Geoscience Reference
In-Depth Information
associated with interindustry production generated in response to a spending
program interpreted in traditional Leontief parlance as a new vector of final
demands presented to the economy.
5
A straightforward and commonly applied
6
approach to accounting for quantifiable
impacts associated with interindustry activity, such as pollution generation, is to first
define a matrix of direct impact coefficients,
[
d
k
p
]. Each element,
d
k
p
, in the case
of pollution impacts as an illustration, is the amount of pollutant type
k
, e.g., sulfur
dioxide, generated per dollar's worth of industry
j
's output. Hence, the level of
pollution associated with a given vector of total outputs can be expressed as
x
p
D
¼
p
*
p
¼
D
x
p
*
is the vector of pollution levels. By adding the traditional Leontief model,
where
x
x
¼
Lf
,where
A
is the matrix of technical coefficients,
f
is the vector of final demands,
p
*
as a
function of final demand, that is, the total pollution of each type generated by the
economy directly and indirectly in supporting that final demand,
)
1
, we can compute
and
x
is the vector of total outputs, and
L
¼
(
I A
x
p
*
p
x
¼
D
Lf
.
p
, is a matrix of total environmental impact coefficients;
that is, an element of this matrix is the total pollution impact generated per dollar's
worth of final demand presented to the economy.
7
Similarly, we can expand the
pollution coefficients matrix with similar coefficients for other factors associated
with interindustry activity that we assume vary linearly with output, such as
employment or energy consumption.
For this illustrative example we restrict the generalized framework to energy
use, environmental pollution, and employment as illustrative of the more general
case in which we define three direct-impact coefficient matrices relating energy
requirements, pollution generation and employment to total output:
The matrix product,
D
L
l
,
respectively, in units such as British thermal units (Btus) of energy of energy used
(coal, oil, electricity, etc.), pounds of pollution emissions (sulfur dioxide,
particulates, carbon dioxide, etc.), and person-years of employment all expressed
per dollar's worth of output. For convenience, we concatenate these matrices to
e
,
p
and
D
D
D
éù
êú
=
ê
ê
ëû
e
D
DD
D
p
yield a direct-impact coefficient matrix
and similarly define a vector of
l
*
, by concatenating
e
*
e
p
*
p
l
*
l
total impacts,
x
x
¼
D
x
,
x
¼
D
x
, and
x
¼
D
x
to yield
éù
êú
=
ê
ê
ëû
x
xx
x
e
*
*
*
p
*
or
x
¼
Dx
. For accounting convenience, we can include
x
along with the
l
*
corresponding final demands associated with the generation of a particular vector of
5
See Blair (
1979
) and Miller and Blair (
2009
), Chap. 10.
6
Beginning with Victor (
1972
) and many others over the past four decades; see Miller and Blair
(
2009
), Chap. 10.
7
Measuring energy and environmental activities in input-output models in monetary units can
create accounting inconsistencies as described in Miller and Blair (
2009
), but adopting hybrid
units for such calculations, e.g., energy units for energy transactions, have limitations as well as
described in Dietzenbacher and Sage (
2006
).
