So in computing the variancecovariance matrix for βhat in an OLS model, we arrive at
VarCov(βhat)=(σ_ε)^2E{[X'X]^1}
However, I'm incredulous as to how X is considered nonstochastic and how we can just eliminate the expectation sign and have
VarCov(βhat)=(σ_ε)^2[X'X]^1
I'm accepting this to be true (since it's so written in the text) but I'm taking a leap of faith here: if this is true, the elements in the VarCov matrix are expressed in terms of sample statistics and are therefore stochastic. I thought that the variance of an estimator of a parameter, if consistent, should be a deterministic parameter itself and should not depend on the sample observations (besides sample size, n), such as the ones we see in using CramerRao lower bound to determine efficiency. Likely I'm understanding something wrong here, any pointers would be greatly appreciated!
