IDEAS home Printed from https://ideas.repec.org/p/kan/wpaper/201102.html
   My bibliography  Save this paper

Bifurcation Analysis of Zellner's Marshallian Macroeconomic Model

Author

Listed:
  • Sanjibani Banerjee

    (Department of Economics, The University of Kansas)

  • William Barnett

    (Department of Economics, The University of Kansas)

  • Evgeniya Duzhak

    (Department of Economics, Baruch College)

  • Ramu Gopalan

    (Department of Economics, Washington and Jefferson College)

Abstract

The Marshallian Macroeconomic Model in Zellner and Israilevich (2005) provides a novel way to examine sectoral dynamics through the introduction of a dynamic entry/exit equation in addition to the usual demand and supply functions found in models of this class. In this paper we examine the possibility of cyclical behavior in the Marshallian Macroeconomic Model and investigate the existence of a Hopf bifurcation with respect to the parameter in the entry/exit equation.

Suggested Citation

  • Sanjibani Banerjee & William Barnett & Evgeniya Duzhak & Ramu Gopalan, 2011. "Bifurcation Analysis of Zellner's Marshallian Macroeconomic Model," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201102, University of Kansas, Department of Economics, revised Apr 2011.
  • Handle: RePEc:kan:wpaper:201102
    as

    Download full text from publisher

    File URL: http://www2.ku.edu/~kuwpaper/2009Papers/201102.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. Gary Mongiovi & Christof Rühl (ed.), 1993. "Macroeconomic Theory," Books, Edward Elgar Publishing, number 322.
    3. Barnett, William A. & Duzhak, Evgeniya Aleksandrovna, 2008. "Non-robust dynamic inferences from macroeconometric models: Bifurcation stratification of confidence regions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3817-3825.
    4. Barnett, William A. & He, Susan, 2010. "Existence of singularity bifurcation in an Euler-equations model of the United States economy: Grandmont was right," Economic Modelling, Elsevier, vol. 27(6), pages 1345-1354, November.
    5. Grandmont, Jean-Michel, 1985. "On Endogenous Competitive Business Cycles," Econometrica, Econometric Society, vol. 53(5), pages 995-1045, September.
    6. He, Yijun & Barnett, William A., 2006. "Singularity bifurcations," Journal of Macroeconomics, Elsevier, vol. 28(1), pages 5-22, March.
    7. William Barnett, 2005. "Monetary Aggregation," Macroeconomics 0503017, University Library of Munich, Germany.
    8. William A. Barnett & Yijun He, 2002. "Bifurcations in Macroeconomic Models," Macroeconomics 0210006, University Library of Munich, Germany.
    9. 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.
    10. Boldrin, Michele & Woodford, Michael, 1990. "Equilibrium models displaying endogenous fluctuations and chaos : A survey," Journal of Monetary Economics, Elsevier, vol. 25(2), pages 189-222, March.
    11. 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.
    12. Benhabib, Jess & Nishimura, Kazuo, 1979. "The hopf bifurcation and the existence and stability of closed orbits in multisector models of optimal economic growth," Journal of Economic Theory, Elsevier, vol. 21(3), pages 421-444, December.
    13. Bergstrom, A. R. & Nowman, K. B. & Wymer, C. R., 1992. "Gaussian estimation of a second order continuous time macroeconometric model of the UK," Economic Modelling, Elsevier, vol. 9(4), pages 313-351, October.
    14. Zellner, Arnold & Israilevich, Guillermo, 2005. "The Marshallian macroeconomic model: A progress report," International Journal of Forecasting, Elsevier, vol. 21(4), pages 627-645.
    15. Benhabib, Jess & Day, Richard H., 1982. "A characterization of erratic dynamics in, the overlapping generations model," Journal of Economic Dynamics and Control, Elsevier, vol. 4(1), pages 37-55, November.
    16. Veloce, William & Zellner, Arnold, 1985. "Entry and empirical demand and supply analysis for competitive industries," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 459-471.
    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. Ngoie, Jacques Kibambe, 2014. "Federal research spending and innovation in the U.S. economy," Journal of Policy Modeling, Elsevier, vol. 36(3), pages 492-506.
    2. Barnett, William A. & Serletis, Apostolos & Serletis, Demitre, 2015. "Nonlinear And Complex Dynamics In Economics," Macroeconomic Dynamics, Cambridge University Press, vol. 19(8), pages 1749-1779, December.
    3. 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.
    4. Barnett, William A. & Ghosh, Taniya, 2013. "Bifurcation analysis of an endogenous growth model," The Journal of Economic Asymmetries, Elsevier, vol. 10(1), pages 53-64.
    5. Barnett, William A. & Eryilmaz, Unal, 2013. "Hopf bifurcation in the Clarida, Gali, and Gertler model," Economic Modelling, Elsevier, vol. 31(C), pages 401-404.
    6. 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.

    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. Barnett, William A. & He, Susan, 2010. "Existence of singularity bifurcation in an Euler-equations model of the United States economy: Grandmont was right," Economic Modelling, Elsevier, vol. 27(6), pages 1345-1354, November.
    2. 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.
    3. Barnett, William A. & Duzhak, Evgeniya Aleksandrovna, 2008. "Non-robust dynamic inferences from macroeconometric models: Bifurcation stratification of confidence regions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3817-3825.
    4. Barnett, William A. & Eryilmaz, Unal, 2013. "Hopf bifurcation in the Clarida, Gali, and Gertler model," Economic Modelling, Elsevier, vol. 31(C), pages 401-404.
    5. Brock, W.A. & Hommes, C.H., 1997. "Models of Compelxity in Economics and Finance," Working papers 9706, Wisconsin Madison - Social Systems.
    6. He, Yijun & Barnett, William A., 2006. "Singularity bifurcations," Journal of Macroeconomics, Elsevier, vol. 28(1), pages 5-22, March.
    7. William A. Barnett & Yijun He, 2002. "Bifurcations in Macroeconomic Models," Macroeconomics 0210006, University Library of Munich, Germany.
    8. Barnett, William A. & Duzhak, Evgeniya A., 2019. "Structural Stability Of The Generalized Taylor Rule," Macroeconomic Dynamics, Cambridge University Press, vol. 23(4), pages 1664-1678, June.
    9. Grandmont, Jean-Michel, 1998. "Introduction to Market Psychology and Nonlinear Endogenous Business Cycles," Journal of Economic Theory, Elsevier, vol. 80(1), pages 1-13, May.
    10. Angeletos, George-Marios & Calvet, Laurent-Emmanuel, 2005. "Incomplete-market dynamics in a neoclassical production economy," Journal of Mathematical Economics, Elsevier, vol. 41(4-5), pages 407-438, August.
    11. Brock, W.A. & Hommes, C.H. & Wagener, F.O.O., 2009. "More hedging instruments may destabilize markets," Journal of Economic Dynamics and Control, Elsevier, vol. 33(11), pages 1912-1928, November.
    12. Akhmet, Marat & Akhmetova, Zhanar & Fen, Mehmet Onur, 2014. "Chaos in economic models with exogenous shocks," Journal of Economic Behavior & Organization, Elsevier, vol. 106(C), pages 95-108.
    13. Philippe Michel & Alain Venditti & Claude Jessua, 1996. "Croissance optimale et cycles dans le modèle à générations imbriquées : un exemple," Revue Économique, Programme National Persée, vol. 47(3), pages 487-497.
    14. William A. Barnett & Yijun He & ., 1999. "Stabilization Policy as Bifurcation Selection: Would Keynesian Policy Work if the World Really were Keynesian?," Macroeconomics 9906008, University Library of Munich, Germany.
    15. Tvede Mich, 2009. "Fluctuations in Overlapping Generations Economies," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 9(1), pages 1-19, May.
    16. Simonovits, Andras, 1999. "Are there cycles in realistic overlapping cohorts models?," Structural Change and Economic Dynamics, Elsevier, vol. 10(2), pages 261-275, June.
    17. Barnett, William A. & Ghosh, Taniya, 2013. "Bifurcation analysis of an endogenous growth model," The Journal of Economic Asymmetries, Elsevier, vol. 10(1), pages 53-64.
    18. Calvet, Laurent-Emmanuel & Grandmont, Jean-Michel & Lemaire, Isabelle, 2018. "Aggregation of heterogenous beliefs, asset pricing, and risk sharing in complete financial markets," Research in Economics, Elsevier, vol. 72(1), pages 117-146.
    19. Luis A. Aguirre & Antonio Aguirre, 1997. "A tutorial introduction to nonlinear dynamics in economics," Nova Economia, Economics Department, Universidade Federal de Minas Gerais (Brazil), vol. 7(2), pages 9-47.
    20. Nijkamp, P. & Poot, J., 1991. "Lessons from non-linear dynamic economics," Serie Research Memoranda 0105, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.

    More about this item

    Keywords

    Marshallian Macroeconomic Model; Dynamic Entry/Exit; Hopf Bifurcation; Limit Cycles;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • L16 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Industrial Organization and Macroeconomics; Macroeconomic Industrial Structure

    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:201102. 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: http://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.