Relaxation oscillations in slow–fast IS–LM economic models

Abstract

We consider the dynamics of the IS–LM economic model, which is a fundamental macroeconomic model describing the relationship between interest rates and assets market. There is generally a long time lag between changes in the interest rate and the consequential effects on the economy. Therefore, most central banks change the interest rates slowly, which yields a slow–fast IS–LM model. Using geometric singular perturbation theory, we establish the sufficient and necessary conditions on the existence of relaxation oscillations for the slow–fast IS–LM model. We also apply our abstract genericity results to study some concrete particular slow–fast IS–LM models. Numerical simulations are presented to validate the theoretical results.