The effects of the proxy information on the iterative Stein-rule estimator of the disturbance variance

In a regression model with proxy variables, we consider the iterative estimator of the disturbance variance to obtain more precise estimates. In the formula of the estimator of the disturbance variance, the estimator is obtained by using Stein-rule (SR) estimator instead of OLS (ordinary least squares) estimator is called Iterative estimator of the disturbance variance. It is shown that, in a regression model with proxy variables the mean square error (MSE) of the iterative estimator of the disturbance variance is greater than the MSE of the disturbance variance related to the OLS estimator under certain conditions.