Public debt games with corruption and tax evasion

Abstract

This study explores the interactions between corruption, tax evasion, and public debt. Public debt accumulation results in disutility, therefore the key issue is whether the time path of the public debt is sustainable or not. Infinite time differential game modeling is used as an appropriate tool for the economic analysis of the sustainability of the time path. The dynamic game is a simple one, and incorporates the well known assumption that the starting point of the public debt model is the accounting identity interrelating public debt, the interest rate and the real government surplus exclusive of interest payments on public debt. In this setting, we consider as stock the public debt and the stress of the regulator as the driver in raising the nation’s primary surplus. Any surplus increase is not only dependent on government measures but is also dependent on the known “culture of corruption” and on tax evasion. Consequently, the process of surpluses’ augmentation should be a function of these two factors. Nash and Stackelberg differential game are used to explore strategic interactions. In the Nash equilibrium, establishment of cyclical strategies during the game between the group of people involved in illegal activities of corruption and tax evasion on the one hand and the government in the other, requires that the discount rate of the group of people involved in illegal actions must be greater than the government’s discount rate. That is, the group of corrupt officials and tax evaders must be more impatient than the government. In the case of hierarchical setting analytical expressions of the strategies and the steady-state value of public debt are provided. Furthermore, a number of propositions are stated.