Does the Supply Network Shape the Firm Size Distribution? The Japanese Case

The relationship between firms' growth rates and firm size distribution has been extensively analyzed in the literature. In particular, the breakdown of Gibrat law for medium and small firms has been identified as the reason for the emergence of a power law only in right tail of the size distribution. However, the growth rates of firms are not mutually independent, since firms are connected in the supply network and idiosyncratic shocks are transmitted through the networks links. This paper presents a stylized empirical and theoretical investigation on the Japanese supply network to shed light on the effects of demand shock on the growth of firms in the different layers of the network. We find that the growth rates are more volatile for small firms, which tend to be located upstream in the supply network, leading to the breakdown of the Gibrat law. The difference in growth volatility depends on the fact that downstream shocks are amplified as they are transmitted upward in the supply chain. The extent of the amplification depends on the level of connectivity of the network and, more precisely, it is larger in more dense networks. Further, the level to which a firm is affected depends on its relative position within the network