Controllability analyses of nation-wide firm networks


Since government fiscal policy stimulates firms and is expected to produce spillover effects, it is important to know the effects on the economy. The government’s approach can be rephrased as control of the economy, because governments have ideal states of the economy, and they want to lead it to the states. Here, we investigate a firm production network observed exhaustively in Japan and determine which firms should be directly or indirectly controlled using the framework of controllability. We can classify firms into three different types: (a) firms that should be directly controlled; (b) firms that should be indirectly controlled; and (c) neither of them. Since there is a direction (supplier and client) in the production network, we can consider controls of two different directions: the demand and supply sides. We obtain the following results: (1) each industry has diverse share of firms that should be controlled directly or indirectly. The configurations of the shares in industries are different between demand and supply sides; (2) advancement of industries that are divided into primary industries or other advanced industries do not show apparent difference in controllability; and (3) if we clip a network in descending order of capital size, we do not lose the control effect for both demand and supply sides.

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    The study that addresses the framework of controllability (Liu et al. 2011) uses weight matrixes of links. However, this paper also proves that we only need to know the existence of directed links with arbitrary weights to calculate controllability.


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Corresponding author

Correspondence to Hiroyasu Inoue.

Additional information

This study is conducted as part of the “Price Network and Dynamics of Small and Medium Enterprises” project undertaken by the Research Institute of Economy, Trade and Industry (RIETI). The authors thank the RIETI for various means of support. We thank Hiroshi Yoshikawa, Hideaki Aoyama, Hiroshi Iyetomi, Yuichi Ikeda, Yoshi Fujiwara, Wataru Soma, Yoshiyuki Arata, and attendees of the internal seminar of RIETI for their helpful comments. In addition, we thank Yang-Yu Liu for sharing his program codes and providing helpful comments. We gratefully acknowledge financial support from the Japan Society for the Promotion of Science (No. 15K01217).

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Inoue, H. Controllability analyses of nation-wide firm networks. Evolut Inst Econ Rev 14, 335–349 (2017).

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  • Network
  • Firm
  • Controllability
  • Demand side
  • Supply side

Mathematics Subject Classification

  • D22
  • H32