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Smoothing and projecting age-specific probabilities of death by TOPALS

Author

Listed:
  • Joop de Beer

    (Nederlands Interdisciplinair Demografisch Instituut (NIDI))

Abstract

Background: TOPALS is a new relational model for smoothing and projecting age schedules. The model is operationally simple, flexible, and transparent. Objective: This article demonstrates how TOPALS can be used for both smoothing and projecting age-specific mortality for 26 European countries and compares the results of TOPALS with those of other smoothing and projection methods. Methods: TOPALS uses a linear spline to describe the ratios between the age-specific death probabilities of a given country and a standard age schedule. For smoothing purposes I use the average of death probabilities over 15 Western European countries as standard, whereas for projection purposes I use an age schedule of ‘best practice’ mortality. A partial adjustment model projects how quickly the death probabilities move in the direction of the best-practice level of mortality. Results: On average, TOPALS performs better than the Heligman-Pollard model and the Brass relational method in smoothing mortality age schedules. TOPALS can produce projections that are similar to those of the Lee-Carter method, but can easily be used to produce alternative scenarios as well. This article presents three projections of life expectancy at birth for the year 2060 for 26 European countries. The Baseline scenario assumes a continuation of the past trend in each country, the Convergence scenario assumes that there is a common trend across European countries, and the Acceleration scenario assumes that the future decline of death probabilities will exceed that in the past. The Baseline scenario projects that average European life expectancy at birth will increase to 80 years for men and 87 years for women in 2060, whereas the Acceleration scenario projects an increase to 90 and 93 years respectively. Conclusions: TOPALS is a useful new tool for demographers for both smoothing age schedules and making scenarios.

Suggested Citation

  • 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.
  • Handle: RePEc:dem:demres:v:27:y:2012:i:20
    DOI: 10.4054/DemRes.2012.27.20
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    References listed on IDEAS

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    1. Booth, Heather, 2006. "Demographic forecasting: 1980 to 2005 in review," International Journal of Forecasting, Elsevier, vol. 22(3), pages 547-581.
    2. John Bongaarts, 2006. "How Long Will We Live?," Population and Development Review, The Population Council, Inc., vol. 32(4), pages 605-628, December.
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    Cited by:

    1. Qian Lu & Katja Hanewald & Xiaojun Wang, 2021. "Subnational Mortality Modelling: A Bayesian Hierarchical Model with Common Factors," Risks, MDPI, vol. 9(11), pages 1-21, November.
    2. Carl P. Schmertmann & Marcos R. Gonzaga, 2018. "Bayesian Estimation of Age-Specific Mortality and Life Expectancy for Small Areas With Defective Vital Records," Demography, Springer;Population Association of America (PAA), vol. 55(4), pages 1363-1388, August.
    3. Ameer Dharamshi & Magali Barbieri & Monica Alexander & Celeste Winant, 2025. "Jointly estimating subnational mortality for multiple populations," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 52(3), pages 71-110.
    4. Kashnitsky, Ilya, 2023. "Non-survival to pension age in Denmark and Sweden: a sub-national investigation," OSF Preprints y9ke4_v1, Center for Open Science.
    5. 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.
    6. Everton Lima & Flavio Freire & Bernardo Lanza Queiroz & Marcos Gonzaga, 2024. "Analyzing regional patterns of mortality data quality and adult mortality for small areas in Brazil, 1980–2010," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 51(44), pages 1411-1428.
    7. Bernard Baffour & James Raymer, 2019. "Estimating multiregional survivorship probabilities for sparse data: An application to immigrant populations in Australia, 1981–2011," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 40(18), pages 463-502.
    8. Kashnitsky, Ilya, 2023. "Non-survival to pension age in Denmark and Sweden: a sub-national investigation," OSF Preprints y9ke4, Center for Open Science.
    9. 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.
    10. Schmertmann, Carl & Gonzaga, Marcos Roberto, 2018. "Bayesian estimation of age-specific mortality and life expectancy for small areas with defective vital records," SocArXiv syzwx_v1, Center for Open Science.
    11. Keilman, Nico, 2016. "Household forecasting: Preservation of age patterns," International Journal of Forecasting, Elsevier, vol. 32(3), pages 726-735.
    12. 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.
    13. 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.

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    More about this item

    Keywords

    population projections; life expectancy at birth; Lee-Carter model; smoothing; relational model; model age schedules; age-specific probabilities of death; Brass model; partial adjustment model;
    All these keywords.

    JEL classification:

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

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