The financial implications of working longer: An application of a micro-economic model of retirement in Belgium

As a result of structurally low fertility and ever-increasing life expectancy, the Belgian population is ageing rapidly. The 2004 report of the ‘Studiecommissie voor de Vergrijzing’ (Commission for the Study of Ageing) (High Council of Finances, 2004: 20), estimates the budgetary cost of ageing to be 3.4% of GDP. It also concludes that an effective way to moderate costs would be to persuade individuals to postpone their retirement, as an increase by one year of the average age at which people retire would decrease the budgetary cost of ageing by 0.9% of GDP. In this, Belgium especially faces a challenge. Figure 1 shows the activity rate and effective retirement age of older employees in European countries.

Figure 1

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For the European Union as a whole, 38.8 % of those older than 55 still have a job. This percentage is 25.1 in Belgium, a figure lower only in Luxembourg. The effective age of retirement is 59.9 in Europe as a whole, and 57 in Belgium. The European countries decided at the European Summit in Barcelona in 2002 that this effective retirement age should be increased by five years before 2010 (EC, 2003). This clearly is even more important for Belgium than for other countries.

The purpose of this paper is to provide an insight into what extent the current public retirement schemes for private-sector wage earners might encourage older workers to voluntarily leave the labour market and enter retirement. What is the penalty for continuing to work? And does this differ between workers of different categories, and between the two main public retirement schemes available in Belgium? These questions are to be answered exploiting the so-called option-value approach. The model to be presented in this paper is based on the notion of actuarial non-neutrality (OECD, 2003: 4) of a retirement scheme, setting the gains from postponing retirement (extra salary) against the losses (foregone expected pension, for all future years until decease) associated with a specific retirement scheme. The which its simulation results will be discussed at length. Finally, conclusions will be drawn.

The well-known replacement ratio compares the last-earned salary with the pension benefit one receives immediately after retirement. This may not be the best variable to reflect a retirement decision, for two reasons. First, it is based on pension benefit in the first year after retirement, and ignores the future development of pension benefit conditional upon the year of retirement. Second, it suggests that working and retirement are two exchangeable strategies, i.e. that a retired individual can re-enter the labour market in any future year. Although this may be theoretically possible, in practise such behaviour is rare. Hence Duval (2003: 34) describes retirement as an “absorbing rather than as a dynamic state”.

The option value approach, developed by Stock and Wise (1990) supposes that a representative agent considers the gains and losses in utility pertaining to every year that he or she could retire. He or she weighs the utility of consumption (i.e. the higher income when working) against leisure (retirement). In this, he or she does not compare just the current alternative incomes, but the expected value of all current and future incomes. Define t as the first year that our individual has the institutional possibility to retire, and define r ≥t as the year that he or she retires. The flow of expected future utilities can then be written as:

Given that r^* = arg max(V_t(r)), it holds that V_t(r^*) − V_t(r) > 0 for each year that r* ≠ r. Considering all the future years that one can choose to retire (i.e. from t to the year one reaches the mandatory retirement age), the option value in t is G_t(r*) = V_t(r*) − V_t(t), and one will postpone retirement from year t for as long as G_t(r*) > 0. In r*, there is no additional expected utility from working, and one will therefore retire. Following Gruber and Wise (2004: 26), the option value can be rewritten as

or

As defined the option value and peak value both assume that the older worker considers all years from t to the legal retirement age in one decision. One might, however, also want to consider year-to-year decisions, in which one decides (not) to retire just for the year to come. This decision is reflected by some additional variables, closely related to the above option and peak value, which are to be presented now. First of all, Social Security Wealth (SSW) can be expressed as the flow of discounted expected utility from retirement in the year r, as seen from t:

The change of SSW as a result of postponing retirement by just one year, is

This is referred to as the wealth accrual. When retirement is postponed by one year, one renounces one year of pension benefits. However, depending on the scheme, the pension benefit may be a function of the career length, and postponing retirement then implies a higher benefit in the remaining years of retirement. If the two effects cancel each other out for an additional year of work, the system is said to be “actuarially neutral at the margin” (OECD, 2003: 34). In practice, however, the first effect usually outweighs the second one (not least because of discounting), so usually ∆SSW_r^t < 0, in which case continuing to work comes with a loss in pension wealth (i.e. total post-retirement pension income).

The option value and peak value reflect a retirement decision to be taken about all the future years from t to the year one reaches the mandatory retirement age. The wealth accrual describes a year-to-year retirement decision, but considers only pension income and neglects labour income. One may therefore want to add variables that compare discounted salaries and pension incomes in a year-to-year-retirement decision.

Write PR as the balance of discounted salaries and changes in pension wealth that result from postponing retirement by one year:

This variable is the balance of expected gains (one additional year of salary) and losses (a decrease of the stream of future pension benefits) if one postpones retirement in r. Income earned usually outweighs the negative wealth accrual, and therefore PRt(r) is usually positive. Gains associated with continuing to work will often outweigh the losses, but we shall see that these increases in wealth as a result of continuing to work are (sometimes considerably) lower than the salary suggests. This may help to account for the fact that that a proportion of wage-earners chooses not to work but to retire instead. Note again the strong relation between the single- and multiple-year retirement decisions; PR and SSW are the single-year ‘versions’ of the option value and peak value.

A second additional variable is used by the OECD (2003: 34), Duval (2003: 18), Börsch-Supan (2000:31) as well as Nelissen (2001: 5) and is referred to as the ‘implicit tax on working through r’. For every year that retirement is postponed, the ratio of expected losses (renounced pension wealth) and gains (salary), shows that the former presses as an implicit tax on the latter.

Following the same line of reasoning explaining that PR usually is positive, one can expect itax to be usually positive as well. If not, it is to be interpreted as an implicit subsidy on work.

The option value approach has been applied in several studies to date. The best known is that of Gruber and Wise (2004), in which the probability that one retires at a certain age is regressed on wealth accrual, peak value and option value. A similar study has been undertaken by Dellis et al. (2004: 41) for Belgium. The broad conclusion is that, even though the estimators of all variables are significant, wealth accrual has the highest explanatory value for both men and women. Subsequently these models have been used to simulate the effect of policy measures on the retirement probability.

The OECD (OECD, 2003; Duval, 2003) also uses this approach to simulate and compare the actuarial nonneutrality of retirement schemes between countries. Their conclusion is that the implicit tax on continuing to work is low for workers of 55-years old, but increases considerably with age. Countries differ significantly, and these differences coincide with differences in replacement ratios.

Similarly, Börsch-Supan (2000) explains labour market status (retired or working) using a regression model, including option value with gender, health, education, age and pension-type. This model is estimated on German data and the results were used to simulate the impact of actuarial changes in retirement benefits on retirement age. In later work, Berkel and Börsch-Supan (2003) concentrate on institutional characteristics of the German retirement system, and simulate the effect of implementing a system of Notional Defined Contributions (NDC) on the effective retirement age.

The above papers all present models which can be classified as static microsimulations (Van Mechelen & Verbist, 2005), for the calculation of the option values are made for a representative sample, and then regressed on the probability that an individual retires. This means that information on specific alternative retirement schemes are combined for existing individuals, and that the information on different individuals is combined in the estimation results. In contrast, the Micro-Economic Pension model (MEP) to be presented in this paper may be classified as a standard model. As in a conventional microsimulation model, the point of departure is the individual; but a standard simulation model concentrates on the calculation of the various indicator variables for four fictional individuals representing male and female blue- and white-collar private-sector wage earners. It also includes two separate ‘first-pillar’ (state) retirement schemes – the early retirement scheme and a conventional early leavers’ scheme. Instead of aggregating outcomes across these schemes and types of individual, MEP keeps them separate, so that comparisons can be made as to the actuarial non-neutrality of the two retirement schemes with respect to male or female white- or blue-collar workers, and the degree to which these schemes may stimulate a step into retirement. Furthermore, an explicit goal of MEP is to bring to the fore the effect of different tax regimes on the implicit costs of continuing to work. For this reason we follow the two OECD studies (OECD, 2003; Duval, 2003) in expressing the variables presented above in monetary units rather than in terms of utility. The advantage of this approach is that it prevents the simulation results being determined to some degree simply by assumptions concerning the difference in utility between a salary or a pension benefit of one euro. Moreover, it is in line with the widely used replacement ratio, which is also a ratio of currency-units. Finally, MEP does not include a behavioural equation relating the option value variables with effective retirement probabilities. So, a higher (lower) implicit cost of retiring is assumed to encourage (discourage) retirement, but it is unknown by how much exactly.

The Belgian retirement system consists of three pillars. The first pillar is provided by public social security programs, which are the most important source of income for current pensioners. The second pillar is that of company pension schemes. Although coverage of these schemes is increasing rapidly, their importance in terms of the income they provide to current pensioners is still limited. The third pillar consists of individual life-insurances and retirement savings. We concentrate upon the first-pillar social security retirement schemes. Ignoring disability schemes, older private-sector wage earners have two ways of retiring before the mandatory age of retirement. The first is via the system of early retirement (‘vervroegd rustpensioen’), and the second is via the conventional early leavers’ scheme (‘brugpensioen’) hereafter abbreviated to CELS. Both will be explained in broad lines in this section.

The retirement system provides former private sector employees a pension benefit which essentially is a function of their past career. The mandatory age of retirement is 65 for males. For females it is gradually increasing from 61 years of age (from July 1997) via 63 years (from 2003 on) up to 65 (from 2009 on). Males become eligible for early retirement from the age of 60 on, if they have a minimum career service 35 years. For females, this minimum career length increased from 20 years in 1997 to 34 years in 2004, and is set to increase further, to 35 years, in 2009. Males and females can in principle therefore retire, and start to drawn public social security pensions, 5 and 3 years before the mandatory retirement age. The remainder of this paper seeks to identify the implicit costs associated with working through to the mandatory retirement age rather than exercise the optional right to retire early.

State pension benefit is calculated as

The wage-base is essentially the sum of past salaries, indexed on the development of prices and with additional discretionary adjustments for the development of wages between the year of earning and the year of retirement. This modified sum of corrected salaries is then multiplied by the length of the career and divided by the length of the career needed for a full pension. The latter equals the age at which one becomes eligible to a full pension benefit minus 20. So, for males, it is 65 – 20 = 45 years. For females, it is gradually increasing to 45 years. As a result, if one does not have a full career, continuing to work causes the pension benefit to move towards the ‘full-career pension benefit’. This wage-base is then multiplied by either 60% or 75%. If the individual is single, 60% is used. If they have a partner, they can choose the ‘family pension benefit’ of 75%, but then their partner loses his or her own pension entitlement. In consequence, this choice is only beneficial if one’s partner has no significant revenues of his/her own.

Redistributive solidarity is embedded in the pension system in several ways. First of all, the wage one earns in a certain year during one’s career is taken into account only up to a certain limit. All incomes higher than this limit do not add to the wage-base, and hence not to the future pension benefit. Those earning a higher income therefore face a lower replacement rate. Second, for those with a career of at least 15 years, the wage-base is calculated substituting a minimum annual allowance for periods of low earnings. Third, there is a minimum pension benefit guaranteed to all, modified for those without a full career history.

An alternative to this system of early retirement is the conventional early leavers’ scheme, which is essentially an unemployment scheme. It allows older workers to exit the labour market and become unemployed on favourable terms until the mandatory retirement age. People generally become eligible for a CELS benefit from the age of 58 onwards. (In practice, many older workers retire to the CELS before the age of 60. But these regulations are of an ad hoc nature and therefore not considered further in this paper.) The benefit consists of two parts. First, there is a general unemployment benefit which is equal to 60 % of the last wage up to a ceiling. Second, there is an additional benefit which equals 50% of the difference between the unemployment benefit and the last wage minus taxes and social-security benefits. The CELS benefit decreases relative to increasing income, because (i) regular unemployment benefit is limited, and (ii) the progressive tax-system causes net income to lag behind gross income as the latter increases.

Unlike early retirement benefit, the CELS benefit does not depend on the number of working years. Furthermore, when one enters the CELS, formally one does not retire but becomes unemployed. The career length, on which the future statue pension will be based upon reaching the mandatory retirement age, therefore continues to increase. Note that one may choose to work after retirement, but the additional income one may earn is very limited. Furthermore, returning to work from a situation of retirement is possible in theory, but rarely seen in practice. Finally, switching from the CELS to the early retirement scheme may be possible, but is not rational and therefore never done. Switching in the opposite direction is not possible.

The Micro-Economic Pensions model (MEP) evaluates Equations 2 to 6 for fictitious individuals representing male and female white- and blue-collar workers. The model is written in the SAS macro language and consists of a body of several modules, accompanied by two modules that read time-dependent parameters, such as gross wages, pensions, minimum and/or maximum benefit levels and wage-ceilings, tax and social contribution rates, survival probabilities, inflation rates, and so forth. Figure 2 shows the technical structure of the model.

Figure 2

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The discussion of the model starts in the top-left quadrant of Figure 2. The user needs to provide the model with information on the gender and labour market status of the fictitious individual, and whether or not he or she applies for a family pension benefit or a single-person pension benefit. Furthermore, one needs to provide a discount rate, and to decide whether results should be expressed in gross or net amounts.

Using this information, MEP will for every year r ≥ t that the individual is eligible to the pension benefit in question, calculate the flow of future expected pension benefits from all future years s until expected death, using the information available at r. All benefits are then discounted back to t using a discount rate and a survival probability. In the case of the CELS, the social security wealth SSW will sum CELS benefits up to the mandatory retirement age, and pension benefits afterwards.

For the calculation of pension or CELS benefit, as well as the various indicators of actuarial non-neutrality, one needs past and current gross-incomes. The model includes a matrix containing wages per day for every combination of gender and labour market status, for all ages between 20 and 64 and for all the years between 1955 and 2004. The creation of this matrix is discussed in the appendix.

For a thorough understanding of the model, two fundamental assumptions need to be discussed briefly. The first assumption pertains to the set of laws, rules and regulations on pensions, taxes and contributions that an individual faces in a certain year. In any year r, potential retirement benefits for all future years s are derived using information on laws, rules and regulations available at r. Suppose that an individual may choose to retire in 2003. His potential pension benefit in the future year 2010 will be derived using information available in 2003. If he or she postpones retirement and reconsiders in 2004, then the potential pension in the same year 2010 will be calculated using the information available in 2004. The second assumption pertains to the individuals who form the basis of the MEP model. To keep things simple, especially with respect to fiscal laws and regulations, it is assumed that an individual is either single or the sole income earner in the household. In other words, the income of the individual is the only income of their household. A consequence of this is that a married individual will by definition choose the family pension benefit of 75% of the wage-base.

Inputs to the model are based on information drawn from Put (various years) and Ministry of Finance (various years) and follow regulations on taxes, social contributions, pension benefits and CELS benefits for the years 1997–2004. It is assumed that the four typical employees are born in 1940 and enter the labour market at the age of 20. Survival probabilities are derived from the 2000 mortality rates (National Institute of Statistics and Federal Planning Bureau, 2003). Finally, and in accordance with Dellis et al. (2004: 5) and Berkel and Börsch-Supan (2003: 3), the discount rate is set at 3%.

One of the possible solutions to limiting the budgetary consequences of demographic ageing is to increase the activity rate of older workers in Europe. Acknowledging the fact that retirement is an absorptive state from which few or none return, a Micro-Economic Pension Model (MEP) expresses the costs of postponing retirement by one or more years, both before and after taxes and social contributions, and this for two early-retirement schemes: the pension scheme and the CELS.

The main conclusion is that the gains from continuing to work in most cases outweigh the losses, so that working longer causes total wealth to increase. However, the implicit costs associated with postponing retirement are in some cases considerable. They may be limited for the gross pension benefit, but they increase considerably when net amounts are simulated. Furthermore, the costs associated with postponing retirement are systematically higher for the CELS benefit than for the pension benefit, and this difference is only partially explained by the higher CELS benefit relative to the pension benefit. The higher costs associated with working longer are more endogenous to the CELS-system and to a lesser extent caused by the fiscal inequality between workers and retirees.

The model has also considered the impact of alternative worker characteristics: singles versus those with a no income partner; longer versus shorter careers. As might be expected, the effect of these different characteristics is more important in the case of the pension benefit. It also comes as no surprise that the cost of postponing retirement is lower if one has a shorter career, although the magnitude of this difference is remarkable.

Furthermore, several changes to the rules and regulations for the pension benefit, CELS benefit and tax and contribution regime have been simulated. This was done not so much to suggest policy measures, as to demonstrate the capabilities of the model. This exercise clearly shows that different measures have different effects, not only upon the four types of workers as a whole, but also between male and female and white- and blue-collar workers. Policy measures designed to increase the activity rate among older workers, should take these differences into account.

Finally, by virtue of being able to disaggregate impacts in this way, the fact that MEP is a standard simulation model and not a genuine microsimulation model is arguably an advantage. But there are also disadvantages. How representative are the results for the population of older workers? Are the differences between categories of workers statistically significant? And by how much will the employment rate of older workers change as a result of a policy change? All these questions cannot be answered at this stage, as they require MEP to be based on a representative dataset of ‘real’ individuals, and not upon a limited selection of fictitious agents. A useful line of future enquiry, therefore, would be to combine MEP outputs with a static microsimulation model to generate representative aggregate costs to the state of alternative policy scenarios.

The calculation of the pension and CELS benefit is based on the income an individual made throughout his or her career. Since the model simulates retirement benefits of male and female white- and blue-collar workers, we ideally need category-specific datasets containing b^t_age, the wage per day, spanning all of the years, t, that the workers were of age between 20 and 65. As this is not available, it has been necessary to construct such wage rate datsets for four fictitious individuals, one in each category. This has been achieved using the following information:

1. The total gross wage mass and total working days from the centralized statistics of the “Rijksdienst Sociale Zekerheid” or RSZ; quarterly data available from the first quarter of 1976 (cf. Bresseleers & Hendrickx, 2003a, b).

2. Long-term time series of gross-wages and employment, available from 1953 (cf. Hendrickx, 2001).

3. Individual information from the “Loonen arbeidstijdengegevensbank” of the RSZ; quarterly data available from the first quarter of 1997 to the last quarter of 2000.

4. Employment figures for blue-collar orkers, white-collar workers and civil servants, specified to gender and age (5 year groups) from the “Enquete arbeidskrachten” of the National Institute of Statistics, available for the years between 1986 and 2003.

5. Population statistics on age and gender and population averages, from the National Institute of Statistics, available from 1948 onward.

First of all, using data source (1), the macroeconomic wage per day w^t in the year t was derived for the four categories of workers. This was extrapolated from 1976 back to 1955 using (2). Figure A1 shows this general wage per day for the four categories of workers.

Starting with this w^t, we use a simple model to derive w^t_age, the wage per day of an individual of a certain age in year t. We use the fact that the macroeconomic wage per day is a weighted average of the unknown w^t_age for every age group at t, where the weight is the proportional number of workers of every age group (4; and 5 for the years before 1986). So, the equation

holds for every category of worker, where Nt^age is the number of workers in the age group age. At the same time the proportional size of the group of age years old in t, may be denoted as

so that

For every t, we have one equation with 45 unknowns, being wt …wt and we therefore need additional information to solve this model. This is provided by data source (3). Suppose a relation f(.) between the gross wage per day at a certain age, and the gross wage per day at a reference age, say 20, and suppose that this relation is the same for all t, giving

Substitution results in

The remaining unknown is w^t₂₀, which of course is

Now all that is left do is to estimate a wage profile f(.), separately for each category of worker, which relates the wage per day of an individual in that category aged age to that of a 20 year old. This has been done using simple quadratic regression on wage data from the 3rd quarter of 1998, again using data source (3). Figure A2 contains the resulting wage profiles.

As might be expected, both male and female blue collar workers have a less steep wage profile than white collar workers. Furthermore, the wage per day of young male blue-collar workers is higher than that of white-collar workers, both male and female; and although the wage of female white-collar workers catches up rapidly at first, it only ends up slightly higher than that of male blue-collar workers from the age of 40 on.

To summarize, the growth of individual wages between two years, t and t + 1 (and, therefore, between age and age + 1) is determined by the growth rate of the macroeconomic wage wt (Figure A1), whereas the wage difference between two individuals of different age at t is determined by the relationships captured in Figure A2.

Figure A1

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Figure A2

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Author details

1. Gijs J. M. Dekkers

   1. Federal Planning Bureau, Belgium
   2. Centre for Sociological Research (CESO), Katholieke Universiteit Leuven, Belgium

   For correspondence

   gd@plan.be