Transcript Chapter 8 PowerPoint document

Chapter 8 Economy wide modelling
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
SO2 and NO2 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 CO2, SO2 and NO2. 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 CO2, by 16% for SO2, and by
63% for NO2. 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.
Input-output accounting 1
Table 8.1 Input-output transactions table, $million
Intermediate
sectors
Primary
inputs
Sales to:
Intermediate sectors
Purchases
from
Agriculture
0
400
0
500
100
Total
outpu
t
1000
Manufacturing
350
0
150
800
700
2000
Services
100
200
0
300
0
600
Imports
250
600
50
Wages
200
500
300
Other value
added
Total input
100
300
100
1000
2000
600
Agriculture
across a row
Agriculture sales
(to)
400
Final demand

Manufacturing
Service
s
Households
Exports
down a column
0
(Agriculture)
0
500



(Manufacturing) (Services) (Households)
100
1000


(Exports) (Total output)
Manufacturing
purchases
(from)

400
0

(Agrculture) (Manufacturing)
200
600
300


(Services) (Imports) (OVA)
2000

(Total input)

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’:
Xi   j Xij  Yi , i  1,..., n
(8.1)
where
Xi = total output of industry i
Xij = sales of commodity i to industry j
Yi = sales of commodity i to final demand
n = the number of industries
Input-output modelling 1
To go from accounting to analysis, the basic assumption is
X ij  aij X j
(8.2)
where aij is a constant.
Substituting 8.2 into 8.1 gives
Xi   j aij X j  Yi , i  1,..., n
(8.3)
as a system of n linear equations in 2n variables, the Xi and Yi, and n2 coefficients, the
aij. If the Yi – the final demand levels – are specified, there are n unknown Xi – the gross
output levels – which can be solved for using the n equations.
Input-output modelling 2
In matrix notation, (8.3) is
X  AX  Y
which can be written
X  AX  Y
(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, Yi. With I as the identity matrix, (8.4) can be written
(I  A)X  Y
which has the solution
X  (I  A)1Y
(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 Leontief inverse, in recognition of inventor of i-o analysis
Input-output modelling 3
X1  l11Y1  l12Y2  l13Y3
X 2  l21Y1  l22Y2  l23Y3
X 3  l31Y1  l32Y2  l33Y3
(8.7) – the lij are the elements of L. The Xi
are the gross output levels for the final
demands Yj.
From the 3-sector transactions table, the coefficients which are the elements of matrix A are
a11  0, a12  400 / 2000  0.2000, a13  0
a21  350 /1000  0.3500, a22  0, a23  150 / 600  0.2500
a31  100 /1000  0.1000, a32  200 / 2000  0.1000, a33  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
X1 = 999.96
Manufacturing
X2 = 2000.01
Services
X3 = 599.94
Solving for Y1 = 700, Y2 = 1800, Y3 = 400 gives
Agriculture
X1 = 1180.51 - for ∆Y1 = 100, ∆X1 = 180.51
Manufacturing
X2 = 2402.79 – for ∆Y2 = 300, ∆X2 = 402.79
Services
X3 = 758.26 – for ∆Y3 = 100, ∆X3 =158.32
Environmental input-output analysis – changes in final demand
Analysing the environmental effect of final demand changes
Suppose that in addition to the data of Table 8.1 we also know that the use of oil by the three industries
was
Agriculture
Manufacturing
Services
50 Pj
400 Pj
60 Pj
With Oi for oil use in industry i, assume
Oi  ri X i
(8.8)
so that
r1  0.05 for agriculture
r2  0.2 for manufacturing
r3  0.1 for services
Then for
Y1  100
Y2  300
Y3  100
get
X1  180.51 X 2  402.79 X 3  158.26
and hence
O1  9.03
O2  80.56 O3  15.83
Attributing resource use and emissions to final demand deliveries 1
O1  r1 X1  rl
1 11Y1  rl
1 12Y2  rl
1 13Y3
O2  r2 X 2  r2l21Y1  r2l22Y2  r2l23Y3
O3  r3 X 3  r3l31Y1  r3l32Y2  r3l33Y3
adding vertically gives
O1  O2  O3  (rl
1 11  r2l21  r3l31 )Y1
(rl
1 12  r2l22  r3l32 )Y2
(rl
1 13  r2l23  r3l33 )Y3
which can be written
O1  O2  O3  i1Y1  i2Y2  i3Y3
(8.10)
where i1 = r1l11 + r2l21 + r3l31 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 i1, 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.
Attributing resource use and emissions to final demand deliveries 2
For the three sector example, the oil intensities are
Agriculture
Manufacturing
0.1525
Servics
0.2467
0.1617
which with final demand deliveries of
Agriculture
Manufacturing
600
1500
Services
300
gives total oil use of 510 PJ, allocated across final demand deliveries as
Agriculture
91.50
Manufacturing
370.05
Services
48.51
As compared with the industry uses of oil from which the ri 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.
Attributing resource use and emissions to final demand deliveries 3
In matrix algebra, which would be the basis for doing the calculations where the number of
sectors is realistically large, n, the foregoing is
O = RX = RLY = iY
(8.11)
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.
CO2 intensities Australia
Extract from Table 8.3 CO2 intensities and levels for final demand deliveries, Australia 1986/7
Sector
CO2 Intensitya
CO2 tonnes
% of total
Ag, forest, fishing
1.8007 (6)
13.836 (8)
4.74
Food products
1.532 (8)
11.540 (10)
4.00
Basic metal
products
4.4977 (4)
20.25 (4)
6.94
Electricity
15.2449(1)
43.747 (1)
14.99
Gas
9.9663 (3)
4.675 (18)
1.60
Construction
0.7567 (19)
28.111 (3)
9.64
Community
services
0.4437 (26)
17.802 (6)
6.10
a. tonnes x 103/($A x 106)
It is frequently stated that about 45% of Australian CO2 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.
Box 8.2 Attributing CO2 emissions to UK households 1
Figure 8.1 Some trends 1992-2004
140
120
100
80
60
40
20
0
Percentage of embedded CO2 due to imports
CO2 emissions attributable to UK households
CO2 intensity household expenditure
CO2 attributable to UK households up 20%
CO2 embedded in imports
CO2 intensity of household expenditure down 20%
Druckman and Jackson’s ‘embedded’ = indirect
Box 8.2 Attributing CO2 emissions to UK households 2
Table 8.4 CO2 emissions attributable to UK households 1992-2004
Total
Tonnes CO2 x 106
Percentage
Embedded
Vehicle Use
Flights
Direct
1992
467.2
49.3
13.2
2.9
34.6
1993
462.1
50.0
13.4
3.1
33.5
1994
454.1
50.2
13.3
3.2
33.2
1995
456.8
51.8
13.0
3.4
31.8
1996
475.0
50.2
13.2
3.3
33.3
1997
460.0
51.0
13.9
3.6
31.6
1998
475.4
51.2
13.3
3.9
31.6
1999
474.8
51.3
13.7
4.3
30.7
2000
490.2
51.3
13.1
4.8
30.9
2001
518.8
52.2
12.5
4.6
30.6
2002
533.0
53.7
12.6
4.6
29.1
2003
542.1
54.0
12.2
4.6
29.2
2004
557.4
54.5
12.0
4.8
28.7
Source: Druckman and Jackson (2009)
Figures in first column correspond to index
numbers in Figure 8.1
Box 8.2 Attributing CO2 emissions to UK households 3
Table 8.5 CO2 emissions attributable to UK Supergroups 2004
Tonnes CO2
Percentage
Per household
Per capita
Embedded
Flights
Vehicle Use
Direct
1.Prospering suburbs
26.5 (1)
10.4 (1)
54.0
5.5
12.6
27.9
2.Countryside
24.9 (2)
10.2 (2)
53.8
5.4
12.4
28.4
3.Typical traits
22.4 (3)
9.2 (3)
55.1
5.0
12.3
27.6
4.City living
18.7 (5)
8.3 (4)
56.1
4.3
11.7
27.9
5.Blue collar
19.5 (4)
8.0 (5)
54.0
4.5
12.0
29.6
6.Muticultural
18.2 (6)
7.7 (6)
55.6
4.0
11.7
28.8
7.Constrained by circumstances
16.1 (7)
7.4(7)
54.2
3.9
11.1
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
Analysing the effects of technical change
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 from 0.35
to 0.25 reduces total economy oil use by 24.13 PJ, 5%.
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
Energy conservation and CO2 emissions reduction can be pursued by materials
saving innovation. In the Australian data, cutting all input coefficients for Basic
Metals by 10% would cut total CO2 emissions by 1.4%.
Cutting the final demand for electricity by 10% would cut total CO2 emissions by
1.5%
Input-output modelling - costs and prices 1
For the columns of the transactions table
Xj   i Xij  M j  Wj  OVAj j  1,..., n
(8.12)
or
X j   i X ij  Vj , j  1,..., n
(8.13)
where Vj is primary input cost. With intermediate inputs as fixed proportions of industry outputs
X j   i aij X j  Vj , j  1,..., n
(8.14)
With prices which are all unity
Pj X j   i aij Pj X j Vj , j  1,..., n
Pj   i aij Pj  Vj / X j , j  1,..., n
Pj   i aij Pj , v j , j  1,..., n
(8.15)
where vj is primary input cost per unit output
Input-output modelling – costs and prices 2
In matrix algebra (8.15) is
P  AP  v
(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)
P  AP  v
which with I as the identity matrix is
(I  A)P  v
which solves for P as
P  (I  A)1v
written more usefully as
P  v(I  A)1  vL
where L is the n x n Leontief inverse
(8.17)
Input-output modelling – costs and prices 3
For the 3 sector illustration transaction table the primary cost coefficients are
Agriculture
0.55
Manufacturing
Services
0.70
0.75
Using these in (8.17) with the Leontief inverse
1.0833 0.222 0.0556 
L  0.4167 1.1111 0.2778 
 0.1500 0.1333 1.0333 
gives P1 = 1, P2 = 1 and P3 =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.
Carbon taxation in the three sector example
CO2 emissions arising in each sector are, kilotonnes
Agriculture
Manufacturing
3660
29280
Services
4392
The change in prices for the changes in the v coefficients is given by
P  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
v1  0.0682, v2  0.2265, v3  0.1277
for which equation 8.18, with L as given above, yields
P1  0.1874, P2  0.2838, P3  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
The regressivity of carbon taxation 1
Extracts from Table 8.7 Price increases due to a carbon tax of A$20 per tonne
Sector
Percentage Price
Increase
Rank
Agriculture, forestry
and fishing
1.77
9
Food products
1.46
16
Basic metals, products
9.00
5
Electricity
31.33
1
Gas
21.41
2
Construction
1.60
13
Community services
0.93
21
The regressivity of carbon taxation 2
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.
CPIh   jβhj Pj ,
h  1,..., m
(8.19)
where CPI stands for Consumer Price Index
h indexes household groups
βhj is the budget share for commodity j for the household group h
The regressivity of carbon taxation 3
Table 8.8 CPI impacts of carbon taxation
Decile
1
Accounting for direct
and indirect impacts
%
2.89
Accounting for
only direct
impacts %
1.53
2
3.00 H
1.66 H
3
2.97
1.60
4
2.85
1.44
5
2.88
1.45
6
2.77
1.35
7
2.80
1.31
8
2.77
1.28
9
2.67
1.16
10
2.62 L
1.10 L
All households
2.79
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.
Box 8.3 Input-output analysis of rebound in Spanish water supply 1
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, Pj0 is the price of the jth commodity initially and Pj1 is the price after the
imposition of the scenario change, and similarly for Xj0 and Xj1. Let k be the ratio, the same
across all sectors, by which expenditure changes when price changes, so that
Pj1Xj1 = kPj0Xj0
and with Pj0 =1 for all j, this means
Xj1 = k(Xj0/Pj1).
gives the quantity demanded by industry j following a price change.
Box 8.3 Input-output analysis of rebound in Spanish water supply 2
Scenario
1
Scenario
2
Scenario
3
20.08
-28.65
-14.30
Water Use change %
Expenditure constant, k=1
Table 8.6 Changes in total
industrial water use
k = 1 is unitary elasticity of demand
Expenditure down 10%,
k=0.9
Expenditure up 10%, k=1.1
8.07
-35.79
-22.87
32.09
-1.52
-5.73
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
Computable general equilibrium models
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.
An illustrative two-sector CGE model - data
Manufacturi
ng
1.3490
Consumption
Agriculture
Agricultur
e
0
3.1615
Total
output
4.5105
Manufacturing
1.1562
0
3.1615
4.3177
Wages
2.5157
1.4844
Other value
added
0.8386
1.4843
Total input
4.5105
4.3177
Table 8.9 Transactions table for
the two-sector economy
Only relative prices matter. Set the price of labour at unity. Then
Agriculture
P1 = 2.4490
Manufacturing
P2 = 3.1355
Labour
W=1
Oil
P = 1.1620
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
Manufacturing
Consumption
Total output
Agriculture
0
0.5508
1.2909
1.8417
Manufacturing
0.3687
0
1.0083
1.3770
Labour
2.5157
1.4844
Oil
0.7217
1.2774
Emissions
52.8484
93.5057
Table 8.10 Physical data
for the two-sector
economy
An illustrative two-sector CGE model – market clearing and
walras
1. Market clearing
X1  X11  X12  C1
X 2  X 21  X 22  C2
In regard to the use of intermediate goods in production use the standard input-output assumption, so
X1  a11 X1  a12 X 2  C1
X 2  a21 X1  a22 X 2  C2
(8.20)
2. Connected markets
Together with demand and supply equations
Y  W ( L1  L2 )  P( R1  R2 )
(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 Ri is oil used in the ith sector.
An illustrative two sector CGE model – household demand
3. Utility maximisation and household demand
C1  C1 (Y , P1 , P2 )
C2  C2 (Y , P1 , P2 )
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
U  C1αC2β
subject to
Y  PC
1 1  P2C2
gives
C1  [α /(α  β) P1 ]Y
C2  [β /(α  β) P2 ]Y
(8.24)
Using the benchmark data this is
α/(α  β)  0.5
β/(α  β)  0.5
(8.25)
with solution α = β. The value α = 0.5 is imposed.
An illustrative two-sector CGE model – intermediate demand
and production
Intermediate demand
From Table 8.9, the transactions table
 0
A
0.2
0.4
0 
Production
X 1  L10.75 R10.25
(8.26)
0.5
X 2  L0.5
R
2
2
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
An illustrative two-sector CGE model
Box 8.4 The illustrative CGE model specification and simulation results
Computable general equilibrium model specification
(1)
C1 = Y/2P1
(10)
L2 = UL2X2
(2)
C2 = Y/2P2
(11)
UR1 = [0.33(W/P)]0.75
(3)
X1 = 0.4X2 + C1
(12)
R1 = UR1X1
18 equations in 18 endogenous
variables – W, P, Y, E, R and for
i=1,2 ULi, URi, Ci, Pi, Xi, Li
Eqtns 1 and 2 – household demands
Eqtns 3 and 4 – commodity balances
(4)
X2 = 0.2X1 + C2
(13)
UR2 = [W/P]0.5
(5)
P1 = 0.2P2 + WUL1 + PUR1
(14)
R2 = UR2X2
(6)
P2 = 0.4P1 + WUL2 + PUR2
(15)
E = E1 + E2 = e1R1 + e2R2
(7)
UL1 = [3(P/W)]0.25
(16)
Y = W(L1 + L2) + P(R1 + R2)
(8)
L1 = UL1X1
(17)
L1 + L2 = L*
Eqtn 16 – household income
(9)
UL2 = [P/W]0.5
(18)
R1 + R2 = R*
Eqtns 17 and 18 – fixed factor
endowments, fully employed
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
The solution algorithm
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 X1 get L1 by eqtn 8 and R1 by eqtn 12
5. L2 = L* - L1
6. Calculate X2 and L2
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 (R1 + R2) with R*.
For (R1 + R2)>R* increase P and repeat steps 1 to 10 until (R1 + R2) is
close enough to R*
For (R1 + R2)<R* reduce P and repeat steps 1 to 10 until (R1 + R2) is close
enough to R*
Stop
Simulation results for the illustrative model
Table 8.11 Computable general equilibrium model results
A and B differ only in
regard to relative prices
Base case A
Base case B
50%
emissions
reduction
Reduction case
as proportion of
base case
W
1
5
1
1
P
1.1620
5.7751
2.3990
2.0645
P1
2.4490
12.2410
3.0472
1.2443
P2
3.1355
15.6702
4.3166
1.3767
X1
1.8416
1.8421
1.4640
0.7950
X2
1.3770
1.3770
1.0341
0.7510
L1
2.5157
2.5164
2.3983
0.9533
X1 and X2 fall
L2
1.4844
1.4836
1.6017
1.0790
L1 down L2 up
R1
0.7216
0.7226
0.3332
0.4618
R2
1.2774
1.2780
0.6677
0.5227
R
2
2
1
0.5000
E1
52.8484
52.8484
24.3902
0.4618
E2
93.5057
93.5057
48.8756
0.5227
E
146.3541
146.3541
73.2658
0.5000
Y
6.324
31.615
6.3990
1.0119
C1
1.2909
1.2912
1.0503
0.8136
C2
1.0083
1.0087
0.7415
0.7354
U
1.1409
1.1412
0.8825
0.7735
A reproduces original price
and quantity data –
calibration
C cuts total emissions by
50%.
P, P1 and P2 increase
The loading of the total
emissions reduction across
sectors is efficient
Households consume less of
both commodities
Higher nominal national
income
Lower utility
Box 8.5 CGE modelling of energy rebound in the UK
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
Rebound is where there is partial offset
Backfire is where the energy demand eventually increases
Rebound/Backfire is an empirical question
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
Rebound definitions
∆EE - the initial percentage change in energy efficiency
∆EM - the percentage change in total energy use after the economy has responded to the initial shock
R - percentage rebound.
  E M
R  100 x 1  
E


  E




with ∆EE<0, four cases can be distinguished:
1. ∆EM < 0 and greater in absolute value than ∆EE implies R < 0.
2. ∆EM < 0 and equal in absolute value to ∆EE implies R = 0.
3. ∆EM < 0 and smaller in absolute value than ∆EE implies 0 < R < 100.
4. ∆EM > 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
UKENVI - industry production structure

Q  A X

1
 (1   ) X

  1 / 
2
: A  0, 0    1,  1    
Constant elasticity of substitution production functions with 2 inputs
Output
Figure 8.2
Production structure
of UKENVI model
Value Added
Intermediates
ROW composite
UK composite
Labour
Energy composite
Non-energy composite
Non-electricity
Electricity
Renewable
Non-renewable
Capital
Non-oil
Oil
Coal
Gas
UKENVI results
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
Real
wage
resistance
GDP
0.17
0.16
-0.33
0.20
-0.04
0.90
Employment
0.21
0.21
0.03
0.26
0.00
0.95
CPI
-0.27
-0.23
0.17
-0.13
-0.10
-0.68
Rebound
Electricity
27.0%
11.6%
-10.4%
26.4%
21.2%
47.4%
Non-electricity
30.8%
13.2%
-3.6%
30.6%
24.0%
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.
International distribution of abatement costs
Table 8.13 Costs associated with alternative
instruments for global emissions reductions
Region
Option 1
Option 2
Option 3
EC
–4.0
–1.0
–3.8
N. America
–4.3
–3.6
–9.8
Japan
–3.7
+0.5
–0.9
Other OECD
–2.3
–2.1
–4.4
Oil exporters
+4.5
–18.7
–13.0
Rest of world
–7.1
–6.8
1.8
World
–4.4
–4.4
–4.2
Figures are for % changes in GDP
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.
Alternative uses of carbon tax revenue
Table 8.14 Effects of carbon taxation
according to use of revenue
S1
S2
Real Gross Domestic Product
0.07
–0.09
Consumer Price Index
–0.18
0.42
Budget Balance*
–0.02
0.31
Employment
0.21
–0.04
CO2 Emissions
–3.9
–4.7
Results from the ORANI CGE model
for Australia.
ORANI has a government sector, and
overseas trade.
S1 Carbon tax to raise A$2 billion, used
to reduce payroll tax
S2 Carbon tax to raise A$2 billion, used
to reduce government deficit
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
Benefits and costs of CGE modelling
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.