Ekonometrika 1Ekonomi Pembangunan

Universitas Brawijaya

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.

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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

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Look at this picture..

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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.

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THERE ARE SEVERAL SOURCES OF MULTICOLLINEARITY Constraints on the model or in the

population being sampled Model specification An overdetermined model

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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

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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

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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

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