A Comparison of Asymptotic Covariance Matrices of Adjusted Least Squares and Structural Least Squares in Error Ridden Polynomial Regression

A polynomial structural errors in variables model with normal underlying distributions is investigated An asymptotic covariance matrix of the SLS estimator is computed includ ing the correcting terms which appear because in the score function the sample mean and the sample variance are plugged in The ALS estimator is also considered which does not need any asumption on the regressor distribution The asymptotic covariance matrices of the two estimators are compared in border cases of small and of large errors In both situations it turns out that under the normality assumption SLS is strictly more e cient than ALS