׉?4ׁB!בCט{u׉׉ 7cassandra://XfMcGLUk7OenBZY3Y-bNgVL6u06MsVslu3bIxVC87yMK` ׉ 7cassandra://bq_fzZxQbD3hejo0wNmdd0u_2XsZEPl3F8iZvRnUMEY``S׉ 7cassandra://A-6DDYVj9bqJPKmPk6g-LOiYVU0Ileic9SHo-j8nppg%`̵׉ 7cassandra://BKpLaqSwZspWigb29U0S5NrJUu3pH8721ZkEnUNClKĂ͠_jL5ט{u׈X3?y׈E_jL5O׉EAKoninklijk Actuarieel Genootschap PROJECTIONS LIFE TABLE AG 2020 ׉ 7cassandra://A-6DDYVj9bqJPKmPk6g-LOiYVU0Ileic9SHo-j8nppg%`̵_jL5P_jL5O{בCט{u׉׉ 7cassandra://s91xQR76LIkD7Xh0FBKhWYRJzKlVHGjT3RwcZ1r521kl` ׉ 7cassandra://aqL89843rDRUAP3QbK8wcSzgGHZQ5LB61jIJjOhy1Gw`S׉ 7cassandra://YFYalGUm4cFFRp4boyz1rhiGrdUhl1J9Zut5F0wX0fA l`̵׉ 7cassandra://YvyHnA1eYzEL9c1ntB44XatIC_fuW80n3caKHCB7NfQ͡:͠_jL5ט{u׉׉ 7cassandra://D-1G_4jn-Iec_80fN1lLaT_8c-B0s32NDGPR72X104Y̓ ` ׉ 7cassandra://FFYnXasaKyfsXqCs9FDIEgX_CnPICF4KIc9NORR3zwU`S׉ 7cassandra://OadBUKP62rFXoiCcyKoc5H8yR6bREbLwyb-L7zxm-kcS`̵׉ 7cassandra://pd2rI-QUJIlbjVJn44wXvWqM6DRn9faENYcCya8Ic3g""͠_jL5נ_jL5o]9ׁHhttp://www.ag-ai.nlׁ ׁ Ј׉E3PROJECTIONS LIFE TABLE AG2020 September 9th 2020 1 ׉ 7cassandra://YFYalGUm4cFFRp4boyz1rhiGrdUhl1J9Zut5F0wX0fA l`̵_jL5Q׉EColophon Publication Royal Dutch Actuarial Association, Groenewoudsedijk 80, 3528 BK Utrecht telephone: 31-(0)30-686 61 50, website: www.ag-ai.nl Design Stahl Ontwerp, Nijmegen Print Selection Print & Mail, Woerden Projections Life Table AG2020 2 ׉ 7cassandra://OadBUKP62rFXoiCcyKoc5H8yR6bREbLwyb-L7zxm-kcS`̵_jL5R_jL5Q{בCט{u׉׉ 7cassandra://Saz6QFDLqvLkP9JxMzPTzkrrHmPgao5S_D3tl56WSyQ9l` ׉ 7cassandra://-vmF882kSRzOzehtNEDaCRenZtvxqvTBlq8dEEwyf6k0M`S׉ 7cassandra://pTCnhaX62UQrrtoDlBlA2yPiJjmQP8RnnxS2V61IJh8`̵׉ 7cassandra://a0Q8smxR1y8v3WE_AhMoAEFjZHDTCy7bdOddYPVFbz08&͠_jL5ט{u׉׉ 7cassandra://epIgAEm61et2FXMLpihm-9t78ErKQDt3So7mDO1rAVQ.` ׉ 7cassandra://iTQKMedSiBG_5bsgemrUeA72sAWYRsx0_kpwCrong5sL`S׉ 7cassandra://VDfoUnhzJhJxUtbPi1qbcxpTchrDOAjLKGHQPgu1Nqg`̵׉ 7cassandra://3uwYurgQu6MbEwbEifqHX2xqLYJGkYw9hr0g_WtN248"͠_jL5׉ECONTENTS 1 Preface – 5 2 Justification – 7 3 Summary – 8 4 Introduction Projections Life Table AG2020 – 12 4.1 Why does AG develop a projection model for mortality probabilities? – 12 4.2 How does the model work? – 12 4.3 What happened since the release of Projections Life Table AG2018? – 13 4.4 Publication of Projections Life Tables on the AG website – 13 5 Data – 14 5.1 Dutch and European data are input for the Projection model AG2020 – 14 5.2 European mortality data: countries with an above-average GDP – 14 5.3 Data range – 15 5.4 Observed mortality has increased in recent years – 16 5.5 Data sources: Human Mortality Database, Eurostat and CBS – 16 6 The projection model – 18 6.1 Model assumptions unchanged – 18 6.2 Adjusted model assumptions – 19 6.3 Effects of adjustments made – 21 6.4 Parameter estimates – 21 7 Results – 26 7.1 Definitions of life expectancy – 26 7.2 Observations with respect to Projections Life Table AG2018 – 26 7.3 From AG2018 to AG2020 – 28 7.4 Projections in perspective – 28 7.5 Link between life expectancy at age 65 and 1st and 2nd pillar retirement age – 30 7.6 Effects on provisions – 31 8 The impact of the Covid-19 pandemic – 34 8.1 Effects in the Netherlands already observed – 34 8.2 Possible long-term effects – 35 8.3 Sensitivity analysis – 35 8.4 Results of the sensitivity analysis – 38 8.5 Future forecasts – 38 Appendices – 39 Appendix A - Projection model AG2020 – 40 Appendix B – Model portfolios Technical provisions – 49 Appendix C – Literature and data used – 51 Appendix D – Glossary – 53 Projections Life Table AG2020 Contents 3 ׉ 7cassandra://pTCnhaX62UQrrtoDlBlA2yPiJjmQP8RnnxS2V61IJh8`̵_jL5S׉E Projections Life Table AG2020 4 ׉ 7cassandra://VDfoUnhzJhJxUtbPi1qbcxpTchrDOAjLKGHQPgu1Nqg`̵_jL5T_jL5S{בCט{u׉׉ 7cassandra://8vx8wEA8hYssTKpvzlsGHHz6memKeSyY9ku_zB3MiT0B` ׉ 7cassandra://rNUCBDp7jXn7eFMmq2Fh8AQOeHuDj-ElAODE_2IXQU40#`S׉ 7cassandra://J2Z3G6qnVyJoEhsfRSsv9ZKFqPVbA6qyIeOYi4uHQGE`̵׉ 7cassandra://C06GPuvn0M7bi0VCdQgxkxU9OpEYodpgPOJlz7PDdNM,4&͠_jL5ט{u׉׉ 7cassandra://sgtqYqX86OhHaBgJF97U5IP5pxPLIEC7ONK0ynDBLTY.` ׉ 7cassandra://wSqfAv1A7b-lbP1LzrpgCJ0XHPar_Es7W1xpRfa3-_w|`S׉ 7cassandra://XQGyLxeAd_5KLqMuFeV6Iy18YB1_voT7ToHBWpZ5lAI`̵׉ 7cassandra://cjvcoIfA7kZN-OmZFW_-TwmqPt3ud4ZF7s5wFT9ONG8 %"͠_jL5׉E1 PREFACE For decades, life expectancy has increased steadily in the Netherlands as well as in the neighbouring countries. This trend has had a large impact on society. It is important for pension funds and life insurers to understand the development of life expectancy in order to be able to estimate future cashflows and thus to set provisions. Every two years The Royal Dutch Actuarial Association (Koninklijk Actuarieel Genootschap or ‘AG’) publishes a new Projections Life table, providing an insight into the expected development of life expectancy in The Netherlands, based on the most recent information at the time. Before you is the publication of the new Projections Life Table AG2020. The underlying model is a fully transparent model with a limited number of parameters, making it easy to explain and exactly reproducible. This complies with AG’s aim to make knowledge available to and applicable by the financial sector. Since the publication of AG2018 various analyses have been conducted that have led to further improvements of the model. The changes from AG2018 will be explained both substantively and numerically. The impact of Covid-19 on life expectancy is as yet hard to predict because of the limited availability of data and the uncertainty in how the pandemic will develop in the future. Therefore, only a number of sensibility analyses have been carried out. I want to thank the members of AG Mortality Research Committee (Commissie Sterfte Onderzoek or ‘CSO’) and the Projections Life Tables Working Group for their efforts and all the work that they have done over the past two years. Wies de Boer AAG Chair AG Mortality Research Committee Projections Life Table AG2020 Preface 5 ׉ 7cassandra://J2Z3G6qnVyJoEhsfRSsv9ZKFqPVbA6qyIeOYi4uHQGE`̵_jL5U׉E Projections Life Table AG2020 6 ׉ 7cassandra://XQGyLxeAd_5KLqMuFeV6Iy18YB1_voT7ToHBWpZ5lAI`̵_jL5V_jL5U{בCט{u׉׉ 7cassandra://RCp6cD8k1kzCwI7Jt73H9wsMQLeNARtCH0lMPjOBr0M` ׉ 7cassandra://bRm65Z5PTNR1pIVL_lnRJ_5Gj057f-vm2wtwdN5E5yYF8`S׉ 7cassandra://o6ZwUn4rP18l19BW3B7DqbNClvYOqZuxFP0jPoXB7zY`̵׉ 7cassandra://qtxaMv3OEGmsPx2B7_GdndJXBtGsbF-7t4CQw3S8C_I6(&͠_jL5ט{u׉׉ 7cassandra://pMemCBQ6XlrVFpPr_Yhaot0XVvPp4hAP5pXn2irlcZY]` ׉ 7cassandra://IF-f7ayV5thmum2ejEpj6mmqJnm7Ie4vau_X8_9R4X0@`S׉ 7cassandra://V8gzMaiA-vE28aGrqj9JiUCTwj89nKVgYVoI3EGUSUI`̵׉ 7cassandra://4dO4lSqWvJo013WTwECaB_CySft3ZUTa7zs2F2p2yyQ4&͠_jL5׉E A2 JUSTIFICATION Mortality Research Committee Monitoring the development of mortality in the Netherlands and developing projections of this has traditionally been an important task of the Royal Dutch Actuarial Association. An expression of this is the long series of period and projections life tables the Association has published. In 2011, the Board of the Association set up the Mortality Research Committee and assigned it the task of publishing a new Projections table every two years, which was to serve as the basis for estimating the future life expectancy of the population of the Netherlands. In 2014, a model was implemented which, in addition to the mortality projections, also reflects the uncertainty in the projection of this model (a so-called stochastic model). This resulted in the publication of Projections Life Table AG2014. Projections Life Table AG2016 is based on the same model as Projections Life Table AG2014, with a number of changes to the data used and the method of estimation. In particular, the correlation between the development of mortality amongst men and women was modelled. After the publication of Projections Life Table AG2016 a number of aspects have undergone further research, but this has not led to any model adjustments. Thus, AG2018 was based on the same model as AG2016. In the past two years further analyses have been performed, that have led to some model adjustments. These adjustments have made the model more robust and this model is the basis for AG2020. The committee consists of members with an academic background, members from the pensions and insurance sector with a technical background and members from these sectors with a managerial background. Mid 2020, the Mortality Research Committee consists of the following members: B.L. de Boer AAG, chair drs. C.A.M. van Iersel AAG CERA, secretary prof. dr. B. Melenberg drs. J. de Mik CFA AAG drs. E.J. Slagter FRM prof. dr. ir. M.H. Vellekoop, vice chair ir. R.E.J.M. Waucomont AAG M.A. van Wijk MSc AAG ir. drs. M.R. van der Winden AAG MBA AG Projections Life Tables Working Group The Mortality Research Committee set up the Association’s Projections Life Tables Working Group at the end of 2012 with the task of supporting the Committee in the development of projection tables. Mid 2020, the Working Group consists of the following members: M.J.A. Klein MSc AAG, chair F. van Berkum PhD F.J. Cuijpers MSc AAG ir. drs. J.H. Tornij J.I. Tol MSc AAG Drs. B.G. ter Veer AAG W. van Wel MSc K. Wittekoek MSc In performing its task, the Working Group has carried out various analyses to obtain Projections Life Table AG2020. These analyses have deepened the Working Group’s insights and resulted in model adjustments. The Mortality Research Committee has validated the Projections Life Table AG2020 as set by the Working Group. Projections Life Table AG2020 Justification 7 ׉ 7cassandra://o6ZwUn4rP18l19BW3B7DqbNClvYOqZuxFP0jPoXB7zY`̵_jL5W׉E 3 SUMMARY By publishing Projections Life Table AG2020 AG presents its most recent estimation of future mortality of the Dutch population to date. This estimation is based on mortality data from both the Netherlands and European countries of similar prosperity. Projections Life Table AG2020 replaces Projections Life Table AG2018. The most important features of the Projections Life Table AG2020 are: • Projections Life Table AG2020 can be used to estimate mortality levels far into the future. Expected future developments in mortality can be factored into calculations of life expectancy and provisions. • In addition to historical mortality in the Netherlands, Projections Life Table AG2020 also uses mortality data from selected European countries with similar prosperity levels. This combination of data leads to a stable model less sensitive to random aberrations in the Dutch data for any one year. • Projections Life Table AG2020 is based on a stochastic model, enabling pension funds and life insurers to also estimate the uncertainty of the forecast. After the publication of AG2018 various analyses were conducted in preparation of Projections Life Table AG2020. These were partly driven by questions and suggestions from the profession. With the analyses further refinements of the model were tested. The selection of the AG2020 model was based on a number of science-based statistical model selection criteria. Model outcomes must be plausible as well as explicable. Stability and robustness of the model are important factors too. Finally, coherence is an important criterion, meaning that future mortality in the Netherlands and the selected European countries will not diverge significantly. All this has resulted in two model adjustments, which are explained in detail in chapter 6. Both adjustments relate to the modelling of the Dutch deviation from the European countries: 1. Constants are added to the modelling of the Dutch deviation for both men and women. This means that the time series that describe the differences between the Netherlands and other countries converge to non-zero numbers. 2. The modelling of the Dutch deviation no longer used data from 1970 onwards, but instead data from 1983 onwards. Dutch data from 1970 is still used in the modelling of the European mortality trend. The changes of Projections Life Table AG2020 as compared to Projections Life Table AG2018 are caused by (1) the two aforementioned model adjustments and (2) the addition of new mortality data from The Netherlands and Europe. Projections Life Table AG2020 Summary 8 ׉ 7cassandra://V8gzMaiA-vE28aGrqj9JiUCTwj89nKVgYVoI3EGUSUI`̵_jL5X_jL5W{בCט{u׉׉ 7cassandra://G4pDQXeuHioFGhuWddOMWl_0Ket0nBVdkBInvr88660` ׉ 7cassandra://ui9uF8vlymjZ0hRA4bcnYdBiCtYEg1IQSqA9wtj8DSk=`S׉ 7cassandra://SWSSHaTV1nfw5NAcYp-SNfpaWPJSrqzniu6UHGUGJwA`̵׉ 7cassandra://jJMWgDoZRumMmU-U1RSvdo-W9QpKJ5SZX1p82iseNQsCZ͠_jL5ט{u׉׉ 7cassandra://NgDvxbMebhk5KtZ79Qxuj5QF-n-D93_CQiUWo-T26-o(` ׉ 7cassandra://JY6yVxQDxLSHwELeT32PJ4X0MW2erxrNY0A2JGcL9Xc/`S׉ 7cassandra://m5imzLVfVkSsP8Cputp4dcQ3TnNaUMqXUfqqA4rraXM`̵׉ 7cassandra://f5g4SNQY_yHBiLeCc66qZ8McD4_6r8MoMC5YOTuxLYE?k͠_jL5׉ETable 3.1 lists the effects of the new projections table. It shows that life expectancy at birth is reduced by about one year for both men and women. The remaining life expectancy at age 65 drops by about six months. Model change is the main cause of the downward adjustment of the prognosis. The impact of adding new mortality data is much smaller. Cohort life expectancy in 2021 AG2018 Model change Adding new data AG2020 At birth Male 90.2 -0.8 -0.1 89.3 Table 3.1 Cohort life expectancy in 2021 The conclusion is that life expectance is still expected to rise in the future, but at a lower rate compared to Projections Life Table AG2018. For a variety of model funds, chapter 7 presents calculations of the impact of the implemented changes on provisions and premium levels. For an average fund, the provision will drop by around 2 per cent at a 1% interest rate. Table 3.2 breaks down the impact of replacing AG2018 by AG2020 for an average model portfolio into two steps. Impact TP 1% interest Male Model change Data update -1.6% -0.5% Average Female -1.4% -0.8% Total -2.1% -2.2% Table 3.2 Impact on technical provision for an average model portfolio at a 1% interest rate It shows that more than two thirds of the reduction in technical provision is explained by the model change. The impact on the premium exceeds that of the provision. This is related to a longer average projection horizon. The premium drops by 2.5 to 3 per cent at a 1% interest rate. The expected development of the State Pension retirement age and standard retirement age using the latest insights based on Projections Life Table AG2020 and the Outline agreement of June 5th, 2019 is summarised in graph 3.1 We wish to emphasise that the actual increase of the State Pension retirement age and standard retirement age is linked to the estimates of Statistics Netherlands (Centraal Bureau voor de Statistiek, CBS) and these values are to be regarded as indicative. Female 92.7 -0.6 -0.4 91.7 Male 20.5 -0.5 0.0 20.0 At age 65 Female 23.3 -0.2 -0.2 22.9 Projections Life Table AG2020 Summary 9 ׉ 7cassandra://SWSSHaTV1nfw5NAcYp-SNfpaWPJSrqzniu6UHGUGJwA`̵_jL5Y׉EU65.5 66.0 66.5 67.0 67.5 68.0 68.5 69.0 69.5 65.0 2020 2024 2028 2032 2036 2040 2044 2048 2052 2056 2060 State Pension age Standard retirement age Graph 3.1 Development of State Pension retirement age and standard retirement age based on AG2020. Adjustment of the State Pension retirement age is done in threemonth steps. According to the AG2020 projections the State Pension retirement age increases to 67 years and 3 months in 2030 and to 68 year in 2042. The impact of Covid-19 on life expectancy is as yet hard to predict. The outbreak was in 2020 and that means that only limited date are available. Future developments related to this virus are uncertain and at this time it is not clear if there will be a lasting effect. For this reason, the 2020 effects have not been included in the projections. To provide some insight into the possible impact on life expectancy, two sensitivity analyses were performed: • An analysis only including excess mortality until mid 2020. • Another analysis assuming that there will be an equal excess mortality in the second half of 2020. In the first analysis the average life expectancy at birth is about six months lower than the AG2020 prognosis. In the second analysis the average life expectancy decreases by more than a year. The effect is stronger for men than for women. Projections Life Table AG2020 Summary 10 ׉ 7cassandra://m5imzLVfVkSsP8Cputp4dcQ3TnNaUMqXUfqqA4rraXM`̵_jL5Z_jL5Y{בCט{u׉׉ 7cassandra://jGU0gZ4D3XrqlCMigeOGWeIGwjLE_aChR8sIG5KBK-o<` ׉ 7cassandra://Kx96lJspFomPAIyCvbzvZONNeL35M1rS4ZCmir-uO98`S׉ 7cassandra://jd7D9IcQ1zHa-xrdZu5IsT6K7tmNUjGx3gV79wYzoPs`̵׉ 7cassandra://PcZILWiC5jZWObw1WvrVfCg103H78hXxFGWFNe-60Mo &͠_jL5ט{u׉׉ 7cassandra://3OA-H2ECYwwZl8p6i1Z0UqzKz9J6gqA5YS71nmUV__Y` ׉ 7cassandra://1fuVJ4Ewt2zx_qZidvqMGfHOJ3H6BQRcuCWxQlnZBogJ`S׉ 7cassandra://ouk-MzhFSNbQMiyNYCZTUGIcShiIdRZ03CzRlE8r8b8 `̵׉ 7cassandra://_GAfK_mAEC2ApHbyxoPxW-11FIRKREH3YhWF6peCDu8=/&͠_jL5׉E.Projections Life Table AG2020 Samenvatting 11 ׉ 7cassandra://jd7D9IcQ1zHa-xrdZu5IsT6K7tmNUjGx3gV79wYzoPs`̵_jL5[׉E 4 INTRODUCTION PROJECTIONS LIFE TABLE AG2020 Through the publication of Projections Life Table AG2020, AG presents an assessment of the expected development of survival rates and life expectancy in the Netherlands. This assessment is based on the most recent mortality data from The Netherlands and from European countries of similar prosperity. The result is a forecast of mortality probabilities by age for each future year for men and women. This introduction describes why the forecast is made, how the model works and what activities were performed since the release of Projections Life Table AG2018. 4.1 Why does AG develop a projection model for mortality probabilities? Every two years AG publishes a projection model to forecast the development of mortality rates in the Dutch population. This model is relevant to, among others, pension funds and life insurance companies. The projection model can be used for the determination of the provisions held by pension funds and insurers, taking into account fund or portfolio specific mortality experience if desired. Pension benefits, in general, are paid as long as a participant or insured person lives and therefore it is important to know how long this person is expected to survive. AG combines expertise from science and the pensions and insurance industry to develop this mortality forecast. The AG model is fully transparent and only uses publicly available data. Based on the model documentation and the data used, the model can be copied and its results reproduced. AG has developed this model for the whole industry and it therefore contributes to market uniformity. 4.2 How does the model work? The projections are based on a stochastic model. This makes it possible to give an impression of the uncertainty in the development of life expectancy. The model estimates parameters that best describe the historical development of European mortality in countries with a prosperity level similar to that of the Netherlands. Based on these parameters a forward projection can be made for these countries. The size of the dataset makes this projection stable. In addition, parameters are estimated that describe the historical aberration between mortality in The Netherlands and these European countries. From 1970 onwards a decreasing difference in mortality probabilities between European countries is clearly discernible. Also, the development of period life expectancy has shown a similar upward trend for decades. See graphs 5.1 and 5.2 in chapter 5. Projections Life Table AG2020 Introduction Projections Life Table AG2020 12 ׉ 7cassandra://ouk-MzhFSNbQMiyNYCZTUGIcShiIdRZ03CzRlE8r8b8 `̵_jL5\_jL5[{בCט{u׉׉ 7cassandra://JLoe6onsL5sA2f8I5QgIunLS5vXtjZtwbXY2Oa9OFV0 F` ׉ 7cassandra://nEXXj_XL8I_kRvcC_4XWLKM1VTa8-Ql8sWKpQzbBcP09`S׉ 7cassandra://vHr_Hc8bpopJr6hVq7EaJpZAT_OwOuEvIgw4ECkOKEY~`̵׉ 7cassandra://T6u6iIHpQILoKsgdt7r9Oazn4sOIaHnkxMf6RFD_RdM4&͠_jL5ט{u׉׉ 7cassandra://2F3jqwAtAa2p6I7MnJtfqB6Sy2RWvLsUyjScbxjZXvQV` ׉ 7cassandra://cvbUIu_ehljCUVWAdJv5XfBdw1gjbOty6KrZxQhpeHg?`S׉ 7cassandra://5xiedGUu6T442aA6CQPknynO7zhIec3jG6Vrg4JnKSc`̵׉ 7cassandra://EfwbKsC9Q1DNSbZe0W7Xdq86-iLHRm8OUk1LF8nLxM81z&͠_jL5נ_jL5'9ׁH*http://www.ag-ai.nl/ActuarieelGenootschap/ׁ ׁ Ј׉E !The current view is, that life expectancy will continue to rise. The evolution of life expectancy is the balance of all (positive and negative) circumstances that impact life expectancy. Implicit in our projections is the assumption that, as in the past, new developments will keep occurring that bring about further increases in life expectancy. This may be, for instance, medical or technological developments or developments related to lifestyle and environment. Mortality developments observed in the past also had multiple causes, such as changes in smoking behaviour, improvements in the treatment of cardiovascular diseases and an increased regard for a healthy lifestyle. The covid-19 outbreak may also impact life expectancy. At this time, it is hard to gauge these effects, because much is still unclear. Although 2020 will show a significant excess mortality, it is unclear what the effects will be in subsequent years. The absence or availability of a vaccine is of great importance to this. Chapter 8 explores the possible effects of covid-19 by calculating a number of sensitivity analyses. Because of the fact that extrapolation techniques had to be used to obtain data points that were not yet available, these sensitivity analyses are not part of the AG2020 model. 4.3 What happened since the release of Projections Life Table AG2018? A number of analyses were conducted to explore further model refinements. The analyses conducted were in part prompted by questions and suggestions from the profession after the publication of AG2018. The analyses have led to two adjustments. Firstly, constant terms were added to the projection of the Dutch deviation from Europe. Also, the sample length for the Dutch deviation was shortened. As a result, the projection model AG2020 is further improved and meets the standards set by the Mortality Research Committee for a good model. 4.4 Publication of Projections Life Tables on the AG website AG published Projections Life Table AG2020, including the technical specifications of the projection model, on its website. Refer to www.ag-ai.nl/ActuarieelGenootschap/ Publicaties. Also listed there are Excel files with the data sets that can be used to reproduce the estimations of the model’s parameters. Projections Life Table AG2020 Introduction Projections Life Table AG2020 13 ׉ 7cassandra://vHr_Hc8bpopJr6hVq7EaJpZAT_OwOuEvIgw4ECkOKEY~`̵_jL5]׉E 5 DATA 5.1 Dutch and European data are input for the Projection model AG2020 The current Projection model AG2020 uses similar data as Projection model AG2018. This implies that, additional to mortality in the Netherlands, data are used on the mortality developments in a number of other European countries. Since 1970 a decrease in the differences in mortality probabilities between these European countries is clearly discernible. Also, the period life expectancies in these countries have shown similar upward trends for decades. Please refer to graphs 5.1 and 5.2. In view of these apparent similarities, as of Projection model AG2014 the choice was made to expand the basis for the Dutch projections to the developments in these European countries. This prevents the forecast from being solely dependent on Dutch data that may include specific historical fluctuations that may not be indicative of future developments. The view is, that the long term increase of life expectancy in the Netherlands can be more accurately predicted by including a broader European population, as this vastly expands the number of observations: from just over 100,000 deaths annually in the Netherlands to over 2,000,000 deaths per year for the included European countries, rendering the model more robust. Consecutive projections are expected to be more stable than when using only Dutch data. 5.2 European mortality data: countries with an above-average GDP The projection model uses European mortality data from countries with an above-average Gross Domestic Product (GDP). GDP is seen as a measure for a country’s prosperity. A positive correlation exists between prosperity and ageing: the higher the prosperity level, the older people get. The Netherlands is a high prosperity country with a GDP above the European average. Based on this criterion, the following European countries have been included: Belgium, Denmark, Germany, Finland, France, Ireland, Iceland, Luxembourg, Norway, Austria, United Kingdom, Sweden and Switzerland. In this publication the aforementioned countries together are referred to as “Europe” or “Western Europe”. The selection of countries was first performed for the publication of the Projection model AG2014. As time passes, other countries may also meet the above-average GDP selection criterion, or countries may cease to do so. In the creation of AG2020 the criterion still generates the same set of countries. Projections Life Table AG2020 Data 14 ׉ 7cassandra://5xiedGUu6T442aA6CQPknynO7zhIec3jG6Vrg4JnKSc`̵_jL5^_jL5]{בCט{u׉׉ 7cassandra://de1iKz3qzGk7mI_xJAXn9Y5tKydhBrHZmV6eH7LmiQA` ׉ 7cassandra://5A0WYl3BB7SvT7U1B7eZa0tkffcrVANmp577Ckc7lwA4`S׉ 7cassandra://c11d3cL3tRMRuFhQPUru0eF2UJMBBKXyLcsCYwU4E14`̵׉ 7cassandra://ycL6jgAgx2iVDqpR1WUipzbiUu59RRYWjQoZ0dkofh8-͠_jL5ט{u׉׉ 7cassandra://VlcUX6MtNhZK0mHTSC9mbcPxO1PXRSBP9FRcXxc6H3Y` ׉ 7cassandra://ACoVGcPDvf4N1VJiXqS2RxqeWkDrWfs5qZ0bN2NlSAUO`S׉ 7cassandra://Jv2fjLhiaWxtKe-ZJXBGU5y55ADB0kCKqrmgg_M8VD0`̵׉ 7cassandra://M307_P8DvbkBB0oGokeX5WApX9vOydmB_iOMGwH6U8URR͠_jL5׉E5.3 Data range Graphs 5.1 and 5.2 show the historical development of life expectancy at birth in the Netherlands and the selected European countries since 1950. The graphs show that in the first part of this period life expectancies are quite far apart, for men in particular. From 1970 onwards a stable development can be seen in life expectancies of both men and women. For the estimation of the European leg of the model, including the Netherlands, we use data from the observation period 1970 through 2018. For the Dutch deviation we use data from 1983 through 2019. 62 64 66 68 70 72 74 76 78 80 82 84 1950 1960 1970 The Netherlands 1980 1990 Other countries Graph 5.1 Period life expectancy at birth male 62 64 66 68 70 72 74 76 78 80 82 84 86 1950 1960 1970 The Netherlands 1980 1990 Other countries Graph 5.2 Period life expectancy at birth females Graphs 5.1 and 5.2 show that life expectancy in the Netherlands after 1970 has risen less than the average over the selected European countries. This is true in particular for women, since the early eighties. The difference between Dutch and European women is even more apparent when looking at the underlying mortality probabilities. Chapter 6 will Projections Life Table AG2020 Data 15 2000 2010 2000 2010 ׉ 7cassandra://c11d3cL3tRMRuFhQPUru0eF2UJMBBKXyLcsCYwU4E14`̵_jL5_׉E uexplore this further and also explain what the effect of this lagging (compared to other European countries) is on the Projection model AG2020. 5.4 Observed mortality has increased in recent years In the publication of Projection model AG2020, attention was given to excess mortality in the years 2016 and 2017 as a result of, among other causes, a wave of influenza in the 2016/2017 season. This led to mortality higher than was to be expected based on Projection model AG2016, in particular for higher ages. This was true for the Netherlands as well as for the selection of European countries. For observation years 2017 and 2018 mortality continues to be higher than expected for higher ages in particular. This too can be partly attributed to the flu season 2017/2018. Mortality caused by influenza has been above average in recent years not only in the Netherlands, but also in other European countries1,2. A strong increase or decrease of mortality in the Netherlands often coincides with a strong increase or decrease in other European countries. This can be seen in the bar charts in graphs 5.3 and 5.4. These represent the numbers of deaths per year in The Netherlands and in Europe. Mortality in 2018 in the over 65 age group is shown to be higher than in previous years. For men this shows in The Netherlands and in Europe, for women it is most prominent in The Netherlands. 10 15 20 25 30 35 0 5 Age 0 to 65 age 65 to 80 age 80 thru 90 2012 2013 2014 2015 2016 2017 2018 100 200 300 400 500 600 700 2012 2013 2014 2015 2016 2017 2018 – Age 0 to 65 age 65 to 80 age 80 thru 90 Graph 5.3 Number of deaths male (x1,000) in The Netherlands (left) and in Europe (right) in the years 2012 – 2018 10 15 20 25 30 35 0 5 Age 0 to 65 age 65 to 80 age 80 thru 90 2012 2013 2014 2015 2016 2017 2018 100 200 300 400 500 600 700 – Age 0 to 65 age 65 to 80 age 80 thru 90 2012 2013 2014 2015 2016 2017 2018 Graph 5.4 Number of deaths female (x1,000) in The Netherlands (left) and in Europe (right) in the years 2012 – 2018 1 – CBS (2018), ‘Meer sterfgevallen in wintermaanden’, CBS. URL visited May 18th, 2020. 2 – EuroMOMO (2020), Graphs and Maps, EuroMOMO. URL visited May 18th, 2020. Projections Life Table AG2020 5.5 Data sources: Human Mortality Database, Eurostat and CBS The data were obtained from the Human Mortality Database (HMD), supplemented with data from Eurostat for years and countries missing in HMD. The 2019 data for the Netherlands was obtained from CBS. The Eurostat data were adapted as required to ensure consistency with HMD. This applies to the 2018 mortality probabilities for the overseas territories of France, see appendix C. Data 16 ׉ 7cassandra://Jv2fjLhiaWxtKe-ZJXBGU5y55ADB0kCKqrmgg_M8VD0`̵_jL5`_jL5_{בCט{u׉׉ 7cassandra://X3mNS-Hcts1Lx5WNPLQO0aa7oAOqVT1gCggbU2DArrIe` ׉ 7cassandra://McQeXMryjWjfnyL8INj18CLz5A2gkNQGHotDqtoqRlg `S׉ 7cassandra://paZPGtGx18hbZ6ehCbFdW_7m6jFlL4n-CB1JWH2DH7s `̵׉ 7cassandra://o7_9LKXVcBRuFNfqaQjA6Sdy_u6lBI-Wr4ZJpR23U0Q7%(͠_jL5ט{u׉׉ 7cassandra://535n2uMBK2PLUxWBrgFseYCQ72rOqg7UjjZVQi1iwlYk` ׉ 7cassandra://qqXalf6Y4qeSYLjmyzVwfyucUdy-m2j2FhV23CpFnuc6R`S׉ 7cassandra://yAF3BlUL0dW42PINUICZp929cYN3UP_9M6QbUFenz9g`̵׉ 7cassandra://RxTmOdB1Mv39QkZvohhwFIzpoSCQi5QpSPvmuXiMsf86&͠_jL5׉ExThe information from these sources is regularly supplemented and sometimes also adjusted retroactively for prior years. The data set used, in the shape of mortality frequencies and exposure for both the Netherlands and the complete group of Western European countries can be found on the AG website and totals more than 115 million deaths. The graph below shows the spread of these deaths across the countries. AUT IRL BEL LUX Deaths (2018) DNK NLD FIN NOR FRA SWE DEU CHE ISL GBR NLD SWE DEU GBR FRA AUT Graph 5.5 Spread by country of deaths (male plus female) in 2018 CHE BEL DNK NOR FIN IRL Projections Life Table AG2020 Data 17 ׉ 7cassandra://paZPGtGx18hbZ6ehCbFdW_7m6jFlL4n-CB1JWH2DH7s `̵_jL5a׉E6 THE PROJECTION MODEL Every two years the Mortality Research Committee, in collaboration with the Working Group, estimates a new projection model, that can be used to determine a best estimate of future mortality probabilities and also to generate stochastic scenarios. In the analyses that precede this, considerations are made whether it is wise to implement model changes. This was not the case when moving from AG2016 to AG2018. The Committee has decided to make some changes for AG2020. These changes are described and explained in this chapter. First, the starting points of the approach are discussed, indicating why adjustments in some areas are desirable. Then the new choices are detailed and the consequences of these changes for the mortality forecast clarified. 6.1 Model assumptions unchanged As in previous years, the forecast is based on the best possible projection of past trends. Again, explicit consideration is given to the fact that mortality probabilities cannot be observed, as we only observe mortality frequencies in a limited sample. The best way to take account of the uncertainty that this entails is to estimate the parameters using a statistical model. The uncertainty in future projections can be visualised by defining stochastic scenarios for future mortality alongside the best estimate mortality probabilities. This offers insurers and pension funds the option to supplement the stochastic scenarios for quantities such as interest, inflation and share prices in their asset and liability management with stochastic scenarios for mortality. This feature makes the Dutch approach stand out from that in many other countries, where the actuarial societies only supply mortality tables. Projections Life Table AG2020 The projection model 18 ׉ 7cassandra://yAF3BlUL0dW42PINUICZp929cYN3UP_9M6QbUFenz9g`̵_jL5b_jL5a{בCט{u׉׉ 7cassandra://r1i7FvkqP_m1hsOnxGuGFXt-K2MgDIACg1iQ6LMNMkE"1` ׉ 7cassandra://7pFRUl_oSBGnAsL3htxpPb9aOvYqppE4DxlvpRIdIIMY_`S׉ 7cassandra://ZDR1WyRnw07O5Sa_Oe58kKijPtlV9ru96rrqx2oD7qw`̵׉ 7cassandra://fciRTt4t65ZJ524OEKUNepp4xtfRwygUUy2IyBessxUL,͠_jL5ט{u׉׉ 7cassandra://CmChcQuNbMgHVpZX_-k8WgsoulN4-Erl3K2IQLTiCrs` ׉ 7cassandra://GL8Q24HH_rTZnd4Ek7pFpebwAIrn7BdYGodoaBoe260O`S׉ 7cassandra://zZqechXeX6T6OpRoCa5mWBW4N8C8M0th_QoFZz_NiPY`̵׉ 7cassandra://iwONroSCWnS8LWzrAhcRsccUTX4V86dyH6z0fDwbLso;&͠_jL5׉EThe fundamentals are unchanged for AG2020: The projections are based on publicly available mortality data in the Netherlands and a number of similar countries in Europe. Chapter 5 discussed the details of the dataset used. As in previous years, the Committee promotes that the parameter calibration can be replicated by everyone. To that end, Appendix A provides a comprehensive description of the estimation procedure. All required datasets can be found on the AG website. The model again builds on the fact that mortality developments in the selected group of European countries clearly shows a linear trend for hazard rates on a logarithmic scale, as we will show later in this chapter. This naturally leads to the use of a random walk with drift model. If we then compare the Dutch hazard rates to the European rates at the same logarithmic scale, we see annual fluctuations occurring, but there seems to be no divergence. Therefore, for the Dutch deviation a first-order autoregressive process was selected again. 3 – See Kannisto, V. (1992). Development of the oldest – old mortality, 1950-1980: evidence from 28 developed countries. Odense University Press. 4 – See Li, N and Lee, R. (2005). Coherent Mortality Forecasts for a Group of Populations: An Extension of the LeeCarter Method. Demography 42 (3), pp. 575 - 594 5 – See Brouhns, N., Denuit, M. and Vermunt, J.K. (2002). A Poisson log-bilinear regression approach to the construction of projected lifetables. Insurance: Mathematics & Economics 31(3), pp. 373-393. 6 – Please note that this does not imply that the deviation between the Netherlands and the other countries also converges to zero, because in addition to this time series the model includes a constant difference that does not vary over time (denoted as αx in the model specification). Projections Life Table AG2020 Males and females are modelled jointly, not separately. Dependencies between developments for men and women and between developments in the Netherlands and elsewhere in Europe are explicitly included in the modelling. There are four stochastic processes that describe the annual changes in mortality probabilities. Two pertain to the dynamics in Europe (one for men and the other for women) and the other two generate the Dutch deviation from the European trend for both sexes. Any dependencies between these four processes are allowed for by estimating all mutual correlations during the calibration. For high ages the common closing method of Kannisto is used. The relatively small numbers of observations available for higher aged persons make that data less reliable for estimating mortality probabilities. The difference between observed mortality frequencies and estimated mortality probabilities could be large here. Therefore, as with AG2018, mortality probabilities over age 90 are determined by extrapolation of mortality probabilities for lower ages, assuming that the development in higher ages corresponds to Kannisto’s parameterisation3. The measurement noise, the difference between observed mortality frequencies and the underlying mortality probabilities, has a Poisson distribution. As before, the basis for AG2020 is a Li-Lee4 model that combines linear specifications for hazard rates in the European countries and the Dutch deviation. Contrary to that model we model measurement noise explicitly5 and allow for dependencies between different stochastic drivers. 6.2 Adjusted model assumptions 6.2.1 Motivation for adjustments During the construction of the previous projections table in 2018 and in the subsequent discussions in the actuarial field a variety of pros and cons of the approach were brought forward. Below we discuss a number of items that were frequently mentioned. Are the time series for the difference between The Netherlands and other European countries expected to converge to zero? AG2018 explicitly assumes that the time series that describe the expected value of the difference between the logarithmic hazard rates in The Netherlands and in other selected European countries converges to zero6. The parameter driving the speed of convergence also drives the stability of the model. During the 2016 and 2018 calibrations it soon turned out that, although the model is stable, the values of this parameter for both men The projection model 19 ׉ 7cassandra://ZDR1WyRnw07O5Sa_Oe58kKijPtlV9ru96rrqx2oD7qw`̵_jL5c׉Eand women is close to the critical threshold for stability7. This begs the question if a more stable model would be found if we allow the expected values of these time series to converge to non-zero values. How much history should be included in the creation of the projections? If convergence to other values is allowed, the question is raised whether these values are constant over time and, more specifically, if they are unchanged since 1970. This question touches upon the choice of historical dataset used for the calibration and that is a subject that the actuarial field has had questions about at earlier projections publications. The choice to start the datasets in 1970 was driven by the relatively stable pattern in the European mortality characteristics since that year. The effects of negative factors such as smoking, aids and the rise of obesity on the one hand and positive developments such as the successful battle against cancer and cardiovascular diseases on the other have yielded an all but constant trend in the logarithmic hazard rates within the selected group of European countries. The observed fluctuations in the Dutch deviation from this trend since 1970 are more ambiguous. Periods of increase and decrease emerge that make convergence (in expected value) to zero less likely if we only look at recent data. It may therefore make sense to exclude some data after 1970 from the estimation of the expected value of the long-term difference between the Netherlands and other European countries. 6.2.2 Adjustments made In light of the above considerations the Committee has decided to implement two adjustments. 7 – The autoregressive parameter values for men and women were 0.975 and 0.993 respectively. The critical threshold for these parameters is 1. 8 – The Akaike Information criterion (AIC) and the Bayesian Information Criterion (BIC) are quantities that measure the plausibility of a fitted model with a loglikelyhood term, but seek to avoid unnecessary complexity by introducing a “penalty term” that increases as more parameters get used in the model. Projections Life Table AG2020 The projection model 20 The European dataset starts in 1970, the Dutch deviation dataset starts in 1983. The choice of 1983 as the starting point for the Dutch calibration data and leaving the starting point for the European data unchanged, is the result of an extensive analysis of the time series involved. The Working Group also analysed several alternatives, including specifications that also adjusted the calibration period for Europe, specifications with different calibration periods for men and women, excluding any dependencies between European changes and the Dutch deviation. The Committee’s deliberations around the model choice included statistical model selection criteria such as log-likelihood, AIC and BIC values8 and the long-term robustness and stability of fitted models and plausibility of the projections. As a matter of fact, entering the start of the calibration period as a free parameter in the model selection procedures almost invariably led to 1983 as preferred option, based on the time series for women. That made the case for this choice. The time series describing the differences between the Netherlands and the other countries converge to values no longer assumed to be zero. These limits are now new parameters included in the calibration, because new constant terms are added to the autoregressive processes describing the Dutch deviation. This leads to a change in the expected value of the difference in the longer term. Because the variance of the time series does not move to zero over time, there will always be fluctuations around this expected value. Dutch mortality probabilities will continue to fall in terms of expected value, as the Dutch deviation is added to the falling European trend. ׉ 7cassandra://zZqechXeX6T6OpRoCa5mWBW4N8C8M0th_QoFZz_NiPY`̵_jL5d_jL5c{בCט{u׉׉ 7cassandra://cEwV51DYXsqwmb6fxSnXzKkrvKNTuTqg5Y2P5Z4JZGY` ׉ 7cassandra://8P-MYk83UHqrDFB1hKuFo6x5XhJX4JARWBcUX2vMK7IG`S׉ 7cassandra://fTvfd9lbVyv0jQ3iDcswip3W2p5suF3BZCe2AUns3B4G`̵׉ 7cassandra://iFR6aoL9EP_dD-suORAXGOY0OlLDnPZvBkTXBeLvEgUCL&͠_jL5ט{u׉׉ 7cassandra://mUtguRUEPlls0tmmustkDgOWI5GlIRPQlKtMZ9LtF_M/` ׉ 7cassandra://PrZafbC0hrKgg6DHNAkzSK-rgnVRKpjA-V1c2RFQ5Ig/`S׉ 7cassandra://bDPBKQ_GvTtBkkHqiNC4mUXXe0LQX7Vu5X0M1Uc85Yc`̵׉ 7cassandra://CTxM2IncXINeFQ2f8JdY2S5dS9OGYRlqEsoVAjKWz9IN&͠_jL5׉E 6.3 Effects of adjustments made The adjustments discussed impact several properties of the model. The times series for the Dutch deviation are more stable The parameter estimates that determine the speed of the convergence (in expected value) for the Dutch deviation time series are now considerably further away from the critical threshold. The introduction of two new constants and the new data points since 2017 also change the estimates of the European trend somewhat, but not by much. The model’s consistency improves An important property of any projection model is time consistency. This means that in a scenario where observed mortality exactly matches a projection, a re-estimate of the model should yield unchanged parameters. In practice minor aberrations will always occur, because after adding new data points there are more observations, altering the estimators’ uncertainty. Adding the two additional parameters (constants) leads to a stronger form of time consistency, that no longer depends on the method applied to rescaling. Moreover, a projection for only the European countries (without adding the Dutch data separately9) then equals the projection for those countries in case the Dutch data are added. This implies that all other European countries in our peer group would find the same European projection as the Netherlands, if they were to apply the AG2020 methodology. 6.4 Parameter estimates Chapter 7 discusses the model results. In this paragraph we discuss the estimation results of AG2020, that drive those model results. The details of the applied estimation procedure are found in Appendix A. The underlying one year mortality probabilities are determined by modelling hazard rates, namely the European hazard rates, ␮x and gender g, and the hazard rate of the Dutch deviation from Europe, ␮x g,EU (t), for year t, age x g,NL (t), for year t, age x and gender g. We model the logarithm of the hazard rates as follows: ln 冠 ␮x ln 冠 ␮x ln g,EU (t) g,NL (t) 冡 = Ax g + Bx g Kt g 冡 = ␣x g + ␤x g ␬t 冠 ␮x g (t) 冡 = ln 冠 ␮x g The hazard rates for the Netherlands, denoted by ␮x g (t), then follow from the equation g,EU (t) 冡 + ln 冠 ␮x g,NL (t) 冡. Graph 6.1 shows the parameter estimates of the hazard rates on a logarithmic scale. The top three graphs (graph 6.1a) show the parameters for Europe and the bottom three graphs (graph 6.1b) show the parameters for the Dutch deviation. The first graph shows the constant age specific effect (Ax second and third graphs yields the age specific time effect (Bx g Kt graph shows the average annual improvement over all ages (Kt g and ␤x g ␬t g and ␬t g): the third g), while the second graph is age specific (Bx g and ␤x g) and represents the degree of change for that age. The interpretation of each of the graphs is linked to the chosen normalisation, but the resulting hazard rate estimates do not depend on this normalisation. 9 – We speak of adding the Dutch data “separately”, because when using European data only, the Dutch data points are in fact included in the aggregated data set. Projections Life Table AG2020 The projection model 21 g and ␣x g respectively). The product of the values in the ׉ 7cassandra://fTvfd9lbVyv0jQ3iDcswip3W2p5suF3BZCe2AUns3B4G`̵_jL5e׉ET-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 A Males Females B 0.005 0.01 0.015 0.02 0.025 0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 K 20 40 60 -60 -40 -20 0 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 Males Females Males Females Graph 6.1a AG2020 model parameter estimates: parameters for the group of European countries Alpha 0.1 0.2 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.01 0.02 0.03 0.04 0.05 -0.02 -0.01 0 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 Kappa 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 Males Females Beta Males Females 1970 1975 1980 1985 1990 1995 2000 2005 2010 2105 Males Females Graph 6.1b AG2020 model parameter estimates: parameters for the Dutch deviation Projections Life Table AG2020 The projection model 22 ׉ 7cassandra://bDPBKQ_GvTtBkkHqiNC4mUXXe0LQX7Vu5X0M1Uc85Yc`̵_jL5f_jL5e{בCט{u׉׉ 7cassandra://z6CjBBFFvqM3ViitiFbv4P3eVtU_eVOiHp4n4aT9LoE{` ׉ 7cassandra://BLV81d7_kPQRE3ZWobRcmfxqOUsbcN-ZswCqwDic-7MG`S׉ 7cassandra://KMnL4qwdWlBFg_S2HcnBROt507GROtNeZFPypTQ7Avc`̵׉ 7cassandra://p9k7edPfKQZ8gptrlqwziKS__iU88ncM_uvcYlfr4IoLo8͠_jL5ט{u׉׉ 7cassandra://T4AKrefGlMCs4Bgqg_qbVDHonjRjXxAaTl7iYnJbGLY` ׉ 7cassandra://i41B-Thf5_U2MXGh1opPhRHZs-yd4FYyA-CkA-dnP2U`S׉ 7cassandra://WQkUFs8sQfQlqjLpSYIqng2m7Vrj7Jze-4my4VOvjdM`̵׉ 7cassandra://A8_fL3VNmFjaEaSl96hKzY0kmhAxdwen9gH6qDyKAg4R&͠_jL5׉E fThe results for Europe in graph 6.1a show that for all ages shown the trend in the hazard rates is downward for both men and women. The Bx series Kt g values are positive while the time g are descending. The trend for lower ages is in general more severe (downward) than for higher ages, because the values in the middle graph are generally higher for lower ages. The results for the Dutch deviation in graph 6.1b show a more varied picture. For women we see in the third graph an upward timeseries until the year 2002 and a more or less flat development after that. The age specific effects for women in the second graph are positive for most ages. This means that for these ages the difference in logarithmic hazard rates between the Netherlands and Europe, or ln 冠 ␮x v,NL (t) 冡 = ln 冠 ␮x v (t) 冡 - ln 冠 ␮x 冠 ␮x v,EU (t) 冡, increases until 2002 and is more or less stationary after that. For men we see in the same graph a time series that goes up until 2002 and drops thereafter. For men too the age specific effects in the middle graph are positive for most ages. For these ages the difference in logarithmic hazard rates between the Netherlands and Europe, ln m,NL (t) 冡 = ln until 2002 and decreases after that. To estimate future hazard rates the time effects in Europe (Kt walk with drift. The time effects of the Dutch deviation (␬t g) are modelled as a random g) are modelled by a first order autoregressive AR(1) model (including the new constant terms cg). This leads to the following equations, with parameters ␪g, ag and cg and noise terms ⑀t g and ␦t Kt g = Kt-1 g + ␪g + ⑀t ␬t g g = ag ␬t-1 g + cg + ␦t g Table 6.1 shows the parameter estimates. The value of ␪g is the estimated drift of the time effects in Europe. The values cg and ag are the estimated constant term and the estimated AR(1) term of the time effects in the Dutch deviation. Male a 0.1951 0.9347 Female ␪ -1.9639 -1.8603 c 0.4071 0.9484 Table 6.1 Time series parameter estimates The future time effects Kt g and ␬t g: 冠 ␮x m (t) 冡 - ln 冠 ␮x m,EU (t) 冡, increases g can be estimated using these estimated models. Combined with the age dependent quantities Ax g, ␣x g, Bx g and ␤x g (which are considered constant over time) these will produce estimates of both the future European hazard rates and the Dutch deviation from Europe. For Europe we find that the hazard rates continue to drop. For identical values of the age specific effects as shown in the middle graph of graph 6.1a the hazards rates for men decrease slightly more than those for women, the ␪value for men being more negative than for women. For the Dutch deviation we observe that the logarithmic hazard rates of that deviation converge to limit values ␣x g + ␤x g ␬∞ g . The limit values of the AR(1) processes ␬∞ g are positive for men and women. This leads to positive limit values for the logarithmic hazards rates of the Dutch deviation, for higher ages in particular. This means that, certainly in the longer term, the estimated mortality probabilities at higher ages for Dutch men and Projections Life Table AG2020 The projection model 23 ׉ 7cassandra://KMnL4qwdWlBFg_S2HcnBROt507GROtNeZFPypTQ7Avc`̵_jL5g׉Ewomen will exceed those of the European peer group. As a result, the estimated future life expectancies of Dutch men and women will grow at a slower pace than those of European men and women. This is confirmed in graphs 7.2 and 7.3 in the next chapter, that show the development of period life expectancy at birth and at age 65 for The Netherlands and the European group of countries. Projections Life Table AG2020 The projection model 24 ׉ 7cassandra://WQkUFs8sQfQlqjLpSYIqng2m7Vrj7Jze-4my4VOvjdM`̵_jL5h_jL5g{בCט{u׉׉ 7cassandra://ne1aO9JcaaUsyTJWcRVGZSxhfWOqWEANFJQvZprS-Hk>d` ׉ 7cassandra://mUmxT3e9x4dBBHJhYsg7EYeaZsU3cWm7ZXpJChBg1E4`S׉ 7cassandra://bmnJx5416IiW2bN_PxiHYUDHSsYoq0C2M477CxpicEw`̵׉ 7cassandra://o-qSQrYI8bRtCiAYM_yulLeNU_NhcgxKPrxPmn_BTO8b&͠_jL5ט{u׉׉ 7cassandra://NosXG_Go_x59Cdb--PzqE3k9eiCLjpg3c70VDAr_ZmI@` ׉ 7cassandra://h7WwzdCTbWt1ps6onq8r65-r2MiM1TIUZxcoJBPgZjo>`S׉ 7cassandra://VA5mIhNQ83CVUglw5J0bK1nR_9fLM-rzQx9kxpiPSIw`̵׉ 7cassandra://-brYK-Wg0LvKpXWiDSdSCOa7XY9W596VLoz7IAclJtg3&͠_jL5׉E3Projections Life Table AG2020 Het Prognosemodel 25 ׉ 7cassandra://bmnJx5416IiW2bN_PxiHYUDHSsYoq0C2M477CxpicEw`̵_jL5i׉E m7 RESULTS This chapter presents the results of Projections Life Table AG2020. The results are compared to those of Projections Life Table AG2018. For a number of example funds the effect on the level of the provisions is evaluated. With the aid of these example funds it is possible to assess the impact for other pension funds. In addition, the AG2020 forecast is confronted with historical developments and compared to the latest forecast by Statistics Netherlands (CBS 2019-2060). 7.1 Definitions of life expectancy A classic definition of life expectancy is the so-called period life expectancy. This period life expectancy is based on mortality probabilities in a certain period, such as one calendar year, and assumes that mortality probabilities will be constant in the future. In period life expectancy current mortality rates are used for mortality rates needed one or two years from now. So, period life expectancy does not allow for expected future developments in the mortality probabilities. This definition is commonly used to compare developments over time, but must never be used to estimate how long people are expected to live. The second definition however, the cohort life expectancy, does take into account expected future mortality developments. When calculating cohort life expectancy at birth, mortality probabilities are required for a new-born, a one-year-old a year from now, a two-year-old two years from now and so on. In cohort life expectancy, for probabilities you need in one- and two-years’ time, you use mortality probabilities projected one and two years into the future. So, cohort life expectancy is based on expected developments in mortality probabilities in future calendar years. To evaluate cohort life expectancy, you need a forward projection of mortality probabilities. In case of an expected decrease in mortality probabilities, cohort life expectancy is therefore higher than period life expectancy. 7.2 Observations with respect to Projections Life Table AG2018 Tables 7.1 and 7.2 present the AG2018 forecast of period life expectancies in the years 2017, 2018 and 2019 and how these relate to the realised life expectancies in these years. Also the table shows the forecast of life expectancies for 2019, 2020 and 2021. In this case, period life expectancies are used, as these can be compared across observation years. Projections Life Table AG2020 Results 26 ׉ 7cassandra://VA5mIhNQ83CVUglw5J0bK1nR_9fLM-rzQx9kxpiPSIw`̵_jL5j_jL5i{בCט{u׉׉ 7cassandra://Kw1QGjUQSgf_ea-C9LTGSY6NuLD_xbKJ3BM6CB7xKSkr` ׉ 7cassandra://jwyj21cpkSbTYUu5TJkoh87-6jnUUVo4OLvqHDv6YzAn͠_jL5ט{u׉׉ 7cassandra://D3v1aXZX4suzl4ixknbVG3LIKHcE6QqNOhpxGwOW8UQ2` ׉ 7cassandra://DSsMXW07-Wvvbtixz6j0sBhDl_H3Tsf1BgwHUF9bN3E5Y`S׉ 7cassandra://7aGNGRoXRhJikWm_pSfciFpYcSTaMlGmTAg3DnhOCME`̵׉ 7cassandra://kK_sRP3a23_UkkfiA8Zi8V1TwS-Xtxj5Xy7d4GywUT0K$͠_jL5׉EdImpact Provision 1% interest rate Average Model change Data update Males -1.6% -0.5% Females -1.4% -0.8% Total -2.1% -2.2% Table 7.9 Impact on provisions for model portfolio “average” at 1% interest rate The table shows that more than 2/3rds of the decrease in provisions is explained by the model change. Table 7.10 shows the provision effect on the separate benefits for various ages. As with the impact on the provisions of the model fund, the impact of the new table is more severe at lower ages. For SP in payment the impact increases for higher ages. Impact Technical Provision Males 3% interest rate 25 45 65 85 1% interest rate 25 45 65 85 OAP Latent SP Females OAP Latent SP Males SP in Females SP in payment* payment -2.6% 2.1% -2.6% 5.3% -0.5% -0.5% -2.5% 1.1% -2.3% 2.0% -0.9% -0.9% -1.8% 0.5% -1.4% -1.1% -1.8% -1.4% -1.9% -1.1% -1.4% -2.2% -1.9% -1.4% OAP Latent SP OAP Latent SP SP in SP in payment* payment -3.2% 1.1% -3.1% 3.9% -1.0% -1.0% -3.1% 0.3% -2.8% 0.8% -1.5% -1.4% -2.3% -0.2% -1.8% -2.0% -2.3% -1.8% -2.1% -1.3% -1.5% -2.5% -2.1% -1.5% Table 7.10 Impact on provisions by age and gender of the transition from AG2018 to AG2020 (difference AG2020 minus AG2018 expressed as a percentage of AG2018) * The effect on the provisions of survivor’s pensions in payment refer to the gender of the surviving partner. Projections Life Table AG2020 Results 33 ׉ 7cassandra://su2oMaGXDkyzcnmuqo8hJSvn48H6PMvsTAn2VRcrgbw`̵_jL5q׉E8 THE IMPACT OF THE COVID-19 PANDEMIC The AG2020 forecast is based on European data until 2018 and Dutch data until 2019. This means that the effects of the Covid-19 pandemic are not included in the estimations of mortality probabilities and life expectancies. In this chapter we discuss the possible impact of the pandemic on the forecast and we argue why the Committee feels that AG2020 at this time is the best possible estimation of future mortality. 8.1 Effects in the Netherlands already observed At the time of writing this publication (August 2020) the spread of Covid-19 in Europe has been pushed back after the spike early in the year as a result of all the measures taken. A resurgence of the number of cases is however visible, giving rise to new localised restrictions. The World Health Organisation (WHO) warns that the worldwide pandemic is far from over. At the presentation of this report more weeks will have gone by and the situation may be quite different again. Males 1,000 1,500 2,000 2,500 3,000 500 0 1 5 9 13 17 21 25 29 33 37 41 45 49 2018 2019 2020 1,000 1,500 2,000 2,500 3,000 500 0 1 5 9 1317212529 3337 414549 2018 2019 Graph 8.1 Mortality in the Netherlands by week in 2018, 2019 and 2020 Projections Life Table AG2020 The impact of the Covid-19 pandemic 34 2020 Females ׉ 7cassandra://7aGNGRoXRhJikWm_pSfciFpYcSTaMlGmTAg3DnhOCME`̵_jL5r_jL5q{בCט{u׉׉ 7cassandra://prIW9PwHHcnolu9Xh6sz_6i_215dGpQjpdANUPuow60{` ׉ 7cassandra://lJNzYt0nRaTw77JZH7USG1DrOHvU3JAScKv_Da59Y-MQ`S׉ 7cassandra://nUsUACVHPWoewO3e8L8eyRktfxniD03HtR9MWfkC1ns`̵׉ 7cassandra://VPBuwiP1vdKyZDATgDwMK30Mot-g2E7b0nA_rOzjeGUEe&͠_jL5ט{u׉׉ 7cassandra://SM7G2fJTOMVnuWhBLajVjW_ZAEfQJSLG7aSJs2LjxCg` ׉ 7cassandra://mFMEq3sHNERq5Sgy11gCh1PE9KsiifAsT83RhZkvpNgF)`S׉ 7cassandra://3dTV_5L3ycEnjjRC1-yRuTF4ZzkRi4YbOF2ObQd_zHk`̵׉ 7cassandra://vbFz-pxc0hawCllh_z2xR6v5r52zFYKiVPzK4WadNsoW͠_jL5Ƒנ_jL5ȁvg 9ׁHhttp://www.mortality.orgׁ ׁ Ј׉E It is already apparent that in the first half of 2020 Covid-19 has caused more deaths than the previous years’ average. Graph 8.1 demonstrates this10. We observe that in years with an influenza epidemic the number of deaths exceed historical averages as well. During the flu epidemic of 2017/2018 for instance, the National Institute for Public Health and the Environment (Rijksinstituut voor Volksgezondheid en milieu, RIVM) reported an excess mortality of over 9,000 cases11. The effect of the influenza epidemic in the spring of 2018 shows clearly in the graph. 8.2 Possible long-term effects Actuarial forecasting has a number of specific properties and targets that sets them apart from other forecasts. For one, the extended time horizon adds to the importance of distinguishing between incidental and structural effects. It is also upon the actuary to make every estimation as objective as possible and to justify any subjective assumptions as clearly as possible. At this time, predictions about the impact of the Covid-19 virus on future mortality rates and life expectancies are highly speculative. There are many uncertainties around the spread of the virus, in addition to which very little reliable data about the impact to date is available. Moreover, data from different countries is often incompatible because of variations in dealing with Covid-19, in areas such as testing policy, prevention measures and the available health care capacity. In years to come the full impact of Covid-19 on long-term life expectancy will emerge. At this point in time it is difficult to assess if the Covid-19 related excess mortality will be structural. If a vaccine is found offering permanent protections, the number of victims will drop sharply from then on. If persons dying from corona in general had a lower life expectancy than their peers, the impact will be further reduced. It may also be the case that elderly person who survive the virus have an above average resilience and therefore have a higher life expectancy. However, if there is permanent damage to the lungs or other organs after recovering from the infection, this could indicate a lower remaining life expectancy. And if the care for patients with other afflictions is impaired because hospitals get overwhelmed, that too will have a major impact on mortality. 10 – Data source: The Short-term Mortality Fluctuations in the Human Mortality Database, www.mortality.org. The Dutch data in that database are provided by CBS. 11 – Data source Reukers et al. (2019), Annual report Surveillance of influenza and other respiratory infections in the Netherlands: Winter 2018/2019, RIVM. Projections Life Table AG2020 All in all, very little can be said about the consequences for life expectancy in 2021 and beyond. Therefore, the choice was made not to make adjustments to the AG2020 forecast, which is based on data until January 1st, 2020, for the time being. In the Committee’s opinion this forecast represents the best possible estimate at this point in time. Nonetheless, in the following paragraphs the results of a sensitivity analysis is presented to get a first impression of the impact of excess mortality in 2020 on life expectancies in 2021. 8.3 Sensitivity analysis For the projections life table AG2020 the Dutch deviation from a European trend is estimated, which is why we include observed excess or below-average mortality in other countries in this sensitivity analysis. Due to limited availability of data the sensitivity analysis only includes data from Germany, France, the UK, Belgium and the Netherlands. On aggregate, these countries represent 83% of the European exposures normally used. The aggregated weekly mortality in these countries can be found in graph 8.2 for 2018, 2019 and the first 21 weeks of 2020. The impact of the Covid-19 pandemic 35 ׉ 7cassandra://nUsUACVHPWoewO3e8L8eyRktfxniD03HtR9MWfkC1ns`̵_jL5s׉E Males Females 5,000 10,000 15,000 20,000 25,000 30,000 35,000 40,000 0 1 5 9 13 17 21 25 29 33 37 41 45 49 2018 2019 2020 5,000 10,000 15,000 20,000 25,000 30,000 35,000 40,000 0 1 5 9 1317212529 3337 414549 2018 2019 2020 Graph 8.2 Aggregated weekly mortality in Germany, France, the UK, Belgium and the Netherlands in 2018, 2019 and the first 21 weeks of 2020 Graph 8.3 presents the same information broken down by country, showing major differences in terms of excess mortality and below average mortality. The German data shows large excess mortality observed in 2018 due to the influenza wave in that year, while 2020 to date shows no notable excess mortality due to Covid-19. Other countries do show clear Covid-19 related excess mortality. Note also that in France and the UK there was hardly any excess mortality in 2018 caused by influenza. The sensitivity analysis for the impact of Covid-19 was done by augmenting the AG2020 data for Europe (through 2018) and the Netherlands (through 2019) with so called virtual data points extending to the end of 2020. The data to do this are not available or not complete yet, so extrapolation was used as required to determine excess or undermortality compared to the AG2020 mortality forecast. Weekly CBS mortality data12 up to and including week 21 was used, plus preliminary data from the Short-term Mortality Fluctuations dataset in the Human Mortality Database (as shown in graph 8.3). Two possible assumptions in the extrapolation were analysed: • Current observed excess mortality The assumption that mortality in the Netherlands and in Europe in the remainder of 2020 (i.e. from week 22 onwards) will develop according to the AG2020 forecast from earlier chapters and no further excess or below-average mortality will occur. • Double the observed excess mortality The assumption that for the weeks after week 21 in 2020 the same total excess or below-average mortality will be recorded (in number of deaths) as in the period up to week 21. This effectively doubles excess mortality in 2020. 12 – A special query was submitted to CBS to be able to use more detailed mortality data by age and by week. We thank the CBS staff involved for their help and quick delivery of the data. Projections Life Table AG2020 In addition to virtual data points for deaths virtual data points for exposures were construed, using population and migration data from Eurostat and projections based on AG2020. Having added the virtual exposures and deaths, the usual calibration method for the model can be applied. In time, the virtual data point now surrounded by much uncertainty will be replaced by actual data points. The impact of the Covid-19 pandemic 36 ׉ 7cassandra://3dTV_5L3ycEnjjRC1-yRuTF4ZzkRi4YbOF2ObQd_zHk`̵_jL5t_jL5s{בCט{u׉׉ 7cassandra://P589cQFCJjYEBXj8L3-GO-ZFsuuS-HbjdTT4h2Upa78V` ׉ 7cassandra://bD1Bo0hVJZgY2MWyJowYBWixPFbjZJvOBbznWWjzU549`S׉ 7cassandra://D9m84pBcbpn8kYkhka_kZxLJX71KNQ6ggPVqIlmt2ak`̵׉ 7cassandra://zvu7e_fdr64tpnpX8NGbkTkLYZH2A0OwABWHpkGUzFcn ͠_jL5ט{u׉׉ 7cassandra://JHw33Pl5DcdYXA9dbBVTT1QQODlJUYBZQ1whuA_1_DoU` ׉ 7cassandra://UOejYRqompxcF7SSswJUW7Ny8QHfsicpFyc_sK3ZG6sK`S׉ 7cassandra://P_j7G_R_mCSWziKTQEt3OTLi8yjv_NY6dDOvQjWbYec`̵׉ 7cassandra://zdCFjwUfpCPFKDbXFlLU1c7TAAuHA3NV29YF3IrbKG0H^`͠_jL5׉EUGermany, Males Germany, Females 2,000 4,000 6,000 8,000 10,000 12,000 14,000 16,000 0 10 2018 France, Males 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000 0 10 2018 the UK, Males 2,000 4,000 6,000 8,000 10,000 12,000 0 10 2018 1,000 1,500 2,000 2,500 3,000 500 0 10 2018 1,000 1,500 2,000 2,500 500 0 10 2018 20 30 40 2019 2020 50 20 Belgium, Males 1,000 1,500 2,000 2,500 500 0 10 2018 20 30 40 2019 2020 Graph 8.3 Mortality by country and by week in Germany, France, the UK, Belgium and the Netherlands in 2018, 2019 and 2020 Projections Life Table AG2020 The impact of the Covid-19 pandemic 37 50 30 40 2019 2020 50 20 30 40 2019 the Netherlands, Males 1,000 1,500 2,000 2,500 3,000 500 0 10 2018 20 Belgium, Females 30 40 2019 2020 50 2020 50 2,000 4,000 6,000 8,000 10,000 12,000 0 10 2018 20 30 40 2019 2020 the Netherlands, Females 50 20 30 40 2019 2020 50 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000 0 10 2018 20 the UK, Females 30 40 2019 2020 50 20 30 40 2019 2020 50 2,000 4,000 6,000 8,000 10,000 12,000 14,000 16,000 0 10 2018 20 France, Females 30 40 2019 2020 50 ׉ 7cassandra://D9m84pBcbpn8kYkhka_kZxLJX71KNQ6ggPVqIlmt2ak`̵_jL5u׉E `8.4 Results of the sensitivity analysis Table 8.1 lists the results of the sensitivity analysis under the assumptions outlined in the previous paragraph. The numbers are cohort life expectancies at birth and at age 65 in 2021 after recalibration of the model with the new, virtual data points. Adding that new data, representing excess mortality for many ages, will shift both the European trend and the Dutch deviation, leading to new life expectancy best estimates. Cohort life expectancy in 2021 AG2020 Current excess mortality Double excess mortality At birth Males 89.3 88.6 87.9 Females 91.7 91.3 91.0 At age 65 Males 20.0 19.6 19.2 Females 22.9 22.7 22.5 Table 8.1 Cohort life expectancies in 2021 based on AG2020, the current excess and below average mortality in 2020 and doubled excess and under-mortality in 2020 Difference relative to AG2020 Cohort life expectancy 2021 Current excess mortality Double excess mortality Male -0.68 -1.37 At birth Female -0.41 -0.73 Male -0.44 -0.87 At age 65 Female -0.19 -0.33 Table 8.2 Difference in cohort life expectancies in 2021 relative to AG2020, based on the current excess and below average mortality in 2020 and doubled excess and below average mortality in 2020 The effect observed in graphs 8.1 and 8.2 that a relatively high number of men die of Covid-19 clearly returns in table 8.1 The effect for men exceeds women by 50 to 150 per cent. We also note that doubling the excess and under-mortality observed to date also doubles the drop. For women this factor is a bit smaller. The sensitivity of the pension scheme provisions can be tentatively assessed by looking at the cohort life expectancies for 65-year-olds. We see that these drop by 2.2 and 0.8% for men and women respectively under the first assumption and by 4.3 and 1.5% under the second. In reality the effects on provisions will be mitigated by interest and by survivor’s pensions. 8.5 Future forecasts CBS and RIVM are working to increase the availability of reliable data on the impact of Covid-19. The Committee, in collaboration with the Working Group, will continue its efforts to include new data in future forecasts. We stress again that calculations around the impact of Covid-19 are currently of a highly speculative nature. Much will depend on the effects turning out to be structural or only temporary. The sensitivity analyses given above need to be assessed in this context. This being the case, the Committee is of the opinion that the AG2020 forecast as outlined in previous chapters provides the best possible assessment at this moment. For this reason too, only the model parameters and mortality probabilities for that forecast are published; the sensitivity analysis is not part of the AG2020 model. In the course of 2021 an update will be published if and when new developments give cause to do so. Projections Life Table AG2020 The impact of the Covid-19 pandemic 38 ׉ 7cassandra://P_j7G_R_mCSWziKTQEt3OTLi8yjv_NY6dDOvQjWbYec`̵_jL5v_jL5u{בCט{u׉׉ 7cassandra://ryz08Zjg3Fy_9U-twdb8v9Y3brHOYTN0LrfMr5QRzsUͧ ` ׉ 7cassandra://upgGd5Ab8TTMrAbP6QNefIxWQL1YrjWpCFqj5BFTDwkW`S׉ 7cassandra://OPWoiaRa7KHKXXYvN0dY1QoSoN8-ecd94wDVy1D6yV4`̵׉ 7cassandra://CCpSLdSwvoN6akM6hSE4utaPBfJt4GgDlZS0UVMo6xw͞Z(͠_jL5ט{u׉׉ 7cassandra://hdUkT3hejFcFspeXeo_E6A6ZSflP1V56iZKfVAzbepY"` ׉ 7cassandra://n6pCc66ZUDJfgclAS_Wsjdi82GQniT7-v4PbbfqXtTI,`S׉ 7cassandra://CIM8LDcbTFLcBkGh56jsvok7sziWGqwsv6I8l_yK564#`̵׉ 7cassandra://f0hSUfhnx9KCCxcoia6ydtfBdCFavIe5rPGQ_DUDrLI\͠_jL5׉E,APPENDICES Projections Life Table AG2020 39 ׉ 7cassandra://OPWoiaRa7KHKXXYvN0dY1QoSoN8-ecd94wDVy1D6yV4`̵_jL5w׉E"APPENDIX A Projection model AG2020 Technical specifications 1 Definitions 2 Dynamic model 13 Li, N. and Lee, R. (2005) Coherent Mortality Forecasts for a Group of Populations: An Extension of the Lee-Carter Method. Demography 42(3), pp. 575-594. Projections Life Table AG2020 Appendix A 40 ׉ 7cassandra://CIM8LDcbTFLcBkGh56jsvok7sziWGqwsv6I8l_yK564#`̵_jL5x_jL5w{בCט{u׉׉ 7cassandra://mjH_KMkvRySeBvuijyBQujRA1JseQUUtkq1fIDz7HR4` ׉ 7cassandra://7bnNwVxGmFiJGpkS5kwAAjtz3vMDcTWZf_3_u7zCEY09`S׉ 7cassandra://HFkMlx6OjlEFtYIL1Vw3Fh_r_jK0i1_MKgz3KwHafXID`̵׉ 7cassandra://4TnSOgW4RkmnLB8Yj2z9yfmYUpDHuSSye1-uE0vV8L8wX͠_jL5ט{u׉׉ 7cassandra://PzO8tRBsmEowRJHPhZpNRSoaPJdj7g9w8HSxJHVYqAs` ׉ 7cassandra://_Jq1JxOfmuA92SrBzJ5u0zxz24qugYcHS8JYBeBz98wGi`S׉ 7cassandra://LhS7ExJJNEyX1-g-qloDq5Ul25Cuuwa4QADaZupQhns `̵׉ 7cassandra://zGZi5_4KdjsFTYAl1JpRnz_4Uy53tYq2uOvYpEtPybsPX͠_jL5Бנ_jL5ҁρ 9ׁH8http://www.mortality.org/Public/Docs/MethodsProtocol.pdfׁ ׁ Ј׉E3 Closure of the table 4 Best estimates for mortality probabilities and life expectancies Projections Life Table AG2020 Appendix A 41 ׉ 7cassandra://HFkMlx6OjlEFtYIL1Vw3Fh_r_jK0i1_MKgz3KwHafXID`̵_jL5y׉EN5 Data set used for calibration 14 Brouhns, N., Denuit, M. and Vermunt, J.K. (2002) A Poisson log-bilinear regression approach to the construction of projected lifetables. Insurance: Mathematics and Economics 31, pp. 373-393. 15 See http://www.mortality.org/Public/Docs/MethodsProtocol.pdf Projections Life Table AG2020 Appendix A 42 ׉ 7cassandra://LhS7ExJJNEyX1-g-qloDq5Ul25Cuuwa4QADaZupQhns `̵_jL5z_jL5y{בCט{u׉׉ 7cassandra://IyezLyw4oTboV2MqNHkkhH4M_sRrW2K61tN71FbhpmM%` ׉ 7cassandra://VZGnPMxJ7-ZYpSmm8RPZSpvtBNUtG9eAC0_N275Zaco?`S׉ 7cassandra://DM2L_xrCOQMc7C2SimAyL2egbYxTEiR3aWhK-agTfRoI`̵׉ 7cassandra://zhs2cWrkhxy8xSNVgLx5ZWFpf_uiB6wl6qzEMvOf7cQT͠_jL5ט{u׉׉ 7cassandra://nFXmx7ji5lsLSt5kTBkHT0WHYx3qQzXXcOa5if7Rf40]` ׉ 7cassandra://lGefZd1905IFKZhDIY-bSnEgvqt9j9x1BXg5okiFe7g&`S׉ 7cassandra://glJIZmBmw4ot5LVjT3lJxPdfL4mpnfK1IhLVGdZr9n0 `̵׉ 7cassandra://MlItKGQVvoj-2V_lGCSgFuABVhcjj_lxbDBvkqHYdaQT͠_jL5׉EA6 Calibration method Projections Life Table AG2020 Appendix A 43 ׉ 7cassandra://DM2L_xrCOQMc7C2SimAyL2egbYxTEiR3aWhK-agTfRoI`̵_jL5{׉EL7 Simulation of the time series Projections Life Table AG2020 Appendix A 44 ׉ 7cassandra://glJIZmBmw4ot5LVjT3lJxPdfL4mpnfK1IhLVGdZr9n0 `̵_jL5|_jL5{{בCט{u׉׉ 7cassandra://Zvqpj3ZoDScl42tyBJQE6rD2f9aEMioeSRbD9p322rYT` ׉ 7cassandra://0xv6h1TUgbka-SDmhbQe3xG2m8YTR-qXn6hLiSe-tO4T`S׉ 7cassandra://JUD8X4edcnBugfHgccXhGvZrGYDzMU43dbB_uOcIMPQ`̵׉ 7cassandra://jEXjuyRdBl8h-DgDp0vnhQtC1Lx-ODvroPVkovSHyy4@͠_jL5ט{u׉׉ 7cassandra://zspfLf0zA3AZwuDDK-_CKeCwEqhDZsCv1mcm3sJOriQZ` ׉ 7cassandra://BG5VFEylRfk_loMFNVE9eyDS2BNacSZG4ouDgw7JhEE#`S׉ 7cassandra://jDi2zd2SQKwifzKduaj-LeDqmfhf-rwzme6us8noggQ `̵׉ 7cassandra://E--TVVktnIHHC-UgWFtOMbjG-wLuC4Dl2MV8aJ20BIA@͠_jL5׉ECParameter values Males Projections Life Table AG2020 Appendix A 45 ׉ 7cassandra://JUD8X4edcnBugfHgccXhGvZrGYDzMU43dbB_uOcIMPQ`̵_jL5}׉E>Males (continued) Projections Life Table AG2020 Appendix A 46 ׉ 7cassandra://jDi2zd2SQKwifzKduaj-LeDqmfhf-rwzme6us8noggQ `̵_jL5~_jL5}{בCט{u׉׉ 7cassandra://-ms1zcZbedNNXE9k-_4SBuW6cAQ-8AVRSlHxCpnHmmo` ׉ 7cassandra://2jN7jNKCgAoDkOIAoHvEq7SOz3wnypV8ASWaWXRVTi0S`S׉ 7cassandra://3ASAiAdeo2uFS28j3aKQMCm2xAXx8_s7LHnh7WBwdfQ`̵׉ 7cassandra://PUF1qLBEqgqRePamv9eFQnR2yNZguhNxrJpyqLGTuz06͠_jL5ט{u׉׉ 7cassandra://hijKTUWCVNecHytZOfkpJTgG8XwSZOdMinhSDVvVIbU` ׉ 7cassandra://yA2l3rWeZ7VXPyEuGERacprKetnDNvsj1nhSVZccZgA0`S׉ 7cassandra://KOnhM2lJfutmAU0ru4L2UDUF137J-t_IoRGGJ3ViVmk `̵׉ 7cassandra://Yjgjof2DA_C8g4XcbunIsNSkCBaaMMShbwtEDt_zVqcF͠_jL5׉E4Females Projections Life Table AG2020 Appendix A 47 ׉ 7cassandra://3ASAiAdeo2uFS28j3aKQMCm2xAXx8_s7LHnh7WBwdfQ`̵_jL5׉EaFemales (continued) Covariance and Cholesky matrices Projections Life Table AG2020 Appendix A 48 ׉ 7cassandra://KOnhM2lJfutmAU0ru4L2UDUF137J-t_IoRGGJ3ViVmk `̵_jL5_jL5{בCט{u׉׉ 7cassandra://2rjdeV8LjAn9k7J_CeTVYVlL8GUHPaVlPH9hEtU9tu4` ׉ 7cassandra://mZHuuXVP_xGb8x-3HLDVHV3NaQwO3qyCrF2XetfX7tc?`S׉ 7cassandra://ZLCZ5cHQs4rm1xPK8vxp92XJEYQrlQmvvx8JuM5fg4s`̵׉ 7cassandra://BnZXSBPs36MnCF-rpFzS3_bW3CnwxaLiUmjAeVhh7_U9r̒͠_jL5ט{u׉׉ 7cassandra://TTghq-dLTw479r3nEgzxiVpKavwUlJoFILI6jkuQKGEHf` ׉ 7cassandra://dY5xmm0HqNvG7wTbU-Hg40rtANPw506TPJxcQalBsts/`S׉ 7cassandra://4Bw6YcyRZIVjBG_AYOaQDobS1q4FGJKNiRjIhktyDvk`̵׉ 7cassandra://rL_1sUR5Nz5shhSB7_DtDWFcOhEt7eujykKIXa2A5BU:D͠_jL5׉EAPPENDIX B Model portfolios Technical provisions To evaluate the impact on the technical provisions of model portfolios six model portfolios were used. The portfolios differ in gender (male and female) and average age (young, average and old). The model portfolios have a weighted (by provision) average age of 45 (young), 55 (average) and 65 (old). The model portfolios contain the benefits lifelong old age pension (OAP) and lifelong Survivor's pension (SP). Listed under male are the benefits accrued by male participants (including widows) and under females the benefits accrued by female participants (including widowers). Males Young Males Average - 1,500 1,050 - 500 Males old Age OAP (65) SP (def) SP (i.p.) OAP (65) SP (def) SP (i.p.) OAP (65) SP (def) SP (i.p.) 30 15,000 10,500 350 40 25,000 17,500 50 10,000 7,000 60 7,500 5,250 70 3,500 2,100 80 1,500 90 - 750 - 150 8,500 5,950 1,000 3,000 2,100 450 15,000 10,500 2,000 7,000 4,900 - - 200 450 15,000 10,500 2,000 15,000 10,500 5,000 600 8,500 5,100 - 3,500 1,750 - 500 200 Table B.1 Accrued rights per type of benefit for model portfolio males Females Young Females Average 40 20,000 14,000 50 15,000 10,500 60 5,000 3,500 70 1,000 80 90 - - 600 - - 50 2,500 1,750 150 7,500 5,250 250 12,500 8,750 50 10,000 7,000 - 7,500 2,250 - 5,000 1,000 - 1,000 100 - 750 Females old Age OAP (65) SP (def) SP (i.p.) OAP (65) SP (def) SP (i.p.) OAP (65) SP (def) SP (i.p.) 30 7,500 5,250 100 1,000 525 700 250 5,000 3,500 250 10,000 7,000 500 - - 250 500 100 12,500 3,750 1,000 - 10,000 2,000 - 5,000 500 250 Table B.2 Accrued rights per type of benefit for model portfolio females Projections Life Table AG2020 Appendix B 49 500 15,000 9,000 10,000 150 15,000 7,500 5,000 - 10,000 4,000 2,000 ׉ 7cassandra://ZLCZ5cHQs4rm1xPK8vxp92XJEYQrlQmvvx8JuM5fg4s`̵_jL5׉E^Modelportfolio premium level For the effect on premium levels a single model portfolio was used. Table B.3 lists the accrual by age in any year. Males age OAP (68) 30 40 50 60 600 750 800 600 Females SP (def) OAP (68) SP (def) 420 525 560 420 400 500 550 400 280 350 385 280 Table B.3 Rights accrual per type of benefit for model portfolio premium levels For the survivor’s pension risk premium 40 years of service are assumed (in service at age 28, retirement at age 68). For schemes with old age pension and risk only survivor’s pension this means assuming 40 service years for all participants. For funds with survivor’s pension accrual, the survivor’s pension risk premium is based on future service years (68 minus current participant age minus 1). Actuarial assumptions The technical provisions and premiums for these portfolios are calculated using the following assumptions: • Life tables: Projections Life Table AG2018 and Projections Life Table AG2020, starting year 2021 • Age corrections and/or experience mortality: none • Discount rate: 1% and 3% • Retirement age: 65 for provisions and 68 for premiums • For deferred survivor’s pensions the following applies: – Undetermined-partner system prior to retirement age with a 100% partner frequency, determined-partner system after that. – 3 years age difference between man and woman (man older than woman) – Different genders for participant and spouse. • Lump sum rates for old age pension and survivor’s pension in payment are set by taking the average of in advance and in arrears payments. Projections Life Table AG2020 Appendix B 50 ׉ 7cassandra://4Bw6YcyRZIVjBG_AYOaQDobS1q4FGJKNiRjIhktyDvk`̵_jL5_jL5{בCט{u׉׉ 7cassandra://5qyWyqPGIRCNzvptSV-HaP564E7t73v4H_9X41QKHwU ` ׉ 7cassandra://Q3NeGj98ciOjeP2mdCKA5PZokEqKBzkNzA7nfUoNcls=`S׉ 7cassandra://I2vUjF-6low92Ojb_Wty9wf_KgpMCrFQIsKwuRamDZ8`̵׉ 7cassandra://Hs5Cl9WqI9Mik-wL3n4s-x75Eb5bbyI52TgMZzZMVqEMD͠_jL5ט{u׉׉ 7cassandra://GxLMaSr6hA0Fl9lBRFTaRIP3rlQagOda-ACAXBvI7vQ^` ׉ 7cassandra://ORtm5N3FXyvP7QUtCPZZLopoJa-l5YMp8av5Fbs7Nxk%`S׉ 7cassandra://zl9-VP7FaYN2OBhGgKpD8sIbOgRKsdbnVL4YEI-ozDg z`̵׉ 7cassandra://7TYzR_BPuUNy0DIw_1XgH9rZlrumgYHhORAHPNjnaHk1&͠_jL5נ_jL5*Q̬9ׁHhttp://www.mortality.org/ׁ ׁ Јנ_jL5*9ׁHJhttp://appsso.eurostat.ec.europa.eu/nui/show.do?dataset=demo_magec&lang=enׁ ׁ Јנ_jL5*9ׁHJhttp://appsso.eurostat.ec.europa.eu/nui/show.do?dataset=demo_mager&lang=enׁ ׁ Јנ_jL5*ׁ9ׁHIhttp://appsso.eurostat.ec.europa.eu/nui/show.do?dataset=demo_pjan&lang=enׁ ׁ Јנ_jL5* 9ׁHNhttps://opendata.cbs.nl/statline/#/CBS/nl/dataset/37168/table?ts=1530802763004ׁ ׁ Јנ_jL5*] 9ׁHNhttps://opendata.cbs.nl/statline/#/CBS/nl/dataset/37325/table?ts=1530795309853ׁ ׁ Ј׉EAPPENDIX C Literature and data used This report makes use of the data as was available in the Eurostat, CBS (Statline) and HMD databases at the end of June 2020. [1] CBS data from Statline for 2019: Exposures-to-Risk (P-values); version of June 10th, 2020. https://opendata.cbs.nl/statline/#/CBS/nl/dataset/37325/table?ts=1530795309853 Observed Deaths (C-values and D-values); version of June 10th, 2020: https://opendata.cbs.nl/statline/#/CBS/nl/dataset/37168/table?ts=1530802763004 [2] Eurostat data (data until 2018): Exposures to Risk (demo_pjan) version of February 24th, 2020: http://appsso.eurostat.ec.europa.eu/nui/show.do?dataset=demo_pjan&lang=en Observed Deaths (demo_mager en demo_magec) version of March 2nd, 2020: http://appsso.eurostat.ec.europa.eu/nui/show.do?dataset=demo_mager&lang=en http://appsso.eurostat.ec.europa.eu/nui/show.do?dataset=demo_magec&lang=en [3] HMD-database: http://www.mortality.org/ Table C.1 shows for each geographical area and each year which data source was used as input for the AG2020 model. The Eurostat data definition for France was changed at the end of 2012: since that time it includes data from overseas territories. This was compensated for in the French Eurostat data using the difference between populations according to both definitions (the P values) as observed at January 1st, 2013 and the difference in mortality for each age (the C values) observed in 2012. GEO Austria Belgium Denmark Finland France (metropolitan) Germany (until 1990 former territory of the FRG) Iceland Ireland Luxembourg Netherlands Norway Sweden Switzerland United Kingdom Table C.1 Data sources AG2020 2013 through 2016 HMD HMD HMD HMD HMD HMD HMD HMD HMD HMD HMD HMD HMD HMD 2017 HMD HMD HMD HMD HMD HMD HMD HMD HMD HMD HMD HMD EUROS EUROS 2018 EUROS HMD HMD HMD EUROS EUROS HMD EUROS EUROS HMD HMD HMD EUROS EUROS 2019 HMD-version HMD 2018.09.03 2019.09.06 2020.03.20 2019.12.02 2019.11.01 2018.12.17 CBS 2020.04.02 2019.10.01 2019.12.10 2020.04.03 2019.11.21 2020.01.09 2020.05.08 2018.05.28 Projections Life Table AG2020 Appendix C 51 ׉ 7cassandra://I2vUjF-6low92Ojb_Wty9wf_KgpMCrFQIsKwuRamDZ8`̵_jL5׉ETo generate the 2020 virtual data points in the Covid-19 impact sensibility analysis the weekly mortality data from CBS up to and including week 21 plus preliminary data from the Short-term Mortality Fluctuations dataset in the Human Mortality Database were used. In addition, the most recent population and migration data from Eurostat were used to derive virtual exposures in 2020. Literature Brouhns, N., Denuit, M. and Vermunt, J.K. (2002) A Poisson log-bilinear regression approach to the construction of projected lifetables. Insurance: Mathematics and Economics 31(3), pp. 373-393. V. Kannisto. (1992). Development of the oldest – old mortality, 1950-1980: evidence from 28 developed countries. Odense University Press. N. Li and R Lee. (2005). Coherent Mortality Forecasts for a Group of Populations: An Extension of the Lee-Carter Method. Demography 42(3), pp. 575-594. Reukers et al. (2019), Annual report Surveillance of influenza and other respiratory infections in the Netherlands: winter 2018/2019, RIVM. CBS (2018), ‘Meer sterfgevallen in wintermaanden’, CBS. URL visited May 18th, 2020. EuroMOMO (2020), Graphs and Maps, EuroMOMO. URL visited May 18th, 2020. Projections Life Table AG2020 Appendix C 52 ׉ 7cassandra://zl9-VP7FaYN2OBhGgKpD8sIbOgRKsdbnVL4YEI-ozDg z`̵_jL5_jL5{בCט{u׉׉ 7cassandra://ZqzhDDV8KHlkVC-b3iuux-q9T5sM6Z8lDXQnBeoGbGI` ׉ 7cassandra://7WWflj4DAuhGRH-ruRRAxEjvTXGCJlTk1ZsCMxVTgbY8`S׉ 7cassandra://k0-L9yMJM2YZcA2jZti1EN0bJSiUBLRielR_r_5U1Rw*`̵׉ 7cassandra://1-EUXDaxSdhCG6JO4wof0WtBYRNWFUL8Y8-igz5emog2&͠_jL5ט{u׉׉ 7cassandra://2hJ0QDdRKGCYcJI-cYRR1HDIN73mMlNmqFAKKWJWPpM` ׉ 7cassandra://rsYKPgSM_OXuiO14rJFOukfSNNmPHP3tei00cSQNS-Q*`S׉ 7cassandra://QrDHqnHYVYG0q3TlsK5_Dy3FqCxX9XOtG0xNNRrBaBE w`̵׉ 7cassandra://6vbBPdEbyu0j4xaHfrx-VQeDZMfCMDTsSr9BbTAuO4g& "͠_jL5׉EAPPENDIX D Glossary State Pension retirement age Age at which a person becomes eligible to receive State Pension retirement benefit (AOW). Best estimate In this publication: the most likely value for a quantity subject to chance, such as a mortality probability, the value of a product or portfolio etc. Cohort life expectancy Life expectancy based on a projections life table allowing for expected future mortality developments in the following calander years. To calculate cohort life expectancy at birth, mortality probabilities are needed for a newborn today, a 1-year-old in one-year’s time, a 2-year-old in two years’ time and so on. Eurostat database The database of Eurostat (the European Union’s bureau of statistics) offers a wide range of data, for use by governments, companies, the education sector, journalists and the broader public. Human Mortality Database (HMD) International database containing population and mortality data from over 40 countries worldwide. Survivor’s pension in payment (SP in payment) An insurance where the surviving spouse (the co-insured) of the main insured person gets periodic payments after the main insured person is deceased. Kannisto closure of the table A method to obtain mortality probabilities for high ages from mortality probabilities of lower ages through extrapolation. Deferred survivor’s pension (deferred SP) An insurance – linked to old age pension – in which a provision is formed to pay out periodic benefits to the survivor after the main insured person is deceased, as long as the survivor lives. Old age pension (OAP) An insurance where the insured participant (main insured person) receives periodic benefit payments after reaching the retirement age for as long as that person lives. Projections Life Table AG2020 Appendix D 53 ׉ 7cassandra://k0-L9yMJM2YZcA2jZti1EN0bJSiUBLRielR_r_5U1Rw*`̵_jL5׉EPeriod life expectancy Life expectancy based on mortality probabilities in a certain period, usually one calender year. This expectancy assumes that mortality probabilities are stationary over time. To calculate period life expectancy current probabilities are used as the probabilities needed for 1 or 2 years from now. Thus, period life expectancy does not account for expected future developments in mortality. This definition is often used to compare developments in time, but must not be used to estimate the expected longevity of individuals. Projection period The number of future years over which -within the model- mortality levels are stated. Projections life table Mortality table in which mortality rates are given for each future year. This provides a mortality probability for each combination of age and observation year. This offers the possibility to calculate a remaining life expectancy for every age and every (future) starting year. Statline Statline is the public database of Statistics Netherlands (CBS). It provides statistics on economics, the Dutch population and our society. Stochastic model Model in which future mortality probabilities are not fixed but are defined by means of probability distributions. Stochastic projections life table Projections life table that results from using a stochastic model and hence assumes different values in different realisations of the random variables (as can be seen in the simulations). Projections Life Table AG2020 Appendix D 54 ׉ 7cassandra://QrDHqnHYVYG0q3TlsK5_Dy3FqCxX9XOtG0xNNRrBaBE w`̵_jL5_jL5{בCט{u׉׉ 7cassandra://bIEkC34SP55EhhbTS9YSiRkTeCL7Ox2ObgUnZQvbSBk.t` ׉ 7cassandra://H8BV8wT7ennmeYjoKHR_oUzV2zynrlNeUFA9Zjvz8AQ͇`S׉ 7cassandra://T7O8uQJN4Kt0AbKX0Ab0wmRI_CRqUQPxjkHRXaBrgNg&`̵׉ 7cassandra://SFo17AXbkzJXkd1QLihfmOK_-FJY439U0J_0_f_M6Po~E.͠_jL5׉EPROJECTIONS LIFE TABLE AG 2020 ׉ 7cassandra://T7O8uQJN4Kt0AbKX0Ab0wmRI_CRqUQPxjkHRXaBrgNg&`̵_jL5׈E_jL5_jL5{)Projections Life Table 2020Every two years The Royal Dutch Actuarial Association (Koninklijk Actuarieel Genootschap or ‘AG’) publishes a new Projections Life Table, providing an insight into the expected development of life expectancy in The Netherlands, based on the most recent information at the time._X3?yzx