Abstract
Bramoullé et al. [3] provided identification conditions for linear social interaction models
through network structures. Despite the importance of their results, the authors omitted
detailed mathematical discussions. Moreover, they consider cases where many identical networks are observed simultaneously within the same dataset. In reality, multiple networks
with different structures, such as families or classrooms, are repeatedly observed within the
same dataset. The purpose of this paper is to fill in the mathematical gaps in their arguments
and establish identification conditions for networks with different structures. In addition, we
reveal the minimum network size as a necessary condition for identifying social effects. We
also discuss the identification conditions of a network model with a network fixed effect.
