Altruism and fairness in a public pension system

13

is due to the logarithmic specification given by the coefficient of Y^m +У⁰, is about 0.281⁰. This means
that (ceteris paribus) on average the utility ofa young individual increases by 0.28% if the income of
the other generations is increased by 1%. Note that the young individual’s own income elasticity
amounts to about 1.38.

The desired or optimal rates of return r^y_k* - only considering significant parameter estimates - show
the following picture from the point of view of the young generation¹¹.

rf≈1.49 (0.16, я = 6)
r^y_m* ≈2.57 (0.01, я =2)
r∕*≈4.72 (0.75, я = 5)

The actual rates of return amount to 1.2 for the young generation, 2.4 for the middle-aged persons and
3.5 for the elderly. So, respondents appear to take the status quo situation as a preferable situation
which should not be amended too drastically. The elasticity of fairness towards the middle-aged
generation is about 0.002 and towards the older generation about 0.001. So, for instance an increase
of 1% (ceteris paribus) in the actual rate of return for the elderly gives the young 0.001% higher
utility¹².

The coefficients of the background characteristics appear to be rather robust. Changes in the system
lead to significantly larger losses when a partner is present. This could be expected as it reduces
consumption possibilities with a given income. Moreover, age sometimes has a small negative effect.
Finally, the intercept term is small. Most of the time it is insignificant as it should be if the specification
chosen is correct.

¹⁰When calculating the elasticities of altruism we only considered the variants in which altruism and fairness
are not both included.

¹¹This includes additional estimates not reported here. The first term between parentheses is the standard
deviation, whereas n gives the number of observations.

¹²Note, however, that the effects of an increase or a decline in the actual rate of return are not symmetric.
For instance, an increase in the actual rate of return of the old brings the value closer to the rate desired by the
young. This positive effect (elasticity) is smaller than the negative effect which a decline in the actual rate would
have.

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