uncorrelated and identically distributed.14 Otherwise, the optimal degree of insurance depends
on the correlation between regional and average income and on the relative volatility of
regional and average income. If all regions have the same variance of regional income, the
optimal degree of insurance approaches zero, as the correlation among the incomes
approaches one. Thus, the more similar income fluctuations are over time, the scope there is
for insurance. But note that even with positive correlations, regions with relatively large
income variances compared to others find insurance attractive, while regions with relatively
low income variance would prefer no insurance at all.
The point of this discussion is that, if the fiscal mechanism must be balanced each period,
regions with different risk profiles demand different degrees of insurance. Designing a
common fiscal insurance then requires finding a compromise among the regions. This can be
done using the state-independent transfers πi to make side payments between the regions.
Specifically, relatively high-risk regions can pay a premium to relatively low-risk regions to
compensate for providing more insurance than the latter would find optimal. Consider the
following example for illustration. Let n=2 and consider a region’s expected utility given
some transfer rate α=a. From equation (9) we have
γ2 2
(11) EUi(a) = y + πi -2[aa var(yt) + 2a(1-a)cov(y,yit)+ (1-a) var(yit)],
where π1 = -π2. Assume that the two countries use Nash bargaining to establish the state-
independent transfers, and that each region’s fall-back position is α = 0. The equilibrium
transfer can be found by maximizing the product [EU1(1)- EU1(0)] [EU2(1)- EU2(0)]. This
yields the equilibrium state-independent transfer:
(12) π1* = -π2 = aY var(yt) [(2 - a)(w2 - w12) + 2(1 - a)[w1ρ1 - w2ρ2].
1 2 2 1 11 22
Assume, first, that the relative variances wi are the same. Then the first term is zero and
equation (12) says that the region whose income is more highly correlated with average
income receives a transfer from the region whose income is less correlated with average
income. Clearly, the former has less interest in fiscal insurance against fluctuations around the
average than the latter. The side payment is used to induce it to agree to the insurance
mechanism. Next, assume that both correlations are negligible such that the second term
disappears. In that case, equation (12) says that the region with the more volatile income pays
a state-independent transfer to the region with the less volatile income.
Generally, this discussion shows that a welfare-maximizing fiscal insurance mechanism will
combine fixed transfers with state-dependent transfers, if it is required to achieve budget
balance each period. Thus, whether or not the fiscal mechanism is allowed to borrow in times
when average income in the monetary union is low to pay back when average income is large
is an important aspect of the design of fiscal insurance.
Consider now the possibility that regional governments can undertake policies that reduce the
variability of regional income, and that doing so requires a fixed tax θi > 0 from all
households. Such policies might consist of running a rainy day fund from which the
government can in draw in times of low income, or in investing in projects improving the
flexibility of local markets and factors of production. An important question then is, how does
the fiscal mechanism at the level of the monetary union interfere with the regional
governments’ optimal policy at the regional level?
To answer this question, we assume that the variance of regional income and its covariance
with average income are functions of θi. Each regional government will choose θi such that
14 To see this, note that wi = √n and ρi = 1∕√n for all i in this case.
11