Debt bailouts and constitutions

Economic Inquiry, July, 2008 by Emanuel Kohlscheen

II. A MODEL WITH BAILOUT RISK

A. The Model

The purpose of this section is to provide an analytical model in which political actors with state-level constituencies have a decisive role in the provision of a bailout. Specifically, it is assumed that the decision to extend a bailout is taken by a simple majority vote by state governors. This may be seen as an approximation of agreements reached within the informal forum of a governor meeting or a Senate, where each state/province has the same number of representatives. As senators and governors have the same political constituency, their interests are likely to overlap to a great extent. In the case of Brazil, to which I will refer in the empirical section, any decision involving state debts has to be approved by the Federal Senate.

Consider a two-period economy in which a federal government, henceforth called the Union, and n states coexist. The utility function of the governor (or, alternatively, the representative citizen) is assumed to be (weakly) concave in consumption. The governor of province i thus maximizes the welfare function u([c.sup.i.sub.1]) [beta]Eu([c.sup.i.sub.2]), where [c.sup.i.sub.t] represents the consumption of state i at time t and [beta] the rate at which future utility is weighted. In each period, state i receives a state-specific endowment [y.sup.i.sub.l], which is taken from an ergodic distribution represented by F[[y.bar], [bar.y]]. In Period 1, states may issue [b.sup.i.sub.2] one-period noncontingent bonds--that are promises to repay 1 unit in Period 2--in a competitive credit market at a price q (which is just the inverse of the gross market interest rate). The number of bonds issued is such that it does not exceed the lowest endowment [y.bar]. Bonds are redeemed with the proceeds accruing from a proportional taxation on the endowment in Period 2. Taxation might be either federal (in which case, the rate is represented by [tau]) or state specific ([[tau].sup.i]). It is not important in the model whether proceeds from debt issuance are transferred to the population of the state or not. There is no debt at the beginning of Period 1.

Assume that a share p of national revenues is pooled in a tax sharing fund. State i has a claim on a fixed share, denoted [[sigma].sup.i] of the fund, where [[summation].sup.n.sub.i=1] [[sigma].sup.i] = 1. In Period 2, states may have a window of opportunity to shift their liabilities to the federal level as long as it is approved by a binding simple majority referendum among state governors. The occurrence or not of this window of opportunity is determined by exogenous factors. All that is known in Period 1 is that it occurs with probability [pi]. Hence, a perfectly credible ex ante no-bailout commitment is represented by the special case where [pi] = 0.

The timing within a period is as follows:

* Nature determines the realization of endowments for each state.

* In Period 2 (only) a binding referendum to decide whether state debts will be shifted to the Union or not occurs with probability [pi].