Reconstructing firm-level interactions: the Dutch input-output network

TL;DR

This paper introduces a novel maximum-entropy method for reconstructing detailed inter-firm networks from limited data, improving understanding of economic resilience and firm interactions under shocks.

Contribution

The paper develops a generalized maximum-entropy reconstruction approach that preserves firm-specific input-output flows, enhancing network modeling accuracy at finer product resolutions.

Findings

The new method reliably reconstructs inter-firm networks with detailed production constraints.

Model likelihood correlates with the system's rewiring capability, indicating network flexibility.

Finer product resolution improves the reconstruction accuracy.

Abstract

Recent crises have shown that the knowledge of the structure of input-output networks at the firm level is crucial when studying economic resilience from the microscopic point of view of firms that rewire their connections under supply and demand shocks. Unfortunately, empirical inter-firm network data are rarely accessible and protected by confidentiality. The available methods of network reconstruction from partial information, which have been devised for financial exposures, are inadequate for inter-firm relationships because they treat all pairs of nodes as potentially interacting, thereby overestimating the rewiring capabilities of the system. Here we use two big data sets of transactions in the Netherlands to represent a large portion of the Dutch inter-firm network and document the properties of one of the few analysed networks of this kind. We, then, introduce a generalized maximum-entropy reconstruction method that preserves the production function of each firm in the data, i.e. the input and output flows of each node for each product type. We confirm that the new method becomes increasingly more reliable as a finer product resolution is considered and can therefore be used as a generative model of inter-firm networks with fine production constraints. The likelihood of the model, being related to the entropy, proxies the rewiring capability of the system for a fixed input-output configuration.