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.