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Age-period cohort models

Author

Listed:
  • Zoë Fannon

    (Somerville College, University of Oxford)

  • B. Nielsen

    (Nuffield College, University of Oxford)

Abstract
Outcomes of interest often depend on the age, period, or cohort of the individual observed, where cohort and age add up to period. An example is consumption: consumption patterns change over the life-cycle (age) but are also affected by the availability of products at different times (period) and by birth cohort-specific habits and preferences (cohort). Age-period-cohort (APC) models are additive models where the predictor is a sum of three time effects, which are functions of age, period and cohort, respectively. Variations of these models are available for data aggregated over age, period, and cohort, and for data drawn from repeated cross-sections, where the time effects can be combined with individual covariates. The age, period and cohort time effects are intertwined. Inclusion of an indicator variable for each level of age, period, and cohort results in perfect collinearity, which is referred to as “the age-period-cohort identification problem”. Estimation can be done by dropping indicator variables. However, this has the adverse consequence that the time effects are not individually interpretable and inference becomes complicated. These consequences are avoided by decomposing the time effects into linear and non-linear components and noting that the identification problem relates to the linear components, whereas the non-linear components are identifiable. Thus, confusion is avoided by keeping the identifiable non-linear components of the time effects and the unidentifiable linear components apart. A variety of hypotheses of practical interest can be expressed in terms of the non-linear components

Suggested Citation

  • Zoë Fannon & B. Nielsen, 2018. "Age-period cohort models," Economics Papers 2018-W04, Economics Group, Nuffield College, University of Oxford.
    • Handle: RePEc:nuf:econwp:1804
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    File URL: https://www.nuffield.ox.ac.uk/economics/Papers/2018/2018W04_age_period_cohort_models.pdf
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    References listed on IDEAS

    as
    1. D. Kuang & B. Nielsen & J. P. Nielsen, 2008. "Forecasting with the age-period-cohort model and the extended chain-ladder model," Biometrika, Biometrika Trust, vol. 95(4), pages 987-991.
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    Cited by:

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    3. Bischofberger, Stephan M. & Hiabu, Munir & Mammen, Enno & Nielsen, Jens Perch, 2019. "A comparison of in-sample forecasting methods," Computational Statistics & Data Analysis, Elsevier, vol. 137(C), pages 133-154.
    4. Valandis Elpidorou & Carolin Margraf & María Dolores Martínez-Miranda & Bent Nielsen, 2019. "A Likelihood Approach to Bornhuetter–Ferguson Analysis," Risks, MDPI, vol. 7(4), pages 1-20, December.

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