Synthetic supply networks

Large-scale economic models require a granular understanding of how money and goods move between entities. To simulate an economy accurately, researchers need a representative population of both households and firms. They also need a map of the transactions that connect them. Scientists have developed reliable ways to create synthetic populations of households (artificial groups of people that mimic real-world demographics). However, creating a synthetic version of the corporate world is significantly harder. It is not enough to simply generate a list of plausible companies. One must also reconstruct the intricate web of supply chain links that dictate who buys from whom and in what volumes.

The bottleneck of confidential micro-data

Economic shocks propagate through the economy via transactions between firms. However, these transactions are rarely observable to the public. In the few nations where high-resolution production network data exists, it is often protected by strict confidentiality laws. This prevents the re-identification of specific businesses. This creates a fundamental bottleneck for researchers. You cannot build a high-fidelity model of a modern economy if the "wiring diagram" of its supply chains is locked away in private databases.

Current attempts to bypass this hurdle generally fall into two camps. One approach involves training machine learning models on confidential data. Researchers then use these models to generate synthetic replacements. While promising, this requires initial access to the very data that is being protected. It also carries the risk that the model might "memorize" sensitive details. Another approach relies on aggregate data, such as input-output tables (IOTs). These are high-level summaries of total value flows between different industrial sectors. While IOTs are publicly available, they are "blunt" instruments. They tell you the total volume of trade between industries but nothing about individual firm-level connections. Bridging the gap between these two scales remains a challenge.

A four-stage reconstruction pipeline

The authors propose a method to synthesize these networks using only publicly available information. Their approach fills in microscopic details while ensuring macroscopic totals remain accurate. The process functions as a multi-stage reconstruction pipeline, as detailed in .

1. Topology Generation: The process begins by sampling "degree sequences" (lists of how many suppliers and customers each firm has). To ensure realism, the authors draw these numbers from Burr XII distributions. These are mathematical tools used to model "fat-tailed" phenomena. In these systems, a small number of entities hold a disproportionately large number of connections. They then couple these sequences to replicate the natural correlation between a firm's number of suppliers and its number of customers.
2. Binary Network Assembly: Using these sequences, the algorithm employs a configuration model to generate a directed, binary network. This is a skeleton of connections that indicates who is connected to whom. It does not yet consider the dollar value of those connections.
3. Weight Attribution: Once the skeleton is built, the algorithm assigns "weights" (transaction values) to each link. The authors use a "gravity-like" formula. This formula considers both the connectivity (degree) of the firms and their "fitness." Fitness is a latent (hidden) variable representing a firm's inherent capacity for high-volume trade.
4. Macro-level Calibration: Finally, the algorithm allocates firms to specific industries and performs a rescaling step. This ensures that when you sum all individual firm-to-firm transactions within an industry pair, the result matches the official, aggregate input-output table exactly.

To find the right balance for these weights, the authors utilize Optuna. This is an automated hyperparameter optimization framework (a tool that automatically finds the best settings for a model). As shown in, the system minimizes a complex "loss function." This function penalizes the model whenever the synthetic network's statistics deviate from empirical reality.

Matching the micro and the macro

The efficacy of this method is demonstrated through a large-scale application. The authors generated a synthetic production network for 100,000 firms modeled after the 2015 Hungarian economy. The results show that the pipeline captures both micro and macro data qualities.

On the micro-scale, the synthetic network mimics the "fat-tailed" nature of real-world commerce. For example, the in-degree tail exponent (a measure of how heavily skewed the number of suppliers is toward a few massive hubs) was 2.53. This nearly hit the empirical target of 2.5. Similarly, the out-degree tail exponent was 1.46, compared to a target of 1.5. On the macro-scale, the agreement is even more striking. The authors measure the error in the aggregated industry flows using Root Mean Square Error (RMSE). The resulting error was a negligible $8.01 \times 10^{-4}$ (relative to 100 million USD). provides visual confirmation.

It shows that the synthetic industry-level transactions overlap almost perfectly with the real-world Hungarian input-output table.

Limitations in topology and accounting

Despite the statistical success, the method is not a perfect mirror of reality. The authors are transparent about two primary limitations. First, the "configuration model" used to build the initial network skeleton is mathematically efficient but structurally simplistic. It does not explicitly account for "clustering" (the tendency of firms to form tight-knit triangles of mutual suppliers) or "reciprocity" (the likelihood that if Firm A buys from Firm B, Firm B also buys from Firm A). Consequently, the specific "shape" of local neighborhoods may lack some real-world nuances.

Second, there is a conceptual friction between the types of data being merged. Input-output tables (IOTs) are constructed using specific accounting conventions. These often smooth over complexities like wholesale versus retail margins or transportation costs. Because the algorithm forces the firm-level data to aggregate into these smoothed IOTs, the synthetic network may inherit these "averaging" biases. For researchers building ultra-high-fidelity simulations of niche markets, these discrepancies could introduce subtle errors in how value moves through the system.

A scalable tool for economic simulation

The verdict is clear: this is an effective tool for large-scale economic modeling. By decoupling the need for confidential micro-data from the need for macro-level accuracy, the authors have provided a way to "democratize" high-resolution economic research. The method is remarkably scalable. The authors report the ability to generate networks of up to 500,000 firms. Computational requirements scale linearly with the number of edges rather than quadratically with the number of firms.

The code is openly available at https://github.com/galvinngkw/synthetic_supply_networks. It provides a functional benchmark for the community. While it may not replace specialized, proprietary datasets for high-stakes supply chain risk management, it serves as a powerful engine for initializing agent-based models. This allows researchers to run stress tests on entire national economies without ever touching private corporate data.

Figures from the paper