(6) U,=ci. - 2var( cit ),
where γ>0. The households’ budget constraint is cit = yit + τit - θi, where θ1 is a constant tax
imposed by the regional government, which means that individuals cannot borrow to smooth
consumption in the presence of shocks For now, assume that θi = 0.
The fiscal transfer mechanism can be designed to make consumers in all regions
better off by paying transfers that partially offset deviations from expected income. A first,
important question is whether or not the fiscal mechanism must be balanced at all times or
not. If budget balance is only required in expectation, the optimal policy is to set consumption
equal to expected income each period and eliminate all variance. In this case, the optimal
transfers are
(7) τit =y-yit,
where y is potential output. Consumers are fully insured against income shocks. This is so,
because it eliminates any variance in consumption over time. Note that each government
could achieve the same outcome by taxing its citizens when income is above its expected
value and paying transfers when income is below its expected value. In this case, each
government would borrow on behalf of its citizens in the international capital market when
income is low and pay back when income is high.
A natural question then is, why should there be a fiscal insurance at the level of the monetary
union? The answer is two-fold. First, small countries in particular may face upward-sloping
credit supply curves in the capital market, implying that they pay higher interest rates for
borrowing funds when income is low than they receive on funds invested when income is
high. Under such circumstances, pooling the individual consumption-smoothing policies will
yield a reduction in the aggregate cost of borrowing (see Hammond and von Hagen, 1998).
Second, if the monetary union imposes restrictions on public debts and deficits to safeguard
the stability of the common currency, as EMU does, a common fiscal insurance mechanism
assures that countries are not forced into suboptimal consumption patterns. By creating a
common fiscal insurance the member countries delegate their borrowing capacity to the
monetary union.
If budget balance is required each period, the transfers are
(8) τit =α(yt -yit)+πi,∑iπi =0.
They consist of a state-dependent part linked to the deviation of a region’s income from
average income in the monetary union, and a state-independent part. Using (8) in (6), we
obtain
(9)
Uit = αyt + (1 - α)У. + πi - γ [α2 var(y. )+ 2α(1 - α)cov(yt, У. )+ (1 - α)2 var(yi.)].
Forcing the system to balance at the aggregate level implies that fiscal insurance now
smoothes fluctuations of regional income around average income in the monetary union,
which itself is a random variable that fluctuates over time. We can use equation (9) to
calculate the optimal, utility-maximizing transfer rate α* from the point of view of households
in each region i,
*
(10) αi*=
wi(wi - ρi) w = ∕var(yit )
1 + wi(wi-2pi)’ i Var(y.),
where ρi is the correlation between income in region i and average income in the monetary
union’ and wi indicates how volatile a region’s income is compared to average income in the
monetary union. Equation (10) shows that’ in this case’ full insurance will generally not be
optimal for all regions. Instead’ different regions have different optimal transfer rates and
each region’s optimal degree of insurance depends on its risk profile compared to the
monetary union. Note’ first’ that αi*=1 for all regions’ if all individual regional incomes are
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