Debt bailouts and constitutions

Economic Inquiry, July, 2008 by Emanuel Kohlscheen

What predictions can be derived in the more realistic case when state governors are risk averse? Substituting the quadratic utility function in the first-order condition and assuming that [y.sub.2] is i.i.d., so that E [[summation].sup.n.sub.i=1][y.sup.i.sub.2] = nEy, we find that the optimal amount of borrowing in Period 1 is given by an expression that includes the degree of risk aversion. (7) In the particular case where an ex ante no-bailout commitment is perceived as credible (i.e., [lambda] = 0) and q = [beta], borrowing reduces to

[b.sup.i.sub.2] = [(1 [beta]).sup.-1] [Ey - [y.sup.i.sub.1]].

In other words, the amount borrowed will be a function of the steepness of the expected income profile and the patience of the state. States expecting a high growth rate and impatient states borrow more. (8) Moreover, when the no-bailout commitment is perceived as credible, revenue sharing clearly has no effect on state borrowing at all.

If the promise not to bail out is not credible however (i.e., [lambda] > 0), the situation changes: from the optimal borrowing expression, we can conclude that state borrowing will be affected by the participation of the state in revenue sharing ([[sigma].sup.i]). Also, in contrast to the risk-neutral case, state borrowing now depends also on expected aggregate borrowing. The expectation of a bailout in Period 2 creates two effects: a common-pool problem that puts upward pressure on the amount borrowed and a contention effect that comes from the fact that states anticipate that they might have to bear the burden of other states in case of a bailout.

D. To Bailout Or Not to Bailout

In the previous subsection, we took the prior probability of a bailout ([lambda]) as parametric. We now endogenize it. Note that here we do not need to specify the utility function. Rational state governors in Period 1 know that in Period 2 each benevolent governor will prefer z such that (1 - z[[tau].sub.2] - (1 - z) [[tau].sup.i.sub.2])[y.sup.i.sub.2] z[[sigma].sup.i] [mu][[tau].sub.2] [[summation].sup.n.sub.i = 1][y.sup.1.sub.2] is maximized. After plugging in the budget constraints for the two levels of government, we find that the optimal strategy will be to favor a bailout if and only if the condition below is expected to be satisfied:

(1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [R.sup.i] denotes the state-specific representation ratio [R.sup.i] = [[sigma].sup.i]/([y.sup.i.sub.2]/[[summation].sup.n.sub.i = 1][y.sup.i.sub.2]). According to this expression, demand for a bailout comes from states with a relatively high indebtness and a high participation rate in the distribution of federal revenues relative to their share in expected income. Once p has been set and overall subnational indebtness is known, the above expression says that these two state-specific statistics are sufficient to define the optimal vote of a state. Note that states with a representation ratio exceeding 1/[mu] would support debt bailouts even if they had no debt at all!

It is easy to see that, in the absence of revenue sharing, Equation (1) reduces to: