Threshold nonlinearities and asymmetric endogenous business cycles

This paper presents a model of endogenous business cycles in the presence of knowledge spillovers and a time-to-build restriction. There are two key assumptions that characterize the model: (i) the payoff to each firm depends on the aggregate state of knowledge, and (ii) the innovation of a project is time-consuming. Under those assumptions, a simple structure is shown to be described by a piecewise linear difference equation with a discontinuity. We show that the resulting dynamics generated by such a dynamical system leads to an asymmetric periodic cycle of arbitrary period that appears to switch repeatedly between different regimes.