Multicollinearity, pronounced as mul-ti-co-lli-nea-ri-ty is the second longest word in the econometrics dictionary after heteroscedasticity. It contains 17 talking words! It occurs when there exists perfect or exact linear dependence or relationships among explanatory variables in a given model. Collinearity is when such exact dependence is between two variables. In that wise, we say that the variables are collinear. For instance, when an explanatory variable is 80 to 100% explained by another explanatory variable, separating the influence of each of them on the dependent variable (regressand) becomes difficult and interpreting the estimated coefficients from that model will also be problematic. This is because variation in one regressor can be completely explained by another regressor in the same model.
With perfect or less than perfect multicollinearity
or collinearity:
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Regression
coefficients are indeterminate (because the collinear variables cannot be
distinguished from one another)
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Standard
errors are infinite (they are very large)
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Estimates
are biased
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Coefficients
cannot be estimated with precision or accuracy
Note:
multicollinearity does not violate any regression assumptions; the OLS
estimators are still BLUE (Best Linear Unbiased Estimators); it does not
destroy the property of minimum variance.
Multicollinearity can be detected using “r” the coefficient of correlation. So,
if r = 1, then multicollinearity or
collinearity exists. So whenever you run your correlation matrix, look out for
those relationship where r > 0.8,
that tells us that the respective variables are collinear. Multicollinearity is
ruled out when regressors in a model have non-linear relationships.
A major problem associated with
multicollinearity is that, if r is
high, then the standard error will be high and the computed t-statistic will be low making it more
likely not to reject the null
hypothesis when is false. Thereby committing a Type II error….that is,
incorrectly retaining a very false null hypothesis.
How do you know if your model suffers
from multicollinearity?
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High
R2
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Few
significant t-ratios
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Wider
confidence intervals
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Contradictory
signs of beta coefficients to expected a
priori
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Estimates
are sensitive to even small changes in model specification
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High
pair-wise correlation statistic among the regressors
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From
the tolerance level and variance inflation factor (VIF). A tolerance level lower than 0.10 and a VIF of 10 are indicative of multicollinearity in a model. A higher VIF provides evidence of
multicollinearity.
Correcting/controlling for
multicollinearity:
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Collect
more data
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Change
the scope of analysis
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Do
not include collinear variables in the same regression
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Drop
the highly collinear variable
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Transform
the collinear variable through differencing (however, the differenced error
term is serially-correlated and violates OLS assumptions).
What I do often, is to drop the
collinear variable and if that variable is very important to my model, I’ll
transform my modelling structure into a step-wise fashion such that collinear
variables are not included together in the same regression.
