we can use ols for ordinary least squares models.
we can use ols for ordinary least squares models.
for what kind of models can we use ols?
ordinary least squares
the ols estimator is identical to the maximum likelihood estimator (mle) under the normality assumption for the error terms. this normality assumption has historical importance, as it provided the basis for the early work in linear regression analysis by yule and pearson. from the properties of mle, we can infer that the ols estimator is asymptotically efficient (in the sense of attaining the cramér–rao bound for variance) if the normality assumption is satisfied.









































section::::alternative derivations.:generalized method of moments.









































in iid case the ols estimator can also be viewed as a gmm estimator arising from the moment conditions
ordinary least squares
whereas gls is more efficient than ols under heteroscedasticity or autocorrelation, this is not true for fgls. the feasible estimator is, provided the errors covariance matrix is consistently estimated, "asymptotically" more efficient, but for a small or medium size sample, it can be actually less efficient than ols. this is why, some authors prefer to use ols, and reformulate their inferences by simply considering an alternative estimator for the variance of the estimator robust to heteroscedasticity or serial autocorrelation.
generalized least squares