Question

Discuss the intuition behind the GLS estimator and how the GLS estimator is different than the OLS estimator when using the OLS residuals to form an heteroscedasticially-robust estimate of the variance-covariance matrix for βˆ.

Answer 1

1) GLS Estimator or Generalised Least Squared Estimator usually uses to estimate the unknown parameters or coefficients of a linear regression when the residuals are usually correlated. it is actually a generalised version of OLS Estimator , to deal with non BLUE OLS Estimator. GLS is also known as weighted least squared method cause it can rule out the problem of heteroscedasticity robust variance .The difference bwtween GLS and OLS is the estimating the error term in the regression model . For OLS the model is where e follows normal distribution with zero mean and ²I (identity matrix)

OLS estimator returns the maximum likelihood for parameter b assuming each parameters has equal variance and they are uncorrelated thus the error term e is homoscedastic.

In the case of GLS Estimator error terms are correlated thus they have unequal variance or heteroscedastocity . the model is

where follows normal dist with zero mean and ²M as std. deviation. (M= covariance matrix of b) thus it actually take into consider the heterscedastically robust variance covariance matrix.

As GLS removes heteroscedasticity or tries to remove it it is specially useful for F/T Statistics but OLS is not.