Modelling of the Lucas critique using fuzzy set approach

In structural time seriesregression models، binary (classic) dummy variables are used to quantify the effects of economic structural breaks، changes or qualitative variables. The binary dummy variable can be challenged using this dummy variable in which 0 or 1 represent absence or presence of structural breaks (or changes)، but presence of the structural breaks (or changes) may not have uniform effect throughout the period and thus use of zero or one does not provide enough fluctuation. The main aim in this paper is to present a suitable method for endogenously modeling structural breaks on structural coefficients. Doing so، instead of using the binary dummy variable، we have used a fuzzy dummy variable which provides more flexibility. First we have presented the fuzzy dummy variable based on fuzzy set with introduction of a method driving the fuzzy set membership concerning qualitative shocks. Then، we have estimated the Iranian aggregate supply and real money demand functions using both binary and fuzzy dummy variables. Estimated results and the comparison indicate that، first; using the fuzzy dummy variable in econometric modeling proveds more accurate (less specification error) estimation. Second; although the Lucas critique may result the structural breaks in econometric modelling، but for a stationary dependent variable، this effects will die down over time and reduces the strength of the Lucas critique reduce.