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Calibrated spline estimation of detailed fertility schedules from abridged data

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  • Carl Schmertmann

    (Max Planck Institute for Demographic Research, Rostock, Germany)

Abstract

OBJECTIVE I develop and explain a new method for interpolating detailed fertility schedules from age-group data. The method allows estimation of fertility rates over a fine grid of ages, from either standard or non-standard age groups. Users can calculate detailed schedules directly from the input data, using only elementary arithmetic. METHODS The new method, the calibrated spline (CS) estimator, expands an abridged fertility schedule by finding the smooth curve that minimizes a squared error penalty. The penalty is based both on fit to the available age-group data, and on similarity to patterns of 1fx schedules observed in the Human Fertility Database (HFD) and in the US Census International Database (IDB). RESULTS I compare the CS estimator to two very good alternative methods that require more computation: Beers interpolation and the HFD's splitting protocol. CS replicates known 1fx schedules from 5fx data better than the other two methods, and its interpolated schedules are also smoother. CONCLUSIONS The CS method is an easily computed, flexible, and accurate method for interpolating detailed fertility schedules from age-group data. COMMENTS Data and R programs for replicating this paper’s results are available online at http://calibrated-spline.schmert.net

Suggested Citation

  • Carl Schmertmann, 2012. "Calibrated spline estimation of detailed fertility schedules from abridged data," MPIDR Working Papers WP-2012-022, Max Planck Institute for Demographic Research, Rostock, Germany.
    • Handle: RePEc:dem:wpaper:wp-2012-022
    DOI: 10.4054/MPIDR-WP-2012-022
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    Cited by:

    1. Vincent Bremhorst & Michaela Kreyenfeld & Philippe Lambert, 2016. "Fertility progression in Germany: An analysis using flexible nonparametric cure survival models," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 35(18), pages 505-534.
    2. Jakub Bijak & John Bryant, 2016. "Bayesian demography 250 years after Bayes," Population Studies, Taylor & Francis Journals, vol. 70(1), pages 1-19, March.
    3. Pavel Grigoriev & Anatoli I. Michalski & Vasily P. Gorlischev & Dmitri A. Jdanov & Vladimir M. Shkolnikov, 2018. "New methods for estimating detailed fertility schedules from abridged data," MPIDR Working Papers WP-2018-001, Max Planck Institute for Demographic Research, Rostock, Germany.
    4. Andrea Verhulst, 2016. "Child mortality estimation: An assessment of summary birth history methods using microsimulation," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 34(39), pages 1075-1128.

    More about this item

    JEL classification:

    • J1 - Labor and Demographic Economics - - Demographic Economics
    • Z0 - Other Special Topics - - General

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