Beyond Six Billion Forecasting the World's Population (2000) / Chapter Skim
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The Uncertainty of Population Forecasts
The Uncertainty of Population Forecasts
Pages 188-217
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From page 188... ...
Users of population projections should be aware of their substantial uncertainty and should not use them without taking this into account. This chapter discusses conceptual issues surrounding forecast uncertainty, considers methods for assessing it, and presents new research to attach probability distributions to U.N.
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From page 189... ...
These estimates might be based on measures of food consumption, carbon dioxide emissions, or energy use. Assuming these estimates remain constant or change in a particular pattern, the analyst could then combine them with the predictive distributions of the population size of each aggregate.
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From page 190... ...
, we review it in some detail. Constructing Scenarios In using the scenario approach to bracket future values, the analyst usually begins by formulating high, medium, and low trajectories for the demographic components: fertility, mortality, and migration.
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From page 191... ...
The Census Bureau scenarios provide a broad range for future population size and growth rates, but a narrow range for the old age dependency ratio. The Social Security Administration scenarios provide a broad range for the old age dependency ratio, but a narrow range for population size and growth rates.
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From page 192... ...
Even if such fluctuations stay within the bounds defined by the high and low scenarios, other demographic parameters (such as the proportion of the population of a given age or particular dependency ratios) may be affected much more and could exceed the levels defined in these scenarios.
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From page 193... ...
This shows that equivalent high-low variants for regions and for the world do not define bounds that have equal probability coverage. The probability coverage of equivalent high-low variants for countries would presumably be still different.
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Old age dependency ratio (20-64/65+) +26% +27% +3% THINKING ABOUT FORECAST ERRORS One view about forecast errors is that they arise largely from limited understanding of the forces governing demographic processes and can be substantially reduced as the knowledge base grows.
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From page 195... ...
Characterizing Errors Through Predictive Distributions We may think of future demographic outcomes as random variables having a probability distribution, which we call a "predictive distribution." The middle forecast (point forecast) is the mean or the median of this distribution, and, given the distribution, the boundaries of a 95-percent probability interval (or any other desired probability interval)
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From page 196... ...
Typically, a much narrower range will have to be chosen for each variable in order to get the desired probability coverage for their joint effect. This type of consideration applies strongly when we make forecasts for groups of countries, and it is essential to study the correlations of forecast errors across the countries in the group.
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From page 197... ...
Error correlations across regions and over time must therefore be considered for fertility, for mortality, and for migration, and the correlations among these components must also be considered. In addition, we must consider the correlations across age and sex for forecast errors in fertility, mortality, and migration.
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From page 198... ...
Correlations of Errors in Vital Rates Errors in vital rates may be correlated for various reasons. First, in developing countries, factors related to economic and social develop2A growing literature provides estimates of the correlations in forecast errors of vital rates across time, age, and sex (e.g., Alho, 1998~.
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From page 199... ...
, and negative correlations also appear for the former Soviet Union and Latin America. On the other hand, a substantial positive correlation appears for
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At any rate, these estimates provide some information necessary to begin to construct consistent probability distributions for U.N. forecasts.
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While the time-series models could then directly produce forecasts with probability intervals of the vital rates, the proper procedure to produce the predictive distribution would be to take the additional step of stochastic simulation (Monte Carlo methods)
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From page 202... ...
and about the correlations of forecast errors over age, sex, and time and among fertility, mortality, and migration. Given the expert judgments and such assumptions, one could use stochastic simulation to calculate prediction intervals for parameters of interest (Tornqvist, 1949; Keyfitz, 1981; Pflaumer, 1988~.
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From page 203... ...
Ex Post Analysis Another approach to producing predictive distributions is to base them on the accuracy of past forecasts. The distribution of past errors can be used as the basis for assigning probability distributions to the errors of current forecasts (Keyfitz, 1981; Stoto, 1983~.
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A naive forecast that keeps population growth rates constant would have had about a third more error than U.N. and World Bank country projections, but about nine times more error than these agencies' world projections (see Appendix B)
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and World Bank forecasts, as analyzed in Appendix B another, fertility starts below the medium projection, then rises above it to 2.3, falls again, and then rises to 2.6 in 2040-2045.
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From page 206... ...
The model, and therefore the estimated prediction intervals, reflect past errors. This is basic to the ex post approach and as we have argued also implies a basic limitation, since neither future forecasts nor future demographic trends can be expected to exactly duplicate the past.6 The model focuses on population growth rates.
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From page 207... ...
Regional Definition and Correlations Regions were defined using geographic proximity as a criterion, taking into account, in borderline cases, a country's average past forecast error. This process resulted in 10 world regions: Western and Middle Africa; North, Eastern, and Southern Africa; the Middle East; South Asia and China; East Asia, excluding China; the Pacific Islands; Latin America and the Caribbean; Northern America and Australia; Western Europe; and Eastern Europe and the former Soviet Union (see Appendix Table F1~.
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From page 208... ...
An exceptional case is that of Eastern Europe and the former Soviet Union, with an average intraregional correlation of 0.50, possibly reflecting parallel national statistical procedures before the Communist bloc fell apart. We will assume that, within a region, forecast errors between countries have identical autocorrelation structures and that the average correlation is 0.375.8 We will also allow, in some estimates for world population, for correlations in errors across regions.
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From page 209... ...
high/low ACE ascot ~~ ~~ AGE FIGURE 7-5 Estimated 95-percent prediction interval (with median projection set equal to 1) for population projected 10 years, and comparable U.N.
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Among developing countries, with the exception of Egypt, prediction intervals increase as population size decreases. This is a consequence of the greater error in projections of smaller than larger countries (see Chapter 2)
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The extreme results for the Middle East where the upper bound of the prediction interval is more than three times the point forecast and the lower bound half of it reflect the region's turbulent recent demographic history: proportionally large and sudden flows of migrants as well as fertility declines that were unaccountably delayed and then proceeded precipitately with few advance indications. Even leaving out the Middle East, the prediction intervals for developing regions are wider than those for industrial regions.
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From page 212... ...
intervals illustrates one serious problem with the scenario method: the probability coverage for different projected units and aggregates is not consistent. We have examined prediction intervals for 10- and 50-year projections from 1995.
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The U.N. low projection indicates population decline after 2040, while the lower bound of our estimated 95-percent prediction interval continues to rise substantially at least up to 2050.
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Finally, scenarios for regions and for the world do not take account of the correlations among the forecast errors for national populations, which determine whether country errors cancel or reinforce each other when countries are combined into an aggregate. Several alternative approaches are available for calculating and communicating the uncertainty of forecasts in a probabilistic manner: judgmental approaches, time-series methods, and ex post analysis.
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Recommendations for Researchers · Extend and deepen the modeling of uncertainty, in order to use ex post analysis to derive probability intervals for forecasts. · Develop ex post models to estimate prediction intervals for component rates.
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From page 216... ...
1998 How accurate are the United Nations world population projections? Population and Development Review 24(Supplement)
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From page 217... ...
1988 Confidence intervals for population projections based on Monte Carlo methods. International Journal of Forecasting 4:135-142.
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