IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v25y2005i1p233-244.html
   My bibliography  Save this article

A dynamic IS-LM model with delayed taxation revenues

Author

Listed:
  • De Cesare, Luigi
  • Sportelli, Mario

Abstract

Some recent contributions to Economic Dynamics have shown a new interest for delay differential equations. In line with these approaches, we re-proposed the problem of the existence of a finite lag between the accrual and the payment of taxes in a framework where never this type of lag has been considered: the well known IS-LM model. The qualitative study of the system of functional (delay) differential equations shows that the finite lag may give rise to a wide variety of dynamic behaviours. Specifically, varying the length of the lag and applying the “stability switch criteria”, we prove that the equilibrium point may lose or gain its local stability, so that a sequence of alternated stability/instability regions can be observed if some conditions hold. An important scenario arising from the analysis is the existence of limit cycles generated by sub-critical and supercritical Hopf bifurcations. As numerical simulations confirm, if multiple cycles exist, the so called “crater bifurcation” can also be detected. Economic considerations about a stylized policy analysis stand by qualitative and numerical results in the paper.

Suggested Citation

  • De Cesare, Luigi & Sportelli, Mario, 2005. "A dynamic IS-LM model with delayed taxation revenues," Chaos, Solitons & Fractals, Elsevier, vol. 25(1), pages 233-244.
    • Handle: RePEc:eee:chsofr:v:25:y:2005:i:1:p:233-244
    DOI: 10.1016/j.chaos.2004.11.044
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077904007519
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2004.11.044?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Semmler, Willi & Sieveking, Malte, 1993. "Nonlinear liquidity-growth dynamics with corridor-stability," Journal of Economic Behavior & Organization, Elsevier, vol. 22(2), pages 189-208, October.
    2. Asea, Patrick K. & Zak, Paul J., 1999. "Time-to-build and cycles," Journal of Economic Dynamics and Control, Elsevier, vol. 23(8), pages 1155-1175, August.
    3. Avinash Dixit, 1991. "The Optimal Mix of Inflationary Finance and Commodity Taxation with Collection Lags," IMF Staff Papers, Palgrave Macmillan, vol. 38(3), pages 643-654, September.
    4. Ioannides, Yannis M. & Taub, Bart, 1992. "On dynamics with time-to-build investment technology and non-time-separable leisure," Journal of Economic Dynamics and Control, Elsevier, vol. 16(2), pages 225-241, April.
    5. Sasakura, Kazuyuki, 1994. "On the dynamic behavior of Schinasi's business cycle model," Journal of Macroeconomics, Elsevier, vol. 16(3), pages 423-444.
    6. Garry J. Schinasi, 1981. "A Nonlinear Dynamic Model of Short Run Fluctuations," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 48(4), pages 649-656.
    7. Schinasi, Garry J., 1982. "Fluctuations in a dynamic, intermediate-run IS-LM model: Applications of the Poincare-Bendixon theorem," Journal of Economic Theory, Elsevier, vol. 28(2), pages 369-375, December.
    8. Kind, Christoph, 1999. "Remarks on the economic interpretation of Hopf bifurcations," Economics Letters, Elsevier, vol. 62(2), pages 147-154, February.
    9. 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 589-596, October.
    10. Manfredi, Piero & Fanti, Luciano, 2004. "Cycles in dynamic economic modelling," Economic Modelling, Elsevier, vol. 21(3), pages 573-594, May.
    11. Burmeister, Edwin & Turnovsky, Stephen J, 1976. "The Specification of Adaptive Expectations in Continuous Time Dynamic Economic Models," Econometrica, Econometric Society, vol. 44(5), pages 879-905, September.
    12. Grasman, Johan & Wentzel, Jolanda J., 1994. "Co-existence of a limit cycle and an equilibrium in Kaldor's business cycle model and its consequences," Journal of Economic Behavior & Organization, Elsevier, vol. 24(3), pages 369-377, August.
    13. Marek Szydlowski & Adam Krawiec, 2001. "Scientific cycle model with delay," Scientometrics, Springer;Akadémiai Kiadó, vol. 52(1), pages 83-95, September.
    Full references (including those not matched with items on IDEAS)

    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. Hiroki Murakami, 2019. "A note on the “unique” business cycle in the Keynesian theory," Metroeconomica, Wiley Blackwell, vol. 70(3), pages 384-404, July.
    2. Dohtani, Akitaka, 2010. "A growth-cycle model of Solow-Swan type, I," Journal of Economic Behavior & Organization, Elsevier, vol. 76(2), pages 428-444, November.
    3. Akio Matsumoto & Ferenc Szidarovszky, 2016. "Delay Dynamics in a Classical IS-LM Model with Tax Collections," Metroeconomica, Wiley Blackwell, vol. 67(4), pages 667-697, November.
    4. Fanti, Luciano & Manfredi, Piero, 2007. "Chaotic business cycles and fiscal policy: An IS-LM model with distributed tax collection lags," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 736-744.
    5. Murakami, Hiroki, 2020. "Monetary policy in the unique growth cycle of post Keynesian systems," Structural Change and Economic Dynamics, Elsevier, vol. 52(C), pages 39-49.
    6. De Cesare, Luigi & Sportelli, Mario, 2022. "A non-linear approach to Kalecki’s investment cycle," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 57-70.
    7. Yüksel, Mustafa Kerem, 2011. "Capital dependent population growth induces cycles," Chaos, Solitons & Fractals, Elsevier, vol. 44(9), pages 759-763.
    8. Giovanni Bella & Paolo Mattana & Beatrice Venturi, 2013. "Kaldorian assumptions and endogenous fluctuations: a note on Schinasi’s IS–LM model," International Review of Economics, Springer;Happiness Economics and Interpersonal Relations (HEIRS), vol. 60(1), pages 71-81, March.
    9. Kitagawa, Akiomi & Shibata, Akihisa, 2001. "Long gestation in an overlapping generations economy: endogenous cycles and indeterminacy of equilibria," Journal of Mathematical Economics, Elsevier, vol. 35(1), pages 99-127, February.
    10. Valls, Claudia, 2012. "Rational integrability of a nonlinear finance system," Chaos, Solitons & Fractals, Elsevier, vol. 45(2), pages 141-146.
    11. Kind, Christoph, 1999. "Remarks on the economic interpretation of Hopf bifurcations," Economics Letters, Elsevier, vol. 62(2), pages 147-154, February.
    12. Murakami, Hiroki, 2014. "Keynesian systems with rigidity and flexibility of prices and inflation–deflation expectations," Structural Change and Economic Dynamics, Elsevier, vol. 30(C), pages 68-85.
    13. Neamţu, Mihaela & Opriş, Dumitru & Chilaˇrescu, Constantin, 2007. "Hopf bifurcation in a dynamic IS–LM model with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 519-530.
    14. Datta, Soumya, 2013. "Robustness and Stability of Limit Cycles in a Class of Planar Dynamical Systems," MPRA Paper 50814, University Library of Munich, Germany.
    15. Ralph Winkler, 2008. "Optimal compliance with emission constraints: dynamic characteristics and the choice of technique," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 39(4), pages 411-432, April.
    16. Joanne S. McGarry & Marcus J. Chambers, 2004. "Party formation and coalitional bargaining in a model of proportional representation," Discussion Papers 04-07, Department of Economics, University of Birmingham.
    17. Chen, Wei-Ching, 2008. "Nonlinear dynamics and chaos in a fractional-order financial system," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1305-1314.
    18. Bazán Navarro, Ciro Eduardo & Benazic Tomé, Renato Mario, 2024. "Qualitative behavior in a fractional order IS-LM-AS macroeconomic model with stability analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 217(C), pages 425-443.
    19. Willi Semmler & Fabio Della Rossa & Giuseppe Orlando & Gabriel R. Padro Rosario & Levent Kockesen, 2023. "Endogenous Economic Resilience, Loss of Resilience, Persistent Cycles, Multiple Attractors, and Disruptive Contractions," Working Papers 2309, New School for Social Research, Department of Economics.
    20. Chen, Wei-Ching, 2008. "Dynamics and control of a financial system with time-delayed feedbacks," Chaos, Solitons & Fractals, Elsevier, vol. 37(4), pages 1198-1207.

    More about this item

    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:eee:chsofr:v:25:y:2005:i:1:p:233-244. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.