  This paper is concerned with upstreamness and downstreamness of industries
and countries in global value chains. Upstreamness and downstreamness measure
respectively the average distance of an industrial sector from final
consumption and from primary inputs, and they are computed from based on the
most used global Input-Output tables databases, e.g., the World Input-Output
Database (WIOD). Recently, Antr\`as and Chor reported a puzzling and
counter-intuitive finding in data from the period 1995-2011, namely that (at
country level) upstreamness appears to be positively correlated with
downstreamness, with a correlation slope close to $+1$. This effect is stable
over time and across countries, and it has been confirmed and validated by
later analyses. We first analyze a simple model of random Input/Output tables,
and we show that, under minimal and realistic structural assumptions, there is
a natural positive correlation emerging between upstreamness and downstreamness
of the same industrial sector/country, with correlation slope equal to $+1$.
This effect is robust against changes in the randomness of the entries of the
I/O table and different aggregation protocols. Secondly, we perform experiments
by randomly reshuffling the entries of the empirical I/O table where these
puzzling correlations are detected, in such a way that the global structural
constraints are preserved. Again, we find that the upstreamness and
downstreamness of the same industrial sector/country are positively correlated
with slope close to $+1$, even though the random reshuffling has destroyed any
underlying economic information about inter-sectorial connections and trends.
Our results strongly suggest that the empirically observed puzzling correlation
may rather be a necessary consequence of the few structural constraints that
Input/Output tables must meet.
