8.1 Input-output analysis
8.2 Environmental input-output analysis
8.3 Costs and prices
8.4 Computable general equilibrium models
Learning objectives
§ learn about the basic input – output model of an economy and its solution
§ find out how the basic input – output model can be extended to incorporate economy – environment interactions
§ encounter some examples of environmental input – output models and their application
§ learn how the input – output models, specified in terms of physical or constant-value flows, can be reformulated to analyse the cost and price implications of environmental policies, such as pollution taxes, and how these results can be used to investigate the distributional implications of such policies
§ study the nature of computable general equilibrium (CGE) models and their application to environmental problems

Box 8.1 Using input-output analysis to consider the feasibility of sustainable development
The Brundtland Report claimed that sustainable development was feasible. This was an assertion rather than a demonstration - the report did not put together the technological and economic possibilities looked at in various parts of the report and examine them for consistency. Duchin and Lange (1994), hereafter DL, is a report on a multisector economic modeling exercise, using input-output analysis, to look at the feasibility of sustainable development as envisaged in the Brundtland Report.
DL used an input-output model of the world economy which distinguished 16 regional economies, in each of which was represented the technology of 50 industrial sectors. This model was used to generate two scenarios for the world economy for the period 1990 to 2020. The reference scenario assumes that over this period world GDP grows at 2.8% per year, while the global population increases by 53%.
DL take 2.8% per year to be what is implied by the Brundtland Report's account of what is necessary for sustainable development. In this reference scenario production technologies are unchanging over the period 1990-2020.
The second scenario is the OCF scenario , where OCF stands for Our Common Future, the title of the
Brundtland Report. This uses the same global economic and demographic assumptions as the reference scenario, but also has technologies changing over 1990-2020.
In the OCF scenario DL incorporate into the input-output model's coefficients technological improvements as envisaged in the Brundtland Report in energy and materials conservation, changes in the fuel mix for electricity generation, and measures to reduce
SO
2 and NO
2 emissions per unit energy use.
As indicators of environmental impact, the analysis uses the input-output model to track fossil fuel use and emissions of CO
2
, SO
2 and NO
2
. In the reference scenario, all of these indicators increase by about 150% over 1990-2020. With the technological changes, there are big environmental improvements in the OCF scenario. But the indicators still go up - by 61% for fossil fuel use, by 60% for CO
2
, by 16% for SO
2
, and by
63% for NO
2
.
Given the assumed economic and population growth, the technological improvements are not enough to keep these environmental damage indicators constant. DL conclude that sustainable development as envisaged in the Brundtland Report is not feasible.

Table 8.1 Input-output transactions table, $million
Sales to: Intermediate sectors Final demand
Intermediate sectors
Purchases from
Agriculture
Agriculture
0
Manufacturing
400
Service s
0
Households
500
Manufacturing 350 0 150 800
300
Primary inputs
Services
Imports across a row
Wages
Other value added
Total input
100
250
200
100
1000
200
600
500
300
2000
0
50
300
100
600
Agriculture sales

(to)
0
(Agriculture)

400

0

500
(Manufacturing) (Services) (Households)

100

1000
(Exports) (Total output)
Exports
100
700
0 down a column
Manufacturing purchases

400

0
(Agrculture) (Manufacturing)
(from)

200

600

300
(Services) (Imports) (OVA)

2000
(Total input)
Total outpu t
1000
2000
600

Input-output accounting 2
Because of the accounting conventions adopted in the construction of an I/O transactions table, the following will always be true:
1.
For each industry: Total output

Total input, that is, the sum of the elements in any row is equal to the sum of the elements in the corresponding column.
2.
For the table as a whole: Total intermediate sales

Total intermediate purchases, and
Total final demand

Total primary input
Note the use here of the identity sign,

, reflecting the fact that these are accounting identities, which always hold in an I/O transactions table.
Reading across rows the necessary equality of total output with the sum of its uses for each industry or sector can be written as a set of ‘balance equations’:
X i
 
X j ij
 i
,

1,..., n (8.1) where
X i
= total output of industry i
X ij
= sales of commodity i to industry j
Y i
= sales of commodity i to final demand n = the number of industries

To go from accounting to analysis, the basic assumption is
X ij
 a X ij j
(8.2) where a ij is a constant.
X i
Substituting 8.2 into 8.1 gives
  a X
 j ij j i
,

1,..., n (8.3) as a system of a ij
. If the Y i n linear equations in 2 n variables, the X i and Y i
, and n 2 coefficients, the
– the final demand levels – are specified, there are n unknown X i
– the gross output levels – which can be solved for using the n equations.

In matrix notation, (8.3) is
X

AX

Y which can be written
(8.4) where X is an n x 1vector of gross outputs, A is an n x n matrix of coefficients a ij
, and Y is an n x 1 vector of final demands, Y i
. With I as the identity matrix, (8.4) can be written which has the solution
X

1
(I A) Y (8.5) where (I – A) -1 is the inverse of (I-A). This can be written
X

LY (8.6)
L is often known as the
, in recognition of inventor of i-o analysis

X
1
 l Y
11 1
 l Y
12 2
 l Y
13 3
X
2
 l Y
21 1
 l Y
22 2
 l Y
23 3
X
3
 l Y
31 1
 l Y
32 2
 l Y
33 3
(8.7) – the l ij are the elements of L. The X are the gross output levels for the final i demands Y j
. a
11
From the 3-sector transactions table, the coefficients which are the elements of matrix A are

0, a
12

400 / 2000

0.2000, a
13

0 a a
21
31


350 /1000

0.3500,
100 /1000

0.1000, a a
22
32


0, a
23

150 / 600

0.2500
200 / 2000

0.1000, a
33

0
Solving the system of three equations with these coefficients for the final demands from the transactions table gives the gross output levels from that table
Agriculture X
1
= 999.96
Manufacturing X
2
= 2000.01
Services X
3
= 599.94
Solving for Y
1
= 700, Y
2
= 1800, Y
3
= 400 gives
Agriculture X
1
= 1180.51 - for ∆Y
1
= 100, ∆X
1
= 180.51
Manufacturing X
2
= 2402.79 – for ∆Y
2
= 300, ∆X
2
= 402.79
Services X
3
= 758.26 – for ∆Y
3
= 100, ∆X
3
=158.32

Analysing the environmental effect of final demand changes was
Suppose that in addition to the data of Table 8.1 we also know that the use of oil by the three industries
Agriculture Manufacturing Services
50 Pj 400 Pj 60 Pj
With O i for oil use in industry i, assume
O i
 r X i i
(8.8) r
2 r
1 so that

0.05 for agriculture

0.2 for manufacturing r
3

0.1 for services
Then for
100 300 100 get
X
1
180.51
and hence
 
1
9.03

X
2

402.79

X
3

158.26
 
2
80.56
 
3
15.83

O
1
 r X
1 1
 r l Y
1 11 1
 r l Y
1 12 2
 r l Y
1 13 3
O
2
 r X
2 2
 r l Y
2 21 1
 r l Y
2 22 2
 r l Y
2 23 3
O
3
 r X
3 3
 r l Y
3 31 1
 r l Y
3 32 2
 r l Y
3 33 3 adding vertically gives
O
1

O
2

O
3

( r l
1 11
 r l
2 21
 r l ) Y
3 31 1

( r l
1 12
 r l
2 22
 r l ) Y
3 32 2

( r l
1 13
 r l
2 23
 r l ) Y
3 33 3 which can be written
O
1

O
2

O
3
 i Y
1 1
 i Y
2 2
 i Y
3 3
(8.10) where i
1
= r
1 l
11
+ r
2 l
21
+ r
3 l
31 etc. The left-hand side of equation 8.10 is total oil use. The righthand side allocates that total as between final demand deliveries via the coefficients i . These coefficients give the oil intensities of final demand deliveries, oil use per unit, taking account of direct and indirect use. The coefficient i
1
, for example, is the amount of oil use attributable to the delivery to final demand of one unit of agricultural output, when account is taken both of the direct use of oil in agriculture and of its indirect use via the use of inputs of manufacturing and services, the production of which uses oil inputs.

For the three sector example, the oil intensities are
Agriculture Manufacturing Servics
0.1525
0.2467
0.1617
which with final demand deliveries of
Agriculture Manufacturing Services
600 1500 300 gives total oil use of 510 PJ, allocated across final demand deliveries as
Agriculture Manufacturing Services
91.50
370.05
48.51
As compared with the industry uses of oil from which the r i were calculated, these numbers have more oil use attributed to agriculture and less to manufacturing and services. This reflects the fact that producing agricultural output uses oil indirectly when it uses inputs from manufacturing and services.

In matrix algebra, which would be the basis for doing the calculations where the number of sectors is realistically large, n , the foregoing is
(8.11) O = RX = RLY = iY to define the intensities, where
O is total resource use (a scalar)
R is a 1
 n vector of industry resource input coefficients i is a 1
 n vector of resource intensities for final demand deliveries and X , L and Y are as previously defined. The resource uses attributable to final demand deliveries can be calculated as
O = R* Y (8.11/) where
O is an n

1 vector of resource use levels
R* is an n
 n matrix with the elements of R along the diagonal and 0s elsewhere.
With suitable changes of notation, all of this applies equally to calculations concerning waste emissions.

2
Extract from Table 8.3 CO
2 intensities and levels for final demand deliveries, Australia 1986/7
Sector CO
2
Intensity a CO
2 tonnes % of total
Ag, forest, fishing 1.8007 (6)
Food products
Basic metal products
Electricity
Gas
Construction
Community services
1.532 (8)
4.4977 (4)
15.2449(1)
9.9663 (3)
0.7567 (19)
0.4437 (26) a. tonnes x 10 3 /($A x 10 6 )
13.836 (8)
11.540 (10)
20.25 (4)
43.747 (1)
4.675 (18)
28.111 (3)
17.802 (6)
4.74
4.00
6.94
14.99
1.60
9.64
6.10
It is frequently stated that about 45% of Australian CO
2 emissions are from electricity supply. Much of that electricity output is input to other sectors, not delivery to final demand for electricity, and here gets attributed to other deliveries to final demand that it is used in the production of.

2
Figure 8.1 Some trends 1992-2004
140
120
100
80
60
40
20
0
Percentage of embedded CO
2 due to imports
CO
2 emissions attributable to UK households
CO
2 intensity household expenditure
CO
2 attributable to UK households up 20%
CO
2 embedded in imports
CO
2 intensity of household expenditure down 20%
Druckman and Jackson’s ‘embedded’ = indirect

2
Table 8.4 CO
2 emissions attributable to UK households 1992-2004
Total
Tonnes CO
2 x 10 6
467.2
462.1
454.1
456.8
475.0
460.0
475.4
474.8
490.2
518.8
533.0
542.1
557.4
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
51.0
51.2
51.3
51.3
52.2
53.7
54.0
54.5
Embedded
49.3
50.0
50.2
51.8
50.2
13.9
13.3
13.7
13.1
12.5
12.6
12.2
12.0
Percentage
Vehicle Use Flights
13.2
2.9
13.4
13.3
13.0
13.2
3.1
3.2
3.4
3.3
4.8
4.6
4.6
4.6
4.8
3.6
3.9
4.3
31.6
31.6
30.7
30.9
30.6
29.1
29.2
28.7
Direct
34.6
33.5
33.2
31.8
33.3
Source: Druckman and Jackson (2009)
Figures in first column correspond to index numbers in Figure 8.1

2
Table 8.5 CO
2 emissions attributable to UK Supergroups 2004
Tonnes CO
2
Per household Per capita Embedded
Percentage
Flights Vehicle Use
1.Prospering suburbs 26.5 (1) 10.4 (1) 54.0
5.5
12.6
Direct
27.9
2.Countryside
3.Typical traits
4.City living
5.Blue collar
6.Muticultural
7.Constrained by circumstances
24.9 (2)
22.4 (3)
18.7 (5)
19.5 (4)
18.2 (6)
16.1 (7)
10.2 (2)
9.2 (3)
8.3 (4)
8.0 (5)
7.7 (6)
7.4(7)
53.8
55.1
56.1
54.0
55.6
54.2
5.4
5.0
4.3
4.5
4.0
3.9
12.4
12.3
11.7
12.0
11.7
11.1
28.4
27.6
27.9
29.6
28.8
30.8
UK mean 21.5
9.0
54.5
4.8
12.0
28.7
Source: Druckman and Jackson (2009)
Figures in brackets are ranks
The worst-off spend a larger share of budget on direct energy use

In 3 sector example
Direct energy conservation
A technological innovation that cuts per unit oil use in Manufacturing by 25% reduces total economy oil use by 100 Pj, 20%.
Indirect energy conservation
An innovation in the use of Manufacturing output in the Agriculture sector which cuts a
21 to 0.25 reduces total economy oil use by 24.13 PJ, 5%.
from 0.35
Combining direct and indirect energy conservation
With both the reduction in oil use in Manufacturing and the use of Manufacturing in Agriculture, total oil use is cut by 118.70 Pj, 23.3%, less than the sum of the independent changes, because the direct cut in oil input to Manufacturing is being applied to a smaller gross output for that sector
2
2
2

For the columns of the transactions table
Xj
X
 j or



X i ij

M j

W j

OVA j j

1,..., n
X i ij

V j
, j

1,..., n (8.13)
(8.12) where V j is primary input cost. With intermediate inputs as fixed proportions of industry outputs
X j
  a X i ij j

V j
, j

1,..., n
(8.14)
With prices which are all unity
P X j
  i a P X j

V j
, j

1,..., n
P j
P j
  i a P j

V j
/ X j
, j

1,..., n
  a P i ij j
 v j j

n (8.15) where v j is primary input cost per unit output

In matrix algebra (8.15) is
P
 
(8.16) where P is an n x 1 vector of prices,
A’ is the transpose of the n x n matrix of input-output coefficients, and v is an n x 1 vector of primary input coefficients. Rearranging (8.16) which with I as the identity matrix is
(I

A )P
 v which solves for P as
P
  
1
A ) v written more usefully as
P
  v (I

A)

1   where L is the n x n Leontief inverse
(8.17)

For the 3 sector illustration transaction table the primary cost coefficients are
Agriculture
0.55
Manufacturing
0.70
Services
0.75
Using these in (8.17) with the Leontief inverse
L

1.0833
0.222
0.0556
 

0.4167 1.1111
0.1500
0.2778
0.1333 1.0333



 gives P
1
= 1, P
2
= 1 and P
3
=1.
The usefulness of the analysis lies in figuring the effects on prices of changes to elements in the vector of primary cost vector, and/or of changes in the elements of the
A matrix.

CO
2 emissions arising in each sector are, kilotonnes
Agriculture
3660
Manufacturing
29280
Services
4392
The change in prices for the changes in the v coefficients is given by
   v L (8.18) where
∆v′ is the transposed vector of changes in the primary input cost coefficients and
∆P′ is the transposed vector of consequent price changes. For the postulated rate of carbon taxation, using the figures above for emissions and the data from Table 8.1 gives
 
1
0.0682,
 
2
0.2265,
 
3
0.1277
for which equation 8.18, with L as given above, yields
 
1
0.1874,
 
2
0.2838,
 
3
0.1987
so that the price of the output of the agricultural sector, for example, rises by 18.74%
The results are conditional on no changes in the elements of the A matrix. If the carbon tax leads to changes in technology – substitution away from fossil fuels/energy conservation – the results here give an upper-bound to the price changes

Extracts from Table 8.7 Price increases due to a carbon tax of A$20 per tonne
Sector Rank Percentage Price
Increase
1.77
9 Agriculture, forestry and fishing
Food products
Basic metals, products
Electricity
Gas
Construction
Community services
1.46
9.00
31.33
21.41
1.60
0.93
16
5
1
2
13
21

Given data on household expenditure patterns across the income distribution, using such with input-output price results can figure the changes in the cost of living for household groups.

CPI h
 
β j hj

P
, h j
 1,..., m
(8.19) where CPI stands for Consumer Price Index h indexes household groups
β hj is the budget share for commodity j for the household group h

Table 8.8 CPI impacts of carbon taxation
Decile
7
8
5
6
3
4
1
2
9
10
All households
2.88
2.77
2.80
2.77
Accounting for direct and indirect impacts
%
2.89
3.00 H
2.97
2.85
2.67
2.62 L
2.79
1.45
1.35
1.31
1.28
Accounting for only direct impacts %
1.53
1.66 H
1.60
1.44
1.16
1.10 L
1.31
Direct impact when accounting only for household expenditure on electricity, gas, and petroleum and coal products.
H is highest CPI impact, L lowest.
Assumption is that expenditure patterns do not change in response to carbon tax.

Rebound is where technological change improving efficiency leads to an increase in use.
Llop (2008) looks at an 18 x 18 A matrix for Spain, where industry 18 is water supply to calculate commodity price changes for 3 scenarios
1.The a coefficients in row 18 are reduced by 20% and in column 18 increased by 20% - water is used and supplied more efficiently
2. Imposition of 40% tax on price industries pay for water
3. Scenarios 1 and 2 combined
With j =1,...18, P j0 is the price of the jth commodity initially and P j1 imposition of the scenario change, and similarly for X j0 is the price after the and X j1
. Let k be the ratio, the same across all sectors, by which expenditure changes when price changes, so that
P j1
X j1
= kP j0
X j0 and with P j0
=1 for all j, this means
X j1
= k(X j0
/P j1
).
gives the quantity demanded by industry j following a price change.

Scenario
1
Scenario
2
Scenario
3 Table 8.6 Changes in total industrial water use
Water Use change %
Expenditure constant, k=1 20.08
Expenditure down 10%, k=0.9
Expenditure up 10%, k=1.1
8.07
32.09
-28.65
-35.79
-1.52
-14.30
-22.87
-5.73
k = 1 is unitary elasticity of demand k = 0.9 is approximately elasticity 0.9
k = 1.1 is approximately elasticity 1.1
These results show
1.The change in total industrial water usage is very sensitive to the elasticity of demand
2. For the elasticities considered, there is rebound – efficiency improvements lead to greater use
3. Scenario 3 – that rebound effects can be offset by the introduction of a tax

CGE models are empirical versions of the Walrasian general equilibrium system and employ standard neoclassical assumptions –
Market clearing
Walras’s law
Utility maximisation by households
Profit maximisation/cost minimisation by firms
Unlike input-output models, CGE models have substitution responses in production and consumption
CGE models have been much used in relation to environmental issues.

Agriculture
Manufacturing
Wages
Agricultur e
0
1.1562
2.5157
Manufacturi ng
1.3490
0
1.4844
Consumption
3.1615
3.1615
Total output
4.5105
4.3177
Other value added
Total input
0.8386
1.4843
4.5105
4.3177
Only relative prices matter. Set the price of labour at unity. Then
Agriculture
Manufacturing
Labour
P
P
2
1
= 2.4490
= 3.1355
W = 1
Oil P = 1.1620
Table 8.9 Transactions table for the two-sector economy
With these prices get an input-output transactions table in physical units. Each Pj of oil gives rise to 73.2 tonnes CO
2 emissions
Agriculture
Agriculture
0
Manufacturing
0.5508
Consumption
1.2909
Total output
1.8417
Table 8.10 Physical data for the two-sector economy
Manufacturing 0.3687
0 1.0083
1.3770
Labour 2.5157
1.4844
Oil
Emissions
0.7217
52.8484
1.2774
93.5057

1. Market clearing
X
1

X
11

X
12

C
1
X
2

X
21

X
22

C
2
In regard to the use of intermediate goods in production use the standard input-output assumption, so
X
1
 a X
11 1
 a X
12 2

C
1
(8.20)
X
2
 a X
 a X
21 1 22 2

C
2
2. Connected markets
Together with demand and supply equations
Y

(
1

L
2
)

(
1

R
2
)
(8.21) ties together the various markets, where Y is total household income, W is the wage rate, P is the price of oil, and R i is oil used in the ith sector.

3. Utility maximisation and household demand
C
1

( , ,
2
)
C
2

( , ,
2
)
In the absence of sufficient data for proper econometric estimation it is usual to assume a plausible functional form and ‘calibrate’ from the benchmark data. Here
Max
 α
U C C
1
β
2 subject to
Y

PC
1 1

P C
2 2 gives
C
1
C
2


[α /(α
 β)
P Y
1
]
[β /(α
 β)
P Y
Using the benchmark data this is
(8.24) with solution α = β. The value α = 0.5 is imposed.
(8.25)

Intermediate demand
From Table 8.9, the transactions table
A

0 0.4
0.2
0


Production
X
1

L 0.75
1
R
1
0.25
 0.5
0.5
X L R
2 2 2
(8.26)
With Constant Returns to Scale , profits are zero always and there is no supply function – firms produce to meet demand.
Factor demand equations derived using cost minimisation.
Numerical values fixed by calibration against benchmark data – Table 8.10

Box 8.4 The illustrative CGE model specification and simulation results
(1)
Computable general equilibrium model specification
C
1
= Y /2 P
1
(10) L
2
= U
L 2
X
2
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
C
2
= Y /2 P
2
X 1 = 0.4
X
2
+ C
1
X
2
= 0.2
X
1
+ C
2
P
1
= 0.2
P
2
+ WU
L 1
+ PU
R 1
P
2
= 0.4
P
1
+ WU
L 2
+ PU
R 2
U
L 1
= [3( P / W )] 0.25
L
1
= U
L 1
X
1
U
L 2
= [ P / W ] 0.5
(11)
(12)
(13)
(14)
(15)
(16)
(17)
(18)
U
R 1
= [0.33( W / P )] 0.75
R
1
= U
R 1
X
1
U
R 2
= [ W / P ] 0.5
R
2
= U
R 2
X
2
E = E
1
+ E
2
= e
1
R
1
+ e
2
R
2
Y = W ( L
1
+ L
2
) + P ( R
1
+ R
2
)
L
1
+ L
2
= L *
R
1
+ R
2
= R *
18 equations in 18 endogenous variables – W, P, Y, E, R and for i=1,2 UL i
, UR i
, C i
, P i
, X i
, L i
Eqtns 1 and 2 – household demands
Eqtns 3 and 4 – commodity balances
Eqtns 5 and 6 – pricing
Eqtns 7,9,11,13 – factor input per unit output
Eqtns 8,10,12, 14 – convert to factor demands
Eqtn 15 – total emissions
Eqtn 16 – household income
Eqtns 17 and 18 – fixed factor endowments, fully employed

1.Take in parameter values and factor endowments
2. Labour is numeraire, W =1 (only interested in relative prices)
3. Assume value for P and use eqtns 7, 9, 11 and 13 to get unit factor demands
4. Use with solutions to eqtns 5 and 6 to get commodity prices and with assumed temporary value for X
1 get L
1 by eqtn 8 and R
1 by eqtn 12
5. L
2
= L* - L
1
6. Calculate X
2 and L
2
7. Get manufacturing demand for oil from eqtn 14
8. Get Y from eqtn 16
9. Get household commodity demands from eqtns 1 and 2
10. Compare (R
1
+ R
2
) with R*.
For (R
1
+ R
2
)>R* increase P and repeat steps 1 to 10 until (R close enough to R*
1
+ R
2
) is
For (R
1
+ R
2 enough to R*
)<R* reduce P and repeat steps 1 to 10 until (R
1
+ R
2
) is close
Stop

Table 8.11 Computable general equilibrium model results
Base case A Base case B
A and B differ only in regard to relative prices
50% emissions reduction
1
Reduction case as proportion of base case
1 W
P
1
1.1620
5
5.7751
2.3990
2.0645
A reproduces original price and quantity data – calibration
P
1
2.4490
12.2410
3.0472
1.2443
P
2
3.1355
15.6702
4.3166
1.3767
C cuts total emissions by
50%.
X
1
1.8416
1.8421
1.4640
0.7950
P, P
1 and P
2 increase
X
2
1.3770
1.3770
1.0341
0.7510
X
1 and X
2 fall
L
1
2.5157
2.5164
2.3983
0.9533
L 2 1.4844
1.4836
1.6017
1.0790
L
1 down L
2 up
R
1
R
2
R
0.7216
1.2774
2
0.7226
1.2780
2
0.3332
0.6677
1
0.4618
0.5227
0.5000
The loading of the total emissions reduction across sectors is efficient
E
1
52.8484
93.5057
52.8484
93.5057
24.3902
48.8756
0.4618
0.5227
Households consume less of both commodities
E
2
E 146.3541
146.3541
73.2658
0.5000
Higher nominal national income
Y 6.324
31.615
6.3990
1.0119
1.2909
1.2912
1.0503
0.8136
Lower utility C
1
C
2
U
1.0083
1.0087
0.7415
0.7354
1.1409
1.1412
0.8825
0.7735

Improvements in energy efficiency may be partially or wholly offset by consequent increases in demand a lower effective price for energy leads to its substitution for other inputs lower production costs increase income and demand
is where there is partial offset
is where the energy demand eventually increases
Allen et al (2007) use the CGE model UKENVI to investigate the question for the UK economy
25 commodities, 5 energy commodities
3 classes of agent – households, firms and government
Rest of the world a single entity
Calibrated on 2000 data base from the 1995 UK input-output tables

∆E E - the initial percentage change in energy efficiency
∆E M - the percentage change in total energy use after the economy has responded to the initial shock
R - percentage rebound.
R

100 x




1


E
M

E
E




 with ∆E E <0, four cases can be distinguished:
1. ∆E M < 0 and greater in absolute value than ∆E E implies R < 0.
2. ∆E M < 0 and equal in absolute value to ∆E E implies R = 0.
3. ∆E M < 0 and smaller in absolute value than ∆E E implies 0 < R < 100.
4. ∆E M > 0 implies R > 100
If all agents respond rationally to a cut in the effective price of energy, as they do in CGE models, case 1 is going to be null, empty.
Case 4 is Backfire

Q

A


X
1
  
( 1
 
) X
2
 


1 /

: A

0 , 0
  
1 ,

1
   
Constant elasticity of substitution production functions with 2 inputs
Output
Figure 8.2
Production structure of UKENVI model Intermediates
Value Added
ROW composite
UK composite Labour Capital
Electricity
Renewable
Energy composite
Non-renewable Oil
Non-energy composite
Non-electricity
Non-oil
Coal Gas

Table 8.12 Selected simulation results from UKENVI
% Change from Base Year
Central case
Elasticity of substitution reduced
Constant costs
Government expenditure adjusts
Exogenous labour supply
GDP
Employment
CPI
Electricity
Non-electricity
0.17
0.21
-0.27
27.0%
30.8%
0.16
0.21
-0.23
11.6%
13.2%
-0.33
0.03
0.17
0.20
0.26
-0.13
-10.4%
Rebound
26.4%
-3.6% 30.6%
-0.04
0.00
-0.10
21.2%
24.0%
Real wage resistance
0.90
0.95
-0.68
47.4%
55.4%
‘Long run’ adjustments to an exogenous shock where all sectors improve energy use efficiency by
5% at third input level in Figure 8.2.
Central case shows rebound, but not backfire . The long run % change is smaller than the initial efficiency improvement
Outcomes for all variables depend on model configuration – rebound can be avoided if efficiency gains accompanied by increased costs.

Table 8.13 Costs associated with alternative instruments for global emissions reductions
Region
EC
N. America
Japan
Other OECD
Oil exporters
Rest of world
Option 1
– 4.0
– 4.3
– 3.7
– 2.3
+4.5
– 7.1
Option 2
– 1.0
– 3.6
+0.5
– 2.1
– 18.7
– 6.8
Option 3
– 3.8
– 9.8
– 0.9
– 4.4
– 13.0
1.8
All options cut global emissions by 50%
Option1 .Each region taxes fossil fuel production
Option2 .Each region taxes fossil fuel consumption
Option3 .A global tax is collected by an international agency which disposes of revenue by grants to regions based on population size
This is least cost for World, but not for all regions, and under it ROW – mostly developing nations – gains.
World – 4.4
– 4.4
– 4.2
Figures are for % changes in GDP

Table 8.14 Effects of carbon taxation according to use of revenue
Real Gross Domestic Product
S1
0.07
S2
– 0.09
Results from the ORANI CGE model for Australia.
ORANI has a government sector, and overseas trade.
Consumer Price Index – 0.18
0.42
S1 Carbon tax to raise A$2 billion, used to reduce payroll tax
Budget Balance* – 0.02
0.31
S2 Carbon tax to raise A$2 billion, used to reduce government deficit
Employment
CO
2
Emissions
0.21
– 3.9
– 0.04
– 4.7
In both, money wage rate is fixed and the labour market does not clear.
‘Short run’ simulations
* as percentage of GDP
Carbon taxation has output and substitution effects in labour market
A reduction in demand on account of GDP contraction due to trade effects of acting unilaterally
An increase in demand due to higher relative price of fossil fuel input relative to labour input – plus reduced payroll tax effect in S1

As compared with input-output models, the main benefit of CGE models is the inclusion of behavioural responses by consumers and producers .
This is modelled as optimising behaviour
– not everybody accepts that economic agents are in fact fully rational, and/or well-informed
But: CGE models are not about short/medium term prediction. They are about insights into underlying tendencies.
Data is a problem for CGE models – calibration rather than estimation
CGE model results typically sensitive to changes in parameter values
There are limits to the accuracy with which the variables that these models track are measured.
Looking at UK annual GDP estimates, current price 1991 to 2004, the change between the first published number and the most recent available in 2006 ranged from
0.4% to 2.8% of GDP.
That CGE model results are consistent with economic theory is not surprising – they incorporate it.