Identification Problems of Linear Social Interaction Models: A General Analysis Based on Matrix Spectral Decompositions

Abstract

This paper develops new social interactions identification methods and develops a framework that includes some important existing results as special cases, such as the identification results in Bramoulle, Djebbari, and Fortin (2009) (except their proposition 3), the section 4.ii of Blume, Brock, Durlauf, and Ioannides(2011) (except their theorems 3 and 5), and Graham (2008). This paper discovers that diameter is a key network property closely related to identification. The proposed methods are based on the matrix spectral decompositions; they address three canonical identification problems. First, this paper offers a method of disentangling endogenous and exogenous interactions by the matrix spectral decompositions. Second, this paper offers a detailed analysis of differencing methods, which solve the endogeneity problem arising from the presence of unobservable group-level heterogeneity (or fixed effects), and provides a method of minimizing the information loss from differencing. Third, this paper develops an identification method based on the spectral decompositions of covariance matrices for the problem arising from the absence of observable individual-level heterogeneity; Graham's (2008) variance contrast method is a special case of this method.