![Sample our Engineering & Technology journals, sign in here to start your access, latest two full volumes FREE to you for 14 days]({"type":"image" , "src" : "/sda/5933/TOC-Subject-Sample-2021-Engineering-Tech.jpg"})
Summary
In econometrics it is common for variables to be related together in a set of linear, multilateral and causal interdependencies. This type of system generally has properties which are unsatisfactory for application of classical regression techniques. Consequently, alternative estimation methods have been developed. This paper explores the relations between several such methods in terms of symmetric idempotents of predetermined variables and their orthogonal complements. Generalizations of two‐ and three‐stage least squares and instrumental variables are considered, including Wicken's estimator.2 The relative efficiencies of the estimators are also discussed.
∗ Some of the ideas in this paper appeared in Reference 1(a), a later version of which was presented to the World Congress of the Econometric Society, Rome, 1965.1(b) Since these papers appeared, the mathematical exposition has been improved, the results made more general and some new results (on efficiency) added. Some of the results reported were developed in connection with the research project: ‘An econometric model of the U.K. and its trading partners’, which is financed in part by a grant from the Social Science Research Council to the University of Southampton.
Notes
∗ Some of the ideas in this paper appeared in Reference 1(a), a later version of which was presented to the World Congress of the Econometric Society, Rome, 1965.1(b) Since these papers appeared, the mathematical exposition has been improved, the results made more general and some new results (on efficiency) added. Some of the results reported were developed in connection with the research project: ‘An econometric model of the U.K. and its trading partners’, which is financed in part by a grant from the Social Science Research Council to the University of Southampton.