IDEAS home Printed from https://ideas.repec.org/p/kan/wpaper/201306.html
   My bibliography  Save this paper

Bifurcation Analysis of an Endogenous Growth Model

Author

Listed:
  • William Barnett

    (Department of Economics, The University of Kansas)

  • Taniya Ghosh

    (Indira Gandhi Institute of Development Research, Reserve Bank of India, Mumbai)

Abstract

This paper analyzes the dynamics of a variant of Jones (2002) semi-endogenous growth model within the feasible parameter space. We derive the long run growth rate of the economy and do a detailed bifurcation analysis of the equilibrium. We show the existence of codimension-1 bifurcations (Hopf, Branch Point, Limit Point of Cycles, and Period Doubling) and codimension-2 (Bogdanov-Takens and Generalized Hopf) bifurcations within the feasible parameter range of the model. It is important to recognize that bifurcation boundaries do not necessarily separate stable from unstable solution domains. Bifurcation boundaries can separate one kind of unstable dynamics domain from another kind of unstable dynamics domain, or one kind of stable dynamics domain from another kind (called soft bifurcation), such as bifurcation from monotonic stability to damped periodic stability or from damped periodic to damped multiperiodic stability. There are not only an infinite number of kinds of unstable dynamics, some very close to stability in appearance, but also an infinite number of kinds of stable dynamics. Hence subjective prior views on whether the economy is or is not stable provide little guidance without mathematical analysis of model dynamics. When a bifurcation boundary crosses the parameter estimates’ confidence region, robustness of dynamical inferences from policy simulations are compromised, when conducted, in the usual manner, only at the parameters’ point estimates.

Suggested Citation

  • William Barnett & Taniya Ghosh, 2013. "Bifurcation Analysis of an Endogenous Growth Model," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201306, University of Kansas, Department of Economics, revised Oct 2013.
  • Handle: RePEc:kan:wpaper:201306
    as

    Download full text from publisher

    File URL: http://www2.ku.edu/~kuwpaper/2013Papers/201306.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. William Barnett & Evgeniya Duzhak, 2010. "Empirical assessment of bifurcation regions within New Keynesian models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 45(1), pages 99-128, October.
    2. Benhabib Jess & Perli Roberto, 1994. "Uniqueness and Indeterminacy: On the Dynamics of Endogenous Growth," Journal of Economic Theory, Elsevier, vol. 63(1), pages 113-142, June.
    3. Lutz G. Arnold, 2000. "Endogenous technological change: a note on stability," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 16(1), pages 219-226.
    4. Banerjee, Sanjibani & A. Barnett, William & A. Duzhak, Evgeniya & Gopalan, Ramu, 2011. "Bifurcation analysis of Zellner's Marshallian Macroeconomic Model," Journal of Economic Dynamics and Control, Elsevier, vol. 35(9), pages 1577-1585, September.
    5. 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.
    6. Barnett William A. & He Yijun, 1999. "Stability Analysis of Continuous-Time Macroeconometric Systems," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 3(4), pages 1-22, January.
    7. Barnett, William A. & Eryilmaz, Unal, 2013. "Hopf bifurcation in the Clarida, Gali, and Gertler model," Economic Modelling, Elsevier, vol. 31(C), pages 401-404.
    8. Charles I. Jones, 2002. "Sources of U.S. Economic Growth in a World of Ideas," American Economic Review, American Economic Association, vol. 92(1), pages 220-239, March.
    9. Mondal, Debasis, 2008. "Stability analysis of the Grossman-Helpman model of endogenous product cycles," Journal of Macroeconomics, Elsevier, vol. 30(3), pages 1302-1322, September.
    10. N. Gregory Mankiw & David Romer & David N. Weil, 1992. "A Contribution to the Empirics of Economic Growth," The Quarterly Journal of Economics, Oxford University Press, vol. 107(2), pages 407-437.
    11. Grossman, Gene M & Helpman, Elhanan, 1991. "Endogenous Product Cycles," Economic Journal, Royal Economic Society, vol. 101(408), pages 1214-1229, September.
    12. Romer, Paul M, 1990. "Endogenous Technological Change," Journal of Political Economy, University of Chicago Press, vol. 98(5), pages 71-102, October.
    13. Barnett, William A. & He, Yijun, 2002. "Stabilization Policy As Bifurcation Selection: Would Stabilization Policy Work If The Economy Really Were Unstable?," Macroeconomic Dynamics, Cambridge University Press, vol. 6(5), pages 713-747, November.
    14. Gong, Gang & Greiner, Alfred & Semmler, Willi, 2004. "The Uzawa-Lucas model without scale effects: theory and empirical evidence," Structural Change and Economic Dynamics, Elsevier, vol. 15(4), pages 401-420, December.
    15. Barnett, William A. & Eryilmaz, Unal, 2016. "An Analytical And Numerical Search For Bifurcations In Open Economy New Keynesian Models," Macroeconomic Dynamics, Cambridge University Press, vol. 20(2), pages 482-503, March.
    16. Bucci, Alberto, 2008. "Population growth in a model of economic growth with human capital accumulation and horizontal R&D," Journal of Macroeconomics, Elsevier, vol. 30(3), pages 1124-1147, September.
    17. Eric M. Leeper & Christopher A. Sims, 1994. "Toward a Modern Macroeconomic Model Usable for Policy Analysis," NBER Chapters, in: NBER Macroeconomics Annual 1994, Volume 9, pages 81-140, National Bureau of Economic Research, Inc.
    18. Grossman, Gene M & Helpman, Elhanan, 1991. "Endogenous Product Cycles," Economic Journal, Royal Economic Society, vol. 101(408), pages 1214-1229, September.
    19. Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Barnett, William A. & Chen, Guo, 2015. "Bifurcation of Macroeconometric Models and Robustness of Dynamical Inferences," Foundations and Trends(R) in Econometrics, now publishers, vol. 8(1-2), pages 1-144, September.
    2. Bosi, Stefano & Desmarchelier, David, 2018. "Natural cycles and pollution," Mathematical Social Sciences, Elsevier, vol. 96(C), pages 10-20.
    3. Barnett, William A. & Bella, Giovanni & Ghosh, Taniya & Mattana, Paolo & Venturi, Beatrice, 2019. "Shilnikov Chaos, Low Interest Rates, And New Keynesian Macroeconomics," Studies in Applied Economics 142, The Johns Hopkins Institute for Applied Economics, Global Health, and the Study of Business Enterprise.
    4. Growiec, Jakub & McAdam, Peter & Mućk, Jakub, 2018. "Endogenous labor share cycles: Theory and evidence," Journal of Economic Dynamics and Control, Elsevier, vol. 87(C), pages 74-93.
    5. William A. Barnett & Taniya Ghosh, 2014. "Stability analysis of Uzawa–Lucas endogenous growth model," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(1), pages 33-44, April.
    6. Meir Russ, 2017. "The Trifurcation of the Labor Markets in the Networked, Knowledge-Driven, Global Economy," Journal of the Knowledge Economy, Springer;Portland International Center for Management of Engineering and Technology (PICMET), vol. 8(2), pages 672-703, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. William A. Barnett & Taniya Ghosh, 2014. "Stability analysis of Uzawa–Lucas endogenous growth model," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(1), pages 33-44, April.
    2. Mondal, Debasis, 2008. "Stability analysis of the Grossman-Helpman model of endogenous product cycles," Journal of Macroeconomics, Elsevier, vol. 30(3), pages 1302-1322, September.
    3. Barnett, William A. & Eryilmaz, Unal, 2013. "Hopf bifurcation in the Clarida, Gali, and Gertler model," Economic Modelling, Elsevier, vol. 31(C), pages 401-404.
    4. Hénock Katuala, 2020. "Intraregional Openness and Dynamics of outgoing growth [Ouverture intra-régionale et Dynamique de la croissance extravertie]," Working Papers hal-02540689, HAL.
    5. Saïd Hanchane & Abdouni Abdeljabbar, 2004. "La dynamique de la croissance économique et de l'ouverture dans les pays en voie de développement : quelques investigations empiriques à partir des données de Panel," Working Papers halshs-00083720, HAL.
    6. Bucci, Alberto, 2013. "Returns to specialization, competition, population, and growth," Journal of Economic Dynamics and Control, Elsevier, vol. 37(10), pages 2023-2040.
    7. Lutz G. Arnold, 2006. "The Dynamics of the Jones R&D Growth Model," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 9(1), pages 143-152, January.
    8. Klaus Waelde, 1994. "Transitional dynamics, convergence and international capital flows in two-country models of innovation and growth," International Trade 9403002, University Library of Munich, Germany, revised 03 Jan 1996.
    9. Barnett, William A. & Chen, Guo, 2015. "Bifurcation of Macroeconometric Models and Robustness of Dynamical Inferences," Foundations and Trends(R) in Econometrics, now publishers, vol. 8(1-2), pages 1-144, September.
    10. Arnold, Lutz G., 2003. "Growth in stages," Structural Change and Economic Dynamics, Elsevier, vol. 14(1), pages 55-74, March.
    11. Panagiotis PEGKAS & Constantinos TSAMADIAS, 2015. "Does Formal Education At All Levels Cause Economic Growth? Evidence From Greece," Review of Economic and Business Studies, Alexandru Ioan Cuza University, Faculty of Economics and Business Administration, issue 15, pages 9-32, June.
    12. Alejandro Diaz-Bautista, 2005. "Convergence and Economic Growth considering Human Capital and R&D Spillovers Convergencia y Crecimiento Economico en Mexico considerando al Capital Humano y derrames en Investigacion y Desarrollo," Urban/Regional 0506012, University Library of Munich, Germany.
    13. Tang, Rongsheng & Wang, Gaowang & Wang, Jin, 2019. "On the transitional dynamics and policy analysis of the Romer (1990) model," MPRA Paper 96132, University Library of Munich, Germany.
    14. Stephen Turnovsky, 2000. "Growth in an Open Economy: Some Recent Developments," Discussion Papers in Economics at the University of Washington 0015, Department of Economics at the University of Washington.
    15. Bloom, David E. et.al., 2013. "Economic impact of non-communicable disease in China and India: Estimates, projections and comparisons," Working Papers 300, Institute for Social and Economic Change, Bangalore.
    16. Cem Ertur & Wilfried Koch, 2006. "The Role of Human Capital and Technological Interdependence in Growth and Convergence Processes: International Evidence," DEGIT Conference Papers c011_029, DEGIT, Dynamics, Economic Growth, and International Trade.
    17. Sequeira, Tiago Neves, 2011. "R&D Spillovers In An Endogenous Growth Model With Physical Capital, Human Capital, And Varieties," Macroeconomic Dynamics, Cambridge University Press, vol. 15(2), pages 223-239, April.
    18. Jochen Hartwig, 2009. "A panel Granger-causality test of endogenous vs. exogenous growth," KOF Working papers 09-231, KOF Swiss Economic Institute, ETH Zurich.
    19. Konstantinos Angelopoulos & Jim Malley & Apostolis Philippopoulos, 2007. "Public Education Expenditure, Growth and Welfare," CESifo Working Paper Series 2037, CESifo.
    20. Maria João Ribeiro, 2003. "Endogenous Growth: Analytical Review of its Generating Mechanisms," NIPE Working Papers 4/2003, NIPE - Universidade do Minho.

    More about this item

    Keywords

    bifurcation; endogenous growth; Jones growth model; Hopf; inference robustness; dynamics; stability.;
    All these keywords.

    JEL classification:

    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • E1 - Macroeconomics and Monetary Economics - - General Aggregative Models

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kan:wpaper:201306. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Professor Zongwu Cai). General contact details of provider: https://edirc.repec.org/data/deuksus.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.