Abstract
A measure of interdependence of a system of equations facilitates e.g. Monte Carlo studies of small sample properties of estimators and tests.
To find such a measure we reorder the equation system such that the sum of the absolute values above the the main diagonal of the coefficient matrix is maximal. If in the reordered system there are only zeroes below the main diagonal, the system is recursive and the degree of interdependence is zero. We use the ‘degree of linearity’ proposed by Helmstädter 1965 for an equivalent problem (triangulation of an input-output matrix) to measure the degree of interdependence. The measure is refined later: First the classes of interdependence are constructed (using the transitive closure operation) and then the measures of interdependence are computed within these classes. This means block-triangulation of the coefficient matrix and corresponds to reordering the equation system so as to achieve a blockrecursive system of equations.
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Bartnick, J. (1991). Optimal triangulation of a matrix and a measure of interdependence for a linear econometric equation system. In: Gruber, J. (eds) Econometric Decision Models. Lecture Notes in Economics and Mathematical Systems, vol 366. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-51675-7_28
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DOI: https://doi.org/10.1007/978-3-642-51675-7_28
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