Indeterminacy and Stability in a Modified Romer Model: A General Case

This paper studies the dynamical properties of an extension of the well—known Romer model of endogenous growth introduced by Benhabib, Perli, and Xie (1994). This model differs from the Romer model by introducing complementarity of intermediate capital goods. It allows an indeterminate steady state for relatively mild degrees of the complementarity. We derive necessary and sufficient conditions for the steady state to be interior and strictly positive, which extend those discussed in Benhabib, Perli, and Xie (1994). We show that Hopf bifurcation to the absolutely stable steady state is impossible and that the steady state is determinate if the model parameter values belong to a certain set. For the set of parameter values that allows indeterminacy, we demonstrate the possibility of Hopf bifurcation using both analytical and numerical approaches. The indeterminate steady state can undergo Hopf bifurcation for a wide range of parameter values.