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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
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    File URL: http://www2.ku.edu/~kuwpaper/2009Papers/201102.pdf
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    References listed on IDEAS

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    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. 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(05), pages 713-747, November.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. Zellner, Arnold & Israilevich, Guillermo, 2005. "Marshallian Macroeconomic Model: A Progress Report," Macroeconomic Dynamics, Cambridge University Press, vol. 9(02), pages 220-243, April.
    13. 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.
    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. 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.
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    Citations

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    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(08), 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(02), pages 482-503, March.
    4. repec:eee:joecas:v:10:y:2013:i:1:p:53-64 is not listed on IDEAS
    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. repec:spr:etbull:v:2:y:2014:i:1:d:10.1007_s40505-013-0024-2 is not listed on IDEAS
    7. 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.

    More about this item

    Keywords

    Marshallian Macroeconomic Model; Dynamic Entry/Exit; Hopf Bifurcation; Limit Cycles;

    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

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