A linear structure is a family of matrices that satisfy a given set of linear restrictions, such as symmetry or diagonality. We add to the literature on linear structures by studying the family of matrices where all diagonal elements are zero, and discuss two econometric examples where these...

Two main approaches are commonly used to empirically evaluate linear factor pricing models: regression and stochastic discount factor (SDF) methods, with centered and uncentered versions of the latter. We show that unlike standard two-step or iterated generalized method of moments (GMM)...