Decomposed Specification Tests for Asymmetric Network Panels

This paper develops specification tests for irregular network panels with time-varying and asymmetric interaction matrices. We decompose each matrix into symmetric and antisymmetric components and show that standard residual quadratic diagnostics, including Moran’s I and the LM-error statistic, are exactly invariant to the antisymmetric component. In contrast, lag-type bilinear diagnostics retain directional information. Building on this dichotomy, we derive a joint score limit for the decomposed lag alternative and propose conditional score tests for directional and contextual relevance. The directional statistic LM tests whether the antisymmetric component contributes information beyond symmetric exposure, while LM provides the corresponding contextual test. The tests have standard chi-square limits under primitive conditions for irregular panels. Monte Carlo evidence shows that the decomposed tests control size and correctly attribute network propagation across contextual and directional channels, whereas conventional quadratic diagnostics are exactly direction-blind and conventional lag diagnostics conflate the two channels.