In the past thirty years, more than 100 censuses gathered fertility data through questions on women's date of last birth. The standard "births last year" (BLY) approach for such data truncates timing information, using binary indicators for births in the prior year only. The first author recently proposed consistent, maximum-likelihood estimation approaches using untruncated date of last birth (DLB).
In this paper we extend DLB techniques to parametric models. We construct estimators for Coale-Trussell M and m parameters from open interval lengths. We apply the new procedure to Brazilian census data, producing maps and spatial statistics for BLY and DLB m estimates in 723 municipalities in Minas Gerais. DLB estimators are less sensitive to sampling error than BLY estimators. This increased precision leads to clearer spatial patterns of fertility control, and to improved regression.
(NOTE from the editorial office: to best view the HTML of this article, you should be using Windows 95 or higher. Readers using other operating systems may not be able to view all of the embedded symbols, and we suggest they use the PDF version instead.)