Annex 3A: The Downstream Index

Using the input-output table, Antràs and Chor (2013) propose a measure to capture the “downstreamness” of an industry in the value chain. Following is a sketch of their measurement and details of an application to the Indian input-output table. The basic input-output identity is as follows:

Yi = Fi + Zi, (3A.1)

where Yi is the total output in industry i; Fi is the output of i that goes toward final use; and Zi is the use of i’s output as inputs in other industries. In a world with N industries, this identity can be expanded as:

Y F i i= + dF dd F dj N ij j j N k ik kj j j N k N l NN 1 1 1 1 1 1∑ ∑ ∑ ∑ ∑ ∑+ + = = = = = = il dd lk kj Fj +… (3A.2)

where dij for a pair of industries is the amount of i used as an input in producing a dollar’s worth of industry j’s output. ∑N =1j dF ij j captures the value of i’s direct use as an input at industry j to produce output that immediately goes to final use. The remaining terms N K 1 1 N ∑ ∑= =j dd ik kj F d j J N N l N K 1 1 1+∑ ∑ ∑= = = ildd lk kj Fj +… that involve higher-order summations reflect the indirect use of i as an input. These indirect inputs enter the value chain for future production at least two production stages away from final use.

The downstream index measures the distance of an industry to the final products consumed by final consumers. In practice, the index is calculated by dividing the direct use of industry i’s product as an input for final use production by the total use of i’s product as inputs in other industries. The higher the ratio in a given industry i, the more intensive is its use as a direct input for final use production, so that the industry is closer to the downstream stage of the value chain. Conversely, a lower ratio indicates that most of the contribution of input i to production processes occurs indirectly and that the industry is located closer to the upstream stage of the value chain.

Based on their methodology, the analysis relies on the Indian input-output table to calculate the relative position of each industry. The input-output table has been constructed for the year 2013–14, which is consistent with the national accounts estimates provided in the 2015 national accounts statistics. The input-output table contains 140 rows (products) and 67 columns (sectors), which have been collapsed and expanded to make the 130*130 input-output table of Singh and Saluja (2018).

First, the analysis calculates the N*N direct requirement matrix D and the N*1 final use vector F by summing over the value of each industry i’s output purchased for consumption and investment by private or government entities and the N*1 output vector Y as the summation of all entries in row i in the input-output table. Then, the analysis calculates the direct use of each industry as DF, and the total input use for each industry as Y−F. The ith element of the direct use vector DF is divided by the corresponding ith element of the input vector Y−F, which generates the downstream index of industry i.