Firm volatilities comove strongly over time, and their common factor is the dispersion of the economy-wide firm size distribution. In the cross section, smaller firms and firms with a more concentrated customer base display higher volatility. Network effects are essential to explaining the joint evolution of the empirical firm size and firm volatility distributions. We propose and estimate a simple network model of firm volatility in which shocks to customers influence their suppliers. Larger suppliers have more customers, and customer-supplier links depend on customers' size. The model produces distributions of firm volatility, size, and customer concentration consistent with the data.