One of the basic assumptions of the regression models is that the parameter vector does not vary across sample observations. If the parameter vector is not constant for all observations in the sample, the statistical model is changed and the usual least squares estimators do not yield unbiased, consistent and efficient estimates. This study investigates the regression model with some or all parameters vary across partitions of the whole sample data when the model permits different response coefficients during unusual time periods. Since the usual test for overall homogeneity of regressions across partitions of the sample data does not explicitly identify the break points between the partitions, the testing the equality between subsets of coefficients in two or more linear regressions is generalized and combined with the test procedure to search the break point. The method is applied to find the possibility and the turning point of the structural change in the long-run unemployment rate in the usual static framework by using the regression model. The relationships between the variables included in the model are reexamined in the dynamic framework by using Vector Autoregression.