pensions and income for those working, i.e. gains from growth are distributed
equally among active and passive members of society. The second part implies
that expenditures on welfare services are proportional to income developments.
This reflects that welfare services are labour intensive and that public wages
follow private wages very closely.31 Notice that all parameters are assumed
to be time-independent, i.e. given rules for pensions and welfare services are
considered.
The following focuses on the requirements to financing given the increase in
the demographic dependency ratio. This is operationalized by considering the
changes in the tax rate needed to finance the expenditures. We consider two
financing strategies, namely, pay as you go with continuous adjustment of taxes
to balance the budget and the sustainable tax rate, which over time is consistent
with the government intertemporal budget constraint.
We consider a "small and open economy" for which the (real) rate of interest
r is exogenous. To simplify, the interest rate is assumed constant over time.
Similarly the growth rate g is exogenous and constant over time. It is assumed
that r>g, i.e. corrected for growth the real rate of interest is positive.
Pay as you go financing
Under pay as you go financing it is a requirement that there is budget balance
on a period-by-period basis, i.e.,32
bt =[τt - α1 - (1 + ρt)(γ + α2)] y1t =0 (11)
which immediately implies
τtPAYG = α1 +(1+ρt)(γ + α2) (12)
It follows straightforwardly that the optimal tax rate is increasing over time if
the demographic dependency ratio is increasing (ρ > 0) and vice versa. The
intuition is that it is necessary to tax the current work force more when a
large fraction of the population has to be supported. It is also an immediate
implication that
Γ1t = Nta1t - Ntτty1t > 0
Γ2t = Nt-1(pt + a2t) < 0
i.e. in net-terms the working population is net-contributors, and the retirees are
net-beneficiaries from the welfare arrangements.
Note that the tax rate under PAYG-financing is independent of the income
level and thus the underlying growth rate. The reason for this neutrality result
31 At the same time, demand will pull in the same direction if the income elasticity in demand
for welfare service is high.
32Can more generally be translated as a requirement for unchanged debt (relative to GDP).
For simplicity, the initial debt is assumed to be zero, and balance in the primary budget will
maintain a zero debt.
34