The problem of network multiple-input multiple-output precoding under distributed channel state information is a notoriously challenging question, for which optimal solutions with reasonable complexity remain elusive. In this context, we assess the value of hierarchical information exchange, whereby an order is established among the transmitters (TXs) in such a way that~a given TX has access not only to its local channel estimate but also to the estimates available at the less informed TXs. Assuming regularized zero forcing (RZF) precoding at the TXs, we propose naive, locally robust, and globally robust suboptimal strategies for the joint precoding design. Numerical results show that hierarchical information exchange brings significant performance gains, with the locally and globally robust algorithms performing remarkably close to the optimal RZF strategy. Lastly, the cost of hierarchical information exchange relative to the cooperation gain is examined and the optimal tradeoff is numerically evaluated.