Killing off cohorts: Forecasting mortality of non-extinct cohorts with the penalized composite link model

Mortality forecasting has crucial implications for insurance and pension policies. A large amount of literature has proposed models to forecast mortality using cross-sectional (period) data instead of longitudinal (cohort) data. As a consequence, decisions are generally based on period life tables and summary measures such as period life expectancy, which reflect hypothetical mortality rather than the mortality actually experienced by a cohort. This study introduces a novel method to forecast cohort mortality and the cohort life expectancy of non-extinct cohorts. The intent is to complete the mortality profile of cohorts born up to 1960. The proposed method is based on the penalized composite link model for ungrouping data. The performance of the method is investigated using cohort mortality data retrieved from the Human Mortality Database for England & Wales, Sweden, and Switzerland for male and female populations.     

The impact of demographic change on human capital accumulation

This paper investigates whether and to what extent demographic change has an impact on human capital accumulation. The effect of the relative cohort size on educational attainment of young adults in Germany is analyzed utilizing data from the German Socio-Economic Panel for West-German individuals of the birth cohorts 1966 to 1986. These are the cohorts which entered the labor market since the 1980s. Particular attention is paid to the effect of changes in labor market conditions, which constitute an important channel through which demographic change may affect human capital accumulation. Our findings suggest that the variables measuring demographic change exert a considerable though heterogeneous impact on the human capital accumulation of young Germans. Changing labor market conditions during the 1980s and 1990s exhibit a sizeable impact on both the highest schooling and the highest professional degree obtained by younger cohorts.     

The age–period–cohort conundrum as two fundamental problems

In general the age–period–cohort (APC) conundrum refers to the problem of separating the effects of age-groups, periods, and cohorts. This formulation, however, fails to differentiate two fundamental problems in APC analysis: (1) the problem of the complete confounding of the linear effects of age with the effects of period and cohort, the linear effects of cohorts with period and age, and the linear effects of period with age and cohort; and (2) the problem of model identification. We elucidate both problems and show how the first problem makes the partitioning of variance between cohort effects, period effects, and age effects and the deviation of their effects from linearity problematic even when these approaches do not suffer from the problems associated with model identification. We conclude by examining the affects of this linear confounding on estimates of the individual effect coefficients for age-groups, periods, and cohorts when a linear constraint it imposed on the matrix of independent variables to produce an identifiable model.     

Age–period–cohort decomposition of aggregate data: an application to US and Japanese household saving rates

This paper compares two methods of analyzing aggregate data that is classified by period and age. Because there is a linear relationship among age, period, and cohort, it is not possible to distinguish the separate effects without employing an identifying assumption. The first method, which is applied in the economics literature, assumes that period effects are orthogonal to a linear time trend. The second method, which is applied in the statistics literature, assumes that the effect parameters change gradually. Simulation results suggest that the performances of both methods are comparable. The results of applying the second method to household saving rates suggest that period effects had a negligible influence in the United States but considerable influence in Japan. Copyright © 2006 John Wiley & Sons, Ltd.     

The Method of Purging Applied to Repeated Cross-Sectional Data

In cross-sectional survey research, it is quite common to estimate the(standardized) effect of independent variable(s) on a dependent variable. However, if repeated cross-sectional data are available, much is to be gained if the consequences of these effects on longitudinal social change are considered.To assess these consequences, we describe a type of simulation in whichlongitudinal shifts in the independent variable's distribution, and longitudinal variation in effect on the dependent variable are `purged' from the data. Although the method of purging is known for many years, we add new practical features by relating the method to logistic and linear regression analysis. Because both logistic and linear regression analysis can be found in all majorstatistical packages, the method of purging is made available to a wider group of social scientists. With the use of repeated cross-sectional data, gathered in the Netherlands between 1970 and 1998, the new practical features of the purging method are shown, using the SPSS package.     

Peer Effects: Evidence from Secondary School Transition in England

We estimate the effect of peers' prior achievement on student progress in secondary school, using administrative data on four cohorts of students in England. Students leaving primary for secondary school experience a big change in their peer group and these changes vary randomly from cohort to cohort. We exploit this variation to identify the effect of new peers on student achievement. We show that peer quality on entry to secondary school has a significant effect on students' subsequent achievement at age 14. The effect sizes are relatively small and are linked to peers' family background and early age achievements.     

Changes in women’s and men’s child care time in China, 2004–2011: the contributions of cohort replacement and intra-cohort change

With the rapid social and economic changes in China, increasing attention has been paid to issues related to child care, such as maternal work and child care, child care support sources, and work-family conflict. But the change in women’s and men’s child care time in the last decade remains under-researched. I use cross-sectional data from the 2004–2011 China Health and Nutrition Survey and linear decomposition regression techniques to examine the mechanisms generating structural change in child care time for men and women. I find that overall women’s child care time is slightly decreasing because the contributions of intra-cohort change and cohort replacement are offsetting one another. However, men’s childcare time is increasing during the same time period because of processes of intra-cohort change. Trends in women’s childcare time indicate a positive but small cohort replacement effect, whereas men’s childcare time is largely impacted by a positive intra-cohort change effect. These results highlight the mechanisms through which the gendered division of childcare time inside Chinese families has been shifting in the direction of increasing egalitarianism from 2004 to 2011.     

Who Gains from the Demographic Dividend? Forecasting Income by Age

Changes in the population age structure are known to influence the total income per person, but little is known about whether the changes are equally shared across the population or are concentrated on particular age groups and/or birth cohorts. The answer to this question has potentially important implications for income inequality, human capital investment, and fertility decision-making. We propose a new model of intergenerational transfers which distinguishes between the effects of changes in population structure and the effects of changes in family age structure. Using age-specific data from annual income and expenditure surveys of Taiwan between 1978 and 1998, we show that changes in age structure have had a very favorable effect on Taiwan's income growth. The gains are not equally shared by all age groups, however. Children and young adults have benefited the most, while the elderly have benefited the least. The population and family age structures have independent effects on per capita income; the effect of the population age structure is most important. Generational differences in per capita income are closely related to intergenerational differences in earnings, suggesting only a weak form of altruism. Finally, we predict that, on average, population aging will adversely influence the per capita income growth in Taiwan in the coming decades.     

Permanent and transitory wages of British men, 1975–2001: year,age and cohort effects

We examine the mean and variance–covariance structure of log-wages over calendar time and the life cycle of British men, hereby controlling for birth cohort effects. We attribute the strong increase in mean log-wage during the 1980s and 1990s to a rise in mean log-wage with the year of birth. This rise is diminishing with the year of birth, which implies lower wage inequality between cohorts with the year of birth. Wage inequality has increased during the 1980s and early 1990s and remained fairly stable in the second half of the 1990s. The year effects, however, show increasing wage inequality up to 2001, mainly due to a strong rise in transitory wage inequality. Transitory wages are strongly correlated over time and an increase in transitory wage inequality therefore has highly persistent inequality consequences. The stable wage inequality in the second half of the 1990s is attributed to lower within-cohort wage inequality for the younger cohorts. The age effects show that permanent wage inequality increases with age, in particular up to age 30 and over age 50. Copyright © 2007 John Wiley & Sons, Ltd.     

Successive Sampling to Estimate Quantiles with P-Auxiliary Variables

The successive sampling is a known technique that can be used in longitudinal surveys to estimate population parameters and measurements of difference or change of a study variable. The paper discusses the estimation of quantiles for the current occasion based on sampling in two successive occasions and using p-auxiliary variables obtained of the previous occasion. A multivariate ratio estimator from the matched portion is used to provide the optimum estimate of a quantile by weighting the estimates inversely to derived optimum weights. Its properties are studied under large–sample approximation and the expressions of the variances are established. The behavior of these asymptotic variances is analyzed on the basis of data from natural populations. A simulation study is also used to measure the precision of the proposed estimator.     

Wages and Ageing: Is There Evidence for the ‘Inverse‐U’ Profile?*

How individual wages change with time is one of the crucial determinants of labour market decisions including the timing of retirement. The focus of this paper is the relationship between age and wages with special attention given to individuals nearing retirement. The analysis is presented in a comparative context for Britain and Germany looking at two longitudinal data sets (BHPS and SOEP, respectively) for the years 1995–2004. We show the importance of cohort effects and selection out of employment which determine the downward‐sloping part of the ‘inverse‐U’ profile observed in cross‐sections. There is little evidence that wages fall with age.     

农村人口老龄化对收入不平等影响的实证研究

利用1989年-2011年的农户微观家计调查数据,采用方差分解和回归分解相结合的方法,考察农村人口老龄化对收入不平等的影响。研究发现农村收入不平等的总体变化主要是由组间效应所引起,即不同出生组之间不平等程度的加剧是收入不平等的主因;无论采用方差分解法还是采用回归分解法得到的研究结论表明,农村人口老龄化的确加剧了收入不平等,其影响程度相对较小,但从时间变化趋势来看,人口老龄化效应有增强之势。     

Event History Data and Making a History out of Cross-Sectional Data

At the turn of 20th century social scientists have built up a large stock of cross-sectional data-sets to study social change. However, scholars more and more collect event history data containing the exact timing of events. Comparing the (dis)advantages event history data are to be preferred. However, for research on value change the event history approach is inapplicable, since it is not possible to ask the timing of a value change retrospectively. I will illustrate that value change (i.e. cohort differences) can be studied adequately with cross-sectional data, if information about the historical context is added. For this purpose I test Inglehart's value change thesis.Interestingly, there are also topics in which cross-sectional data-sets are unnecessarily being used. Using research on secularization as an example, I show that the event-history approach can be used to answer the question whether the decreasing number of religious people concerns a cohort-effect. However, whatever data-set is being used, to study cohort differences, one should always give a theoretical answer to the key-question: what exactly makes cohorts different     

The hierarchical age–period–cohort model: Why does it find the results that it finds?

It is claimed the hierarchical-age–period–cohort (HAPC) model solves the age–period–cohort (APC) identification problem. However, this is debateable; simulations show situations where the model produces incorrect results, countered by proponents of the model arguing those simulations are not relevant to real-life scenarios. This paper moves beyond questioning whether the HAPC model works, to why it produces the results it does. We argue HAPC estimates are the result not of the distinctive substantive APC processes occurring in the dataset, but are primarily an artefact of the data structure—that is, the way the data has been collected. Were the data collected differently, the results produced would be different. This is illustrated both with simulations and real data, the latter by taking a variety of samples from the National Health Interview Survey (NHIS) data used by Reither et al. (Soc Sci Med 69(10):1439–1448, 2009) in their HAPC study of obesity. When a sample based on a small range of cohorts is taken, such that the period range is much greater than the cohort range, the results produced are very different to those produced when cohort groups span a much wider range than periods, as is structurally the case with repeated cross-sectional data. The paper also addresses the latest defence of the HAPC model by its proponents (Reither et al. in Soc Sci Med 145:125–128, 2015a). The results lend further support to the view that the HAPC model is not able to accurately discern APC effects, and should be used with caution when there appear to be period or cohort near-linear trends.     

Mixed Hidden Markov Models for Longitudinal Data: An Overview

In this paper we review statistical methods which combine hidden Markov models (HMMs) and random effects models in a longitudinal setting, leading to the class of so‐called mixed HMMs. This class of models has several interesting features. It deals with the dependence of a response variable on covariates, serial dependence, and unobserved heterogeneity in an HMM framework. It exploits the properties of HMMs, such as the relatively simple dependence structure and the efficient computational procedure, and allows one to handle a variety of real‐world time‐dependent data. We give details of the Expectation‐Maximization algorithm for computing the maximum likelihood estimates of model parameters and we illustrate the method with two real applications describing the relationship between patent counts and research and development expenditures, and between stock and market returns via the Capital Asset Pricing Model.     

The cost and technological structure of aluminium smelters worldwide

A cost model is developed for the estimation of several technological parameters describing the production process of aluminium smelters worldwide. The model is similar to Baltagi and Griffin's ( 1988 ), but, instead of estimating technological change using a panel data set of firms, we estimate, among other things, the vintage effect, using a cross‐section of aluminium smelters in operation throughout 1994. The vintage effect is defined as the variable cost differential that may be attributed to the utilization of a specific technical vintage in the production of aluminium in relation to another. Other technological measurements are also discussed: the scale effect or returns to scale and technological characteristic effects, i.e. the variable cost elasticities with respect to pot size and current intensity. The results show that considerable cost reductions may be expected from the change of old technical vintages to more recent ones. Also, results show that for a majority of smelters in the sample, returns to scale seem to be exhausted. Finally, variable costs are very sensitive to pot size in the sense that large cost reductions can be expected from the increase in pot size, an important characteristic of the technology used by smelters. Copyright © 2000 John Wiley & Sons, Ltd.     

Maximum likelihood estimation of seemingly unrelated stochastic frontier regressions

This paper explores the changes in value added (VA) of a sample of schools for cohorts of students finishing secondary education between 2005 and 2008. VA estimates are based on distance measures obtained from DEA models. These measures are computed for each pupil in each school, and evaluate the distance between the school frontier in a given year and a pooled frontier comprising all schools analysed. The school VA is then computed by aggregating the VA scores for the cohort of pupils attending that school in a given year. The ratio between VA estimates for two consecutive cohorts, that attended the school in different years, is taken as the index of VA change. However, the evolution of school performance over time should consider not only the movements of the school frontier, but should also take into account other effects, such as the proximity of the students to the best-practices, represented by the school frontier, observed over time. For that purpose we developed an enhanced Malmquist index to evaluate the evolution of school performance over time. One of the components of the Malmquist index proposed measures VA change, and the other measures the ability of all school students to move closer to their own school best practices over time. The approach developed is applied to a sample of Portuguese secondary schools.     

中国人口年龄结构对消费的影响研究

改革开放以来,中国经济保持持续高增长,但居民消费一直处于低迷状态,在人口老龄化的大背景下,研究人口老年化对我国消费增长的作用具有重要意义。在假设年龄是消费函数的内生变量前提下,对家庭的跨期消费选择进行建模,针对人口结构函数的不同形式分别给出消费函数的几种重要的性质,并着重讨论了人口结构与消费总量的关系。研究表明:老龄人口的增多不仅没有拉低消费,反而显著促进消费增长。再利用我国2005—2010年间各省面板数据,在检验变量内生性之后选择动态面板GMM方法进行估计,得到的结果和理论假设契合,即老年抚养比的提高对消费具有促进作用。最后,针对人口老年化和消费给出相关政策建议。     

Data collection frequency effect in the National Medical Care Expenditure Survey.

The National Medical Care Expenditure Survey (NMCES) was characterized by a longitudinal survey design, with data collection targeted to five points in time covering the survey year. Field conditions did not allow for all interviews to be conducted over the targeted time periods. A subset of sampled households (holdovers) were not contacted for a particular wave of the survey and data were gathered at the subsequent time period for the two time intervals that were spanned. National estimates for a representative set of health care utilization and expenditure measures were derived from the sample of holdovers and compared with estimates derived from the respondents with five complete waves of data collection. Controlling for relevant predispositional factors in the estimation of health care utilization and expenditure measures, a test for data collection frequency effect is also considered.     

Ethnic enclaves in the classroom

We use data on elementary-school students to investigate how the home language and other characteristics of a student's same-grade schoolmates influence that student's academic achievement. We exploit the availability of multiple cohorts of data within each school to control for endogenous selection by incorporating school fixed effects in the model. We also exploit the longitudinal structure of the data to estimate value-added models of the educational production function. We find that attending an “enclave” school provides a slight net benefit to Chinese home-language students and a large net cost to Punjabi home-language students. The results are consistent with a simple peer effects mechanism in which the academic achievement or behavior of peers is much more important than their home language.