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Smoothing migration intensities with P-TOPALS

Author

Listed:
  • Sigurd Dyrting

    (Charles Darwin University)

Abstract

Background: Age-specific migration intensities often display irregularities that need to be removed by graduation, but two current methods for doing so, parametric model migration schedules and non-parametric kernel regression, have their limitations. Objective: This paper introduces P-TOPALS, a relational method for smoothing migration data that combines both parametric and non-parametric approaches. Methods: I adapt de Beer’s TOPALS framework to migration data and combine it with penalized splines to give a method that frees the user from choosing the optimal number and position of knots and that can be solved using linear techniques. I compare this method to smoothing by model migration schedules and kernel regression using one-year and five-year migration probabilities calculated from Australian census data. Results: I find that P-TOPALS combines the strengths of both student model migration schedules and kernel regression to allow a good estimation of the high-curvature portion of the curve at young adult ages as well as a sensitive modelling of intensities beyond the labour force peak. Conclusions: P-TOPALS is a useful framework for incorporating non-parametric elements to improve a model migration schedule fit. It is flexible enough to capture the variety of profiles seen for both interstate and regional migration flows and is naturally suited to small populations where observed probabilities can be highly irregular from one age to the next. Contribution: I demonstrate a new method for migration graduation that brings together the strengths of both parametric and non-parametric approaches to give a good general-purpose smoother. An implementation of the method is available as an Excel add-in.

Suggested Citation

  • Sigurd Dyrting, 2020. "Smoothing migration intensities with P-TOPALS," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 43(55), pages 1607-1650.
    • Handle: RePEc:dem:demres:v:43:y:2020:i:55
    DOI: 10.4054/DemRes.2020.43.55
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    References listed on IDEAS

    as
    1. Tom Wilson, 2010. "Model migration schedules incorporating student migration peaks," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 23(8), pages 191-222.
    2. Joop de Beer, 2011. "A new relational method for smoothing and projecting age-specific fertility rates: TOPALS," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 24(18), pages 409-454.
    3. Joop de Beer, 2012. "Smoothing and projecting age-specific probabilities of death by TOPALS," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 27(20), pages 543-592.
    4. M. Bell & M. Blake & P. Boyle & O. Duke‐Williams & P. Rees & J. Stillwell & G. Hugo, 2002. "Cross‐national comparison of internal migration: issues and measures," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 165(3), pages 435-464, October.
    5. Aude Bernard & Martin Bell, 2015. "Smoothing internal migration age profiles for comparative research," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 32(33), pages 915-948.
    6. Aude Bernard & Martin Bell & Elin Charles-Edwards, 2014. "Life-Course Transitions and the Age Profile of Internal Migration," Population and Development Review, The Population Council, Inc., vol. 40(2), pages 213-239, June.
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    Citations

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    Cited by:

    1. Sigurd Dyrting & Andrew Taylor & Tom Wilson, 2024. "Application of P-TOPALS for Smoothing Input Data for Population Projections ‘At the Edge’," Population Research and Policy Review, Springer;Southern Demographic Association (SDA), vol. 43(2), pages 1-28, April.
    2. Ameer Dharamshi & Monica Alexander & Celeste Winant & Magali Barbieri, 2025. "Jointly estimating subnational mortality for multiple populations," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 52(3), pages 71-110.
    3. Sigurd Dyrting & Andrew Taylor, 2021. "Smoothing destination-specific migration flows," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 67(2), pages 359-383, October.
    4. Sigurd Dyrting & Abraham Flaxman & Ethan Sharygin, 2022. "Reconstruction of age distributions from differentially private census data," Population Research and Policy Review, Springer;Southern Demographic Association (SDA), vol. 41(6), pages 2311-2329, December.
    5. Jan Weymeirsch & Julian Ernst & Ralf Münnich, 2024. "Model Recalibration for Regional Bias Reduction in Dynamic Microsimulations," Mathematics, MDPI, vol. 12(10), pages 1-25, May.
    6. Tom Wilson & Irina Grossman & Monica Alexander & Phil Rees & Jeromey Temple, 2022. "Methods for Small Area Population Forecasts: State-of-the-Art and Research Needs," Population Research and Policy Review, Springer;Southern Demographic Association (SDA), vol. 41(3), pages 865-898, June.
    7. Agnieszka Orwat-Acedańska, 2024. "Accuracy of small area mortality prediction methods: evidence from Poland," Journal of Population Research, Springer, vol. 41(1), pages 1-20, March.

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    JEL classification:

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

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