A stochastic version of the brass PF ratio adjustment of age-specific fertility schedules

Estimates of age-specific fertility rates based on survey data are known to suffer down-bias associated with incomplete reporting. Previously, William Brass (1964, 1965, 1968) proposed a series of adjustments of such data to reflect more appropriate levels of fertility through comparison with data on children-ever-born by age, a measure of cohort-specific cumulative fertility. His now widely-used Parity/Fertility or PF ratio method makes a number of strong assumptions, which have been the focus of an extended discussion in the literature on indirect estimation. However, while it is clear that the measures used in making adjusted age-specific fertility estimates with this method are captured with statistical uncertainty, little discussion of the nature of this uncertainty around PF-ratio based estimates of fertility has been entertained in the literature. Since both age-specific risk of childbearing and cumulative parity (children ever born) are measured with statistical uncertainty, an unknown credibility interval must surround every PF ratio-based estimate. Using the standard approach, this is unknown, limiting the ability to make statistical comparisons of fertility between groups or to understand stochasticity in population dynamics. This paper makes use of approaches applied to similar problems in engineering, the natural sciences, and decision analysis--often discussed under the title of uncertainty analysis or stochastic modeling--to characterize this uncertainty and to present a new method for making PF ratio-based fertility estimates with 95 percent uncertainty intervals. The implications for demographic analysis, between-group comparisons of fertility, and the field of statistical demography are explored.