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Producing the Dutch and Belgian mortality projections: a stochastic multi-population standard

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Abstract

The quantification of longevity risk in a systematic way requires statistically sound forecasts of mortality rates and their corresponding uncertainty. Actuarial associations have a long history and continue to play an important role in the development, application and dispersion of mortality projections for the countries they represent. This paper gives an in depth presentation and discussion of the mortality projections as published by the Dutch (in 2014) and Belgian (in 2015) actuarial associations. The goal of these institutions was to publish a stochastic mortality projection model in line with both rigorous standards of state-of-the-art academic work as well as the requirements of practical work such as robustness and transparency. Constructed by a team of authors from both academia and practice, the developed mortality projection standard is a Li and Lee type multi-population model. To project mortality, a global Western European trend and a country-specific deviation from this trend are jointly modelled with a bivariate time series model. We motivate and document all choices made in the model specification, calibration and forecasting process as well as the model selection strategy. We show the model fit and mortality projections and illustrate the use of the model in several pension-related applications.

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Notes

  1. We refer to Chapter 4. The financial impact of longevity risk.

  2. We refer to Part II: Long-term projections of age-related expenditure and unemployment benefits.

  3. See Table II.1.15 in European Commission (DG ECFIN) and Economic Policy Committee (Ageing Working Group) [27], p. 79.

  4. See, for example, the ‘Algemene Ouderdomswet’ (AOW-law): http://wetten.overheid.nl/BWBR0002221/. The definition of period life expectancy is given in Sect. 5.1.

  5. The specific law was published on 21 August 2015, see http://reflex.raadvst-consetat.be/reflex/pdf/Mbbs/2015/08/21/131341.pdf.

  6. See, for example, their 2014 and 2015 reports: Commissie Pensioenhervorming 2020–2040 [14, 15].

  7. More history on the \({\textsf {CMI}}\) can be found in Institute of Actuaries and Faculty of Actuaries [33], pp. 1–5.

  8. For example, the 2012 IAM and IAR, GAM–83 and GAR–94, see National Association of Insurance Commissioners [41], section 3.

  9. A complete description of the model is in Koninklijk Actuarieel Genootschap [36].

  10. We refer to Institute and Faculty of Actuaries [32] and Society of Actuaries [48] for more information.

  11. The multi-population models in this report consist of various combinations of mortality models for the multi-population trend and the country-specific deviation.

  12. For the Belgian calibration, see http://www.iabe.be/nl/iabe-mortality-tables. For the Dutch calibration, see http://www.ag-ai.nl/view.php?action=view&Pagina_Id=480.

  13. For example, these definitions are used by ‘Centraal Bureau voor Statistiek’ (\({\textsf {CBS}}\), http://www.cbs.nl/en-GB/menu/home/default.htm?Languageswitch=on) in The Netherlands and ‘Algemene Directie Statistiek—Statistics Belgium’ (\({\textsf {ADS}}\), http://statbel.fgov.be/en/statistics/figures/) in Belgium.

  14. We use the \({\textsf {CBS}}\) definitions where the age-time subscript ‘x, t’ refers to people born in year \(t-x\). Other institutions, such as the \({\textsf {ADS}}\), use ‘x, t’ to refer to people born in year \(t-x-1\).

  15. This mortality database is available at http://www.mortality.org.

  16. Source: World Bank Data for 2013 on \({\textsf {GDP}}\) per capita in US dollar, http://data.worldbank.org/indicator/NY.GDP.PCAP.CD.

  17. See bottom of page 6 in the \({\textsf {HMD}}\) protocol: http://www.mortality.org/Public/Docs/MethodsProtocol.pdf.

  18. Since we reproduce the results and forecasts as published by \({\textsf {KAG}}\) on 9 September 2014 and by \({\textsf {IA}\vert \textsf {BE}}\) on 18 February 2015 we use the data used by the authors of these publications, as downloaded on 29 May 2014.

  19. On 30 December 2015, data until 2012 for both The Netherlands and Belgium was available on \({\textsf {HMD}}\). This data was used to stay as close as possible to the original dataset used by \({\textsf {KAG}}\) and \({\textsf {IA}\vert \textsf {BE}}\).

  20. This protocol is available from http://www.mortality.org/Public/Docs/MethodsProtocol.pdf.

  21. The number of deaths per year, age and gender are available at http://alturl.com/dz7mc.

  22. Data from, for example, \({\textsf {CBS}}\) shows that the yearly net migration in recent years is around 0.2% of the total population and for specific ages is almost always less than 2%. We consider these effects small enough to not have a significant impact on the calculations. Population data from http://statline.cbs.nl/Statweb/publication/?DM=SLNL&PA=7461BEV&D1=0&D2=1-2&D3=1-100&D4=45-66&HDR=G1,G3,T&STB=G2&VW=T and migration data from http://statline.cbs.nl/Statweb/publication/?DM=SLNL&PA=03742&D1=3&D2=1-2&D3=1-96&D4=0&D5=0&D6=a&HDR=G3,T,G1,G5&STB=G4,G2&VW=T.

  23. Proper scoring rules are out-of-sample evaluation criteria. They are used to assess model predictions by allocating a score for each prediction, based on its accuracy and sharpness. Examples of these scores are the predictive deviance, the squared Pearson residuals or the Dawid–Sebastiani scoring rule from Dawid and Sebastiani [19].

  24. A complete set of all Dutch parameters can be found at the last pages of http://www.ag-ai.nl/download/20470-Prognosetafel+14-Appendix+A.pdf. The full set of Belgian parameters can be found at http://www.iabe.be/sites/default/files/bijlagen/mortality_tables_iabe_2015_parameters.xls.

  25. The Pearson residuals for the Poisson regression in our model are defined as \(\frac{d_{x,t}^{(c)} - E_{x,t}^{(c)}\hat{\mu }^{(c)}_{x,t}}{\sqrt{E_{x,t}^{(c)}\hat{\mu }^{(c)}_{x,t}}}\).

  26. In R we use Seemingly Unrelated Regression through the package systemfit, we use the function systemfit with options method=“SUR” and methodResidCov=“noDfCor”.

  27. For the Dutch tables, see http://www.ag-ai.nl/view.php?action=view&Pagina_Id=480. For the Belgian tables, see http://www.iabe.be/nl/iabe-mortality-tables.

  28. The Dutch calibration for this backtest initially led to an unstable \({\textsf {AR}}\)(1) parameter in the country specific time series: \(a>1\). The results shown here are with an inequality constrained calibration for the time series to keep them stationary.

  29. We note that the \({\textsf {KAG}}\) uses a slightly different definition of life expectancies, available on page 34 of Koninklijk Actuarieel Genootschap [37].

  30. The interest rate i is set to a constant 1% and inflation g is ignored, i.e. 0%. The red band in the left panel of Fig. 13 are period calculations of \(\text{PV}_{65,t}(10{,}000)\), obtained by replacing \(q_{x+l,t+l}\) in (31) with \(q_{x+l,t}\).

  31. The age at which one reaches a full career, i.e. the normal pension age, can be different from person to person depending, amongst others, on the age one starts working and any period of inactivity on the way.

  32. The quantities are actually ‘curtate’ cohort life expectancies, see, for example, Dickson et al. [23].

  33. This is the benefit one would receive in case of retiring at normal pension age \(x_n\) in year \(t_n\) but calculated using the individual’s situation regarding pension variables (such as career length, social security status,\(\ldots\)) at age \(x_r\) in year \(t_r\). Thus, only the timing/mortality aspect of benefits is taken into account.

  34. As such, it is possible that one person has a normal pension age of 67 while another has a normal pension age of 62, depending on career length, type of profession, etc. See Commissie Pensioenhervorming 2020–2040 [14] for more information.

  35. Since there are 10,000 simulations for the reference point and 10,000 simulations for all period life expectancies from 2014 onwards, the quantiles were calculated on \(10{,}000\times 10{,}000\) evaluations of the correction factor \(\gamma\). For the year 2013, only 10,000 evaluations were necessary since \(e_{60,2013}^{\text{per}}\) is known and observed.

  36. Of course, the benefit \(B_{x_r,t_r}\) is still dependent on the situation of the underlying individual, but the numerator numerator of the actuarial correction \(\gamma\) in (33) is now the same for the whole population.

  37. This section is based on the Dutch retirement law (AOW-law) as consulted on 29 April 2016: http://wetten.overheid.nl/BWBR0002221/.

  38. This approach is slightly different from the unisex methodology of \({\textsf {CBS}}\).

  39. The value 20.26 is obtained by filling in \(P_{2021} = 67\) in (35) and simplifying, leading to \(e_{65,2022}^{\text{per}}\) being compared with \(18.26+2\). If the predicted \({\textsf {PLE}}\) is significantly higher than this number (e.g. 8 months higher), subsequent yearly three month increases are necessary to compensate for this difference.

  40. See Appendix B of the English version of the \({\textsf {KAG}}\) publication: http://www.ag-ai.nl/view.php?action=view&Pagina_Id=625.

  41. For example, all people in the portfolio aged 40-49 are in class \(c=2\) and have their age rounded to \(x_c=40\). This is assumed because we do not have full portfolio data but only exposures per age class.

  42. As in Table 1.3.1 on http://www.dnb.nl/statistiek/statistieken-dnb/financiele-markten/rentes/index.jsp.

References

  1. Albrecher H, Embrechts P, Filipović D, Harrison G, Koch P, Loisel S, Vanini P, Wagner J (2016) Old-age provision: past, present, future. Eur Actuar J 6(2):287–306

    Article  MathSciNet  MATH  Google Scholar 

  2. Antonio K (2012) Sluiten van de periodetafel GBM/V 2005–2010. http://www.ag-ai.nl

  3. Antonio K, Devolder L, Devriendt S (2015) The IA\(\mid\)BE 2015 mortality projection for the Belgian population. https://lirias.kuleuven.be/bitstream/123456789/487077/1/AFI_15101.pdf

  4. Barrieu P, Bensusan H, El Karoui N, Hillairet C, Loisel S, Ravanelli C, Salhi Y (2012) Understanding, modelling and managing longevity risk: key numbers and main challenges. Scand Actuar J 3:203–231

    Article  MATH  Google Scholar 

  5. Börger M, Fleischer D, Kuksin N (2014) Modeling the mortality trend under modern solvency regimes. ASTIN Bull 44(1):1–38

    Article  MathSciNet  Google Scholar 

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

    Article  MATH  Google Scholar 

  7. Cairns A (2007) LifeMetrics open source R code. http://www.macs.hw.ac.uk/~andrewc/lifemetrics/. JPMorgan Chase Bank

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

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  10. Cairns A, Blake D, Dowd K, Kessler A (2016) Phantoms never die: living with unreliable population data. J R Stat Soc Ser A (Stat Soc) 179(4):975–1005

    Article  MathSciNet  Google Scholar 

  11. Cairns A, El Boukfaoui G (2017) Basis risk in index based longevity hedges: a guide for longevity hedgers. Working Paper, Heriot-Watt University, Edinburgh. http://www.macs.hw.ac.uk/~andrewc/papers/HedgingLongevityRisk2017.pdf

  12. Carter L, Lee R (1992) Forecasting demographic components: modeling and forecasting US sex differentials in mortality. Int J Forecast 8:393–411

    Article  Google Scholar 

  13. Chen H, MacMinn R, Sun T (2015) Multi-population mortality models: a factor copula approach. Insur Math Econ 63:135–146

    Article  MathSciNet  MATH  Google Scholar 

  14. Commissie Pensioenhervorming 2020–2040 (2014). Een sterk en betrouwbaar sociaal contract. Voorstellen van de Commissie Pensioenhervorming 2020–2040 voor een structurele hervorming van de pensioenstelsels. http://www.pensioen2040.belgie.be

  15. Commissie Pensioenhervorming 2020–2040 (2015) Zware beroepen, deeltijds pensioen en eerlijke flexibiliteit in het pensioensysteem. Aanvullend advies van de Commissie Pensioenhervorming 2020–2040. http://www.pensioen2040.belgie.be

  16. Czado C, Gneiting T, Held L (2009) Predictive model assessment for count data. Biometrics 65(4):1254–1261

    Article  MathSciNet  MATH  Google Scholar 

  17. D’Amato V, Haberman S, Piscopo G, Russolillo M, Trapani L (2014) Detecting common longevity trends by a multiple population approach. N Am Actuar J 18(1):139–149

    Article  MathSciNet  MATH  Google Scholar 

  18. D’Amato V, Haberman S, Piscopo G, Russolillo M, Trapani L (2016) Multiple mortality modeling in a Poisson Lee–Carter framework. Commun Stat Theory Methods 45(6):1723–1732

    Article  MathSciNet  MATH  Google Scholar 

  19. Dawid A, Sebastiani P (1999) Coherent dispersion criteria for optimal experimental design. Ann Stat 27:65–81

    Article  MathSciNet  MATH  Google Scholar 

  20. De Waegenaere A, Melenberg B, Boonen T (2012) Het koppelen van de pensioenleeftijd en pensioenaanspraken aan de levensverwachting. Netspar Design Papers, 12

  21. Denuit M, Goderniaux A-C (2005) Closing and projecting life tables using log-linear models. Bull Swiss Assoc Actuar 1:29–48

    MathSciNet  MATH  Google Scholar 

  22. Devolder P, Maréchal X (2007) Réforme du régime belge de pension légale basée sur la longévité. Belg Actuar Bull 7:34–38

    MathSciNet  Google Scholar 

  23. Dickson D, Hardy M, Waters H (2009) Actuarial mathematics for life contingent risks. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  24. Doray L (2008) Inference for the logistic-type models for the force of mortality. In: Living to 100 and beyond, SOA Monograph M-LI08-01, pp 1–18

  25. Dowd K, Cairns A, Blake D, Coughlan G, Epstein D, Khalaf-Allah M (2010) Backtesting stochastic mortality models. N Am Actuar J 14(3):281–298

    Article  MathSciNet  MATH  Google Scholar 

  26. Enchev V, Kleinow T, Cairns A (2017) Multi-population mortality models: fitting, forecasting and comparisons. Scand Actuar J 2017(4):319–342

    Article  MathSciNet  Google Scholar 

  27. European Commission (DG ECFIN) and Economic Policy Committee (Ageing Working Group) (2015) The 2015 ageing report: Economic and budgetary projections for the 28 EU member states (2013–2060). Eur Econ 3. http://ec.europa.eu/economy_finance/publications/european_economy/2015/pdf/ee3_en.pdf

  28. Haberman S, Kaishev V, Millossovich P, Villegas A, Baxter S, Gaches A, Gunnlaugson S, Sison M (2014) Longevity basis risk: a methodology for assessing basis risk. Technical report, Institute and Faculty of Actuaries. https://www.actuaries.org.uk/documents/longevity-basis-risk-methodology-assessing-basis-risk

  29. Haberman S, Renshaw A (2011) A comparative study of parametric mortality models. Insur Math Econ 48:35–55

    Article  MathSciNet  Google Scholar 

  30. Hyndman R, Booth H, Yasmeen F (2013) Coherent mortality forecasting: the product-ratio method with functional time series models. Demography 50(1):261–283

    Article  Google Scholar 

  31. IMF (2012) Global financial stability report—the quest for lasting stability. http://www.imf.org/External/Pubs/FT/GFSR/2012/01/pdf/text.pdf

  32. Institute and Faculty of Actuaries (2012) CMI Working paper 63. http://www.actuaries.org.uk/research-and-resources/pages/cmi-working-paper-63

  33. Institute of Actuaries and Faculty of Actuaries (1973) Continuous mortality investigation reports. http://www.actuaries.org.uk/research-and-resources/documents/cmi-report-1-whole-volume

  34. Kannistö V (1992) Development of the oldest-old mortality, 1950–1990: evidence from 28 developed countries. Odense University Press, Odense

    Google Scholar 

  35. Kleinow T (2015) A common age effect model for the mortality of multiple populations. Insur Math Econ 63:147–152

    Article  MathSciNet  MATH  Google Scholar 

  36. Koninklijk Actuarieel Genootschap (2012) Prognosetafel AG2012. http://www.ag-ai.nl/view.php?action=view&Pagina_Id=496

  37. Koninklijk Actuarieel Genootschap (2014) Prognosetafel AG2014. http://www.ag-ai.nl/view.php?action=view&Pagina_Id=535

  38. Lee R, Carter L (1992) Modeling and forecasting the time series of US mortality. J Am Stat Assoc 87:659–671

    MATH  Google Scholar 

  39. Li J (2013) A Poisson common factor model for projecting mortality and life expectancy jointly for females and males. Popul Stud J Demogr 67(1):111–126

    Article  Google Scholar 

  40. Li N, Lee R (2005) Coherent mortality forecasts for a group of populations: an extension of the Lee–Carter method. Demography 42(3):575–594

    Article  Google Scholar 

  41. National Association of Insurance Commissioners (2013) NAIC model rule (regulation) for recognizing a new annuity mortality table for use in determining reserve liabilities for annuities. http://www.naic.org/store/free/MDL-821.pdf. MDL-821

  42. Niu G, Melenberg B (2014) Trends in mortality decrease and economic growth. Demography 51(5):1755–1773

    Article  Google Scholar 

  43. Pitacco E, Denuit M, Haberman S, Olivieri A (2009) Modeling longevity dynamics for pensions and annuity business. Oxford University Press, Oxford

    MATH  Google Scholar 

  44. Plat R (2009) On stochastic mortality models. Insur Math Econ 45:393–404

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  46. Schwarz G (1978) Estimating the dimension of a model. Ann Stat 6(2):461–464

    Article  MathSciNet  MATH  Google Scholar 

  47. Shang H (2016) Mortality and life expectancy forecasting for a group of populations in developed countries: a multilevel functional data method. Ann Appl Stat 10(3):1639–1672

    Article  MathSciNet  MATH  Google Scholar 

  48. Society of Actuaries (2014) Mortality improvement scale MP-2014. http://www.soa.org/Research/Experience-Study/Pension/research-2014-mp.aspx

  49. Stevens R (2016) Managing longevity risk by implementing sustainable full retirement age policies. J Risk Insur. doi:10.1111/jori.12153

    Google Scholar 

  50. Van Berkum F, Antonio K, Vellekoop M (2016) The impact of multiple structural changes on mortality predictions. Scand Actuar J 2016(7):581–603

    Article  MathSciNet  Google Scholar 

  51. Villegas A, Haberman S (2014) On the modeling and forecasting of socioeconomic mortality differentials: an application to deprivation and mortality in England. N Am Actuar J 18(1):168–193

    Article  MathSciNet  Google Scholar 

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Acknowledgements

The authors would like to thank the two anonymous referees who provided helpful suggestions to improve an earlier draft of this paper. The authors acknowledge the support of the Koninklijk Actuarieel Genootschap and the Institute of Actuaries in Belgium. Katrien and Sander are grateful for the financial support of Ageas Continental Europe, Fonds voor Wetenschappelijk Onderzoek (\(\textsf {FWO}\)) and the support from KU Leuven through the C2 COMPACT research project.

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Authors and Affiliations

  1. Faculty of Economics and Business, KU Leuven, Belgium

    Katrien Antonio & Sander Devriendt

  2. Faculty of Economics and Business, University of Amsterdam, Amsterdam, The Netherlands

    Katrien Antonio, Wilbert Ouburg & Michel Vellekoop

  3. Center for Economic Research (CentER), Tilburg University, Tilburg, The Netherlands

    Anja De Waegenaere

  4. Commissie Sterfte Onderzoek, Koninklijk Actuarieel Genootschap, Utrecht, The Netherlands

    Wouter de Boer, Robert de Vries, Egbert Kromme, Tim Schulteis, Marco van der Winden, Corné van Iersel & Michel Vellekoop

  5. Werkgroep Prognosetafels, Koninklijk Actuarieel Genootschap, Utrecht, The Netherlands

    Katrien Antonio, Anja De Waegenaere, Hok-Kwan Kan, Wilbert Ouburg & Erica Slagter

  6. Aegon, The Hague, The Netherlands

    Hok-Kwan Kan & Erica Slagter

  7. Delta Lloyd, Amsterdam, The Netherlands

    Wilbert Ouburg

  8. Algemene Pensioen Groep (APG), Heerlen, The Netherlands

    Tim Schulteis

  9. PGGM, Zeist, The Netherlands

    Marco van der Winden

  10. KPMG, Amstelveen, The Netherlands

    Egbert Kromme

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Correspondence to Sander Devriendt.

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Hok-Kwan Kan, Egbert Kromme, Wilbert Ouburg, Tim Schulteis, Erica Slagter, Marco van der Winden: This paper reflects the personal views of the author and not the views of his or her company.

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Antonio, K., Devriendt, S., de Boer, W. et al. Producing the Dutch and Belgian mortality projections: a stochastic multi-population standard. Eur. Actuar. J. 7, 297–336 (2017). https://doi.org/10.1007/s13385-017-0159-x

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