Probabilistic projection of subnational total fertility rates

BACKGROUND

We consider the problem of probabilistic projection of the total fertility rate (TFR) for subnational regions.

OBJECTIVE

We seek a method that is consistent with the UN’s recently adopted Bayesian method for probabilistic TFR projections for all countries and works well for all countries.

METHODS

We assess various possible methods using subnational TFR data for 47 countries.

RESULTS

We find that the method that performs best in terms of out-of-sample predictive performance and also in terms of reproducing the within-country correlation in TFR is a method that scales each national trajectory from the national predictive posterior distribution by a region-specific scale factor that is allowed to vary slowly over time.

CONCLUSIONS

Probabilistic projections of TFR for subnational units are best produced by scaling the national projection by a slowly time-varying region-specific scale factor. This supports the hypothesis of Watkins (1990, 1991) that within-country TFR converges over time in response to country-specific factors, and thus extends the Watkins hypothesis to the last 50 years and to a much wider range of countries around the world.

CONTRIBUTION

We have developed a new method for probabilistic projection of subnational TFR that works well and outperforms other methods. This also sheds light on the extent to which within-country TFR converges over time.

Contemporary Developments in Applied Demography within the United States

Changes in technology and methodological developments have significantly changed the field of applied demography in the U.S. over the last decade. These have been accompanied by alterations in perceptions of how the demographic perspective contributes to addressing public and private sector issues. This paper focuses on contemporary developments with the goal of identifying areas of future direction. Following a brief history of applied demography, recent developments are placed into five categories: training, including programs; courses and course materials; institutional structures such as the Population Association of America, the Southern Demographic Association and funding agencies; career opportunities in government, educational institutions and the private sector; technological developments in communication and data storage and retrieval; and methodological developments, such as GIS, that allow researchers to extract additional information from data. These developments provide an overall picture of applied demography in the U.S. early in the twenty-first century and provide ideas about the state of the art in applied demography in the near future.

Forecast Accuracy and Uncertainty of Australian Bureau of Statistics State and Territory Population Projections

Errors from past rounds of population projections can provide both diagnostic information to improve future projections as well as information for users on the likely uncertainty of current projections. This paper assesses the forecast accuracy of official Australian Bureau of Statistics (ABS) population projections for the states and territories of Australia and is the first major study to do so. For the states and territories, it is found that, after 10-year projection durations, absolute percentage errors lie between about 1% and 3% for the states and around 6% for the territories. Age-specific population projections are also assessed. It is shown that net interstate migration and net overseas migration are the demographic components of change which contributed most to forecast error. The paper also compares ABS projections of total population against simple linear extrapolation, finding that, overall, ABS projections just outperformed extrapolation. No identifiable trend in accuracy over time is detected. Under the assumption of temporal stability in the magnitude of error, empirical prediction intervals are created from past errors and applied to the current set of ABS projections. The paper concludes with a few ideas for future projection rounds.

More on the cohort-component model of population projection in the context of HIV/AIDS: A Leslie matrix representation and new estimates

This article presents an extension of the cohort-component model of population projection (CCMPP) first formulated by Heuveline (2003) that is capable of modeling a population affected by HIV. Heuveline proposes a maximum likelihood approach to estimate the age profile of HIV incidence that produced the HIV epidemics in East Africa during the 1990s. We extend this work by developing the Leslie matrix representation of the CCMPP, which greatly facilitates the implementation of the model for parameter estimation and projection. The Leslie matrix also contains information about the stable tendencies of the corresponding population, such as the stable age distribution and time to stability. Another contribution of this work is that we update the sources of data used to estimate the parameters, and use these data to estimate a modified version of the CCMPP that includes (estimated) parameters governing the survival experience of the infected population. A further application of the model to a small population with high HIV prevalence in rural South Africa is presented as an additional demonstration. This work lays the foundation for development of more robust and flexible Bayesian estimation methods that will greatly enhance the utility of this and similar models.

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.

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.

An evaluation of population projections by age

A number of studies have evaluated the accuracy of projections of the size of the total population, but few have considered the accuracy of projections by age group. For many purposes, however, the relevant variable is the population of a particular age group, rather than the population as a whole. We investigated the precision and bias of a variety of age-group projections at the national and state levels in the United States and for counties in Florida. We also compared the accuracy of state and county projections that were derived from full-blown applications of the cohort-component method with the accuracy of projections that were derived from a simpler, less data-intensive version of the method. We found that age-group error patterns are different for national projections than for subnational projections; that errors are substantially larger for some age groups than for others; that differences in errors among age groups decline as the projection horizon becomes longer; and that differences in methodological complexity have no consistent impact on the precision and bias of age-group projections.

A note on the measurement of accuracy for subnational demographic estimates

Mean absolute percentage error (MAPE), the measure most often used for evaluating subnational demographic estimates, is not always valid. We describe guidelines for determining when MAPE is valid. Applying them to case study data, we find that MAPE understates accuracy because it is unduly influenced by outliers. To overcome this problem, we calculate a transformed MAPE (MAPET) using a modified Box-Cox method. Because MAPE-T is not in the same scale as the untransformed absolute percentage errors, we provide a procedure for calculating MAPE-R, a measure in the same scale as the original observations. We argue that MAPE-R is a more appropriate summary measure of average absolute percentage error when the guidelines indicate that MAPE is not valid.

An evaluation of population projection errors for census tracts

"In this article we evaluate the accuracy and bias of projections of total population and population by age group for census tracts in three counties in Florida. We use [U.S. census] data from 1970 and 1980 and several simple extrapolation techniques to produce projections for 1990; we then compare these projections with 1990 census counts and evaluate the differences. For the total sample, we find mean absolute errors of 17%-20% for the three most accurate techniques for projecting total population and find no indication of overall bias. For individual age groups, mean absolute errors range from 20%-29%." This is a revised version of a paper presented at the 1993 Annual Meeting of the Population Association of America.

Evaluating the forecast accuracy and bias of alternative population projections for states

"A common perception among producers (and users) of population projections is that complex and/or sophisticated techniques produce more accurate forecasts than simple and/or naive techniques. In this paper we test the validity of that perception by evaluating the forecast accuracy and bias of eight commonly used projection techniques drawn from...four categories [trend extrapolation, ratio extrapolation, cohort-component, and structural]. Using data for [U.S.] state population projections from a number of different time periods, we find no evidence that complex and/or sophisticated techniques produce more accurate or less biased forecasts than simple, naive techniques."

An Empirical Analysis of the Effect of Length of Forecast Horizon on Population Forecast Errors

Many studies have found that population forecast errors generally increase with the length of the forecast horizon, but none have examined this relationship in detail. Do errors grow linearly, exponentially, or in some other manner as the forecast horizon becomes longer? Does the error-horizon relationship differ by forecasting technique, launch year, size of place, or rate of growth? Do alternative measures of error make a difference? In this article we address these questions using two simple forecasting techniques and population data from 1900 to 1980 for states in the United States. We find that in most instances there is a linear or nearly linear relationship between forecast accuracy and the length of the forecast horizon, but no consistent relationship between bias and the length of the horizon. We believe that these results provide useful information regarding the nature of population forecast errors.

The relationship between the length of the base period and population forecast errors

"The base period of a population forecast is the time period from which historical data are collected for the purpose of forecasting future population values. The length of the base period is one of the fundamental decisions made in preparing population forecasts, yet very few studies have investigated the effects of this decision on population forecast errors. In this article the relationship between the length of the base period and population forecast errors is analyzed, using three simple forecasting techniques and data from 1900 to 1980 for states in the United States. It is found that increasing the length of the base period up to 10 years improves forecast accuracy, but that further increases generally have little additional effect. The only exception to this finding is long-range forecasts of rapidly growing states, in which a longer base period substantially improves forecast accuracy for two of the forecasting techniques."