To examine the factors that might explain the changes over time in the domestic supply
chain, we conduct a shift-share analysis. This analysis allows us to decompose
the aggregate changes in the supply chain indices into changes in the relative
sizes of sectors with differing supply chain characteristics (‘between
effects’) and changes in the supply chain characteristics of individual
sectors (‘within effects’).

Denote aggregate fragmentation and upstreamness for the economy as a whole by and respectively. The changes in aggregate…