Controlling Endogenous Cycles in an OLG Economy by the OGY Method

We show that very complicated dynamics arising, e.g. from an overlapping generations model (OLG) with production and an endogenous intertemporal decision between labour and leisure, which produces hyperchaos (both eigenvalues with modulus higher than 1), can in fact be controlled or managed with relative simplicity. The aperiodic and very complicated motion that stems from this model can be subject to control by very small perturbations in its parameters and turned into a stable steady state or into a regular cycle. Therefore, the system can be controlled without a change of its original properties. To perform the control of chaos in this economic model we apply the pole-placement technique, developed by Romeiras, Grebogi, Ott and Dayawansa (1992). The application of control methods to chaotic economic dynamics may raise serious reservations, at least on mathematical and logical grounds, to some recent views on economics which have argued that economic policy becomes useless in the presence of chaotic motion (and thus, that the performance of the economic system cannot be improved by public intervention, i.e., that the amplitude of cycles cannot be controlled or reduced). In fact, the fine tuning of the system (that is, the control) can be performed without having to rely only on infinitesimal accuracy in the perturbation to the system, because the control can be performed with larger or smaller perturbations, but neither too large (because these would lead to a different fixed point of the system, therefore modifying its original nature), nor too small because the control becomes too ineffcient.