Correlation between upstreamness and downstreamness in random global value chains

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 analyze a simple model of random Input/Output tables, and we show that, under minimal and realistic structural assumptions, there is a positive correlation between upstreamness and downstreamness of the same industrial sector, 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. Our results suggest that the empirically observed puzzling correlation may rather be a necessary consequence of the few structural constraints (positive entries, and sub-stochasticity) that Input/Output tables and their surrogates must meet.