Can a GLS estimate be unbiased in OLS?
It is important to know that the OLS estimates can be unbiased, even if the underlying (true) data generating process actually follows the GLS model. If GLS is unbiased then so is OLS (and vice versa). You can very easily proof this, but basically the assumptions for consistency/unbiasedness do not rely on the variance of the estimates at all.
What’s the difference between a GLS and an OLS?
The real difference between OLS and GLS is the assumptions made about the error term of the model. In OLS we (at least in CLM setup) assume that $Var(u)=\\sigma^2 I$, where I is the identity matrix – such that there are no off diagonal elements different from zero.
What is the equation for GLS with OLS?
With GLS this is no longer the case (it could be, but then GLS = OLS). With GLS we assume that V a r ( u) = σ 2 Σ, where Σ is the variance-covariance matrix. Many text books introduce GLS with WLS, which is the GLS function that eliminates heteroskedasticity (or tries to).
Can you prove that GLS is unbiased but only consistent?
If GLS is unbiased then so is OLS (and vice versa). You can very easily proof this, but basically the assumptions for consistency/unbiasedness do not rely on the variance of the estimates at all. A more subtle point is that, unless you know the actual GLS function, it is not unbiased but only consistent.
What does AR ( 1 ) term mean in OLS?
I don’t use Eviews but, as I understand it, that equation means an OLS regression with a constant, one independent variable and an AR (1) term. I tried running this in R:
How to use GLS with T / F statistics?
With GLS we assume that V a r ( u) = σ 2 Σ, where Σ is the variance-covariance matrix. Many text books introduce GLS with WLS, which is the GLS function that eliminates heteroskedasticity (or tries to). This means that the usual t/F statistics can be valid for the GLS estimation, but not for the OLS.