Chapter 7. Indirect environmental requirements: the domestic
7.3.1 The hypothetical two country case
Figure 7.1c shows that a consistent allocation of indirect environmental requirements addresses the final users or the consumers in both countries. This section illustrates the estimation of such a reallocation of environmental requirements in a hypothetical two country case: the domestic economy and the rest of the world.
This is done with the help of an input-output model. Similar to figure 7.1c, both countries depend via trade on each other’s outputs. Suppose for simplicity reasons and for the time being that the total emission of a particular type of pollution in these two countries, denoted by the variables and , only results from production activities and that this pollution can be determined as a function of the total output of these production activities, denoted by vectorsx1andx2.
(7.1) The vectorse1ande2containing the emission coefficients are determined by
and
wherex$1–1andx$–21denote the inverse diagonal matrices of output vectorsx1andx2. Element vl j
x
, of vlx corresponds to the total amount of pollution by production activity (j) in country (1) while elementel j, ofe1represents the emission coefficient or the pollution intensity,i.e.amount of pollution emitted per money unit of output of production activity (j).
With the help of a Leontief inverse, pollution in both countries can be determined as a function of final demand in both countries, denoted by the vectorsy1andy2. Suppose that matricesA1andA2represent the technical coefficients with respect to domestic production in both countries while matricesM1andM2represent the technical coefficients with respect to import,i.e.:
A1=D x1x$1–1andA2=D x2x$2–1
where matrices D1x and D2x represent the domestically produced intermediate deliveries in both countries;
M1=D xm1 $1–1andM2=D xm2 $2–1
⎟⎟⎠⎞
⎜⎜⎝⎛
⎟⎟⎠⎞
⎜⎜⎝⎛
⎟⎟⎠=
⎜⎜⎝ ⎞
⎛
2 1 2 1
x x e' 0
0 e'
x 2 x 1
v v
x 1 1 1
1 x v
e = ˆ− e2 =xˆ2−1vx2
where matricesDm1 andDm2 represent the imported intermediate deliveries in both countries;
Then the pollution model for the two countries can be formulated as follows.
Both equations can be jointly presented as follows.
(7.2) From equation (7.2) the Leontief inverse can be derived in a similar way as the derivation of the Leontief inverse of a regular one-country open Leontief model.
Substitution of equation (7.1) into (7.2) then leads to the following two-country pollution model.
or
(7.3) This model determines the pollution levels in both countries as a function of the final demands in both countries. Pollution in country (1) is jointly determined by the final demands in both countries. Similarly, pollution in country (2) is jointly determined by the final demands in both countries. The partitioning of the Leontief-inverse as shown in the second part of equation (7.3) is determined as follows.
where
L11contains the technical coefficient multipliers representing the output requirements of country (1) with respect to one unit of final demand in country (1);
⎟⎟⎠⎞
⎜⎜⎝⎛
⎟⎟⎠⎞
⎜⎜⎝⎛
⎟⎟⎠⎞
⎜⎜⎝⎛
⎟⎟⎠=
⎜⎜⎝ ⎞
⎛
2 1
y y L L
L L e ' 0
0 e '
2 2 2 1
1 2 11 2 1 2x
1x
v v
( ) 1 1
1 1 1 2 2 1 1
11 I (I A ) M (I A ) M (I A )
L = − − − − − − − −
( 1 1 2 2 1 1)1 1 1 2 2 1
12 I (I A ) M (I A ) M (I A ) M (I A )
L = − − − − − − − − − −
( ) 1 1 1
1 2 1 2 1 1 1 1 2
21 I (I A ) M (I A ) M (I A ) M (I A )
L = − − − − − − − − − −
( ) 2 1
1 2 1 1 1 1 2
22 I (I A ) M (I A ) M (I A )
L = − − − − − − − −
⎟⎟⎠⎞
⎜⎜⎝⎛
⎟⎟⎠+
⎜⎜⎝ ⎞
⎟⎟⎠⎛
⎜⎜⎝ ⎞
=⎛
⎟⎟⎠⎞
⎜⎜⎝⎛
2 1 2 1 2 1
2 1 2
1
y y x x A M
M A x
x
⎟⎟⎠⎞
⎜⎜⎝⎛
⎟⎟⎠⎞
⎜⎜⎝⎛
−
−
−
⎟⎟⎠ −
⎜⎜⎝ ⎞
=⎛
⎟⎟⎠⎞
⎜⎜⎝⎛ −
2 1 1
y y A I M
M A
I e' 0
0 e'
2 1
2 1
2 1 x
2 x 1
v v
2 1 1 2 2
2 A x M x y
x = + +
1 2 2 1 1
1 A x M x y
x = + +
L12contains the technical coefficient multipliers representing the output requirements of country (1) with respect to one unit of final demand in country (2);
L21contains the technical coefficient multipliers representing the output requirements of country (2) with respect to one unit of final demand in country (1);
L22contains the technical coefficient multipliers representing the output requirements of country (2) with respect to one unit of final demand in country (2).
The variablesv1xandv2xin equations (7.1) and (7.3) represent the direct emissions from production in each two countries. Equations (7.4a) and (7.4b) show that the final demand vectors in both countries,i.e.y1andy2, equal the sum of domestic final uses, represented by vectord, and foreign final uses or export, represented by vectorf.
(7.4a) and
(7.4b) Sof1represents that part of final outputy1exported to country (2) and vectorf2 represents the final output of country (2) exported to country (1). Subsequently, total final consumption in both countries (including net capital formation and inventory changes), represented by the vectorsc1andc2,equals:
(7.5a) and
(7.5b) Subsequently, pollution attributed to consumption in both countries,i.e.c1andc2, is determined with the help of equations (7.6a) and (7.6b). The aggregatesvc1andvc2 in these equations correspond to the attributed part of the ‘environmental consumption’ indicators of both countries. The environmental consumption indicator (IV) in table 7.1 includes in addition the direct emissions of households (vh).
(7.6a) (7.6b) Trade flows between countries (1) and (2) contain intermediate and final products.
Vectors1denotes the export of country (1). In our two country model, export of
(e1'L11+e2'L21)d1+(e1'L12+e2'L22)f2 c =
v1
(e1'L12 +e2'L22)d2 +(e1'L11 +e2'L21)f1 c =
v2
1 1
1 d f
y = +
2 2
2 d f
y = +
2 1
1 d f
c = +
1 2
2 d f
c = +
country (1) equals by definition the import of country (2). The latter is indicated by vectort2. Vectorss2andt1are defined accordingly.
(7.7a) (7.7b) Finally, the environmental balance of trade of country (1),i.e.indicator (III) in table 7.1, can be determined as the difference between direct output of pollution in the domestic economy and pollution attributed to final consumption, or, as the difference between pollution attributed to export minus pollution attributed to import.
(7.8) (7.9a) (7.9b) When looking at equation (7.9a), the terme1‘L12y2expresses the pollution attributed to country (1)’s export of intermediate requirements to country (2) while the term (e1‘L11+e2‘L21)f1expresses all pollution attributed to country (1)’s export of final products. As such, equations (7.9a) and (7.9b) express the total amount of pollution attributed to export (or import). Since pollution attributed to the export (or import)
1 21 2 11 1 2 12
1'L y (e 'L e 'L )f
e + +
s = v1
2 12 1 22 2 1 21
2'L y (e 'L e 'L )f
e + +
t = v1
Table 7.2
Origin and destination of carbon dioxide (CO2) pollution attributed to product flows in the Netherlands, 1997
Gross recording Net recording
billion kg Origin
Domestic production (vx) 163 (vx) 163
Import (vt) 125 (vt- vts) 66
Total, origin 288 229
Destination
Domestic use (vc) 133 (vc) 133
Export (vs) 156 (vxs) 97
From domestic production (vxs) 97
From import (vts) 59
Total, destination 288 229
1t 1s 1c
1x v v v
v − = −
2 1 1 1
2 t M x f
s = = +
1 2 2 2
1 t M x f
s = = +
of final products contains pollution fractions originating from both countries, certain pollution fractions are transferred twice. To be precise, both equations (7.9a) and (7.9b) include fractions e1‘L12f2 and e2‘L21f1, i.e.pollution attributed to the foreign intermediate requirements of final product exports. In fact, the partitioned Leontief matrix presented in equation (7.3) shows that, at different stages in a production process, attributed pollution to intermediate products may be transferred several times between both countries. These loop effects are a general feature of input-output models. The multiple displacement of pollution underlines that the environmental balance of trade indicator is a more meaningful indicator compared to a separate attribution of environmental requirements to either import or export. The environmental balance of trade indicator balances-out these multiple pollution reallocations. Also, these loop effects do not disturb the environmental consumption indicator. From equations (7.6a) and (7.6b) it becomes clear that the model consistently allocates all generated pollution to the final demand in both countries.
Table 7.2 shows that one may decide to follow a gross or net recording in the attribution of pollution to import and export. The net recording excludes pollution originating from the production of foreign intermediate requirements of final product exports,i.e.the fractionse1‘L12f2ande2‘L21f1in the equations (7.9a) and (7.9b), indicated by variablevtsin table 7.2. Variablevxsdenotes pollution attributed to export originating from domestic production. In the Netherlands in 1997, the gross-net difference in the recording of import and export,i.e. vts, corresponds to 59 billion kilogram of carbon dioxide emissions.
Finally, it must be noted that the attributed part of the environmental consumption indicatorsi.c. vc, presented in the tables 7.1 and 7.2 for various pollutants, represents the pollution attributed to all domestic final demand categories, that is, consumption of households, consumption of government andnetfixed capital formation (as well as net inventory changes). Pollution attributed to replacement investments are in the input-output calculations, presented here, reallocated according to the use of capital at the industry level. As such, replacement investments serve as a proxy for the pollution attributable to the use of capital,i.e.capital services. In other words, capital services are represented as an additional industry in the input-output model.