Question

Explain the FGLS (Feasible Generalized Least Squares) method and how we can apply it step by step. The following notation is suggested :V(u) =σ2Ω(explain what areσandΩ). Then how do we interpret it?

ECONOMETRICS

Answer 1

Generalized least squares(GLS) is a method for estimating the unknown parameters in a linear regression model when there is a certain degree of correlation between the residuals in a regression model.

If the covariance of the errors

f the covariance of the errors   $\Omega$ is unknown, we can get a consistent estimate of $\Omega$ , $\widehat \Omega$ using an implementable version of GLS known as the feasible generalized least squares (FGLS) estimator.

In FGLS, modeling proceeds in two stages:

(1) the model is estimated by OLS or another consistent (but inefficient) estimator, and the residuals are used to build a consistent estimator of the errors covariance matrix

(2) using the consistent estimator of the covariance matrix of the errors, one can implement GLS ideas.

$\Omega$ is a non-singular covariance matrix and σ2 is a variance of the error term.

V(u) =σ2Ω is the consistent estimator of the variance term.