Heterogeneity and selection in multistate population analysis

If one subgroup of individuals in a population has a higher death rate than the others, then over time the surviving population will include a larger share of those with the lower death rate. As a result, the aggregate average death rate for this increasingly more robust population will decline. This conclusion, however, can be drawn only for nonrecurrent events experienced by populations that do not exchange members with one another--that is, for noninteracting populations. Studies of changes in marital status, labor force activity, residential location, and active life, for example, all should focus on patterns of recurrent events among interacting populations (that is, multistate populations). Selection arising from heterogeneity will occur, but the consequences for average measures become unpredictable a priori. This paper explores such aspects of the selection effects of heterogeneity in multistate populations and illuminates some of their consequences for commonly used rates.     

愚昧还是文明,哪一个离我们更近-中国人口素质逆淘汰的实证分析

中国的人口素质逆淘汰问题不仅是多学科的研究对象,而且是学术界争论的焦点。本文从城乡不同的生育率是造成人口素质逆淘汰的原因出发,采取定性分析和定量分析相结合的方法,指出静态社会中的确存在人口素质逆淘汰,但城镇化不仅控制了人口数量,而且提高了人口素质,因此,加大高等教育的投入和改善医疗卫生条件等提高我国人口素质的根本途径应和推进城镇化相结合,才能达到事半功倍的效果。     

Constrained vs unconstrained labor supply: the economics of dual job holding

This paper develops a unified model of dual and unitary job holding based on a Stone-Geary utility function. The model incorporates both constrained and unconstrained labor supply. Panel data methods are adapted to accommodate unobserved heterogeneity and multinomial selection into six mutually exclusive labor supply regimes. We estimate the wage and income elasticities arising from selection and unobserved heterogeneity as well as from the Stone-Geary Slutsky equations. The labor supply model is estimated with data from the British Household Panel Survey 1991–2008. Among dual job holders, our study finds that the Stone-Geary income and wage elasticities are much larger for labor supply to the second job compared with the main job. When the effects of selection and unobserved heterogeneity are taken account of, the magnitudes of these elasticities on the second job tend to be significantly reduced.     

Methods For Comparing The Mortality Experience of Heterogeneous Populations

Methods are presented which produce Maximum Likelihood Estimates (MLE) of the degree of heterogeneity in individual mortality risks under a variety of assumptions about the age trajectory of those mortality risks. With these estimates of the degree of population heterogeneity it is possible to adjust comparisons of mortality risks across populations for the effects of population heterogeneity, differential mortality selection, and different age trajectories of the force of mortality. These methods are demonstrated by applying a variety of standard assumptions about the age trajectory of the force of mortality to the analysis of a broad range of cohort mortality data for the U.S. and Swedish populations. The estimates of the degree of heterogeneity, produced under all of the selected force of mortality models, consistently indicated a considerable degree of heterogeneity in mortality risks.     

Why is there so much genetic variation for wing dimorphism?

Wing dimorphism appears in general to be determined either by a single locus, 2 allele system in which brachyptery is dominant, or by the additive action of numerous loci. In the latter case studies indicate that the heritability is typically quite large. It is generally postulated that wing dimorphism is under strong selection: why then is genetic variation not eroded? In this paper I consider three possible explanations. First, genetic variation may not be exposed to selection because environmental heterogeneity effectively makes heritability zero. Because wing dimorphisms are known to evolve it seems unlikely that this is the primary factor. Second, directional selection on a threshold trait may push the population almost to monomorphism but erodes genetic variance at a very slow rate. This mechanism cannot preserve variation but makes it possible for other factors to more easily maintain variability. Finally, I demonstrate that in a heterogeneous environment spatio-temporal variation in fitness will itself maintain a genetic polymorphism for wing dimorphism. This paper is dedicated to Professor Sinzo Masaki, whose work on the evolution of wing dimorphism and diapause has been so important to our understanding of the evolution of dimorphic variation.     

On a Pandemic Threshold Theorem of the Early Kermack–McKendrick Model with Individual Heterogeneity

A pandemic threshold theorem of the Kermack–McKendrick epidemic system with individual heterogeneity is proved from the definition of R ₀ by Diekmann, Heesterbeek, and Metz. The early Kermack–McKendrick epidemic model is extended to recognize individual heterogeneity, where the state variable indicates an epidemiological state or genetic, physiological, or behavioral characteristics such as risk of infection. With the basic reproduction number R ₀ for the heterogeneous population, the final size equation of the limit epidemic starting from a completely susceptible steady state at t = ?∞ has a unique positive solution if and only if R ₀  > 1. The main result is that the positive solution of the final size equation gives the lower bound of the intensity of any epidemic starting from a host population composed of susceptible and a few infected individuals who spread on a noncompact domain of the trait variable.     

Sex selection with biased technologies and its effect on the population sex ratio

Current biomedical research on sex selection techniques may soon offer couples the opportunity to choose the sex of their children with greater certainty. A technique planned for marketing by mid-1978 can increase the probability of bearing a son to as much as 0.90. However, couples who wish to improve their chances of bearing a daughter have no such opportunity. The purpose of this paper is two-fold. First, a decision-making model is provided which describes how couples should choose among alternative sex-selection methods so as to maximize the probability of bearing their desired number of sons and daughters. Second, the effect of the widespread use of sex-selection techniques on the population sex ratio is explored. It is shown that even if populations have unbiased sex preferences, or sex preferences biased towards daughters, the use of biased sex-selection technologies may result in very high population sex ratios.     

Aging, fertility, social security and political equilibrium

We analyze the effect of population aging on the political choice of the size of a pay-as-you-go (PAYG) social security system, incorporating the heterogeneity of individuals in their preference for having children, and hence the endogenous fertility choices of individuals, into a simple overlapping generations model. We show that population aging may result in an increase in the contribution rate, increasing the share of the retired population who prefer a higher contribution rate; and that, if the system involves redistribution between retirees with different contributions, the increased contribution rate raises the number of individuals who have children, i.e., future contributors.     

Population regulation by dispersal over patchy environment;

Summary A mathematical model for the population regulation is presented, which takes into account the environmental heterogeneity and the animal dispersal, and does not contain any direct density effect on reproduction or death processes. Generally speaking, there are two kinds of dispersal, one is the density independent dispersal, the other is the density dependent. It is shown that a population equilibrium can be maintained by the density dependent dispersal or threshold dispersal which occurs only when the population density exceeds a certain threshold level, but that density independent dispersal by itself can not continue to maintain a population equilibrium.     

区域研究中的常用人口预测模型

人口是一国和地区发展的重要因素。准确的人口预测是制定国民经济计划、区域发展规划的基础。文章以甘肃省为例,介绍了线性回归模型、马尔萨斯模型、Logistic模型和GM（1,1）模型在人口预测中的应用,包括模型的建立、参数的求解以及精度检验。并分别用这几种模型对甘肃省2006—2020年的总人口进行预测。结果表明几种模型的拟合精度都比较高,预测值比较接近。取几种模型的预测平均值作为甘肃省总人口规模的预测结果。几种模型的平均预测结果为：2010年甘肃省总人口将达到2745．84万人,2015年将达到2840．91万人。2020年将达到2934．23万人．     

Estimates of Spatial Prices in India and Their Sensitivity to Alternative Estimation Methods and Choice of Commodities

This paper provides Indian evidence on sub-national PPPs that point to considerable spatial price heterogeneity within the country, based on Indian National Sample Survey (NSS) data. The prices of various commodities have been generated from the household specific unit values obtained from the information on expenditures and quantities from the NSS unit records. This paper shows that the CPD model, proposed in the cross country context, can be adapted to the household context to estimate spatial prices in the intra country context. The proposed CPD based model is shown to be formally equivalent to certain well known fixed weight price indices under certain parametric configurations. The empirical contribution includes a systematic comparison between the spatial price indices from alternative models, namely the CPD and utility based models, and the result that the utility based methods point to a much greater extent of spatial price heterogeneity than is suggested by the CPD type models. The results also record the sensitivity of the spatial price indices to the choice of commodities in the utility based approach. The pairwise comparison of estimates suggests that commodity selection may be more important than model selection in its impact on the spatial price estimates, though the latter is important as well. The study provides estimates of rural–urban differentials in spatial price indices that suggest some interesting differences between the constituent states. The results make a strong case for further research on the topic of sub-national PPPs in the context of large heterogeneous countries.     

Mortality Deceleration and Mortality Selection: Three Unexpected Implications of a Simple Model

Unobserved heterogeneity in mortality risk is pervasive and consequential. Mortality deceleration—the slowing of mortality’s rise with age—has been considered an important window into heterogeneity that otherwise might be impossible to explore. In this article, I argue that deceleration patterns may reveal surprisingly little about the heterogeneity that putatively produces them. I show that even in a very simple model—one that is composed of just two subpopulations with Gompertz mortality—(1) aggregate mortality can decelerate even while a majority of the cohort is frail; (2) multiple decelerations are possible; and (3) mortality selection can produce acceleration as well as deceleration. Simulations show that these patterns are plausible in model cohorts that in the aggregate resemble cohorts in the Human Mortality Database. I argue that these results challenge some conventional heuristics for understanding the relationship between selection and deceleration; undermine certain inferences from deceleration timing to patterns of social inequality; and imply that standard parametric models, assumed to plateau at most once, may sometimes badly misestimate deceleration timing—even by decades.     

人口规模、结构对区域碳排放的影响研究——基于中国省级面板数据的经验分析

目前关于人口对碳排放影响的经验研究,得出大相径庭的结论。基于这种背景,本文以STIRPAT模型为研究起点,运用中国1997～2009年30个省份的面板数据,采用Driscoll和Kraay基于固定效应中纠正异方差、序列相关和截面相关的估计方法,具体考察了地区人口规模、结构对碳排放量的影响。研究表明,在考虑人口结构因素的情况下,人口规模的排放弹性显著为1,因此,以中国为样本研究碳库兹涅茨曲线(CKC)并不会产生太大偏误。在反映人口结构的变量中,劳动年龄人口对碳排放有显著的正向影响,家庭户规模有显著负向影响,而城镇化率对于碳排放的影响并不显著。     

On the Survival of Centenarians and the Span of Life

It has been argued in the literature that the observed mortality crossover among older black Americans relative to the white population is a result of ‘differential early mortality which selects the least robust persons from the disadvantaged population at relatively earlier ages so that, at advanced ages, the disadvantaged population has proportionately more robust persons’ (Kenneth G. Manton). The authors examine the plausibility of the observed black mortality crossover and the heterogeneity argument supporting its existence. In addition to citing evidence from the literature, they use life tables from various countries known to have good mortality data to explore the relation between mortality in childhood and at younger adult ages and mortality in old age for cohorts and periods. Analysis suggests that the association between childhood and old-age mortality for cohorts is positive, implying that observed mortality crossovers are produced by deficient data rather than population heterogeneity.     

Comment on ‘The random variation in rates based on total enumeration of events’ by J. R. Udry,C. Teddlie,C. M. Suchindran

This comment builds on the work of Udry et al., developing a model of random variation of vital rates in small geographical areas. The model is based on the division of the variance of vital rates into three parts; that which would occur in a homogenous population; that due to population heterogeneity; and that due to yearly fluctuations in the underlying basis for the mean value of the probability of the vital event in question. Contrary to Udry et al., this model demonstrates that population heterogeneity must decrease the overall vital rate variance. Using birth rates presented in Udry et al., a test of the new model demonstrates the importance of the third factor, yearly fluctuations, in determining year-to-year variation in birth rates.     

流动人口的择偶模式及其影响因素——以厦门市流动人口为例

利用“厦门市流动人口婚姻家庭抽样调查”的数据,描述流动人口择偶模式的主要特征,对流入厦门的流动人口的择偶意愿、目的、时间、标准以及途径等进行多元回归分析,在此基础上提出优化流动人口择偶模式的对策建议。分析结果表明,流动人口在对择偶模式的选择和实践上越来越重视自身的需要和体验;在各种假想的影响因素中,教育、性别和年龄的作用最大,流出的时间和收入水平的影响却相对比较微弱。     

不同预测模型下西藏自治区人口发展状况及对策研究

针对西藏自治区人口数据的有限性、数据序列的不平滑性等特点,分别采用一元回归、马尔萨斯模型、lo-gistic模型、GM(1,1)模型等4种方法,利用西藏自治区1980—2009年统计年鉴数据进行人口预测,综合考虑各种方案预测值,确定西藏自治区2010-2030年的人口数,在此基础上探讨基于人口增长的西藏经济发展模式与对策。结果表明,几种预测模型中平均相对误差率最小的是一元线性预测模型Ⅲ,仅0.2611%,马尔萨斯预测模型Ⅲ的平均相对误差率最大,也只有2.0767%;从预测结果看,Logistic模型的预测结果最为保守,仅为339.61万人,马尔萨斯模型预测最为乐观,高达380.10万人,未来相关研究中,可应用Logistic模型预测值作为下限,马尔萨斯模型预测值为上限;为综合应用四种模型的优势,研究中综合平均四个不同模型的预测结果,则西藏2010年人口将达到294.07万人,2015年达到311.34万人,2020年328.81万人,2025年346.54万人,2030年364.57万人,未来20年总人口增长趋势逐渐加快,区域发展中有一定人口压力。     

Modelling the evolution of heterogeneity in residential mobility

Migration probabilities are known to vary over the population (heterogeneity) and over time (nonstationarity). It is shown that if the heterogeneity is represented by an SB mixing distribution and the nonstationarity by a set of arbitrary logistic scaling functions, then not only may all sources of heterogeneity, including tastes, be modelled, but heterogeneity at different points in time may be readily compared. The model is calibrated using data previously published by Clark et al. (1977, 1979) for a sample of 1,176 older renters and is found to fit well. The-changing heterogeneity over the ten-year period of observation is represented graphically.     

Longer Life and Population Growth

Enthusiasm about the prospect of large increases in human life expectancy is often dampened by fears that lower mortality will increase population size, hence population pressure. A simple mathematical model of life-cycle stretching demonstrates that if increased longevity is accompanied by later childbearing, a trend that is already underway, future declines in mortality will not increase population size.     

Simulation of movement and egglaying inDanaus plexippus (Lepidoptera: Nymphalidae)

Summary A model simulating the movement and oviposition of monarch butterflies over a female's life time is presented. The model's predictions compare favourably with observed data and suggest that females who lay eggs in an optimal fashion should have low directionalities in areas with high host plant density (patches and single plants) and high directionalities in areas with low host plant density. The model also provides one means of combining individual animal processes and spatial heterogeneity into population dynamics.