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First suppose production of sector j increases due to a shock on final demand.
Figure 8 shows the detailed distribution of the effect on production of a shock on final demand according to different targets.
We relate the ranking provided by global centralities to the diffusion properties of sectors using the idea that the effect of a shock on final demand has an effect on sectoral and aggregate production.
where s i is the fraction of the effect on production of a shock on final demand that is absorbed by sector i, l ji is the jith element of the Leontief inverse, and n is the number of sectors in the economy.
The method consists on computing input-output linkages and authority and hub centralities of sectors in the network and comparing the most central sectors to the sectors that bring about a high aggregate effect on production when they receive a shock on final demand, while having a good diffusion of the effect across the economy.
Dietzenbacher and Romero (2007) proposed the mean of average propagation lengths that measures the average number of steps it takes for a shock on final demand of sector i to reach sector j and show that the average distance between these two sectors does not depend on whether the backward or forward perspective is adopted.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com