A system of model fertility schedules with graphically intuitive parameters

Carl Schmertmann

doi:10.4054/DemRes.2003.9.5

Volume 9 - Article 5 | Pages 81–110

A system of model fertility schedules with graphically intuitive parameters

By Carl Schmertmann

Date received:

28 May 2003

Date published:

10 Oct 2003

Word count:

5200

Keywords:

age-specific fertility rate (ASFR), age-specific rates, Coale-Trussell model, estimation, fertility, models, splines

DOI:

10.4054/DemRes.2003.9.5

Supplementary Material:

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)

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Abstract

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.