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A system of model fertility schedules with graphically intuitive parameters

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  • Carl Schmertmann

    (Florida State University)

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.

Suggested Citation

  • Carl Schmertmann, 2003. "A system of model fertility schedules with graphically intuitive parameters," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 9(5), pages 81-110.
    • Handle: RePEc:dem:demres:v:9:y:2003:i:5
    DOI: 10.4054/DemRes.2003.9.5
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    References listed on IDEAS

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    1. Ansley Coale & A. John & Toni Richards, 1985. "Calculation of age-specific fertility schedules from tabulations of parity in two censuses," Demography, Springer;Population Association of America (PAA), vol. 22(4), pages 611-623, November.
    2. Jan Hoem & Dan Madien & Jørgen Nielsen & Else-Marie Ohlsen & Hans Hansen & Bo Rennermalm, 1981. "Experiments in modelling recent Danish fertility curves," Demography, Springer;Population Association of America (PAA), vol. 18(2), pages 231-244, May.
    3. Hans-Peter Kohler & Dimiter Philipov, 2001. "Variance effects in the bongaarts-feeney formula," Demography, Springer;Population Association of America (PAA), vol. 38(1), pages 1-16, February.
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    Cited by:

    1. Gianni Corsetti & Marco Marsili, 2013. "Previsioni stocastiche della popolazione nell’ottica di un Istituto Nazionale di Statistica," Rivista di statistica ufficiale, ISTAT - Italian National Institute of Statistics - (Rome, ITALY), vol. 15(2-3), pages 5-29.
    2. Rueda, Cristina & Rodríguez, Pilar, 2010. "State space models for estimating and forecasting fertility," International Journal of Forecasting, Elsevier, vol. 26(4), pages 712-724, October.
    3. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.
    4. Rebecca Folkman Gleditsch & Astri Syse, 2020. "Ways to project fertility in Europe. Perceptions of current practices and outcomes," Discussion Papers 929, Statistics Norway, Research Department.
    5. Roberto Impicciatore & Francesco Billari, 2011. "MAPLES: A general method for the estimation of age profiles from standard demographic surveys (with an application to fertility)," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 24(29), pages 719-748.
    6. Carl Schmertmann, 2021. "D-splines: Estimating rate schedules using high-dimensional splines with empirical demographic penalties," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 44(45), pages 1085-1114.
    7. Ezra Gayawan & Samson B. Adebayo & Reuben A. Ipinyomi & Benjamin Oyejola, 2010. "Modeling fertility curves in Africa," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 22(10), pages 211-236.
    8. Anastasia Kostaki & Javier Moguerza & Alberto Olivares & Stelios Psarakis, 2009. "Graduating the age-specific fertility pattern using Support Vector Machines," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 20(25), pages 599-622.
    9. Paraskevi Peristera & Anastasia Kostaki, 2007. "Modeling fertility in modern populations," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 16(6), pages 141-194.
    10. Marc Luy, 2012. "Estimating Mortality Differences in Developed Countries From Survey Information on Maternal and Paternal Orphanhood," Demography, Springer;Population Association of America (PAA), vol. 49(2), pages 607-627, May.
    11. Cristina Rueda-Sabater & Pedro Alvarez-Esteban, 2008. "The analysis of age-specific fertility patterns via logistic models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(9), pages 1053-1070.
    12. Renato Assunção & Carl Schmertmann & Joseph Potter & Suzana Cavenaghi, 2005. "Empirical bayes estimation of demographic schedules for small areas," Demography, Springer;Population Association of America (PAA), vol. 42(3), pages 537-558, August.
    13. Alina Ștefania CHENIC (CREȚU) & Alin Ioan CREȚU & Laurențiu TEȘCAN, 2018. "A Long Term Analysis of Two Undeniable Realities of the XXI Century - Global Economic Crisis and Demographic Aging," REVISTA DE MANAGEMENT COMPARAT INTERNATIONAL/REVIEW OF INTERNATIONAL COMPARATIVE MANAGEMENT, Faculty of Management, Academy of Economic Studies, Bucharest, Romania, vol. 19(2), pages 196-212, May.
    14. Mikko Myrskylä & Joshua R. Goldstein & Yen-hsin Alice Cheng, 2012. "New cohort fertility forecasts for the developed world," MPIDR Working Papers WP-2012-014, Max Planck Institute for Demographic Research, Rostock, Germany.

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    More about this item

    Keywords

    fertility; estimation; models; splines; age-specific fertility rate (ASFR); age-specific rates; Coale-Trussell model;
    All these keywords.

    JEL classification:

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

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