10
higher than the older generation does. The last two situations are the situations with ageing effects.
The elderly evaluate the situation with lower public pension benefits (LB) better than the other
generations do. Notice, however, that situation LB as well as EB pertain to future changes that barely
harm the income positions of the elderly. Finally, the situation with higher contributions (EB) has been
evaluated higher than the situation with lower public pensions (LB) by all generations.
As noted in Section 3, one of the basic goals is to estimate whether altruism and notions of fairness
play an independent role in the individual evaluation of public pension systems. The variants described
in Section 3.2 produce changes in pension contributions, savings, income and rates of return in the
public pension system for the individual respondent and for the members of other generations. The
changes have been communicated to the respondents during the survey. The evaluations and the
(changed) values of the variables mentioned above are used as data. Thus, for each individual four
observations on the dependent and independent variables in eqs. (1) are available8.
To compensate for individual-specific effects, first differences of the variables are used. That is to say,
for each variable the difference between the alternative situation and the basic situation is calculated9.
This yields the equations that we will estimate:
(3Uk' = ao+akYk'+pk(Yh' + Yi')+ V (γ*r*' + δ*√2) k,g=y,m,o, h≠i≠k (3)
ʊ SS SS
g=y,mio
8Notwithstanding the variation in independent variables, several income variables and the variables taking
account of fairness are plagued by multicollinearity problems. So, for instance, a change in the contribution rate
moves current and middle-aged income of the current young in the same direction which prevents detecting their
independent influence on the evaluation of the pension system. For respondents of other generations analogous
effects hold. This multicollinearity problem was partly circumvented by taking discounted individual lifetime
income as an explanatory variable. Furthermore, we had to combine the lifetime income of members of the other
two generations in one variable.
9If we do not take first differences the following problem occurs. One of the assumptions of OLS or WLS
is that the error terms are normally distributed i.e. ei~N(0,σ2). In our case the disturbance terms are likely to
reflect background characteristics and some common unmeasurable or omitted factors that are probably individual-
dependent. The assumption is, therefore, likely to be violated as we use a vector in which every individual arises
four times. This problem disappears if we take first differences. However, background characteristics are still
assumed to play a role, so the terms ak0 appear in eqs. (3). Furthermore, it is likely that taking first differences
decreases possible generational differences in the perception of grades, e.g the chance that an old person perceives
a 7 differently than a young person does (and therefore gives a 6 or an 8) is larger than the chance that a
difference of 2 between two grades is perceived differently.