Public debt stabilization via a stochastic differential game paradigm

Abstract

In this paper, we examine a public debt stabilization in a country under inflation targeting by arguing that bond yields are sensitive to inflation risks. Endogenously defining the convenience premium function, we focus on fiscal and monetary strategic interactions within an optimal control setting. The level of the debt-to-gross domestic produced (GDP) ratio and current inflation rate of the country are considered as the state variables in the game. We then focus on the convenience risk premium and rate of inflation as market-based disciplining devices, to articulate the Nash noncooperative equilibria, cooperative equilibria and Stackelberg equilibria via a feedback control strategy. We show that the outcome of the game depends on the parameters of the game, the type of equilibrium one considers and the decision horizon. When the current inflation rate follows an uncontrolled Ornstein–Uhlenbeck dynamic process, we highlight its effects on the growth rate of the debt ratio. Hence, our model provides a novel framework in which monetary and fiscal authorities can simultaneously achieve their individual interests, while achieving an optimal debt stabilization policy in the presence of inflation. We also highlight the need for governments to adopt policy-approaches which maintain the debt-to-GDP ratio under an inflation-dependent ceiling.