Numerical Simulation of Non-cooperative and Cooperative Equilibrium Solutions for a Stochastic Government Debt Stabilization Game

In this article, we consider the impact uncertainty has on policies and realization of targets aimed at the stabilization of government debt. The problem is motivated by the fact that in many countries revenues are to a large extent uncertain. Following Tabellini (TEDC 4: 427–442, 1986), we model the debt stabilization problem as a dynamic game between government and central bank. However, different from Tabellini (TEDC 4: 427–442, 1986) we assume that nominal income in this problem setting is uncertain and model its price dynamics by a stochastic differential equation. By employing the quotient rule from stochastic calculus, government debt, primary fiscal deficit, and base money are scaled by this nominal income process. Then, the debt stabilization problem is formulated within this stochastic framework. Assuming a feedback information structure we solve the problem both within a non-cooperative and cooperative mode of play. To explore the effects of uncertainty on government and central bank polices and debt stability, we perform a simulation study and sensitivity analysis. One of the major conclusions from this study seems to be that cooperation has a smoothing effect on pursued policies but that this does not necessarily lead on average to a better tracking of the debt target. Furthermore, we observe that the more uncertainty there is, the more policymakers are inclined to emphasize the stabilization of debt.