We use data from the U.S. airline industry to test the hypothesis, consistent with the general equilibrium oligopoly model of Azar and Vives (2021), that inter-industry common ownership should be associated with lower prices in product markets. We find that, as the model predicts, increases over time in intra-industry common ownership are associated with higher prices, while increases in inter-industry common ownership are associated with lower prices. The aggregate effect is nil. We also find that common ownership by the ``Big Three'' (BlackRock, Vanguard and State Street) is associated with lower airline prices, while common ownership by shareholders other than the Big Three is associated with higher prices. The results highlight the limitations of partial equilibrium oligopoly theory in the context of common ownership, and the need to consider a general equilibrium perspective.