1. Ekonometrika 1 Ekonomi Pembangunan Universitas Brawijaya

2. WHAT IS THAT..?  Assumption of the classical linear regression model (CLRM) is that there is no multicollinearity among the regressors included in the regression model. 2 almuiz 2009

3. THE NATURE OF MULTICOLLINEARITY  The term multicollinearity is due to Ragnar Frisch. Originally it meant the existence of a “perfect,” or exact, linear relationship among some or all explanatory variables of a regression model 3 almuiz 2009

4. Look at this picture.. almuiz 2009 4

5. NEXT..  Why does the classical linear regression model assume that there is no multicollinearity among the X’s?  If multicollinearity is perfect in the sense of the regression coefficients of the X variables are indeterminate and their standard errors are infinite. almuiz 2009 5

6. THERE ARE SEVERAL SOURCES OF MULTICOLLINEARITY  Constraints on the model or in the population being sampled  Model specification  An overdetermined model almuiz 2009 6

7. PRACTICAL CONSEQUENCES OF MULTICOLLINEARITY  Although BLUE, the OLS estimators have large variance and covariance, making precise estimation difficult.  The confidence intervals tend to be much wider.  The t-ratio of one or more coefficients tend to be statistically insignificant.  R-square can be very high  The OLS estimators and their standard errors can be sensitive to small changes in the data almuiz 2009 7

8. DETECTION OF MULTICOLLINEARITY  High R-square but few significant t-ratio  High pair-wise correlation among regressors  Examination of partial correlations (Farrar and Glauber)  Auxiliary regressions (Fi)  Klein’s rule of thumb (R2 aux; overall R2)  Eigenvalues and condition index  Tolerance and variance inflation factor almuiz 2009 8

9. REMEDIAL MEASURES  A priori information  Combining cross-sectional and time-series data  Dropping a variable(s) and specification bias  Transformation of variables  Additional or new data  Reducing collinearity in polynomial regressions  Factor analysis, principal component and ridge regression almuiz 2009 9

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