A Dutch uniform policy pension study : the welfare loss of the transition towards an actuarially fair system

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A Dutch uniform policy pension study

— The welfare loss of the transition

towards an actuarially fair system

M.P.G.W. Th¨

onissen

Master’s Thesis to obtain the degree in Actuarial Science and Mathematical Finance University of Amsterdam

Faculty of Economics and Business Amsterdam School of Economics Author: M.P.G.W. Th¨onissen Student nr: 10517685

Email: maxthonissen@gmail.com Date: July 12, 2018

Supervisor: Dr. S. van Bilsen Second reader: Dr. T. Boonen

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This document is written by Max Th¨onissen who declares to take full responsibility for the contents of this document. I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it. The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.

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Abstract

This master thesis examines the transition of the au courant pay-as-you-go pension system towards a new actuarially fair pension system based on uniform accrual and uniform contribution. The calculations of Frehen et al. (2017) and Chen and Van Wijnbergen (2017) are used as the common thread for this research. The calculations are done in Rstudio to provide a stable solution for numerous scenarios, furthermore several different situations are considered to find the sensitivity of the market de-pendent and individual specific parameters. One of the results of this examination is that the welfare loss per generation is at least 1.2 percent and that the transition cost for the society is approximately 36 billion euros. Furthermore, it is concluded that the inflation rate has a big influence on the welfare loss. Also situations with different levels of risky assets in the portfolio are considered.

Keywords Actuarially fair system, Pay-as-you-go, Pension system transition, System of uniform accrual and uniform contribution

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In this foreword I want to thank my first supervisor Dr. S. van Bilsen for his active and supporting accompaniment during this four month lasting project. His avail-ability and critical eye about the nowadays pension discussion were useful when the theoretical basis was created and when the calculations were made. This col-laboration was as pleasant as during the period of my actuarial science bachelor thesis.

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Chapter 1 Introduction

Cabinet Rutte III aims for a renewed pension system in 2020. This is one of the main goals of the recently formed cabinet of VVD, CDA, D66 and ChristenUnie in The Netherlands. This new cabinet follows the path that cabinet Rutte II has chosen where the cabinet presupposes that the present pension system is outdated. Unfortunately, due to several factors the progress towards a new system disappoints, but on the other hand cabinet Rutte III has the abolishing of the system of uniform accrual and uniform contribution, also known as the doorsneesystematiek, in their own hands. This transition towards a new pension system involves advantages and disadvantages.

One of the main goals of a new pension system includes the possibility of per-sonal pension accumulation relative to the collective uniform policy pension system. On the other hand, this does not facilitate the solidarity between and within gen-erations that comes with the pension system nowadays. Younger participants pay in comparison to older participants relatively more. This is not actuarially fair. The actuarially fairness of the new pension system has to overcome this problem.

When the aim of cabinet Rutte III becomes reality, it involves several questions. One of them is, how much will the transition cost the society and who has to pay for it. Especially for the people who are building up pension for several years in the au courant system and will switch towards the new system. The already accrued pension rights cannot disappear, so they have to be compensated for the transition. Even more, how will the pension accrual be defined for someone who starts in the new system without any accrued pension rights. This problem can be described as

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a zero-sum game. Every advantage for a particular generation is a disadvantage for another generation, this problem also comes through if there is a switch towards an actuarially fair system. This results in the main question of this thesis:

How much is the welfare loss for the active generation when switching towards a new actuarially fair pension system in The Netherlands?

To find a solution for this question, the theoretical basis is formed in the second chapter. This section is divided into four subchapters, where at first the solidarity and the structure of the Dutch pension system are explained. Furthermore, the uni-form policy pension is clarified and the reason is mentioned why there has to be a transition towards an actuarially fair system. Additionally, this switch has a few financial consequences. This is declared in the third subchapter, where inferences of earlier studies are compared and is explained why there are some major differences between the outcomes of the costs for the society of the transition towards a new system. Finally a short introduction of the own study is given.

After the theoretical part, the mathematical calculations are discussed. The cur-rent situation is modelled, after which the new situation is described. To find a well-funded solution, how much the real burden will be, there is a verification of how much a change in parameter value influences the transition costs. These calcu-lations are given in the sensitivity analysis. The final mathematical computations are done such that the real impact on the society can be quantified. One of the main results of this examination is that the total cost of the transition is approximately 36 and 50 billion euros when taking two different parameter assumptions into ac-count. Additionally, the welfare loss strongly depends on the parameter choice. The inflation rate influences the premium accrual in the old system more than in the actuarially fair system. The graphical representation of these results can be found in paragraph 4.3. Furthermore, the value loss per generation is at least 1.2 %, see Figure 4.11.

The other results are also explained in chapter four where the analysis of the results is given per different category. These results and analysis form the basis of the conclusion which is stated in the final chapter of this thesis. On the last page the references and used sources are enumerated.

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Chapter 2 Theoretical background

2.1 Dutch pension system

The current Dutch pension system came into existence after the second world war when the collective regulations with solidarity between participants became key. Back then it was important for the older participants to create a sufficient pension sum in a short amount of time, which resulted in equal premium for employers that fitted the spirit of that particular time period (Bonenkamp, Cox and Lever, 2013).

Solidarity between participants became one of the up-front issues in the pension discussion. Participants were now able to share risks among other participants such as longevity risk and financial risks. Subsidising solidarity is one less desirable char-acteristic, because for example, a poorly-educated man has a lower life expectancy in comparison to a well-educated woman. This results in the fact that this man pays a relatively high premium in comparison to that woman. There is a one-sided value transfer from one group to another without a compensation the other way around. Unfortunately this situation will always occur since there are no perfectly homogene participation groups.

One of problems of the solidarity of the system is the aging society, this started with the babyboom after the second world war. Nowadays, we have reached the period that all the babyboomers are retiring and in comparison to the retirees there are fewer participants to pay for the pay-as-you-go system. This results in higher premia for active participants. A solution for this problem is the increase in

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sionable age to have more people that can pay for the retirees but this also results in a bigger difference among active participants and so the premia pay off differ, per saldo the younger participants are worse off.

The system nowadays is build up out of three pillars, at first the pillar that provides a pension for everybody that belongs to the working class. The fact that this first pillar pension is a collective pension plan, hereby it creates a minimum pension for individuals that live and work in The Netherlands. This base pension is also known as the Algemene Ouderdomswet (AOW).

The second building block is the possibility to create an additional pension where the employee can build up his pension with the help of the employer to stabilise their purchasing power even after retirement. The main goal of the second pension pillar is the preservation of the standard of living when the fruits of labour drop out. In this thesis, the focus will be on the second pension pillar.

The last possibility to accrual a pension is by taking life annuities, lump sums or life insurances. These opportunities are primarily used by freelancers. Au courant these freelances are only able to use the first and third pension pillar but the third block also functions as an additional pension possibility for someone who belongs to the working class and has an employer.

2.2 Uniform policy pension

The second pension pillar in The Netherlands is subjected to some interventional transformation. Next to the fact that there is a transition from a Defined Benefit regulation towards a Defined contribution regulation, the uniform policy pension system will probably be abolished in the next couple of years by cabinet Rutte III. The question arises, why will the system of uniform accrual and uniform contribu-tion be abolished and what is it exactly. The uniform policy pension system can be seen as a combination of a pension premium that is a fraction of the pensionable salary that is equal for every participant with also an equal pension accrual per-centage. This system involves several strengths and weaknesses. One of the major weaknesses is the uniformity. The premium and accrual percentage are independent of the personal characteristics of individual, thinking of age, gender and career pat-tern. This is one of the conclusions of the CPB Netherlands Bureau for Economic

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6 M.P.G.W. Th¨onissen — _{The welfare loss of the transition}

Policy Analysis (2013) at the request of the Dutch Ministry of Social Affairs and Employment. The actuarially value per participant differs, so there is an ex-ante redistribution between participants. When an individual participant accesses the pension regulation, the individual already knows beforehand whether it would be beneficial or not to participate, think of a well-educated woman by comparison to a poorly-educated man.

The structural redistribution within supplementary pension plans can be down-graded into two causes, on one hand the time value of the premium, where premia of younger participants have higher expected pay off than premia of older participants, due to the fact that they can render longer. On the other hand the life expectancy among participants, people with a lower life expectancy subsidise older people. A persons career path can be divided into two parts. Approximately the first half the younger people subsidise the older people, but the benefits of the second half do not equal the negative effects in the first half of someones career path.

Besides the time value and life expectancy redistribution, there is a so-called pay-as-you-go (omslagelement) effect. The CPB has published this pay-pay-as-you-go effect in their report. This element is quantified by approximately eight percent. It means that someone who accedes the system of uniform accrual and uniform contribution faces an eight percent decrease in value of their pension where six percent is due to the consistent premium and the other two percent is due to increasing life expectancy (Koninklijk Actuarieel Genootschap, 2014). The pay-as-you-go-element can be seen as the difference between the uniform premium and the generation premium, where the generation premium is the uniform premium for the concerning generation. The Royal Dutch Actuarial Agency states that the redistribution depends on the current situation, because in general the time value and life expectancy redistribution will lead to an unfavourable effect for younger, poorly-educated and less healthy par-ticipants. On the other hand, in more denominational conditions, for example an increasing population, the redistribution can lead to more favourable effects. It is im-portant notice that this eight percent depends on the interest rate, salary increase and age distribution of the population. Next to the effects of the pay-as-you-go-element, an incomplete career and differences in income patterns will lead to welfare losses of the pension regulation. Especially in the first half of the career path where there is subsidising solidarity. Even more, the differences in life expectancy will lead

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to a redistribution from poorly to well-educated participants. This redistribution is an ex-ante redistribution, participants already know beforehand that this downside will affect them. In the end, it looks like that the system of uniform accrual and uniform contribution also has a positive effect. It could be beneficial for the labour participation of older people, due to the fact that there is an increase in labour demand.

If the uniform policy pension system is abolished, the question arises, how the transition towards an actuarially fair system will be. Every pension system can be described as a zero-sum game. So when one system is abolished the active par-ticipants have to take the burden. Those active parpar-ticipants will miss out of the subsidising solidarity in the second phase of their career path. The question arises how much the value will be, how and to whom the transition value has to be dis-tributed. In the current system, the active generations pay for the older generations, but if this chain is broken, the active generations will miss out on the premia of the future generations. Thus they have to be compensated for that. By this fact, it is important to know how much the current active generations will miss out.

Among earlier studies there is a disagreement as to what the real transition value will be. It varies between approximately 100 billion from the calculations of the Koninklijk Actuarieel Genootschap (2014) and 37 billion at Chen and Van Wijnbergen (2017). This discussion will be analysed in the next subsection.

After abolishing the system of uniform accrual and uniform contribution, there are a few possibilities to change into an actuarially fair system. One of those possibil-ities is the change towards a degressive accrual system where the premia and accrual are balanced and the pension costs are equal for every participant. Hereby the age-specific accrual percentage decreases when participants become older. Unfortunately, this transition will take some time and is quite complex to compensate the current active participants. This also counts for progressive systems where older participants pay an increasing premium over time. The actuarial fairness of these two solutions is identical. Moreover, there are some age-dependent premia systems where the to-tal premium (employee plus employer) or the individual premia are age-dependent. This only involves several problems. The individual premium varies per employer and employee. Apart from this characteristic, these systems overshadow the positive effect of the pay-as-you-go-element. The Koninklijk Actuarieel Genootschap (2014)

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concludes that older people possibly get a better position on the labour market.

2.3 Comparison of earlier studies

Until now there had been no consensus about how much the transition burden will be for the active participants. The opinions are widely spread from approximately 37 billion towards about 100 billion euros. In Frehen et al. (2017) the burden is divided into two parts, where the complete transition cost will be approximately 100 billion, but the burden on the participants who suffer a loss, will be about 68 billion. The remaining costs are the compensation for the saving on the premium of the current generations. The difference between Bonenkamp and Lever (2015) working for the CPB and Frehen et al. (2017) is that the CPB calculated the transition burden and Frehen et al. calculated the loss in value for the current generation.

In Bonenkamp and Lever (2015) this loss in value takes the implicit debt of the future premia into account, the real burden per participant is also calculated where there are about six million full time working participants. This results in a loss of 17.000 euros per full time working individual.

When Chen and Van Wijnbergen (2017) use comparable parameter and model assumptions, they conclude the same transition burden as Lever et al. (2017). The outcome strongly depends on the parameter settings. One of the main differences is that Chen and Van Wijnbergen (2017) do not model the survivor’s pension, fur-thermore the starting pension base differs among the two studies. The pension base in Lever et al. (2017) is about 42.8 percent higher, respectively 112 to 160 billion euros. Supplementary, the applied yield curve by Lever et al. (2017) differs with the flat yield curve of Chen and Van Wijnbergen (2017). Lastly, the outcomes of Lever et al. (2017) are based on a stochastic approach in comparison to the deterministic setting of Chen and Van Wijnbergen (2017). The big difference between the results of these two studies is based on the larger transition effect due to the difference in pension base and accrual.

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2.4 Own study

In addition to the earlier studies of Bonenkamp and Lever (2015), Frehen et al. (2017), Chen and Van Wijnbergen (2017) and Lever et al. (2017) in this mathe-matical analysis of the burden that individuals have to face due to the transition towards a new actuarially fair system a sensitivity analyses on ω is performed, differ-ent values for the premia are taken into consideration and in the end a value for the total transition cost for the society is computed. Furthermore indexation is taken into account when defining the value for the benefits. This analysis can be found in section 4.3. The more detailed mathematical explanation of the calculations are presented in chapter 3.4 and 3.5.

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Chapter 3 Mathematical model

3.1 Assumptions

After analysing the au courant pension discussion, the assumptions and mathemat-ical computations will be explained. Some of the assumptions will differ when the sensitivity analysis is performed in section 3.4. The assumptions are given in Table 3.1.

The complete group of participants consists of 60 generations aged 25 to 85 (Ω), divided into 40 active generations and the last 20 (n) generations are retirees. To derive a well-funded solution it is assumed that the old system is working for the last one-hundred years and now the system will be abolished such that there will be a switch towards a new actuarially fair system. This is calculated in 10.000 different scenarios.

Among the more economical assumptions the accrual rate ρ is chosen equal to the weighted average of the accrual rates of Dutch pension funds in 2016. Furthermore it is assumed that the wage-increase will be constant over time and is denoted as 1+π. Next to the wage-increase, the wages are indexed such that the wages grow with the inflation rate and the value of the wages per age does not decrease over time.

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Table 3.1: Assumption setting

Assumptions Description Value

r Interest rate 1 % ρ Accrual rate 1.829 % π Inflation rate 2 % µ Mean return 5 % σ Standard deviation 20 % p Premium percentage 20 %

ω Amount of portfolio in risky assets 50 %

β Time discount vector 97 %

γ Degree of risk aversion 5 Ti Number of generations (25...85) 60

Tchange Moment in time when switching to new system 100

Tt Number of time periods 200

S Number of scenarios 10000

3.2 Current situation

After the explanation of the assumptions, the mathematical routines are explained in chronological order. In the beginning of the year on the first of January the total amount of wealth of the pension fund is equal Wt. On the first date it is assumed that

the value of W0 is equal to the premium percentage p times the 40 active generations

(Ti-n). These premia render over this full year which gives a new value:

Wt+1 = Wt(1 + r + ω(µ − r)) + Wtσωεt (3.1)

Furthermore, the benefits are calculated in a matrix B with dimensions (10.000,60,200), so the value of B[1,2,3] is the value of the benefits of an individual of a 26 year old at time 3 in the first scenario. A pension fund has to know how the liabilities and the assets behave during the year, the funding ratio becomes an important issue. For every year and scenario the pension fund knows whether they have to index their benefits and liabilities. The liabilities L are defined as the total amount of wealth that have to be redistributed among the retirees. The indexation method is defined as follows:

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12 M.P.G.W. Th¨onissen — _{The welfare loss of the transition} Indexation =          0 if Ft< 1.05 Ft−1.05 1.4−1.05π if 1.05 < Ft< 1.4 π if Ft> 1.4

When the funding ratio exceeds 1.4 the indexation is chosen such that the funding level is reset towards 1.4, otherwise the funding ratio can explode when it remains increasing. This would lead to an unreal situation. After knowing the height of the indexation, the liabilities are adjusted and then the cycle goes on in the same pattern for each of the 200 years.

Since the values of the benefits and liabilities are known, these values have to be valued towards the same moment. This is done by the next formula:

Nt= e

−rt−1₂λ2_t−λt−1P

i=0

ε_i+Tchange

(3.2) This is also known as the pricing kernel where λ is the Sharpe ratio (µ−r_σ ) and ε is the matrix which is used to model the uncertainty among the different scenarios. With this formula the values of an individual in the current situation is known, the results are given in the next chapter.

3.3 Transition towards a new actuarially fair

sys-tem

When modelling the transition towards a new actuarially fair system, there are similarities and differences. The major difference is the premium accrual method where there is no equal premium for every participant but an actuarial fair premium per generation. This premium will be calculated on the basis of the next formula. Let x be the actuarial fair premium:

p = x 20 P i=1 (1 + r)i+j x = p ₂₀ 1 P i=1 (1 + r)i+j (3.3)

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Where p is the premium percentage and j is the amount of years until someone reaches their pension age (j=0, ... , 39).

To compute a substantiated comparison, the same assumptions of Table 3.1 are needed. Furthermore, the pension fund takes the same decisions with respect to indexation and the portfolio (ω = 0.5). The matrix ε is computed in such way that the first 100 years (Tchange) are zero, so everyone will have the same uncertainty in

their generation.

3.4 Sensitivity analysis

After the computations of the old situation, the actuarially fair system and the transition effects, there is a sensitivity analysis on the parameter values of Table 3.1. One of the changed assumptions is the inflation rate π, due to the fact that the inflation rate nowadays is quite low. It is good to know what the influences are if the inflation rate starts rising again or even decreases towards zero. It is assumed that the inflation rate will be positive so there will be no deflation due to the stability of the Dutch economy.

Another possible situation is that there is a mutation in the portfolio composi-tion, so various heights of ω will be used. The most realistic portfolio composition is the lifecycle method due to the fact that someone aged 25 will invest in a different way than someone who is near his pension age. Young people are more risk-seeking by comparison to the older risk-averse generations. This is a result of the fact that younger people have more time to come up if a setback occurs. Moreover, the younger generations have substantial human capital. Human capital reflects someones abil-ity to earn and save throughout their lives. Younger generations typically have had little time to accumulate wealth, so the financial wealth of an individual is low in the beginning but is increasing over time and human capital is decreasing during the active phase. These are well-known elements in scientific studies which uses various portfolio compositions for different ages.

This sensitivity analysis will be done for the old and the new situation so that we know how much the effect will be in case of a transition.

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3.5 Impact on the society

The value for the impact on the society is a valuable supplement to the sensitivity analysis and the valuation for the transition due to the fact that this will give a better insight in how much the real burden is in a realistic scenario. This is calculated as follows: as usual the pension base of a modal individual consists of the modal income in The Netherlands as it is 37500 euros in 2018 minus the AOW-franchise of 13.344 euros. This results in a pensionable salary of 24.156 euros. Since we are interested in the situation after the transition, the premium on time Tchange is set to 20 percent

of the pensionable salary at that moment. The modal income is chosen since that the complete income distribution is not known and furthermore 50 percent of the working class earns more and 50 percent earns less than the modal income of 37500 euros, so the modal income to some extent reflects the Dutch income distribution.

Moreover, based on the papers of Chen and Wijnbergen (2017) and Frehen et al. (2017), a comparable analysis of the transition cost for the society is computed. These calculations are computed under the same assumptions as in the paper of Chen and Wijnbergen (2017). The assumptions can be found in Table 4.3.

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Results and analysis

4.1 Current situation

After computing the transition effects and a sensitivity analysis on the parameters the results are presented. The findings are divided in several subchapters. In the beginning the value per generation in the old system is given. These are the pension values for every individual if someone leaves the system, a small side note that this value is the value for someone of a particular age who steps out of the system but not in the case of death. For example, someone aged 30 has a pension value of approximately 50 in the old situation. Figure 4.1 shows the value of accrued pension rights in the old system.

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Figure 4.1: Accrued pension rights per generation in the old system

The figure above differs in comparison to the current situation where an indi-vidual is fully in the current system. This Figure 4.2 shows the value of accrued pension rights plus the value of future pension rights (pension rights that still need to be accrued) in the old system. It is visible that there first is a decrease in value

Figure 4.2: Value of accrued pension rights plus the value of future pension rights

and after fourteen periods the pension value increases again. This phenomenon can be explained by the indexation and discount effect. The value of pension of the younger generations will typically be higher than value of pension of the old because

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the younger generations get more compensation for inflation, that is why it is called the indexation effect. On the other hand, there is the discount effect. That is the value of pension of the young that will typically be lower than value of pension of the old because pension of the young is discounted at a higher rate. The difference in shape of the graph in Figure 4.1 and 4.2 is that in the beginning the value of an individual is much lower in Figure 4.1. This difference can be explained by the fact that if someone steps out of the system the value is lower than someone who participates all his working life. Specifically the explanation for the higher value for younger generations in Figure 4.2 is that an individual will participate for all of his life, so they will pay premia for a longer period and those premia render for forty years.

4.2 Transition towards a new actuarially fair

sys-tem

Additionally, the findings of the new actuarially fair system are presented. The ma-jor difference is the pension accrual by the fact that in comparison to the old system there is now an actuarially fair premium, see equation 3.1. One important assump-tion is that an individual will fully use their accrued pension rights so there will be no legacy for heirs, the value after age 85 is zero. The results are presented in the following two barplots, where the first plot shows the value of an individual that partly participates in the new system and in the figure on the right the values of the partly new, partly old and the sum of both are given. The value of an individual that partly participates in the old system is also presented in Figure 4.1.

Figure 4.4 is built up from three different graphs; in green the pension value for an individual that will partly participate in the old system, in red the value for an individual that will participate for a fraction of his working life in the old system and in blue the sum of both systems is chosen to find the value of the pensions in case of a transition. The difference in graph of the old and new system is due to the fact that in the new system an actuarially fair premium is used as equation (3.3). The fact that the last two generations are equal is a result of the fact that the value after age 85, so generation 60, has to be zero.

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Figure 4.3: Partly in the new system Figure 4.4: New, old and the sum of both

This results in the comparison between the value the accrued pension rights plus the value of future pension rights in Figure 4.2 and the value of the full accrued pension rights in case of a transition from the old towards the new system in blue in Figure 4.4, this can be seen in the following graph:

Figure 4.5: Comparison of the lifelong value in the old system and partly in the old and new system

At first it is worth noticing that the pension value in case of a transition, in the turquoise color, that the last value in the active phase is substantial higher than the one but last value. This is due to the accrued behaviour in the old situation. See the red graph in Figure 4.4. Even more it becomes clear that a transition decreases

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the value for the younger generations but the difference between the two situations reduces due to the earlier explained indexation and discount effect.

Beside these two effects, another remarkable issue rises. In Figure 4.5 it becomes visible that there is a difference in value at the starting age. This can be explained by two effects. On one hand, inflation has an important role, the used inflation rate of 2 percent increases the premia in the old system for Tchange years and on the

other hand also the ρ in the old system is equal to 0.01829, this is not a breakeven premium percentage. So to explain this difference in value, the value for ρ is changed to 0.012. This displays an actuarial fair premium and the inflation rate π is changed to 0 percent to compute a well-founded comparison. Now the inflation effect and the actuarially unfairness effect diminish due to similar circumstances.

Figure 4.6: Comparison with (ρ, π) = (0.012,0)

Even though when considering the normal situation where actuarial fair premium in the old system is neglected and individuals still use the breakeven premium with ρ is equal to 1.829% the inflation effect elucidates. Since the pension accrual is quite sensitive with respect to the inflation, the welfare loss is computed in four different situations where the inflation differs from zero to two percent in steps of one percent. Inflation in The Netherlands is stable due to the long-term objective of monetary policy of the European Central Bank. The most likely situation is that inflation will be between zero and two percent because otherwise consumers will postpone their expenses in case of deflation and consumers will not consume at all if inflation is

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high. The effect of the different heights of inflation can be seen in the following three subfigures:

To finalise the analysis of the value gap between current system and the new actuarially fair system, the descriptive statistics are given. Table 4.1 shows that an increase in inflation rate π will lead in general to lower funding ratios of the pension fund. This results in the fact that the liabilities increase in comparison to the assets. So when the inflation starts to rise, the liabilities of the pension fund also start to rise. This explains the value gap between both systems.

Table 4.1: Descriptive statistics of the funding ratio Statistics π = 0.00 π = 0.01 π = 0.02 Minimum 0.61 0.60 0.59 Mean 1.29 1.24 1.18 Median 1.33 1.25 1.17 Maximum 2.08 2.05 2.02 Standard deviation 0.18 0.18 0.14

4.3 Sensitivity analysis

After computing the lifetime values per generation in the two different systems, now the real transfer value will be presented. The transition on different ages is verified, so for example what is the value if the transition occurs for someone who is aged 25, 30 or possibly 50. This gives an insight in the value of the transition for individuals of different generations.

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Now the sensitivity analysis is performed where it is shown how much the amount of risky assets in the portfolio influences the accrued pension rights. The standard amount of risky assets in the portfolio is chosen here at 50 percent. A sensitivity analysis is performed on nine different levels of risky assets in a portfolio, from ten up to ninety percent in steps of ten percent. By this sensitivity analysis the behaviour of the pension rights with respect to ω becomes visible when someone fully participates in the old system. This sensitivity analysis of an individual that fully participates in the old system with respect to ω can be seen in the following nine subplots.

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When the different outcomes are compared, the result of a lower amount of risky assets in a portfolio becomes visible. The indexation effect increases since the value of the pension is decreasing over time. The indexation effect has a stronger influence than the discount effect. This influence decreases when ω increases. Furthermore, it can be concluded that someone has to invest at least 50 percent in risky assets when using multiple-of-ten heuristics in computing an investment portfolio, otherwise the final value is not bigger than the starting value. A person has to take into account that these situations are based on a simulation of ten thousand replications, the final values in case of ω is 0.6, 0.7, 0.8 and 0.9 are quite high in comparison to the results with portfolios with lower amounts invested in risky assets. This also involves excessive risk taking, since in a situation of economic growth this possibly will have a positive effect but in recession this will lead to less favourable effects as the premia will not render that much over the working lifespan. In addition the difference between the starting value for an 25 year old individual in the old situation and in case of the transition is due to fact that in the old system it is possible to take more risk, so ω increases, but since the collective character of the pension system people now have the possibility of risk sharing and diversification. This feature is not possible in the individual actuarially fair system. That is a possible explanation for the higher starting value in the old system.

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Additionally, a congeneric sensitivity analysis can be computed for the situations where someone partly participates in the old and new system instead of an individual which fully lives in the old system. To reduce the amount of graphs, the form of Figure 4.4 is replicated for every of the eight different values for ω. In these graphs the value for an individual which lives partly in the new or old system can be seen. Furthermore, the sum of both systems are given in blue. It becomes visible that the effect of the old system outweighs the effect of the new actuarially fair system since the slope of the green barplot increases when ω increases. This results in a less convex shape of the blue plot.

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When checking the influence of ω on the welfare loss we see the following be-haviour:

It becomes visible that the amount of ω does influence the welfare loss. As if ω rises, the difference increases between the values of the old situation and the situation where a transition occurs. Especially in the first half of the active phase. This is a result of the fact that the new actuarially fair system is not influenced that much by a change in ω in comparison to the old system. If you take sum of the differences between both systems you get the following welfare losses given in Table 4.2.

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Table 4.2: Value loss per different ω Omega values Value loss

ω = 0.1 190.89 ω = 0.2 193.30 ω = 0.3 196.47 ω = 0.4 230.51 ω = 0.5 280.55 ω = 0.6 337.34 ω = 0.7 388.17 ω = 0.8 432.65 ω = 0.9 480.76

Moreover, it is interesting to know how the values will behave under similar but different circumstances with respect to different heights of the interest rate and the premium. Primarily the height of the premium is changed from 20 percent towards 22.8 percent, this is the premium that a person has to pay that builds up pension at the ABP, the biggest pension fund in The Netherlands. This is the pension fund for people that work for the government or in educational organizations. From this 22.8 percent, 16.03 percent is paid by the employer and the other 6.87 percent is paid by the employee such that 70 percent of the premium is covered by the employer.

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A trivial conclusion is that an increase in premium that has to be paid results in a higher value for the starting generations. This effect can be explained by the idea that a person pays more premium 40 years long and this bigger premium will render for the forty years. Since an individual pays more premium, he or she will build up more pension if the pension rights are not cut.

This can also be seen in Figure 4.9, in comparison to Figure 4.5 the most re-markable visible difference is the vertical deviation of the value. This is a result of the higher pension premium that participants have to pay at ABP.

Figure 4.9: Comparison of the lifelong value in the old system and partly in the old and new system

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4.4 Impact on the society

The value of the impact on the society is calculated on the basis of the modal income, see section 3.5. Since for every of the 10.000 scenario’s the first 100 years will follow the same pattern to create an equal situation on time Tchange. This results

in a premium equal to 7000.07 euros on a full time yearly basis on Tchange if the

premium increases by 2 percent per year. (p · (1+ π)Tchange · p · 24156=7000.07).

Furthermore, to compute the value for the individual in a realistic scenario, the values of paragraph 4.1 and 4.2 are multiplied by a factor 4831.20. This is the discounted value of the premium, since 7000.07 divided by p · (1+ π)Tchange _gives

4831.20. Figure 4.10 shows the realistic values for an individual.

Figure 4.10: Realistic value loss estimation

At the same time it is possible to compute the welfare loss percentage per ac-tive generation by the help of utility optimization. For this method β and γ are introduced as two new parameters, where β is the time discount vector and the γ parameter is the risk averse parameter. The value for γ is chosen equal to 5, this rep-resents a moderately risk-averse individual. Moreover, it is not possible to compare different nut levels on their value, one simple and clear understandable method is the so-called certainty equivalent principle where an individual prefers a guaranteed value X over the choice of having the possibility of acquiring a value that can be higher than X but is uncertain. In this situation it can be explained based on the following equation:

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28 M.P.G.W. Th¨onissen — _{The welfare loss of the transition} U = 60 X t=0 βt 1 1 − γX 1−γ X = U (1 − γ) P60 t=0βt !_1−γ1

These values for X for the situation in case of a transition from the old situation towards the situation and situation where the old system holds are compared by normal differences in terms of percentage. From this calculation the conclusion can be formed that this transition will at least lead to a value loss of 1.2 percent, in case of the optimal situation. If suboptimal choices are made this welfare loss percentage will rise. This result is illustrated in Figure 4.11. The increase in welfare loss decreases due to the indexation and discount effect in the old system, also referring to Figure 4.5.

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Additionally to the welfare loss in percentage per active generation, a welfare loss for the complete society is calculated as Chen and Wijnbergen (2017) and Frehen et al. (2017) already have calculated. But since there were no consensus, it is valuable to find the transition costs for the society. To provide a solid transition value, the same assumptions as in the paper of Chen and Wijnbergen (2017) are used in two different situations. These assumptions are given in Table 4.3. This results in at least a transition effect of 35 billion euros in the first situation and 50 billion euros in the second situation where Chen and Wijnbergen (2017) concluded that it should be approximately 37 billion and 48 billion euros.

Table 4.3: Assumptions for the transition effect

Description Situation 1 Situation 2

Working cohorts 40 40

Retired cohorts 20 20

Interest rate 1 % 1.5 %

Wage inflation 0.5 % 1 % Pension base (in billion euros) 112 112 Accrual rate 1.829 % 1.829 % Transition effect (in billion euros) 35.52 50.28

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Chapter 5 Conclusion

This master thesis explores the value and welfare loss in case of a transition from the au courant pay-as-you-go pension system towards a new actuarially fair sys-tem based on uniform accrual and uniform contribution in The Netherlands. Hereby a comprehensive study is presented, where a sensitivity analysis is presented and where a realistic scenario is sketched. This research has been done due to the fact that the recent cabinet Rutte III follows the path of the cabinet Rutte II, since they stated the present pension system in The Netherlands is outdated. Furthermore, the solidarity became one of the key points in the pension discussion as the au courant pension system does not provide an actuarially fair situation for younger generations. The abolishing of this system results in a welfare loss as the active generations built up pension for older generations but the young do not get a pension from the not yet active generations as the chain is broken. This results in the main question:

How much is the welfare loss for the active generation when switching towards a new actuarially fair pension system in The Netherlands?

Earlier studies have elaborated the Dutch pension pillar system where the second pillar is subjected to most of the present-day pension discussion. These studies also have shown the strengths and weaknesses of this pension pillar. One of arguments in favour of the transition is the actuarially fair character of the new system but the old system is based on collectivity. Especially this transition is important for the younger active generations as they do not profit from the subsidising solidarity in

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the second phase of their career path. Therefore it is important to know how much these active generations will miss out in their final pension accrual. However, until the moment of writing of this thesis there were no consensus about the height of the burden that the active generations have to face. The deviation between earlier studies is noteworthy, it varies from 37 billion euros by the calculations of Chen and Van Wijnbergen (2017) up to 100 billion euros by the calculation of the Konin-klijk Actuarieel Genootschap (2014). Other studies have compared what the ideal actuarially fair system is in case of a transition. One of these possibilities was the degressive accrual system which came forward as the best of the rest system since the age-dependent systems involve several problems, among other things the indi-vidual premie varies per employer and employee and even more so these systems overshadow the pay-as-you-go element.

This master thesis provides several new results in the Dutch pension discussion. One of these findings is that the real burden for the society can be approximated by 36 and 50 billion euros when taking two different scenarios into consideration. Moreover, the inflation rate plays a key-role in the welfare loss, the inflation rate strongly influences the welfare loss because the au-courant system is more influenced by the inflation due to the premium accrual method in comparison to the actuarially fair method. At the same time, the value loss per generation can be at least 1.2 per-cent per active generation in case of optimal choices, if suboptimal choices are used this will result into a higher percentage. In addition the results and welfare losses for different values for the amount of risky assets in the portfolio ω are presented. Subsequently two realistic scenarios are given in case someone builds up a pension at the biggest Dutch Pension fund ABP and for modal individual.

Considering in this research the value loss per active generation is only a per-centage, it is worthwhile translating this percentage into values so not only the full burden for the society is known, but also the distribution of the total value loss per active generation. Then it becomes clear which generation has to be compensated the most for the transition. This could be examined in further studies concerning a transition from the au courant pay-as-you-go pension system towards a new ac-tuarially fair system based on uniform accrual and uniform contribution in The Netherlands.

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References

Bonenkamp, J., Cox, R. and Lever, M. (2013), Eindrapportage Voor- en nadelen van de doorsneesystematiek, Centraal Planbureau.

Bonenkamp, J., Lever, M. (2015), Transitie doorsneesystematiek: een kwantitatieve analyse, Centraal Planbureau.

Chen, D.H.J., Van Wijnbergen, S.J.G. (2017), Redistributive Consequences of Abol-ishing Uniform Contribution Policies in Pension Funds, Network for Studies on Pensions, Aging and Retirement.

Frehen, L., Van Wel, W., Van Ewijk, C., Bonekamp, J., Van Valkengoed, J., Boei-jen, D. (2017), Heterogeniteit in doorsneeproblematiek, Network for Studies on Pensions, Aging and Retirement.

Lever, M., Van Ewijk, C., Werker, B., Van Wijnbergen, S. (2017), Overgangseffecten bij afschaffing doorsneesystematiek, Centraal Planbureau.

Utrecht, Koninklijk Actuarieel Genootschap (2014), Doorsneesystematiek Veran-deren of behouden?

Wolzak, M. (2017), Rutte III zet in op vernieuwing pensioenstelsel in 2020. Found on

https://fd.nl/economie-politiek/1221749/doorsneepremie-afgeschaft, consulted on April 28, 2018.

A Dutch uniform policy pension study : the welfare loss of the transition towards an actuarially fair system