Koninklijk Actuarieel Genootschap PROJECTION TABLE AG 2018
PROJECTION TABLE AG2018 12 September 2018 1
Colophon 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 Projection Table AG2018 2
1 PREFACE Life expectancy has increased steadily in The Netherlands over the past 50 years. This trend has had a considerable impact on society. It is important for pension funds and life insurers to have a continuous insight into this development, if they are to keep promises made. The Royal Dutch Actuarial Association (Koninklijk Actuarieel Genootschap or ‘AG’) considers it its role to provide the financial sector with an opinion with regard to these developments with the aid of Projections tables. The latest Projections Life Table AG2018 is based on the same model that the Projections Life Table AG2016 was based upon. It 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. In this publication the AG Mortality Research Committee (Commissie Sterfte Onderzoek or ‘CSO’) describes the development and the outcomes of the Projections Life Table AG2018. As chairman of AG I owe a large debt of gratitude to the members of the CSO and to the members of the Projections Life Tables Working Group for all the good work that they have done. On behalf of the Board of the Royal Dutch Actuarial Association, drs. Ron van Oijen AAG Chairman Projection Table AG2018 Preface 3
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2 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 this model (a so-called stochastic model). This resulted in the publication of Projections Life Table AG20141. 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. 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 2018, 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 dr. H.J. Plat AAG RBA drs. E.J. Slagter FRM prof. dr. ir. M.H. Vellekoop ir. R.E.J.M. Waucomont 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 2018, the Working Group consists of the following members: W.G. Ouburg MSc AAG FRM (chair) F. van Berkum PhD drs. K.K. Keijzer AAG M.J.A. Klein MSc AAG ir. drs. J.H. Tornij W. van Wel MSc M. van der Werf MSc AAG M.A. van Wijk MSc AAG K. Wittekoek MSc 1 – Prognosetafel AG2014 of 9 september 2014. Projection Table AG2018 In performing its task, the Working Group has carried out various analyses to obtain Projections Life Table AG2018. While deepening the Working Group’s insights, these analyses have not yielded any model adjustments. The CSO has validated the Projections Life Table as set by the Working Group. Justification 5
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3 CONTENTS 1 Preface –3 2 Justification –5 3 Contents –7 4 Summary –8 5 Introduction Projections Life Table AG2018 –10 5.1 Why does AG develop a projection model for mortality probabilities? – 10 5.2 How does the model work? – 10 5.3 What happened since the release of Projections Life Table AG2016? – 11 5.4 Definitions of life expectancy – 11 5.5 Publication of Projections Life Tables on the AG website – 11 6 Mortality data and model assumptions –12 6.1 Dutch and European mortality – 12 6.2 Model assumptions – 15 6.3 Research – 16 6.4 Summary of changes and research Projections Life Table AG2018 – 18 7 Uncertainty –19 7.1 Parameter uncertainty – 19 7.2 The effect of the choice of model – 20 7.3 Alternative parameterisation of the model – 21 7.4 Consistency over time – 21 8 Results –22 8.1 Observations with respect to Projections Life Table AG2016 – 22 8.2 From AG2016 to AG2018 – 23 8.3 Future cohort life expectancy – 24 8.4 Projections in perspective – 24 8.5 Link between life expectancy at age 65 and 1st and 2nd tier retirement age– 25 8.6 Effects on provisions – 27 9 Applications of the model –29 9.1 Simulations for life expectancy – 30 9.2 Simulations for obligations – 31 9.3 Simulations for life expectancy over a one-year horizon – 33 9.4 Simulations for the best estimate over a one-year horizon – 35 10 Appendices –37 Appendix A - Projection model AG2018 - Technical description – 38 Appendix B – Model portfolio – 47 Appendix C – Literature and data used – 49 Appendix D – Glossary – 51 Projection Table AG2018 Contents 7
4 SUMMARY By publishing Projections Life Table AG2018 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 AG2018 replaces Projections Life Table AG2016. The most important features of the Projections Life Table AG2018 are: • It is based on a stochastic model, enabling pension funds and life insurers to also estimate the uncertainty around the forecast. This is essential in pricing financial derivatives and in setting buffers to be held in connection with mortality uncertainty. • In addition to historical mortality in The Netherlands, Projections Life Table AG2018 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 AG2018 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. The model specifications being unchanged, the changes of Projections Life Table AG2018 as compared to Projections Life Table AG2016 are caused solely by the addition of new mortality data from The Netherlands and Europe. Most notably for higher age groups, the past two years have shown higher mortality than expected based on Projections Life Table AG2016. This explains the drop in the expected life expectancy increase based on AG2018 in comparison with AG2016. Life expectancy at birth in 2019 Period life expectancy Cohort life expectancy based on AG2016 Cohort life expectancy based on AG2018 Decrement Table 4.1 Life expectancy at birth The conclusion is that the Dutch are still reaching higher ages, but that the expected increase has fallen in comparison with Projections Life Table AG2016. Based on the latest insights the life expectancy of a girl born in 2019 is 92.5 years and of a boy born in 2019 Projection Table AG2018 Summary 8 Male 80.6 90.4 90.0 0.4 Female 83.9 93.3 92.5 0.8
it is 90.0 years. These are so called cohort life expectancies; they take into account expected future mortality developments. It is expected that the life expectancy of boys and girls born in 50 years’ time will have increased by a further 4 years. The decrease in life expectancy as shown in table 4.1 is within acceptable statistical boundaries of Projections Life Table AG2016 and is not extreme. The fact that the Dutch are reaching ever-higher ages also shows in table 4.2 Life expectancy in 2019 based on Projections Life Table AG2018 Age 0 Age 65 Difference Table 4.2 Cohort life expectancy for the ages 0 and 65 based on AG2018 Male 90.0 85.3 4.7 Female 92.5 88.1 4.4 The expectation is that a boy, now aged 0, will live 4.7 years longer than a man now aged 65. For women the difference is 4.4 years. Pension funds and insurance companies may use Projections Life Table AG2018 to set and validate their technical provisions and premium rates. The effects will vary across portfolios. In particular, the ages and genders of the members will determine the effects for a portfolio. As a general statement, at 3% interest rate for a predominantly male portfolio, technical provisions will decrease about 0.9% and for a predominantly female portfolio, technical provisions will decrease about 1.2%. At an aggregated level, Projections Life Table AG2018 is lighter than Projections Life Table AG2016 in terms of provisions. If Projections Life Table AG2018 were to be used for the upcoming determination (end of 2018) of the State Pension retirement age in the year 2024, then, according to current legislation, the State Pension retirement age would be unchanged at 67 years and 3 months in 2024, but would rise in subsequent years to 68 years in 2029. Projection Table AG2018 Summary 9
5 INTRODUCTION PROJECTIONS LIFE TABLE AG2018 Through the publication of Projections Life Table AG2018, 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 and for whom the forecast is made, how the model works and what activities were performed since the release of Projections Life Table AG2016. 5.1 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 pension funds and life insurance companies. A projection model is required for the determination of the provisions held by pension funds and insurers. Pension benefits, for example, are paid as long as a member 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: 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. 5.2 How does the model work? Since the publication of Projections Life Table AG2014, the projections have been based on a stochastic model. This makes it possible to give an impression of the uncertainty in the development of life expectancy. Firstly, the model projects forward European mortality in countries with a prosperity level similar to Dutch prosperity. This is done by continuing European trends from the past into the future. Then a projection is made of the difference between this European mortality and mortality in The Netherlands. By including European trends a large amount of data becomes available. This leads to a stable forecast of future life expectancy. In the approach taken, 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. We take into consideration that at any time new developments may occur that will bring about a further increase in life expectancy. This may relate to, 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 and prevention of cardiovascular diseases and an increased regard for a healthy lifestyle. Projection Table AG2018 Introduction Projections Life Table AG2018 10
5.3 What happened since the release of Projections Life Table AG2016? The model has not changed: no alterations have been made in the model specification. The changes in the forecast AG2018 versus AG2016 are caused solely by adding mortality data of the two most recent years to the data set underlying Projections Life Table AG2016 and moving up the start year from 2016 to 2018. Research was done into some of the assumptions. This research is further discussed in chapter 6. 5.4 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 on board 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-yearold 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. In this publication, wherever the term ‘life expectancy’ is used, cohort life expectancy is intended. Where needed, the intended definition of life expectancy is explicitly specified. At the moment, period life expectancy is 80.6 years for men and 83.9 years for women. Cohort life expectancy is 90 years for men and 92.5 years for women, if the forward projection of mortality probabilities is based on Projections Life Table AG2018. Cohort life expectancy is higher because we expect mortality probabilities to drop in the future. The State Pension retirement age is determined on the basis of a forecast by Statistics Netherlands (Centraal Bureau voor de Statistiek or ‘CBS’). According to the most recent insights within AG, using its own model and the most recent available data, the expectation is that the State Pension retirement age will be 68 years in 2029. That is one year sooner than can be derived from the most recent CBS forecast (2030). 5.5 Publication of Projections Life Tables on the AG website AG published Projections Life Table AG2018, 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. Projection Table AG2018 Introduction Projections Life Table AG2018 11
6 MORTALITY DATA AND MODEL ASSUMPTIONS 6.1 Dutch and European mortality The current Projection model AG2018 is equal to Projection model AG2016. This implies that, additional to mortality in The Netherlands, data is 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 discernable. Also, the period life expectancies in these countries have shown similar upward trends for decades. Please refer to graphs 6.1 and 6.2 for representations of this. In view of these clear similarities the choice was made to partly base the Dutch projections on developments in these European countries. This prevents the forecast from depending only on Dutch data, in which specific fluctuations may have occurred in the past that may not be relevant to future developments. The thought is that the long term increase in life expectancy in The Netherlands can be predicted more precisely by including a broader European population, because it strongly increases the number of observations: from over 100,000 deaths annually in The Netherlands to over 2,000,000 deaths per year for the included European countries. This makes the model more robust. The expectation is that subsequent projections are more stable than they would be if only Dutch data were used. European mortality data 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”. Data range Since 1970 a stable development can be seen in mortality probabilities for both men and women (see also graphs 6.1 and 6.2). For modelling, data is used from the observation period 1970 through 2016. For The Netherlands the most recent 2017 mortality probabilities are available and hence added. By selecting this timeframe historical data from a 47 year long period is used. Projection Table AG2018 Mortality data and model assumptions 12
Period life expectancy at birth males 60 65 70 75 80 85 1950 1960 1970 1980 1990 2000 2010 Belgium Denmark France Netherlands Sweden Ireland Norway Switzerland Graph 6.1 Convergence of period life expectancies in a number of European countries, new-born males Period life expectancy at birth females 65 70 75 80 85 90 1950 1960 1970 1980 1990 2000 2010 Belgium Denmark France Netherlands Sweden Ireland Norway Switzerland Graph 6.2 Convergence of period life expectancies in a number of European countries, new-born females Compared to Projections Life Table AG2016 two years of data are added to the data set. For The Netherlands this means mortality probabilities from the years 2016 and 2017. In graphs 6.3 and 6.4 these observed mortality probabilities in The Netherlands are compared to the mortality probabilities expected before, based on Projections Life Table AG2016. The horizontal line at level 1 represents AG’s expectations based on Projections Life Table AG2016. Where the number of deaths exceeds expectation the observed value is above this line. In case of lower mortality the mortality probabilities are under this line. The bars in the bar chart represent actual death frequencies per age in the years 2016 and 2017. As the numbers of deaths are lower for younger ages, we see higher volatility in the results there. Projection Table AG2018 Mortality data and model assumptions 13 Germany Iceland Austria Finland Luxembourg United Kingdom Germany Iceland Austria Finland Luxembourg United Kingdom
Observed/expected mortality, males 0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 25 30 35 40 45 50 55 60 65 70 75 80 85 90 Deaths 2016 Observed/expected mortality 2016 Deaths 2017 Observed/expected mortality 2017 Graph 6.3 Observed mortality divided by expected mortality based on AG2016, males Observed/expected mortality, females 0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 25 30 35 40 45 50 55 60 65 70 75 80 85 90 Deaths 2016 Observed/expected mortality 2016 Deaths 2017 Observed/expected mortality 2017 Graph 6.4 Observed mortality divided by expected mortality based on AG2016, females Graph 6.3 shows that for males the observed mortality probabilities between ages 65 and 85 are lower than expected based on Projections Life Table AG2016. Over age 85 they are higher than expected. For females there is higher than expected mortality upwards of age 60, see graph 6.4. The higher mortality is the result of, among other causes, more influenza fatalities. During the 2016/2017 influenza season almost 8,000 more people died than expected (Teirlinck et al., 2017). It is likely that this ‘excess mortality’ is related to influenza2. 2 – https://www. volksgezondheidenzorg. info/onderwerp/ influenza/cijferscontext/sterfte#nodesterfte-3 3 – https://www. cbs.nl/nl-nl/nieuws/ 2018/07/meersterfgevallen-inwintermaanden Projection Table AG2018 The higher than average influenza related mortality in recent years does not occur in The Netherlands only, it is the same in other European countries as well3. A strong increase or decrease in mortality in The Netherlands quite often coincides with a strong increase or decrease in other European countries. This is demonstrated in the bar chart in diagram 6.1. Represented in it are death frequencies in The Netherlands and in Europe. It shows that for men mortality in the years 2015 and 2016 for ages over 65 exceeded mortality in previous years. For women this effect is evident mainly in The Netherlands. 1,000 1,500 2,000 2,500 3,000 3,500 4,000 500 0 1,000 1,500 2,000 2,500 3,000 500 0 Mortality data and model assumptions 14
Number of deaths Number of deaths The Netherlands, males (1,000) 10 15 20 25 30 35 0 5 Age 0 to 65 Age 65 to 80 Age 80 thru 90 Number of deaths Europe, males (1,000) 100 200 300 400 500 600 700 0 Age 0 to 65 Age 65 to 80 Age 80 thru 90 2012 2013 2014 2015 2016 100 200 300 400 500 600 700 0 Age 0 to 65 Age 65 to 80 Age 80 thru 90 2012 2013 2014 2015 2016 10 15 20 25 30 35 0 5 Age 0 to 65 Age 65 to 80 Age 80 thru 90 Number of deaths Europe, females (1,000) 2012 2013 2014 2015 2016 The Netherlands, females (1,000) 2012 2013 2014 2015 2016 Diagram 6.1 Number of deaths in The Netherlands and in Europe in the years 2012 – 2016. Data sources The data was obtained from the Human Mortality Database (HMD), supplemented with data from Eurostat for years and countries missing in HMD. The 2017 data for The Netherlands was obtained from CBS. The Eurostat data were adapted as required to insure consistency with HMD. This applies to the 2016 mortality probabilities for the overseas territories of France, see appendix C. The 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 100 million deaths. 6.2 Model assumptions Fundamentals of model • The long term development of the Dutch life expectancy is based on the observed development of life expectancy in European countries with a GDP above the European average; • No separate cohort effects (such as the effects of smoking behaviour) are included, as this would considerably increase the complexity of the model; • For high ages mortality probabilities are extrapolated using Kannisto’s method; • Only data from the public domain has been used. The Projection model AG2016 was used, only adding two years’ observations. The Projection model AG2018 is a multi population mortality model as proposed by Lee an Li with a two tier approach to the estimation of the required parameters (see appendix A). In this approach the European trend is estimated by gender with the Lee-Carter model. Subsequently the Lee-Carter mortality model is used again to represent the deviations of The Netherlands from the common trend. By combining data from different, but similar countries the model becomes robust with more stable trends and a lower sensitivity to the calibration period used. Moreover, we explicitly consider the fact that we can never exactly observe mortality probabilities; we only have mortality frequencies at our disposal. This implies a certain ‘measurement noise’, also referred to as ‘Poisson noise’ in connection with the distribution we assume for the observed number of deaths. Projection Table AG2018 Mortality data and model assumptions 15
The model for the development of mortality probabilities is based on four stochastic processes: a) the development of mortality in Europe for males; b) the development of the deviation of Dutch mortality from Europe, for males; c) the development of mortality in Europe for females; d) the development of the deviation of Dutch mortality from Europe, for females; For the European developments a) and c) a random walk with drift model is used. For the Dutch deviations b) and d) a first order autoregressive process without constant term is used. This means that the Dutch mortality development is expected to follow the European trend over time. The four processes are estimated jointly so as to also estimate the correlations between the various processes. For European mortality, data is available up to and including 2016. For Dutch mortality, data is available up to and including 2017. To estimate the four stochastic processes jointly all processes must be based on the same period of data history. Because 2017 data is only available for The Netherlands, the European development for 2017 is determined by extrapolation of the data until 2016 (see appendix A). The correlations between the four different quantities are shown in diagram 6.2. European males -0.27 (AG2016: 0.45) 0.45 Dutch deviation males 0.54 0.93 0.40 -0.23 (AG2016: -0.21) European females Dutch deviation females Diagram 6.2 Mutual correlations between development of European mortality and development of Dutch deviation, males and females For ages over 90 there are relatively few observations. This may lead to fluctuations in the estimations of mortality probabilities. Therefore the mortality tables are ‘closed’. This means that the mortality probabilities for high ages are determined by means of an extrapolation method. As with Projections Life Table AG2016, the method of Kannisto was selected for Projections Life Table AG2018. Appendix A provides a comprehensive specification of the stochastic model used, including the model estimation method. In combination with the data set made available through the AG website, Projections Life Table AG2018 can be reconstructed exactly. Projection Table AG2018 Mortality data and model assumptions 16
6.3 Research 6.3.1 Smoothing the time series The latest fitted values from the historical time series (see a) to d) in the previous paragraph) are the starting point for the estimations of the European trend and the Dutch deviation from it. A change in the starting point for the European trend is particularly determinative for the projections table. For insurers and pension funds the impact of an update to the projections table can be significant. The purpose of smoothing is to prevent unnecessary fluctuations in the provisions year on year. Smoothing time series makes sense if adjustments in the projections can be seen to have alternating signs year on year. This would imply that a rise in one year is often followed by a drop in the next year and vice versa. A risk of smoothing is that a potential trend break is detected at a later stage. We have investigated the benefit of smoothing the time series by adding a term to the specification of the European trend. This so-called moving average term allows for shock in the time series for a particular year to be correlated with a shock in the previous year. This can prevent positive shocks in one year being followed by negative shocks in the next and vice versa. The parameters of this moving average effect turned out to be very close to zero. Consequently, we elected not to complicate the model unnecessarily. Other smoothing mechanisms are statistically less tenable. Moreover, additional subjective choices would need to be made. CSO has elected not to implement this in Projections Life Table AG2018. 6.3.2 Sensitivities of the model to changes in the input The sensitivities of the model have been plotted by calculating the consequences of potential changes in the input, such as the impact of new mortality data, the country selection and the length of the data set used. These analyses do not give rise to changes in the choices made before. Sensitivity of the model to changes in the input – country selection It turns out that the results of the model are dominated by the three large countries: Germany, France and the United Kingdom. Removing or adding other countries has only a limited effect on the results. Sensitivity of the model to changes in the input – starting year 1970 The starting year 1970 was kept. The reasons are: 1. Mortality data from all countries included in the modelling are available as of 1970; 2. For males, there appears to be a trend break around 1970; mortality drops quicker because men stop smoking. For women this effect only becomes apparent at a later moment; 3. Males and females are estimated jointly, including correlations between the two. Therefore the same observation period must be used for both men and women; 4. With starting year 1970, 47 observation years are available. Postponing the starting year reduces the volume of available data. Projection Table AG2018 Mortality data and model assumptions 17
6.4 Summary of changes and research Projections Life Table AG2018 Projections Life Table AG2016 Data set from countries with a GDP above the European average. Data set Europe until 2014, extrapolated to 2015. Data set The Netherlands until 2015. All possible correlations between Europe and Dutch deviation and between males and females. Projections Life Table AG2018 No change. Data set Europe until 2016, extrapolated to 2017. Data set The Netherlands until 2017. No change in system, correlation values do change. Projection Table AG2018 Mortality data and model assumptions 18
7 UNCERTAINTY The projection model presented in this publication is based on mortality data from the past. Trends observed in the historical data are extended into the future in the best possible way. The future being uncertain, the values that will be found for the actual mortality rates in the Netherlands will deviate from the best possible estimations at this moment in time. AG elects to explicitly chart this uncertainty too. The model equations in Appendix A invite users to not only apply a fixed projections table. Actuaries can use them to generate stochastic scenarios by simulation. That yields a collection of possible future mortality probability scenarios, similar to scenarios produced for future interest rate curves and investment yields. There are other forms of uncertainty as well. The parameters in the projection model are estimated from observed deaths, which constitute a limited sample. That implies that there is also uncertainty in the projection model’s estimated parameters. Below, besides this ‘parameter risk’, we also discuss the uncertainty about the validity of the chosen model, the so-called ‘model risk’. 7.1 Parameter uncertainty We assume that the number of deaths follows a Poisson distribution with a mean depending on the modelled trend. The observed numbers of deaths constitute a sample from that distribution. This raises the question what the effect on the estimated parameters is of the limited sample size. Through Eurostat, the HMD and CBS we possess reliable data on the numbers of deaths in the past. As the parameters are based on a multitude of observations over multiple years from both The Netherlands and the rest of Europe, the estimation is far less uncertain than if only a smaller population would have been used. Nonetheless, it is advisable to analyse the effect of using a sample. The statistical method that can be used for this, the bootstrap, is based on a so-called resampling technique. In this method, myriad possible numbers of deaths are simulated for a given set of parameters from the corresponding Poisson distribution. For each of these samples the parameters are recorded that would be found if that sample had been used to calibrate the model. This provides an insight into the uncertainty of the parameter values found. If roughly the same parameter values are found in each of the possible samples, the effect of the sample on the parameters is small. If, on the other hand, a large variation shows in the parameter values generated in this way, then parameter uncertainty is large. Table 7.1 shows the results of the bootstrap procedure for 10,000 AG2018 model samples. For all parameters the 2.5%, 25%, 50%, 75% and 97.5% quantiles are given. Projection Table AG2018 Uncertainty 19
Quantile ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ M V aM aV C11 C22 C33 C44 C21 C31 C32 C41 C42 C43 2.5% -2.44 -2.48 0.84 0.79 1.33 0.09 1.81 0.90 0.07 1.37 0.05 -0.93 0.10 -1.13 Table 7.1 Bootstrap results Table 7.1 gives an impression of the uncertainty in the parameters describing the time series for the European trend and the Dutch deviation. Because these values are obtained via simulations, the results from a new bootstrap could be slightly different. In general the medians of the bootstrap results are close to the parameter best estimates, but not in all cases. More specifically, it appears that somewhat lower values are found for parameters aM and aF, which describe the dynamics of the Dutch deviation from the European trend. Parameter uncertainty and Poisson noise are not included in the confidence intervals shown in chapter 9. If they were, the confidence intervals would widen. To determine – for instance- the 2.5% quantile of the combined uncertainties, one would not use the 2.5% quantile parameter values shown here, as this would result in a value that relates to the 2.5% times 2.5% equals 0.0625% quantile. 7.2 The effect of the choice of model Before the transition to a new stochastic model in 2014 the CSO and the working group of that time compared numerous models. Any model current in actuarial practice and scientific literature at the time that had a semblance of plausibility was included in this survey. This has resulted in the current model being chosen. The current model assumes that the gradual improvements in mortality probabilities observed in recent decades will continue in the future and that there will not be any sudden structural breaks in the trends. On the one hand, major successes have been achieved in the medical field and by our healthier lifestyles, while on the other hand very many additional lives were unfortunately lost to smoking. Despite all these major effects we still see a relatively steady pattern in the observed mortality frequencies. The CSO therefore opted not to explicitly model the structural breaks in the trends. Doing so would further complicate the model. Moreover, many additional subjective assumptions would need to be made about future medical and other potential developments. At the same time we would point out that our model represents a stochastic scenario generator. Anyone who wants to add scenarios to the model to include their own Projection Table AG2018 Uncertainty 20 25.0% -2.20 -2.16 0.91 0.91 1.88 0.15 2.69 1.26 0.18 2.05 0.19 -0.60 0.19 -0.67 50.0% -2.08 -1.99 0.94 0.95 2.23 0.18 3.23 1.47 0.25 2.48 0.27 -0.43 0.24 -0.45 75.0% -1.95 -1.82 0.96 0.97 2.61 0.21 3.85 1.70 0.32 2.95 0.36 -0.28 0.31 -0.25 97.5% -1.70 -1.49 0.99 0.99 3.43 0.29 5.12 2.19 0.47 3.96 0.54 0.01 0.44 0.13
convictions about future developments, may do so within the current transparent model structure. The CSO opts to limit itself to estimations based on data from the public domain and not to include extreme scenarios that experts are not agreed upon. 7.3 Alternative parameterisation of the model The model description we give in Appendix A is in line with current actuarial literature. A unique specification of parameters is forced by demanding that the sum of all fitted K’s and kappas equals zero and the sum of all fitted B’s and betas equals one (1). Both choices have evolved historically, although other choices were possible. If one sets not the average of kappas, but the first kappa to zero, this also yields a unique specification of parameters, without the need to average a different number of points at each addition of new data points. That would simplify the comparison of time series over the years. And setting the squared sum of betas to one instead of the sum would eliminate the prerequisite of betas being positive. We would stress that a different choice in these normalisation steps leads to parameter values that describe the same model results in ‘different coordinates’. To preserve compliance with existing literature, we have therefore maintained the notation from the previous publication. 7.4 Consistency over time If the best estimate forecasts from a model that has been estimated deviate little from the actuals observed in subsequent years, one would expect the new parameter estimation to be close to the old parameter values. This desirable property in estimation procedures is sometimes called consistency over time. In reality, even if the best estimate forecasts come true exactly, different values will be found for the new parameters. After all, there are more observations, there are additional assumptions in our model specification (such as the absence of a constant term in the AR process for the Dutch deviation) and we also rescale the K and kappa values to set the average back to zero. Having stated this, the application of the maximum likelihood method implies that we can expect minor adjustments to parameters if new observations are close to earlier projections. It is therefore no surprise that the Projections Life Table AG2018 parameter values are close to the Projections Life Table AG2016 values. Projection Table AG2018 Uncertainty 21
8 RESULTS This chapter presents the results of Projections Life Table AG2018. The results are compared to those of Projections Life Table AG2016. 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 AG2018 forecast is confronted with historical developments and compared to the latest forecast by Statistics Netherlands (CBS 2017-2060). 8.1 Observations with respect to Projections Life Table AG2016 The table below shows the AG2016 forecast of life expectancies for the years 2015, 2016 and 2017 and how these relate to the realised life expectancies in these years. Also the table shows the forecast of life expectancies for 2017 and 2018. In this case, period life expectancies are used, as these can be compared across observation years. Males 2015 2016 2017 2018 2019 Realised 79.7 79.9 80.1 AG2016 79.8 80.0 80.2 AG2018 80.1 80.3 80.4 Table 8.1 Period life expectancy at birth Males 2015 2016 2017 2018 2019 Realised 18.2 18.4 18.6 AG2016 18.2 18.4 18.5 AG2018 18.5 18.6 18.8 Table 8.2 Period life expectancy at age 65 The new observations after the release of Projections Life Table AG2016 in general show a more moderate increase in period life expectancies than was included in Projections Life Table AG2016. The following graph shows the development of period life expectancy at birth for the period until 2050. The graph is based on realised mortality rates until 2017 and AG2018 projections thereafter. Projection Table AG2018 Results 22 Females Realised 83.1 83.1 83.3 AG2016 83.1 83.3 83.5 AG2018 83.3 83.5 83.6 Females Realised 20.9 21.0 21.1 AG2016 21.0 21.1 21.3 AG2018 21.2 21.3 21.4
90 85 80 Females 75 Males 70 The Netherlands European selection AG2018 NED AG2018 Europe 65 1970 1980 1990 2000 2010 2020 2030 2040 2050 Graph 8.1 Period life expectancy in The Netherlands and selected European countries Graph 8.1 demonstrates that period life expectancy for Dutch women, as in the previous projections, is still below life expectancy of women in selected European countries. Life expectancy of Dutch men on the other hand is, as before, higher than life expectancy of men in selected European countries. 8.2 From AG2016 to AG2018 To further clarify the differences between the old and the new projections tables, Projections Life Tables AG2016 and AG2018, cohort life expectancy is used. Cohort life expectancy includes all future mortality developments. Below the step-by-step impact on cohort life expectancy for starting year 2019 of each added set of datapoints is shown. Cohort life expectancy in 2019 AG2016 Add EU2015 Add NL2016 Add EU2016 Add NL2017 AG2018 At birth Males 90.4 -0.4 -0.1 0.1 0 90 Table 8.3 Cohort life expectancy in 2019 It is apparent that the addition of year 2015 observations from the European countries in particular has caused a downward adjustment to the projections. This is demonstrated clearly in Diagram 6.1 in paragraph 6.1. That diagram shows that the number of deaths in 2015 is higher than in 2014, while in the subsequent year the numbers remained the same or dropped slightly. Projection Table AG2018 Results 23 Females 93.3 -0.5 -0.2 0 -0.1 92.5 Males 20.4 -0.1 -0.1 0.1 0 20.3 At age 65 Females 23.5 -0.2 -0.1 0 -0.1 23.1
8.3 Future cohort life expectancy Projections Life Table AG2018 offers the possibility to calculate future life expectancies. Table 4 shows future cohort life expectancies in the years 2019, 2044 and 2069. Year 2019 2044 2069 Males 90.0 92.3 94.0 At birth Females Difference 92.5 94.6 96.1 2.5 2.3 2.1 Males 20.3 23.2 25.6 Table 8.4 Future cohort life expectancies based on AG2018 The numbers stated here again demonstrate that the model implies that life expectancies for men and women will continue to rise, slightly faster for men than for women, thus reducing the gap in life expectancies between the sexes. 8.4 Projections in perspective Graph 8.2 compares the developments in period life expectancy at birth for AG2016, AG2108 and CBS2017-2060. It is apparent that the AG2018 trend forecast for Dutch women converges to the trend forecast for women in selected Western European countries and that the projections have been adjusted downwards from AG2016. The AG2018 forecast for men shows a similar motion versus AG2016; the trend is close to the trend in Western European countries, keeping the difference in life expectancy fairy stable through time. For men, the CBS2017-2060 forecast shows a life expectancy development almost identical to AG2018. The life expectancy in 2050 based on CBS2017-206 is slightly higher than AG2018 for women and slightly lower for men. 90 At age 65 Females Difference 23.1 25.8 28.0 2.8 2.6 2.4 85 Females 80 Males 75 2000 2010 2020 2030 2040 2050 Graph 8.2 Development of period life expectancy at birth Graph 8.3 shows the development of period life expectancy at age 65. The Netherlands European selection AG2018 NED AG2018 Europe CBS-2017 AG2016 Projection Table AG2018 Results 24
10 12 14 16 18 20 22 24 26 Females Males The Netherlands European selection AG2018 NED AG2018 Europe CBS-2017 AG2016 1970 1980 1990 2000 2010 2020 2030 2040 2050 Graph 8.3 Development of period life expectancy at age 65 The different projections of life expectancy at age 65 for men are close together. For women the downward adjustment from AG2016 is clearly visible. Table 8.5 lists the cohort life expectancies for AG2016, AG2018 and CBS2017-2060. The differences between AG2018 and CBS2017-2060 in cohort life expectancy at age 65 are moderate. Year 2019 Projection AG2016 AG2018 CBS2017 At birth Males 90.4 Females 93.3 90.0 92.5 20.3 Not available 20.3 Table 8.5 Life expectancies for AG2016, AG2018 and CBS2017 8.5 Link between life expectancy at age 65 and 1st and 2nd tier retirement age The Raising of the State Pension Retirement Age and Standard Pension Retirement Age Act (Wet Verhoging AOW- en Pensioenrichtleeftijd) of 12 July 2012 links the first tier (State pension) retirement age and the standard retirement age in the second tier (employers’ pension schemes) to period life expectancy. Raising the State Pension age is done in three month steps and depends on the level of the macro average remaining period life expectancy at age 65 (L), as estimated by CBS, versus a value of 18.26 and on the difference between the then prevailing State Pension retirement age and 65. The reference value of 18.26 is legally defined and based on CBS observations in the period 2000-2009. Because at the end of 2016 L was expected to exceed 20.51 years before 2022, an increase in State Pension retirement age of a quarter of a year (0.25) was necessary (because (20.51 – 18.26) – (67 – 65) equals 0.25), as was announced in 2016. No increase was announced in 2017 for the year 2023. Projection Table AG2018 Results 25 At age 65 Males 20.4 Females 23.5 23.1 22.8
According to Projections Life Table AG2018 L will equal 20.70 in 2024, eliminating the need to raise the State Pension retirement age to 67 years and 6 months applying the formula above. This expectation concurs with the latest CBS forecast from 2017. By 1 January 2019 at the latest there will need to be clarity about the raise in 2024 based on the recent CBS forecast. Estimating the macro average remaining period life expectancy at age 65 for the years after 2024 reveals the following years in which the State Pension age is expected to increase by a full year4. Expected State Pension retirement age 68 69 70 71 CBS 2017-2060 2030 2039 2048 2057 AG2018 2029 2038 2047 2057 Table 8.6 Expected years in which the State Pension retirement age will have risen by a full year according to the latest CBS and AG projections The raising of the standard retirement age in the second tier is based on the same formula as for the State Pension retirement age, except that by law expected increases in life expectance are to be anticipated sooner. Legislation states that a change in the standard retirement age must be announced at least one year before it takes effect and that the macro average remaining life expectancy at age 65 expected ten years after the implementation of a change is to be considered. This means that, for instance, an adjustment to the standard retirement age in 2020 must be announced prior to 1 January 2019 and that this adjustment is to be based on the macro average remaining life expectancy at age 65 in 2030. Based on Projections Life Table AG2018 L is not expected to have risen in 2030 to such an extent that it would warrant a standard retirement age of 69 in 2020. A rise of the standard retirement age to 69 not expected before 2028. The developments of State Pension retirement age and standard retirement age based on Projections Life Table AG2018 are summarised in the graph below. 4 – For the sake of calculating simplicity the macro average remaining life expectancy is defined as the unweighted average of male and female life expectancy. In reality more precise weights would be allocated, giving women a slightly higher influence. The impact of this is marginal. Projection Table AG2018 65 66 67 68 69 70 71 2018 2022 2026 2030 2034 2038 Standard Retirement Age State Pension Age 2042 2046 2050 Graph 8.4 Development of State Pension retirement age and standard retirement age based on AG2018 Results 26
In general, current AG projection can be said not to deviate much from the CBS forecast, which means that differences in future State Pension and standard retirement ages will not be very large. 8.6 Effects on provisions In order to analyse the effects of Projections Life Table AG2018 on the technical provisions of pension portfolios six fictitious example funds have been constructed. Three of the funds have male participants and three have female participants. For both sexes a young, an old and an average funds has been constructed. The average fund is the average of the first two funds. These example funds were partly based on actual portfolios. Besides an old age pension the example funds contain a latent survivor’s pension and a survivor’s pension in payment. For male portfolios spouses receiving survivor’s benefits are assumed to be females. For female portfolios the opposite applies. The benefits used are a retirement benefit commencing at age 65 and an “unspecified partner” type survivor’s benefit with a partner frequency of 100%. A fixed age gap of 3 years is assumed between male and female partners, the male partner being assumed older than the female. The effects are shown for interest rates 3 and 1%, so that the effects can be compared to the previous publication (AG2016). Effect Technical Provision 3% interest rate Young OP (65) NP OP+NP 1% interest rate Young OP (65) NP OP+NP Males Females Average Old Young Average Old -0.8% -0.7% -0.6% -2.0% -1.9% -1.8% -1.2% -1.4% -1.5% 2.9% 2.4% 2.2% -0.9% -0.9% -0.9% -1.3% -1.2% -1.2% Old Average Young Average Old -1.0% -0.9% -0.8% -2.5% -2.3% -2.2% -1.8% -1.9% -2.0% 3.5% 2.8% 2.5% -1.2% -1.2% -1.2% -1.7% -1.6% -1.6% Table 8.7 Impact on model portfolio provisions of a transition from AG2016 to AG2018 (difference AG2018 minus AG2016 expressed as percentage of AG2016). The separate percentages as listed for OAP and SP do not add up to the percentages listed for the OAP+SP combination. This is caused by the difference in the provisions for the separate benefits Table 8.7 indicates that the differences, in terms of provision, for men are limited. For an average portfolio the provision will be reduced by about 1%. For women the impact is higher (average reduction of 1.2 and 1.6% respectively). At 1% interest the low interest rate creates an additional impact. In table 8.8 the impact of AG2016 to AG2018 is split into 2 steps: • Data update to ‘AG2017’, i.e. adding EU15 en NL16; • Data update to AG2018, adding EU16 en NL17. Projection Table AG2018 Results 27
Effect Technical Provision Males 3% interest rate Young Average 1) AG2016 → "AG2017" → AG2016 → Old Females Young Average Old OAP (65) -1.0% -0.9% -0.8% -1.7% -1.6% -1.5% SP -0.5% -0.7% -1.0% 2.0% 1.6% 1.4% "AG2017" OAP+SP -0.9% -0.9% -0.9% -1.1% -1.1% -1.1% 2) OAP (65) 0.2% 0.2% 0.2% -0.3% -0.3% -0.3% SP -0.7% -0.6% -0.6% 0.8% 0.8% 0.8% AG2018 OAP+NP 0.0% 0.0% 0.0% -0.1% -0.1% -0.1% 1) + 2) OAP (65) -0.8% -0.7% -0.6% -2.0% -1.9% -1.8% SP -1.2% -1.4% -1.5% 2.9% 2.4% 2.2% AG2018 OAP+SP -0.9% -0.9% -0.9% -1.3% -1.2% -1.2% Table 8.8 Impact on provisions for model portfolios of a transition from AG2016 to AG2018, with AG2017 as intermediate step This demonstrates that in the transition from AG2016 to AG2017 the increase in mortality probabilities has a significant impact. What stands out is, that for men the provision for both OAP and SP generally drops, while for women the SP provision goes up. Mortality probabilities have risen for men and women. For SP this means that payment starts earlier (increase), but then has a shorter payment period (decrease). The combination of both effects is different for male and female portfolios, because in general the increase of mortality probabilities is higher for women than for men. We also note that in tables 8.7 and 8.8 both latent SP and SP in payment are included and the change in technical provision values is dependent on both. Table 8.9 shows the effect on the separate benefits for various ages. Males 3% interest rate 25 45 65 85 1% interest rate 25 45 65 85 OAP Latent SP SP in payment OAP Females Latent SP SP in payment -1.3% 0.4% -0.5% -2.2% 8.4% -0.3% -1.2% -0.3% -0.8% -2.1% 5.8% -0.5% -0.5% -1.9% -1.4% -1.4% 4.1% -0.5% 0.3% -2.8% -1.5% -1.5% 2.6% 0.3% SP in OAP Latent SP payment OAP Latent SP SP in payment -1.5% -0.9% -0.9% -2.6% 8.2% -0.5% -1.3% -1.4% -1.3% -2.5% 5.7% -0.7% -0.6% -2.6% -1.7% -1.7% 4.0% -0.6% 0.3% -3.0% -1.6% -1.6% 2.6% 0.3% Table 8.9 Impact on provisions for individual benefits and ages of the transition from AG2016 to AG2018 (difference AG2018 minus AG2016 expressed as a percentage of AG2016) Projection Table AG2018 Results 28
9 APPLICATIONS OF THE MODEL Using a stochastic model offers additional possibilities for analysing mortality risks. In particular, it is possible to gain insight into the variability on the values of insurance portfolio obligations. As Projections Life Table AG2018 is based on a stochastic model, a statement can be made about the spread of future mortality probabilities around best estimates. The model used not only generates best estimate mortality developments, but can also be used to analyse the uncertainty in future scenarios, based on fluctuations observed in the historical data. It is important to note that the uncertainty intervals presented in this chapter do not take account of parameter or model uncertainty. That is to say, our calculations take the assumed model and the estimated parameters as given fundamentals. Only mortality probabilities are simulated and we assume that we can observe these mortality probabilities exactly. We therefore do not take into account that in practice, working as we do with finite populations, we have at our disposal not the exact mortality probabilities, but only observed ones (the measurement or Poisson noise). In this chapter a number of potential applications of the stochastic model are shown for illustrational purposes. The results listed in this chapter are based on the model portfolios also mentioned in chapter 8, see Appendix B. Firstly, we show in paragraph 9.1 the confidence intervals around the life expectancy produced by the model over the whole horizon. In paragraph 9.2 we discuss the value of the obligations for all potential developments of future mortality probabilities. While the best estimate value of obligations is attained by using best estimate mortality probabilities, we also look at various possible scenarios for mortality probability developments as given by the stochastic model. This provides an insight into the potential increase of the value for the entire portfolio run off at for instance the 95% quantile. In practice, the stochastic distribution of the value of obligations after a one-year shock is also often looked at. To do this, possible shocks during the first year are simulated. Then, for each scenario (shock) the model is recalibrated after adding the new (simulated) observation to the original data set. Based on parameters calibrated per scenario, best estimate mortality probabilities are determined for the remaining years. Paragraph 9.3 shows the confidence intervals this yields for a one-year horizon. Paragraph 9.4 shows the consequences of the resulting stochastic distribution of the value of obligations after a one-year shock and recalibration. Projection Table AG2018 Applications of the model 29
In the applications above no statement is made about the consequences for the calculation of Solvency II buffers. Deriving the amount of capital to be held for mortality risk solely from the spread that the stochastic model produces could lead to an underestimation of the required capital, in view of what is mentioned above on parameter uncertainty, model uncertainty and Poisson noise. 9.1 Simulations for life expectancy Best estimate mortality probabilities can be obtained by assuming that future mortality probabilities will develop according to the model equations from Appendix A, setting all error terms to zero. It is also possible to simulate possible scenarios in which the error terms are drawn from the multivariate normal distribution specified there. On the basis of this, confidence intervals around life expectancy can be determined for the whole horizon. The 95% confidence intervals for men and women are presented in the graph below. Period life expectancy at birth 90 85 80 Females 75 Males 70 95% confidence interval Observations The Netherlands Observations European selection Projection The Netherlands Projection European selection 65 1970 1980 1990 2000 2010 2020 2030 2040 2050 Graph 9.1 Confidence interval around the best estimate of the period life expectancy for Dutch males and females Graph 9.1 demonstrates that, as expected, the uncertainty in the projection of period life expectancy increases as the projection moves further into the future. The graph below shows the uncertainty in cohort life expectancy per age of Dutch men and women in 2018. Projection Table AG2018 Applications of the model 30
Life expectancy in The Netherlands 2018 105 100 95% confidence interval Males Females 95 90 85 80 0 10 20 30 40 50 60 70 80 90 100 Present Age Graph 9.2 Confidence interval around the best estimate cohort life expectancy of Dutch males and females in 2018 Graph 9.2 shows that uncertainty decreases as age increases. This follows from the fact that the number of years projected decreases as age goes up. Also visible is that life expectancy decreases until age 60 and increases after that. Two effects play their parts here. An older person has already survived a certain period, so life expectancy grows as one ages. On the other hand, a younger person will benefit more from expected future mortality improvements. Please note that the confidence intervals presented only include uncertainty in future mortality probabilities and do not apply to any single individual. As mortality probabilities for, for instance, a 90-year-old change very little over time, we observe hardly any differences for their expected age at death when we simulate all kinds of future scenarios with our model. But of course this does not mean that the actual moment of death for a 90-year-old individual is already fixed. Low uncertainty in mortality probabilities does not imply low uncertainty about the actual time of death of a single individual. 9.2 Simulations for obligations For each of the mortality probability scenarios described in paragraph 9.1 the value of obligations can be determined. By assessing all scenarios together a distribution of the value of obligations is obtained. Table 9.1 lists the average and 95%, 97.5 and 99.5% quantiles of the technical provision after simulating 10,000 such scenarios. The average male and female model portfolios were used at fixed interest rates of 3% and 1%. The results are expressed as a percentage of best estimate values. Projection Table AG2018 Applications of the model 31 Life expectancy
Results simulation of technical provision (relative to best estimate) Interest 3% Males OAP Standard deviation Quantiles 50% 95% 97.50% 99.5% SP OAP + SP OAP Females SP OAP + SP 2.2% 1.7% 1.4% 1.8% 2.1% 1.4% 99.9% 100.0% 100.0% 99.9% 100.0% 99.9% 103.5% 102.8% 102.2% 102.8% 103.5% 102.3% 104.2% 103.4% 102.7% 103.4% 104.2% 102.7% 105.5% 104.4% 103.4% 104.2% 105.6% 103.4% Table 9.1 Results simulation of provisions at 3% interest for model portfolios (males and females average) Bij 1% rekenrente is de spreiding in de resultaten groter. Uitkomsten simulatie VPV (in verhouding tot de best estimate) Interest 1% Males OAP Standard deviation Quantiles 50% 95% 97.50% 99.5% SP OAP + SP OAP Females SP OAP + SP 2.6% 2.0% 1.7% 2.2% 2.7% 1.8% 99.9% 100.0% 99.9% 99.9% 100.0% 99.9% 104.2% 103.3% 102.8% 103.5% 104.4% 102.9% 105.1% 104.0% 103.3% 104.2% 105.3% 103.5% 106.7% 105.3% 104.3% 105.3% 107.1% 104.4% Table 9.2 Results simulation of provisions at 3% interest for model portfolios (males and females average) The distribution that ensues from the simulations strongly resembles a normal distribution. As demonstrated in the tables above, the spread in the separate benefits is much higher than in the OAP and SP combination, especially in the old age pensions for men and survivor’s pensions for women. As an example graph 9.3 shows the distribution of simulated values for OAP, SP and the combination of both around the best estimate. The model portfolio is male average and the interest rate is 3%. Please note that the distributions shown are not entirely regular due to the inherent simulation uncertainty at 10,000 simulations. Projection Table AG2018 Applications of the model 32
Distribution of Technical Provisions based on AG2018 Combination Survivor’s pension Old age pensions 85% 90% 95% 100% 105% 110% 115% Graph 9.3 Distribution results around the best estimate of simulation of provisions (interest 3%) for male average model portfolio 9.3 Simulations for life expectancy over a one-year horizon As mentioned above, life expectancy can also be simulated after a shock in the first year, including the impact of that shock on the best estimates for remaining years after recalibration. On the basis of this life expectancy confidence intervals with a one-year horizon can be determined. The 95% confidence intervals based on 5,000 scenarios are represented in the graph below for men and women. Period life expectancy at birth 90 85 80 Females 75 Males 70 95% confidence interval Observations The Netherlands Observations European selection Projection The Netherlands Projection European selection 65 1970 1980 1990 2000 2010 2020 2030 2040 2050 Graph 9.4 Confidence interval around the best estimate period life expectancy for Dutch males and females, one-year horizon Projection Table AG2018 Applications of the model 33
The graph shows that the confidence intervals for a one-year horizon are considerably smaller that those for the complete run off (see graph 9.1). The reason for this is, that for the one-year horizon only the uncertainty in the first projection year is included (including the impact of this first year on the parameters), while in graph 9.1 the uncertainty is represented across the whole run off period of the obligations. The graph below shows the uncertainty in cohort life expectancy of Dutch men and women in 2018, again over a one-year horizon. Life expectancy in The Netherlands 2018 105 100 95% confidence interval Males Females 95 90 85 80 0 10 20 30 40 50 60 70 80 90 100 Present Age Graph 9.5 Confidence interval around the best estimate cohort life expectancy of Dutch males and females in 2018, one-year horizon Here too, the confidence intervals are shown to be significantly smaller for a one-year horizon, compared to those of the complete run off (see graph 9.2). Projection Table AG2018 Applications of the model 34 Life expectancy
9.4 Simulations for the best estimate over a one-year horizon For each of the 5,000 mortality probability scenarios described in paragraph 9.4 the value of obligations after recalibration can be determined, which will yield a distribution of the value of obligations over a one-year horizon. The results of this are listed in the tables below. Results simulation of technical provision (relative to best estimate) over one year Interest 3% Males OAP Standard deviation Quantile 50% 95% 97,50% 99,5% SP OAP + SP OAP Females SP OAP + SP 0.7% 0.8% 0.5% 0.8% 1.1% 0.5% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 101.1% 101.3% 100.8% 101.2% 101.7% 100.8% 101.3% 101.5% 100.9% 101.5% 102.2% 101.0% 101.7% 102.0% 101.2% 101.9% 103.1% 101.3% Table 9.3 Results simulation of provisions at 3% interest for model portfolios (males and females average) over a one-year horizon Results simulation of technical provision (relative to best estimate) over one year Interest 1% Males OAP Standard deviation Quantile 50% 95% 97,50% 99,5% SP OAP + SP OAP Females SP OAP + SP 0.8% 1.0% 0.6% 1.0% 1.3% 0.7% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 101.2% 101.6% 101.0% 101.5% 102.1% 101.1% 101.5% 101.9% 101.1% 101.8% 102.6% 101.2% 101.8% 102.4% 101.5% 102.3% 103.9% 101.6% Table 9.4 Results simulation of provisions at 1% interest for model portfolios (males and females average) over a one-year horizon These results show that, as suggested by the results in paragraph 9.3, the spread over a one-year horizon is much lower than in a simulation over all years. The impact of the transition from AG2016 to AG2018 on provisions is listed in table 8.7 in chapter 8. Because the transition from AG2016 to AG2018 adds on two years of new observations, the impact must be split into the impact of the AG2016 to AG2017 and the AG2017 to AG2018 transitions (see table 8.8 in chapter 8) to obtain a clean comparison. Only then can we speak of the impact for a single year. It turns out that in the AG2016 to AG2017 transition the observed impact on old age pensions for women just exceeds the 97.5 percentile. Other benefits remain within the 97.5% confidence interval. In the AG2017 to AG2018 transition the results for all benefits are close to the 50% quantile. We would again point out that the calculated one-year uncertainty only relates to uncertainty in the development of mortality probabilities and does not take into account that the observed mortality frequencies will not exactly match those mortality probabilities. Projection Table AG2018 Applications of the model 35
Projection Table AG2018 36
APPENDICES Projection Table AG2018 37
APPENDIX A Projection model AG2018 Technical description 1 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. Projection Table AG2018 Appendix A 38
Projection Table AG2018 Appendix A 39
2 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. Projection Table AG2018 Appendix A 40
3 See http://www.mortality.org/Public/Docs/MethodsProtocol.pdf 4 For this, the working group has used the R package systemfit with the options method=”SUR” and methodResidCov=”noDfCor”. Projection Table AG2018 Appendix A 41
Projection Table AG2018 Appendix A 42
Parameter values Males Projection Table AG2018 Appendix A 43
Males (continued) Projection Table AG2018 Appendix A 44
Females Projection Table AG2018 Appendix A 45
Females (continued) Covariance and Cholesky matrices Projection Table AG2018 Appendix A 46
APPENDIX B Model portfolio The model portfolio contains only the benefits lifelong old age pension and lifelong survivor pension. There are six model portfolios, which distinguish young/average/old and male/female. Only multiples of 10 are included as ages of members, pensioners and survivors. The average portfolio is defined as the average of young and old. The benefits granted to male participants (including widows’ benefits) are labelled as ‘male’ and the benefits granted to female members (including widowers’ benefits) are labelled ‘female’. The weighted average age for the various categories is listed in table B1. Young Males Active and deferred members Pensioners Survivors (SP) Females Active and deferred members Pensioners Survivors (SP) 49.3 71.7 61.1 40.6 73.3 55.0 50.8 72.9 68.1 46.4 73.3 62.2 Table B1 Weighted average age in the model portfolios The distribution in numbers is presented in tables B2 and B3. Males Young Males Average 30 500 350 0 40 1200 840 0 50 2000 1400 150 60 1800 1260 150 70 1500 800 100 80 300 150 50 90 0 0 0 (65) (def.) (i.p) 300 210 0 53.4 73.7 70.9 49.8 73.3 64.3 Average Old Males Old Age OAP SP SP OAP SP SP OAP SP SP (65) (def.) (i.p) (65) (def.) (i.p) 100 70 0 850 595 0 1400 980 125 1800 1260 175 1650 950 250 550 275 175 50 25 50 Table B2 Number of members model portfolios males 500 350 0 800 560 100 1800 1260 200 1800 1100 400 800 400 300 100 50 100 Projection Table AG2018 Appendix B 47
Females Young Females Average 30 750 525 0 40 1000 700 0 50 500 350 50 60 200 140 50 70 100 50 0 80 50 20 0 (65) (def.) (i.p) 500 350 0 Females Old Age OAP SP SP OAP SP SP OAP SP SP (65) (def.) (i.p) 1000 700 0 1000 700 50 800 560 100 300 200 50 150 50 25 1000 700 0 1500 1050 50 1400 980 150 500 350 100 250 80 50 90 000 000 000 Table B3 Number of members model portfolios females The technical provisions for these portfolios are calculated using the following assumptions: • Retirement age is 65 years; • Payment is continuous; • Survivor’s benefit is of the type ‘undefined partner’ until retirement date and ‘defined partner’ thereafter; • Partner frequency is 100% until retirement age; • A partner’s gender is opposite to the member’s; • In any partnership the man is three years older than the woman. (65) (def.) (i.p) 250 175 0 Projection Table AG2018 Appendix B 48
APPENDIX 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 May 2018. [1] CBS data from Statline for 2017: Exposures-to-Risk (P-values); version of 14 May 2018. https://opendata.cbs.nl/statline/#/CBS/nl/dataset/37325/table?ts=1530795309853 Observed Deaths (C-values and D-values); version of 8 May 2018: https://opendata.cbs.nl/statline/#/CBS/nl/dataset/37168/table?ts=1530802763004 [2] Eurostat data (data until 2016): Exposures to Risk (demo_pjan) version of 27 February 2018: http://appsso.eurostat.ec.europa.eu/nui/show.do?dataset=demo_pjan&lang=en Observed Deaths (demo_mager en demo_magec) version of 15 March 2018: 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/ The table below shows for each geographical area and each year which data source was used as input for the AG2018 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 by adding the difference between the two definitions as observed in 2012 to the Eurostat data in 2016. GEO Austria Belgium Denmark Finland France (metropolitan) Germany (until 1990 former territory of the FRG) Iceland Ireland Luxembourg Netherlands Norway Sweden Switzerland United Kingdom 2013 HMD HMD HMD6 HMD HMD6 HMD HMD6 HMD HMD HMD6 HMD HMD HMD HMD6 2014 HMD HMD HMD6 HMD HMD6 HMD HMD6 HMD HMD HMD6 HMD HMD HMD HMD6 HMD = Human Mortality Database, protocol v5 HMD6 = Human Mortality Database, protocol v6 EUROS = Eurostat Statline = Statline EUROS = Eurostat, modified Table C1 Sources Projection Table AG2018 Appendix C 49 2015 EUROS HMD HMD6 HMD HMD6 HMD HMD6 EUROS EUROS HMD6 EUROS HMD EUROS HMD6 2016 EUROS EUROS HMD6 EUROS EUROS EUROS HMD6 EUROS EUROS HMD6 EUROS HMD EUROS HMD6 2017 HMD-version 2015.09.02 2016.08.12 2018.04.23 2016.10.07 2017.09.26 2017.03.29 Statline 2018.03.26 2015.11.20 2015.10.19 2018.05.10 2015.08.28 2017.08.28 2016.05.20 2018.05.08
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 form 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 Teirlinck, A.C., van Asten, L., Brandsema, P.S., Dijkstra, F., Trab Damsgaard, M., van Gageldonk-Lafeber, A.B., Hooiveld, M., de Lange, M.M.A., Marbus, S.D., Meijer, A., and van der Hoek, W. (2017) Surveillance of influenza and other respiratory infections in the Netherlands: winter 2016/2017, RIVM, Bilthoven. Projection Table AG2018 Appendix C 50
APPENDIX D Glossary State Pension retirement age Age at which a person becomes eligible to receive State Pension retirement benefit (AOW). This age is raised step by step from 65 to 67 in the period 2014 to 2021. Further increases will depend on the future development of (estimated) life expectancy. 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. This means that the life expectancy of an individual is based on mortality probabilities from a mortality table corresponding to the observation year in which that individual has a certain age. Deterministic projections life table Projections life table in which mortality rates for future years are determined on the basis of a model that does allow for uncertainties. Hence there is 1 (deterministic) result. 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 35 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. Life expectancy In most publications the term life expectancy denotes the expected (remaining) lifespan of a new-born. The publication Projections Life Table AG2014 refers to remaining life expectancy, because this term applies to any age. The term may denote to period life expectancy or cohort life expectancy. Projection Table AG2018 Appendix D 51
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. Period life expectancy Life expectancy based on a period life table. Period life table Mortality table based on actual mortality rates from one or more observation years. AG bases its period life tables on actual mortality in the five most recent completed calendar years. A period life table does not allow for mortality developments and thereby assumes constant mortality probabilities in future years. Projection period The number of years for which –within the model- mortality figures 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). Projection Table AG2018 Appendix D 52
PROJECTION TABLE AG 2018
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