Teaching Econometric Theory from the Coordinate-Free Viewpoint

The principal aim of this paper is to demonstrate how the coordinate-free methods of linear statistical models may be adapted to the analysis of econometric models, and to explain why such methods are useful for teaching purposes. The application of coordinate-free methods to linear statistical models cast in Euclidean space was first introduced by Kruskal(1961). Later, the methodology was extended to multivariate analysis by Dempster (1968) and Eaton (1970). Drygas (1970) and Philoche (1971) give coordinate-free expositions of minimum-variance linear unbiased [or Gauss-Markov (GM)] estimation, and Seber (1964a,b,c and 1980) makes use of coordinate-free methods in a comprehensive treatment of the linear hypothesis.