Does the supply network shape the firm size distribution? The Japanese case

The paper examines the relationship between the structure of the Japanese supply network and the firm size distribution. We obtain five main original results through a combination of empirical analysis, analytical decomposition of growth rate volatility, and numerical simulations. First, Gibrat's law only holds for larger firms, which are typically located upstream in the supply network, while it breaks down for smaller firms, which are more likely to be located downstream. Second, this structural asymmetry explains why downstream firms are concentrated in the power-law tail of the size distribution. Third, final demand shocks are amplified when propagating to upstream firms, explaining their higher growth rate volatility and consequently smaller average growth. Fourth, the magnitude of this amplification is determined by the degree of complexity of the network structure and the market power of the downstream firms. Finally, the power-law tail disappears in completely connected networks that lack layers or hierarchical structure. A significant implication of our findings is that aggregate demand shocks can affect the economy both directly, by reducing output for downstream firms, and indirectly, by shaping the firm size distribution.