Reconstructing firm-level interactions in the Dutch input–output network from production constraints

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 try to rewire their connections under supply and demand constraints. Unfortunately, empirical inter-firm network data are protected by confidentiality, hence rarely accessible. The available methods for network reconstruction from partial information treat all pairs of nodes as potentially interacting, thereby overestimating the rewiring capabilities of the system and the implied resilience. 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 its properties. 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 in reconstructing the empirical network as a finer product resolution is considered and can, therefore, be used as a realistic generative model of inter-firm networks with fine production constraints. Moreover, the likelihood of the model directly enumerates the number of alternative network configurations that leave each firm in its current production state, thereby estimating the reduction in the rewiring capability of the system implied by the observed input–output constraints.

Reconstructing supply networks

“…In [19], visual inspection of the results shows a substantial enhancement in weight reconstruction when applying sector-specific constraints to firms' inputs, further underscoring the crucial role the economy's sectoral structure plays in the accurate reconstruction of production networks.…”

“…Topological indicators gauge how effectively the reconstruction captures the network 'coarse-grained' features. For instance, Ialongo et al [19] validate their reconstruction methodology by assessing how accurately it replicates the network degree distribution.…”

“…Ialongo et al [19] introduced a method that tackles this issue and simultaneously reconstructs the whole network topology and link weights (see section 4 for the weights). Following a well-known approach in network reconstruction [3], they compute a probability distribution P(G) over the set of all possible graphs G that maximizes the Shannon Entropy S,…”

Revealing production networks from firm growth dynamics

“…A similar approach was used in [16] to predict links between firms using their financial, industrial, and geographical features. Additional efforts have been carried out to adapt maximum-entropy models [17][18][19][20][21][22][23], already popular for models of international trade [21,[24][25][26][27], to the reconstruction of firm-level networks. The motivation of this research effort is that economic models conceived to represent the economy at the firm level require a good knowledge of the production network and should lead to a better understanding of economic dynamics and forecast.…”

Deterministic, quenched or annealed? Differences in the parameter estimation of heterogeneous network models

“…Over the last twenty years, the growth of network science has impacted several disciplines by establishing new, empirical facts about the structural properties of those systems. Prominent examples are provided by economics and finance: the growing availability of data has motivated researchers to explore, and model, the architecture of interbank networks [1], production networks [2], trading networks [3][4][5][6].…”