The parameter estimation for this model no longer uses the OLS method because this method cannot produce an efficient estimator
under the REM assumption.
The estimators [[??].sub.1] and [[??].sub.2] are both consistent under the null hypothesis, but [[??].sub.1] is designated to be the more efficient estimator
. If, under the alternative hypothesis, [[??].sub.1] is no longer a consistent estimator for b, but [[??].sub.2] remains consistent, then it is possible to construct a test of the null hypothesis using the difference between [[??].sub.1] and [[??].sub.2].
However, Coal is efficient estimator
then other energy resources.
The general consensus of opinion, however, is that, thus far, two-stage least squares is the cheapest, easiest, and most efficient estimator
in most situations .
This latter work takes advantage of a GMM efficient estimator
for dynamic panels.
Regarding specific goals, it is necessary to establish efficient criteria to select the optimal lag-length (parametric), as well as the approach of an efficient estimator
of the long-run variance (semi-parametric).
As a consequence, an estimator that provides a non-optimal solution close to the correct value is preferred instead of a much efficient estimator
that provides an absurd solution when any assumption does not fulfil.
Since m, our estimator of [Mu], has a covariance matrix that is not a constant times the identity matrix, we must resort to a weighted least squares (WLS) approach to obtain the most efficient estimator
for [Gamma] (the trend line), and in particular [[Gamma].sub.1] (the trend).
It should be noted that since the overidentifying restrictions of the model are not rejected, we could, in principle, combine the various estimators for the change in the black-white earnings gap into a more efficient estimator
The sample 10 percent trimmed mean is clearly the most efficient estimator
, with an RMSE that is more than 15 percent below that of the sample mean, with a 30 percent lower variance!
Three versions of each model (zero lag, geometric lag, and almon lag) are estimated using, in each case, an efficient estimator
. The residual and predicted time series from structural estimation are utilized to test the truth of each specification against rival specifications using the non-nested hypothesis tests proposed by Davidson and MacKinnon.
The quantile regression estimator described above is not an efficient estimator