Debilitation's aftermath: stochastic process models of mortality

A stochastic differential equation model is developed to clarify the interaction of debilitation, recuperation, selection, and aging. The model yields various insights about the lingering mortality consequences of disasters such as wars, famines, and epidemics that may weaken the survivors. A key result is that debilitation and selection are interdependent: debilitation that increases population heterogeneity will result in subsequent selection; selection, by altering the distribution of population heterogeneity, will influence the impact of debilitating events.     

Three strikes and you're out: Demographic analysis of mandatory prison sentencing

Much of the debate about the costs and benefits of “three-strikes” laws for repeat felony offenders is implicitly demographic, relying on unexamined assumptions about prison population dynamics. However, even state-of-the-art analysis has omitted important demographic details. We construct a multistate life-table model of population flows to and from prisons, incorporating age-specific transition rates estimated from administrative data from Florida. We use the multistate life-table model to investigate patterns of prison population growth and aging under many variants of three-strikes laws. Our analysis allows us to quantify these demographic changes and suggests that the aging of prison populations under three-strikes policies will Significantly undermine their long-run effectiveness.     

The multistate stable population model with immigration

This paper outlines the discrete‐time and continuous‐time formulations of the stable population model with immigration, showing their commonality. It then illustrates how the model can be extended to include multiple interacting populations, and goes on to consider a multistate version of reproductive value that further illuminates the evolutionary dynamics of an “open”; model of multistate population growth and redistribution. Attention is restricted to results arising from a fertility regime that is below replacement level.     

Intrinsically Dynamic Multistate Models

Multistate life table models, which follow persons through more than one living state, have found increasing use in demographic analyses. Multistate stable populations, however, are infrequently used because the constant rate assumption is quite strong and such populations can take centuries to approach stability. Dynamic models, that is models where the rates can change over time, are examined to derive a new solution for the size and composition of a multistate population in terms of the sequence of underlying population projection matrices (PPMs). Constraints on the subordinate eigenvalues and the subordinate eigenvectors of the time-varying PPMs produce a model population that grows according to the dominant eigenvalues of each time-specific PPM and has a state composition that depends only on the most recent PPM. The two living state model is examined in detail, relationships between the PPM elements and the size and composition of the model are explored, and two illustrative applications of the model are presented.     

Age,period, and cohort effects in demography: a review

This paper considers only the vital events of demographic measurement, the factors influencing the rate at which those events occur and then investigates the consequences of patterns of these events. It reviews the state of the art of age, period and cohort analysis for demographic dependent variables. Major examples of such analyses are given in both mortality and fertility studies. In the area of mortality the conventional approach to such analysis apears to be well suited to a wide range of applications yielding useful results. The reasons for this suitability are: early childhood experience is important in many major disease and death processes, so that cohorts are legitimately viewed as acquiring early on a certain fixed susceptibility; data sometimes stretch back far enough that stationary standards of age patterns can be developed empirically, and applied to later experience; and, logarithmic or logistic transformations linearize comparisons of age schedules or mortality so that standard statistical procedures are suitable. Applications of age, period, and cohort analysis are not always routine; external constraints are required, in the form of theoretically based and mathematically expressed age patterns of mortality, in order to distinguish effectively between period and cohort effects. A set of models of age patterns of mortality that are based on cohort as well as period experience could be constructed with useful applications. With fertility analysis the conventional approach is much less suitable. Once goal directed behavior is introduced, empirical examinations must be based on theories or assumptions about how such goals are formulated and pursued. Conventional analysis might suffice only if one is prepared to accept the assumption that all pertinent goals and strategies are formulated before the initiation of childbearing and remain unaffected by subsequent events. This assumption is untenable for modern developed populations and the forms of analysis appropriate to age period cohort investigations of fertility will have to develop along with theories of reproductive behavior.     

A preliminary inquiry into the interrelationship between population growth and economic development in Hong Kong]

Hong Kong includes Hong Kong Island, Kowloon, New Territory, and more than 230 islands. During World War ii, the population of Hong Kong decreased sharply, and the total number decreased to less than 600,000. Since the war ended in 1945, the population of Hong Kong has been increasing rapidly at an annual rate of 20%. By the end of 1981, its total population had increased to 5.2 million, including 1.25 million newly arrived immigrants. The average age is 24.8. People above the age 65 constitute only 6% of the total population. This shows that there is a sufficient supply of labor for local economic development. Because of continued economic growth, there has been a constant demand for more labor. Low wages provide an excellent condition for high-speed industrial development. An improved quality of professional workers and management personnel also contributes much to Hong Kong's industrial modernization. Because of high employment among the labor population, the general population earns income and spends a great deal, and this has created a rather active economy. General population growth trends include: 1) continued population growth will bring the total population to 6.3 million by the end of 1981, and the housing problem will become more serious; 2) a stable decline in the natural population growth rate will gradually change the population pattern to a low birth, low death, and low natural growth situation; and 3) improvements in science and technology, health care, and living conditions will reduce the death rate, and the average age will lengthen, and with the increase in old people, the demand for social welfare will also increase; and 4) there will be a shortage in experienced labor (professional technicians and high management personnel) in the 1980s. Facing the new situation, Hong Kong's economic structure needs reform, moving from a labor intensive enterprise to a capital-technological intensive enterprise. The market will be expanded and Hong Kong will earn more profit in China's mode rnization process.     

Urban growth in China: past, prospect, and its impacts

Rapid growth and globalization of the domestic economy have dramatically accelerated urbanization in China, resulting in significant environmental impacts and challenges for sustainable development. Using a multistate model accounting for distributional aspects of age, sex, education, and migration in rural and urban regions, we estimate the magnitude of urbanization in China through 2030 and examine some major associated sustainability issues. Results indicate that: (1) for a range of assumptions, China’s urban population will nearly double from 2000 to 2030; (2) the labor force will constitute a larger share of total population in urban areas than rural due to internal migration of younger workers—this appears particularly true for the mega-urban metropolises of Beijing and Shanghai; (3) rural populations will experience more aging than urban; and (4) level of education among China’s rural labor force will remain low, which could pressure China’s industrial structural transition from an agricultural to a service-based economy.     

Changing mortality and morbidity rates and the health status and life expectancy of the older population

This paper demonstrates the consequences of changes in mortality and health transition rates for changes in both health status life expectancy and the prevalence of health problems in the older population. A five-state multistate life table for the mid-1980s provides the baseline for estimating the effect of differing mortality and morbidity schedules. Results show that improving mortality alone implies increases in both the years and the proportion of dependent life; improving morbidity alone reduces both the years and the proportion of dependent life. Improving mortality alone leads to a higher prevalence of dependent individuals in the life table population; improving morbidity alone leads to a lower percentage of individuals with problems in functioning.     

生育率演变的生态学逻辑及人口增长的长期趋势

人口增长的长期过程一直是充满困惑与引发争论的话题,将人类复归到生态系统的普通成员,按照生态学逻辑构建一个由替代生育率内生引导、人口容量外生制约的人口增长新模型,以代替用具体社会经济因子解释短周期人口变动的传统思路,探讨生育率转变的一般模式及人口发展的长期趋势。工业革命以来,全球人口已经或正在经历着第一次、第二次生育率转变,全球生育率演变可以聚类为欧美、亚非拉、撒哈拉以南非洲和东亚四种区域模式;在计划生育政策的推动下,我国在短短的三十年内完整经历了两次生育率转变。极限替代生育率是生育率演变的长期目标,但当前已有一些国家跌破更替水平,这也许会成为各个国家的普遍经历,预示着人口容量约束的日益显性化;世界及主要国家的人口规模正在日益逼近其容量极限,并会在惯性驱动下突破容量限制,达到峰值后再以负增长方式趋近人口容量,同期的生育率也将向极限替代生育率递增复归。按趋势模拟世界和中国的可持续人口容量分别约为65亿人和12亿人。研究设计出测量人口增长惯性的新指标——人口增长惯性系数,它是生育率与实时替代生育率之比或出生率与死亡率之比,相比常用的人口惯性因子更为简便易行。     

Divergent Patterns in the Ethnic Transformation of Societies

The uneven timing of the demographic transition in different countries of the world will lead to divergence between countries in ethnic and religious homogeneity. Developed‐country populations that began their fertility transitions relatively early are becoming increasingly diverse with respect to the ethnic origin and religion of their inhabitants, primarily as a result of high recent levels of immigration. Many demographic patterns of the developed world, such as low death and birth rates, are becoming universal. It might be expected that less developed countries will also turn from emigration to experiencing immigration, as their populations age and their economies develop. This essay suggests, however, that future ethnic diversity arising from immigration may be less marked in many of those developing countries than in the West, especially among latecomers to the fertility transition. Five reasons are advanced as impediments to the globalization of ethnic heterogeneity arising from immigration: demographic, economic, political, and factors related to resource constraints, and climate change. The essay considers what social, economic, and political consequences might arise if high levels of ethnic diversity, and possibly ethnic replacement, remained an idiosyncratic peculiarity of today's developed countries, which would therefore diverge in important ways from the rest of the world as the twenty‐first century unfolds.     

Problems and solutions in forecasting geographical populations

This paper asks the question: how does the multistate population model need to be adjusted to provide forecasts of geographical populations? Following an exposition of the standard model, ossible solutions to the problems posed by excessive number of parameters are discussed. ecomposition, aggregation and parameterization are described, drawing on some new results. ssues in the temporal forecasting of model components are outlined and the alternative approach of using a spatial interaction model is considered. The paper concludes by arguing that the design of forecasting models is a powerful learning device for both designers and users.     

Heterogeneity,dependence among causes of death and Gompertz

Heterogeneity in a population with respect to mortality, or variation in “frailty”; among members of that population, which has been discussed extensively in the literature over the last decade and a half is essential to any realistic model of dependence among causes of death. The main problem then is the development of a mortality model incorporating heterogeneity and cause of death which is both realistic and of manageable proportions.

In a recent paper (J. H. Pollard, 1991), it has been shown that many life table results are remarkably insensitive to the strict shape of the mortality curve, at least for more developed populations, and that accurate approximations can in many cases be obtained knowing only the mortality rates at two representative ages (e.g. 50 and 70). These results and the Gompertz “law”; of mortality can be used to develop manageable approximate formulae for the expectation of life under heterogeneity and correlation among the causes of death. The formulae are confirmed by simulation.

Numerical results indicate, somewhat surprisingly, that the effects of correlation among causes of death, even at quite high levels, on expectation of life and changes on expectation of life when particular causes of death are reduced or eliminated are relatively minor.     

A dynamic multistate model of robustness and frailty

Dynamic multistate models can show realistic population dynamics over time, model complex cycles, and encompass the life history of a cohort. This paper uses a recently developed approach to obtain the analytic solution of a time‐dependent multidimensional differential equation. The illustrative robust/frail model presented shows that the assumption of fixed individual frailty can be abandoned in a two living state model that allows transitions between health statuses and nonproportional hazards of death.     

各地区死亡率比较方法的改进及实证分析

长期以来,人们在分析各地区的人口死亡率时,都是用直接死亡率进行分析比较。然而在我国各地区人口基数不同的情况下,采用直接死亡率进行比较会带来很大的误差。本文对传统的死亡率进行了调节,并利用五普时各地区的死亡率进行了实证分析。     

Multistate projections by level of education for Portugal, 2011–2031

Educational attainment is an attribute that leads to a great distinction between the members of a population, including when considering their health and well-being, which are features to pursue within an aging society. The aim of this work was to produce demographic projections for the Portuguese population by sex, age group and level of educational attainment, for the period 2011–2031. Considering fertility, mortality and migration differentials by level of education, the population was projected using the multistate cohort-component method with a block Leslie matrix. Two scenarios were considered, one where educational attainment before 2011 remains constant and another in which educational attainment will follow the trend observed over the last decade, being the trend in the state proportion modelled using continuation ratio models. The results show an increase in the proportion of individuals who complete higher educational levels in almost all age groups of both sexes. Among women, only 13.6 % had completed some level of higher education in 2011, a figure that will rise to approximately 23.4 % in 2031, whereas among men this value was only 9.7 % and will also rise by 2031, reaching 15.5 %. We can expect the proportion of people with higher educational levels to continue to rise as the education of younger cohorts seems to evolve positively. This work will be particularly useful to study how the aging population and the rising levels of education can contribute to the planning and monitoring of public policies, although these findings can also be used in other research contexts.     

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.     

Working Life Expectancy at Age 50 in the United States and the Impact of the Great Recession

A key concern about population aging is the decline in the size of the economically active population. Working longer is a potential remedy. However, little is known about the length of working life and how it relates to macroeconomic conditions. We use the U.S. Health and Retirement Study for 1992–2011 and multistate life tables to analyze working life expectancy at age 50 and study the impact of the Great Recession in 2007–2009. Despite declines of one to two years following the recession, in 2008–2011, American men aged 50 still spent 13 years, or two-fifths of their remaining life, working; American women of the same age spent 11 years, or one-third of their remaining life, in employment. Although educational differences in working life expectancy have been stable since the mid-1990s, racial differences started changing after the onset of the Great Recession. Our results show that although Americans generally work longer than people in other countries, considerable subpopulation heterogeneity exists. We also find that the time trends are fluctuating, which may prove troublesome as the population ages. Policies targeting the weakest performing groups may be needed to increase the total population trends.     

Immigrants’ ages and the structure of stationary populations with below-replacement fertility

A sustained regime of low fertility plus immigration yields an unusual kind of stationary population. The author demonstrates that all stationary populations have a common structure, and that the familiar replacement-level fertility population is the youngest among the many stationary populations corresponding to a particular life table. This finding has important consequences for policy because although fertility increase and immigration are equally effective at halting population decline, immigration is inferior as a means of rejuvenating low-fertility populations. In fact, an immigration-based policy could make a low-fertility population older rather than younger. The paper includes examples using U.S. and West German vital rates.     

灾难事件对生育率的影响：历史经验与现实思考

纵观人类历史,任何一次重大灾难事件都会导致生育率波动变化。灾难事件周期与生育率变动的一般规律为:生育率在灾难事件发生短期内会受挫下降,灾难事件恢复中期内回升反弹,灾后长周期内则回归灾难事件前的变动大趋势。从外在因素的影响看,灾难事件范围越广,波及人口越多且致死率越高,生育率波动越剧烈,疫情和与环境有关的灾难事件可能会对生育能力产生负面影响。从内在因素的影响看,灾害发生地的经济发展水平、教育水平与家庭经济能力、人口年龄结构以及政府的应对能力等会影响生育率波动幅度,但不会改变波动方向。通过影响机制分析,初步观察新冠肺炎疫情所造成的生育率下降是高死亡数量带来的心理冲击、经济衰退、停工停产以及对未来生活预期不明朗和信心减弱综合作用的结果。     

Estimating intercensal age schedules by intracohort interpolation

"This paper describes a procedure for estimating intercensal age schedules of rates of occurrence of demographic events (birth, death, marriage) from tabulations at two points in time of a status of the population (average children ever born, persons surviving, proportion ever married) classified by age." The procedure is called iterative intracohort interpolation. The paper describes a more general version than that originally developed by Ansley J. Coale and provides a probabilistic interpretation of the age-specific rates estimated by the procedure.