APPENDIX

B

Accuracy of Population Projections from the 1970s to the 1990s

The accuracy of multicountry population projections from the 1970s to the 1990s is assessed against current estimates. This assessment is meant to provide insight into the factors that affect accuracy and indirectly some understanding of the uncertainty of current and future projections.

Assessments are made of projections for individual countries rather than aggregates, although we also consider the accuracy of projections for the world as a whole. The projections are assessed against the most convenient source, U.N. data from the 1998 revision of its estimates and projections. Both population and the components of growth (fertility, mortality, and migration) are examined, but not the age-sex structure. Attempts are made both to account for inaccuracy and to predict it.

DATA AND MEASURES

Data

The projections to be covered are from the U.N. Population Division and the World Bank, plus one additional set from the U.S. Census Bureau. Each set of projections is referred to as a forecast, to distinguish the entire set from the individual projections that comprise it. The reference years for these forecasts and the sources are as follows:



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BEYOND SIX BILLION: Forecasting the World's Population APPENDIX B Accuracy of Population Projections from the 1970s to the 1990s The accuracy of multicountry population projections from the 1970s to the 1990s is assessed against current estimates. This assessment is meant to provide insight into the factors that affect accuracy and indirectly some understanding of the uncertainty of current and future projections. Assessments are made of projections for individual countries rather than aggregates, although we also consider the accuracy of projections for the world as a whole. The projections are assessed against the most convenient source, U.N. data from the 1998 revision of its estimates and projections. Both population and the components of growth (fertility, mortality, and migration) are examined, but not the age-sex structure. Attempts are made both to account for inaccuracy and to predict it. DATA AND MEASURES Data The projections to be covered are from the U.N. Population Division and the World Bank, plus one additional set from the U.S. Census Bureau. Each set of projections is referred to as a forecast, to distinguish the entire set from the individual projections that comprise it. The reference years for these forecasts and the sources are as follows:

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BEYOND SIX BILLION: Forecasting the World's Population Agency Forecast dates Sources U.N. Population Division 1973, 1980, 1984, 1994 United Nations (1977, 1982, 1987, 1994) World Bank 1972, 1983, 1988, 1990 Zachariah and Cuca (1972); Vu and Zachariah (1983); Vu et al. (1988); Bos et al. (1991) U.S. Census Bureau 1987 McDevitt (1999) The forecasts covered start, somewhat arbitrarily, in the 1970s. Various earlier U.N. projections have been evaluated elsewhere (e.g., Keyfitz, 1981; Stoto, 1983). Similar evaluations have not been done for the World Bank, for which the 1972 forecast was the earliest that covered the world or a good part of it. For the U.S. Census Bureau, earlier projections were not of the cohort-component type, and the 1987 forecast was the only such available (see McDevitt, 1999; Jamison et al., 1987). Some forecasts involve a limited number of countries. The 1972 World Bank forecast includes only member countries, about 70 percent of the world's population at the time. The 1987 U.S. Census Bureau forecast covers only developing countries. The other forecasts all cover between 170 and 250 countries, but comparisons never involve more than the 219 in the 1998 U.N. estimates, none of which has a population smaller than 75,000. Because countries have rearranged themselves over time, the units in the different forecasts do not always coincide. Data for different countries were aggregated when necessary to permit comparisons, especially in the cases of Czechoslovakia, Ethiopia-Eritrea, Germany, the Soviet Union, Yemen, and Yugoslavia. Although we consistently refer to “countries,” some cases in the analysis, such as these, may not actually be countries; some others also lack full sovereignty and are territories, economies, or overseas departments, such as Puerto Rico and Martinique. Projected population and projected components in these forecasts are examined for every 5 years from the base date of each projection to 2000. The base date is taken to be the year divisible by five preceding the date of the forecast. Not all the data are available from this date to 2000 in each case; the earlier forecasts in particular are less fully reported. The 1972 World Bank forecast does not provide life expectancy or infant mortality, and in addition reports results for decades rather than 5-year periods. The 1973 and 1980 U.N. forecasts do not provide infant mortality and give the gross reproduction rate, which is multiplied by 2.05 to obtain total fertil

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BEYOND SIX BILLION: Forecasting the World's Population ity. The 1987 Census Bureau data do not provide results for 1995, although they do give them for 1990 and 2000, and have fertility projected to only one point and no projected mortality. The criterion against which the projections are compared is the 1998 U.N. population forecast, issued toward the end of November 1998 and published in June 1999 (United Nations, 1999). It would be preferable to compare agency projections instead with the same agency's own current estimates, which can differ in particulars from those of the U.N. This is not easy to do, however. The World Bank historical estimates are sometimes for individual years and sometimes for multiyear periods and therefore not always directly comparable to projections, and the U.S. Census Bureau does not update its historical estimates annually. The 1998 U.N. estimates have their own drawbacks. Given limited data on some countries, some historical estimates may themselves involve backward projections. To try to ensure that solid criteria are used, the analysis was intended to focus mainly on countries with good recent population data, principally a census in the 1990s or, for a few European countries, reliable vital registration. Although there are many exceptions and inconsistencies, countries with a recent census tend to be more developed than those without one and presumably have at least demonstrated the national capacity to conduct such a statistical exercise. As will be seen, however, this criterion proved problematic and was not applied throughout. Measures Two aspects of projection accuracy are of interest: whether the projected parameter is too high or too low relative to the 1998 U.N. forecast and how close it comes to the current estimate. The first aspect, measured as the signed difference between the projected figure and the current estimate divided by the current estimate, is referred to as proportional error. For country i projected to year t the proportional error (pe) will therefore be peit = (it − Pit)/Pit where P stands for actual population and for projected population. The second aspect—how close the projected parameter comes to the true value—will be measured as the absolute value of proportional error, or |peit|. In the literature, these two measures may be averaged, e.g., across projections of different lengths or lead times. They may then be referred to as mean percentage error (MPE, or mean algebraic percentage error,

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BEYOND SIX BILLION: Forecasting the World's Population MALPE) and mean absolute percentage error (MAPE), usually being expressed as percentages (e.g., Keilman, 1998; Tayman and Swanson, 1996). Somewhat confusingly, however, MPE and MAPE have sometimes been applied even when means are not taken. Since in addition we often use proportions rather than percentages, we avoid the abbreviations here. For growth components, similar measures of error and absolute error are calculated. In this case, however, raw differences rather than proportions are taken for total fertility, life expectancy, and infant mortality, given that component rates are already expressed in relation to population. Migration assumptions are similarly assessed but require some explanation. Net migration is examined, since neither immigration nor emigration is projected separately. Historical estimates of net migration are often obtained as residuals, by comparing estimated population growth with births and deaths (Zlotnik, 1999). One might assume therefore that historical net migration estimates are less reliable than fertility, mortality, or growth estimates. This is not the complete story, however, because forecasters can be assumed to examine carefully cases in which net migration is believed to be substantial. These few cases —in which absolute net migration rates may be 10 or 15 times the average —carry much more weight, in statistical analysis, than the many cases in which net migration is close to zero. In addition, the equation that relates growth to components (Population growth = Births − Deaths + Net migrants) is an exact equation, with no residual error. Any measurement error for migration must be exactly balanced by measurement error for growth, births, or deaths. The migration estimates, therefore, should have no greater (and no less) error than the other variables combined. We assume that the other measurement errors are not perfectly correlated, so they will cancel each other at least occasionally. This may still leave the migration estimates with greater proportional measurement error, because net migration rates are generally small. However, we are not examining proportional error in projected growth components but raw error. In analyzing the error in these projections, various country classifications and related variables are used: Whether or not a country has had a national population census in the 1990s. National censuses in this period have covered 80 percent of the world's population. The existence of such a census is used, in some analysis, essentially as a proxy for presumed population data quality. Population size at the start of a projection. Countries are divided into those of at least one million people and smaller countries, on the assumption that forecasts have often paid less attention to small countries.

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BEYOND SIX BILLION: Forecasting the World's Population Initial total fertility rate, dichotomized at 4.5 children. A high fertility level may mean more scope for error in specifying rates. Initial life expectancy and initial net migration are also used in some analyses. Developing country and industrial country (or developed country) status, as defined by the U.N. World region, with countries divided into six regions: Europe and the former Soviet Union; other industrial countries around the Pacific Rim; Latin America and the Caribbean; Asia and Oceania; the Middle East and North Africa; and Sub-Saharan Africa. The Soviet Union is treated as a unit because forecasts did not distinguish its subunits until its breakup. The Pacific Rim industrial countries include the United States and Canada (and the rest of Northern America, which is sometimes defined to include Bermuda, Greenland, and St. Pierre and Miquelon), Japan, and Australia and New Zealand and are generally referred to, for shorthand, as the United States, Australia, and Japan. Asia and Oceania excludes Japan and the Middle East but still contains the majority of the world's population. In regard to number of countries, however, it is similar to other regions, and variation in the relevant parameters within the region is no greater than elsewhere. The presence of significant discontinuities in recent population history. These discontinuities, referred to as “demographic quakes, ” are measured by changes in a country's annual population growth rate of at least 2.5 percentage points between one 5-year period and the next. Further explanation of this concept is provided below. The analysis relies initially on means, across countries and across forecasts. Some multivariate analysis is then reported to explain inaccuracy. ACCURACY OF PROJECTED POPULATION Table B-1 shows proportional error and absolute proportional error derived by comparing projected population and population as currently reported by the U.N. Each row of the table presents means for a single forecast assessed against the 1998 U.N. estimates. These forecasts all project population for a succession of 5-year periods, usually starting with the year divisible by five immediately preceding the date of the projection, designated as year 0 in the table. The comparison for year 0, therefore, is a check on the accuracy of what we consider the base population estimate used in the projection. Since the earliest forecasts examined have base years of 1970, the longest projection that can be checked is for 30 years, up to the year 2000.

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BEYOND SIX BILLION: Forecasting the World's Population Error Past projections are, on average across countries and forecasts, biased upward relative to current estimates. The bias increases the longer is the projection period, from 1 percent for a 5-year projection to 6 percent for a 30-year projection. This pattern of increasing bias with longer projection horizons holds across all forecasts. Longer projections appear to have greater error. Projection length itself is the main reason, but two other factors may be considered because they may contribute slightly. The longer projections are primarily those made earlier, in the 1970s, whereas shorter projections also include more recent ones. One might hypothesize that earlier projections were less accurate. But the table does not support this. For 10-year projections, for instance, the two earliest forecasts were among the least biased. Another possible factor is suggested in Table B-2. Proportional error appears to increase as one tries to predict later and later target years. Bias is higher for projections to 2000 than for projections to earlier years. Perhaps 1995 and 2000 in particular have simply been more difficult to project accurately. However, much of this pattern is explained by projection length, because projections to 1995 and 2000 include more long-duration projections than do projections to earlier years. Absolute Error Looking at absolute proportional error (also given in Table B-1 and Table B-2) makes the projections look somewhat less satisfactory. The base-year estimate of population is off, on average across countries and forecasts, by 3 percent in either direction, a projection of 10 years is off on average by 6 percent, a projection of 20 years is off by 11 percent, and a projection of 30 years is off by 15 percent. This pattern is consistent across all forecasts. No substantial improvement from earlier to later forecasts is evident, although the last two forecasts in the 1990s may have been somewhat better. Since only the short-term results of these last two forecasts can be evaluated, and since the criterion data were produced relatively soon after the forecasts and could share similar errors with them, this apparent improvement cannot be confirmed at this date. (It is reexamined below as part of the multivariate analysis.) Although the absolute errors in these projections may appear large, the projections are a considerable improvement over holding population or population growth rates constant. In comparison with simulated projections that simply keep population constant, these projections have only a third as much absolute proportional error over a projection horizon of 20 years. In comparison with simulated projections that keep previous

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BEYOND SIX BILLION: Forecasting the World's Population TABLE B-1 Error in projected population: Means across countries, by forecast and projection length   Projection length (years) Forecast 0 5 10 15 20 25 30 (n) Proportional error Mean 0.003 0.008 0.015 0.024 0.034 0.035 0.058 1,375 1972 World Bank −0.007 — 0.011 — 0.039 — 0.079 113 1973 U.N. −0.006 −0.004 0.006 0.012 0.023 0.036 0.043 163 1980 U.N. 0.007 0.012 0.011 0.016 0.028 0.033 — 163 1983 World Bank 0.003 0.005 0.015 0.037 0.048 — — 145 1984 U.N. 0.015 0.013 0.017 0.029 0.036 — — 164 1987 U.S. Census 0.004 0.009 — 0.037 — — — 124 1988 World Bank 0.005 0.008 0.019 0.023 — — — 160 1990 World Bank 0.001 0.004 0.014 0.018 — — — 162 1994 U.N. 0.004 0.015 0.022 — — — — 181 Means for countries with: Census in 1990s 0.008 0.012 0.017 0.029 0.038 0.043 0.071 880 No 1990s census −0.004 0.000 0.011 0.017 0.026 0.021 0.032 490  

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BEYOND SIX BILLION: Forecasting the World's Population Absolute proportional error Mean 0.033 0.048 0.069 0.094 0.122 0.142 0.172 1,375 1972 World Bank 0.043 — 0.088 — 0.134 — 0.179 113 1973 U.N. 0.041 0.062 0.093 0.113 0.134 0.154 0.167 163 1980 U.N. 0.032 0.050 0.065 0.087 0.116 0.129 — 163 1983 World Bank 0.034 0.051 0.075 0.103 0.123 — — 145 1984 U.N. 0.036 0.046 0.067 0.092 0.107 — — 164 1987 U.S. Census 0.047 0.065 — 0.112 — — — 124 1988 World Bank 0.032 0.047 0.070 0.083 — — — 160 1990 World Bank 0.027 0.040 0.062 0.072 — — — 162 1994 U.N. 0.015 0.033 0.041 — — — — 181 Means for countries with: Census in 1990s 0.030 0.043 0.061 0.086 0.109 0.123 0.152 880 No 1990s census 0.039 0.058 0.084 0.108 0.147 0.178 0.213 490 Means for simulated projections with: Constant population 0.000 0.092 0.174 0.244 0.306 0.362 0.410 5,564 Constant 5-year growth rate 0.000 0.026 0.057 0.094 0.145 0.189 0.226 4,494 Constant 10-year growth rate 0.000 0.028 0.059 0.097 0.144 0.177 — 3,210 — No data. Note: Year 0 is the base year for the forecast, taken to be the year divisible by five preceding the date of the forecast. Number of cases is given for this year and declines for longer projections. The mean rows pool all countries from all forecasts. The simulations attempt to project population, either keeping it constant or using the preceding population growth rate, by country to the years 1975-2000. The simulations use 1998 estimates of population or growth rate as of the base year, therefore assuming no base error, and should properly be compared with adjusted error measures in Table B-3.

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BEYOND SIX BILLION: Forecasting the World's Population TABLE B-2 Error in projected population by target year: Means across countries and forecasts Target year Proportional error Absolute proportional error (n) 1975 −0.004 0.062 163 1980 0.009 0.076 439 1985 0.010 0.069 635 1990 0.016 0.080 1,194 1995 0.025 0.089 1,138 2000 0.036 0.109 1,375 growth rates constant, these projections have only two-thirds as much absolute error. (The “proportionate reduction in error” [Tayman and Swanson, 1996] in the latter case is therefore around 35 percent. These comparisons require adjustments for base population error, which are discussed below. See Appendix E for some explanation of similar simulated projections.) Countries with a recent census, and therefore presumably better data, can be contrasted with countries with no recent census (Figure B-1). Projections actually appear less biased without a recent census, as if fewer “inconvenient” real data mean fewer revisions in subsequent forecasts. However, projections for these countries also have greater variability around subsequent estimates, producing larger absolute errors. This contrast indicates that a focus on countries with good criterion data may lead to overestimating the accuracy of projections. The analyses to follow, therefore, do not distinguish between countries with and without a recent census. Comparisons across agencies cannot safely be made from these results. Only U.N. data are available as criteria. Using these data as criteria for a different agency's projections, rather than the other agency 's own current estimates, could produce apparent error that is actually disagreement between agencies about historical demographic trends. For instance, the mean base absolute proportional error in the 1983 World Bank forecast, in Table B-1, is 0.034. If the base estimates had been compared not with 1998 U.N. estimates but with essentially contemporaneous estimates used in the 1984 U.N. forecast, the mean absolute proportional error would still have been of comparable size, at 0.026. Much of the apparent error in this case, therefore, could conceivably be due to disagreements between agencies. Estimates of demographic trends made more recently, in 1998 or 1999, conceivably differ less across agencies, but one obviously needs to be cautious in making cross-agency comparisons.

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BEYOND SIX BILLION: Forecasting the World's Population FIGURE B-1 Proportional error and absolute proportional error by existence of a recent census and projection length. Some Sources of Error The variability in country projections is demonstrated even more clearly in Figure B-2, which gives percentiles of the distribution across countries. Positive bias in the base population is confirmed as more serious than negative bias. In 10-year projections, 8 out of 10 countries are within ± 10 percent of the currently estimated population total. But in 30-year projections, 1 out of 10 is more than 30 percent too high, and another 1 out of 10 is more than 20 percent too low. Specifically among countries without a 1990s census (not distinguished in the figure), the range of error is wider, so that, to encompass 95 percent of the distribution in a 30-year projection, one would have to go from 100 percent above to 70 percent below the criterion estimate. The countries with large errors are sometimes small countries to which little demographic attention has been paid but sometimes also large and important countries with insufficient data. Large errors have occurred for various small countries with poor base population estimates, such as

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BEYOND SIX BILLION: Forecasting the World's Population FIGURE B-2 Proportional error by projection length: Percentiles for all countries. the Western Sahara, the Netherlands Antilles, and Djibouti. But large base errors have also occurred for such large and important countries as Nigeria and Saudi Arabia. Most forecasts include between five and eight countries in which the base population estimate is off by at least 20 percent (plus or minus), except for the two most recent forecasts, which may have improved slightly. Another important explanation for projection error is unexpected events that have substantial demographic consequences. Without a precise account of the demographic futures envisioned at the time a projection was made, one cannot determine which events were indeed unexpected. As a rough guide, however, one can look at sharp turning points in actual population growth, such as those illustrated for five countries in Figure B-3. Bosnia-Herzegovina, Lebanon, and Liberia experienced civil wars (with some external participation), Kuwait was invaded, and Albania went through social upheaval and a temporary collapse of civil order. Their population trends reflect these upheavals. Demographic upheavals of this sort, or demographic quakes, might be identified from sharp increases or decreases in the annual population growth rate, of at least 2.5 percentage points from one 5-year period to the next. (This quantity is equal to twice the standard deviation for such period-to-period growth-rate changes.) Such quakes affected two dozen

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BEYOND SIX BILLION: Forecasting the World's Population TABLE B-14 Absolute proportional error in projected world population, by forecast, projection length, and target year Forecast World error As % of country error Projection length World error As % of country error Target year World error As % of country error 1973 U.N. 0.017 16% 0 0.005 16% 1970 0.023 56% 1980 U.N. 0.004 5% 5 0.006 13% 1975 0.014 24% 1983 World Bank 0.007 9% 10 0.009 15% 1980 0.006 9% 1984 U.N. 0.004 5% 15 0.011 14% 1985 0.002 3% 1988 World Bank 0.011 18% 20 0.009 8% 1990 0.003 5% 1990 World Bank 0.010 19% 25 0.014 10% 1995 0.009 10% 1994 U.N. 0.010 33% 30 0.033 20% 2000 0.020 20% Note: Error in base estimates is included in the calculations.

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BEYOND SIX BILLION: Forecasting the World's Population FIGURE B-14 Mean country proportional error and world proportional error, by projection length and target year. jected country populations and comparing this with current estimates of the total for the same group of countries (unlike the two previous tables, which used the reported world totals). In contrast to mean country proportional error, world proportional error shows no increase by projection length, and possibly a small decrease. It does however increase fairly clearly from 1990 to 1995 to 2000 at every projection length, indicating that world population in the 1990s became increasingly difficult to project. Explaining Increased Error The increase in world absolute error in the 1990s is not explained by an increase in average country error. Figure B-14 shows no consistent increase in average country error by target year, and weighting these means by population size does not alter the conclusion. Instead, world absolute error has increased because country errors offset each other to a more limited extent. To show this, we calculate the proportion of unoffset error (u) as

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BEYOND SIX BILLION: Forecasting the World's Population Entirely random errors would be as often negative as positive, and, in a large sample, u would be close to zero. However, consistently positive (or consistently negative) errors across countries would make u equal to one. Figure B-15 shows, first, that unoffset error is fairly high for base estimates and short projections and declines with longer projections. Errors in initial parameters appear nonrandom, but errors in longer projections by contrast tend not to reflect any consistent bias. More critically for present purposes, the figure also shows that unoffset error increases from 1990 to 1995 to 2000, although for earlier target years no trend can be confirmed. Unoffset error therefore appears to be the likely explanation for the increase in world projection error as target years move from 1990 to 2000. FIGURE B-15 Proportion of country error unoffset in world projections across six exercises, by projection length and target year.

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BEYOND SIX BILLION: Forecasting the World's Population FIGURE B-16 World total fertility rate in various forecasts, by target period. NOTE: UN stands for the U.N. Population Division and WB for the World Bank, with the following digits indicating forecast date. Fertility and Mortality One possible reason why errors in country projections might increasingly be going in a single direction is that too-high fertility might have been projected, both among high-fertility and low-fertility countries. Figure B-16 examines this possibility. Projected trends in total fertility are compared with the estimated trend from the 1998 U.N. forecast. The forecast from the 1970s (the 1973 U.N. forecast) was off almost from its inception. Forecasters in the 1970s appear to have missed the sharp acceleration of fertility decline in that period, almost entirely attributable to China. Using population-weighted total fertility rates, one can estimate that almost 60 percent of fertility decline between 1965-1970 and 1970-1975 took place in China. This is equivalent to over 80 percent of fertility decline in the developing regions in this period. This is even more remarkable because so many other large developing countries actually contributed to an increase in world fertility, either because their fertility rose (e.g., Bangladesh, the Democratic Republic of the Congo) or because fertility decline was small and offset by population increase (e.g., India, Nigeria).

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BEYOND SIX BILLION: Forecasting the World's Population Most of the projected trends in post-1970s forecasts in Figure B-16 are fairly close together. They all differ, however, from the currently estimated trend, which shows a fairly sharp dip around 1990. Whereas fertility decline in the world as a whole appeared to be leveling off in the late 1980s, by the early 1990s it accelerated again, and all these forecasts missed the turning point. Why did fertility decline accelerate? Perhaps more countries unexpectedly started fertility transition, or fertility declined more rapidly in midtransition developing countries, or fertility declined unexpectedly in industrial countries. To evaluate such possible explanations, total-fertility change in each country was estimated between 1985-1990 and 1990-1995, weighted by population size. Three-fourths of the total weighted change was in the negative direction. The bulk of the total negative change was accounted for by just four countries: China (36 percent of total negative change), Bangladesh (12 percent), India (9 percent), and Russia (7 percent). Fertility error might not be the complete explanation for increasing error in projections to the 1990s, however, and mortality error is also worth investigating. Mortality appears to have reached a similar turning point around 1990, with progress in life expectancy moderating somewhat around that date (Figure B-17). However, the effect on projection accuracy is ambiguous, since some forecasts projected higher life expectancy and some projected lower life expectancy. This turning point in mortality, therefore, made some forecasts look slightly better and others look slightly worse, unlike the turning point in fertility around 1990, which made them all look bad. SUMMARY AND DISCUSSION To summarize the results for world projections first, we note that the error in projected world population is small, less than 1 percent (on average across various forecasts) in projections as long as 20 years. The error seems to be larger, however, for projections to the years 1995 and 2000. Projections to these years have been consistently too high. The explanation lies in fertility trends since 1990. World fertility declined sharply, around that date, at a faster rate than in the previous decade. Four countries—China, Bangladesh, India, and Russia —accounted for the largest part of this fertility decline. While the decline might represent the start of a new era of faster fertility decline, it could as well reflect highly particular circumstances affecting these specific countries. To interpret projection error, therefore, it is useful to look at the errors for specific countries. Country population projections have been assessed

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BEYOND SIX BILLION: Forecasting the World's Population FIGURE B-17 World life expectancy in various forecasts, by target period. NOTE: UN stands for the U.N. Population Division and WB for the World Bank, with the following digits indicating forecast date. from nine forecasts dated from 1972 to 1994, each forecast covering most of the world population. The scale of projection errors and the reasons for them are summarized here. Projection Error and Its Explanation Proportional error in either direction in projected country populations ranges from 5 percent, in 5-year projections, to 17 percent, in 30-year projections. When countries are aggregated, errors tend to cancel each other out, so that, although projections have been biased upward, the average bias is more modest at 1 to 6 percent over projections of 5 to 30 years. This slight upward bias appears across forecasts, which were all assessed against the current 1998 U.N. historical estimates. Some bias in these historical estimates is of course also possible but cannot be assessed and is unlikely to be the complete explanation. Projection error has three broad types of explanations. First, the base demographic estimates from which the projection starts may be wrong, producing subsequent errors. The base population may be misestimated, as may be the base levels of fertility, mortality, and net migration. Errors

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BEYOND SIX BILLION: Forecasting the World's Population in each of these factors have been shown to be related to error in projected population. What causes such errors? Two possibilities appear to have some empirical support. On one hand, countries that have received less careful attention—in these world projections, smaller populations of less than 1 million people—are more likely to be assigned erroneous base estimates of population, net migration, and mortality (though not necessarily fertility). On the other hand, where there is more scope for error, error is more likely. Countries with more births, more deaths, and more net migrants have on average larger errors in base estimates. The second major explanation for projection error is misspecified trends in component rates, which produce increasing error as projections lengthen. Long projections have substantially more error than short projections. When projections reach 30 years in length, 1 out of 4 will be off by at least 20 percent and 1 out of 10 by at least 40 percent. A misspecified component rate can cause increasing error in projected population as a projection lengthens, and in addition projected levels of fertility and mortality become increasingly poorly specified. The third major explanation for projection error is unexpected events that substantially alter demographic prospects. Extreme events of this type, labeled demographic quakes, have been identified from changes in population growth rates, between successive 5-year periods, of at least 2.5 percentage points. Since the 1970s, the majority of such events have been associated with substantial and sudden flows of migrants. Some events have also been associated with mortality crises. Demographic quakes double or triple the error in projected population. The relative importance of these three major explanations is difficult to directly assess, but one can compare instead the importance of error in base population, fertility, mortality, and migration. Error in base population is the predominant explanation for error in shorter projections but declines in importance as one looks at longer projections. Fertility error and migration error (including here base error in these component rates) are roughly comparable in importance, but fertility error increases with longer projections, whereas migration error does not. Mortality error also contributes but is of lesser importance, probably because the pace of progress in extending life expectancy has been more predictable than the pace of fertility change or the levels of migration in the last few decades. Projection errors vary by region, for all the reasons just considered. Projections for countries of the Middle East and North Africa have on average the most error. The reasons are straightforward: base population estimates have been worse for these countries generally than for countries in other regions, and fertility, mortality, and migration—the last one especially—have each been projected more poorly for this region than for others. These factors almost entirely explain the poorer projections.

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BEYOND SIX BILLION: Forecasting the World's Population Projections for Sub-Saharan countries are distinctive in a different way. Several aspects of these projections have fairly high levels of error, but the errors tend to offset. Base population error, to begin with, is substantial, but appears to go in both directions, so that country populations are neither systematically over- or underestimated. Mortality has been systematically underprojected for this region and accounts for proportionally more error in projected population than in other regions. This may be due to slower than expected economic progress, lagging development of health care systems, or the HIV/AIDS epidemic, or to all three factors combined, but this analysis was not designed to test such explanations. Note that fertility has been slightly underprojected (unlike the average country in every other region), offsetting the mortality error. Sub-Saharan countries have had a larger number of deaths and births than the typical projection has shown, experiencing greater population turnover but not much faster or slower growth than projected. The populations of industrial countries appear to be more accurately projected than the populations of developing countries. Better data may be a factor in this, as may lower levels of fertility and mortality, from which only smaller deviations are possible. However, gains in life expectancy have been underestimated, as have net migrants. Unresolved Issues This analysis has not been limited to countries with good criterion data. In principle such a limitation might have been the conservative choice, given the possibility that errors for countries with poorer criterion data might escape detection. However, initial tabulations for countries with and without a census in the 1990s—a possible operationalization of good criterion data—showed contradictory results. Projections for countries without such a census had relatively less bias but greater absolute error. Attempting to impose the more stringent standard that good criterion data ordinarily imply would therefore have led to underestimates, not overestimates, of projection error. Whether projection results for countries with poorer data really are more variable and less precise, as they appear to be, awaits further clarification once their demographic histories can be more reliably ascertained. Differences in the accuracy of projections from different agencies have also not been clarified. The criterion data available were only from the U.N. These data may differ substantially from the historical estimates underlying projections from other sources, just as contemporaneous population estimates have differed in the past. Obtaining historical data from other sources may clarify the situation. Even better, of course, would

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BEYOND SIX BILLION: Forecasting the World's Population be an independently reviewed set of historical estimates, but producing such a set for the whole world is a considerable enterprise. Looking at forecasts over time, regardless of their source, suggests that, with other factors controlled, 1990s forecasts have been slightly better than earlier ones. This needs some verification. The 1998 criterion data could have been contaminated, in a sense, by expectations based on the fairly recent 1990s forecasts—but whether this is true or not, and how serious an issue it is, cannot be determined. Some data also suggest that population projections to the mid-1980s were worse than for other periods. Whether this is true, and what factors could have been responsible, cannot be conclusively determined. Improving Projections One important conclusion deals less with how projections can be improved than with how they can be better utilized. Clearly, users should be more aware of the limits to the accuracy of long-term projections. Perhaps, as occasionally suggested, projections should not be made at all for periods longer than a few decades, given the increasing error in longer projections. Others argue, however, that longer projections are useful to make concrete the implications of various demographic assumptions. This issue cannot be resolved here. What does seem worth arguing for, however, is greater effort at providing users with an appreciation of potential error, especially in longer projections. Aggregated projections, interestingly enough, appear to be considerably more precise. Whereas country projections are off in either direction by 12 percent on average after 20 years, world projections are off by only 1 percent after that period. One implication is that the careful country-by-country work performed by the agencies whose projections have been considered helps in producing more accurate aggregate estimates, even if the country projections themselves have substantial error. Producing aggregate projections directly, as is done in some other cases, is a less desirable exercise if these regional projections are no more accurate than typical country projections. There could conceivably even be some advantage in producing, where feasible, subnational projections, especially for large and heterogeneous countries. A fairly direct way to improve projections is to improve base demographic estimates. Base estimates are responsible for much projection error, especially in the short term, when projection results are most useful for planning. Base estimates for population, age structure, and component rates can be improved, in general, through better data from censuses, surveys, and vital registration and through improved methods of estimating demographic parameters. Of the world population, 20 percent have

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BEYOND SIX BILLION: Forecasting the World's Population not been covered by a census in the 1990s. So while small countries are particularly subject to error in base population and base net migration rates, better data could affect projections for an important portion of world population. More accurate projections of component trends could also improve projections, particularly longer ones. Accuracy may improve naturally, as high levels of fertility and mortality become less common, reducing the scope for error. Since long projections are more problematic, sufficient attention should be paid to long-term levels of fertility and mortality to ensure that they are determined from the best available research. Overall, past forecasts appear to have underprojected demographic progress, assuming too slow a decline in both fertility and mortality —except in Sub-Saharan Africa, where demographic progress has been overprojected. This was still true for fertility in the most recent forecasts that could be examined, but was no longer true for mortality. Whether this weakness in procedures still obtains today cannot be determined, but procedures should be reviewed to ensure it does not. For migration, improvements are difficult to prescribe. Over the period studied, projections would have been more accurate with slightly more net immigration into industrial countries. One cannot be certain, however, whether this pattern will continue, subject as it is to political decisions and controls. Migration is heavily implicated in the majority of demographic quakes, and what to do about these is a vexing problem. Successful prediction of such quakes seems unlikely at present. What one might hope for is that such quakes become less common, as countries become more stable and emergency support systems more effective. When such quakes do occur, obviously, one needs to discount past projections and to prepare new ones as soon as feasible. Rapid updating may be the best that can be recommended and would also contribute in relation to the problem of base error. Providing new projections as soon as better base data become available is one way to limit any damage that may be done by inaccurate projections. REFERENCES Arnold, F. 1989 Revised Estimates and Projections of International Migration, 1980-2000 . Policy, Planning, and Research Working Paper 275. World Bank, Washington, D.C. Bos, E., P.W. Stephens, M.T. Vu, and R.A. Bulatao 1991 Africa Region Population Projections; Asia Region Population Projections; Latin America and the Caribbean Region Population Projections; Europe, Middle East, and North Africa Region Population Projections, 1990-91 Edition. Policy, Research, and External Affairs Working Papers 568-601. World Bank, Washington, D.C.

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BEYOND SIX BILLION: Forecasting the World's Population Jamison, E., P.D. Johnson, and R.A. Engels 1987 World Population Profile: 1987. Washington, D.C.: U.S. Census Bureau. Keilman, N. 1998 How accurate are the United Nations world population projections? Population and Development Review 24(Supplement):15-41. Keyfitz, N. 1981 The limits of population forecasting. Population and Development Review 7(4):579-593. McDevitt, T. 1999 Knowledge-Based Population Projections: New Statistical Evidence and a Word on Making Projections under Real World Conditions. Poster presented at the Population Association of America meetings, New York, March. Sanderson, W.C. 1998 Knowledge can improve forecasts: A review of selected socioeconomic population projection models. Population and Development Review 24(Supplement):88-117. Stoto, M.A. 1983 The accuracy of population projections. Journal of the American Statistical Association 78(381):13-20. Tayman, J., and D.A. Swanson 1996 On the utility of population forecasts. Demography 33(4):523-528. United Nations (U.N.) 1977 World Population Prospects as Assessed in 1973. New York: United Nations. 1982 Demographic Indicators by Country: Estimates and Projections as Assessed in 1980. New York: United Nations. 1987 Global Estimates and Projections of Population by Sex and Age: The1984 Assessment. New York: United Nations. 1994 The Sex and Age Distribution of the World Populations: The 1994 Revision . New York: United Nations. 1999 World Population Prospects: The 1998 Revision, Vol. 1, Comprehensive Tables. New York: United Nations. Vu, M.T., and K.C. Zachariah 1983 Short-Term Population Projection, 1980-2020 and Long-Term Projection, 2000 to Stationary Stage by Age and Sex for All Countries of the World. Policy and Research Unit, Population, Health and Nutrition Department [World Bank, Washington, D.C.]. Vu, M.T., E. Bos, and R.A. Bulatao 1988 Africa Region Population Projections; Asia Region Population Projections; Latin America and the Caribbean Region Population Projections; Europe, Middle East, and North Africa Region Population Projections, 1988-89 Edition. Policy, Planning, and Research Working Papers 114-117. World Bank, Washington, D.C. Wheeler, D. 1984 Human Resource Policies, Economic Growth, and Demographic Change in Developing Countries. Oxford, Eng.: Clarendon Press. Zachariah, K.C., and R. Cuca [ 1972] Population Projections for Bank Member Countries 1970-2000. Development Economics Department, International Bank for Reconstruction and Development [ Washington, D.C.]. Zlotnik, H. 1999 World Population Prospects: The 1998 Revision. Paper prepared for the Joint ECE-Eurostat Work Session on Demographic Projections, Perugia, Italy, May 3-7.