A Test for Strong Hysteresis

The mathematical definition of systems with hysteresis, that is nonlinear input-output systems with memory, is different from the definition usually applied to economic systems. Economic theory and modelling practice have almost always specified simple dynamic systems with regular leads and lags in their responses, corresponding to input-output systems with unit or zero (or at least stable) roots. These models cannot capture the `selective memoryʹ feature of hysteretic behaviour, that is, the influence only of certain past events (typically, non-dominated sequences of previous peaks and troughs). There is therefore a difficulty in testing for and validating economic models containing hysteretic behaviour; appropriate empirical tests have not been developed. In particular, the usual unit vs. zero (or stable) root tests used in econometric analysis are unable to detect hysteretic behaviour or to distinguish it from more conventional economic behaviour. The purpose of this paper is to propose a new way of testing for hysteresis, by drawing on some ideas in the mathematical/control theory literature and adapting them to fit into the economic frameworks with elements of hysteresis.