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The United Nations regularly publishes projections of the populations of all the world's countries broken down by age and sex. These projections are the de facto standard and are widely used by international organizations, governments and researchers. Like almost all other population projections, they are produced using the standard deterministic cohortcomponent projection method and do not yield statements of uncertainty. We describe a Bayesian method for producing probabilistic population projections for most countries which are projections that the United Nations could use. It has at its core Bayesian hierarchical models for the total fertility rate and life expectancy at birth. We illustrate the method and show how it can be extended to address concerns about the UN's current assumptions about the long-term distribution of fertility. The method is implemented in the R packages bayesTFR, bayesLife, bayesPop and bayesDem.

In 2015, the United Nations (UN) issued probabilistic population projections for all countries up to 2100, by simulating future levels of total fertility and life expectancy and combining the results using a standard cohort component projection method. For the 40 countries with generalized HIV/AIDS epidemics, the mortality projections used the Spectrum/Estimation and Projection Package (EPP) model, a complex, multistate model designed for short-term projections of policy-relevant quantities for the epidemic. We propose a simpler approach that is more compatible with existing UN projection methods for other countries. Changes in life expectancy are projected probabilistically using a simple time series regression and then converted to age- and sex-specific mortality rates using model life tables designed for countries with HIV/AIDS epidemics. These are then input to the cohort component method, as for other countries. The method performed well in an out-of-sample cross-validation experiment. It gives similar short-run projections to Spectrum/EPP, while being simpler and avoiding multistate modelling.

Population projections provide predictions of future population sizes for an area. Historically, most population projections have been produced using deterministic or scenario-based approaches and have not assessed uncertainty about future population change. Starting in 2015, however, the United Nations (UN) has produced probabilistic population projections for all countries using a Bayesian approach. There is also considerable interest in subnational probabilistic population projections, but the UN's national approach cannot be used directly for this purpose, because within-country correlations in fertility and mortality are generally larger than between-country ones, migration is not constrained in the same way, and there is a need to account for college and other special populations, particularly at the county level. We propose a Bayesian method for producing subnational population projections, including migration and accounting for college populations, by building on but modifying the UN approach. We illustrate our approach by applying it to the counties of Washington State and comparing the results with extant deterministic projections produced by Washington State demographers. Out-of-sample experiments show that our method gives accurate and well-calibrated forecasts and forecast intervals. In most cases, our intervals were narrower than the growth-based intervals issued by the state, particularly for shorter time horizons.

Accurate estimates of subnational populations are important for policy formulation and monitoring population health indicators. For example, estimates of the number of women of reproductive age are important to understand the population at risk of maternal mortality and unmet need for contraception. However, in many low-income countries, data on population counts and components of population change are limited, and so subnational levels and trends are unclear. We present a Bayesian constrained cohort component model for the estimation and projection of subnational populations. The model builds on a cohort component projection framework, incorporates census data and estimates from the United Nation's World Population Prospects, and uses characteristic mortality schedules to obtain estimates of population counts and the components of population change, including internal migration. The data required as inputs to the model are minimal and available across a wide range of countries, including most low-income countries. The model is applied to estimate and project populations by county in Kenya for 1979–2019 and is validated against the 2019 Kenyan census.

This article presents the core methodological ideas and empirical assessments of an extended cohort-component approach (known as the \"ProFamy model\"), and applications to simultaneously project household composition, living arrangements, and population sizes-gender structures at the subnational level in the United States. Comparisons of projections from 1990 to 2000 using this approach with census counts in 2000 for each of the 50 states and Washington, DC show that 68.0 %, 17.0 %, 11.2 %, and 3.8 % of the absolute percentage errors are <3.0%, 3.0% to 4.99 %, 5.0 % to 9.99 %, and > 10.0 %, respectively. Another analysis compares average forecast errors between the extended cohort-component approach and the still widely used classic headshiprate method, by projecting number-of-bedrooms-specific housing demands from 1990 to 2000 and then comparing those projections with census counts in 2000 for each of the 50 states and Washington, DC. The results demonstrate that, compared with the extended cohort-component approach, the headship-rate method produces substantially more serious forecast errors because it cannot project households by size while the extended cohort-component approach projects detailed household sizes. We also present illustrative household and living arrangement projections for the five decades from 2000 to 2050, with medium-, small-, and large-family scenarios for each of the 50 states; Washington, DC; six counties of southern California; and the Minneapolis-St. Paul metropolitan area. Among many interesting numerical outcomes of household and living arrangement projections with medium, low, and high bounds, the aging of American households over the next few decades across all states/areas is particularly striking. Finally, the limitations of the present study and potential future lines of research are discussed.

Population projections commonly suffer from a decreasing accuracy with a higher degree of disaggregation. We suggest combining the cohort-component model and an averaged projection technique to improve precision of forecasts for small areas. Calculating ex-post population projections, we evaluate the precision and bias of the proposed method by contrasting error patterns of commonly used techniques using official population data from 46 districts of a German state for the years 1980-2013. In comparison to the individual methods considered, the combined approach results in the highest accuracy and lowest bias both for the total population and for age groups. The proposed method is also more robust regarding past growth.

Success in producing a population projection predominately depends on the accuracy of its migration rates. In developing an interregional, cohort-component projection methodology for the U.S. city of Boston, Massachusetts, we created an innovative approach for producing domestic migration rates with synthetic populations using 1-year, American Community Survey (ACS), and Public Use Microdata Samples (PUMS). Domestic in- and out-migration rates for Boston used 2007–2014 ACS data and developed synthetic Boston and United States populations to serve as denominators for calculating these rates. To assess the reliability of these rates, we compared the means and standard deviations of eight years of these rates (2007–2014) with synthetic populations by single-year ages for females and males to rates produced from two ACS samples using the same migration data in the numerator but the prior year’s age data in the denominator. We also compared results of population projections for 2015 using these different migration rates to several 2015 U.S. Census Bureau population estimates for Boston. Results suggested our preferred rates with synthetic populations using one ACS sample for each year’s migration rates were more efficient than alternative rates using two ACS samples. Projections using these rates with synthetic populations more accurately projected Boston’s 2015 population than an alternative model with rates using the prior year’s age data.

Population projection for many developing countries could be quite a challenging task for the demographers mostly due to lack of availability of enough reliable data. The objective of this paper is to present an overview of the existing methods for population forecasting and to propose an alternative based on the Bayesian statistics, combining the formality of inference. The analysis has been made using Markov Chain Monte Carlo (MCMC) technique for Bayesian methodology available with the software WinBUGS. Convergence diagnostic techniques available with the WinBUGS software have been applied to ensure the convergence of the chains necessary for the implementation of MCMC. The Bayesian approach allows for the use of observed data and expert judgements by means of appropriate priors, and a more realistic population forecasts, along with associated uncertainty, has been possible.

Projecting populations that have sparse or unreliable data, such as those of many developing countries, presents a challenge to demographers. The assumptions that they make to project data-poor populations frequently fall into the realm of \"educated guesses,\" and the resulting projections, often regarded as forecasts, are valid only to the extent that the assumptions on which they are based reasonably represent the past or future, as the case may be. These traditional projection techniques do not incorporate a demographer's assessment of uncertainty in the assumptions. Addressing the challenges of forecasting a data-poor population, we project the Iraqi Kurdish population using a Bayesian approach. This approach incorporates a demographer's uncertainty about past and future characteristics of the population in the form of elicited prior distributions.

Three widely used classes of methods for forecasting national populations are reviewed: demographic accounting/cohort-component methods for long-range projections, statistical time series methods for short-range forecasts, and structural modeling methods for the simulation and forecasting of the effects of policy changes. In each case, the major characteristics, strengths, and weaknesses of the methods are described. Factors that place intrinsic limits on the accuracy of population forecasts are articulated. Promising lines of additional research by statisticians and demographers are identified for each class of methods and for population forecasting generally.