[Paper Review] Reconstructing firm-level input-output networks from partial information

Andrea Bacilieri, Pablo Austudillo-Estevez|arXiv (Cornell University)|Mar 31, 2023

Economic and Technological InnovationEconomics, Econometrics and Finance3 citations

TL;DR

This paper proposes a maximum entropy method to reconstruct firm-level input-output network weights from partial data, using binary supplier-customer links and firm-level financial aggregates. It demonstrates strong performance in recovering microscale distributions but shows divergent results for systemic importance measures, particularly due to network structure and sampling bias in missing firms and links.

ABSTRACT

There is a large consensus on the fundamental role of firm-level supply chain networks in macroeconomics. However, data on supply chains at the fine-grained, firm level are scarce and frequently incomplete. For listed firms, some commercial datasets exist but only contain information about the existence of a trade relationship between two companies, not the value of the monetary transaction. We use a recently developed maximum entropy method to reconstruct the values of the transactions based on information about their existence and aggregate information disclosed by firms in financial statements. We test the method on the administrative dataset of Ecuador and reconstruct a commercial dataset (FactSet). We test the method's performance on the weights, the technical and allocation coefficients (microscale quantities), two measures of firms' systemic importance and GDP volatility. The method reconstructs the distribution of microscale quantities reasonably well but shows diverging results for the measures of firms' systemic importance. Due to the network structure of supply chains and the sampling process of firms and links, quantities relying on the number of customers firms have (out-degrees) are harder to reconstruct. We also reconstruct the input-output table of globally listed firms and merge it with a global input-output table at the sector level (the WIOD). Differences in accounting standards between national accounts and firms' financial statements significantly reduce the quality of the reconstruction.

Motivation & Objective

• Address the scarcity and incompleteness of firm-level supply chain data, which hinders accurate macroeconomic modeling of shock propagation.
• Evaluate the performance of a maximum entropy method for reconstructing transaction values in input-output networks when only binary links and aggregate financial data are available.
• Assess the method’s accuracy on microscale, higher-order, and macroscale economic quantities, including systemic risk indicators and GDP volatility.
• Investigate the impact of network structure and sampling bias on reconstruction quality, especially for measures dependent on firm out-degrees (number of customers).
• Explore the feasibility of enhancing global firm-level datasets by merging them with sector-level input-output tables (e.g., WIOD), despite accounting standard mismatches.

Proposed method

• Applies a conditional maximum entropy method (Parisi et al., 2020) to infer transaction values from known binary topology and firm-level revenue/expenditure data.
• Uses the administrative dataset from Ecuador’s SRI as ground truth to calibrate and validate the reconstruction method.
• Reconstructs technical and allocation coefficients by normalizing inferred weights relative to total inputs or outputs per firm.
• Employs a general equilibrium input-output model (Acemoglu et al., 2012) to simulate shock propagation and assess GDP volatility under reconstructed networks.
• Introduces a proxy node to represent the unobserved portion of the economy, testing its impact on reconstruction accuracy.
• Merges the FactSet dataset of globally listed firms with the WIOD sector-level input-output table, applying the same reconstruction method to the augmented network.

Experimental results

Research questions

• RQ1 How accurately can the maximum entropy method reconstruct firm-level transaction weights when only partial links and aggregate financial data are available?
• RQ2 To what extent does the reconstruction method preserve the distribution of microscale quantities such as technical and allocation coefficients?
• RQ3 How well does the method recover higher-order measures of systemic importance, such as output multipliers and influence vectors?
• RQ4 Why do certain systemic risk indicators—particularly those based on firm out-degrees—show poorer reconstruction performance?
• RQ5 How does the inclusion of a proxy node for the unobserved economy affect the accuracy of reconstructed network quantities and aggregate GDP volatility?

Key findings

• The method reconstructs the distribution of microscale quantities—such as technical and allocation coefficients—reasonably well, despite imperfect absolute values.
• Output multipliers are reconstructed with remarkable accuracy, closely matching empirical values in the Ecuador dataset.
• The influence vector, a measure of systemic importance based on firm out-degrees, is systematically overestimated due to missing firms and links in the sampling process.
• Aggregate GDP volatility is overestimated in the reconstruction, indicating that the method fails to fully capture the true network structure’s stabilizing effects.
• Firms with higher out-degrees (more customers) are more adversely affected by missing data, due to the network’s inherent structure and sampling bias.
• Including a proxy node improves the reconstruction of microscale and higher-order quantities but does not reduce the overestimation of aggregate GDP volatility.