Test for strong hysteresis

The mathematical definition of systems withhysteresis, that is nonlinear input-output systemswith memory, is different from the definition usuallyapplied to economic systems. Economic theory andmodelling practice have almost always specified simpledynamic systems with regular leads and lags in theirresponses, corresponding to input-output systems withunit or zero (or at least stable) roots. These modelscannot capture the ‘selective memory’ feature ofhysteretic behaviour, that is, the influence only ofcertain past events (typically, non-dominatedsequences of previous peaks and troughs). There istherefore a difficulty in testing for and validatingeconomic 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 todetect hysteretic behaviour or to distinguish it frommore conventional economic behaviour. The purpose ofthis paper is to propose a new way of testing forhysteresis, by drawing on some ideas in themathematical/control theory literature and adaptingthem to fit into the economic frameworks with elementsof hysteresis.