Stability switches in a linear IS-LM model having dual time delay

Abstract

Keynesian theory focuses on identifying the money supply as a constant.\@ But recent trends show that post-Keynesian theory emphasizes the endogeneity of the money supply. Thus, we will be considering the money supply as an endogenous variable i.e., not a constant.\@ Taking in account the business cycle Investment Savings-liquidity preference Money supply (IS-LM) model, we incorporated dual time delays in the capital accumulation equation. Thus, the model we propose is a four-dimensional system with dual delay inspired from new Keynesian theory. In order to keep the model simple yet approachable we have considered a linear model. While scrutinizing the system, we evaluate equilibrium points and then consider three separate cases according to the delays viz., when both delays are absent, only one delay is absent and no delay is absent. Linear Stability analysis is done around the equilibrium point. Delays have been observed to cause stability switches in the dynamic behavior of the system. Our system thus experiences switches in stability and undergoes Hopf bifurcation when the parameter time delay crosses a critical value. The delay dependent stability regions are identified. Lastly, numerical simulations are executed to validate our analyses.