Before revision:  In our framework, an input is technologically more relevant if a shock on that upstream market can hit harder the marginal costs of a downstream buyer , considering the topology of the supply structure. A higher labor intensity at each stage buffers the transmission of upstream shocks in the network. In addition, we provide for the possibility that producers have limited knowledge of inputs in the supply network, hence they can underestimate the relevance of more distant inputs. After applications, the Input Rank returns a matrix of technological centralities that order any direct or indirect input for a representative firm in any output industry. We compute the Input Rank on U.S. and world input-output tables .
After revision:  In our framework, an input is technologically more relevant if a shock on that upstream market can hit harder the marginal costs of a downstream buyer , considering the topology of the supplier relative to the buyer, ii) the patterns of intermediate inputs vs labor intensities connecting the buyer and the supplier, iii) and the competitive pressures along supply chains. After we compute the Input Rank on U.S. and world input-output tables .