Determination of Linear Relations Between Systematic Parts of Variables with Errors of Observation the Variances of Which are Unknown

摘要: Given a sufficient number of instrumental variables significantly correlated with the investigational variables, consistent estimates coefficients linear relations can be determined (if they exist), without knowledge disturbance variances. The are discussed from viewpoint probability convergence. In case two and one variable, all three distributed on normal surface, distribution estimate coefficient is found exactly for sample sizes, certain hypotheses. function remarkably simple. applicability theorem to economic time series by (a) comparing inferences derived this Model A those simplest stationary time-series model, termed B, (b) large-sample variances several models. It that theory used confidence when not too short error large. applied particular series, showing accuracy depends correlation between variable variables. which reference made in Sections II, III, IV, relating two-investigational-variable case, extended many tests given, applicable samples small, determining significance estimates.