Chapter 8 Economy wide modelling

1
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
inputoutput model of an economy and its
solution          find out how the basic
inputoutput model can be extended to incorporate
economy environment interactions         
encounter some examples of environmental
inputoutput models and their application        
  learn how the inputoutput 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
2
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.
3
Input-output accounting 1
Table 8.1 Input-output transactions table,
million
 
   
across a row
down a column
4
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
(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
5
Input-output modelling 1
To go from accounting to analysis, the basic
assumption is
(8.2)
where aij is a constant. Substituting 8.2 into
8.1 gives
(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.
6
Input-output modelling 2
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 aij, 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
7
Input-output modelling 3
(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
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
8
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
(8.8)
so that
Then for
get
and hence
9
Attributing resource use and emissions to final
demand deliveries 1
adding vertically gives
which can be written
(8.10)
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.
10
Attributing resource use and emissions to final
demand deliveries 2
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.
11
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.
12
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.
13
Box 8.2 Attributing CO2 emissions to UK
households 1
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 Jacksons
embedded indirect
14
Box 8.2 Attributing CO2 emissions to UK
households 2
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
15
Box 8.2 Attributing CO2 emissions to UK
households 3
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
16
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
17
Input-output modelling - costs and prices 1
For the columns of the transactions table
(8.12)
or
(8.13)
where Vj is primary input cost. With intermediate
inputs as fixed proportions of industry outputs
(8.14)
With prices which are all unity
(8.15)
where vj is primary input cost per unit output
18
Input-output modelling costs and prices 2
In matrix algebra (8.15) is
(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
which solves for P as
written more usefully as
(8.17)
where L is the n x n Leontief inverse
19
Input-output modelling costs and prices 3
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.
20
Carbon taxation in the three sector example
CO2 emissions arising in each sector are,
kilotonnes
The change in prices for the changes in the v
coefficients is given by
(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     for which
equation 8.18, with L as given above, yields  
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
21
The regressivity of carbon taxation 1
Extracts from Table 8.7 Price increases due to a
carbon tax of A20 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
22
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.
(8.19)
where CPI stands for Consumer Price Index
h indexes household groups ßhj is
the budget share for commodity j for the
household group h
23
The regressivity of carbon taxation 3
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.
24
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.
25
Box 8.3 Input-output analysis of rebound in
Spanish water supply 2
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
26
Computable general equilibrium models
CGE models are empirical versions of the
Walrasian general equilibrium system and employ
standard neoclassical assumptions Market
clearing Walrass 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.
27
An illustrative two-sector CGE model - data
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
CO2 emissions
Table 8.10 Physical data for the two-sector
economy
28
An illustrative two-sector CGE model market
clearing and walras
1. Market clearing
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.
29
An illustrative two sector CGE model household
demand
3. Utility maximisation and household demand
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
subject to
gives
(8.24)
Using the benchmark data this is
with solution a ß. The value a 0.5 is
imposed.
(8.25)
30
An illustrative two-sector CGE model
intermediate demand and production
Intermediate demand
From Table 8.9, the transactions table
Production
(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
31
An illustrative two-sector CGE model
Box 8.4 The illustrative CGE model specification
and simulation results
Computable general equilibrium model specification
18 equations in 18 endogenous variables W, P,
Y, E, R and for i1,2 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
32
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)gtR increase P and repeat
steps 1 to 10 until (R1 R2) is close enough to
R For (R1 R2)ltR reduce P and repeat steps 1
to 10 until (R1 R2) is close enough to
R Stop
33
Simulation results for the illustrative model
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
Table 8.11 Computable general equilibrium model
results
34
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
35
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.
with ?EElt0, four cases can be distinguished   1.
?EM lt 0 and greater in absolute value than ?EE
implies R lt 0.   2. ?EM lt 0 and equal in absolute
value to ?EE implies R 0.   3. ?EM lt 0 and
smaller in absolute value than ?EE implies 0 lt R
lt 100.   4. ?EM gt 0 implies R gt 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
36
UKENVI - industry production structure
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
Capital
Non-energy composite
Energy composite
Non-electricity
Electricity
Non-oil
Renewable
Non-renewable
Oil
Coal
Gas
37
UKENVI results
Table 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.
38
International distribution of abatement costs
Table 8.13 Costs associated with alternative
instruments for global emissions reductions
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.
Figures are for changes in GDP
39
Alternative uses of carbon tax revenue
Table 8.14 Effects of carbon taxation according
to use of revenue
Results from the ORANI CGE model for
Australia. ORANI has a government sector, and
overseas trade. S1 Carbon tax to raise A2
billion, used to reduce payroll tax S2 Carbon tax
to raise A2 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
40
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.