An increasing trend in the dependency ratio increases the sustainable tax
rate. For the case where the dependency ratio is increasing (ρ>0), it follows
that an increase in the growth rate increases the sustainable tax rate, as does an
increase in the interest rate. The intuition is that the sustainable tax distributes
the financing requirements over time. Since increasing growth means increasing
expenditures in the future, and since current generations are contributing to the
financing it follows that the tax rate has to go up. Similar reasoning applies for
the interest rate effect.
With a trend in the demographic dependency ratio, the initial budget balance
is
b0 =[τb - α1 - (1 + ρ)(γ + α2)] y1t
(γ + α2)(1 + ρ)
(1 + g)ρ
.(1 + r) - (1 + g)(1 + ρ)J y1t
which implies that the sustainable tax rate implies an initial budget surplus if the
demographic dependency ratio is increasing, and vice versa if it is decreasing,
i.e. b0 > 0 for ρ> 0, and b0 < 0 for ρ< 0. With an underlying trend in
the dependency ratio, it follows that the sustainable tax rate causes an initial
consolidation to create a financial basis from which to finance future expenditure
increases. With an underlying demographic trend, the sustainable tax rate thus
induces savings to ensure a constant tax rate over time.
With an underlying upward trend in the dependency ratio, it is straightfor-
ward to compare the sustainable tax rate with the PAYG-tax rate, since
i.e.
PAYG
τt
^
τ
α1 +(1+ρ)i+1(γ+ α2)
α1 +(γ+ α2)(1 + ρ)
(1 + r) - (1 + g)
(1 + r) - (1 + g)(1 + p)
PAYG
τtPAYG - τb
α1 +(1+ρ)i(γ+ α2) -
α1 +(γ + α2)(1 + ρ)
(1 + r) - (1 + g)
(1 + r) - (1 + g)(1 + p)
(γ+α2)(1+ρ)
(1 + ρ)i -
(1 + r) - (1 + g)
(1 + r) - (1 + g)(1 + p)
It follows that for p > 0 : τPAYG--T < 0, and there exists a t, where τPAYG-T >
0. This shows that the sustainable tax rate smooths the financial burden caused
by the trend increase in the demographic dependency ratio.
PAYG-taxes and the sustainable tax rate
It follows immediately by use of () defining the PAYG-tax that the sustain-
able tax from () can be written
[b - αι - (1 + pt)(γ + α2)] y1t + 1 + r £b - α1 - (1 + pt+ι)(γ + α2)] y1t+1
U ) 2fT -
α1
- (1 + pt+2)(γ + α2) y1t+2
37
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