Population momentum for gradual demographic transitions

Population momentum is the ratio of a population's ultimate size after a demographic transition to its initial size before the transition. For an instantaneous drop to replacement fertility, Nathan Keyfitz found a simple expression M K for the momentum. However, as Keyfitz pointed out, `no one thinks that any country will drop immediately to stationary reproduction patterns'. We present results concerning the momentum of a population whose demographic transition is completed within a finite time. First, we provide an exact analytical formula for such a population's momentum. Second, for rapid fertility transitions, we obtain a simple exact expression for momentum that reduces to Keyfitz's M K if the transition is instantaneous. We show, by example, that our simpler formulae are accurate approximations to population momentum for transitions that take as long as 100 years. Finally, we show that the speed of fertility decline makes a substantial difference to population momentum.     

Family Benefits and Fertility: An Econometric Analysis

A population's growth potential is significantly underestimated by conventional calculations of population momentum which assume an immediate drop to replacement level fertility. Here we assume that the growth rate of births linearly declines to zero over a specified time interval, and find simple and intuitively meaningful expressions for the size of the ultimate birth cohort and the resultant population momentum. In particular, we find that the increase in the number of births over the transition is equal to growth at the initial rate for half the time needed to attain a constant birth level. Thus our formula readily calculates the growth potential of a population under a gradual approach to stationarity without the need for a numerical projection. Calculations for actual and hypothetical populations are presented to show the demographic impact of such gradual approaches to zero growth.     

Modeling momentum in gradual demographic

The analysis of population momentum following a gradual decline in fertility to replacement level provides valuable insights into prospects for future population growth. Here, we extend recent work in the area by applying a new form of the quadratic hyperstable (QH) model, which relates exponentially changing fertility to the resultant exponentiated quadratic birth sequence. Modeling gradual transitions from an initial stable population to an ultimate stationary population indicates that such declines in fertility increase momentum by a product of two factors. The first factor is a previously noted continuation of stable growth for half the period of decline. The second is a not previously appreciated offsetting factor that reflects the interaction between the decline in fertility, the changing age pattern of fertility, and the changing age composition of the population. Numerical examples using both hypothetical and actual populations demonstrate that for declines of any length, the product of the two factors yields momentum values that closely agree with the results of population projections. The QH model can examine monotonic transitions between any two sets of constant vital rates. As a generalization of the fixed-rate stable model, it has great potential value in numerous areas of demographic analysis.     

Population momentum across the demographic transition

Population momentum is the main driver of global population growth today, and this makes an appreciation of momentum critical to understanding contemporary worldwide growth dynamics. This article traces population momentum along with two recently defined measures of momentum decomposed—stable and nonstable momentum—across the demographic transition. We use historical data and population projections from 16 countries to illustrate some previously ignored empirical regularities of the demographic transition in both the developed and the developing world. We also demonstrate the dynamic nature of stable and nonstable momentum, as changes in stable momentum lead to predictable changes in current and future nonstable momentum. These results suggest that momentum, which by definition is measured at a point in time, can also be considered as a process that unfolds over time.     

Population momentum for gradual demographic transitions: an alternative approach

In this article, I derive a simple formula for approximating the ultimate size of a population that undergoes a gradual transition to replacement fertility. I model the fertility transition by specifying a linear frontier on the Lexis surface across which a change in fertility is instantaneous. Gradual transitions result from variations in the slope of this frontier. This framework can be used to reproduce and understand previous studies of population momentum and gradual transitions.     

Completing the Demographic Transition

Despite ongoing declines in fertility in many countries, the population of the world is experiencing a period of rapid expansion, and its size is expected to reach 10 billion by the end of the demographic transition. Three causes of this growth are identified and quantified: 1) fertility above the replacement level of two surviving children per woman, 2) continuing declines in mortality, and 3) population momentum resulting from a young age structure. A set of simple analytic expressions is proposed for estimating these factors from standard demographic indicators. Population momentum is shown to be the main cause of future growth in most countries and regions.     

Stages of the Demographic Transition from a Child's Perspective: Family Size,Cohort Size,and Children's Resources

This article provides a new characterization of stages of the demographic transition from the perspective of children competing for resources within families and cohorts. In Stage 1 falling mortality increases the size of both families and birth cohorts. In Stage 2 falling fertility overtakes falling mortality to reduce family size, but population momentum causes continued growth in cohort size. In Stage 3 falling fertility overtakes population momentum to produce declining cohort size. We apply our framework to census microdata for eight countries and to United Nations population projections for a larger set of countries. The results suggest that most countries spend two to three decades in Stage 2, with declining family size offset by increasing cohort size. From the perspective of children aged 9–11, many countries enter Stage 3 between 2000 and 2010. Other countries, especially in Africa, will continue to experience increasing cohort size for several more decades.     

Population momentum expresses population aging

Population momentum and population aging occur when an initially growing population experiences a reduction in fertility to replacement level. Conceptually and empirically, momentum and aging express the same change, albeit on different scales. Fundamentally, they are two manifestations of the underlying process of demographic transformation. We consider three measures of aging over the transition to stationarity: the increase in mean population age, the decrease in the proportion under age 30, and the increase in the proportion over age 65. The three measures of aging are highly correlated, though the relationship to momentum is weakest for the increase in the proportion over age 65. We find that momentum is linearly related to aging. In both model and actual populations, a one-year increase in mean age translates into about 4.5% more population growth. The population below age 30 does not grow over the transition to stationarity, and the ratio of initial to ultimate proportions under age 30 is virtually identical to momentum.     

On the distribution of completed parities when fertility is heritable

"Over the last one hundred years, there has been, in many developed countries, a demographic convergence towards the two child family. The possible implications for population growth of such a tendency are considered in this paper in terms of both family limitation and also the intergenerational transmission of fertility. These two effects interact so that as the proportion of two-child families increases, the possible influence of mother-daughter fertility associations on population growth decreases, though even now it could override otherwise significant changes in either or both of the birth and death intensities. In particular, it is shown that according...to how fertility is transmitted through generations, it is still possible to have zero growth rates consistently with a widely dispersed stable distribution of family size as well as a typical mortality regime." (SUMMARY IN FRE)     

On the distribution of completed parities when fertility is heritable

Over the last one hundred years, there has been, in many developed countries, a demographic convergence towards the two child family. The possible implications for population growth of such a tendency are considered in this paper in terms of both family limitation and also the intergenerational transmission of fertility. These two effects interact so that as the proportion of two‐child families increases, the possible influence of mother‐daughter fertility associations on population growth decreases, though even now it could override otherwise significant changes in either or both of the birth and death intensities. In particular, it is shown that according as to how fertility is transmitted through generations, it is still possible to have zero growth rates consistently with a widely dispersed stable distribution of family size as well as a typical mortality regime.     

Relative cohort size: source of a unifying theory of global fertility transition

Using United Nations estimates of age structure and vital rates for 184 countries at five‐year intervals from 1950 through 1995, this article demonstrates how changes in relative cohort size appear to have affected patterns of fertility across countries since 1950—not just in developed countries, but perhaps even more importantly in developing countries as they pass through the demographic transition. The increase in relative cohort size (defined as the proportion of males aged 15–24 relative to males aged 25–59), which occurs as a result of declining mortality rates among infants, children, and young adults during the demographic transition, appears to act as the mechanism that determines when the fertility portion of the transition begins. As hypothesized by Richard Easterlin, the increasing proportion of young adults generates a downward pressure on young men's relative wages (or on the size of landhold‐ings passed on from parent to child), which in turn causes young adults to accept a tradeoff between family size and material wellbeing, setting in motion a “cascade” or “snowball” effect in which total fertility rates tumble as social norms regarding acceptable family sizes begin to change.     

Options for Fertility Policy Transition in China

This article compares five currently debated scenarios for fertility policy transition in China, in terms of their implications for future population growth and population aging, the proportions of elderly living alone, labor force trends, pension deficits, economic costs, the marriage squeeze, and other socioeconomic outcomes. Based on these comparative analyses, the author concludes that China needs to begin a gradual modification of its fertility policy as soon as possible. He proposes a three‐stage “soft‐landing” strategy for fertility policy transition: (1) a 7‐year initial smooth transition period; (2) from approximately 2014‐15 to 2032‐35 a universal two‐child policy combined with late childbearing in both rural and urban areas; (3) after 2032‐35 all Chinese citizens would be free to choose family size and fertility timing. This strategy will enable China to have much more favorable demographic conditions and socioeconomic outcomes, as compared to keeping the current policy unchanged.     

Population pressure and fertility in pre-transition Thailand

Before the demographic transition in Thailand, fertility was high, but not uniformly so. As in other pre-transition settings, Thai fertility responded to pressures and opportunities created by socioeconomic structure and land availability. Drawing upon provincial data from the 1947 and 1960 censuses of Thailand, we find a strong 'frontier effect' on Thai fertility in the 1950s. Fertility was higher in sparsely settled frontier provinces and lower in provinces with higher population density relative to cultivatable land. This finding is robust and holds up with controls for agricultural employment, land quality, and the sex ratio (an indicator of sex-selective migration). The effect of population pressure lowers the likelihood of marriage and of marital fertility. The findings from Thailand are consistent with the research of Easterlin on the nineteenth century United States and with other pre-transition societies. We suggest how demographic transition theory might be broadened to include fertility dynamics in pre-transition societies.     

曲折、艰难、辉煌的中国生育转变

从1979～2009年30年人口变动的历程来看,中国人口转变是成功的,其结果是辉煌的,但其转变的历程,尤其是生育转变的历程是曲折和艰难的,历史留给人们的经验和教训是深刻的。本文将近30年来的生育转变历程为四个阶段,从而突显了不同阶段生育水平的变化,以及生育水平与社会经济变革、生育行为以及生育政策博弈的结果。1979～1984年生育水平反弹波动,反映出严格的生育政策遇到强大阻力,结果是欲速而不达。1985～1991年生育高峰如期而至,显示了人口内在规律的强大威力,从而最大限度地调动了人口控制的力量。1992～1999生育率再次下降,并穿透替代水平生育率,宣告人口转变基本完成。2000～2009低生育水平持续稳定,人口结构性问题逐步显现,统筹解决人口问题势在必行。     

Fertility Transition in China:A Zigzag and Splendid Course

Examining China’s population changes in the past three decades demonstrates that China’s demographic transition has been successfully completed with a splendid and zigzag path.There are profound historical experiences and lessons.This paper reviews China’s fertility transition which is divided into four periods and argues that fertility changes are a result of the interactions between socioeconomic development,fertility behaviors and fertility policies.Substantial resistance to the "one-childpolicy" during 1979 to 1984 resulted in rebounding and fluctuating fertility.The baby boom occurred in the period 1985 to 1991 was a manifestation of the inherent laws of demographic dynamics,and subsequently forceful birth control was again mobilized.The period from 1992 to 1999 witnessed large declines in fertility which penetrates the replacement zone,showing that China was completing the fertility transition.China’s stabilizing low fertility and emerging population structural issues since 2000 call for comprehensive ways in addressing the population problems.     

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.     

The evaluation of China's population policy]

China's population policy has had tremendous effects on the reduction of fertility. The impact of the population policy is manifested in the following aspects. 1) Reducing the size of the total population by 200 million in 17 years. If the population growth rate had remained at its 1970 level of 2.6/1000, the total population would have been 1.28 billion in 1987. 2) The implementation of the population policy accelerated the process of demographic transition. The mortality decline which began in the early 1950s initiated the demographic transition. The Fertility decline began after the birth control policy was implemented and shifted the transition to a low population growth stage even before the socioeconomic conditions which are considered to be the determinants of fertility decline appeared. The fertility decline, in turn, promoted the socioeconomic development of the country. 3) Solving the problem of food; feeding 21.6% of the world's population on 7.1% of the world's farm land is no easy task. The success of population control, no doubt, played an important role in lowering the population growth rate so that the growth of food production could keep pace with the needs of the population. 4) A decline in the dependency ratio is a favorable condition to socioeconomic development. China's dependency ratio of 59.7 is among the lowest in developing countries and is close to the level in developed countries. Therefore, more production output can be used in investment rather than consumption. 5) The fertility decline facilitated a balanced economic growth. The ratio of population growth as compared to the growth of major economic indicators should be considered an important issue in maintaining macroeconomic control. The population policy made it possible for economic growth to surpass population growth.     

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.     

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.     

Research on Feasible Transition of Age Structure in China

With comparison of demographic changes between the developed European countries and China,this paper has discussed the shortcomings of the Western demographic transition theories.Furthermore,the paper has proposed the direction of demographic transition and the criteria of such transition’s completion.With the establishment of age-structure transition theory,and helped with strict definitions of both surplus population and appropriate population,the paper points out the distinction of demographic age-structure between those developing countries that are undergoing demographic transition and those developed countries with a near completion of such demographic transition.Finally it concludes that China’s transition of age structure is moving towards a feasible direction.