Relating Period and Cohort Fertility

Abstract

From a population perspective, the trajectories of both the total fertility at successive time periods and the total fertility of successive birth cohorts are derived from the same array of age-specific fertility rates. This analysis uses the assumption of constant age-specific fertility proportions to derive new explicit relationships between period and cohort fertility. In short, period total fertility is approximately equal to the total fertility of the cohort born a generation earlier, with a modest additive adjustment. A simple relationship also links both period and cohort total fertility to ACF, the average fertility of the childbearing cohorts in a given year. Assuming that fertility levels follow a cubic curve, cohort values from the derived relationships are then compared to observed cohort fertility values for the United States in 1917–2019. Despite substantial violations of the constant proportional fertility assumption, the calculated values deviate from the observed values by an average of only 7–8%. Short-term projections suggest that U.S. cohort fertility will continue to decline.