What is it about?
In this article, we carry out the structural analysis of an IS-LM-AS macroeconomic model with adaptive inflation expectations, exploring the presence of a possible local bifurcation. We prove that the model is structurally unstable when the speed with which economic agents adjust their expectations about future inflation is equal to the inverse of the semi-elasticity of real money demand with respect to the nominal interest rate since the periodic solutions are lost when the adaptive expectations parameter suffer any small change, ceteris paribus. Additionally, the phase portraits of the instantaneous rate of change of the real interest rate, the inflation rate, and the instantaneous rate of change of the inflation rate are numerically simulated in with MATLAB for three asymptotically and locally stable cases and for the degenerate Hopf bifurcation. Finally, our results show that, specifically, in the case of pure conjugate complex eigenvalues, the economy could enter periods of an inflationary/deflationary spiral when the adaptive expectations parameter is of greater magnitude to the inverse of the semi-elasticity of real money demand balances with respect to the nominal interest rate, regardless of its initial state.
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Why is it important?
Our model permit us examine the possible qualitative changes in the dynamic nature of the model’s phase paths in the neighborhood of its equilibrium point as a consequence of variation in any of its parameters to study the possibility of the presence of a local bifurcation.
Perspectives
As a potential line of future research, the option of using functional forms that incorporate nonlinear elements into the model remains open so that it is possible to analyze under what circumstances a single limit cycle could arise, which would allow the endogenous representation of the permanent periodic fluctuations that characterize the cycle of the main economic aggregates. Another line of future research is to consider dynamic IS-LM-AS models with fractional calculus and with delays to analyze their stability. There is very little literature on this subject.
Professor Ciro Eduardo Bazán Navarro
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Read the Original
This page is a summary of: Structural Stability Analysis in a Dynamic IS-LM-AS Macroeconomic Model with Inflation Expectations, International Journal of Differential Equations, October 2022, Hindawi Publishing Corporation,
DOI: 10.1155/2022/5026061.
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