Measuring the Input Rank in Global Supply Networks

In this paper, we introduce the Input Rank as a measure to study the organization of global supply networks at the firm level. We model the case of a firm that needs assessing the technological relevance of each direct and indirect supplier on a network-like production function with labor and intermediate inputs. 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. Finally, we test how it correlates with choices of vertical integration made by 20,489 U.S. parent companies controlling 154,836 affiliates worldwide. We find that a higher Input Rank is positively associated with higher odds that that input is vertically integrated, relatively more when final demand is elastic. A supplier's Input Rank remains a significant predictor of a firm's decision to integrate even after controlling for the relative positions on upstreamness(downstreamness) segments.