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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
Sales to: Intermediate sectors Final demand
Purchases from
Agriculture Manufacturing Services
Households Exports Total output
Intermediate sectors
Agriculture 0 400 0 500 100 1000
Manufacturing 350 0 150 800 700 2000
Services 100 200 0 300 0 600
Primary inputs
Imports 250 600 50
Wages 200 500 300
Other value added
100 300 100
Total input 1000 2000 600
Table 8.1 Input-output transactions table, $million
Agriculture sales 0
(to) (Agriculture)
400 0 500
(Manufacturing) (Services) (Households)
100 1000
(Exports) (Total output)
across a row
Manufacturing400 0
purchases(Agrculture) (Manufacturing)
(from)
200 600 300
(Services) (Imports) (OVA)
2000
(Total input)
down a column
Input-output accounting 2Because 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’:
, 1,...,i j ij iX X Y i 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
ij ij jX a X (8.2)
To go from accounting to analysis, the basic assumption is
where aij is a constant.
Substituting 8.2 into 8.1 gives
, 1,...,i j ij j iX a X Y i 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
X AX Y
(I A)X Y
1X (I A) Y
X LY
X AX Y In matrix notation, (8.3) is
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, Yi. With I as the identity matrix, (8.4) can be written
which has the solution
(8.5)
where (I – A)-1 is the inverse of (I-A). This can be written
(8.6)
L is often known as the Leontief inverse, in recognition of inventor of i-o analysis
Input-output modelling 3
1 11 1 12 2 13 3
2 21 1 22 2 23 3
3 31 1 32 2 33 3
X l Y l Y l Y
X l Y l Y l Y
X l Y l Y l Y
(8.7) – the lij are the elements of L. The Xi are the gross output levels for the final demands Yj.
11 12 13
21 22 23
31 32 33
0, 400 / 2000 0.2000, 0
350 /1000 0.3500, 0, 150 / 600 0.2500
100 /1000 0.1000, 200 / 2000 0.1000, 0
a a a
a a a
a a a
From the 3-sector transactions table, the coefficients which are the elements of matrix A are
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 demandAnalysing 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 Services50 Pj 400 Pj 60 Pj
With Oi for oil use in industry i, assume
i i iO r X
1
2
3
0.05 for agriculture
0.2 for manufacturing
0.1 for services
r
r
r
1 2 3100 300 100Y Y Y
1 2 3180.51 402.79 158.26X X X
1 2 39.03 80.56 15.83O O O
(8.8)
so that
Then for
get
and hence
Attributing resource use and emissions to final demand deliveries 1
1 1 1 1 11 1 1 12 2 1 13 3
2 2 2 2 21 1 2 22 2 2 23 3
3 3 3 3 31 1 3 32 2 3 33 3
O r X rl Y rl Y r l Y
O r X r l Y r l Y r l Y
O r X r l Y r l Y r l Y
1 2 3 1 11 2 21 3 31 1
1 12 2 22 3 32 2
1 13 2 23 3 33 3
( )
( )
( )
O O O rl r l r l Y
r l r l r l Y
r l r l r l Y
1 2 3 1 1 2 2 3 3O O O i Y i Y i Y
where i1 = r1l11 + r2l21 + r3l31 etc. The left-hand side of equation 8.10 is total oil use. The right-hand 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.
(8.10)
adding vertically gives
which can be written
Attributing resource use and emissions to final demand deliveries 2
Agriculture Manufacturing Servics
0.1525 0.2467 0.1617
Agriculture Manufacturing Services
600 1500 300
Agriculture Manufacturing Services
91.50 370.05 48.51
For the three sector example, the oil intensities are
which with final demand deliveries of
gives total oil use of 510 PJ, allocated across final demand deliveries as
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 coefficientsi is a 1 n vector of resource intensities for final demand deliveriesand 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 levelsR* 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
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
Extract from Table 8.3 CO2 intensities and levels for final demand deliveries, Australia 1986/7
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.
Figure 8.1 Some trends 1992-2004
0
20
40
60
80
100
120
140
Percentage of embedded CO2 due to imports
CO2 emissions attributable to UK households
CO2 intensity household expenditure
Box 8.2 Attributing CO2 emissions to UK households 1
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
TotalTonnes 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
Table 8.4 CO2 emissions attributable to UK households 1992-2004
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
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
Table 8.5 CO2 emissions attributable to UK Supergroups 2004
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 a21 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
1,..., i ij j j jXj X M W OVA j n For the columns of the transactions table
(8.12)
, 1,..., j i ij jX X V j n or
(8.13)
where Vj is primary input cost. With intermediate inputs as fixed proportions of industry outputs
, 1,..., j i ij j jX a X V j n (8.14)
With prices which are all unity
, 1,..., j j i ij j j jP X a P X V j n / , 1,..., j i ij j j jP a P V X j n
, , 1,..., j i ij j jP a P v j n (8.15)
where vj is primary input cost per unit output
Input-output modelling – costs and prices 2
P A P v (8.16)
P A P v
(I A )P v
1P (I A ) v
1P v (I A) v L (8.17)
In matrix algebra (8.15) is
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
which solves for P as
written more usefully as
where L is the n x n Leontief inverse
Input-output modelling – costs and prices 3
Agriculture Manufacturing Services
0.55 0.70 0.75
1.0833 0.222 0.0556
L 0.4167 1.1111 0.2778
0.1500 0.1333 1.0333
For the 3 sector illustration transaction table the primary cost coefficients are
Using these in (8.17) with the Leontief inverse
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
P v L (8.18)
The change in prices for the changes in the v coefficients is given by
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
for which equation 8.18, with L as given above, yields
1 2 30.0682, 0.2265, 0.1277v v v
1 2 30.1874, 0.2838, 0.1987P P P
Agriculture Manufacturing Services
3660 29280 4392
CO2 emissions arising in each sector are, kilotonnes
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
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
Extracts from Table 8.7 Price increases due to a carbon tax of A$20 per tonne
The regressivity of carbon taxation 2
CPI β , 1,..., h j hj jP h m
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.
(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
Decile Accounting for direct and indirect impacts %
Accounting for only direct impacts %
1 2.89 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
Table 8.8 CPI impacts of carbon taxation
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
1Scenario 2
Scenario 3
Water Use change %
Expenditure constant, k=1 20.08 -28.65 -14.30
Expenditure down 10%, k=0.9
8.07 -35.79 -22.87
Expenditure up 10%, k=1.1 32.09 -1.52 -5.73
Table 8.6 Changes in total industrial water use
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
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
Agriculture
Manufacturing
Consumption Total output
Agriculture 0 1.3490 3.1615 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
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
Only relative prices matter. Set the price of labour at unity. ThenAgriculture P1 = 2.4490Manufacturing P2 = 3.1355Labour W = 1Oil 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
Table 8.9 Transactions table for the two-sector economy
Table 8.10 Physical data for the two-sector economy
An illustrative two-sector CGE model – market clearing and walras
1. Market clearing
1 11 12 1
2 21 22 2
X X X C
X X X C
1 11 1 12 2 1
2 21 1 22 2 2
X a X a X C
X a X a X C
1 2 1 2( ) ( )Y W L L P R R
In regard to the use of intermediate goods in production use the standard input-output assumption, so
(8.20)
2. Connected markets
Together with demand and supply equations
(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
1 1 1 2
2 2 1 2
( , , )
( , , )
C C Y P P
C C Y P P
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 β1 2U C C
subject to
1 1 2 2Y PC P C
gives
1 1
2 2
[α /(α β) ]
[β /(α β) ]
C P Y
C P 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
From Table 8.9, the transactions table
0 0.4A
0.2 0
Intermediate demand
Production 0.75 0.25
1 1 1
0.5 0.52 2 2
X L R
X L R
(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
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
(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*
(9) UL2 = [P/W]0.5 (18) R1 + R2 = R*
An illustrative two-sector CGE model
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
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
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
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
L2 1.4844 1.4836 1.6017 1.0790
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
Simulation results for the illustrative modelTable 8.11 Computable general equilibrium model results A and B differ only in
regard to relative prices
A reproduces original price and quantity data – calibration
C cuts total emissions by 50%.
P, P1 and P2 increase
X1 and X2 fall
L1 down L2 up
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
E
M
E
ExR 1100
∆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.
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
1,10,0:)1(
/1
21 AXXAQ
Constant elasticity of substitution production functions with 2 inputs
Output
Intermediates Value Added
ROW composite UK composite Labour Capital
Non-energy compositeEnergy composite
Electricity Non-electricity
Renewable Non-renewable Oil Non-oil
Coal Gas
Figure 8.2 Production structure of UKENVI model
% Change from Base Year
Centralcase
Elasticity ofsubstitutionreduced
Constantcosts
Governmentexpenditureadjusts
Exogenouslaboursupply
Realwageresistance
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%
UKENVI resultsTable 8.12 Selected simulation results from UKENVI
‘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
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
Table 8.13 Costs associated with alternative instruments for global emissions reductions
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
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
Table 8.14 Effects of carbon taxation according to use of revenue
* as percentage of GDP
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
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.
