Population of the United States

Calculating the change in a population is easy:$$\text{Population change} = \text{Births} - \text{Deaths} + \text{Immigration} - \text{Emigration}$$ Estimating the number of births and deaths—and the effects of migration—in any given year is difficult.  The number of births can be estimated from the total fertility rate (TFR)—the average number of children a woman will have during her life time.  The number of deaths can be inferred from a life-table, like those used by actuaries.  I've put these statistics together into a simple model for forecasting populations.  Today, we'll look at two hypothetical futures—two assumptions about the behavior of people in the 21st century.

The darker line assumes a constant fertility rate, equal to that of 2012.  The lighter line assumes a decreasing fertility rate.

In the 1960s the United States entered  a period of relatively low fertility.  The population hasn't decreased, because of immigration.  In the past few years, approximately one million people have come to this country each year—compared to about four million births per year.  In the graph above, the darker line shows the expected population if the fertility rate and immigration continue as they were in 2012.  In this case, we would expect the population to level off by mid-century around 350 million people.

The United States has also experienced declining fertility since the mid 2000s.  The lighter line assumes that fertility will continue to fall to 1.4 by the year 2025—this fertility rate would be similar to that of South Korea today.  If you were born in the 1990s, it is likely that none of your children will be born during the 2040s—the decade where the curves diverge.  The parents of these children already exist though—they are young children today.  After this point, the population would decline rapidly, as those born near the end of the 20th century begin to age and die.  We currently face an aging population, but the effects would be much more pronounced in this scenario.