Page 292 - Special Topic Session (STS) - Volume 4

STS587 Guangwu C.
driven model and Ghosh supply-driven model to quantifying production of
the new goods and services, consumption from consumers and the labour and
capital income. This integrated study plans to give a whole picture for
assessing the size and growth of the digital economy and its possible
contributions to household’s welfare.

2. Methodology: Leontief and Ghosh models
Our model start with Leontief’s famous demand-side (Leontief, 1936;
Leontief, 1949) and Leontief and Strout (1963). Assume that an economy can
be categorized into n sectors. Let = ( ) be a × intermediate
×
transaction matrix with representing the input from the ith sector to the jth

sector in the economy, = ( ) be an × 1 vector of the total output
×1
with being the ith sectoral total output, = ( ) be an × direct
×

requirement coefficient matrix with showing the direct input from the ith

sector to the jth sector to produce one unit of output, = ( − ) be the
−
famous Leontief Inverse Matrix representing both direct and indirect input in
order to produce on unit of output; and = ( ) be an × flow matrix
×
including m categories of final demand and with being the ith sectoral final

demand. The standard Leontief’s demand-driven input-output model can be
) .
shown as: = = ( − ) − = ( − ̂ − −
The supply-side input-output model was developed by Ghosh (Ghosh,
1958) as a supplement to the Leontief demand-driven input-output model.
Ghosh’s input-output model is an allocation model with the column balance
equation x’=i’T+v, v is the row vector of value added, i is a suitable unitary
vector.
The direct output coefficients B is calculated by dividing each row of T by

the gross output of the sector associated with that row. Its matrix = ̂ − ,
namely allocation coefficients, represents that the distribution of outputs of
the original sectors. The outputs across all sectors of the economy show inter-
industrial sectors buying input from the original sectors.
′
′
′
Using the column balance equation, we have = + = ̂ + =
′
+ = ( − ) − = . The matrix G is called the Ghosh inverse, relating
sectoral gross production to the primary inputs — a unit of value entering the
inter-industry (supply chain) system at the beginning of the process. It is
termed a supply inverse and measures the production values of sectors that
come in the supply chain system caused by per unit of primary input in sectors
(Miller and Blair, 2009).
Attaching the satellite accounts to the supply chain system, the extended
Leontief and Ghosh models can be shown respectively as = and
Q=vGq, where Q represents total digitalisation and q is the sectoral intensity
vector that is calculated by = ̂ − , indicating digitalised impacts caused by
producing per unit of sectoral output. Accordingly, the vector Ly in the

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