Local stability in endogenous growth models

The local stability of balanced paths in endogenous growth models is investigated. Under the fulfillment of transversality conditions, a general instability result is established. It has been proved that models with one state variable are completely unstable, whereas two alternatives are possible in models with two states: complete instability or saddle point property. Balanced paths of models with three state variables can either be completely unstable, satisfy the saddle point property with a one-dimensional stable manifold, or have a two-dimensional manifold approaching them. Necessary and sufficient conditions for the saddle point property to occur are given. Transversality conditions guarantee that closed contours and periodic sinuoidal motions around the balanced path are ruled out.