Fertility estimation from open birth-interval data

Censuses and surveys frequently collect information on period fertility through questions on the timing of last births. The standard approach to estimating fertility with open-interval data uses the proportion of women giving birth in the year before the interview. I propose a more efficient, maximum likelihood method for estimating fertility from open-interval data. I illustrate a mathematical derivation of the new method, perform sensitivity analyses, and conduct empirical tests with Brazilian census data. The new estimators have small biases and lower variance than standard estimators for open-interval data. Consequently, the new method is more likely to generate accurate results from small or moderately sized samples.