The Algebra of Government Debt

A fiscal policy which achieves a reduction of the debt to GDP ratio below its initial level is labeled as fiscal retrenchment policy. In this paper we investigate four types of fiscal retrenchment policies. Type 1 describes a policy where the government chooses a constant primary budget surplus to GDP ratio, type 2 a policy where the government chooses a constant overall budget deficit to GDP ratio to achieve the reference value of the debt to GDP ratio. Following type 3, the Strong Gros-Rule, the government reduces the debt to GDP ratio every year by 5% of the discrepancy observed at the beginning of the fiscal retrenchment program and the target value. Finally, a type 4 policy (the Weak Gros-Rule) is investigated where the debt to GDP ratio declines every year by 5% of the difference between the one-period lagged debt ratio and the reference value.