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EVALUATING THE ACCURACY OF U.S. POPULATION PROJECTION MODELS 307 NATURE OF POPULATION PROJECTION MODELS To appreciate the simplified nature of most population projection models, âsimpleâ at least in relation to models commonly used in more elaborate microsimulation exercises, imagine an analyst in the Office of Management and Budget who has been given the task of preparing annual forecasts of the gross national product (GNP) until the year 2010, starting from a baseline of $4.53 trillion in 1987 (Bureau of the Census, 1990).1 Suppose also that the analyst has access to a forecasting model of the macroeconomy, one of whose equations is for the growth rate of the GNP. Assume that (1) the model is correctly specified with no error term, so that all relevant factors have been identified; (2) all of the model's coefficients are precisely known; (3) the proper functional form has been used; and (4) there will be no structural changes in the relationships during the forecast period. To obtain an accurate prediction of GNP growth rates (and therefore of the future size of the GNP) 2, 3, 5, 10, or 20 years from now, it is necessary to be able to accurately foresee future trends in savings rates, labor force growth, interest rates, investments in human capital, foreign trade, and all other factors on the right-hand side of the forecasting equation. Even though the situation described above is hypothetical, it is analogous to the circumstance faced when making population projections, especially those performed with the aid of cohort component projection models. The work involves a closed analytical system for which all relevant variables have been properly and precisely accounted, and the hard part is deciding how fertility, mortality, and migration are likely to behave in the future. Most current population projections, whether performed by central statistical bureaus, other federal administrative units charged with population forecasting, or groups outside the government, are made by using a cohort component method of population projection. The method is easy to understand, and its associated calculations are transparent and relatively few in number. In making a projection of national aggregates, for example, the initial requirement is to specify a baseline population (usually for July 1 of a particular calendar year) arrayed by age and sex and often by race or other characteristics as well. Population ages are typically given in 1-year or 5-year intervals. The analyst must also indicate the specific paths that future trends in fertility, mortality, and migration are assumed to take. Trend variables are usually given in as much detail as that contained in the baseline population. For example, it is minimally expected that age and gender patterns will be articulated. Assumptions 1A 23-year planning horizon is probably longer than needed for most economic policy purposes, even for long-range planning. Population projections, on the other hand, typically take us much farther into the future than either microsimulation or macroeconometric forecasting models. For example, the most recent projections of the population of the United States prepared by the Census Bureau use 1986 as the base year and extend to the year 2080 (Spencer, 1989).
EVALUATING THE ACCURACY OF U.S. POPULATION PROJECTION MODELS 308 regarding the international movement of persons may be given as net flows or as separate gross flows of immigrants and emigrants. Once the baseline population and underlying assumptions about birth rates, death rates, and international migration have been delineated, the cohort component method proceeds in two steps. First, those persons alive at the start of the projection interval are âsurvivedâ 5 years into the future by performing separate computations on each 5-year age group or cohort.2 If July 1, 1985, defines the baseline population, for example, the numbers of males and females in the 0â4 age group are multiplied separately by appropriate survival proportions computed from gender-specific life tables to project the expected number of persons of each sex in the 5â9 age group on July 1, 1990.3 This process is repeated for successively older age groups in the baseline population. Following an adjustment for the net number of international migrants into each age-sex group over the 5-year period, the first part of the cohort component method is complete. Thus far it has produced a projection of the July 1, 1990, population by sex and by 5-year age groups for ages 5 and over. The second step of the method projects the population aged 0â4 on July 1, 1990. To do this, the average number of women between July 1, 1985, and July 1, 1990, in each 5-year age group in the childbearing ages is multiplied by an assumed age-specific fertility rate to derive the total number of births expected during the 5- year period. These births can be separated into males and females by an empirically based sex ratio at birth. Then appropriate gender-specific mortality ratios are applied to the expected number of births to project the expected number of survivors under age 5 on July 1, 1990. To continue the projection beyond 1990, the process is repeated using the projected population on July 1, 1990, as the new baseline and the same (or possibly different) assumptions about the underlying behavior of fertility, mortality, and migration for the next projection interval. One advantage of the cohort component model is that its method of making population projections mirrors the actual population dynamics involved; the mechanics of the calculations parallel exactly the demographic processes of growth and change. The model also yields projections by age and sex, not just total population. Other relevant demographic indicators, such as rates of population growth, birth, or death, can be derived from these primary outputs. Whether the cohort component model yields âbetterâ forecasts than less elegant approaches (e.g., trend extrapolations of total population size or the growth rate of the total population) is an empirical issue. It is also clear that projections issued by cohort component models are conditional forecasts of the population. Even with the same baseline population, choosing a different set of fertility, mortality, or immigration assumptions would 2If single years of age are used instead, the baseline population can be survived 1 year into the future. 3These life tables are derived from the underlying mortality assumptions.