Bayes plus Brass: Estimating total fertility for many small areas from sparse census data

Estimates of fertility in small areas are valuable for analysing demographic change, and important for local planning and population projection. In countries lacking complete vital registration, however, small-area estimates are possible only from sparse survey or census data that are potentially unreliable. In these circumstances estimation requires new methods for old problems: procedures must be automated if thousands of estimates are required; they must deal with extreme sampling variability in many areas; and they should also incorporate corrections for possible data errors. We present a two-step procedure for estimating total fertility in such circumstances and illustrate it by applying the method to data from the 2000 Brazilian Census for over 5,000 municipalities. Our proposed procedure first smoothes local age-specific rates using Empirical Bayes methods and then applies a new variant of Brass's P/F parity correction procedure that is robust to conditions of rapid fertility decline.<italic>Supplementary material at the project website http://schmert.net/BayesBrass will allow readers to replicate all the authors' results in this paper using their data and programs</italic>.