Sunspots and Hopf bifurcations in continuous time endogenous growth models

Abstract

First we treat a three‐dimensional continuous time abstract stationary model that includes one predetermined variable and two non‐predetermined variables. We construct stationary sunspot equilibria in this model under the following two alternative conditions: (i) a steady state has two stable roots and one unstable root; and (ii) A closed orbit has a two‐dimensional manifold on which it is asymptotically stable. Next, we apply these results to the models due to Lucas and Romer that undergo Hopf bifurcations for some parameter values. We construct sunspot equilibria in these models.