[Paper Review] Estimating the loss of economic predictability from aggregating firm-level production networks

Christian Diem, András Borsos+3 more|arXiv (Cornell University)|Feb 22, 2023

Economic and Technological Innovation4 citations

TL;DR

This study compares shock propagation in firm-level production networks (FPNs) versus aggregated industry-level networks (IPNs) using a comprehensive Hungarian dataset of 243,399 firms. It demonstrates that IPN-based models systematically underestimate economic losses by up to 37% due to unaccounted firm heterogeneity within sectors, revealing a fundamental limitation in using aggregated IO models for predicting economic resilience and policy impacts.

ABSTRACT

To estimate the reaction of economies to political interventions or external disturbances, input-output (IO) tables -- constructed by aggregating data into industrial sectors -- are extensively used. However, economic growth, robustness, and resilience crucially depend on the detailed structure of non-aggregated firm-level production networks (FPNs). Due to non-availability of data little is known about how much aggregated sector-based and detailed firm-level-based model-predictions differ. Using a nearly complete nationwide FPN, containing 243,399 Hungarian firms with 1,104,141 supplier-buyer-relations we self-consistently compare production losses on the aggregated industry-level production network (IPN) and the granular FPN. For this we model the propagation of shocks of the same size on both, the IPN and FPN, where the latter captures relevant heterogeneities within industries. In a COVID-19 inspired scenario we model the shock based on detailed firm-level data during the early pandemic. We find that using IPNs instead of FPNs leads to errors up to 37% in the estimation of economic losses, demonstrating a natural limitation of industry-level IO-models in predicting economic outcomes. We ascribe the large discrepancy to the significant heterogeneity of firms within industries: we find that firms within one sector only sell 23.5% to and buy 19.3% from the same industries on average, emphasizing the strong limitations of industrial sectors for representing the firms they include. Similar error-levels are expected when estimating economic growth, CO2 emissions, and the impact of policy interventions with industry-level IO models. Granular data is key for reasonable predictions of dynamical economic systems.

Motivation & Objective

• To quantify the error introduced in economic loss predictions when aggregating firm-level production networks (FPNs) into industry-level networks (IPNs).
• To investigate how firm heterogeneity within sectors distorts shock propagation estimates in input-output (IO) models.
• To evaluate the accuracy of IPN-based models in predicting production losses during crises, such as the early COVID-19 pandemic.
• To demonstrate that aggregated IO models systematically underestimate actual firm-level losses due to structural oversimplification.

Proposed method

• The study constructs a nearly complete nationwide firm-level production network (FPN) with 243,399 firms and 1,104,141 supplier-buyer relationships in Hungary.
• It models shock propagation on both the FPN and the IPN using identical initial shock sizes, comparing downstream production losses.
• A COVID-19-inspired scenario is simulated using detailed firm-level data to assess shock propagation under real-world conditions.
• The study uses 1,000 synthetic shock scenarios on the FPN and compares the resulting loss distributions with those from the IPN.
• It calculates the mean absolute error (MAE) between IPN-based and FPN-based loss estimates to quantify model inaccuracy.
• The analysis includes both linear and non-linear production function assumptions, with a focus on labor shock propagation.

Experimental results

Research questions

• RQ1 How do production loss estimates differ when shocks are modeled at the firm level versus the aggregated industry level?
• RQ2 To what extent does firm heterogeneity within sectors distort the accuracy of input-output models in predicting economic shocks?
• RQ3 What is the magnitude of error introduced by aggregating firm-level production networks into sector-based IO models?
• RQ4 How does the variability of loss outcomes differ between FPN and IPN models under identical initial shock conditions?
• RQ5 To what extent do IPN-based models underestimate or overestimate actual firm-level economic losses during crises?

Key findings

• The use of industry-level input-output models leads to an average underestimation of economic losses by 31.1% compared to firm-level network models.
• In extreme cases, IPN-based predictions underestimated actual firm-level losses by up to 75.5%, particularly in sectors like K65 (financial services).
• The maximum loss in some industries varied by a factor of up to 41.1 (sector K65) across different firm-level shock scenarios, despite identical initial shocks at the industry level.
• Firm-level production losses showed strong right-skewness and high inter-shock variability, which IPNs failed to capture entirely.
• Even under linear production functions, IPN-based models systematically underestimated the true scale of losses, with an average error of -45.35%.
• The study attributes the large discrepancy primarily to the low degree of intra-industry trade: on average, firms within the same sector only transact 23.5% of their sales and 19.3% of their purchases with other firms in the same sector.