Designing a linear pension scheme with forced savings and wage heterogeneity

This paper studies the optimal linear pension scheme when society consists
of rational and myopic individuals. Myopic individuals have, ex ante, a strong preference
for the present even though, ex post, they would regret not to have saved enough.
While rational and myopic persons share the same ex post intertemporal preferences,
only the rational agents make their savings and labor supply decisions according to
these preferences. Individuals are also distinguished by their productivity. The social
objective is “paternalistic”: the utilitarian welfare function depends on ex post
utilities. We examine how the presence of myopic individuals affects both the size
of the pension system and the degree of redistribution it operates, with and without
liquidity constraints. The relationship between proportion of myopic individuals and
characteristics of the pension system turns out to be much more complex than one
would have conjectured. Neither the impact on the level of pensions nor the effect on
their redistributive degree is unambiguous. Nevertheless, we show that under some
plausible assumptions adding myopic individuals increases the level of pension benefits
and leads to a shift from a flat or even targeted scheme to a partially contributory
one. However, we also provide an example where the degree of redistribution is not
a monotonic function of the proportion of myopic individuals.