Altruism and fairness in a public pension system

3 Specification and data

3.1 Specification

In our survey individuals are supposed to belong to one of three generations, namely the young (25-44
years old), the middle aged (45-64 years) or the old (older than 65 years). For an individual of
generation k (k=y, m, o) the evaluation function is supposed to be determined by the following
logarithmic function:

1п{7* = а* ₊ а*УМ*(Г^А + Г')₊ V (γ‰* ₊ δ*r*²) k,g=y,m,o, h≠i≠k (1)
⁴*                             OO   OO

g=y,m,o

where U^k denotes the utility of an individual belonging to generation k, Y^k indicates measured
discounted lifetime income of the respondent and Y^h + Y^t indicates measured total discounted lifetime
income of the representative individuals of the other two generations. Altruism is assumed to be
measurable by means of the income of other generations, so by the parameter βⁱ. r_g (r_g ) is the
actual rate of return for a representative member of generation g (squared)¹. These terms are assumed
to represent notions of fairness regarding oneself and members of other generations. We expect that
fairness can be represented by a parabolic function². Therefore, γ^k_g is expected to be positive, whereas δ*
is expected to be negative. The ’optimal’ rate of return for generation g as perceived by generation
к                                                                              y^k

k (r^k* ) can be calculated from the estimated parameters as —-. Note, however, that the feelings
²⁸S

towards one’s own ratio may be different from the feelings towards the ratios of others. It might be
possible that people consider their own rate of return never to be too high. In particular, the rater/*

¹The actual rate of return is defined as the discounted pension benefits divided by the discounted pension
contributions made during the entire life. The actual rates of return are calculated from Nelissen (1994), assuming
a real discount rate of 2% and a real growth rate of the economy of 2%. The actual rate of return for the
respondent is the average rate of return for the 5 years age category s/he belongs to, whereas the actual rates
of return for the other two generations are given by the average rates of return for the representative members
of those generations.

²The idea is that we expect individuals to dislike rates of return on public pension systems for members of
other generations that are too high or too low compared with an ’optimal’ rate of return r_g (k≠g). More specific,
it seems reasonable to assume that individual’s notions of fairness are determined by the function (r_g -r_g )².
By including r and r separately in the regression equations we are able to calculate the ’optimal’ rate of
⅛*      °          °                                     k*2∣                                                         fa

return r_g (k≠g) (see Section 4). Implicitly, the r_g -part is contained in the constant term a₀. The parabolic
specification of the fairness function is supported by the data (see Section 4).

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