Pension system in the Netherlands

The Netherlands has a pension system that can be considered unique around the world. The Dutch pension system consists of three so called pillars. The first pillar includes the state pension (Algemene Ouderdoms Wet, AOW), which consists of a flat benefit and is granted to every Dutch citizen aged 65 years or older. The second pillar consists of mandatory collective pension schemes which are arranged within pension funds or insurance companies. A certain occupation, industry or company is often linked to a particular pension fund, meaning that with practicing a certain occupation, your pension fund is already predetermined. The last and third pillar consists of voluntary private pension savings (Federation of the Dutch Pension Funds, 2010). Although the pillar structure of Dutch pension system itself does not differ much from the pillar structure of other western countries, the size and relative importance of each of the pillars is rather different. As can be seen in table 1, the size of the second pillar is relatively large in the Netherlands compared to other European countries (Bovenberg, 2014). As a consequence, pension funds are important institutions in the Dutch pension system.
Table 1 size of the different pillars of pension systems in European countries
The Netherlands Germany France Italy Spain Swiss UK US
1st pillar 50 85 79 74 92 42 65 45
2nd pillar 40 5 6 1 4 32 25 13
3rd pillar 10 10 15 25 4 26 10 42

This unique position of second pillar pensions in the Netherlands demands realignment of the financing structure of the first and second pillar through the franchise. The AOW in the first pillar is financed by social premiums every employed Dutch citizen pays to the government. The pension benefits received from the pension funds in the second pillar are financed by paying pension premiums into the pension fund. Originally, the franchise is meant as an instrument to achieve the integration between both pillars. In order to establish this integration, part of the labor income is exempted from paying pension premiums over into a pension fund; the franchise (Schols ‘ van Oppen, 2009). Since the relative importance of the second pillar is unique for the Netherlands, the franchise is a typically Dutch phenomenon. Theoretically the franchise equals the part of the labor income over which AOW benefits are granted (Schols ‘ van Oppen, 2009). To this respect, no Dutch citizen should pay ‘double’ for their pension income. Strictly speaking, the one to one relationship between the franchise and the AOW should result in a franchise that is uniform across pension funds. In practice the level of the franchise differs between pension funds (Eberhardt, 2014), although it has a uniform character within the funds itself (Schols ‘ van Oppen, 2009). Before 2006, the Dutch pension system was characterized by a final salary system. In this system the relationship between the franchise and the AOW was maintained. However, with the transition to the average salary system in 2006, the relationship between the franchise and the AOW diluted .
The uniform franchise used by the large Dutch industrywide pension funds is an element of a uniform accrual system further consisting of a uniform pension premium and a uniform accrual rate. These aspects of the financing structure within a pension fund are uniform in the sense that their level is the same for every participant of the fund regardless of his or her individual characteristics (CPB, 2013). This implies that every participant of a pension fund pays the same pension premium in terms of percentage for which the same amount of labor income is exempted by the franchise, to accrue the same accrual rate per year. Especially the franchise and accrual rate are highly interdependent. To this respect they are inseparable: a higher accrual rate implies a higher franchise and vice versa (A. Paulis, personal communication, May 22, 2015). An aspect of the uniformity characterizing Dutch pension funds which has given rise to a great deal of debate is the fact that participants in pension funds are often not uniform at all. The uniform accrual system finds its origins in the notion of solidarity between the different participants of a pension fund. Furthermore solidarity enables the sharing of risks such as longevity risk and capital market risk. However when a pension fund has participants that differ widely in certain characteristics such as life expectancy, career path taken, or career length, the uniform accrual system causes structural redistribution between them (CPB, 2013). A system is then said to be actuarially unfair. A measure of this redistribution is the net gain. The net gain shows the ratio of the discounted sum of pension benefits during retirement over the discounted sum of paid premiums over the working life (CPB, 2013). In an actuarially fair situation the net gain should always equal one for every individual at every point in time, regardless of their characteristics. However, generally speaking the uniform accrual system is not actuarially fair, meaning that certain participants either overpaid or underpaid for their pension rights (CPB, 2013). Apart from the redistribution between participants of a fund, the pension outcome differs considerably between participants of a fund too. The pension outcome can be thought of as the replacement rate. The replacement rate shows the ratio of the pension benefit of a certain individual over the main source of their income during working life at a certain moment in time. Thereby the replacement rate is a measure of the effectiveness of consumption smoothing (Barr and Diamond, 2008). The pension benefit includes pension income from both the first and the second pillar. Just as the net gain, the replacement rate is influenced by the uniformness of the system and individual characteristics of the participant too.
Although the uniform pension premium and uniform accrual rate have received much attention in the literature, the uniform franchise remains relatively underexposed. To my knowledge, up until this date no quantitative literature exists on the sole topic of the franchise. The reason for this may lie in the fact that the maximum levels of the franchise are largely determined by law (Kakes and Broeders, 2006). Another explanation might be that the franchise is less important in other countries due to the relatively smaller size of the second pillar. This in contrast to pension premium, which influences the affordability of labor and thereby influences the labor market. Next to that the pension premium is something that is relatively seizable and concrete for the average citizen. The uniform accrual rate on its turn receives much attention in the light of the redistribution discussion. Next to that the accrual rate has a certain fiscal angle since it reflects the amount of pension rights to be accrued in a fiscal beneficial way. It is however unjust that the franchise receives little attention. Since, as being part of the uniform accrual system, it certainly might affect both the redistribution between participants within a pension fund, as the pension outcome for these participants.
Therefore the research question of this thesis is the following:
‘How are the redistribution between – and pension outcome of individual participants of a pension fund influenced by their individual characteristics in terms of starting salary, career path and length of career, and to what extend does the level of the uniform franchise and accrual rate change the redistribution and pension outcome?’
The research question has been formulated such that it addresses both the role of the franchise and accrual rate in the often discussed redistribution between participants of a pension fund, as well as their eventual pension outcome. Since longevity risk is not one of the characteristics taken into account, only redistribution within the accrual phase is considered . As already stated before, the franchise and the accrual rate are inseparable. Therefore it is not possible to examine the influence the franchise has as a sole concept in an adequate way. The net gain is used as the outcome variable for the redistribution, while the replacement rate will be used as the outcome variable for the pension outcome. The replacement rate and net gain are not necessarily linked. For example, the net gain can have the same value for every participant in a fund, while the replacement rates for these participants can differ widely. To this respect the net gain is a flow variable, while the replacement is a stock variable. Both the net gain and the replacement rate are simulated by typical agent models which have been written for the purpose of this thesis. Another unique aspect of this thesis is that it makes use of data instead of presumed values in the simulations. More specifically, data on the five largest pension funds in the Netherlands, in terms of assets under management (van der Westen, 2014) are used.
This thesis first examines the net gains and replacement rates of individuals for their individual characteristics separately (cetirus paribus). Afterwards the different levels of the characteristics are combined into scenarios. Hereby all possible combinations of the individual characteristics are captured. The scenarios are determined in the following manner:
# scenarios = # starting salaries*# career paths*# lengths of career
For reasons of variation in outcomes and keeping in mind the scope of this thesis, these scenarios are simulated for the replacement rates.
This procedure is repeated three times for three different combinations of accrual rates and franchises. Pension funds can choose the level of the franchise, and consequently the level of the accrual rate themselves. However, not all combinations are allowed. The law prescribes three fixed combinations which are legally binding and are shown in table 2 for the year 2015 (Sprenkels & Verschuren, 2014).
Table 2 Lawful Combinations of Franchise and Accrual rate, 2015
Combination Accrual Rate Maximum Franchise Level
Combination 1 Maximum of 1,875% ‘ 12.642,-
Combination 2 Maximum of 1,788% (but not lower than 1,701%) ‘ 11.395,-
Combination 3 Maximum of1,701% ‘ 10.095,-

These fixed combinations represent maximum levels of the franchise and accrual rate combination. Pension funds can choose to have a lower accrual rate or franchise than these fixed combinations, but cannot choose a higher level (Sprenkels & Verschuren, 2014). Therefore these three combinations are used in this research. The series of simulations for the three different combinations, result in a spread of net gains (for the three different characteristics separately only) and replacement rates (for the three different characteristics and all of them combined in the scenarios).
Next, the magnitude of above described effects the individual characteristics and the combination of the franchise and accrual rate have on the replacement rates is estimated using a log linear model. In this way the marginal effects can be quantified. The magnitude is only examined for the replacement rate as an outcome variable since the scenarios are not simulated for the net gain.
The remainder of this paper is organized as follows. Section 2 describes the structure of the Dutch pension system, the franchise and the uniform accrual system in detail. Furthermore, previous literature on relevant topics is discussed. Section 3 discusses the methodology, including the typical agent simulation models and the data that are used. The results and implications are discussed in section 4. Subsequently, section 5 examines possible policy implication. Section 6 describes and discusses the general conclusions. Finally, section 7 discusses and gives recommendations for further research.

Literature Review
Structure of the Dutch Pension System
The Dutch three pillar pension system is a system that is rather complex to understand. Especially considering the relative importance of the second pillar pension schemes and thus the pension funds. Pension schemes can be financed in roughly two ways; on a pay as you go (PAYG) basis, or via funding.
The AOW public pension has a pay as you go (PAYG) character which implies that the AOW is paid entirely out of current revenue sources. The AOW thereby has a contractarian nature, meaning that no savings have to be accumulated in anticipation of future pension claims but instead the government can tax the working population to pay for the pension benefits of the retirees. Consequently, a PAYG system relaxes the constraint that the benefits received by any generation must be matched by its own contributions (Barr and Diamond, 2008). A PAYG financed pension scheme usually has two main objectives. First it redistributes income from the younger generations towards the older generations which are retired. Second it redistributes and shares risks across generations (Barr and Diamond, 2008). The level of the AOW benefit depends on the household’s composition. And the number of years which an individual has been insured. Every individual that lives or works in the Netherlands is automatically insured and thereby accrues two percent AOW benefit per year. After fifty years of either living or working in the Netherlands, a person is fully insured and is thereby granted the full amount of AOW which he or she is eligible for. This amount depends on the household composition. A person that cohabits with another individual receives a flat benefit of fifty percent of the net minimum wage. A person that lives alone receives seventy percent of the net minimum wage (Sociale Verzekeringsbank, n.d.). Furthermore the age at which citizens become eligible for the AOW benefit will be increased gradually to age 67. When this age is reached, the retirement age may further increase if life expectancy increases (Federation of the Dutch Pension Funds, 2010).
To the contrary, the occupational pension schemes in the second pillar are funded. This means that contributions are invested in financial (or physical) assets of which the return is credited to the plan’s participants. Funded schemes can be either individual or collective. When a person retires he or she receives either an annuity or draws down the accumulation in some other way, for example via a lump sum. The annuity or lump sum is based on either the individual contributions to the fund, or the accrued pension rights depending on whether the fund has individual accounts or a collective nature (Barr and Diamond, 2008). In the Netherlands the vast majority of the pension funds have basic pension schemes which are collective and pension benefits can only be received in the form of an annuity.
Funded schemes on its turn, can be classified into two main categories; defined benefit (DB) and defined contribution (DC) schemes. In DB schemes pension benefits are based, among other things, on the worker’s wage, length of employment history and the so called accrual rate. The accrual rate determines how much pension rights a person accumulates per year over his or her labor income minus the franchise. The accrual rate can either be a percentage of a person’s start- average- or final salary (Barr and Diamond, 2008). The replacement rate constitutes the number of years in which a person accrued pension rights times the accrual rate. Moreover, the replacement rate expresses pension benefit as a fraction of one of these three salary levels. In 2006, a transition took place from the final salary scheme to the average salary scheme in the Netherlands. Therefore the average salary scheme is the most common. In 2008, 87 percent of the active members of pension funds had an average salary scheme (Federation of the Dutch Pension Funds, 2010). As of the first of January 2015, the fiscal regulation surrounding the accrual of pension rights has been adjusted with the adaptation of the ‘Witteveenkader’. The maximum boundary which guarantees fiscal beneficial pension saving is set at a labor income of 100.000 euros. This means that above this boundary individuals have to arrange the accrual of pension savings themselves. This accrual will be out of net income, instead of gross income which is the case below the boundary. Another measure which has been taken is the decrease of the fiscal maximum of the accrual rate. This maximum is lowered from 2,15% for average salary schemes in 2014, to 1,875% for average salary schemes in 2015 (Staatsblad van het Koninkrijk der Nederlanden, 2014).
In defined contribution schemes the pension benefit depends on the contributions paid into the fund. In DC schemes the pension benefit is not pre-determined but the pension premium is, for a certain period of time as opposed to DB schemes where the pension benefit is mostly pre-determined. Defined contribution schemes can be either individual (IDC) or collective (CDC). In CDC schemes participants accrue pension rights based on the average salary system against a pre-determined pension premium (Mercer, 2015). The eventual pension benefit is not predetermined since it depends on the factual funding ratio of the pension fund at the time of retirement (Chen, 2014). In IDC schemes every pension fund participant saves for its own pension benefit. The eventual pension benefit is the sum of the paid pension premiums and the realized return on them (Chen, 2014). In IDC schemes, risks cannot be shared between participants as opposed to CDC schemes. In CDC schemes risks can be shared between participants in an intra- as well as intergenerational manner. Intragenerational since pension benefits are paid out in the form of an annuity which enables the sharing of, for example, longevity risk (Barr and Diamond, 2008) and intergenerational since shocks in the funding ratio can be spread out over a number of years and thereby shared between various generations (Chen, 2014). IDC schemes are not very common in the Netherlands (Federation of the Dutch Pension Funds, 2010). Most pension funds that do have a DC scheme implement a CDC scheme. Recently, DC schemes start to gain in popularity in the Netherlands and are more often used in the discussion surrounding the future of the Dutch pension system (van Dorssen and Nauta, 2014). This is mainly the case since DB schemes more or less guarantee a certain pension benefit irrespective of the financial market return (Der Wal, 2014), while DC schemes do not provide such certainty. This implies that contributing participants in a pension fund with a DB scheme bear the risks surrounding the pension benefits of the pension fund retirees, while those risks are shared between contributing participants and pension fund retirees in DC schemes.
The Franchise
The franchise exempts a certain amount of the labor income of pension fund participants over which pension premium needs to be paid. The franchise relates to the accrual rate. Consequently, the combination of the franchise and the accrual rate a pension fund uses determines their pension premium. Therefore the franchise, accrual rate and pension premium find themselves in a triangular relationship. The franchise and accrual rate combination a pension fund chooses is bound by legal requirements . Reasons for this may lie in the fact that by legally binding the choice of the combination, the premium stays within a certain bound and cannot take an outrageous level. Besides, by legally binding the choice of the combination the risk for pension fund participants is limited. For example a low franchise in combination with a high accrual rate would result in either a relatively high premium, or a pension fund taking more risk in their investment strategy in order to be able to finance the accrued pension rights. Therefore such a combination is not allowed.
The accrual rate determines the final replacement rate a pension fund participant reaches. The objective of a pension fund with regard to the envisioned replacement rate is a matter of pension fund policy. Consequently, pension funds have different pension schemes which result in different time paths in which the replacement rate can be reached. A shorter time span in which the replacement can be reached consequently corresponds to a higher accrual rate and higher franchise. The replacement rate is applicable to both pension income coming from the first ‘ and the second pillar which, theoretically, should result in a uniform franchise of 10/7th times the AOW benefit (Schols ‘ van Oppen, 2009). Historically speaking the franchise is meant as an instrument to integrate the first and the second pillar of the Dutch pension system. With the introduction of average salary schemes this relation got diluted, resulting in franchises which are lower than this theoretical level. Some pension funds even wield a franchise of exactly ‘0 (Eberhardt, 2014). As of 2015 the relationship diluted even further, since the levels of the franchise which are connected to the fiscally allowed maximum accrual rates are lower than they would be if they were at a level of 10/7th times the AOW. Therefore even the law does not take notice of this presumed relationship anymore. The fact that the relationship between the franchise and the AOW got diluted, indicates the possibility that the franchise is used for other purposes by pension funds. Nowadays, one of this main purposes is to keep the pension scheme affordable for the pension fund (A. Paulis, personal communication, May 22, 2015).
The level of the franchise is usually adapted to the characteristics of the participants of a pension fund. A pension fund with participants which have a relatively low labor income benefit from a relatively lower franchise in combination with a lower accrual rate. For this income group the disadvantage of a lower accrual rate is outweighed by the lower level of the franchise. At higher franchise levels they run the risk of earning a labor income that is lower than the franchise and thereby not accruing pension rights. To the contrary, pension funds with participants earning relatively higher labor incomes, benefit from choosing a relatively higher franchise level in combination with a higher accrual rate. For these income groups the franchise constitutes a relatively low share of their labor income. Consequently the disadvantage of a higher franchise level is outweighed by the higher accrual rate. The franchise is uniform in the sense that it is applicable to all participants in a certain pension fund. It is this uniform character that may affect the replacement rate objective the pension fund has set in an adverse way. This is the case for two reasons. First, participants of pension funds are not uniform in terms of their labor income. Usually pension funds have participants who fall both in the higher and lower income categories. Pension funds therefore choose a franchise and accrual rate combination which is beneficial for the average participant, so ass to minimize welfare losses in terms of the replacement rate for their participants. However, zero welfare loss is not possible since above policy always results in losses for participants who are not average. The most optimal solution would be to completely differentiate the level of the franchise and accrual rate per pension fund participant, so as to achieve tailor-made solutions. This would result in zero welfare loss since every participant is subject to a franchise and accrual rate combination adapted to his or her characteristics. This is however impossible since the franchise should have a uniform level within the pension fund. Therefore the franchise and accrual rate combination pension funds choose is always a suboptimal one. Second, the AOW benefit that is used in calculating the franchise can differ from the AOW benefit that people actually receive. Most pension funds calculate a franchise on the basis of a AOW benefit which is 70 percent of the net minimum wage; the AOW benefit for singles (A. Paulis, personal communication, May 22, 2015). However, married or cohabiting couples receive an AOW benefit of 50 percent of the net minimum wage each, resulting in a combined AOW benefit of 100% of the net minimum wage (Frericks, 2006). Moreover, employees who deviate from the ‘average’ participant in others ways than their labor income or level of the AOW benefit, can experience problems in reaching the desired replacement rate. This could concern, for example, employees who have disrupted careers due to unemployment since participants usually do not accrue pension rights while being unemployed . Considering all this, it can be stated that the franchise could have implications for the final outcome of the pension plan; the pension income in terms of the replacement rate and the redistribution in terms of the net gain (Schols ‘ van Oppen, 2009).
The Uniform Accrual System
Besides the franchise being at a uniform level, the accrual rate and the pension premium are uniform too. The uniform accrual system causes certain losses and redistribution. First, part of the pension rights in pension funds is financed on a PAYG basis as younger workers subsidize the older ones (Bovenberg, 2014). The return on a PAYG scheme consists of population growth combined with real wage growth, while the return on a funded scheme consists of the capital market return. Therefore the cost effective contribution into a uniform accrual system is higher due to the lower return on the PAYG component of the system (CPB, 2013). Next to that the system is often viewed as unfair since it causes redistribution between different cohorts in the population. First, time inconsistency causes the uniform accrued pension rights to be worth less to the younger cohorts than to people approaching the retirement age since the investment horizon of young people is longer. Second, structural differences in life expectancy are not taken into account which is beneficial for cohorts with a longer life expectancy as opposed to cohorts with a lower life expectancy (Lever, 2014). Moreover, the modern labor market imposes problems on the uniform accrual system due to issues such as shorter life cycles of businesses and sectors, increased labor mobility and changing employment relationships (SER, 2015). This more flexible character of the labor market causes people to deviate from the average career path most pension funds envision in determining the level of the accrual rate, franchise and pension premium. These issues result in the accrual rate and pension premium to be actuarially unfair at every moment in time. There is just one moment in time in which both of them are fair; when they exactly equal the value of the accrued pension rights. Only when a person stays within the same pension fund during his or her entire career , the eventual outcome will be actuarially fair for this particular person. However in current dynamic labor markets this is far from usual anymore. Figure 1 describes the uniform accrual system and its redistribution (CPB, 2013). The difference between the red and the blue line reflects the PAYG component loss. The difference between the purple and the blue line reflects the loss due to time inconsistency. Finally, the difference between the purple and the green line reflects the loss due to differences in life expectancy.

Figure 1 Decomposition of the Redistribution
In light of above described losses and redistributions, the Dutch parliament recently decided that the uniform accrual system will be abolished in phases. This process will be concluded in 2020 (Rijksoverheid, 2015). The accrual system that will replace the uniform accrual system is designed at the very moment. Several proposals for this redesign have been made already. Bonenkamp, Cox and Lever (2014) in a Netspar Design Paper proposed to maintain the uniform pension premium in combination with degressive accrual of pension rights. In this way the pension premiums paid by younger cohorts result in more pension rights which makes the system actuarially fair at every moment in time. Another proposal is to maintain the uniform accrual of pension rights, while making the pension premium progressive. However this proposal could cause wage profiles to become even steeper since part of this increase in the pension premium will be paid by the employer resulting in relatively higher wages for older employees. This could cause harm for the older cohorts of the working population. Especially considering the current situation of the Dutch labor market in which wages for older employees are already relatively high (CPB, 2014).
Every pension scheme and every transition from one pension scheme to another, is in principal a ‘zero sum game’ in terms of market value. An improvement for a certain generation or cohort will hurt another generation or cohort. Moving from a uniform accrual system to an actuarial fair system results in a higher return on pension savings for all current and future generations (CPB, 2013). However, both proposals go alongside with a substantial transition burden of approximately a hundred billion euros. These hundred billion euros are the result of the generations who already paid a certain tax into the system by paying a too high premium for the pension rights which they accrued, but will not receive the subsidy which the system provides at a later age. This burden is also referred to as implicit debt. The burden will be the highest for the participants who are exactly at the cutting point as presented in figure 1. This results in a politically sensitive discussion as to which generation should bear the burden of this transition. Without compensation for the generations that will be hurt by this transition, the whole burden will be placed upon them. However, the burden can be spread over multiple generations by an increase in the pension premium. This will hurt younger cohorts. Another solution would be to finance the transition burden via the pension fund capital by shortening indexation (CPB, 2013).
Previous Research
This thesis can be considered a first attempt to fill the gap in the quantitative literature concerning the franchise, by examining the influence the combination of the franchise and the accrual rate has on both the net gain and the replacement rate. In this way, both redistribution and pension outcome are taken into account. Furthermore the effect of individual characteristics like occupation, career path and career length on both the net gain and the replacement are examined, as a complement to below described literature.
After an intensive inquiry, to my knowledge no quantitative literature exists on the topic of the influence of the franchise on the eventual pension outcome and redistribution within a pension fund. Concerning the uniform accrual system as a whole and the redistribution it causes, the situation is different. Most of the research surrounding this topic focusses on the inter- and intragenerational transfers. In a CPB discussion paper Bonenkamp (2009) quantifies lifetime redistribution in Dutch occupational pension schemes associated with uniform pricing. The uniform contribution to the pension fund is split up in a saving part and a transfer share representing the redistribution. The transfer share is split up in an inter- and intragenerational part. Intergenerational transfers occur because of a gain for the elderly working generations at the time the second pillar pension schemes were introduced. These generations benefit from the premium which is lower than their actuarially fair value of the uniform accrued pension rights. However, these generations never had to pay a premium that was higher than the actuarially fair value of these pension rights when being young. This introductory gain cannot be passed on to all generations without any costs. This results in an intergenerational transfer. Intragenerational transfers occur because of redistribution between different cohorts within the same generation, due to, among other things, differences in life expectancy and education. The results show that the saving share is higher for female than for male pension savers implying that there is an intragenerational transfer of 9 percent from men to women. Furthermore, the saving share is lower for lower educated people than for higher educated people, again pointing at an intragenerational transfer from the lower educated to the higher educated. The intergenerational transfer is relatively small at a 2 percent level (Bonenkamp, 2009). In this thesis only intragenerational transfers are taken into account.
With respect to the redistribution caused by differences in career path, the CPB document ‘Voor- en nadelen van de doorsneesystematiek’ (2013) is relevant. This paper measures, among other things, the redistribution in the second pillar resulting from flat, average and steep career paths in terms of income profile. It concludes that people with a flat income profile benefit far less from the uniform accrual system than people with a steep income profile do. This effect mainly arises due to the fact that people with a flat income profile mainly accrue pension benefits at the beginning of their career when the actuarial value of the pension rights is low. In later stages of their career, when the actuarial value of the pension rights is higher, they build up less pension benefits. For people with a steep income profile the opposite is true (CPB, 2013).

Simulation Model Characteristics
Both the net gain and the replacement rate are modelled using a typical agent simulation model. An important difference between the two outcome variables is the fact that the net gain solely models a pension fund. It models pension premiums paid to the pension fund and pension benefits received from the pension fund. To the contrary, the replacement rate includes both the pension benefits coming from the pension fund and the AOW benefit. Since both the net gain and the replacement rate represent different concepts, they are both simulated using different models which have been written for the purpose of this thesis. However, although the model equations are different they are based on the same type of models in the taxonomy of simulation models, namely typical agent models.
The taxonomy of simulation models regarding pensions is presented in table 3 (G��l, 2009).
Table 3 Taxonomy of Simulation Models for Pensions
Microsimulation Models Standard Models
1.1 Static microsimulation models Standard cohort models
1.2 Dynamic microsimulation models 2.2 Typical agent models

Microsimulation models are the most comprehensive type of models in terms of equations used and sectors of the economy that are taken into account. Moreover, they need a large amount of data as input. Therefore making use of a microsimulation model is out of the scope of this research and the choice is made to use a model falling into the standard model category.
Microsimulation models simulate changes in a sample of a large number (G��l, 2009). The sample can be either cross sectional or a panel. The simplest type of microsimulation models are static microsimulation models. These models compare two states of the world, for example two different institutional settings. In these type of models time is not included as a factor. To the contrary, dynamic microsimulation models do include time. Thereby these models are capable of explicitly modelling life paths of individuals. They take into account both behavioral responses and the policy environment (G��l, 2009).
Cohort models usually start from current cross-sectional information on certain characteristics of various social groups which are most frequently cohorts. This current set of information is then simulated into the future. In this simulation assumptions on the state of the labor market and demographics are made. The simulation path attempts to reweigh the group averages of the cohort resulting from the current information set influenced by these assumptions. The major advantage of cohort models is that aggregate conclusions can be obtained (G��l, 2009).
Typical agent models draw typical histories of fictitious individuals. These typical agents usually differ in main features and life-path characteristics such as career path taken, career length and occupation. Based on the typical histories the level of the pension benefit is simulated and expressed in a certain way, for example by using the replacement rate as an outcome variable (G��l, 2009). Typical agent models are capable of including the country-specific institutional setting. Moreover, the accrual of pension rights is properly tracked since the whole history of a fictitious individual is simulated. Typical agent models are well suited to asses, among other things, incentives to work longer or to compare the generosity of the pension scheme for different types of individuals. They are, however, incapable of producing aggregate outcomes (G��l, 2009). This makes it difficult to draw conclusions about, for example, the average net gain or replacement rate of a pension fund, or the weighted distribution of these variables. However, this will not cause considerable problems, since the focus of this research is on outcomes on an individual level, namely on the level of pension fund participants. Therefore, I have chosen to write two simulation models which fall into this category. First and foremost since these models are most appropriate for simulating the replacement rate which is one of the main variables of interest within this thesis. Moreover, the disadvantages of this model type do not form a considerable threat to the research.
Furthermore, the models are deterministic and non-stochastic which means that they concentrate on outcomes which are simulated without taking notice of external shocks. Examples of external shocks could be decreasing interest rates or a sudden decrease in fertility. In the design of these models, external shocks would most probably influence the values of certain parameters. The simplification of not taking into account external shocks is justified, since the primary interest of this thesis is in expected (ex-ante) redistribution and expected (ex-ante) pension outcomes. However, this simplification also causes the model to be stylized. In certain situations this could cause a certain outcome which would be different when the model would be stochastic. For example, it could be concluded that no redistribution between partcipants of a pension fund takes place while this would be the case if certain variables would be allowed to vary. An example of this is described in appendix (‘).

Net Gain Model
The model that is used to simulate the net gain took the model of Joop Hartog (2013) as a starting point. This model can be found in appendix II. In this thesis the net gain is simulated using equation the following model/equations :

‘NG’_i=(‘_(W_i+P)^(W_i)”(��_i ((‘_0^(W_i)”(y_i e^(n_i s)-f)Me^gs ‘)/W_i ) e^g(W_i/2) ds) e^(-rW_i ) e^(-rt) e^gt dt’)/(‘_0^(W_i)’�� (y_i e^(n_i t)-f)Me^gt e^(-rt) dt)

��_i= ��*W_i
List of variables:
NG = net gain

W = length of working life in years

P = duration of retirement period in years

�� = replacement rate (length of working life times the accrual rate)

r = discount rate (real rate of return on standard life cycle investment scheme)

g = inflation

y = starting salary as a fraction of the minimum wage

n = individual real growth of the wage

f = franchise as a fraction of the minimum wage

�� = pension premium (as a fraction of the salary minus the franchise)

�� = accrual rate

Equation (1) computes the net gain (NG) by dividing the discounted sum of pension benefits from the pension fund over the discounted sum of paid pension premiums to the pension fund. Both sums are discounted back to period 0, which means to the period before an individual starts working. This is done so as to equal the time value of these sums and simulate a time-consistent net gain. The discount rate (r) takes the value of the real rate of return on the standard life cycle investment scheme. The nominator represents the sum of discounted pension benefits. The sum is computed by multiplying the replacement rate (��) with the average salary, since the accrual system in the Netherlands is characterized by an average salary system. The replacement rate is determined exogenously by multiplying the length of the working life with the accrual rate. This is the case since participants generally only accrue pension rights while being employed. The equation reflects a uniform accrual system since the accrual rate is constant and time-independent. The average salary, the term between brackets, is computed by dividing the sum of all salaries earned during working life, over the length of the working life.
The denominator represents the sum of discounted pension premiums. The pension premium (��) is multiplied with every year’s salary, which increases every year with the inflation (g) and the individual growth of the wage (n). Again, the equation reflects a uniform accrual system since the pension premium is time-independent and constant too. Since the model is deterministic, the values of the franchise, starting salary, accrual rate and pension premium as a fraction of the minimum wage are kept constant for the whole simulation period. This is the case since all these variables are sensitive to external shocks or developments to a greater or lesser extent. Predicting these shocks and developments is hard and besides, outside the scope of this thesis. Furthermore, the minimum wage increases with the inflation. Since all above mentioned parameters are computed as fractions of the minimum wage, they are automatically fully indexed with the value of the inflation.
The net gain is only computed for the pension fund. Therefore the first pillar pension benefit is not taken into account. The franchise is used in equation (1) to reflect this. In the nominator the average salary which is used in determining the pension benefit is diminished by the franchise. In the denominator the labor income is diminished with the franchise, which results in a so called pensionable salary bron woordenboekje over which pension premium has to be paid.

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