Altruism and fairness in a public pension system

14

[ INSERT TABLE 4.5 ABOUT HERE ]

In table 4.5 the regression results for the middle-aged generation are reported. What stands out quite
remarkably is the less robust effect of their own lifetime incomes ( Y^y ). Again, altruism and / or fairness
improves the estimation results. This holds in particular for the fairness measures. Altruistic feelings
increase the explanatory power of the equation to a fairly small degree (.R² increases from 0.11 to 0.12;
see variants 0 and 1), but it is significant at the 5% level. The lifetime incomes of the middle-aged
appear to interfere with the notion of fairness, in particular regarding the elderly, r “ and r “² (compare
e.g. variants 3 and 5 or 4 and 6). Moreover, notions of fairness regarding one’s own contribution to
the public pension system and fairness with respect to other generations apparently cannot be
established independently from each other. In particular, as soon as fairness with respect to other
generations is introduced, the coefficients of the rates of return of the middle-aged themselves become
statistically insignificant (compare variant 3 with the other variants). Without incorporation of the rates
of returns with respect to the other generations, the own ratio clearly affects utility and the fairness
function then has a reversed U-shape. Estimation of the equation without taking account of one’s own
ratio results in an on average higher coefficient for one’s own lifetime income У¹”¹³. This can be seen
as an indication that the (egoistic) feelings about one’s own situation influence both the coefficient of
one’s own fairness ratio and the coefficient of one’s own income, or in other words, the (egoistic)
feelings are divided over these two variables.

Just as in the case of the young generation, multicollinearity problems prevent us from getting precise
and significant estimates of the notions of fairness. To get an idea we calculated the fair return Q^mx
for generations k (k=y, m, o) from the significant estimates. The estimates are remarkably robust with
respect to the young, whereas some more variation exists with respect to the elderly. The estimated
optimal rates are:

r_y^m*≈0.97 (0.026, « = 6)
r“*=2.67 (0.00, n =2)
r₀^m*≈5.24 (0.50, n= 6)

¹³These results are not reported here. The concerning tables are available from the authors upon request.

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