[Paper Review] Revealing production networks from firm growth dynamics

Luca Mungo, José Alberto Moráis Morán|arXiv (Cornell University)|Feb 20, 2023

Firm Innovation and GrowthEconomics, Econometrics and Finance3 citations

TL;DR

This paper proposes a novel, unsupervised method to reconstruct firm-level production networks using correlations in firm growth dynamics, leveraging Gaussian Markov models and spectral decomposition of correlation matrices. It demonstrates that supply chain-connected firms exhibit significantly higher growth correlation than unconnected firms, enabling partial network recovery with accuracy outperforming random benchmarks when topological constraints are applied.

ABSTRACT

We study the correlation structure of firm growth rates. We show that most firms are correlated because of their exposure to a common factor but that firms linked through the supply chain exhibit a stronger correlation on average than firms that are not. Removing this common factor significantly reduces the average correlation between two firms with no relationship in the supply chain while maintaining a significant correlation between two firms that are linked. We then investigate if this observation can be used to reconstruct the topology of a supply chain network using Gaussian Markov Models.

Motivation & Objective

• To investigate whether firm growth rate correlations encode traceable information about underlying production network topology.
• To develop a method for reconstructing firm-level supply chains using only observable firm growth dynamics, without requiring direct transaction data.
• To test whether the correlation structure of firm growth rates can distinguish between supply chain-connected and unconnected firms.
• To evaluate the performance of a spectral-based, unsupervised reconstruction method against random network benchmarks.

Proposed method

• The authors analyze the correlation matrix of firm growth rates from FactSet’s supply chain dataset to identify patterns linked to supply chain relationships.
• They decompose the correlation matrix into diagonal (within-industry) and off-diagonal (cross-industry) blocks based on firm industries.
• Using spectral decomposition, they reconstruct adjacency matrices by matching the eigenvalue spectra of Erdős-Rényi random graphs for within-industry blocks and stochastic block models for cross-industry blocks.
• The reconstruction procedure uses a parameter α to match empirical network density and is applied independently to each block, then reassembled into a full network.
• The method is unsupervised and does not require model training, relying instead on statistical constraints derived from empirical correlation structures.
• Performance is evaluated using standard metrics: True Positive Rate, Accuracy, and F1 Score, compared against Erdős-Rényi and block model benchmarks.

Experimental results

Research questions

• RQ1 Do firms connected in a supply chain exhibit significantly higher correlation in their growth rates than unconnected firms?
• RQ2 Can the correlation structure of firm growth rates be used to reconstruct the topology of a production network?
• RQ3 How does the correlation between firm growth rates decay with increasing network distance along the supply chain?
• RQ4 To what extent does a spectral-based, unsupervised reconstruction method outperform random network benchmarks in recovering supply chain structure?
• RQ5 Can the method be improved by incorporating known topological features such as industry sector membership?

Key findings

• Firms linked through the supply chain exhibit significantly higher average correlation in growth rates than unconnected firms, even after removing a common macroeconomic factor.
• The average correlation between unconnected firms drops substantially after removing the common factor, while the correlation between connected firms remains high, indicating a structural signal.
• The correlation between firm growth rates decays gradually with increasing network distance along the supply chain, suggesting a measurable spatial correlation structure.
• The proposed spectral reconstruction method achieves higher accuracy than both Erdős-Rényi and block model benchmarks, though it does not consistently outperform the block model on F1 score or True Positive Rate.
• The method is fully unsupervised and relies only on accessible data—such as firm sales or stock returns—making it broadly applicable and robust to data substitution.
• The approach is scalable to subnetworks of 300–500 firms and shows promise for future integration with generative models of production networks.