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Indeterminacy and Stability in a Modified Romer Model

  • Sergey Slobodyan


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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Paper provided by The Center for Economic Research and Graduate Education - Economics Institute, Prague in its series CERGE-EI Working Papers with number wp205.

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Date of creation: Dec 2002
Date of revision:
Handle: RePEc:cer:papers:wp205
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  1. Paul Romer, 1989. "Endogenous Technological Change," NBER Working Papers 3210, National Bureau of Economic Research, Inc.
  2. Arnold, Lutz G., 2000. "Stability of the Market Equilibrium in Romer's Model of Endogenous Technological Change: A Complete Characterization," Journal of Macroeconomics, Elsevier, vol. 22(1), pages 69-84, January.
  3. 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.
  4. Benhabib, Jess & Farmer, Roger E.A., 1999. "Indeterminacy and sunspots in macroeconomics," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 6, pages 387-448 Elsevier.
  5. Benhabib, Jess & Miyao, Takahiro, 1981. "Some New Results on the Dynamics of the Generalized Tobin Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 22(3), pages 589-96, October.
  6. Lutz G. Arnold, 2000. "Endogenous technological change: a note on stability," Economic Theory, Springer, vol. 16(1), pages 219-226.
  7. Benhabib, Jess & Perli, Roberto & Xie, Danyang, 1994. "Monopolistic competition, indeterminacy and growth," MPRA Paper 37411, University Library of Munich, Germany, revised 1994.
  8. 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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