What is it about?
We analyze the conditions for the structural stability of a fractional order IS-LM-AS dynamic model with adaptive expectations. It is a generalization of our previous research lately published in the literature. We also present the conditions that the structural parameters of the model must meet for the economic system to present a periodic movement when the critical value of the fractional order of the system, q*, guarantees the presence of a degenerate Hopf bifurcation. The theoretical analysis is complemented with numerical simulations of the phase portraits in the three-dimensional space of the set of real numbers and of the temporal trajectories of the solutions of the model in MATLAB software. Lastly, our qualitative results show that all the structural parameters of the model are essential in determining its global asymptotic stability and Hopf bifurcation.
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Why is it important?
To analyze macroeconomic fluctuations in a closed economy, we recently developed a dynamic IS-LM-AS model with adaptive inflation expectations. To do this, we analyzed theoretically and numerically as well as qualitatively and quantitatively the structural stability of the model using Ordinary Differential Equations (ODEs) techniques. We found that the stability of the model depended solely on two of its parameters: the adaptive expectations parameter and the parameter that represents the percentage change in the demand for real balances in terms of an absolute change in the nominal interest rate. The cause behind this is because ODEs do not contemplate the Memory Effect (ME) of the economic variables involved in the model. In this paper, in order to take into account the ME, we considering fractional derivatives instead of derivatives of integer order and we demonstrate that all model parameters intervene in the qualitative behavior of the model solutions, which considerably improves the result obtained in the model analyzed with ODEs.
Perspectives
As future lines of research we propose the following: 1. Develop an IS-LM-AS model of a non-linear nature that allows the appearance of chaos and/or fractals using Systems of Fractional Equations. 2. Incorporate delays in the dynamics of our fractional macroeconomic model.
Professor Ciro Eduardo Bazán Navarro
Universidad San Ignacio de Loyola
Read the Original
This page is a summary of: Qualitative behavior in a fractional order IS-LM-AS macroeconomic model with stability analysis, Mathematics and Computers in Simulation, March 2024, Elsevier,
DOI: 10.1016/j.matcom.2023.11.003.
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