Reconstructing firm-level input-output networks from partial information: inferring link weights and assessing shock propagation

The COVID-19 pandemic, the recent war in Ukraine and the evermore frequent natural disasters have highlighted the fragility of global supply chains. These recent events also make it clear that shocks to supply chains are localised geographically and/or firm-specific but have repercussions on the global economy. Therefore, firm-level data would be much more useful than aggregate data since aggregation washes away key processes taking place at the micro-level and can also introduce substantial biases. However, data on supply chains at the fine-grained, firm level are scarce. Indeed, the most widely used data are at the sector level and remain highly aggregated.

For listed firms, some commercial data sets 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 value of the transactions (the weighted production network) based on information about the existence of transactions (the binary production network) and standard information about firms disclosed in their financial statements. We test the method on the administrative data set of Ecuador and reconstruct a commercial data set (FactSet).

We test the performance of the reconstruction method on the weights, the technical and allocation coefficients (normalised weights), and three multipliers (node centrality measures). We find that the method reconstructs the weight (normalised or not) distribution reasonably well and we can recover the power-law exponent of the weight distribution. The reconstructed multipliers remarkably agree with the empirical ones. We also test the reconstruction using two standard input-output models to assess how well the method performs in recovering the growth rates of firms’ revenues and aggregate volatility. For more than half of the firms, we correctly predict the sign of the growth rates of firms’ revenues but whether growth rates tend to be over or underestimated depends on the data set. We assess aggregate volatility for Ecuador only, where it is overestimated.

We also reconstruct the input-output table of globally listed firms using the data set collected by FactSet and merge it with a global input-output table at the sector level (the WIOD). Differences in accounting standards between national accounts and financial statements reduce the quality of the final data set.