Empirical Prediction Intervals for County Population Forecasts

Population forecasts entail a significant amount of uncertainty, especially for long-range horizons and for places with small or rapidly changing populations. This uncertainty can be dealt with by presenting a range of projections or by developing statistical prediction intervals. The latter can be based on models that incorporate the stochastic nature of the forecasting process, on empirical analyses of past forecast errors, or on a combination of the two. In this article, we develop and test prediction intervals based on empirical analyses of past forecast errors for counties in the United States. Using decennial census data from 1900 to 2000, we apply trend extrapolation techniques to develop a set of county population forecasts; calculate forecast errors by comparing forecasts to subsequent census counts; and use the distribution of errors to construct empirical prediction intervals. We find that empirically-based prediction intervals provide reasonably accurate predictions of the precision of population forecasts, but provide little guidance regarding their tendency to be too high or too low. We believe the construction of empirically-based prediction intervals will help users of small-area population forecasts measure and evaluate the uncertainty inherent in population forecasts and plan more effectively for the future.     

MAPE-R: a rescaled measure of accuracy for cross-sectional subnational population forecasts

Accurately measuring a population and its attributes at past, present, and future points in time has been of great interest to demographers. Within discussions of forecast accuracy, demographers have often been criticized for their inaccurate prognostications of the future. Discussions of methods and data are usually at the centre of these criticisms, along with suggestions for providing an idea of forecast uncertainty. The measures used to evaluate the accuracy of forecasts also have received attention and while accuracy is not the only criterion advocated for evaluating demographic forecasts, it is generally acknowledged to be the most important. In this paper, we continue the discussion of measures of forecast accuracy by concentrating on a rescaled version of a measure that is arguably the one used most often in evaluating cross-sectional, subnational forecasts, Mean Absolute Percent Error (MAPE). The rescaled version, MAPE-R, has not had the benefit of a major empirical test, which is the central focus of this paper. We do this by comparing 10-year population forecasts for U.S. counties to 2000 census counts. We find that the MAPE-R offers a significantly more meaningful representation of average error than MAPE in the presence of substantial outlying errors, and we provide guidelines for its implementation.     

Modeling and forecasting populations by time series: The Swedish case

Time series analysis techniques are used to model and to forecast populations. An autoregressive (AR) and a moving average (MA) model, which seem to fit the population of Sweden very well, are found. Forecasts are calculated using both models and are compared with the forecasts obtained by other methods. This comparison is very favorable for the time series models. Although our study is confined to the mid-year population of Sweden, there are good reasons to expect that the technique can be successfully applied to other population parameters.     

Assessing Uncertainty in Small Area Forecasts: State of the Practice and Implementation Strategy

Forecasts are needed for everyday decisions and must be in the form of numbers. Yet forecasts invariably turn out to be different than the numbers that actually occur. Yet, most producers of forecasts only present a deterministic view of the future in the form of point predictions. However, the presence of uncertainty is inherent in management or policy decisions and there is often concern that benefits are overstated and risks are understated. Such concerns are difficult to address by providing only point forecasts with no assessment of their uncertainty. Having a better understanding of uncertainty can enhance the usefulness of forecasts and make the work of forecasting agencies an even more valuable product for planners, policy makers, and the public. The purpose of this paper is twofold. First, it presents an overview of the current state-of-the-practice is assessing forecast uncertainty. Second, it offers a guidelines and options for implementing and building uncertainty into small area forecasting processes. There are options for assessing forecasting uncertainty that can and should be implemented by most, if not all, producers of forecasts.     

Facing up to uncertain life expectancy: The longevity fan charts

This article uses longevity fan charts to represent the uncertainty in projections of future life expectancy. These fan charts are based on a mortality model calibrated on mortality data for English and Welsh males. The fan charts indicate strong upward sloping trends in future life expectancy. Their widths indicate the extent of uncertainty in these projections, and this uncertainty increases as the forecast horizon lengthens. Allowing for uncertainty in the parameter values of the model adds further to uncertainty in life expectancy projections. The article also illustrates how longevity fan charts can be used to stress-test longevity outcomes.     

Precision,bias, and uncertainty for state population forecasts: an exploratory analysis of time series models

Many researchers have used time series models to construct population forecasts and prediction intervals at the national level, but few have evaluated the accuracy of their forecasts or the out-of-sample validity of their prediction intervals. Fewer still have developed models for subnational areas. In this study, we develop and evaluate six ARIMA time series models for states in the United States. Using annual population estimates from 1900 to 2000 and a variety of launch years, base periods, and forecast horizons, we construct population forecasts for four states chosen to reflect a range of population size and growth rate characteristics. We compare these forecasts with population counts for the corresponding years and find precision, bias, and the width of prediction intervals to vary by state, launch year, model specification, base period, and forecast horizon. Furthermore, we find that prediction intervals based on some ARIMA models provide relatively accurate forecasts of the distribution of future population counts but prediction intervals based on other models do not. We conclude that there is some basis for optimism regarding the possibility that ARIMA models might be able to produce realistic prediction intervals to accompany population forecasts, but a great deal of work remains to be done before we can draw any firm conclusions.     

Insights from the Evaluation of Past Local Area Population Forecasts

Local area population forecasts have a wide variety of uses in the public and private sectors. But not enough is known about the errors of such forecasts, particularly over the longer term (20 years or more). Understanding past errors is valuable for both forecast producers and users. This paper (i) evaluates the forecast accuracy of past local area population forecasts published by Australian State and Territory Governments over the last 30 years and (ii) illustrates the ways in which past error distributions can be employed to quantify the uncertainty of current forecasts. Population forecasts from the past 30 years were sourced from State and Territory Governments. Estimated resident populations to which the projections were compared were created for the geographical regions of the past projections. The key features of past forecast error patterns are described. Forecast errors mostly confirm earlier findings with regard to the relationship between error and length of projection horizon and population size. The paper then introduces the concept of a forecast ‘shelf life’, which indicates how far into the future a forecast is likely to remain reliable. It also illustrates how past error distributions can be used to create empirical prediction intervals for current forecasts. These two complementary measures provide a simple way of communicating the likely magnitude of error that can be expected with current local area population forecasts.     

Evaluating Population Forecast Accuracy: A Regression Approach Using County Data

Many studies have evaluated the impact of differences in population size and growth rate on population forecast accuracy. Virtually all these studies have been based on aggregate data; that is, they focused on average errors for places with particular size or growth rate characteristics. In this study, we take a different approach by investigating forecast accuracy using regression models based on data for individual places. Using decennial census data from 1900 to 2000 for 2,482 counties in the US, we construct a large number of county population forecasts and calculate forecast errors for 10- and 20-year horizons. Then, we develop and evaluate several alternative functional forms of regression models relating population size and growth rate to forecast accuracy; investigate the impact of adding several other explanatory variables; and estimate the relative contributions of each variable to the discriminatory power of the models. Our results confirm several findings reported in previous studies but uncover several new findings as well. We believe regression models based on data for individual places provide powerful but under-utilized tools for investigating the determinants of population forecast accuracy.     

Modeling and Forecasting Health Expectancy: Theoretical Framework and Application

Life expectancy continues to grow in most Western countries; however, a major remaining question is whether longer life expectancy will be associated with more or fewer life years spent with poor health. Therefore, complementing forecasts of life expectancy with forecasts of health expectancies is useful. To forecast health expectancy, an extension of the stochastic extrapolative models developed for forecasting total life expectancy could be applied, but instead of projecting total mortality and using regular life tables, one could project transition probabilities between health states simultaneously and use multistate life table methods. In this article, we present a theoretical framework for a multistate life table model in which the transition probabilities depend on age and calendar time. The goal of our study is to describe a model that projects transition probabilities by the Lee-Carter method, and to illustrate how it can be used to forecast future health expectancy with prediction intervals around the estimates. We applied the method to data on the Dutch population aged 55 and older, and projected transition probabilities until 2030 to obtain forecasts of life expectancy, disability-free life expectancy, and probability of compression of disability.     

Coherent Mortality Forecasting: The Product-Ratio Method With Functional Time Series Models

When independence is assumed, forecasts of mortality for subpopulations are almost always divergent in the long term. We propose a method for coherent forecasting of mortality rates for two or more subpopulations, based on functional principal components models of simple and interpretable functions of rates. The product-ratio functional forecasting method models and forecasts the geometric mean of subpopulation rates and the ratio of subpopulation rates to product rates. Coherence is imposed by constraining the forecast ratio function through stationary time series models. The method is applied to sex-specific data for Sweden and state-specific data for Australia. Based on out-of-sample forecasts, the coherent forecasts are at least as accurate in overall terms as comparable independent forecasts, and forecast accuracy is homogenized across subpopulations.     

Risk, uncertainty and family formation: The social context of poverty groups

Abstract Despite the assumptions of many demographers that the net returns from children for non-elite groups in underdeveloped areas are likely to be negative, high fertility persists in most of these societies. Both cultural and institutional explanations have been proposed to account for this. We attempt to provide some mediation between these competing models, by introducing the elements of risk and uncertainty as factors likely to induce poverty and lead works to opt for the 'high fertility, low quality' pattern of investment of time and money in family formation. Drawing upon the work of Wharton in subsistence agriculture practices, several alternative decision-making models are proposed to account for both the persistence of high fertility, and the declines that have been registered in selected areas, such as Taiwan and perhaps China. The empirical work of Mueller on Taiwanese expectations of returns on children and the concomitant variation in family-size preferences is consistent with the models proposed. Some implications for uncertainty and risk-reduction strategies in family planning and other social welfare programmes are drawn.     

中国人口时间序列预测模型的探讨

以 1 95 2～ 2 0 0 2年人口序列数据为基础 ,构建了中国人口时间序列预测模型 ,采用一般回归法、后退法和逐步回归法三种方法对所设计的模型进行估计 ,得到 72个模型。然后 ,从中筛选出估计标准误较小 ,自相关影响基本消除的预测模型。作为中国人口总量的预测模型 ,我们提出的预测模型有估计精度高 ,误差低的特点 ,是目前用自回归方法估计得出的较好的中国人口预测模型。     

A multi-level,bipolar view of the urban residential environment: Local community vs. mass societal forces

A multidisciplinary review of the urban literature reveals that theory can be ranged along two bipolar continua—individual vs. aggregate levels of analysis and equilibrium vs. conflict models of behavior. Research employed such bipolar conceptualizations to examine the persistence or deterioration of local community structure in a contemporary urban environment. A two-year ethnographic community study was conducted in Syracuse, New York and Onondaga County. Also examined were program processes of an experimental program designed to enhance neighborhood organization and social networks of 157 families living in ten randomly selected neighborhoods. Data collection methods included participant observation supplemented by archival research and in-depth interviews with community leaders. It was found that both bipolar models were necessary to illuminate processes at work within a city experiencing a sharp decline in population and in economic activity. Three coping strategies employed by city institutions to counter this decline were distinguished, but it was observed that often such strategies led to disruption of residential neighborhoods. We concluded that while local community structure remains in some neighborhoods, conflict between residential and nonresidential interests poses an ever more serious threat.     

Statistically tested comparisons of the accuracy of forecasting methods for age-specific and sex-specific mortality and life expectancy

Although there are continuing developments in the methods for forecasting mortality, there are few comparisons of the accuracy of the forecasts. The subject of the statistical validity of these comparisons, which is essential to demographic forecasting, has all but been ignored. We introduce Friedman's test statistics to examine whether the differences in point and interval forecast accuracies are statistically significant between methods. We introduce the Nemenyi test statistic to identify which methods give results that are statistically significantly different from others. Using sex-specific and age-specific data from 20 countries, we apply these two test statistics to examine the forecast accuracy obtained from several principal component methods, which can be categorized into coherent and non-coherent forecasting methods.     

The role of population size in the determination and prediction of population forecast errors: An evaluation using conifidence intervals for subcounty areas

Producers of population forecasts acknowledge the uncertainty inherent in trying to predict the future and should warn about the likely error of their forecasts. Confidence intervals represent one way of quantifying population forecast error. Most of the work in this area relates to national forecasts; although, confidence intervals have been developed for state and county forecasts. A few studies have examined subcounty forecast error, however, they only measured point estimates of error. This paper describes a technique for making subcounty population forecasts and for generating confidence intervals around their forecast error. It also develops statistical equations for calculating point estimates and confidence intervals for areas with different population sizes. A non-linear, inverse relationship between population size and forecast accuracy was found and we demonstrate the ability to accurately predict average forecast error and confidence intervals based on this relationship.     

On the utility of population forecasts

Many customers demand population forecasts, particularly for small areas. Although the forecast evaluation literature is extensive, it is dominated by a focus on accuracy. We go beyond accuracy by examining the concept of forecast utility in an evaluation of a sample of 2,709 counties and census tracts. Wefind that forecasters provide “value-added” knowledge for areas experiencing rapid change or areas with relatively large populations. For other areas, reduced value is more common than added value. Our results suggest that new forecasting strategies and methods such as composite modeling may substantially improve forecast utility.     

Bayesian demography 250 years after Bayes

Bayesian statistics offers an alternative to classical (frequentist) statistics. It is distinguished by its use of probability distributions to describe uncertain quantities, which leads to elegant solutions to many difficult statistical problems. Although Bayesian demography, like Bayesian statistics more generally, is around 250?years old, only recently has it begun to flourish. The aim of this paper is to review the achievements of Bayesian demography, address some misconceptions, and make the case for wider use of Bayesian methods in population studies. We focus on three applications: demographic forecasts, limited data, and highly structured or complex models. The key advantages of Bayesian methods are the ability to integrate information from multiple sources and to describe uncertainty coherently. Bayesian methods also allow for including additional (prior) information next to the data sample. As such, Bayesian approaches are complementary to many traditional methods, which can be productively re-expressed in Bayesian terms.     

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。     

Interrelated family-building behaviors: Cohabitation, marriage, and nonmarital conception

Data from the National Longitudinal Study of the High School Class of 1972 are used to estimate a series of models of entry into marriage, entry into cohabitation, and nonmarital pregnancy. Our models account explicitly for the endogeneity of one outcome as a predictor of another by taking into account both heterogeneity across individuals due to unmeasured factors that may affect all these outcomes and the correlation in the unmeasured factors across processes. We find that these heterogeneity components are strongly and positively related across the outcomes. Women who are more likely to cohabit, marry, or become pregnant while unmarried are also more likely to do each of the others. Although black and white women differ in the likelihood of these behaviors, the interrelations of the behaviors are quite similar across groups.     

Using Mokken methods to develop robust cross-national scales: American and West German attitudes toward abortion

A fundamental methodological issue in cross-national research on attitudes is the comparability of the attitude measures across populations. We address this issue by presenting the Mokken method and accompanying Mokken test as a means for developing equivalent attitude scales. We apply these methods to an analysis of the responses to seven abortion items in the 1982 NORC GSS and West German ALLBUS combined files. We find that the seven items form a unidimensional scale in both countries and that four of these items constitute a scale that is robust across the two populations. We conclude by describing how such results can be used to guide the development of Rasch and LISREL models.