I am reading Greene's textbook Econometric Analysis where he says that, if there's multicollinearity, then:
- Small changes in data lead to large swings in parameter estimates.
- Coefficients have high standard errors even though they're jointly significant.
- Coefficients have the "wrong" sign or implausible magnitudes.
I have three question:
- What are the consequences for the unbiasedness and consistency of the OLS estimators in the presence of multicollinearity?
- Is the efficiency of the estimators reduced in the presence of multicollinearity?
- Do Greene's points hold (yet to a lesser extent) for slightly correlated independent variables? For example, would all three points hold (to a small extent) if the correlation between the regressors is $\rho = 0.1$, for example?