Estimating Parametric Fertility Models
with Open Birth Interval Data

Carl P. Schmertmann, Ph.D.
André Junqueira Caetano, M.S.

Date Received: 6 August 1999
Date Published: 22  September 1999

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.

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Authors' affiliation:
Carl P. Schmertmann, Ph.D. is an Associate Professor of Economics, Center for the Study of Population, Florida State University, Tallahassee, Florida, USA

André Junqueira Caetano, M.S. is a Doctoral Student in Sociology/Demography, University of Texas, Austin, Texas, USA

Table of Contents:
1 Introduction
2 Statistical Background
   2.1 DLB Data
   2.2 Estimating a Simple Fertility Schedule with DLB Data
   2.3 Summary Indices for Piecewise-Constant Models
   2.4 Poisson Estimation
   2.5 Discussion
3 Empirical Examples: Methods and Data
   3.1 Poisson Regression for Coale-Trussell Parameters
   3.2 Brazilian Census Data
   3.3 Simulated Small-Sample Properties of BLY and DLB estimators
4 Improvements in Small-Area Demographic Analysis with DLB Data
   4.1 Example 1: Spatial Analysis
   4.2 Example 2: Regression Analysis
5 Conclusion
6 Acknowledgments

Keywords: fertility, open birth intervals, Coale-Trussell model, Brazil, statistics
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Estimating Parametric Fertility Models
with Open Birth Interval Data
Carl P. Schmertmann
André Junqueira Caetano
© 1999 - 2000 Max-Planck-Gesellschaft ISSN 1435-9871