Two Papers on Linear Models

When coefficients of endogenous variables are known, it is demonstrated that two-stage least squares and instrumental variable estimators are invariant to the form in which these variables enter computations, as raw data or estimates. Exclusion of instruments and knowledge of coefficients are related to identifiability testing, and a test presented. -- This paper discusses the traditional specification problem from a geometric viewpoint. While the traditional emphasis is on the properties of estimators, the geometric approach also allows an easy development of corresponding results for inference. Errors arising from artificial inclusion or exclusion of variables are considered in terms of augmentations or restrictions on a given maintained hypothesis, and this allows a corresponding interpretation of tests based upon the Wald and Lagrange Multiplier Principles. It is demonstrated that biases arising from incorrect exclusion of variables do not invalidate the traditional F-test