Constrained Randomization for Motif Detection in Attributed Hierarchical Networks: Evidence from Tax-Haven Routing in Multinational Firm Networks

Abstract

Network motif analysis asks whether observed subgraph patterns reflect meaningful organization or the mechanical consequences of network structure. The question is especially difficult in attributed hierarchical networks, where a valid counterfactual must preserve the degree sequence, categorical node attributes, and connectivity while randomizing the feature hypothesized to encode design, a combination that classical motif-detection methods do not provide. This paper develops a constrained-randomization framework for such settings. It combines a connectivity-preserving edge-swap null, which holds the directed degree sequence, node labels, and weak connectivity fixed while randomizing topology, with a depth-stratified label-shuffle null, which holds topology fixed and randomizes labels within each hierarchical level; an Erdős–Rényi baseline shows the cost of ignoring structure. The framework is applied to tax-haven "sandwich" motifs, directed ownership paths that leave and re-enter the same haven through a distinct intermediary haven, in firm-level networks for 1,033 U.S. multinationals over 2012 to 2022 from Bureau van Dijk's Orbis database. Across 590 sandwich-containing firm-years, the connectivity-preserving null rejects random formation at p<0.05 in 63.7% of cases and the label-shuffle null at p<0.05 in 93.1%, while the baseline rejects near-universally with zero edge overlap with the observed structure. Haven density strongly predicts sandwich counts under the Erdős–Rényi baseline (Spearman ρ = 0.75), but only weakly in the observed networks (ρ = 0.12), indicating that observed sandwiches reflect how haven nodes are wired rather than how many are present. The null model formulation developed here extends to a variety of settings, including interbank lending, trade, and patent citations.

Keywords: Network Motifs, Orbis, Random Graphs, Tax Havens, Multinational Enterprises, Double Irish, Tax Planning, Transfer Pricing, Corporate Ownership, Motif Detection, Dutch Sandwich, Hierarchical Networks, Profit Shifting

JEL Classification: H26, F23, C63, H25, L22