PROJECTIONS AND FORECASTS, POPULATION

Population size and structure can be projected into the future based on current knowledge about population size; age and sex composition; and rates of birth, death, and migration; and on assumptions about how these rates may change over time. The projection may cover very different geographic areas, time horizons, or population characteristics, and they may be targeted for a number of different uses. Spatial dimensions can range from local areas such as counties or cities to the entire world. Localarea projections tend to use shorter time horizons, often ten years or less, whereas national and global projections typically extend decades into the future–in some cases, for more than a century. Short- and medium-term projections are more likely than long-term (50-plus-year) projections to include more detail than just the size and age and sex composition of the future population. They may project such socioeconomic characteristics as educational and labor force composition, ethnicity, urban residence, or household type.

While individual researchers and national statistical institutions have made significant contributions to the methods used to project population, especially at the national level (or below), global projections have been the province of relatively few institutions: principally, the United Nations (UN) Population Division, the U.S. Bureau of the Census, the World Bank, and the International Institute for Applied Systems Analysis (IIASA). These institutions have different ways of dealing with uncertainty, make varying assumptions about future fertility, mortality, and migration trends, and begin with slightly different estimates of current population size

Projection Techniques

While some projections for individual countries or regions have been made with other techniques, long-term global population projections commonly employ the cohort-component method. Initial populations for countries or regions are grouped into cohorts defined by age and sex, and the projection proceeds by updating the population of each age- and sex-specific group according to assumptions about the three components of population change: fertility, mortality, and migration. Each cohort is "survived" forward to the next age group according to assumed age-specific mortality rates. Five-year age groups (and five-calendar-year time steps) are commonly used (although IIASA uses single years of age and time) for long-range projections. As an example, the number of women in a particular population aged 20 to 25 in 2005 is calculated as the number of women aged 15 to 20 in 2000 multiplied by the assumed probability of survival for women of that age over the period from 2000 to 2005. This calculation is made for each age group and for both sexes and is repeated for each time step as the projection proceeds. Migration can be accounted for by applying age- and sex-specific net migration rates to each cohort as well, and, in the case of global projections, by ensuring that immigration equals emigration when summed over all regions. The size of the youngest age group is calculated from the number of births during the most recent time period by applying an appropriate survival rate. For example, those under age five in 2005 will be the survivors of births during the preceding five years. Births are calculated by applying assumed age-specific fertility rates to female cohorts in the reproductive age span. An assumed sex ratio at birth is used to divide total births into males and females.

Development of this approach was a major innovation in the evolution of projection methodology, bringing it beyond the mere application of growth rates to an unstructured population. It was first proposed by the English economist Edwin Cannan in 1895. The technique was elaborated by demographer Pascal K. Whelpton in the 1930s, and the method was first employed in producing a global population projection by demographer Frank W. Notestein in 1945. Prior to the mid-twentieth century, the few global population projections that had been made were based on extrapolations of the population growth rate applied to estimates of the total population of the world or by application of some mathematical formula, such as the logistic function.

Since Notestein's 1945 projection, the cohort-component method has become the dominant means of projecting population and has remained essentially unchanged, except for extensions to multistate projections and innovations in characterizing uncertainty. The cohort-component method is nothing more than a particularly useful accounting scheme: It works out the numerical consequences of the size and age structure of the population at the beginning of the period and the fertility, mortality, and migration rates assumed to prevail over the projection period. This was once a laborious operation, but computers have greatly simplified the mechanics of preparing projections. The real work in producing projections lies not in carrying out the necessary calculations but in estimating the population size and age structure in the base period and in selecting appropriate assumptions for specifying future trends of fertility, mortality, and migration. Demographers can draw on specialized knowledge of each of these components of population change to inform projections, and institutions therefore normally project trends in vital rates based on expert opinion. Often, however, it has been difficult to determine precisely how knowledge has been applied in making the assumptions for such projections.

In general, fertility has the greatest effect on the trajectory of a population over time because of its multiplier effect: Children born today will have children in the future, and so on. The fertility component of population projections is summarized by the total fertility rate (TFR), the average total number of children a woman will have assuming that current age-specific birth rates remain the same throughout her childbearing years. In long-term projections the TFR generally reflects the assumption that fertility will eventually stabilize at a specific level in a country or region and an assumption about the time path the TFR will follow in reaching that level. Once fertility stabilizes at that level, assuming mortality and migration rates also remain the same, the population age structure will eventually stabilize as well. Thereafter, the population size will change at a constant rate. If there is no net migration (that is, if the number of in-migrants is canceled out by the number of out-migrants), and the TFR stabilizes at replacement level (when mortality is low, a little more than two children per woman), the growth rate will eventually be zero. Both the projected pace of fertility decline and the assumed eventual fertility level are important in determining trends in population size and age structure. The two factors also interact: The lower the assumed eventual fertility level, the more important the pace of fertility decline becomes in determining the long term projected population size.

Mortality projections are based on projecting life expectancy at birth–that is, the average number of years a child born in a given year can expect to live if current age-specific mortality levels continued in the future. Projections of mortality must specify how the distribution of mortality over different age and sex groups may change over time. Changes in mortality at different ages have different consequences for population growth and age structure. When child and infant mortality decline, for example, a greater proportion of babies will survive to adulthood to have their own children and contribute to future growth. Mortality declines among the older population have a smaller effect on population growth because the survivors are already past reproductive age.

Future international migration is more difficult to project than fertility or mortality. Migration flows often reflect short-term changes in economic, social, or political factors, which are impossible to predict. And, because no single, compelling theory of migration exists, projections are generally based on past trends and current policies, which may not be relevant in the future.

Projection Results and Uncertainty

Projection results are generally produced in one of three forms: as a single projection, as a set of scenarios, or as probability distributions. Many projections present to their users just one path of future population, which is considered most likely at the time of the production. Population projections according to alternative scenarios, called variants in some cases, show what the future population would be if fertility, mortality, and migration follow different paths. Some scenarios are purely illustrative–such as the UN's constant fertility scenario, which projects world population assuming that fertility remains constant at its current level. In other cases, users are given a "plausible" range as indicated by some high and low scenarios or variants. The best known among such projections are those of the UN (revised every two years), which are elaborated in three variants: "medium," "high," and "low." Figure 1 shows the results of these three variants (along with the constant-fertility scenario) on the global level for the period 2000 to 2050 as progressively divergent continuations of the estimated 1950 to 2000 trend. In these UN projections, the four population paths differ only by the fertility trends assumed while disregarding mortality and migration uncertainty. Users of population projections sometimes require projections that conform to various "story lines." For example, population projections might form just part of a scenario of future energy use and greenhouse gas emissions that presuppose particular socioeconomic, technological, or political developments.

Presenting just one best guess projection (e.g., as done by the World Bank and the U.S. Bureau of the Census)

FIGURE 1

may satisfy the needs of most users, but it does not convey the message that this future path is uncertain. The scenario approach also has several weaknesses. The most important is that users cannot interpret the probability that population will actually follow a higher or lower scenario or lie within that range. The UN provides little information about the likelihood of a particular scenario, except that it suggests that both the high and low scenarios are unsustainable over the very long run. These scenarios produce a global population that doubles or is halved every 77 years. Theoretically, they would eventually lead to implausible crowding or to extinction. In the real world, however, fertility will almost certainly not stay constant over extended period but rather show some ups and downs.

Another shortcoming of scenario approaches lies in the fact that they have usually been used to represent the uncertainty induced by only one of the three components, mostly fertility. But mortality and migration uncertainties also significantly influence population outcomes. For example, Figure 2 shows IIASA probabilistic projections for the proportion above age 80 in Western Europe over 2000–2100, taking into account uncertainty in fertility, mortality, and migration. The proportion is not expected to change much over the first two decades but, after 2030, it increases significantly while at the same time the uncertainty range widens dramatically, with the 95 percent uncertainty interval covering a range from 3 to 43 percent aged 80+ by 2100, due mainly to high uncertainty in the future path of old age mortality. In contrast, the most recent UN long range projections for 2100 foresee a proportion above age 80 that ranges from 7 percent in the high scenario to 17 percent in the low scenario, with the other UN scenarios all lying within this narrow interval. Because the UN projections do not include mortality uncertainty, they significantly underestimate the uncertainty in the number of elderly.

Finally, aggregation of the low and high scenarios to regional and global totals is typically based on the highly unlikely assumption that these extreme paths occur in all countries of the world simultaneously, an approach termed probabilistically inconsistent by the U.S. National Research Council (NRC).

An alternative way to communicate the uncertainty in population projection results is to derive probability distributions for the projected size and characteristics of a population by using a range of different fertility, mortality, and migration rates. There have been three main bases for determining the probabilities associated with vital rates: expert opinion, statistical time series analysis, and analysis of errors in past projections.

Researchers at IIASA pioneered a methodology for assessing uncertainty in population projections based on asking a group of experts to give a likely range for future fertility, mortality, and migration rates–that is, that the vital rates for a given date would be within the specified range 90 percent of the time. Thousands of cohort-component projections are then produced, drawing from these distributions. Unlike other methods, this approach is also applicable in geographic areas where data on historical trends are sparse.

The expert opinion approach has several drawbacks. For example, the task of deciding who constitutes an expert will always be problematic, and research has shown that, on average, experts tend to be too conservative in their expectations for future

FIGURE 2

changes. Demographer Ronald D. Lee has questioned whether experts can meaningfully distinguish between different confidence levels they may place on estimates of future vital rates. He also argued that the original IIASA methodology, which was based on (piece-wise linear) random scenarios, excluded the possibility of fluctuations in vital rates that deviate from a general trend, which could underestimate uncertainty in outcomes.

Statistical analysis of historical time series data can be used either to project population size directly or to generate probability distributions for population size or vital rates assuming no structural changes. While statistical methods also employ expert judgment, they do not rely on it as much as the purely expert-based method. Statistical analysis methods based on times series have been applied to some national projections but not to global projections because their wide application is severely constrained by lack of data.

Population projections made in the past can be evaluated for how well they forecast the actual population, and these errors–the difference between the projected and actual population size–can be used to calculate probability distributions for new projections. An NRC report issued in 2000 calculated probability distributions from the errors of UN medium-variant projections for 2000 that were made between 1957 and 1998. The NRC found the UN was somewhat more likely to overestimate than to underestimate future population size at the world level, although the size of the error was small. Errors were much greater for projections of country populations, but these errors tended to cancel out over the long term at the global level. The average error in UN projections for individual countries varied from 4.8 percent for five-year projections to 17 percent for 30-year projections, according to the NRC report.

In general, projections of population size tend to be more uncertain, or less accurate, under particular circumstances. They are less accurate for:

1. Less developed countries than for more developed countries, partly because less developed countries tend to have limited and less reliable data and, because they are still in the process of demographic transition, their demographic outlook is very sensitive to the timing of fertility decline;
2. Smaller countries than for larger ones, perhaps stemming in part from the greater attention devoted to larger countries and from greater heterogeneity within large countries, which allows errors at the level of sub-populations to cancel;
3. Younger and older age groups than in middle age groups, because incorrect assumptions about fertility and mortality have a greater effect at older and younger ages; and
4. The country level than at regional or global levels, because errors at the country level partly cancel each other when aggregated to regions or to the world.

These three methods of producing probabilistic projections are not mutually exclusive. Early-twenty-first-century projections from IIASA combine all three elements: Expert opinion is used to define a central path for fertility, mortality, and migration in all world regions. It is also used, in conjunction with historical errors, to define the uncertainty ranges for these values. Time series methods are used to generate paths for each variable that can show realistic short-term fluctuations over time.

Current Projections

Given the difficulties of estimating baseline data accurately and the inherent uncertainty in projecting trends in vital rates, different population projections can produce widely varying population sizes, age structures, and distributions. Nevertheless, the U.S. Census Bureau and World Bank projections, the medium or "most likely" projection from the UN, and the median future population from IIASA's probabilistic projection are similar in some respects. The Census Bureau foresees a world population of 9.1 billion in 2050, compared with 9.3 billion for the 2000 medium UN series (reduced to 8.9 million in the 2002 series) and 8.7 billion for the World Bank, while IIASA's median value for 2050 is 8.8 billion.

Differences between the UN medium variant and the median path of IIASA's probabilistic long-range projections increase over time. By 2100, projected world population differs by 11 percent: IIASA projects a median population of 8.4 billion that is already declining by 2100, whereas the UN projects a population of 9.5 billion that is nearly stable. For total population size, the UN high and low variants span a wide range (of undefined probability) that is also generally higher than the IIASA 95 percent uncertainty range. The UN projects a global population of five billion to 16 billion by 2100, based on its low and high variants, while IIASA projects a 95 percent uncertainty interval of 4.3 to 14.4 billion. IIASA's projections are generally lower primarily because they assume that fertility will, in the long run, fall below replacement level in all world regions.

Projections following different scenarios differ less in the short term than in the long term because they generally start from the same base population, and because it takes years for changes in vital rates to alter the built-in momentum that drives population growth. Momentum refers to the effects of population age structure on demographic trends: In a population with a young age structure, even if fertility falls sharply, the numbers of children will continue to increase for about a generation as the large cohorts of young people pass through their reproductive years. As a result, such populations will continue to grow for decades even if fertility were to be instantly reduced to replacement level. In contrast, some low-fertility industrialized countries are subject to negative population momentum. Because of past fertility decline, their populations have relatively small cohorts under age 30 and, therefore, even if fertility were to rise to replacement level, population size would decline for some time.

Under any plausible scenario for future growth, the world age structure will grow older, greater percentages of people will live in urban areas, and the regional balance will shift. These changes will be more dramatic further into the future. In 2000 the global population below age 15 was about three times the size of the population age 60 or older. The proportion age 60 or older is projected to swell in all scenarios, while the proportion below age 15 shrinks. World population is youngest under the higher fertility rates in the UN high-variant projections. In the UN medium-variant and the IIASA median, the proportion age 60 or older is likely to surpass the proportion below age 15 by the middle of the twenty-first century.

Based on the high and low projections prepared by these institutions, however, the older age group could overtake the below-15 age group as early as 2030 or as late as the twenty-second century. This reflects the uncertainty in the rates of change in each of these age groups considered separately. While in all cases the proportion of the population below 15 is expected to fall, it could reach anywhere from 10 percent to 22 percent of the total population in 2100. Similarly, while the percentage age 60 or older will grow, the figure could be as low as 22 percent or as high as 44 percent of the population by the end of the century.

All of the global projections show that the regional balance of world population will shift over time. Under the UN long-range projections, the share of the global population made up by the current more developed countries of North America and Europe declines from 17.2 percent in 2000 to about 10 percent in 2100. Africa's share of the total grows the most over this period, from 13.1 percent to about 23 percent, while the population share of China actually falls from 21 percent to 14 percent. These conclusions are qualitatively consistent across other scenarios, as well as across institutions.

See also: Cannan, Edwin; Cities, Future of; Momentum of Population Growth; Multistate Demography; Notestein, Frank W.; Pearl, Raymond; Thompson, Warren S.; Whelpton, P. K.; World Population Growth.

bibliography

Cannan, Edwin. 1895. "The Probability of a Cessation of the Growth of Population in England and Wales during the Next Century." Economic Journal 5(20): 505–515.

Frejka, Tomas. 1996. "Long-Range Global Population Projections: Lessons Learned." In The Future Population of the World: What Can We Assume Today? 2nd edition, ed. Wolfgang Lutz. London: Earthscan.

Lee, Ronald D., and Shripad Tuljapurkar. 1994. "Stochastic Population Projections for the United States: Beyond High, Medium, and Low." Journal of the American Statistical Association 89: 1175–1189.

Leslie, P. H. 1945. "On the Use of Matrices in Certain Population Mathematics." Biometrika 33:183–212.

Lutz, Wolfgang, ed. 1996. The Future Population of the World: What Can We Assume Today? 2nd edition. London: Earthscan.

Lutz, Wolfgang, Warren C. Sanderson, and Sergei Scherbov. 2001. "The End of World Population Growth." Nature 412: 543–546.

Lutz, Wolfgang, James W. Vaupel, and Dennis A. Ahlburg, eds. 1999. Frontiers of Population Forecasting, Supplement to Volume 24 of Population and Development Review. New York: Population Council.

National Research Council. Committee on Population. Panel on Population Projections. 2000. Beyond Six Billion: Forecasting the World's Population, ed. John Bongaarts and Rodolfo A. Bulatao. Washington, D.C.: National Academy Press.

Notestein, Frank W. 1945. "Population: The Long View." In Food for the World, ed. Theodore W. Schultz. Chicago: University of Chicago Press.

O'Neill, Brian C., Deborah Balk, Melanie Brickman, and Markos Ezra. 2001. "A Guide to Global Population Projections." Demographic Research 4(8): 203–288.

O'Neill, Brian C., Sergei Scherbov, and Wolfgang Lutz. 1999. "The Long-Term Effect of the Timing of Fertility Decline on Population Size." Population and Development Review 25: 749–756.

United Nations. 2001. World Population Prospects: The 2000 Revision, Vol. 1: Comprehensive Tables. New York: United Nations.

United Nations. Population Division. 2000. Long-Range World Population Projections: Based on the 1998 Revision. New York: United Nations.

U.S. Bureau of the Census. 1999. World Population Profile, 1998. Washington, D.C.: U.S. Government Printing Office.

Whelpton, Pascal K. 1936. "An Empirical Method of Calculating Future Population." Journal of the American Statistical Association 31: 457–473.

World Bank. 2000. World Development Indicators, 2000. Washington, D.C.: World Bank.

Brian C. O Neill

Wolfgang Lutz