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The mixed results of the estimated coefficient on earnings is another indication that the assumption that there is a positive and homogeneous relation between price and earnings is doubtful, even within the same industry group.
The negative price-earnings relation for firms that report losses, as reported by Jan and Ou (1995) and documented by Burgstahler and Dichev (1997) and Kothari and Aimmerman (1995), raises questions about the validity of the assumption of a positive and homogeneous relation between price and earnings, as expressed by the simple earnings capitalization model.
We deal with quadratic algebras generated in degree one, that is, algebras given by homogeneous relations of degree 2: