IDEAS home Printed from https://ideas.repec.org/a/spr/jecstr/v10y2021i1d10.1186_s40008-021-00239-3.html
   My bibliography  Save this article

Revisiting Samuelson’s models, linear and nonlinear, stability conditions and oscillating dynamics

Author

Listed:
  • Fabio Tramontana

    (Department DiMSEFA Università Cattolica del Sacro Cuore)

  • Laura Gardini

    (University of Urbino)

Abstract

In this work, we reconsider the dynamics of a few versions of the classical Samuelson’s multiplier–accelerator model for national economy. First we recall that the classical one with constant governmental expenditure, represented by a linear second-order difference equation, is able to generate oscillations converging to the equilibrium for a wide range of values of the parameters, and give its analytic solution for all the possible cases. A delayed version proposed in the recent literature, represented by a linear third-order difference equation, is also considered. We show that also this model is able to produce converging oscillations, and give a complete analysis of the stability region of the equilibrium. A new simple nonlinear model is proposed, showing that it keeps oscillatory behavior, although coupled with other dynamics related to global effects. Our analysis confirms that the seminal work of Samuelson and simple modifications of it, may give powerful tools in the study of the business cycles.

Suggested Citation

  • Fabio Tramontana & Laura Gardini, 2021. "Revisiting Samuelson’s models, linear and nonlinear, stability conditions and oscillating dynamics," Journal of Economic Structures, Springer;Pan-Pacific Association of Input-Output Studies (PAPAIOS), vol. 10(1), pages 1-15, December.
    • Handle: RePEc:spr:jecstr:v:10:y:2021:i:1:d:10.1186_s40008-021-00239-3
    DOI: 10.1186/s40008-021-00239-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1186/s40008-021-00239-3
    File Function: Abstract
    Download Restriction: no
    File URL: https://libkey.io/10.1186/s40008-021-00239-3?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Ioannis K. Dassios & Mel T. Devine, 2016. "A macroeconomic mathematical model for the national income of a union of countries with interaction and trade," Journal of Economic Structures, Springer;Pan-Pacific Association of Input-Output Studies (PAPAIOS), vol. 5(1), pages 1-15, December.
    2. Dassios, Ioannis K. & Baleanu, Dumitru I., 2018. "Caputo and related fractional derivatives in singular systems," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 591-606.
    3. Frank Westerhoff, 2006. "Samuelson's multiplier-accelerator model revisited," Applied Economics Letters, Taylor & Francis Journals, vol. 13(2), pages 89-92.
    4. Fernando Ortega & Maria Filomena Barros, 2020. "The Samuelson macroeconomic model as a singular linear matrix difference equation," Journal of Economic Structures, Springer;Pan-Pacific Association of Input-Output Studies (PAPAIOS), vol. 9(1), pages 1-10, December.
    5. Ioannis Dassios & Alexandros Zimbidis & Charalambos Kontzalis, 2014. "The Delay Effect in a Stochastic Multiplier–Accelerator Model," Journal of Economic Structures, Springer;Pan-Pacific Association of Input-Output Studies (PAPAIOS), vol. 3(1), pages 1-24, December.
    6. Gemmell, Norman, 1990. "Wagner's Law, Relative Prices and the Size of the Public Sector," The Manchester School of Economic & Social Studies, University of Manchester, vol. 58(4), pages 361-377, December.
    7. Maria Filomena Barros & Fernando Ortega, 2019. "An optimal equilibrium for a reformulated Samuelson economic discrete time system," Journal of Economic Structures, Springer;Pan-Pacific Association of Input-Output Studies (PAPAIOS), vol. 8(1), pages 1-10, December.
    8. Ilias Kostarakos & Stelios Kotsios, 2017. "Feedback policy rules for government spending: an algorithmic approach," Journal of Economic Structures, Springer;Pan-Pacific Association of Input-Output Studies (PAPAIOS), vol. 6(1), pages 1-10, December.
    9. Puu, Tonu & Gardini, Laura & Sushko, Irina, 2005. "A Hicksian multiplier-accelerator model with floor determined by capital stock," Journal of Economic Behavior & Organization, Elsevier, vol. 56(3), pages 331-348, March.
    10. Dollery, Brian & Singh, Sukhvinder, 1998. "A Note on the Empirical Analysis of Wagner's Law," Economic Analysis and Policy, Elsevier, vol. 28(2), pages 245-257, September.
    11. Dalla, Eleni & Varelas, Erotokritos, 2016. "An economic model for the interpretation of business cycles and the efficiency of monetary policy," The Journal of Economic Asymmetries, Elsevier, vol. 14(PA), pages 29-38.
    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. Yamina Soula & Hadi Jahanshahi & Abdullah A. Al-Barakati & Irene Moroz, 2023. "Dynamics and Global Bifurcations in Two Symmetrically Coupled Non-Invertible Maps," Mathematics, MDPI, vol. 11(6), pages 1-13, March.

    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. Vasileios Spyrakis & Stelios Kotsios, 2021. "Public debt dynamics: the interaction with national income and fiscal policy," Journal of Economic Structures, Springer;Pan-Pacific Association of Input-Output Studies (PAPAIOS), vol. 10(1), pages 1-22, December.
    2. Ioannis K. Dassios & Mel T. Devine, 2016. "A macroeconomic mathematical model for the national income of a union of countries with interaction and trade," Journal of Economic Structures, Springer;Pan-Pacific Association of Input-Output Studies (PAPAIOS), vol. 5(1), pages 1-15, December.
    3. Fernando Ortega & Maria Filomena Barros, 2020. "The Samuelson macroeconomic model as a singular linear matrix difference equation," Journal of Economic Structures, Springer;Pan-Pacific Association of Input-Output Studies (PAPAIOS), vol. 9(1), pages 1-10, December.
    4. Dalla, Eleni & Varelas, Erotokritos, 2016. "An economic model for the interpretation of business cycles and the efficiency of monetary policy," The Journal of Economic Asymmetries, Elsevier, vol. 14(PA), pages 29-38.
    5. Maria Filomena Barros & Fernando Ortega, 2019. "An optimal equilibrium for a reformulated Samuelson economic discrete time system," Journal of Economic Structures, Springer;Pan-Pacific Association of Input-Output Studies (PAPAIOS), vol. 8(1), pages 1-10, December.
    6. Paulo Reis Mourao & Irina Alina Popescu, 2022. "Revisiting a Macroeconomic Controversy: The Case of the Multiplier–Accelerator Effect," Economies, MDPI, vol. 10(10), pages 1-15, October.
    7. Dalla, Eleni & Varelas, Erotokritos, 2016. "Second-order accelerator of investment: The case of discrete time," International Review of Economics Education, Elsevier, vol. 21(C), pages 48-60.
    8. Todorova, Tamara & Kutrolli, Marin, 2019. "An Expanded Multiplier-Accelerator Model," MPRA Paper 107480, University Library of Munich, Germany.
    9. Wegener, Michael & Westerhoff, Frank & Zaklan, Georg, 2009. "A Metzlerian business cycle model with nonlinear heterogeneous expectations," Economic Modelling, Elsevier, vol. 26(3), pages 715-720, May.
    10. Jean-François Verne, 2021. "Relevance of Chaos and Strange Attractors in the Samuelson-Hicks Oscillator," Economic Thought, World Economics Association, vol. 10(1), pages 32-45, July.
    11. Robert Calvert Jump & Engelbert Stockhammer, 2023. "Building blocks of a heterodox business cycle theory," Journal of Post Keynesian Economics, Taylor & Francis Journals, vol. 46(2), pages 334-358, April.
    12. Matsumoto, Akio & Szidarovszky, Ferenc, 2015. "Nonlinear multiplier–accelerator model with investment and consumption delays," Structural Change and Economic Dynamics, Elsevier, vol. 33(C), pages 1-9.
    13. Ilias Kostarakos & Stelios Kotsios, 2017. "Feedback policy rules for government spending: an algorithmic approach," Journal of Economic Structures, Springer;Pan-Pacific Association of Input-Output Studies (PAPAIOS), vol. 6(1), pages 1-10, December.
    14. Dalla, Eleni, 2023. "Asymmetries in banking conduct: A Cournot - Bertrand model," Economics Letters, Elsevier, vol. 233(C).
    15. Gerasimos T. Soldatos, 2018. "Multiplier–Accelerator Interaction in the Presence of an Underground Economy and Taxation," Margin: The Journal of Applied Economic Research, National Council of Applied Economic Research, vol. 12(2), pages 244-256, May.
    16. Tramontana, F. & Gardini, L. & Ferri, P., 2010. "The dynamics of the NAIRU model with two switching regimes," Journal of Economic Dynamics and Control, Elsevier, vol. 34(4), pages 681-695, April.
    17. Tawfik, Ashraf M. & Abdelhamid, Hamdi M., 2021. "Generalized fractional diffusion equation with arbitrary time varying diffusivity," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    18. Westerhoff Frank H., 2006. "Nonlinear Expectation Formation, Endogenous Business Cycles and Stylized Facts," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 10(4), pages 1-17, December.
    19. Gerasimos T. Soldatos, 2021. "In/Estabilidad bajo el impuesto sobre la renta ideal y el impuesto sobre el consumo ideal," Cuadernos de Economía - Spanish Journal of Economics and Finance, Asociación Cuadernos de Economía, vol. 44(124), pages 33-42, Enero.
    20. Frank Westerhoff, 2006. "Samuelson's multiplier-accelerator model revisited," Applied Economics Letters, Taylor & Francis Journals, vol. 13(2), pages 89-92.

    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:spr:jecstr:v:10:y:2021:i:1:d:10.1186_s40008-021-00239-3. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.