The Cohort-Component Method
The cohort-component method is the most commonly used technique to project future population size. The method, covered rigorously by Smith, Taymen, and Swanson (2001), is relatively standardized. However, small variations in the application of the method are often needed to account for the type of data available for input. One such modification was necessary for this study.
The basic concept behind the cohort-component method is that behaviors that prevailed recently will continue in the future. For example, if 10 percent of females age 25 to 29 moved out of a county during the last five-year period, it is expected that 10 percent of females in that age group in that county will do the same during the next five years. This assumption is quite strong and often erroneous. However, the results of the cohort-component method compare favorably to other methods of population projection.
Though not mandatory, most projections made using the cohort-component method use the date of census counts as starting, or launch, points. In this study, the launch date is the year 2000, the time of the last decennial census. Another subjective decision made by demographers who utilize the method is the determination of interval length, the time between the launch and target dates. Usually five year intervals are used. This occurs as most of the data needed to implement the cohort-component method that is freely available to the public is classified in five-year periods.
In the cohort-component method three components of change migration, birth, and death, drive changes in population from one period to the next. Projections are made for age-gender groups as migration and mortality rates tend to differ significantly by age and sex. Similarly, birth rates depend on the age of the potential mother. For the cohort-component method, the three components are addressed individually then combined to project the population.
A mastery of the notation used in population-projection models, which is relatively cumbersome, is needed to understand the mechanics behind the method and to properly build and use a population-projection model. Three symbols are used to manage the notation of time: the launch date, l, target date, t, and interval length, z. Individuals are grouped by their gender, g, and their age, where x is the youngest age in an age group and n is the number of years in each age group.
Migration
In- and out-migration rates are calculated for each age-gender combination using equations (1) and (2). The in-migration rate for individuals of gender g age x to x + n during the period l-t and l is found by dividing the number of individuals of gender g age x + z to x + z + n that move into the area during period l-t to l by the number of individuals of gender g age x to x + n that live outside the geographic region of interest at the beginning of the period, that is l-t. This value is typically expressed as the difference between the total population of the United States of gender g age x to x +n, in year l-t less that residing in the region of interest.
.............(1)
The calculation of the out-migration rate is similar, with the exception that the population of the community of interest is the denominator (2).
.............(2)
To project in-migration between the launch year, l, and the target date, t, the rate calculated in equation (1) is multiplied by the population of the United States less that of the community in the launch year (3) for each age-gender class. Similarly, out-migration is projected by multiplying the out-migration rate from (2) times the population by age-gender group at year l (4).
.............(3)
.............(4)
Mortality
The second step in projecting population using the cohort-component method is to project the number of deaths for each age-gender group. Here the number of surviving individuals nSURVPgx,l is equal to the number of residents of gender g and age x to x + n at time l, nPgx,l, times the survival rate for that age-sex combination nSgx(5). The survival rate can either be determined using site specific location or from state or national data. As survival rates are relatively uniform across the United States, use of national data is common as is the case in this study.
.............(5)
Natality
Next, the number of births for the region is projected. The first step in this process is to determine the age-specific birth rate, which is traditionally noted as births per 1,000 women in their childbearing years (ASBR). This is done by dividing the number of births born to a mother age x to x + n, nBx, divided by the total number of women in that age group, nFPx, and then multiplying that number by one thousand as shown in equation (6).
.............(6)
To accommodate the fact that half of the women in an age group at the beginning of a period will pass into the next age group, the adjusted age-specific birth rate is needed. This is calculated by finding the arithmetic average of successive age-specific birth rates as shown in equation (7).
.............(7)
The number of women of childbearing age, referred to as the at-risk female population, is calculated using (8). This value is equal to the female population in the launch year plus in-migrants, less the number projected to out-migrate or die. It is assumed that the women who die live for half of the interval.
.............(8)
The projected number of births between the launch and target years to mothers age x to x +n is equal to the adjusted age-specific birthrate times the at-risk female population divided by one thousand (9). The total number of births is found by summing across all ages of mothers (10).
.............(9)
.............(10)
The total number of births, Bl to l, is multiplied by rate of male births, PCTM, to determine the number of males born in the period, MBl to l (11). Similarly, the number of births is multiplied by 1 minus the male birth rate to determine the number of females born, FBl to l(12).
.............(11)
.............(12)
These values are then multiplied by the gender-specific survival rate to project the number of male, nMo, z, and female, nF0, z, residents age zero to z in the geographic region (13,14).
.............(13)
.............(14)
Combining the Components
The determination of the projected value of the remaining age-sex groups is done by adding the surviving population with the number of in-migrants less the number of out-migrants as shown in (15).
.............(15)
Projecting Special Populations
To project the population of individuals with trait γ, the ratio of individuals with the trait by age and gender to the total population of the gender-age group are calculated (16). To project the population, this rate is then multiplied by the projected population of that age-gender group calculated previously. The total number of individuals projected with trait γ is found by summing over age and gender (17).
.............(16)
.............(17)
To project the number of households with trait γ, it is further assumed that the household size will remain the same across time, a strong assumption. Household size is calculated by dividing the launch population by the number of households in the launch year (18). To project the number of households in the target year, the projected population in the target year is divided by this rate (19). Equations (20) and (21) project the number of households with trait γ in the same manner as (16) and (17).
.............(18)
.............(19)
.............(20)
.............(21)
Data Requirements
To make use of the cohort component method, migration, mortality, natality (birth rate), and population data are needed. In- and out-migration data by county, age, and gender between the years 1995 and 1999 was taken from the U.S Census. Survival rates were taken from the National Center from Health Statistics. Birth data by age and county of mother was collected from the North Dakota Department of Vital Records. Total population data for the United States and each of North Dakota's counties by age and gender for 2000 were taken from the decennial census.
A modified estimate of U.S. population by age and gender for 1995 was calculated as the values provided by the U.S. Census proved to be out of sync when compared to the actual census counts taken in 2000. These estimates generated nonsensical projections. To address the issue, a 1995 estimate was generated using the 1990 and 2000 census counts and exponential growth between the two dates. This method resulted in significantly improved results, though the underlying theory behind its use is relatively weak.