  Ranking sectors and countries within global value chains is of paramount
importance to estimate risks and forecast growth in large economies. However,
this task is often non-trivial due to the lack of complete and accurate
information on the flows of money and goods between sectors and countries,
which are encoded in Input-Output (I-O) tables. In this work, we show that an
accurate estimation of the role played by sectors and countries in supply chain
networks can be achieved without full knowledge of the I-O tables, but only
relying on local and aggregate information, e.g., the total intermediate demand
per sector. Our method, based on a rank-$1$ approximation to the I-O table,
shows consistently good performance in reconstructing rankings (i.e.,
upstreamness and downstreamness measures for countries and sectors) when tested
on empirical data from the World Input-Output Database. Moreover, we connect
the accuracy of our approximate framework with the spectral properties of the
I-O tables, which ordinarily exhibit relatively large spectral gaps. Our
approach provides a fast and analytical tractable framework to rank
constituents of a complex economy without the need of matrix inversions and the
knowledge of finer intersectorial details.
