Tie-formation process within the communities of the Japanese production network: application of an exponential random graph model

This paper studies the driving forces behind the formation of ties within the major communities in the Japanese nationwide network of production, which contains one million firms and five million links between suppliers (“ upstream " firms) and customers (“ downstream " firms). We apply the Infomap algorithm to reveal the hierarchical structure of the production network. At the second level of the hierarchy, we find a reasonable community resolution, where the community size distribution follows a power law decay. Then, we estimate the tie formation within 100 communities of different sizes. The studied model considers a large set of attributes, including both endogenous attributes (network motifs, e.g., stars and triangles) and exogenous attributes (economic variables, e.g., net sales and firm size). The estimation results show that the considered model converges and presents a high goodness of fit (GoF) for all communities. Moreover, it is found that the forces explaining the formation of links between suppliers and customers differ among communities. Some attributes, such as reciprocity, popularity, activity, location homophily, bank homophily and sales statistics, are common drivers of internal link formation for most of the studied communities. However, transitivity is rejected as a significant influencing factor for most communities, reflecting an absence of a sense of trust and reliability between firms with a common partner. Finally, we show that sector homophily does not serve as an obvious mechanism of partnership at the community level in the production network.