The Efficiency of OLS Estimators of Structural Parameters in a Simple Linear Regression Model in the Calibration of the Averages Scheme

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Abstract

A simple linear regression model is one of the pillars of classic econometrics. Multiple areas of research function within its scope. One of the many fundamental questions in the model concerns proving the efficiency of the most commonly used OLS estimators and examining their properties. In the literature of the subject one can find taking back to this scope and certain solutions in that regard. Methodically, they are borrowed from the multiple regression model or also from a boundary partial model. Not everything, however, is here complete and consistent. In the paper a completely new scheme is proposed, based on the implementation of the Cauchy-Schwarz inequality in the arrangement of the constraint aggregated from calibrated appropriately secondary constraints of unbiasedness which in a result of choice the appropriate calibrator for each variable directly leads to showing this property. A separate range-is a matter of choice of such a calibrator. These deliberations, on account of the volume and kinds of the calibration, were divided into a few parts. In the one the efficiency of OLS estimators is proven in a mixed scheme of the calibration by averages, that is preliminary, and in the most basic frames of the proposed methodology. In these frames the future outlines and general premises constituting the base of more distant generalizations are being created.

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