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We extend the econometric literature on the role of production networks in the propagation of monetary policy shocks along two dimensions. First, we allow for time‐varying industry‐specific responses, reflecting non‐linearities and heterogeneity in direct transmission channels. Second, we allow for time‐varying network structures and dependence. This captures both variation in the structure of the production network and differences in cross‐industry demand elasticities. Spillover effects among industries appear to be important in periods of elevated economic and financial uncertainty, often coinciding with tight credit market conditions and financial stress. Cross‐sectional differentials can be explained by how close industries are to end‐consumers.