2. Institutional framework

The Belgian public retirement system is characterized by three large sectoral schemes, one for the private sector wage-earners, one for the public sector and one for the self-employed.Footnote ² The main system is the wage-earners public pension scheme. Individuals are eligible to full benefits at the age of 65 but it allows voluntary retirement from age 60. The pension benefit corresponds to 75% of average lifetime earnings for one-earner couples and to 60% for others. There are floors and ceilings for earnings taken into account, fully updated for inflation but only partially for real wages growth. A full career corresponds to 45 years of earnings or assimilated periods. Indeed a peculiar feature of the system is that period of one's life spent on replacement income (such as unemployment or disability) fully counts as years worked in the computation of the retirement benefits. For any such periods, wages from previous periods at work are inserted into individuals’ records file. Benefits are shielded against inflation through an automatic price adjustment and are subject to an earning test.Footnote ³

The system for self-employed is very similar to the wage-earners. Full public pension benefits are available at age 65 with a complete earnings history of 45 years, as in the private sector scheme. Benefits are based on average earnings but for the years before 1984, a lump-sum amount is taken into account. However, in practice, wage-earners pension benefits are in average near 50% higher that self-employed benefits.Footnote ⁴ The main reason explaining this gap is that professional earnings entering in the computation of self-employed pensions are only partially considered. More precisely, earnings are multiplied by a fraction which corresponds to the ratio between self-employed and wage-earners payroll taxes rates (0.541 and 0.663 for earnings above or below the €31,820 threshold in 2016, respectively (INASTI-RSVZ, 2017)).

Civil servants face compulsory retirement at the latest at age 65 but it is possible to opt for early retirement. Public sector pensions are based on the income earned during the last 5 years before retirement. Benefits are equal to 75%, at maximum, of the average wages over the last 5 years. The system also applies floors and ceilings which are much more generous than in the private sector. Public pensions are indexed on average wages in the public sector, which make them much more advantageous for higher-income individuals. In average, €28.296 is the average annual amount of before tax civil-servant pensions in 2015. That is more than double of wage-earner pensions (PDOS-SDPSP, 2016).

Overall it is possible to accumulate rights in several schemes and to obtain a kind of a mixed pension. This case is frequent and then each scheme accounts for a part of the total pension benefits. Nevertheless, Belgian public pension benefits reflect generosity differences across schemes and are highly dispersed. As a direct consequence, public pension wealth is also unequally distributed across individuals and households, and in this paper we try to estimate how, and to which degree, pension rights are substitute for wealth accumulation.

3. Theoretical framework and empirical specification

We follow Engelhardt and Kumar (Reference Engelhardt and Kumar2011) and Alessie et al. (Reference Alessie, Angelini and van Santen2013) who consider a simple life-cycle model formulated by Gale (Reference Gale1998). Especially we follow Alessie et al. (Reference Alessie, Angelini and van Santen2013) who derive the equation of interest from a simple discrete-time counterpart of the model. We assume that an individual lives from period 1 to period T and retirement occurs at time R. Utility is derived from consumption and is assumed to be isoelastic and exhibits constant relative risk aversion. The consumer maximizes lifetime utility:

(1)$$\mathop {\max} \limits_{C_\tau} \mathop \sum \limits_{\tau = 1}^T (1 + \rho )^{1-\tau} \displaystyle{{C_\tau ^{1-\gamma}} \over {1-\gamma}} $$

subject to the intertemporal budget constraint

(2)$$\eqalign{\mathop \sum \limits_{\tau = 1}^T (1 + r)^{1-\tau} C_\tau & = \mathop \sum \limits_{\tau = 1}^T (1 + r)^{1-\tau} Y_\tau \cr & = \mathop \sum \limits_{\tau = 1}^R (1 + r)^{1-\tau} E_\tau + \mathop \sum \limits_{\tau = R + 1}^T (1 + r)^{1-\tau} B_\tau \;} $$

where C _τ and Y _τ denote respectively consumption and income at time τ wherein E _τ is labor-market earnings and B _τ is public pension benefits; r is the constant real interest rate, ρ is the discount rate and γ is the coefficient of relative risk aversion.

Maximization of (1) subject to (2) implies:

(3)$$C_\tau = C_1\left( {{\left( {\displaystyle{{1 + r} \over {1 + \rho}}} \right)}^{1/\gamma}} \right)^{\tau -1}\; \; $$

(4)$$C_1 = \displaystyle{{\sum\limits_{\tau = 1}^T {{(1 + r)}^{1-\tau} (E_\tau + B_\tau )}} \over {\sum\limits_{\tau = 1}^T {\lambda ^{\tau -1}}}} $$

where

$$\lambda = (1 + r)^{-1}\left( {\displaystyle{{1 + r} \over {1 + \rho}}} \right)^{1/\gamma} $$

Because we are interested in the impact of public pension wealth on wealth accumulation, we can express non-pension wealth at a given age t, A _t, as the cumulative difference between income and consumption and substituting (3) and (4), we obtain:

(5)$$\eqalign{A_t & = \mathop \sum \limits_{\tau = 1}^t (1 + r)^{t-\tau} (Y_\tau -C_\tau ) = \mathop \sum \limits_{\tau = 1}^t (1 + r)^{t-\tau} Y_\tau \cr & -Q_t\mathop \sum \limits_{\tau = 1}^T (1 + r)^{t-\tau} Y_\tau} $$

where $Q_t = \sum\nolimits_{\tau = 1}^t {\lambda ^{\tau -1}} /\sum\nolimits_{\tau = 1}^T {\lambda ^{\tau -1}} $ is the Gale's Q, which when λ ≠ 0, takes into account the time the consumer has had since the introduction of the pension to adjust the lifetime consumption stream (Gale, Reference Gale1998). Finally, using equation (2), equation (5) can be rewritten

(6)$$A_t = \underbrace{{\mathop \sum \limits_{\tau = 1}^t {(1 + r)}^{t-\tau} Y_\tau -Q_t\mathop \sum \limits_{\tau = t}^R {(1 + r)}^{t-\tau} E_\tau}} _{{I_t}}-\underbrace{{Q_t\mathop \sum \limits_{\tau = R + 1}^T {(1 + r)}^{t-\tau} B_\tau}} _{{P_t}}$$

where P _t which denotes the Gale's-Q-adjusted pension wealth and I _tis the adjusted lifetime income. Based on equation (6), our empirical strategy is to estimate the following regression:

(7)$$A_t = \beta _0 + \beta _1I_t + \beta _2P_t + {X}^{\prime}_t\gamma + \varepsilon _t$$

where X _t is a vector of individual characteristics that may affect savings. Indeed there are factors that are not taken into account in the theoretical model that may affect the relationship between wealth and the flow of earning and pensions. In equation (7), the primary variable of interest is P _t and β ₂ measures the impact of an additional euro of pension wealth on non-pension wealth.

4. Data

The empirical analysis uses data from the SHARE. The survey is a cross-national panel database of micro data on health, socio-economic status and social and family networks of European individuals aged 50 and over conducted since 2004–05. It covers a broad range of variables of special interest for this study such as information on employment, income, real and financial assets and the household context. The first wave of collection was in 2004/05 and there are now five waves available. Our sample of analysis is based on individuals aged between 55 and 85 in wave 2 (2006/07) in Belgium.Footnote ⁵

The third wave of data from SHARE, known as SHARELIFE (collected in 2008–09), asked all previous respondents (waves 1 and 2) and their partners to provide information not on their current situation but on their entire life-histories. This provides retrospective information on childhood, health, living and professional career. Thanks to the data from SHARELIFE we are able to reconstruct the individual's career history. SHARELIFE asks the respondents to provide start and end dates of each paid job they had, the characteristics of the job, as well as the first monthly wage. For those who are still employed at the time of the interview, the last monthly wage is asked and for those who are already retired the last monthly wage in the main job is asked. All these amounts are after taxes, as are the amount in wave 2 of SHARE.

This information is used to construct a panel with one observation per year for each individual, from the first job until the interview year. These data are used to calculate the various income flows entering I _t. The wage path is obtained using linear interpolation between the years for which we have wage information; that is between the different wages declared along the career and the last wage of the main job or the current wage of the employed. For years spent under replacement income (i.e., unemployment, disability, sickness etc.), we use actual rules applied in Belgium to calculate the benefit given occupation, earnings and family status.Footnote ⁶ Once computed in this way the complete career path, the amounts are converted in euros of the interview year. In the paper we use a constant annual interest rate (r) of 0.03, as in Alessie et al. (Reference Alessie, Angelini and van Santen2013) and compounded labor income is obtained starting from the year of the first job for the retirees. Future labor income is calculated for the employed assuming constant real wages. Retirement is assumed to start in the year that the individuals declare as their expected retirement age or the statutory retirement age (65 in Belgium) if they did not specify their expectations. All future incomes are weighted by the individual probability of survival using life tables from the Human Mortality Database (2015).Footnote ⁷

Public pension benefits are obtained through two channels. For those who are already retired, the level of benefits is the one declared in the survey. For those still employed, we use a microsimulation developed for Belgium on the basis of SHARE data (see Jousten and Lefebvre, Reference Jousten and Lefebvre2013; Jousten et al., Reference Jousten, Lefebvre, Perelman and Wise2016). This allows us to calculate precise value of the entitlement of each individual in the survey given the actual rules applied in Belgium. Pension wealth,P _t, is calculated applying survival probabilities from the Human Mortality Database and assuming constant real benefits as well as discount rate (ρ) of 0.03.Footnote ⁸ The Gale's-adjustment factor, Q, is obtained with λ = 1.03⁻¹.

The non-pension wealth, A _t, is available in wave 2 at the household level. We use household net worth and its decomposition into net real wealth and net financial wealth. In SHARE data, missing values for individual and household level economic information are replaced by five imputed values for each missing ones (see Christelis, Reference Christelis2011). This is the case of wealth variables so that in all estimations below we use multiple imputations techniques (see Rubin, Reference Rubin1987). The net real wealth is the sum of the value of the main residence minus any mortgage, the value of other real estate, the value of own share of businesses and the value of own cars. The net financial wealth is the sum of gross financial assets minus (non-mortgage) debts.

Finally we include a set of explanatory variables, X _t, to capture individual differences. In the following regressions we use age, gender, marital status, education level, self-declared health, number of children and spouse.

Our sample of analysis is based on individuals in wave 2 (2006/07) of SHARE in Belgium and for whom we have information in SHARELIFE. This amounts to 2,340 observations. We concentrate on individuals aged between 55 and 85 (1531 observations) and we exclude those who have never worked or for whom we do not have enough career information in order to construct the wage path (449 observations). We keep those who had a short career since the Belgium system does not penalize short career and applies fictitious wages to period under replacement income (see Section 2). We end up with a sample of 1,082 observations.

Our sample is rather large compared to previous studies using SHARE in a cross-country analysis because the microsimulation allows our sample not being too much affected by missing values and erroneous answers. Furthermore, it is even more valuable at the time of calculating the pension entitlement. Alessie et al. (Reference Alessie, Angelini and van Santen2013) calculated the pension entitlement of those still working by multiplying the expected replacement rate by the current salary. The microsimulation developed for Belgium allows us to obtain much more accurate measures. As an example, when we compare the average annual pension benefit according to the two methods, we obtain diverging results both in terms of average and standard deviation. Individuals would systematically overestimate their forthcoming pension.Footnote ⁹

Table 1 presents descriptive statistics for the sample. It is well balanced between men and women and the average age is about 69 years old. The length of working career is about 34 years and women have shorter career than men. Almost 80% of the sample is retired and surprisingly this number rises to 88.6% for men while it is only 69.4% for women. Looking at the proportion that is married, we observe that only 60.3% of women are married while 84.9% of men are. Thus women in our sample are more active than men and this likely comes from our sample making constraint in which we have excluded individuals who have never worked. In the female population, it is a kind of all or nothing career decision. Those who were married and never worked, particularly women, are thus not represented in our sample. This also explains why in our sample we have more single active women than single men. Table 1 also presents the total net wealth and shows that the main part of the wealth is non-financial, especially for women. In Table 1 we also find the non-adjusted value of pension wealth (that is before Gale Q-adjustment) and lifetime income.

Table 1. Sample descriptive statistics

6. Robustness tests and sensitivity analysis

One important aspect of our estimation is concerned with the measurement errors. Even if there is no correlated measurement error between I and P, there is still a possibility to have measurement error in P. This may causes an attenuation bias. As exposed above, Alessie et al. (Reference Alessie, Angelini and van Santen2013) used the same SHARE data for a series of countries. They approximated the pension benefits by the individual expectation and they obtained counterintuitive results when they estimated the same model as ours. They push forward the effect of the correlation of measurement errors between the lifecycle income and the pension wealth to explain their results and they show that under the validity of the lifecycle model, by imposing that β ₁ = 1, they are able to sign the bias associated with the measurement error problem. Their estimation of the displacement effect is still biased but it has the same sign as the true value. Our results exposed above do not seem to be affected by such a problem since we do not find counterintuitive results, especially regarding the sign of the coefficients associated to our variables of interest. This tends to show that the use of full microsimulation model reduce the effects of the measurement errors.

However for sake of comparison, we also estimated the displacement effect using the same pension wealth obtained through the use of the expected replacement rate. This is done in a complete specification as presented above and in a constrained linear regression model. In addition, we present the same constrained model when we use our pension wealth obtained through the microsimulation model. The results in Table 4 show that indeed when we use their approach to estimate P, we obtain counterintuitive results with I _t being negative and significant and P _t not significant. Once we constraint β ₁ to be equal to one, we obtain a significant displacement effect but it is much bigger and close to the one obtained in Alessie et al. (Reference Alessie, Angelini and van Santen2013). When we run the same constraint regression with our definition of pension wealth, we still obtain a high displacement effect. These results show the importance of correctly measuring the flow of income from the work career and the pension system. It appears that our strategy to rely on full microsimulation model allows us to circumvent part of the problems related to the measurement errors.

Table 4. Effect of public pension wealth (median regression) based on expected replacement rate + constrained linear regression

*p < 0.1, **p < 0.05, ***p < 0.01.

Note: Robust standard errors in parentheses. Each regression includes age, age squared, marital status, gender, the number of children, education and health as controls, detailed results are available in the Appendix (Table A7).

In Table 5, we perform a series of additional robustness tests. First we make the distinction between financial and non-financial wealth. Financial wealth, because of its narrowed nature and because it is more dependent on contemporaneous situation, may be unable to detect crowding-out effects, as pension wealth is accumulated over a long period (Gale, Reference Gale1998; Alessie et al., Reference Alessie, Angelini and van Santen2013). However Hurd et al. (Reference Hurd, Michaud and Rohwedder2012) argued that since financial wealth is more liquid it can then be easily displaced by pension wealth. Our results are in accordance with Gale (Reference Gale1998) and we find a smaller offset when we use a narrowed definition of wealth.

Table 5. Effect of public pension wealth on net financial and real wealth – full sample

*p < 0.1, **p < 0.05, ***p < 0.01.

Note: Robust standard errors in parentheses. Each regression includes age, age squared, marital status, gender, the number of children, education and health as controls, detailed results are available in the Appendix (Table A8).

Finally, in Table 6, we test for the addition of other covariates that might be relevant in determining non-pension wealth. Since our results so far are qualitatively identical we run these last regressions for the full sample and present only median regressions. First individuals may have different tastes for saving or, saying differently, have different risk preferences. Risk averse individuals are likely to delay retirement age and save more for retirement than risk lovers. We introduce self-declared individual risk preferences taken from a question in SHARE.Footnote ¹⁵ Vieider et al. (Reference Vieider, Lefebvre, Bouchouicha, Chmura, Hakimov, Krawczyk and Martinsson2015) have shown that self-declared measure of risk preferences are good measures of the true risk preferences. We introduce a dummy variable equal to 1 if the individual is risk averse. We also control for the partner situation and add in column 2 a dummy variable equal to 1 if the partner is still working and if his/her level of education is higher than 12 years of education in total. Following Alessie et al. (Reference Alessie, Angelini and van Santen2013) we control for whether the individual has ever received inheritances or gifts worth more than 5,000 euros as well as for the amount received. In columns 1, 2 and 3, our results show that the displacement effect is still in the same range as in Table 2 and significantly different from 0.

Table 6. Effect of public pension wealth on net non-pension wealth – adding covariates and interactions (median regressions)

*p < 0.1, **p < 0.05, ***p < 0.01.

Note: Robust standard errors in parentheses. Each regression includes age, age squared, marital status, gender, the number of children, education and health as controls, detailed results are available in the Appendix (Table A9).

Finally, we go one more step forward in identifying different response of household wealth to pensions benefit according to two specific dimensions: education and marital status. As shown in previous works (see Gale, Reference Gale1998; Engelhardt and Kumar, Reference Engelhardt and Kumar2011; Alessie et al., Reference Alessie, Angelini and van Santen2013), the displacement effect can be different according to the level of education. Especially, the question of financial literacy (expected to be highly correlated to the level of education) may be important in explaining the various plans for retirement (Solomon, Reference Solomon and Juster1975; Bernheim and Garrett, Reference Bernheim and Garrett1996; Haurin et al., Reference Haurin, Hendershott and Wachter1996; Bernheim, Reference Bernheim, Mitchell and Schieber1998 and Laibson et al., Reference Laibson, Repetto and Tobacman1998). There can be substantial variation across individuals in the displacement of pensions to saving, with the bulk of crowd-out occurring in the upper levels of education. In Table 6, we split our sample according to education and report the estimate for the low and high level of education.Footnote ¹⁶ We find that the displacement effect is not significantly different from 0 for the less educated individuals. This tends to confirm previous results that show that less educated people would be less financially literate and thus less able to correctly plan for retirement.

In Table 6, we also look at the differentiated displacement effect according to the marital status. The last columns show that there is no significant displacement effect for the non-married individuals but a significant one for the married. This is surprising but Section 2 has shown how being married or not may affect the pension benefit calculation. Furthermore pension wealth inequality can be higher among two-partner households than among single households. Indeed the two-partners households with one single-earner are generally more liquidity constrained than single individuals and will be more affected by a potential reduction of their pension benefits. On the contrary, the two-earner households are less liquidity constrained and a reduction of pensions should trigger saving reaction.