Predicting childlessness for recent cohorts of American women

Over 50% of the American women now in the midst of the childbearing years have never borne a child. These levels of childlessness for women in their 20s are the highest ones in a time series that spans most of the twentieth century. Will postponed parenthood be translated into very high levels of permanent childlessness? Or will these cohorts "catch-up" with a late fertility flurry in their 30s and 40s? The authors examine 3 projection strategies: one using women's stated fertility expectations, a second relying on the patterns of previous cohorts, and a third which posits that current rates will persist into the future. The predictive validity of these different projection strategies are tested with data for the 1980-87 period. They show that the projection based on current period rates performs well. Further, the authors argue that it better captures the first birth process than other models. They forecast levels of 20% childless for cohorts of white women born in the early 1960s. Recent trends for nonwhites are very different from those for whites: levels of 4% are forecast for nonwhite women.     

Response to updated mortality forecasts in life cycle saving and labor supply

Historical evidence shows that demographic forecasts, including mortality forecasts, have often been grossly in error. One consequence of this is that forecasts are updated frequently. How should individuals or institutions react to updates, given that these are likewise expected to be uncertain? We discuss this problem in the context of a life cycle saving and labor supply problem, in which a cohort of workers decides how much to work and how much to save for mutual pensions. Mortality is stochastic and point forecasts are updated regularly. A Markovian approximation for the predictive distribution of mortality is derived. This renders the model computationally tractable, and allows us to compare a theoretically optimal rational expectations solution to a strategy in which the cohort merely updates the life cycle plan to match each updated mortality forecast. The implications of the analyses for overlapping generations modeling of pension systems are pointed out.     

Life Expectancies for Small Areas: A Bayesian Random Effects Methodology

Monitoring small area contrasts in life expectancy is important for health policy purposes but subject to difficulties under conventional life table analysis. Additionally, the implicit model underlying conventional life table analysis involves a highly parametrized fixed effect approach. An alternative strategy proposed here involves an explicit model based on random effects for both small areas and age groups. The area effects are assumed to be spatially correlated, reflecting unknown mortality risk factors that are themselves typically spatially correlated. Often mortality observations are disaggregated by demographic category as well as by age and area, e.g. by gender or ethnic group, and multivariate area and age random effects will be used to pool over such groups. A case study considers variations in life expectancy in 1 118 small areas (known as wards) in Eastern England over a five-year period 1999–2003. The case study deaths data are classified by gender, age, and area, and a bivariate model for area and age effects is therefore applied. The interrelationship between the random area effects and two major influences on small area life expectancy is demonstrated in the study, these being area socio-economic status (or deprivation) and the location of nursing and residential homes for frail elderly.     

Mortality Forecasting and Trend Shifts: an Application of the Lee–Carter Model to Swedish Mortality Data*

In this paper we examine how the Lee–Carter model fares with Swedish data for the period 1901–2001 and for segments of this period. We have choosen to censor ages less than age 40 as those ages only are of marginal interest to the forecast. At age 40 some 98 to 99 percent of the birth cohorts are survivors. In the study we only consider the unweighted K¹ estimates. The Lee–Carter model provides very good fits to the data. When splitting up the base period there seems to be an interaction beween the age and time components of the model. In order to deal with the different phases of falling mortality for males and females possibly one should choose the past 25 years as a base in the model. Selecting the base period is however a judgmental issue depending on the main focus of the forecast. Is it long‐term, short‐term or, as in Sweden, a combination of both.?     

Stochastic demographic forecasting

"This paper describes a particular approach to stochastic population forecasting, which is implemented for the U.S.A. through 2065. Statistical time series methods are combined with demographic models to produce plausible long run forecasts of vital rates, with probability distributions. The resulting mortality forecasts imply gains in future life expectancy that are roughly twice as large as those forecast by the Office of the Social Security Actuary....Resulting stochastic forecasts of the elderly population, elderly dependency ratios, and payroll tax rates for health, education and pensions are presented."     

Forecasting sales using online review and search engine data: A method based on PCA–DSFOA–BPNN

Traditional sales forecasting methods are mainly based on historical sales data, which result in a certain lag. The relationship between sales volume and its influencing factors is intricate and often non-linear. In view of this, we propose a novel product forecasting method using online reviews and search engine data. Firstly, a dictionary-based sentiment analysis method is developed to convert the textual review concerning each attribute of the product into the corresponding sentiment score. And by combining the prospect theory and relevant online review data, sentiment indices in each period are calculated. Subsequently, data of product-related Baidu search words with different lag orders are collected and screened by time difference correlation analysis. Finally, the forecast model, PCA–DSFOA–BPNN, is constructed by combining the principal component analysis (PCA), the back propagation neural network (BPNN), and the improved fruit fly optimization algorithm (DSFOA), in which sentiment indices, Baidu search data, and historical sales volume are input data. Taking the monthly sales forecast of 14 automobile models as a case study, we observe that the proposed forecast method can effectively improve the forecast accuracy with good robustness.     

Distinguishing aging,period and cohort effects in longitudinal studies of elderly populations

In the analysis of longitudinal data sets describing the characteristics of elderly populations it is useful to distinguish aging, period, and cohort effects. An aging effect is a change in variable values which occurs among all cohorts independently of time period, as each cohort grows older. A cohort effect is a change which characterizes populations born at a particular point in time, but which is independent of the process of aging. A period effect is a change which occurs at a particular time, affecting all age groups and cohorts uniformly. In this paper a dummy variable regression technique and a parallel graphical technique are introduced as means of identifying aging, cohort, and period effects in a longitudinal data set. These techniques are applied to data describing Los Angeles County which appeared in the censuses of 1940, 1950, 1960 and 1970. Trends in residential density, home ownership, housing value, apartment living, rental rates, one-person households and racial composition are investigated, and aging, cohort and period effects are noted and interpreted.     

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.     

Population forecasting theory,methods and assessments of accuracy. The magnitude of error due to different vital processes in population forecasts

The accuracy of population forecasts depends in part upon the method chosen for forecasting the vital rates of fertility, mortality, and migration. Methods for handling the stochastic propagation of error calculations in demographic forecasting are hard to do precisely. This paper discusses this obstacle in stochastic cohort-component population forecasts. The uncertainty of forecasts is due to uncertain estimates of the jump-off population and to errors in the forecasts of the vital rates. Empirically based of each source are presented and propagated through a simplified analytical model of population growth that allows assessment of the role of each component in the total error. Numerical estimates based on the errors of an actual vector ARIMA forecast of the US female population. These results broadly agree with those of the analytical model. This work especially uncertainty in the fertility forecasts to be so much higher than that in the other sources that the latter can be ignored in the propagation of error calculations for those cohorts that are born after the jump-off year of the forecast. A methodology is therefore presented which far simplifies the propagation of error calculations. It is noted, however, that the uncertainty of the jump-off population, migration, and mortality in the propagation of error for those alive at the jump-off time of the forecast must still be considered.     

火炮身管寿命预测技术发展研究

火炮身管寿命问题受到了从事火炮研究、设计、生产和使用人员的高度关注。通过概述火炮身管寿命的定义及其预测技术的发展历程,基于火炮身管寿命预测技术已经取得的成果,提出了对大口径火炮身管寿命实施实时动态预测的方法,并对该方法进行了初步的探讨,确定了实现该方法的关键技术所在。     

主成分分析—BP神经网络在备件需求预测中的应用

备件需求预测在装备维修保障中占据重要的地位,针对当前主要以经验为主进行估计,与实际需求相差较大,提出基于主成分分析—BP神经网络模型的备件需求预测方法。首先利用主成分分析方法去除原始输入数据的相关性,降低数据维度,减小网络规模,选择合适的隐含层的BP神经网络。最后通过结合实例进行分析,取得较好的效果。     

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.     

Efficient estimation of factor models with time and cross‐sectional dependence

This paper studies the efficient estimation of large‐dimensional factor models with both time and cross‐sectional dependence assuming (N,T) separability of the covariance matrix. The asymptotic distribution of the estimator of the factor and factor‐loading space under factor stationarity is derived and compared to that of the principal component (PC) estimator. The paper also considers the case when factors exhibit a unit root. We provide feasible estimators and show in a simulation study that they are more efficient than the PC estimator in finite samples. In application, the estimation procedure is employed to estimate the Lee–Carter model and life expectancy is forecast. The Dutch gender gap is explored and the relationship between life expectancy and the level of economic development is examined in a cross‐country comparison.     

Cohort and target age effects on subjective survival probabilities: Implications for models of the retirement phase

Subjective survival scaling factors are often estimated from one observation of life expectancy and treated as constant to any target age. Using new survey data on subjective survival probabilities, we estimate a model incorporating cohort- and target age-varying beliefs in scaling factors. Both cohort age and target age matter: respondents are pessimistic about overall life expectancy but optimistic about survival at advanced ages, and older respondents are more optimistic than younger. We propose a new theoretical model incorporating cohort- and target age-varying beliefs and illustrate their effects on the perceived value of annuities and on retirement phase consumption plans.     

The natural resource curse and economic transition

Using cross-country regressions, we examine the relationship between “point-source” resource abundance and economic growth, quality of institutions, investment in human and physical capital, and social welfare (life expectancy and infant mortality) for all countries and for the economies in transition. Contrary to most literature, we find little evidence of a natural resource curse for all countries. Only the “voice and accountability” measure of institutional quality is negatively and significantly affected by oil wealth. In the economies in transition, there is some evidence that natural resource wealth is associated with lower primary school enrollment and life expectancy and higher infant mortality compared to other resource rich countries. Compared to other economies in transition, however, natural resource abundant transitional economies are not significantly worse off with respect to our indicators.     

Selecting stochastic mortality models for the Italian population

The future revision of capital requirements and a market-consistent valuation of non-hedgeable liabilities lead to an increasing attention on forecasting longevity trends. In this field, many methodologies focus on either modeling mortality or pricing mortality-linked securities (as longevity bonds). Following Lee–Carter method (proposed in 1992), actuarial literature has provided several extensions in order to consider different trends observed in European data set (e.g., the cohort effect). The purpose of the paper is to compare the features of main mortality models proposed over the years. Model selection became indeed a primary task with the aim to identify the “best” model. What is meant by best is controversial, but good selection techniques are usually based on a good balance between goodness of fit and simplicity. In this regard, different criteria, mainly based on residual and projected rates analysis, are here used. For the sake of comparison, main forecasting methods have been applied to deaths and exposures to risk of male Italian population. Weaknesses and strengths have been emphasized, by underlying how various models provide a different goodness of fit according to different data sets. At the same time, the quality and the variability of forecasted rates have been compared by evaluating the effect on annuity values. Results confirm that some models perform better than others, but no single model can be defined as the best method.     

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.     

Physics-informed Gaussian process regression for states estimation and forecasting in power grids

Real-time state estimation and forecasting are critical for the efficient operation of power grids. In this paper, a physics-informed Gaussian process regression (PhI-GPR) method is presented and used for forecasting and estimating the phase angle, angular speed, and wind mechanical power of a three-generator power grid system using sparse measurements. In standard data-driven Gaussian process regression (GPR), parameterized models for the prior statistics are fit by maximizing the marginal likelihood of observed data. In the PhI-GPR method, we propose to compute the prior statistics offline by solving stochastic differential equations (SDEs) governing the power grid dynamics. The short-term forecast of a power grid system dominated by wind generation is complicated by the stochastic nature of the wind and the resulting uncertainty in wind mechanical power. Here, we assume that the power grid dynamics are governed by swing equations, with the wind mechanical power fluctuating randomly in time. We solve these equations for the mean and covariances of the power grid states using the Monte Carlo simulation method.We demonstrate that the proposed PhI-GPR method can accurately forecast and estimate observed and unobserved states. For the considered problem, PhI-GPR has computational advantages over the ensemble Kalman filter (EnKF) method: In PhI-GPR, ensembles are computed offline and independently of the data acquisition process, whereas for EnFK, ensembles are computed online with data acquisition, rendering real-time forecast more challenging. We also demonstrate that the PhI-GPR forecast is more accurate than the EnKF forecast when the random mechanical wind power is non-Markovian. In contrast, the two methods produce similar forecasts for the Markovian mechanical wind power.For observed states, we show that PhI-GPR provides a forecast comparable to the standard data-driven GPR; both forecasts are significantly more accurate than the autoregressive integrated moving average (ARIMA) forecast. We also show that the ARIMA forecast is more sensitive to observation frequency and measurement errors than the PhI-GPR forecast.     

The evolution of the disability-adjusted life year (DALY)

The disability-adjusted life year (DALY) is a summary health measure that combines mortality and morbidity into a single measure as a way to estimate global disease burden and the effectiveness of health interventions. We review the methodological progression of the DALY, focusing on how the use of life expectancy estimates, disability weights, age weighting, and discounting has evolved since the first DALY reports were published in 1993. These changes have generally improved the metric but have made it difficult for researchers to interpret, compare, and conduct DALY studies.