Coupled Dynamics in a Phillips Machine Model of the Macroeconomy
In this paper it is claimed that the Phillips machine, contrary to what is sometimes believed, is a nonlinear mechanism. Phillips (1950) presented his machines, as formally described, with linear differential equations. In doing so, he fell into what Samuelson came later to define as the linearity dogma. It is argued here that the Phillips machines are not linear mechanisms but are coherent with a system of nonlinear difference-differential equations. Here, this system is in turn approximated with a set of nonlinear differential equations, which are isomorphic with the Hicks-Goodwin flexible multiplier accelerator models. Consistent with this conjecture and following a Goodwin-Phillips' suggestion, we have presented a «digital» simulation of two coupled would-be Phillips machines. Whether the data generated with the set of nonlinear difference equations is consistent with the observations emerging from the actual coupled Phillips machines could be verified by comparing the data emerging from the two systems - the digital and the analogue ones.
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