Score-Augmented Frobenius Distance and Its Applications in Causal Inference
This paper develops a framework for comparing networks that is invariant to node labeling and interpretable within standard econometric settings. I define a node’s structural role as its expected importance within the network given observable features and show that ordering nodes by these expected roles yields a canonical, label-invariant representation. Based on this representation, I propose the Score-Augmented Frobenius Distance, a metric that quantifies structural differences between networks while isolating genuine shifts in connectivity from compositional variation in node characteristics. The framework can be applied within causal inference designs such as difference-in-differences and synthetic control: by aligning networks through structural roles, it recovers parallel trends and treatment effects that are otherwise obscured when networks are compared under fixed labels. In an application to China’s value-added tax (VAT) reform, the method reveals substantial reorganization of production networks that conventional, industry-based comparisons miss. Overall, the approach provides a tractable and interpretable bridge between network analysis and econometric inference, enabling causal analysis defined directly over network structure.
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