  A multivariate errors-in-variables (EIV) model with an intercept term, and a
polynomial EIV model are considered. Focus is made on a structural
homoskedastic case, where vectors of covariates are i.i.d. and measurement
errors are i.i.d. as well. The covariates contaminated with errors are normally
distributed and the corresponding classical errors are also assumed normal. In
both models, it is shown that (inconsistent) ordinary least squares estimators
of regression parameters yield an a.s. approximation to the best prediction of
response given the values of observable covariates. Thus, not only in the
linear EIV, but in the polynomial EIV models as well, consistent estimators of
regression parameters are useless in the prediction problem, provided the size
and covariance structure of observation errors for the predicted subject do not
differ from those in the data used for the model fitting.
