Delay Dynamics in a Classical IS‐LM Model with Tax Collections

Abstract An IS‐LM model is developed for the dynamics of income, interest rate and money stock with delay in tax revenue. The main aim is to show that the delay matters in macro dynamics. Two different delays, fixed time delays and continuously distributed time delays, are considered explicitly and described by delay‐differential equations and integro‐differential equations, respectively. Conditions for the local stability of the two models are derived and compared. The destabilizing effects caused by the delay are numerically examined. Appearance of wide spectrum of dynamics ranging from simple cyclic oscillations to complex dynamics is described through Hopf bifurctions.