Indeterminacy in a two-sector endogenous growth model with productive government spending

We construct a two-sector endogenous growth model in which productive government spending is essential for sustaining an economy's long-run growth. It is shown that, like the original one-sector [Barro, R.J., 1990. Government spending in a simple model of endogenous growth. Journal of Political Economy 98, 103-125] model, the balanced growth path (BGP) equilibrium is unique under some conditions. Unlike Barro (1990), however, our two-sector framework exhibits transitional dynamics. In fact, when the intertemporal elasticity of substitution for consumption is large, around the BGP equilibrium, there is a continuum of equilibrium paths whose growth rates commonly converge to a balanced growth rate. That is, the BGP equilibrium is indeterminate.