Debt policy rule, productive government spending, and multiple growth paths: a note

In a very interesting endogenous growth model, Futagami, Iwaisako, and Ohdoi [Macroeconomic Dynamics 12 (2008), 445-462] study the long-run growth effect of borrowing for public investment. Their model exhibits (i) the ltiplicity of balanced growth paths (BGPs) in the long run (two steady states) and (ii) a possible indeterminacy of the transition path to the high-growth BGP. The goal of this note is to show that their results depend on a sharp assumption, namely the definition of the public debt target as a ratio to private capital. If the target is defined in terms of public debt-to-GDP ratio, both results vanish: the model exhibits a unique BGP (no multiplicity) and the adjustment path to this unique equilibrium is determinate (no indeterminacy)