Demographic Modeling: An Overview
Demography involves the study of the structure and dynamics of human populations or subpopulations, focusing on their size and composition and how they change over time. The changes result from flows into and out of these populations, reflecting births, deaths, and migration. The composition of a population or subpopulation will change when there are disproportionate flows of people with a particular set of characteristics. Although these models were originally developed to forecast population growth and size, they can also be used to model change in other populations of interest. Models of the labor force are an example. If the labor force is considered to be a population and the propensity of a sub-population to enter that population changes, the result will be a change in the share of the population whose propensity has changed. More specifically, the proportion of the labor force that is female (a sub-population) will increase if a disproportionately large number of new entrants to the labor force (the equivalent of births) are female, other factors held equal.
One of the simplest demographic models, a ''cohort-survival'' model, involves projecting the effects of mortality on the size and composition of a given cohort.3 For example, the size of the cohort at time t, Pt at the next time, Pt+1, is projected by multiplying the base population by a "survival rate," 1 -dt, where dt is the proportion of that cohort expected to die during period t:
This type of model is called a "decrement" model because the cohort can only decline over time.
Any measurable process that involves a time pattern of attrition from or accession to a particular state (e.g., in the above example attrition from life) can be analyzed using "life tables"—a statistical device that helps present in an elegant and convenient way the information in a sequence of age- or duration-specific rates. Life tables can be used to generate projections of the size and characteristics of future populations based on some initial base populations. In the simple example above, where the projection is made over a single period for a single cohort, the life-table contains two elements: Pt and 1 - dt.
The model can be made more complex by considering multiple periods and/or multiple cohorts. To project for multiple periods, the model must make some assumption about the death rate. Frequently, it is assumed that this rate will remain stable over time. In this case, the life table used to project the future size of the
cohort after n years, Pt+n, would include only one survival rate, 1 - dt. The equation used to project the cohort to period t+n would be
The alternative assumption—that death rates will rise, fall, or vary in some irregular way—will require more than one survival rate in the life table. In this case, the life table would include a set of n survival rates.
To project for more than one cohort, the model must have death rates for each cohort being examined. For example, one might wish to project both the future size and age composition of the male and female population in period t+n. To do so the model would require survival rates for both males and females. In this case, there would be two life tables—one for each gender. Each table would include a set of survival rates for each age group, as well as a set of numbers representing the size of the initial population for each age group.
One can further complicate the cohort-survival model outlined above by adding inflows and other outflows. For example, to project the future size of the "biomedical workforce,"4 inflows would include (1) the number of new Ph.D.s entering the workforce, (2) the number of reentrants to the workforce, and (3) the number who have emigrated to this workforce from other fields or other countries. Outflows would include (1) the number who leave because of death or retirement or other nonworkforce states (e.g., unemployment or nonlabor force activity), and (2) those who leave to jobs in other fields or other countries. These models are typically called "increment-decrement" models because, given both inflows and outflows, the population can either increase or decline, depending on whether inflows exceed or fall short of outflows.
Life tables for these models would include estimates of rates of inflow and outflow. Such tables are generally referred to as "multi-state life tables" because they incorporate many modes of entry and exit from the cohort, as well as movements between states within the cohort. These rates are then applied to an initial distribution of the population of interest across the states to generate a forecast or projection.
