4.2  Industry interconnectedness (continued)

Figure 10: Column entropy (final demand weighted)

(12)    

where and for all i and j .

Note that is generally replaced by (Theil 1971).

The row and column entropy are conceptually similar to the backward and forward concentration index, but take into account final demand. Figures 9 and 10 plot the row and column entropy measures. Taking into account final demand sales has the effect of raising the relative importance of wood and paper products, printing; and agriculture, forestry, fishing in New Zealand in terms of backward industry connectedness (Figure 9). The relative importance of agriculture, forestry, fishing also increases in Australia.

Moreover, a comparison of the row and column entropy (Figures 9 and 10) with the backward and forward concentration index (Figures 7 and 8) shows that taking into account final demand lowers the relative importance of finance in New Zealand, Belgium and Finland. This suggests that the finance industry in New Zealand, Belgium and Finland probably offers similar products to that in other countries and provides services across all industries in the economy, but the amount of credit channelled through the final system for final demand is lower.

The measures discussed so far rank industries by sales and purchases with other industries. To take into account inter industry transactions as well as deliveries to final demand, an extended version of the entropy measure can be used. The entropy of total sales flows is calculated by normalising

(13)    

and then dividing both sides of (13) by x_i and applying the following entropy formula to the proportions, ,

(14)    

The entropy for total sales flows is plotted in Figure 11. When taking into account intermediate and final sales, communication services; finance; chemical, petrol, rubber etc; and transport and storage have the largest entropy in New Zealand. That is, a large number of households and exporters, for example, will buy additional output from these industries following an increase in these industries’ output. Moreover, other industries will also buy additional output from these industries in the form of intermediate products.

Figure 11: Entropy for total sales flows

 

The entropy for total sales flows is high across all countries for communication services and generally large for chemical, petrol, rubber etc; and transport and storage. The entropy for total sales flows is also high for finance in the United Kingdom. The finding that finance ranks more highly in New Zealand for the total sales entropy than the column entropy supports the hypothesis that finance is more important in terms of lending to industries than for final demand.

The relative importance of electricity, gas, and water is lower in New Zealand compared to other countries. Electricity, gas, and water has the highest entropy for total sales flows in Belgium, Finland and Germany. It ranks second in Australia and third in Denmark, Norway and the United Kingdom. In New Zealand electricity, gas, and water has the eighth largest entropy for total sales flows. A lower degree of inter industry connectedness for this industry is in line with the finding in Black, Guy and McLellan (2003) of a decline in productivity in the electricity, gas, and water over the 1993-2002 period.