Indeterminacy and Stability in a Modified 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 modification 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 find specific parameter values producing the indeterminate steady state. For the modified 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 simplified 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.
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- Paul Romer, 1989.
"Endogenous Technological Change,"
NBER Working Papers
3210, National Bureau of Economic Research, Inc.
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- Sergey Slobodyan, 2002.
"Indeterminacy and Stability in a Modified Romer Model,"
CERGE-EI Working Papers
wp205, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
- Slobodyan, Sergey, 2007. "Indeterminacy and stability in a modified Romer model," Journal of Macroeconomics, Elsevier, vol. 29(1), pages 169-177, March.
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- Benhabib, Jess & Perli, Roberto & Xie, Danyang, 1994. "Monopolistic competition, indeterminacy and growth," MPRA Paper 37411, University Library of Munich, Germany, revised 1994.
- Asada, Toichiro & Semmler, Willi & Novak, Andreas J., 1998. "Endogenous growth and the balanced growth equilibrium," Research in Economics, Elsevier, vol. 52(2), pages 189-212, June.
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