Volume 9 - Article 5 | Pages 81-110

A system of model fertility schedules with graphically intuitive parameters

By Carl Schmertmann

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Date received:28 May 2003
Date published:10 Oct 2003
Word count:5200
Keywords:age-specific fertility, age-specific rates, Coale-Trussell, estimation, fertility, models, splines
Additional files:All Files (zip) (zip file, 323 kB)
 FILE I QS Model (Excel file, 88 kB)
 FILE II CT and QS fits to international schedules (pdf file, 226 kB)
 FILE III CT and QS fits to international schedules (Excel file, 80 kB)
 FILE IV QS fits to Swedish time series (Excel file, 132 kB)
Weblink:Please also see the new software with publication 12-5.


I propose and examine a new family of models for age-specific fertility schedules, in which three index ages determine the schedule's shape. The new system is based on constrained quadratic splines. It has easily interpretable parameters, is flexible enough to fit a variety of "noiseless" schedules well, and is inflexible enough to avoid implausible estimates from noisy data. Across a set of over two hundred contemporary ASFR schedules, the new model fits a majority better, and in some cases much better, than the Coale-Trussell model.
When fit to a recent Swedish time series, model parameters exhibit simple, regular changes over time, suggesting utility in forecasting applications. In simulated small-sample data the new model produces plausible ASFR estimates, with errors similar to Coale-Trussell.

Author's Affiliation

Carl Schmertmann - Florida State University, United States of America [Email]

Other articles by the same author/authors in Demographic Research

» Stationary populations with below-replacement fertility
Volume 26 - Article 14

» Quadratic spline fits by nonlinear least squares
Volume 12 - Article 5

» Estimating Parametric Fertility Models with Open Birth Interval Data
Volume 1 - Article 5

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