Skip to main content

Forecasting the Retirement Age: A Bayesian Model Ensemble Approach

  • Conference paper
  • First Online:
Trends and Applications in Information Systems and Technologies (WorldCIST 2021)

Abstract

In recent decades, most countries have responded to continuous longevity improvements and population ageing with pension reforms. Increasing early and normal retirement ages in an automatic or scheduled way as life expectancy at old age progresses has been one of the most common policy responses of public and private pension schemes. This paper provides comparable cross-country forecasts of the retirement age for public pension schemes for selected countries that introduced automatic indexation of pension ages to life expectancy pursuing alternative retirement age policies and goals. We use a Bayesian Model Ensemble of heterogeneous parametric models, principal component methods, and smoothing approaches involving both the selection of the model confidence set and the determination of optimal weights based on model’s forecasting accuracy. Model-averaged Bayesian credible prediction intervals are derived accounting for both stochastic process, model, and parameter risks. Our results show that statutory retirement ages are forecasted to increase substantially in the next decades, particularly in countries that have opted to target a constant period in retirement. The use of cohort and not period life expectancy measures in pension age indexation formulas would raise retirement ages even further. These results have important micro and macroeconomic implications for the design of pension schemes and individual lifecycle planning.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

Notes

  1. 1.

    In private individual or employer-sponsored pension plans, insurance and non-insurance longevity risk-sharing devices have been proposed and/or implemented, the benefit structure switched from DB to DC and conservative ALM strategies have been adopted [4,5,6,7,8,9, 15].

  2. 2.

    See, e.g., [21,22,23,24,25,26,27,28] and references therein.

  3. 3.

    This contrasts with previous approaches focusing either on the selection of optimal combination schemes and weights [17] or assigning equal weights to the set of superior models [18].

  4. 4.

    On July 2, 2019, the Dutch parliament passed a law that slows the rate of scheduled increases in the retirement age for public pensions, under which the retirement age will remain at the 2019 through 2021 and will rise gradually to age 67 from 2022 to 2024. Starting in 2025, the retirement age will automatically rise based on increases in life expectancy at age 65.

  5. 5.

    Voluntary early retirement pension (VERP).

  6. 6.

    See [1] and references there in for technical details.

References

  1. Bravo, J.M., Ayuso, M., Holzmann, R., Palmer, E.: Addressing the Life Expectancy Gap in Pension Policy. Insurance: Mathematics and Economics (2021, accepted/in press)

    Google Scholar 

  2. Ayuso, M., Bravo, J.M., Holzmann, R.: Getting life expectancy estimates right for pension policy: period versus cohort approach. J. Pension Econ. Finan. 20(2), 212–231 (2021). https://doi.org/10.1017/S1474747220000050

  3. European Commission: Pension Reforms in the EU since the Early 2000’s: Achievements and Challenges Ahead. Brussels: European Economy Discussion Paper 42 (2016)

    Google Scholar 

  4. Bravo, J.M., Pereira da Silva, C.M.: Immunization using a stochastic process independent multifactor model: the Portuguese experience. J. Bank. Finan. 30(1), 133–156 (2006)

    Article  Google Scholar 

  5. Milevsky, M., Salisbury, T.: Optimal retirement income tontines. Insur.: Math. Econ. 64, 91–105 (2015)

    MathSciNet  MATH  Google Scholar 

  6. Bravo, J., El Mekkaoui de Freitas, N.: Valuation of longevity-linked life annuities. Insur. Math. Econ. 78, 212–229 (2018)

    Article  MathSciNet  Google Scholar 

  7. Bravo, J.M.: Funding for longer lives: retirement wallet and risk-sharing annuities. Ekonomiaz 96(2), 268–291 (2019)

    Google Scholar 

  8. Bravo, J.M.: Longevity-linked life annuities: a Bayesian model ensemble pricing approach. In: CAPSI 2020 Proceedings. Atas da 20ª Conferência da Associação Portuguesa de Sistemas de Informação 2020, p. 29 (2020). https://aisel.aisnet.org/capsi2020/29

  9. Bravo, J.M., Coelho, E.: Forecasting subnational demographic data using seasonal time series methods. Atas da Conferência da Associação Portuguesa de Sistemas de Informação (2019)

    Google Scholar 

  10. Bravo, J.M., Ayuso, M., Holzmann, R., Palmer, E.: Intergenerational actuarial fairness when longevity increases: amending the retirement age to cope with life expectancy developments. Scand. Actuar. J. (2021, submit for publication)

    Google Scholar 

  11. Human Mortality Database: University of California, Berkeley (USA), and Max Planck Institute for Demographic Research (Germany) (2020)

    Google Scholar 

  12. Ayuso, M., Bravo, J.M., Holzmann, R.: On the heterogeneity in longevity among socioeconomic groups: scope, trends, and implications for earnings-related pension schemes. Glob. J. Human Soc. Sci.-Econ. 17(1), 31–57 (2017)

    Google Scholar 

  13. Holzmann, R., Ayuso, M., Bravo, J.M., Alaminos, E., Palmer, E.: Reframing lifecycle saving and dissaving by low-, middle-, and high-income groups: initial hypotheses, literature review, and ideas for empirical testing (2021, submitted for publication)

    Google Scholar 

  14. Bravo, J.M., Ayuso, M.: Previsões de mortalidade e de esperança de vida mediante combinação Bayesiana de modelos: Uma aplicação à população portuguesa. RISTI - Revista Iberica de Sistemas e Tecnologias de Informacao, E40, 128–144 (Dec 2020). https://doi.org/10.17013/risti.40.128-145

  15. Bravo, J.M.: Pricing participating longevity-linked life annuities: a Bayesian model ensemble approach. Eur. Act. J. (2021, revised and resubmitted)

    Google Scholar 

  16. Hansen, P., Lunde, A., Nason, J.: The model confidence set. Econometrica 79, 453–497 (2011)

    Article  MathSciNet  Google Scholar 

  17. Andrawis, R., Atiya, A., El-Shishiny, H.: Forecast combinations of computational intelligence and linear models for the NN5 time series forecasting competition. Int. J. Forecast. 27(3), 672–688 (2011)

    Article  Google Scholar 

  18. Samuels, J.D., Sekkel, R.M.: Model confidence sets and forecast combination. Int. J. Forecast. 33(1), 48–60 (2017)

    Article  Google Scholar 

  19. Turek, D., Fletcher, D.: Model-averaged wald confidence intervals. Comput. Stat. Data Anal. 56(9), 2809–2815 (2012)

    Article  MathSciNet  Google Scholar 

  20. Makridakis, S., Spiliotis, E., Assimakopoulos, V.: Statistical and machine learning forecasting methods: concerns and ways forward. PLoS ONE 13(3), e0194889 (2018)

    Article  Google Scholar 

  21. Brouhns, N., Denuit, M., Vermunt, J.: A Poisson log-bilinear regression approach to the construction of projected life tables. Insur. Math. Econ. 31, 373–393 (2002)

    Article  Google Scholar 

  22. Renshaw, A.E., Haberman, S.: A cohort-based extension to the Lee–Carter model for mortality reduction factors. Insur.: Math. Econ. 38(3), 556–570 (2006)

    MATH  Google Scholar 

  23. Currie, I.: Smoothing and forecasting mortality rates with P-Splines. Heriot Watt Un (2006)

    Google Scholar 

  24. Cairns, A., Blake, D., Dowd, K.: A two-factor model for stochastic mortality with parameter uncertainty: theory and calibration. J. Risk Insur. 73, 687–718 (2006)

    Article  Google Scholar 

  25. Hyndman, R., Ullah, S.: Robust forecasting of mortality and fertility rates: a functional data approach. Comput. Stat. Data Anal. 51, 4942–4956 (2007)

    Article  MathSciNet  Google Scholar 

  26. Plat, R.: On stochastic mortality modeling. Insur. Math. Econ. 45(3), 393–404 (2009)

    Article  MathSciNet  Google Scholar 

  27. Hunt, A., Blake, D.: On the structure and classification of mortality models. North Am. Actuar. J. (2020). https://doi.org/10.1080/10920277.2019.1649156

    Article  Google Scholar 

  28. Bravo, J.M., Nunes, J.P.V.: Pricing longevity derivatives via fourier transforms. Insur. Math. Econ. 96, 81–97 (2021)

    Article  MathSciNet  Google Scholar 

  29. European Commission: The 2018 ageing report: economic and budgetary projections for the EU Member States (2016-2070), European Economy, Institutional Paper 079 (2018)

    Google Scholar 

  30. Bravo, J.M., Herce, J.A.: Career breaks, broken pensions? Long-run effects of early and late-career unemployment spells on pension entitlements. J. Pension Econ. Finan. 1–27 (2020). https://doi.org/10.1017/S1474747220000189

  31. Bravo, J.M.: Taxation of pensions in Portugal: a semi-dual income tax system. CESifo DICE Rep. – J. Inst. Comp. 14(1), 14–23 (2016)

    Google Scholar 

  32. Cairns, A., Blake, D., Dowd, K., Coughlan, G., Epstein, D., Ong, A., Balevich, I.: A quantitative comparison of stochastic mortality models using data from England and Wales and the United States. North Am. Actuar. J. 13(1), 1–35 (2009)

    Article  MathSciNet  Google Scholar 

  33. Shang, H.L., Booth, H., Hyndman, R.J.: Point and interval forecasts of mortality rates and life expectancy: a comparison of ten principal component methods. Demogr. Res. 25, 173–214 (2011)

    Article  Google Scholar 

  34. Camarda, C.G.: Smooth constrained mortality forecasting. Demogr. Res. 41(38), 1091–1130 (2019)

    Article  Google Scholar 

  35. Huang, J.Z., Shen, H., Buja, A.: The analysis of two-way functional data using two-way regularized singular value decompositions. J. Am. Stat. Assoc. 104(488), 1609–1620 (2009)

    Article  MathSciNet  Google Scholar 

  36. Brouhns, N., Denuit, M., Van Keilegom, I.: Bootstrapping the Poisson log-bilinear model for mortality forecasting. Scand. Actuar. J. 3, 212–224 (2005)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jorge M. Bravo .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Bravo, J.M., Ayuso, M. (2021). Forecasting the Retirement Age: A Bayesian Model Ensemble Approach. In: Rocha, Á., Adeli, H., Dzemyda, G., Moreira, F., Ramalho Correia, A.M. (eds) Trends and Applications in Information Systems and Technologies. WorldCIST 2021. Advances in Intelligent Systems and Computing, vol 1365. Springer, Cham. https://doi.org/10.1007/978-3-030-72657-7_12

Download citation

Publish with us

Policies and ethics