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Stochastic modelling and projection of mortality improvements using a hybrid parametric/semi-parametric age–period–cohort model

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  • Erengul Dodd
  • Jonathan J. Forster
  • Jakub Bijak
  • Peter W. F. Smith

Abstract

We propose a comprehensive and coherent approach for mortality projection using a maximum-likelihood method which benefits from full use of the substantial data available on mortality rates, their improvement rates, and the associated variability. Under this approach, we fit a negative binomial distribution to overcome one of the several limitations of existing approaches such as insufficiently robust mortality projections as a result of employing a model (e.g. Poisson) which provides a poor fit to the data. We also impose smoothness in parameter series which vary over age, cohort, and time in an integrated way. Generalised Additive Models (GAMs), being a flexible class of semi-parametric statistical models, allow us to differentially smooth components, such as cohorts, more heavily in areas of sparse data for the component concerned. While GAMs can provide a reasonable fit for the ages where there is adequate data, estimation and extrapolation of mortality rates using a GAM at higher ages is problematic due to high variation in crude rates. At these ages, parametric models can give a more robust fit, enabling a borrowing of strength across age groups. Our projection methodology assumes a smooth transition between a GAM at lower ages and a fully parametric model at higher ages.

Suggested Citation

  • Erengul Dodd & Jonathan J. Forster & Jakub Bijak & Peter W. F. Smith, 2021. "Stochastic modelling and projection of mortality improvements using a hybrid parametric/semi-parametric age–period–cohort model," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2021(2), pages 134-155, February.
  • Handle: RePEc:taf:sactxx:v:2021:y:2021:i:2:p:134-155
    DOI: 10.1080/03461238.2020.1815238
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    Cited by:

    1. Xiaobai Zhu & Kenneth Q. Zhou & Zijia Wang, 2024. "A new paradigm of mortality modeling via individual vitality dynamics," Papers 2407.15388, arXiv.org, revised Oct 2024.
    2. Philip Rees & Tom Wilson, 2023. "Accuracy of Local Authority Population Forecasts Produced by a New Minimal Data Model: A Case Study of England," Population Research and Policy Review, Springer;Southern Demographic Association (SDA), vol. 42(6), pages 1-30, December.

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