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A dynamic IS-LM model with delayed taxation revenues

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  • 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
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    1. 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.
    2. Sasakura, Kazuyuki, 1994. "On the dynamic behavior of Schinasi's business cycle model," Journal of Macroeconomics, Elsevier, vol. 16(3), pages 423-444.
    3. Kind, Christoph, 1999. "Remarks on the economic interpretation of Hopf bifurcations," Economics Letters, Elsevier, vol. 62(2), pages 147-154, February.
    4. 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.
    5. 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.
    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. Manfredi, Piero & Fanti, Luciano, 2004. "Cycles in dynamic economic modelling," Economic Modelling, Elsevier, vol. 21(3), pages 573-594, May.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. Marek Szydlowski & Adam Krawiec, 2001. "Scientific cycle model with delay," Scientometrics, Springer;Akadémiai Kiadó, vol. 52(1), pages 83-95, September.
    13. 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.
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