Multi-scale reconstruction of large supply networks

Abstract: The structure of the supply chain network has important implications for modelling economic systems, from growth trajectories to responses to shocks or natural disasters. However, reconstructing firm-to-firm networks from available information poses several practical and theoretical challenges: the lack of publicly available data, the complexity of meso-scale structures, and the high level of heterogeneity of firms. With this work we contribute to the literature on economic network reconstruction by proposing a novel methodology based on a recently developed multi-scale model. This approach has three main advantages over other methods: its parameters are defined to maintain statistical consistency at different scales of node aggregation, it can be applied in a multi-scale setting, and it is computationally more tractable for very large graphs. The consistency at different scales of aggregation, inherent to the model definition, is preserved for any hierarchy of coarse-grainings. The arbitrariness of the aggregation allows us to work across different scales, making it possible to estimate model parameters even when node information is inconsistent, such as when some nodes are firms while others are countries or regions. Finally, the model can be fitted at an aggregate scale with lower computational requirements, since the parameters are invariant to the grouping of nodes. We assess the advantages and limitations of this approach by testing it on two complementary datasets of Dutch firms constructed from inter-client transactions on the bank accounts of two major Dutch banking institutions. We show that the model reliably predicts important topological properties of the observed network in several scenarios of practical interest and is therefore a suitable candidate for reconstructing firm-to-firm networks at scale.