Backward Linkage

Definition

Backward Linkage captures the interconnection of an industry to other industries from which it purchases its inputs in order to produce its output.

In the simplest forms linkages are measured as summations of the appropriate IO matrix

Direct Backward Linkage

The proportion of intermediate consumption to the total output of the sector. In terms of the Technical Coefficient Matrix this is expressed as the sum

$b_j = \sum_{i=1}^{n} a_{ij}$

Expressed in terms of transactions (Z, Input-Output Matrix not A) it captures the value of total intermediate inputs for a sector j as a proportion of the value of j’s total output.

Total Backward Linkage

The proportion of intermediate consumption to the total output requirement (capturing both direct and indirect linkages in an economy) can be expressed as the column sums of the total requirements matrix (Leontief Inverse Matrix) L.

$c_j = \sum_{i=1}^{n} l_{ij}$

An industry has significant backward linkages when its production of output requires substantial intermediate inputs from many other industries.

See Also

• Forward Linkage

Further Resources

• Crash Course on Input-Output Model Mathematics
• Introduction to Input-Output Models using Python