Relating Period and Cohort Fertility

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.