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Environmentally extended
input-output analysis
Jan Weinzettel
9th April 2014 IES, CUNI
Content
Computational framework
Supply, use and symmetric input-output
tables
Contributional and structural path
analysis
Structural decomposition analysis
Multiregional input-output analysis
2
Computational Framework
Iron production: consumes 10 tons of coal and 1 ton of iron and produces 50 tons of iron
Coal production: consumes 5 tons of iron and 5 tons of coal and produces 75 tons of coal
How much coal is needed to produce 5 tons of steel including the full production chain?
What are the related CO2 emissions?
3
Computational framework
iron
coal
10 tons coal
1 ton iron
5 tons iron
5 tons coal
50 tons iron
75 tons coal
Demand
\
Supply
Iron Coal Outside Total
Iron 1 5 44 50
Coal 10 5 60 75
50 – 5 – 1 =
44 tons iron
75 – 10 – 5 =
60 tons coal
Z y x
4
Computational framework
A . x + y = x
x* = (I – A)-1 . y* if (I – A) is regular
Demand
\
Supply
Iron Coal Outside Total
Iron 1 5 44 50
Coal 10 5 60 75
Z y x
2
1
2221
1211
2
1
y
y
zz
zz
x
x Z . 1 + y = x
A = Z . diag(x)-1
1
11
5
Computational framework
6
Demand \
Supply
Iron Coal Outside Total
Iron 1 5 44 50
Coal 10 5 60 75
Environmental
extension
CO2 (t) 100 20
Z y x
Fr
F = Fr . diag(x)-1
E = F . x*
x* = (I – A)-1 . y*
E* = F . (I – A)-1 . y*
0
5*
2
1
y
y
General equalities
(I – A)x = y
(I – A’)p = v
p'y = v‘x
7
Supply table
Which commodities are supplied by
which industries
8
Sector
Product
Sector 1 … Sector n Import Total
supply
Product 1
Supply matrix S
m1 q1
… m… q…
Product n mn qn
Use table
Which commodities are consumed by which industries
Sector
Product
Sector 1 … Sector n Final
demand
Total use
Product 1
Use matrix U
y1 q1
… y… q…
Product n yn qn
Value
added VA
Environme
ntal
extension
Fr
9
Domestic x Imports
Use table can be split by origin of
products into domestic and imported
U = Ud + Um
Two types of analysis
◦ Domestic environment
◦ Global environment (under domestic
technology assumption)
10
Domestic technology assumption
In a single region IOA imported products
are assumed to be produced by the same
technology as the domestic products
11
Symmetric input-output table
12
„Product by product“
◦ All products of one sector are produced with the same
structure of inputs (industry technology assumption)
◦ Each product is produced using the same technology regardless
the production sector (product technology assumption)
„Sector by sector“
◦ Each product has fixed sales structure
◦ Each sector has its own fixed sales structure regardless the
products on the output
Differences caused by bi-products
◦ For diagonal supply table all the models are equivalent
Transformation of supply and use
tables Intermediate consumption
Value added
Final demand
Environmental extension
Symmetric IOT looks like use table, but it
is symmetric (product by product or
sector by sector)
13
Input coefficient and Leontief
inverse matrix A = Z . (diag(domestic output)-1)
L = (I – A)-1
x* = L . y*
Note inequality:
q ≠ (I - A)-1(y)
But
q = (I - A)-1(y – m)
14
Environmental extension
Usually similar position as value added
Environmental interventions of economic sectors (denote Fr)
Transformation and normalization to unit output
Environmental interventions of the full supply chain of final demand y*
e* = F . L . y*
15
Environmental extension
Needs to be transformed according to
type of IOT
Can include unlimited number of rows
(environmental interventions)
16
Value added
Wages and salaries
Employers’ social contributions
Other taxes on production
Other subsidies on production
Consumption of fixed capital
Operating surplus, net
Mixed income, net
17
Final demand
Final consumption Gross fixed
capital
formation
incl. changes
in valuables
Changes in
inventories
Exports
(FOB)
expenditure
Households Governments NPISH
18
Valuation
Countries differ in valuation concepts
EU: ◦ Supply table and IOT: basic prices
◦ Use table: purchaser prices
◦ The difference is: Taxes
Subsidies
Transport margins
Trade margins
US IOT: ◦ Producer prices – includes non deductible taxes
on products (VAT is deductible)
19
Contribution analysis
How much different products on final
contribute to total environmental impact?
E = F . L . diag(y)
How much different sectors contribute to
total environmental impact?
E = F . diag(L . y)
20
Structural path analysis
Which processes of which production paths contribute
the most to the total environmental impact?
While contribution analysis focuses on total impact of
each sector, SPA aims at distinguishing particular
production paths
e = F . L . y = F . (I – A)-1 . y = F . (I + A + A2 + … + An) . y
eijk = Fk . Akj . Aji . yi
Need for an algorithm to calculate impacts from all
paths (limits needed) and sort those.
21
Structural decomposition analysis
It is used to analyze the drivers behind changes
Includes Leontief inverse matrix
Options for environmental input output analysis: ◦ Direct intensity of sectors
◦ Economic structure – intermediate inputs
◦ Structure of final demand
◦ Contribution of final demand categories
◦ Total volume of final demand (per capita)
◦ Total population
e = F . L . M . D . G . P
Optional: to merge any of the factors
22
Structural decomposition analysis
Example for two variables (additive decomposition)
z = x . y
What is the change due to x? y?
◦ Equal share of higher orders effects
zx = y1.Δx + ½ Δx. Δy
zy = x1.Δy + ½ Δx. Δy
Δq = q2 – q1
Becomes too
complicated
for more variables.
23
x
y
x1 x2
y1
y2
1
2
z1 zx
zy z?
Structural decomposition analysis
Logarithmic mean divisia index
y = x1 . x2. … . xn
Complete decomposition (without residues
Not defined for zeroes and negatives (when a variable changes sign)
Matrix algebra?
24
ixi x
y
ydy ln
ln
Structural decomposition analysis
eijkl = Fli . Lij . Mjk . D1k . G . P,
Δeijkl = dFijkl + dLijkl + dMijkl + dDijkl+ dGijkl + dPijkl
25
m
l
d
k
n
ji
lkjieE1 1 1.
,,,
m
l
d
k
n
ji
lkjieE1 1 1.
,,,
li
ijkl
ijkl
ijkl Fe
edF ln
ln
m
l
d
k
n
ji
ijklijklijklijklijklijkl dPdGdDdMdLdFE1 1 1.
m
l
d
k
n
ji
ijkldFdF1 1 1.
Structural decomposition analysis
Negatives
◦ Not so common in IOA
◦ Suitable to treat negatives separately
◦ E.g. Changes in stocks and inventory
Zeroes
◦ Only relevant if zero in time and non zero
other time
◦ Specific treatment for each case
26
SDA: Case study
Structural decomposition analysis of raw
material input, Czech Republic, 1995 –
2011
RMI = F . L . y (material footprint of the
total final demand)
RMI = F . L . M . D . G . P + F . L . B . Z +
F . L . S
27
SDA: Case study
RMI = F . L . M . D . G . P + F . L . B . Z + F . L . S
RMIr = F . L . M . D . G . P
RMIe = F . L . B . Z
RMIs = F . L . S
ΔRMI = Δ(F . L . M . D . G . P) + Δ (F . L . B . Z) + Δ(F . L . S)
ΔRMI = ΔRMIr + ΔRMIe + ΔRMIs
ΔRMI = Δ(Fr . Lr . M . D . G . P) + Δ (Fe . Le . B . Z) + Δ(F . L . S)
dF = dFr + dFe
dL = dLr + dLe,
RMIrijkl = Fli . Lij . Mjk . Dk . G . P
28
m
l
d
k
n
ji
li
ijkl
ijklFr
RMIr
RMIrdFr
1 1 1.
lnln
SDA: Case study - results
Material F L M D G P B Z S
Crude oil -4 209 -2 527 - 866 310 2 959 156 -1 423 8 211 509
Natural gas 2 801 -3 245 -1 088 350 3 427 143 -1 672 9 671 665
Hard coal -2 149 -19 268 - 934 394 4 845 139 -7 788 17 939 1 062
Lignite 18 962 -59 310 -3 554 1 261 13 669 493 -23 047 46 281 2 995
Iron ore 2 996 -8 436 -1 076 - 49 3 038 143 -1 933 16 300 - 782
Non iron ores 2 962 -1 777 67 - 166 5 480 358 -2 872 33 848 - 159
Industrial minerals -10 153 - 797 - 877 81 4 432 167 -3 567 15 839 253
Construction
minerals -12 635 18 550 -24 493 -3 630 24 500 1 414 -1 829 11 853 - 769
Food crops 4 366 -7 797 -3 675 1 092 5 424 231 -2 685 8 339 777
Feed crops -3 665 -6 479 -2 894 926 4 322 135 -2 467 6 513 633
Wood -2 259 -1 376 61 79 2 049 109 -2 533 8 791 292 29
Multiregional input-output
framework Connection of multiple economies in
order to avoid the domestic technology
assumption
Detail international trade
Which product of one economy
consumed by which sectors of other
economy
Assumptions
Databases
30
31
Product 1
Product 2
…
Product n
Product 1
Product 2
…
Product n
Product 1
Product 2
…
Product n
Regi
on 1
R
egi
on …
R
egi
on m
Pro
duct
1
Pro
duct
2
…
Pro
duct
n
Pro
duct
1
Pro
duct
2
…
Pro
duct
n
Pro
duct
1
Pro
duct
2
…
Pro
duct
n
Region 1 Region … Region m Final demand
Regi
on 1
…
Regi
on 2
Regi
on m
Displacement of CO2 emissions
Source: Peters, G.P., Minx, J.C., Weber, C.L., Edenhofer, O., 2011. Growth in emission transfers via international trade from 1990 to 2008. Proc. Natl. Acad. Sci. U. S. A. 108, 8903-8908. 32
Material extraction
Source: Wiedmann, T.O., Schandl, H., Lenzen, M., Moran, D., Suh, S., West, J., Kanemoto, K., 2013.
The material footprint of nations. Proc. Natl. Acad. Sci. U. S. A. 33
Land use
Source: Weinzettel, J., Hertwich, E.G., Peters, G.P., Steen-Olsen, K., Galli, A., 2013. Affluence
drives the global displacement of land use. Global Environmental Change 23, 433-438. 34
Land use
Units: million gha
Source: Weinzettel, J., Hertwich, E.G., Peters, G.P., Steen-Olsen, K., Galli, A., 2013. Affluence
drives the global displacement of land use. Global Environmental Change 23, 433-438. 35
Biodiversity threats
Source: Lenzen, M., Moran, D., Kanemoto, K., Foran, B., Lobefaro, L., Geschke, A., 2012.
International trade drives biodiversity threats in developing nations. Nature 486, 109-112. 36
Literature Eurostat, 2008. Eurostat Manual of Supply, Use and Input-Output Tables.
European Communities, Luxembourg.
Hertwich, E.G., 2005. Life cycle approaches to sustainable consumption: A critical review. Environmental Science & Technology 39, 4673-4684.
Lenzen, M., Moran, D., Kanemoto, K., Foran, B., Lobefaro, L., Geschke, A., 2012. International trade drives biodiversity threats in developing nations. Nature 486, 109-112.
Peters, G.P., Minx, J.C., Weber, C.L., Edenhofer, O., 2011. Growth in emission transfers via international trade from 1990 to 2008. Proc. Natl. Acad. Sci. U. S. A. 108, 8903-8908.
Peters, G.P., Hertwich, E.G., 2006. The importance of imports for household environmental impacts. J.Ind.Ecol. 10, 89-109.
Schoer, K., Weinzettel, J., Kovanda, J., Giegrich, J., Lauwigi, C., 2012. Raw material consumption of the European union - concept, calculation method, and results. Environmental Science & Technology 46, 8903-8909.
Weinzettel, J., Kovanda, J., 2011. Structural Decomposition Analysis of Raw Material Consumption. J.Ind.Ecol. 15, 893-907.
Wood, R., Lenzen, M., Foran, B., 2009. A Material History of Australia. J.Ind.Ecol. 13, 847-862.
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