Controllability Analyses on Firm Networks Based on Comprehensive Data

TL;DR

This paper analyzes the controllability of a comprehensive Japanese firm network using control theory, classifying firms into control categories and examining industry and network size effects on controllability.

Contribution

It applies control theory to a large-scale firm network, revealing industry and size-related differences in controllability and the impact of network clipping.

Findings

Industry-specific control share variations

No significant difference in controllability between advanced and primary industries

Controlling only the largest firms maintains control effectiveness

Abstract

Since governments give stimulus to firms and expect the spillover effect by fiscal policies, it is important to know the effectiveness that they can control the economy. To clarify the controllability of the economy, we investigate a firm production network observed exhaustively in Japan and what firms should be directly or indirectly controlled by using control theory. By control theory, we can classify firms into three different types: (a) firms that should be directly controlled; (b) firms that should be indirectly controlled; (c) neither of them (ordinary). Since there is a direction (supplier and client) in the production network, we can consider controls of two different directions: demand and supply sides. As analyses results, 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, such like, primary industries or other advanced industries, does not show apparent difference in controllability; (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.