Input-Output Accounting
UNSD SEEA Training of Trainers Seminar
July 7-10, 2014, New York
Joe St. Lawrence
Statistics Canada
The Economy and The Environment
-Natural Resources
-Ecosystem Services
Stocks
The
Economy
Flows
Expenditures
2
Statistics Canada • Statistique Canada
-Residuals
2016-07-23
SNA view
Final demand
Sectors
Industries
Assets
Financial and
produced assets,
opening balance
Industrial intermediate
demand
Final demand
Gross fixed capital
formation
Wastes
Commodities
Industrial output of
goods and services
Sectors
Other changes in volume
& holding gains/losses on
financial & produced
assets
3
Statistics Canada •
Financial and
produced assets,
closing balance
Statistique
Canada
2016-07-23
Flow Accounting
United Nations, 2012, System of Environmental-Economic Accounting: Central Framework (white cover draft), New York. http://unstats.un.org/unsd/envaccounting/White_cover.pdf
4
Statistics Canada • Statistique Canada
2016-07-23
Flow Accounting
United Nations, 2012, System of Environmental-Economic Accounting: Central Framework (white cover draft), New York. http://unstats.un.org/unsd/envaccounting/White_cover.pdf
5
Statistics Canada • Statistique Canada
2016-07-23
Integration – the IO tables
235
U
473
280
1
F
q
473
primary
473
primary
473
1
V
235
6
g
235
Statistics Canada • Statistique Canada
2016-07-23
Integration – the common denominator
α = E/g
α
235
7
1
1
1
=
E
235
Statistics Canada • Statistique Canada
/
g
235
2016-07-23
Integration – the IO model
• Basic identity: supply = demand
q + inv- + m = u + fd + x + inv+
By substituting for market share (D=V/q) and technology
(B=U/g), we get:
g = (I -
-1
DB) Df
• Allows an estimate of the gross production (g)
required from each industry to satisfy a given final
demand (f) based on pre-defined relationships of
market-share (D) and technology (B)
8
Statistics Canada • Statistique Canada
2016-07-23
Sample results – attribution to demand
g* = (I -
-1
DB) Df
pe
Greenhouse Gas Emissions (carbon dioxide equivalents) attributable to
household purchases and consumption, 2002
1
α
235
9
1
Indirect emissions
Motor vehicles, parts & repairs
Furniture and household appliances
Other durable goods
Clothing and footwear
Other semi-durable goods
Food and non-alcoholic beverage
Motor fuels and lubricants
Electricity
Natural Gas
Other fuels
Other non-durable goods
Gross rent (imputed and paid)
Restaurants & hotels
Other services
Sub total, indirect emissions
Direct emissions
Heating, lighting and appliances
Motor fuels and lubricants
Sub total, direct emissions
Total GHG emissions attributable to households
=
*
g*
235
Statistics Canada • Statistique Canada
kilotonnes
5,023
3,066
3,741
4,750
5,521
38,874
15,554
43,343
7,315
2,281
10,781
14,555
15,972
39,011
209,787
41,719
69,557
111,276
321,064
%
1.6%
1.0%
1.2%
1.5%
1.7%
12.1%
4.8%
13.5%
2.3%
0.7%
3.4%
4.5%
5.0%
12.2%
65.3%
13.0%
21.7%
34.7%
100.0%
2016-07-23
Sample results – time series
10
Statistics Canada • Statistique Canada
2016-07-23
Sample results – direct and indirect
intensities (multipliers)
Direct plus indirect energy intensity by industry, 1990-2007
Industry1
1
α
235
11
235
*
235
(I - DB) -1
=
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
1990
1991
1992
1993
1994
1
Crop and animal production
18.70
Forestry and logging
11.80
Fishing, hunting and trapping
11.81
Support activities for agriculture and forestry
11.78
Oil and gas extraction
32.49
Coal mining
18.18
Metal ore mining
17.78
Non-metallic mineral mining and quarrying
22.87
Support activities for mining and oil and gas extraction
14.87
Electric power generation, transmission and distribution
62.63
Natural gas distribution, water and other systems
12.34
Residential building construction
8.94
Non-residential building construction
7.87
Transportation engineering construction
18.63
Oil and gas engineering construction
11.59
Electric power engineering construction
6.97
Communication engineering construction
7.58
Other engineering construction
8.17
Repair construction
8.06
Other activities of the construction industry
9.53
Animal food manufacturing
15.57
Sugar and confectionery product manufacturing
9.74
Fruit and vegetable preserving and specialty food manufacturing13.12
Dairy product manufacturing
15.46
Meat product manufacturing
15.87
Seafood product preparation and packaging
10.45
Miscellaneous food manufacturing
12.04
Soft-drink and ice manufacturing
10.73
Breweries
8.95
20.57
11.96
12.56
10.91
37.12
19.21
19.49
23.82
14.42
57.47
10.67
9.37
8.37
19.36
12.26
7.12
8.66
8.69
8.33
10.40
16.16
11.03
12.54
16.25
16.67
11.13
10.82
11.12
8.09
21.63
12.24
11.41
11.30
36.93
18.80
18.76
22.70
17.02
57.87
12.06
9.69
8.57
18.94
12.87
7.27
8.57
9.14
8.56
10.42
16.44
10.23
12.71
16.98
17.11
11.42
11.24
10.26
8.46
19.70
10.73
9.60
10.83
33.72
16.99
20.00
22.37
16.09
51.07
13.52
9.41
8.65
18.08
11.95
7.14
8.48
8.80
8.19
10.41
15.73
9.58
12.50
15.88
16.34
10.25
11.31
10.97
8.08
18.68
10.48
13.57
10.53
31.93
17.24
17.93
21.75
13.54
49.54
11.65
9.12
8.26
17.64
11.17
6.70
8.21
8.11
7.92
10.02
15.32
9.54
12.57
15.43
15.67
11.21
11.45
11.45
7.55
1
1
1
Statistics Canada • Statistique Canada
2016-07-23
3
1
1
2
1
5
1
1
1
1
1
1
1
1
1
1
Numerical example
USE (U)
cattle
iron ore
milk
cheese
fuel
steel
cars
advertising
12
farms
mines
food manuf. other manuf. services
10
0
80
10
0
0
0
0
100
0
10
5
100
0
5
0
5
0
0
5
100
200
10
50
50
0
5
0
145
0
10
5
5
5
10
5
15
20
40
20
Statistics Canada • Statistique Canada
2016-07-23
Numerical example
USE (U)
cattle
iron ore
milk
cheese
fuel
steel
cars
advertising
farms
mines
food manuf. other manuf. services
10
0
80
10
0
0
0
0
100
0
10
5
100
0
5
0
5
0
0
5
100
200
10
50
50
0
5
0
145
0
10
5
5
5
10
5
15
20
40
20
MAKE (V)
cattle
iron ore milk
farms
100
0
mines
0
100
food manuf.
0
0
other manuf.
0
0
services
0
0
13
cheese
100
0
80
0
0
fuel
10
0
200
0
0
steel
0
1000
0
10
0
cars
0
0
0
150
0
advertising
0
0
0
0
0
0
200
0
0
100
Statistics Canada • Statistique Canada
2016-07-23
Numerical example
USE (U)
cattle
iron ore
milk
cheese
fuel
steel
cars
advertising
farms
mines
food manuf. other manuf. services
10
0
80
10
0
0
0
0
100
0
10
5
100
0
5
0
5
0
0
5
100
200
10
50
50
0
5
0
145
0
10
5
5
5
10
5
15
20
40
20
MAKE (V)
cattle
iron ore milk
farms
100
0
mines
0
100
food manuf.
0
0
other manuf.
0
0
services
0
0
14
cheese
100
0
80
0
0
fuel
10
0
200
0
0
steel
0
1000
0
10
0
Final Demand
0
0
60
200
600
0
165
0
cars
0
0
0
150
0
advertising
0
0
0
0
0
0
200
0
0
100
Statistics Canada • Statistique Canada
2016-07-23
Numerical example
USE (U)
cattle
iron ore
milk
cheese
fuel
steel
cars
advertising
farms
mines
food manuf. other manuf. services
10
0
80
10
0
0
0
0
100
0
10
5
100
0
5
0
5
0
0
5
100
200
10
50
50
0
5
0
145
0
10
5
5
5
10
5
15
20
40
20
MAKE (V)
cattle
iron ore milk
farms
100
0
mines
0
100
food manuf.
0
0
other manuf.
0
0
services
0
0
cheese
100
0
80
0
0
fuel
Final Demand
0
0
60
200
600
0
165
0
10
0
200
0
0
steel
0
1000
0
10
0
cars
0
0
0
150
0
advertising
0
0
0
0
0
0
200
0
0
100
210
1010
150
200
g
Σ
210
1100
280
360
100
Σ
q
100
15
100
180
Statistics Canada • Statistique Canada
100
2016-07-23
Numerical example
B (U/g)
cattle
iron ore
milk
cheese
fuel
steel
cars
advertising
Σ
farms
mines
0.05
0.00
0.05
0.00
0.48
0.00
0.05
0.02
0.6
16
other
food manuf. manuf.
0.00
0.29
0.00
0.00
0.00
0.36
0.00
0.00
0.18
0.04
0.00
0.00
0.00
0.02
0.01
0.07
0.2
0.8
0.03
0.28
0.00
0.00
0.14
0.40
0.01
0.11
services
0.00
0.00
0.05
0.05
0.50
0.00
0.10
0.20
0.97
0.9
Statistics Canada • Statistique Canada
2016-07-23
Numerical example
B (U/g)
cattle
iron ore
milk
cheese
fuel
steel
cars
advertising
Σ
farms
mines
0.05
0.00
0.05
0.00
0.48
0.00
0.05
0.02
0.6
other
food manuf. manuf.
0.00
0.29
0.00
0.00
0.00
0.36
0.00
0.00
0.18
0.04
0.00
0.00
0.00
0.02
0.01
0.07
0.2
D (V/q)
cattle
iron ore milk
farms
1.00
0.00
mines
0.00
1.00
food manuf.
0.00
0.00
other manuf.
0.00
0.00
services
0.00
0.00
Σ
1
17
1
0.8
0.03
0.28
0.00
0.00
0.14
0.40
0.01
0.11
services
0.00
0.00
0.05
0.05
0.50
0.00
0.10
0.20
0.97
0.9
cheese
fuel
steel
cars
0.56
0.00
0.44
0.00
0.00
0.05
0.00
0.95
0.00
0.00
0.00
0.99
0.00
0.01
0.00
0.00
0.00
0.00
1.00
0.00
1
1
1
1
advertising
0.00
0.00
0.00
0.00
0.00
0.00
1.00
0.00
0.00
1.00
1
Statistics Canada • Statistique Canada
1
2016-07-23
Numerical example
other
(I-DB)ˉ¹
farms
mines
food manuf. manuf.
farms
1.11
0.01
0.65
mines
0.74
1.26
0.59
food manuf.
0.04
0.01
1.22
other manuf.
0.13
0.03
0.14
services
0.07
0.03
0.16
meaning?
18
0.08
1.13
0.03
1.80
0.27
services
0.12
1.01
0.12
0.27
1.32
dollars of output from industry at row to deliver (to final demand) a dollar of output from industry at column
Statistics Canada • Statistique Canada
2016-07-23
Numerical example
other
(I-DB)ˉ¹
farms
mines
food manuf. manuf.
farms
1.11
0.01
0.65
mines
0.74
1.26
0.59
food manuf.
0.04
0.01
1.22
other manuf.
0.13
0.03
0.14
services
0.07
0.03
0.16
meaning?
19
0.08
1.13
0.03
1.80
0.27
services
0.12
1.01
0.12
0.27
1.32
g=(I-DB)ˉ¹De
210
1100
280
360
100
g
210
1100
280
360
100
dollars of output from industry at row to deliver (to final demand) a dollar of output from industry at column
Statistics Canada • Statistique Canada
2016-07-23
Numerical example
other
(I-DB)ˉ¹
farms
mines
food manuf. manuf.
farms
1.11
0.01
0.65
mines
0.74
1.26
0.59
food manuf.
0.04
0.01
1.22
other manuf.
0.13
0.03
0.14
services
0.07
0.03
0.16
services
0.08
0.12
1.13
1.01
0.03
0.12
1.80
0.27
0.27
1.32
De
42.86
594.06
217.14
170.94
0.00
farms only
47.51138
7.0069
141.1847
14.29702
0
210
g=(I-DB)ˉ¹De
210
1100
280
360
100
decompostion of row one of (I-DB)ˉ¹ times column one of De (Row 1 of (I-DB)ˉ¹ times column of De)
1.11 * 42.86 ($1.11 of production from farms is required to deliver a dollar of production from farms, so to get
42.86 of final demand we need farms to produce 47.5 dollars of output)
Plus: 0.01 * 594.06 ($0.01 of production from farms is required to deliver a dollar of production from mines,
so to get 594.06 of final demand we need farms to produce 7 dollars of output)
Plus: 0.65 * 217.14 ($0.65 of production from farms is required to deliver a dollar of production from food
manufacturers, so to get 217.14 of final demand we need farms to produce 141.2 dollars of output)
Plus: 0.08 * 170.94 ($0.08 of production from farms is required to deliver a dollar of production from other
manufacturers, so to get 170,94 of final demand we need farms to produce 14.3 dollars of output)
Plus: 0.12 * 0 ($0.12 of production from farms is required to deliver a dollar of production from services, so to
get 0.00 to final demand we need farms to produce 0 dollars of output)
So, to deliver all of final demand, farms must produce 210 dollars of gross output
20
Statistics Canada • Statistique Canada
2016-07-23
Sample results – direct and indirect
intensities (multipliers)
Direct plus indirect energy intensity by industry, 1990-2007
Industry1
1
α
235
21
235
*
235
(I - DB) -1
=
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
1990
1991
1992
1993
1994
1
Crop and animal production
18.70
Forestry and logging
11.80
Fishing, hunting and trapping
11.81
Support activities for agriculture and forestry
11.78
Oil and gas extraction
32.49
Coal mining
18.18
Metal ore mining
17.78
Non-metallic mineral mining and quarrying
22.87
Support activities for mining and oil and gas extraction
14.87
Electric power generation, transmission and distribution
62.63
Natural gas distribution, water and other systems
12.34
Residential building construction
8.94
Non-residential building construction
7.87
Transportation engineering construction
18.63
Oil and gas engineering construction
11.59
Electric power engineering construction
6.97
Communication engineering construction
7.58
Other engineering construction
8.17
Repair construction
8.06
Other activities of the construction industry
9.53
Animal food manufacturing
15.57
Sugar and confectionery product manufacturing
9.74
Fruit and vegetable preserving and specialty food manufacturing13.12
Dairy product manufacturing
15.46
Meat product manufacturing
15.87
Seafood product preparation and packaging
10.45
Miscellaneous food manufacturing
12.04
Soft-drink and ice manufacturing
10.73
Breweries
8.95
20.57
11.96
12.56
10.91
37.12
19.21
19.49
23.82
14.42
57.47
10.67
9.37
8.37
19.36
12.26
7.12
8.66
8.69
8.33
10.40
16.16
11.03
12.54
16.25
16.67
11.13
10.82
11.12
8.09
21.63
12.24
11.41
11.30
36.93
18.80
18.76
22.70
17.02
57.87
12.06
9.69
8.57
18.94
12.87
7.27
8.57
9.14
8.56
10.42
16.44
10.23
12.71
16.98
17.11
11.42
11.24
10.26
8.46
19.70
10.73
9.60
10.83
33.72
16.99
20.00
22.37
16.09
51.07
13.52
9.41
8.65
18.08
11.95
7.14
8.48
8.80
8.19
10.41
15.73
9.58
12.50
15.88
16.34
10.25
11.31
10.97
8.08
18.68
10.48
13.57
10.53
31.93
17.24
17.93
21.75
13.54
49.54
11.65
9.12
8.26
17.64
11.17
6.70
8.21
8.11
7.92
10.02
15.32
9.54
12.57
15.43
15.67
11.21
11.45
11.45
7.55
1
1
1
Statistics Canada • Statistique Canada
2016-07-23
3
1
1
2
1
5
1
1
1
1
1
1
1
1
1
1
Numerical example
Intensity indicators
emissions per unit of output (direct emissions intensity)
a
farms
co2/g
mines
0.5
0.8
food manuf.other manuf.
services
0.3
0.4
0.1
alpha inverse
1.218388 1.030774 1.234589 1.698604 1.139405
(I-DB)ˉ¹
farms
mines
food manuf.other manuf.
services
farms
1.11
0.01
0.65
0.08
0.12
mines
0.74
1.26
0.59
1.13
1.01
food manuf.
0.04
0.01
1.22
0.03
0.12
other manuf.
0.13
0.03
0.14
1.80
0.27
services
0.07
0.03
0.16
0.27
1.32
So, a*(I-DB)ˉ¹ for row of a times column 1 of (I-DB)ˉ¹ is...
0.5 *
0.8 *
0.3 *
0.4 *
0.1 *
farms is required to deliver a dollar of production from farms. Farms emit .05 CO2 per dollar of output,so in terms of emissions this is:)
0.554299
mines is required to deliver a dollar of production from farms. Mines emit .8 CO2 per dollar of output, so in terms of emissions this is:)
0.594947
food manuf. Is required to deliver a dollar of production from farms. Food manuf. Emit .3 CO2 per dollar of output, so in terms of emissions:) 0.011714
other manuf. Is required to deliver a dollar of output from farms. Other manuf. Emit .4 CO2 per dollar of output, so in terms of emissions:)
0.05075
services is required to deliver a dollar of output from farms. Services emit .1 CO2 per dollar of output, so in terms of emissions this is:)
0.006678
SUM
1.218388
This is the total emissions required (direct plus indirect) from all industries per dollar of output from farms.
plus
plus
plus
plus
22
1.11 (1.11 dollars
0.74 (0.74 dollars
0.04 (0.04 dollars
0.13 (0.13 dollars
0.01 (0.01 dollars
of production from
of production from
of production from
of production from
of production from
Statistics Canada • Statistique Canada
2016-07-23
Questions?
Joe St. Lawrence
Environment Accounts and Statistics | Comptes et statistique de l'environnement
R.H. Coats Building | Immeuble R.-H.-Coats / Floor | Étage 25 M
Statistics Canada | 100 Tunney's Pasture Driveway, Ottawa ON K1A 0T6
Statistique Canada | 100, promenade Tunney's Pasture, Ottawa ON K1A 0T6
Joe.St.Lawrence@statcan.gc.ca
Telephone | Téléphone 613-951-7709
Facsimile | Télécopieur 613-951-0634
Government of Canada | Gouvernement du Canada
23
Statistics Canada • Statistique Canada
2016-07-23