A Nonsmooth Extension of Samuelson’s Multiplier-Accelerator Model

Abstract

Dynamical-systems approaches have historically been used in business-cycle theory to generate sustained oscillations in macroeconomic variables. We aim to contribute to this literature by extending the original Samuelson multiplier-accelerator model with a discontinuous stabilization policy in terms of government expenditure. We show that the nonsmoothness yields dynamics in terms of periodic orbits and irregular fluctuations, not found in the original Samuelson model. We also note with particular interest that our model is able to generate localized nonstationary dynamics, which is in contrast to the most standard models found in the literature.