Question

what are the theoretical consequences of multicollinearity?

Answer 1

Multicollinearity means when independent variable are itself linearly correlated

1) Least square estimator cannot be defined. Estimation is not possible for estimates and standard error.

(ii) For variables that are highly related to one another (but not perfectly related), theOLS (Ordinary Least Squares) estimators have large variances and covariances,making precise estimation difficult.

(iii) Because of the consequences of point 2, confidence intervals tend to be much wider, leading to the acceptance of the null hypothesis more readily. This is due to the relatively large standard error. The standard error is based, in part, on the correlation between the variables in the model.

(iv)Although the t ratio of one or more of the coefficients is more likely to be insignificant with multicollinearity, the R^2 value for the model can still be relatively high.

(v)The OLS estimators and their standard errors can be sensitive to small changes in the data. In other words, the results will not be robust.