In the analysis of endogenous growth models often projections are used which map the balanced growth path into a single point. This is done in order to draw conclusions about the stability of the system or the determinacy of transition paths. This procedure hinges on the homogeneity of the models under consideration, whereas the possible existence of a balanced growth path or a more general asymptotic attractor does not. Furthermore, exponential asymptotic stability cannot be proved on the basis of a model reduced by projection. We show that one has to be careful in drawing conclusions from the projected system in order to judge upon the behavior near the balanced growth path. And with two standard examples of endogenous growth we demonstrate an analytical method to study exponential stability in the full model.
