4.2 Industry interconnectedness (continued)
- Figure 8: Forward concentration index
where 
and 
for all i and j
The larger is the measure of concentration, the more industries’ transactions or the higher the degree of outsourcing and diversification. Conversely, the smaller the measure of concentration is, the fewer inter industry sales or purchases.[18]
Figures 7 and 8 plot the backward and forward concentration index. Food, beverages, tobacco; construction; trade, restaurant, hotels; and public administration in New Zealand are important in terms of how much they purchase from other industries directly and indirectly (backward linkage, Figure 3), but also in terms of the number of industries they buy products from (backward concentration index, Figure 7). In contrast, in other countries, the relative importance of industries appears to differ more than in New Zealand depending on whether backward linkages or the backward concentration index is used. One interpretation is that industries in New Zealand tend to purchase many inputs from many industries, whereas in other countries, industries tend to either buy many inputs from some industries or purchase some inputs from many industries.[19]
The relative importance of industries changes in New Zealand measured in terms of forward concentration compared to forward linkages. The forward concentration index, which shows the dispersion across industries of a unit increase in final demand output on industries’ sales to other industries, is largest for communication services in New Zealand. The importance of communication services also increases in other countries in terms of the number of industries selling to relative to the magnitude of sales.
Overall, the importance of dwellings, property and business services generally declines across countries when adjustment is made for the magnitude of transactions. The relative importance of finance increases in New Zealand and Belgium, and to a lesser extent in Finland, when measured by the number of industries transacting with rather than value of sales and purchases.
An alternative measure of industry interconnectedness is entropy. Entropy, which has its origin in physics, is a measure of disorder.[20] The higher (lower) is the entropy, the more (less) integrated and thus specialised industries are.
The row entropy of sector i is calculated as follows
(11) 
and the column entropy of sector j as
Figure 9: Row entropy (final demand weighted)
Notes
- [18]The index would probably be more adequately called a “de-concentration” index.
- [19]It should be noted that the indexes will be affected by the extent to which countries take out secondary production.
- [20]Consider, for example, two gases, one with all A molecules and one with all B molecules. Mixing the two gases leads to a final mixture of A and B molecules that is less ordered than the initial system of pure A and B molecules. The mixed state is more probable than the unmixed state, i.e. it has a higher entropy, because there are more ways of distributing the molecules of A and B so as to yield mixed states than there are ways to yield pure states. The two gases in the example can be interpreted as industries in an economy.
