Topic 9: Multicollinearity

Question 1

What is meant by the assupmtion of no collinearity between X variables?

Answer 1

That there is no perfect linear relationship between the regressors

Question 2

List some sources of Multicollinearity

Answer 2

• Data collection method employed
• Constraints on the model, where there is some causal reason for variables to be correlated
• Model specification problems (adding needless polynomials)
• Overdetermined model (more regressors then observations)
• In time series data, regressors share a common trend

Question 3

Why does regression fail given perfect multicollinearity?

Answer 3

Because estimates represent the expected change in the regressant for a unit change in the regressor, all other variables held constant. But with perfect multicollinearity, there is no way to examine the effects of one variable without a change in the other

Question 4

What is the effect of imperfect multicollinearity? Is it an assumption violation?

Answer 4

No The CLRM remains BLUE and the CNLRM remains BUE Standard errors are larger, just as the case when there are fewer observations or small data variation

Question 5

How does multicollinearity affect the F test that B₁ = B₂ = B₃ = 0? and R²?

Answer 5

It does not affect either. A key sign of multicollinearity is high R² but insignificant t-tests

Question 6

Why is multicollinearity a sample phenomena?

Answer 6

Because if one could run a proper experiment, then they could set all inputs, hence it has little to do with the PRF and all to do with the sample / data that we have

Question 7

How reliably can pairwise correlation detect multicollinearity problems?

Answer 7

Only when there is a pairwise correlation. Issues arise when X_h = aX_i+ bX_j

Question 8

How can we counter multicollinearity?

Answer 8

• Use prior knowledge to assume a constraint
• Different polynomial model
• Drop variables if it is clearly a case of perfect collinearity
• Can transform variables, take difference, but make cause correlation between error terms
• Combine cross sectional & time series to make panel data
• More data

Question 9

What applications does multicolinearity matter for?

Answer 9

• When trying to establish causal relationships
• But not when forecasting, because R² is not affected