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

Abstract

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.

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.

Keywords:

• fertility
• small areas
• indirect estimation
• spatial statistics
• Bayesian statistics
• Empirical Bayes
• Brass's parity correction
• Brazil

Notes

1. Carl P. Schmertmann is at Center for Demography and Population Health, Florida State University, 601 Bellamy Building, 113 Collegiate Loop, Tallahassee, FL 32306-2240, USA. E-mail: [email protected]. Suzana M. Cavenaghi is at Escola Nacional de Ciências Estatísticas; Renato M. Assunção is at Universidade Federal de Minas Gerais; Joseph E. Potter is at the University of Texas–Austin.

2. This research was supported by two grants from the Eunice Kennedy Shriver National Institute of Child Health and Human Development: R01 HD41528 (awarded to Joseph E. Potter at the University of Texas at Austin), and R24 HD042849 (awarded to the Population Research Center at the University of Texas at Austin). We thank two anonymous reviewers for insights and suggestions that have significantly improved the paper. We also thank participants at the June 2011 IUSSP seminar on ‘Current Issues and Frontiers in Demographic Research’, held in honour of Professor José Alberto Magno de Carvalho, for helpful comments on an earlier draft.