A widely used demographic technique called the "cohort-component" method is used to project Missouri's population. The basic equation is "population at the beginning of the time period + births for the time period - deaths for the time period ± migration for the time period = projected population at the end of the time period."
The formula is applied to the population after it is grouped in five-year age increments - broken out by male and female (e.g., females age 0-4, females age 5-9, females age 10-14, etc.). These groupings are referred to as "age-sex cohorts." The equation is applied to population counts on a county-by-county basis for each of the age-sex cohorts.
With population at the beginning of the process being the 2000 Census counts, the model is iterated six times to generate projections out to the year 2030 - at five-year intervals (six separate five-year time periods). The population projected at the end of a given five-year time period serves as the "beginning population" for the next five-year time period (iteration).
Because it is not known who will die in the future, survival rates must be projected based on historic trends for each of the age cohorts (e.g., x% of males age 55-59 historically survive to age 60-64). These survival rates are then applied to the population in each county in the state. Furthermore, because life expectancies have been increasing in recent decades, these survival rates will increase with each iteration of the model, for most age-sex cohorts. The rate at which they increase is based on historic trends for each of the age-sex cohorts.
Similarly, because it is not known who will move into, or out of, a given county in the future, migration rates must be projected on a county-by-county basis based on past migration tendencies for each of the age-sex cohorts.
Furthermore, historical birthrates are used to project births during future time periods in order to populate the 0-4 year-old age-sex cohorts at the beginning of each iteration of the model. These mathematically derived population counts are then aged through the projection horizon as though they were actual person counts.
Special consideration is given to areas with large concentrations of college students, military personnel, or prison inmates. These groups are given the term "special populations." Because these "special populations" are not native to the county and are not likely to spend the remainder of their lives there, they are not aged forward through the model. These persons must be removed from the base population before the model begins to age the county's population through the projection horizon. The special populations are extracted from the appropriate age-sex cohorts at the beginning of the iteration for that county, the model is run, and at the end of the time period they are added back to the original age-sex grouping from which they were extracted at the beginning of the iteration. These special populations move to a specific county where a facility is located. They remain there for a certain period of their lives and then move on to other locations. The counties in which the facilities are located will always have bulges in their population that correlate to these age-specific periods during which people are located in or near the facilities.
In the cohort-component method used to produce this set of Missouri population projections, the components of population change (births, deaths, and net migration) are projected separately for each age-sex cohort (males and females in five-year age groups). The beginning, or base, populations are 2000 Census counts. These are advanced at five-year intervals to the year 2030 by using projected survival rates and net migration rates by age and sex. Every five years, a new age 0-4 cohort is added for males and females by applying projected fertility rates to the female population.
To be consistent with the decennial census date on April 1, projected populations apply to this date in each projection year. Each county's population is projected independently and is not controlled to a state or regional total. Missouri total state projections are the sums of projections for all 114 counties and St. Louis City, an independent city not within any county.
This set of population projections is labeled the "preferred series" because of the particular assumptions made about future births, deaths, and migration in Missouri. Specifically, the preferred series of projections assumes that recent migration trends will continue and that fertility and mortality will also follow recent historical patterns. These assumptions and the procedures to implement them are described below.
The population projections are "launched" from base census populations for the 115 areas by age and sex. These base populations reflect corrections in initial published census enumerations, which were made through the Count Question Resolution program sponsored by U.S. Census Bureau. The program handled external challenges to official 2000 counts of housing units and group quarters population received from state, local, or tribal officials.
Middle Fertility in the Preferred Series
Area births are projected for each five-year interval by applying age-specific fertility rates to the number of women in each of the childbearing age groups from ages 10-14 through ages 45-49. An age-specific fertility rate is the number of live births to women of a given age group divided by the total number of women in that age group. Fertility rates are based on total live births reported in each area by the Missouri Department of Health and Senior Services for the period 1998-2002, which centers on the 2000 Census. Births over the period for each age group are divided by 2000 Census counts of women in that age group.
Total fertility rates have been stable over the last thirty years, ranging between 1.8 and 2.0 children per woman on average. Middle fertility rates in the preferred series are assumed to hold at their initial 2000-centered levels throughout the projection horizon.
Middle Mortality in the Preferred Series
Each cohort is aged over each projection interval by applying age-sex-specific survival rates assumed for that period. Initial rates for each area are calculated using abridged life tables provided by the Missouri Department of Health and Senior Services. The life tables are based on 2000 Census counts and recorded area deaths by age and sex for the period 1998-2002.
Life expectancies have generally increased over the last two decades. It is assumed in the preferred series that survival rate changes experienced statewide, by male and female age groups from 1980 to 2005, will continue at the same levels for all age-sex groups in all areas throughout the projection horizon.
Recent Migration in the Preferred Series
Migration assumptions are particularly critical because migration has generally changed area populations more than the birth and death components. The recent migration scenario is applied in the preferred projection series. It assumes that migration trends over the period 2000-2007, the most recent period for which post-census population estimates are available, will continue with some constraints throughout the projection horizon.
Migration is derived from net rates for males and females in each five-year age group in each area. The rates are calculated in four stages. First, 1990-2000 net migration totals are computed as residuals using a vital statistics method, where recorded births and deaths by the Department of Health and Senior Services over the course of the decade are employed. For each area, resident births from April 1990-March 1995 and April 1995-March 2000 are applied, along with resident deaths to 1990 age-sex cohorts. Net migration equals the total population change according to 1990 and 2000 Census counts, minus natural change (births minus deaths) during the 1990s. Net migration rates are highly sensitive to undercount and overcount in the populations on which the rates are based. Therefore, for the purpose of calculating net migration rates, the 1990 and 2000 enumerated census populations are adjusted based on the Census Bureau's estimates of net undercount and overcount to approximate "true" populations.
In the second stage of the migration rate calculations, area net migration totals are converted to ten-year rates by dividing them by the 2000 "expected" population, that is, the survivors of the 1990 population at the end of the decade. These ten-year rates are then converted to five-year rates (the interval of each projection cycle) applying an adjacent cohort averaging technique.
In the third stage of the migration rate calculations, both 2000-2005 and 2000-2007 total net migration controls are developed for all areas. Independent estimates of net migration are calculated as the residual differences between estimated total population change since the 2000 Census and the reported natural change (births minus deaths) over the respective periods. The 2000-2005 controls are used to project 2005 area populations by age and sex. The 2000-2007 controls are converted to five-year controls and are applied starting with the 2005-2010 projection cycle.
In the fourth and final calculation stage, net migration controls are constrained at five-year intervals beginning in 2010-2015 to the final 2025-2030 projection cycle. A root function is used to progressively decay the net migration controls at each successive interval. The 1990-2000 area age-sex net migration rates for each area are adjusted to the constrained net migration control set for the area.
Exceptions to the migration calculations described above occur in 25 counties where large college, military, and prison populations, termed "special populations," reside. An opening, closing, or changed mission of a facility significantly affects the age structure of an area population. Moreover, the cohort-component projection framework does not work properly for age-sex groups with large contingents of special populations, if those large groups are allowed to "age in place" in the county. For this reason, the cohort-component model is modified. Special populations in the 15-64 age range are treated separately from the rest of the population, which is projected with the cohort-component methodology described above. Independent estimates of special populations are separated out at the beginning of each projection cycle and added back to the county's projected "native population" at the end of each cycle. The initial 1990-2000 residual net migration rates for each affected area were also generated after the special population counts were removed from the native age-sex cohorts. Sources of area special populations typically come from the decennial censuses, but also include updated corrections facility data for 2005 from the Missouri Department of Corrections. College enrollments were considered to be special populations only if they comprised eight percent or more of the county's total population. This eight percent threshold identified 12 counties with college special populations.
Missouri Department of Corrections, 1994, 2008. Institutional Admission and Release Reports.
Missouri Department of Health and Senior Services, 1987, 1993, 1994, 2003. Total Fertility Rates and Age-Specific Birth Rates: 1977-1983, 1988-1992, 1998-2002; Abridged Life Tables by Sex, 1977-1983, 1988-1992, 1998-2002; Live Births by Sex: April 1, 1990-1995 and 1995-2000; Resident Deaths by 1990 Age and Sex Cohort: April 1, 1990-2000.
U.S. Census Bureau, 1993. 1990 Census of Population and Housing: Summary File 4, Missouri.
U.S. Census Bureau, 1993. 1990 Census of Population and Housing: Public Use Microdata Sample, 5%, Missouri.
U.S. Census Bureau, 2002. 2000 Census of Population and Housing: Summary File 1, Missouri.
U.S. Census Bureau, 2003. 2000 Census of Population and Housing: Summary File 3, Missouri.
U.S. Census Bureau, 2003. 2000 Census of Population and Housing: Public Use Microdata Sample, 5%, Missouri.
U.S. Census Bureau, 2005. 2000 Census of Population and Housing: Notes and Errata, Missouri.
U.S. Census Bureau, Missouri Office of Administration, 2007. Cumulative Estimates of the Components of Population Change for the United States, Regions, and States: April 1, 2000 to July 1, 2007; Cumulative Estimates of the Components of Population Change for Counties of Missouri: April 1, 2000 to July 1, 2006.
Voss, Paul R., McNiven, Hammer, Johnson, Fuguitt, 2004. County-Specific Net Migration by Five-Year Age Groups, Hispanic Origin, Race and Sex 1990-2000.