4  Inter industry linkages

To assess countries’ industrial structures in terms of industry linkages this section applies input output coefficients. They are calculated from the inter industry transactions matrix and take into account both direct and indirect transactions. The production structures are examined using six types of measure: (i) backward and forward linkages, (ii) indices of industry interconnectedness, (iii) a value added index, (iv) a value added production multiplier, (v) a cumulated primary input coefficient for compensation of employees and (vi) a measure of import content of final demand output. To compare countries’ production structures, these measures are calculated for each industry of the eight countries. The number of industries varies across countries and to facilitate comparison across economies, countries’ industries are grouped into 16 industry categories, except for Norway, where the number of categories is 14 and the United Kingdom, where it is 17.[8] We then calculate category averages for all measures (apart for import content) and rank the averages from highest to lowest.[9] The graphs plot the inter industry linkages measures for each industry ranked according to their category averages.

4.1  Backward and forward linkages[10]

Backward and forward linkages are descriptive measures of the economic interdependence of industries in terms of the magnitude of transactions. They can be interpreted as an estimate of the direct and indirect increase in output following an increase in final demand. Backward and forward linkages, which were first proposed by Rasmussen (1956), are calculated from the Leontief inverse or total requirement matrix [I - A]^-1 .[11] The Leontief inverse is weighted by final demand (discussed further below).

The elements of the final demand weighted Leontief inverse are denoted by and calculated as follows

(4)    

The average of the elements in column j [12]

(5)    

shows the input requirements for a unit increase in the final demand for industry j’s output given each industry’s share in total final demand. It is called the backward linkage as it measures the impact on the supplier industries of a unit increase in final demand.[13] If the Leontief inverse was not weighted, the backward linkage would be an estimate of the direct and indirect increase in output to be supplied by an industry chosen at random following an increase in final demand for industry j’s output. The weighting can thus be interpreted as applying a probability measure (Rasmussen, 1956).[14]

Expressing the backward linkage as an index

(6)    

allows inter industry comparisons to be made. The numerator in equation (6) measures the average stimulus to other industries, according to each industry’s share in total final demand, resulting from a unit increase in the final demand for industry j’s output. The denominator measures the average stimulus to the whole economy resulting from a unit increase in the final demand for the output of all industries.

Conversely, the index of forward linkage is given by

(7)    

where the average of the elements in row i

(8)    

shows the increase in the output of sector needed to supply the inputs required to produce an additional unit of final demand output given each industry’s share in total final demand. Weighting the total requirement coefficient matrix is important for the forward index as it avoids a possible bias. The forward linkage would be subject to a bias noted in Chatterjee (1989) if the total requirement matrix wasn’t weighted. This is because “for the row sum to measure the forward linkage in an unbiased fashion, it is necessary to make the assumption that the demands for all sectors increase by one unit. All sectors are unlikely in practice to be of equal importance in the structure of demand, so if a small sector j uses inputs from sector i disproportionately largely, the forward linkage index will be blown up artificially by the assumption of equal expansion of all sectors” (Chatterjee 1989, p. 96). Weighting the total requirement matrix avoids this problem.