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In this paper, we introduce the Input Rank as a measure to study the organization of supply networks at the firm level. We assume that a Markov process of exploration may be started by a producer throughout her web of direct and indirect suppliers, to assess the technological relevance of each direct and indirect input, when her ability to outreach in the supply network may be limited. Therefore, each producer ends up with an input-output eigenvector centrality, which is higher when a direct or indirect input is relatively more requested to produce other direct or indirect inputs, and when that input is relatively more requested to produce other highly-requested inputs. Finally, we compute the Input Rank on U.S input-output tables and test its empirical validity for choices of vertical integration on a dataset made of 20,489 U.S. parent companies controlling 154,836 affiliates worldwide. Results show that a higher Input Rank is positively associated to a higher probability that that input is vertically integrated, relatively more when the demand faced by the parent company is more elastic. We argue that a producer reduces the risk of disruption in her supply network when a central input is vertically integrated. In this framework, the Input Rank is at least complementary to previous sequential metrics (e.g. upstreamness or downstreamness), because it better catches the recursive nature of real-world supply networks, whereas linear technological sequences may be just corner solutions.
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