  We introduce the Input Rank as a measure of relevance of direct and indirect
suppliers in Global Value Chains. We conceive an intermediate input to be more
relevant for a downstream buyer if a decrease in that input's productivity
affects that buyer more. In particular, in our framework, the relevance of any
input depends: i) on the network position 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 from both U.S. and world Input-Output
tables, we provide useful insights on the crucial role of services inputs as
well as on the relatively higher relevance of domestic suppliers and suppliers
coming from regionally integrated partners. Finally, we test that the Input
Rank is a good predictor of vertical integration choices made by 20,489 U.S.
parent companies controlling 154,836 subsidiaries worldwide.
