Probing the effects of fiscal policy delays in macroeconomic IS–LM model

In this paper, we address the effects of two fiscal policy delays on the dynamical analysis of macroeconomics. First, a time gap between the accrual of taxes and their payment is considered. Second, the time spent between the purchasing decisions and the actual expenditure is also taken into conside...

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Bibliographic Details
Published in:Computational & applied mathematics 2024-07, Vol.43 (5), Article 289
Main Authors: Rajpal, Akanksha, Bhatia, Sumit Kaur, Kumar, Praveen
Format: Article
Language:English
Subjects:
Applications of Mathematics
Centre manifold theory
Computational Mathematics and Numerical Analysis
Critical point
Differential equations
Fiscal policy
Hopf bifurcation
Macroeconomics
Mathematical Applications in Computer Science
Mathematical Applications in the Physical Sciences
Mathematical models
Mathematics
Mathematics and Statistics
Stability analysis
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Summary:In this paper, we address the effects of two fiscal policy delays on the dynamical analysis of macroeconomics. First, a time gap between the accrual of taxes and their payment is considered. Second, the time spent between the purchasing decisions and the actual expenditure is also taken into consideration. Since both these delays are significant in controlling macroeconomic conditions, this paper incorporates aforementioned delays into the IS–LM model. At first, a mathematical model is developed using delayed differential equations. Then a unique steady state solution is obtained. Around the equilibrium point, linear stability analysis is done. Also, the occurance of Hopf bifurcation is observed when delay crosses a critical point and switches in stability are also detected. Properties of Hopf bifurcation using center manifold theorem are discussed. Lastly, numerical simulations are run to verify our analysis. In this work, we considered a case study to perform simulation wherein GDP of India for last ten years is recorded for estimating some parameters. In different investment scenarios, numerical simulations corroborate the analytical findings of the model. Furthermore, rigorous analysis shows that adding the right mix of delays can help in maintaining/ regaining the stability after periods of instability, or even gaining stability in the long run.
ISSN:2238-3603
1807-0302
DOI:10.1007/s40314-024-02804-5