U.S. Population Projections

Details of the Cohort-Component Method

Reference: Population Division Working Paper No. 38, by By Frederick W. Hollmann, Tammany J. Mulder, and Jeffrey E. Kallan (http://www.census.gov/population/www/documentation/twps0038.html)

The Cohort-Component Method

The cohort-component method for estimating and projecting a population is distinguished by its ability to preserve knowledge of an age distribution of a population (which may be of a single sex, race, and Hispanic origin) over time. It is a special case of a component method, which is defined simply by the use of estimates or projections of births, deaths, and net migration to update a population.  In its simplest statement, the component method is expressed by the following equation:

P_t = P_t-1 + B_t-1,t - D_t-1,t + M_t-1,t     (1)

where P_t = population at time t;
P_t-1 = population at time t-1;
B_t-1,t = births, in the interval from time t-1 to time t;
D_t-1,t = deaths, in the interval from time t-1 to time t; and
M_t-1,t = net migration, in the interval from time t-1 to time t.

Components of population change are estimated or projected separately, and applied to equation (1) recursively to produce a series of populations. We have not specified the measurement unit of time, so the interval from t-1 to t may be of any duration.

The cohort-component method is based on similar logic for individual age groups, recognizing that the source population for a given age group is the population at time t-1 in the adjacent younger age group. For the initial age group, it is births during the interval from t-1 to t. For the moment, let us assume that the time unit is one year. The equation is replaced by two equations, depending on whether the age group is zero (meaning under 1) or any other age as of the last birthday, denoted by a.

P_t(0) = B_t-1,t - D_t-1,t(0) + M_t-1,t(0)            (2)

P_t(a) = P_t-1(a-1) - D_t-1,t(a) + M_t-1,t(a)     (3)

In the case of deaths (D) and net migration (M), a denotes age of decedents or migrants at time t, which is not necessarily equal to age at time of death or migration. Each of the terms in equations (2) or (3), whether defined as a population or a number of events, relates to people born in a particular year (from t-a-1 to t-a). Such a group is known as a birth cohort, hence the term "cohort component method." While it is essential that age and time in equations (2) and (3) be measured in the same unit, there is no requirement that the interval be one year. The Census Bureau’s 2008 projections of the U.S. population are done by single years.