of birth control, adoption, and slavery on fertility.     

China's demographic dilemmas

The year 2000 marks the end of a tumultuous century in China's population history, which weathered the demographic effects of devastating famines, wars, and epidemics and population growth and change. This paper examines the effect of population policies on the demographic dilemmas of China. In the 1950s, China had seen the fastest demographic transition in history, with a dramatic decline in mortality rates, followed by a decrease in fertility rates. However, in the 1970s, revisions in population control measures, changes in age structure, and fluctuations in age at marriage resulted in lower fertility rates. The struggles encountered by China in regulating fertility are described; these include the different methods of birth control, gender preference, marriage, population aging, and minority populations. Population and development issues within the context of urbanization, employment, education, health care, economy, and environment are also discussed. Future implications of these findings indicate the need for a systematic, effective, and complete environmental clean-up, as well as fertility and population policies.     

Estimation of vital rates by means of monte carlo simulation

Monte Carlo simulation has been used to estimate age-specific fertility and mortality rates for a small population,the French-derived isolate of Northside on St. Thomas, U. S. Virgin Islands. Estimates were based on data collected in a household census and genealogical survey and on birth, death, and marriage records for the years 1916to 1966. During this 50-year period (in which the population size increased from 202 to 657), the numbers of births and deaths were too, small to estimate age-specific rates directly, and in addition, death registration was incomplete. Mortality rates were estimated using a simulation program in which mortality was the only stochastic variable. A model mortality schedule was chosen which most accurately reproduced the growth pattern of the population over the 50-year period. To estimate fertility rates, a more complex simulation model was used in which fertility, nuptiality, and mortality were random variables with probability distributions. Preliminary estimates of fertility were made from the birth records and used as input to this simulation program. Birth probabilities were adjusted empirically from one set of simulation runs to the next, until population growth rates, as well as other demographic characteristics, were similar in the real and simulated populations. The birth rates which produced the best fit to the real population data were taken as the estimated age-specific fertility schedule. To reproduce the real population age structure more closely, secular changes in birth probabilities were applied.     

A demographic perspective on the Muslim world

A demographic perspective is relevant to understanding the position of Muslims in today’s world. This paper examines the size and growth of Muslim populations, and whether most Muslims live in overwhelmingly Muslim countries. It also examines indices of poverty and human development for Muslimmajority countries, and the growth of the youth population; finally, it examines the key components of population growth: mortality and fertility. Mortality has declined sharply over the past 15 years in many Muslim countries, though not in all, and Muslim countries are no longer prominent among the ‘outliers’ with higher mortality than expected on the basis of their income levels. Fertility rates are also declining sharply in a number of major Muslim-majority countries, raising interesting issues about attitudes of different schools of Islamic jurisprudence, village-level religious leaders and ordinary Muslims towards contraception and abortion, as well as the role of socio-economic development and family planning programs in fertility declines. Despite these declines, past high fertility in many Muslim-majority countries leaves as a legacy a rapidly growing adolescent population and a burgeoning, inadequately educated labour force.     

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.     

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.

     

The UN Population Division on Replacement Migration

The most salient demographic trend pictured by the influential set of population projections prepared by the Population Division of the United Nations (a unit in the UN's Department of Economic and Social Affairs) is the continuing substantial increase—albeit at a declining rate—of the global population during the coming decades. According to the “medium” variant of the most recent (1998) revision of these projections, between 2000 and 2050 the expected net addition to the size of the world population will be some 2.85 billion, a figure larger than that of the total world population as recently as the mid‐1950s. All of this increase will occur in the countries currently classified as less developed; in fact, as a result of their anticipated persistent below‐replacement levels of fertility, the more developed regions as a whole would experience declining population size beginning about 2020, and would register a net population loss of some 33 million between 2000 and 2050. A report prepared by the UN Population Division and released on 21 March 2000 addresses some of the implications of the changes in population size and age structure that low‐fertility countries will be likely to experience. The 143‐page report, issued under the eyecatching title Replacement Migration: Is It a Solution to Declining and Ageing Populations?, highlights the expected magnitude of these changes by the imaginative device of answering three hypothetical questions. The answer to each of these questions is predicated on the assumption that some specified demographic feature of various country or regional populations would be maintained at the highest level that feature would exhibit, in the absence of international migration, in the United Nations' medium population projections (as revised in 1998) during the period 1995–2050. The selected demographic features are total population size, the size of the working‐age population (15–64 years), and the so‐called potential support ratio: the ratio of the working‐age population to the old‐age population (65 years and older). The illustrative device chosen for accomplishing the specified feats of preserving the selected demographic parameters (i.e., keeping them unchanged up to 2050 once their highest value is attained) is international migration. Hence the term “replacement migration.” Given the low levels of fertility and mortality now prevailing in the more developed world (and specifically in the eight countries and the two overlapping regions for which the numerical answers to the above questions are presented in the report), and given the expected future evolution of fertility and mortality incorporated in the UN population projections, the results are predictably startling. The magnitudes of the requisite compensatory migration streams tend to be huge relative both to current net inmigration flows and to the size of the receiving populations; least so in the case of the migration needed to maintain total population size and most so in the case of migration needed to counterbalance population aging by maintaining the support ratio. Reflecting its relatively high fertility and its past and current record of receiving a large influx of international migrants, the United States is a partial exception to this rule. But even for the US to maintain the support ratio at its highest—year 1995—level of 5.21 would require increasing net inmigration more than tenfold. The country, the report states, would have to receive 593 million immigrants between 1995 and 2050, or a yearly average of 10.8 million. The extreme case is the Republic of Korea, where the exercise calls for maintaining a support ratio of 12.6. To satisfy this requirement, Korea, with a current population of some 47 million, would need 5.1 billion immigrants between 1995 and 2050, or an average of 94 million immigrants per year. (In the calculations, the age and sex distribution of migrants is assumed to be the same as that observed in the past in the main immigration countries. The fertility and mortality of immigrants are assumed to be identical with those of the receiving population.) The “Executive Summary” of the report is reproduced below, with the permission of the United Nations. Chapters of the full report set out the issues that prompted the exercise; provide a selective review of the literature; explain the methodology and the assumptions underlying the calculations; and present the detailed results for the eight countries and two regions selected for illustrative purposes. A brief discussion of the implications of the findings concludes the report. As is evident even from the figures just cited, immigration is shown to be at best a modest potential palliative to whatever problems declining population size and population aging are likely to pose to low‐fertility countries. The calculations, however, vividly illustrate that demographic changes will profoundly affect society and the economy, and will require adjustments that remain inadequately appreciated and assessed. The criteria specified in the UN calculations—maintenance of particular demographic parameters at a peak value—of course do not necessarily have special normative significance. Past demographic changes, with respect notably to the age distribution as well as population size, have been substantial, yet they have been successfully accommodated under circumstances of growing prosperity in many countries. But the past may be an imperfect guide in confronting the evolving dynamics of low‐fertility populations. As the report convincingly states, the new demographic challenges will require comprehensive reassessments of many established economic and social policies and programs.     

On the scale of global demographic convergence, 1950-2000

The second half of the twentieth century saw global demographic change of unprecedented magnitude, with pronounced falls in both mortality and fertility in many developing countries. This article assesses the extent to which these changes have led to the convergence of demographic patterns around the world. It considers not just the levels of fertility and mortality in each country at different points in time, but also the size of each population. It also disaggregates China and India into their constituent provinces and states in order to provide estimates for units more typical of the size of the populations of other countries. The note presents proportions of the world's population according to the levels of life expectancy and total fertility they experienced in the early 1950s, the late 1970s, and around 2000. The graphs and tables thus produced give a convenient and novel way to view the scale and nature of demographic convergence over the last 50 years.     

Mortality and fertility in Arctic Communities Greenland - A case study

Summary The purpose of this paper is to estimate the present level of mortality and fertility as well as its history amongst the indigenous population of Greenland during the period 1834-1953 on the basis of a series of censuses taken during that time. Mortality and fertility parameters have been estimated by techniques particularly suited for the analysis of incomplete demographic data - e.g. stable population analysis. During the period studied Greenland was a Danish colony. It did not become constitutionally part of Denmark until 1953. The paper shows that even though the importance of Danish - and other European - influence should not be underestimated, the socio-economic structure of Greenland was relatively stable until 1953. The results show an extremely high mortality and a correspondingly high fertility. There is also evidence that mortality fluctuated considerably during the period. This might also be true of fertility, but it is impossible to establish this by means of the techniques used. These results are supported by an analysis of registrations of births and deaths for part of the period. The paper concludes with an evaluation of the validity of the techniques of estimation, having regard to the nature of the Greenland censuses. It is pointed out that the empirical material from which model stable populations must have been constructed varies somewhat from that applicable to an Arctic population.     

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.     

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     

A Relational Gompertz Model of Male Fertility: Development and Assessment

Brass has proposed a relational Gompertz model of female fertility which, in combination with the standard fertility distribution developed by Booth, has proved useful in a range of applications, such as indirect estimation, demographic modelling, and population projections. This paper develops a standard distribution of male fertility for use in conjunction with the relational Gompertz model. The derivation of the standard takes advantage of the similarity between the shape of male and female fertility distributions. It entails ‘stretching’ the female standard, so that it extends to age 80, and then transforming it, using the Gompertz model into a pattern which is more typical of male fertility distributions in the developing world. An assessment of this new standard by fitting the relational Gompertz model based on it to a series of male fertility distributions from diverse populations, suggests that it performs very well.     

Age structure,growth, attrition and accession: A new synthesis

This paper shows that each equation describing relationships among demographic parameters in a stable population is a special case of a similar and equally simple equation that applies to any closed population and demonstrates some implications of these new equations for demographic theory and practice. Much of formal demography deals with functions that pertain to individuals passing through life, or to a stationary population in which births of individuals are evenly distributed over time. These functions include life expectancy, probabilities of survival, net and gross reproduction rates, expected years spent in various states and the probability that certain events will occur in the course of life. The stable population model permits the translation of population structure or processes in a more general type of population, with constant growth rates, back into equivalent populations for a stationary population. The method for translation developed in this paper, requiring only a set of age-specific growth rates is even more general, applying to any population. Age specific growth rates may also be useful for performing reverse translations, between a population's life table and its birth rate or its age distribution. Tables of numbers of females by single years of age in Sweden are used to illustrate applications. Tables summarize the basic relations among certain functions in a stationary population, a stable population and any population. Applications of new equations, particularly to demographic estimation of mortality, fertility and migration, from incomplete data, are described. Some other applications include; the 2 sex problem, increment decrement tables, convergence of population to its stable form, and cyclical changes in vital rates. Stable population models will continue to demonstrate long term implications of changes in mortality and fertility. However, in demographic estimation and measurement, new procedures will support most of those based on stable assumptions.     

Was there a neolithic mortality crisis?

The case that mortality rose either with the Neolithic Revolution or subsequent urbanization is made by both medical ecologists and anthropologists. The former point out that only dense farming or urban populations could sustain epidemic disease. Many anthropologists believe that Palaeolithic society either controlled population numbers or experienced low natural fertility, and that both fertility and mortality rose with denser, sedentary populations. Given that the evidence for low hunter-gatherer fertility is unsatisfactory, and that the balance of fertility and mortality was inevitably approximately maintained into the Neolithic period, it is possible that there was no Neolithic mortality crisis. This paper examines how the case was built for near-consensus on such a mortality crisis, and the implications of this case being wrong.     

The fall in household size and the rise of the primary individual in the United States

The long-term fall in household size in the United States is discussed within the framework of the aging of the population, continuing as the effects of fertility and mortality decline accumulate. Using distributions of households by size from U.S. census data 1790–1970 and a components of change analysis on primary individuals for 1950–1974, household changes are related to demographic change for the periods 1790–1900, 1900–1950, and 1950–1974. Fertility and mortality declines have unambiguous impact on household size until the increases in primary individuals begin. But these, too, have a theoretically interesting, if indirect relationship to population structure.