Government Debt, Fiscal Rules and Singular Growth Dynamics

Abstract

A fiscal rule controlling the government surplus as a function of the deviation of the actual debt ratio from a target level is introduced in an otherwise benchmark endogenous growth model in which productive government expenditures are financed by taxes and government debt. This generates a feedback mechanism from the government debt ratio to expenditure that can generate impasse-singular dynamics, in the sense that rates of growth can become locally infinitely valued. We characterize locally the different impasse-singular dynamics that can exist and discuss their consequences for the existence and characterization of general equilibrium endogenous growth paths, for different parameterizations of the fiscal rule. We present some consequences of impasse-singular dynamics generated by particular fiscal rules, which are not present in regular models: existence of multiple over-determinate balanced growth paths (BGP), existence of constraints in the domain of existence of determinate equilibrium paths converging to a regular BGP, and the existence of singular BGP’s.