(13)
∂EU
∂θi
-1-γ[(1-α2)∂var(yit)
2 ∂θi
+ 2α(i — α )d covCy'. ■y ) + α
∂θi
∂var(yt)] = 0
∂θi .
It is plausible to assume that the derivatives of the two variances with respect to θi are
negative, since reducing the variance of regional income is likely to result in a reduction in
the variance of aggregate income. Whether or not such policies reduce the covariance,
however, is uncertain. Using condition (13), we can derive the effect of an increase in the
degree of fiscal insurance on the optimal policy of a regional government:
(14)
∂θ*
∂α
2(1-α)∂var(yit)
∂θi
-2(1-2α)∂cov(yit,yt)-2α∂var(yt)
∂θ ∂θ
2 ∂2 var(yit) ∂2 cov(yit, yt) 2
(1-α)2 it +2α(1-α) it t +α2
∂θi2 ∂θi2
∂2 var(yt)
∂θi2
Assume that policies to reduce income risk have declining marginal returns, i.e., the second
derivatives are all positive. Equation (14) then says that the effect of fiscal insurance on the
optimal regional policy depends crucially on the effect a region’s variance has on the variance
of average income. If this effect is small, as it would be for small regions, regional policies
have small effects only on the covariance of regional and average income and the variance of
average income, and (14) is negative. Thus, an expansion of the fiscal insurance mechanism
reduces efforts for less income variance at the regional level. The opposite may be true,
however, for large regions, whose policies have strong effects on the monetary union’s
average income variability.
Furthermore, equation (14) shows that the response of regional policies to a small increase in
fiscal insurance provided by the monetary union depends on the degree of insurance already
in place. Assuming that the changes in the covariances are of smaller magnitude than the
changes in the variances, (11) shows that an increase in fiscal insurance reduces local efforts
to reduce income variance if α is initially close to zero. The opposite is true, however, if the
degree of insurance is already large. In that case, regions have an incentive to engage in
policies reducing regional income variance as this contributes to a more stable average
income.
This discussion shows that a fiscal insurance mechanism changes the incentives for regional
governments to protect their citizens against income fluctuations, a point discussed also by
Persson and Tabellini (1996) and Migué (1993). However, it is not clear a priori which way
these incentive effects go. One can only conclude that a fiscal insurance mechanism may
require additional policies at the level of the monetary union that rectify or amplify the
incentive effects on local governments.
Turning from a simple endowment economy to a macroeconomic environment raises
additional concerns. In an economy with production, household welfare will depend not only
on consumption but also on employment. To offset the effects of asymmetric shocks, a fiscal
insurance mechanism should then aim at stabilizing fluctuations in employment and
consumption. In the simple, traditional Keynesian framework with fixed prices and Keynesian
unemployment considered by Mundell (1961) and Kenen (1969), stabilizing household
income through fiscal insurance would still be sufficient. In a more general, dynamic macro
economic framework, it is not.15 An important aspect of fiscal insurance then is whether the
15 For recent analysis of these issues in the framework of a New-Keynesian dynamic general
equilibrium model see Evers (2006).
12