Saddle Path Stability, Fluctuations, and Indeterminacy in Economic Growth

We present a macroeconomic growth model in which investment in physical capital exhibits positive externalities which raise the stock of knowledge. Treating physical capital and knowledge as two separate variables, we show that the model can generate endogenous growth. It is demonstrated that there exist at most two balanced growth paths (BGPs) with endogenous growth. If the BGP is unique it is always saddle-point stable. If there are two BGPs, the first is always stable in the saddle point sense, whereas the second cannot be a saddle point. Instead, the second is either totally stable, giving rise to local indeterminacy, or completely unstable. Further, we can demonstrate that a Hopf bifurcation may occur at the second BGP, leading to persistent fluctuations. Besides local indeterminacy, the model may also give rise to global indeterminacy.