Indeterminacy and Stability in a ModiÞed Romer Model

This paper considers the well known Romer model of endogenous technological change and its extension where different intermediate capital goods are complementary, introduced in (Benhabib, Perli, and Xie 1994). They have shown that this modiÞcation allows indeterminate steady state for relatively mild degrees of the complementarity. The authors were able to derive analytically sufficient conditions for the indeterminacy and to Þnd speciÞc parameter values producing the indeterminate steady state. For the modiÞed Romer model of (Benhabib, Perli, and Xie 1994), I derive necessary and sufficient conditions for the steady state to be interior and strictly positive. I show that Hopf bifurcation to the absolutely stable steady state is impossible and the steady state is determinate if the model parameter values belong to a certain set. Considering a simpliÞed version of the model, I calculate necessary conditions for a Hopf bifurcation in one special case and show that it is impossible in another. Using numerical algorithm for multigoal optimization, I obtain several sets of parameter values leading to the loss of stability of the indeterminate steady state through Hopf bifurcation.