is that all welfare arrangements (services and pensions) and the tax system are
proportional to the current income level. Increased growth will thus lead to
a proportional income in revenues and expenditures for the public sector and
therefore in net-terms not change anything. This neutrality result depends on
the way welfare arrangements and taxation have been arranged, which can be
seen by considering two special cases.
i) The tax system includes tax bases dependent on income in past period,
e.g. via taxation of pensions or the return on savings. The budget restriction
or the requirement to budget balance is in this case
bt = [τt - αι - (1 + ρt)(γ + α2)] yιt + μyιt-i = 0
where μy1t-1, is the revenue from taxation related to tax bases dependent on
earlier periods’ income (here income in the previous period). The balanced
budget requirement can be rewritten
bt = £tt - αι - (1 + ρt)(γ + α2) + μ(1 + g) 1] yιt = 0
where g is the growth rate in income (y1t = (1 + g)y1t-1). The tax rate under
PAYG-financing becomes
τ PAYG = αι + (1 + ρt)(γ + α2) — μ(1 + g) 1
i.e. increased growth will increase the tax rate. The intuition is that while
expenditures are increasing proportionally to income, this is not the case for
the tax base since it also depends on previous periods’ income. Therefore the
needed tax rate to finance given welfare arrangements goes up.
ii) Pensions are proportional to earlier labour income, i.e.
pt = γy1t-1
In this case pensions are seen relative to the income (and [ this-?] consumption
possibilities) while working and not relative to those currently working. In this
case the budget restriction becomes
bt = £tt — αι - (1 + Pt)(γ(1 + g)-1 + α2)] yιt = 0
and the tax rate under PAYG-financing
τtPAYG = α1 + (1 + ρt)(γ(1 + g)-1 + α2)
i.e. increased growth will reduce the PAYG-tax. The intuition is that expendi-
tures on pensions are not affected by growth since they depend on last period’s
income.
Sustainable tax rates
An alternative financing strategy is to keep tax rates constant over time to avoid
varying tax rates and possibly minimizing tax distortions (Barro (1979)). The
sustainable tax rate is defined as the tax rate τb, which it is possible to maintain
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