Government spending in a model where debt effects output gap

In this paper I present a simple model of government spending where the level of government debt affects the output gap. The structure of the economy is specified such that the output gap has a structural part, which is a function of debt. Based on empirical research, the structural part is assigned a specific functional form. The government faces an optimization problem where they attempt to close the output gap. The optimal change in government debt is found by solving a nonlinear equation. Numerical results show that the optimal change in debt has nonlinear behaviour. The solution to the unconstrained problem is an alternating equilibrium, whereas the solution to the constrained problem is a non linear cycle around the government's upper bound of admissible debt.