Transcript Accounting for the environment

Chapter 19: Accounting for the environment
19.1 Environmental indicators and state of the environment
reporting
19.2 Environmental accounting: theory
19.3 Environmental accounting: practice
19.4 Wealth and genuine saving
19.5 Sustainable development indicators
Environmental indicators and state of the environment reporting: terminology
‘Environmental indicators’/’Environmental statistics’ - biophysical data organised
around environmental issues
‘State of the environment report’ – a compilation of environmental
indicators/statistics
For the USA see Table 19.1 for EPA coverage: go to http://www.epa.gov/roe for the
EPA’s SOER
For the UK see Table 19.2 for DEFRA coverage: go to
http://www.defra.gov.uk/environment/statistics, and see also The environment in your
pocket published by DEFRA.
‘Environmental accounting’ – monetary, sometimes biophysical, data organised
around economic categories
An almost practical step toward sustainability
An almost practical step toward sustainability is the title of a lecture given in 1992 by
Robert Solow. Based on the analysis of a simple model economy with Q=KαRβ with
α+β=1 and β< α, Solow advanced two ‘key propositions’:
1.‘properly defined net national product’ ‘measures the maximum current
level of consumer satisfaction that can be sustained forever’ so it is ‘a
measure of sustainable income’
2.‘Properly defined and properly calculated, this year’s net national product
can always be regarded as this year’s interest on society’s total stock of
capital’
Putting these together gives a rule for sustainability as constant consumption
3.Maintain the total stock of capital by consuming only the interest on it
In the simple model analysed, this implies adding to the stock of reproducible capital,
K, an amount equal to the depreciation of the stock of the non-renewable resource, R.
With depreciation measured as the Hotelling rent arising in extraction this is
Hartwick’s Rule.
Two important hedges
For Hartwick’s rule to work in practice, the prices used have to be the ‘right’ ones,
ie to reflect perfect foresight, as eg with the rent evolving according to the Hotelling
Rule. According to Solow it is
Obvious that everyday market prices can make no claim to embody that
kind of foreknowledge. Least of all could the prices of natural resource
products…..The hope has to be that a careful attempt to average out
speculative movements and to correct for other the other imperfections I
listed earlier would yield adjusted prices that might serve as rough
approximations to the theoretically correct ones….The important hedge is
not to claim too much.
There is another ‘hedge’ to be examined shortly. The ‘right’ prices are those that go
with a constant consumption path. They are not those that hold along the optimal
path unless that involves constant consumption, which it will not given standard
assumptions.
A resource owner in a competitive economy 1
B is the size of the bank account, units £s
C is consumption expenditure, units £s
Bt – Bt–1 = iBt–1 + (1 + i)ht–1Rt–1 – Ct
(19.2)
Vt = ht(Xt–1 – Rt–1)
(19.3)
ht = (1 + i)ht–1
so
W is total wealth, units £s
Vt = (1 + i)(Vt–1 – ht–1Rt–1)
R is the total of permit sales, units tonnes
or
X is the size of the remaining stock of
mineral, units tonnes
Vt – Vt–1 = iVt–1 – (1 + i)ht–1Rt–1
h is the price of a permit, £s per tonne
Wt – Wt–1 = (Bt – Bt–1) + (Vt – Vt–1)
V is the value of the mine, units £s
gives
i is the interest rate, assumed constant
over time
Wt – Wt–1 = iWt–1 – Ct
(19.4)
(19.5)
Then (19.2) and (19.5) in
(19.6)
(19.8)
where Wt = Wt-1 implies
Ct = iWt–1
(19.9)
and
Ct = iW0
(19.10)
is the maximum constant consumption stream
A resource owner in a competitive economy 2
Given that PV of x forever is x/i
Ct = iW0
B is the size of the bank account, units £s
forever gives
C is consumption expenditure, units £s
W* = W0
W is total wealth, units £s
Income is
R is the total of permit sales, units tonnes
Yt = iBt–1 + (1 + i)ht–1Rt–1
X is the size of the remaining stock of
mineral, units tonnes
For Wt = Wt-1
h is the price of a permit, £s per tonne
V is the value of the mine, units £s
i is the interest rate, assumed constant
over time
(19.10)
(19.11)
(19.12)
Ct = iBt–1 + iVt–1
for which
It = Yt – Ct = iBt–1 + (1 + i)ht–1Rt–1 – iBt–1 –
iVt–1
= (1 + i)ht–1Rt–1 – iVt–1
(19.13)
which by (19.5) is
It = –(Vt – Vt–1)
which is Hartwick’s rule.
(19.14)
A resource owner in a competitive economy 3
For sustainable income as what can be consumed without reducing wealth
Ysus,t = iWt–1
(19.15)
which is Solow’s ‘properly’ measured income – the level of consumption that can be
maintained forever and the interest on wealth.
Would a resource owner choose constant consumption? It depends.
In 11.4.1 it was established that a necessary condition for maximising the discounted
sum of utilities over time, subject to consumption equal to the change in wealth, is (in
the notation used here)
Uct/Uct-1 = (1+ρ)/(1+i)
so that
ρ<i implies Uct<Uct-1 implies Ct>Ct-1
ρ=i implies Uct=Uct-1 implies Ct=Ct-1
ρ>i implies Uct>Uct-1 implies Ct<Ct-1
given the assumption of diminishing marginal utility.
Optimal and sustainable consumption paths 1
For a representative agent closed model
economy where
Qt=KαtRβt : α + β = 1 and β<α
C0t is the optimal path
CS0 is the highest feasible level of
constant
consumption at t =0
CSt is the time path under the optimal plan
Figure 19.1 Optimal and
sustainable consumption
paths
for the maximum level of constant
consumption that would thereafter be
sustainable indefinitely – at T, COT is
optimal and CST is maximum sustainable
consumption from T onwards, given that
the optimal path was followed up to T.
Optimal and sustainable consumption paths 2
At T, having followed the
optimal path, C0T is not
sustainable.
The maximum constant
consumption level from T on
would be CST.
Using the prices and quantities
from the optimal path will not
generally give correct signals
about the future level of
sustainable income.
Figure 19.1 Optimal and sustainable
consumption paths
To get the right signals it is
necessary to use the prices and
quantities that hold at T on the
path CST.
Measuring national income: theory 1
Consumption is the purpose of economic activity, so why is the National Income
measure of economic performance defined as consumption plus investment?
Because current investment contributes to future consumption.
For

 U(C )e dt
 ρt
Max
t
0
  Q(K )  C
K
St
t

U(C )  U K
t
C
t
t
is a function of current levels of the variables consumption
and investment that gives a single valued measure of
performance in terms of the objective function.
Measuring national income: theory 2

U(C )  U K
t
C
t
UC is the marginal utility of consumption. For a linear utility function so that
U(Ct) = UCCt, and using It for the change in the size of the capital stock, this is
UCCt + UCIt
a performance measure in utils. Dividing through by UC gives the
performance measure
NDPt = Ct + It
(19.17)
where NDP is Net Domestic Product, also known as NNI for Net National
Income.
From (19.17), NDPt – Ct = It so that Ct>NDPt implies It<0, which implies
Kt+1<Kt and Qt+1<Qt.
For sustainable income as the maximum that can be consumed without
reducing the size of the capital stock, NDPt is sustainable income.
Measuring national income: theory - taking account of the
environment 1
The adjustments to the measurement of national income required on account of
economy-environment interdependence are derived by considering optimal
growth models where the specification of the constraint set reflects the nature of
the interdependence.
For the model which is the basis for Fig 19.1 – production uses a costlessly
extracted non-renewable resource – the result is
EDPt = NDPt – QRtRt = NDPt – htRt
(19.18)
where EDP stands for Environmentally Adjusted Domestic Product, QRt is the
marginal product of the resource in production, Rt the amount used, and ht the
Hotelling rent.
The second term on the rhs is the depreciation of the resource stock.
With NDPt = Ct + It, (19.18) is
EDPt = Ct + It – htRt
so that for total net investment zero, It = htRt, the Hartwick Rule, consumption is
equal to sustainable income.
Measuring national income: theory – taking account of the
environment 2
For a model where the extraction of the non-renewable is costly, and new reserves
can be established at cost,
EDPt = NDPt – (QRt – GRt)(Rt – Nt) = NDPt – ht(Rt – Nt)
(19.20)
where QRt is the marginal product of the resource in production, GRt is marginal
extraction cost, and Nt is additions to the known stock.
For a model where the resource input is a renewable
EDPt = NDPt – (QRt – GRt)(Rt – F{St}) = NDPt – ht(Rt-F{St}) (19.21)
where GRt is the marginal cost of harvesting, F{St} is the stock’s growth function,
and St stock size.
For sustainable yield exploitation, Rt = F{St} and there is no depreciation –
EDPt = NDPt
Measuring national income: theory – taking account of the
environment 3
Renewable resources, such as forests, can yield amenity services direct to
consumption as well as provide inputs to production.
EDPt = NDPt + (USt/UCt)St – ht(Rt – F{St})
(19.22)
where USt is the marginal utility of standing timber and UCt is the marginal
utility of produced commodity consumption.
Typically USt is unobservable, there is no market price. Chapter 12 methods
are needed.
-------------------------------------------------------------------------------------These models are not mutually exclusive – production uses non-renewables,
renewables, flow resources. Production and consumption generate waste
flows. The environment provides amenity and life support services. A
comprehensive model needs to capture all such linkages.
Environmental accounting: practice
It is generally agreed that, leaving aside environmental considerations, the proper
measure of economic performance is Net Domestic Product, NDP, which is Gross
Domestic Product, GDP, less the depreciation of reproducible capital. In fact, GDP
is more widely used than NDP. This is, largely, because it is difficult to measure
the depreciation of reproducible capital.
Environmentally driven criticism of current accounting conventions focuses on
three issues
Natural resource depletion - should be treated in the same way as depreciation of
reproducible capital – measurement and valuation problematic
Environmental degradation – air, water and land quality reductions should be
treated as depreciation – how to measure degradation from what benchmark?
Defensive expenditure – , eg clean-up costs, on the environment should be
deducted – why not other defensive expenditure?
The UNSTAT proposals: satellite accounting 1
System of integrated Environmental and Economic Accounting, SEEA
Balance Sheets and Satellite Accounts
EC   a v   a v
n
t
i 1
n
it
it
i 1
it  1
it  1
(19.23)
Environmental Cost is the change in the balance sheet value,
i.e. depreciation, of all environmental assets, natural capital.
Environmentally Adjusted NDP could be defined as
EDPt ≡ NDPt – ECt ≡ (GDPt – DMt) – DNt
where DNt ≡ ECt
(19.24)
The UNSTAT proposals: satellite accounting 2
SEEA does not envisage national statistical agencies reporting EDP instead of
GNP/NDP.
SEEA does envisage complementing the current GDP/NDP accounts with balance
sheets for natural capital – Satellite Accounts.
Some counties do this already for a limited range of environmental assets – some
of those commercially exploited – eg fossil fuels, minerals, timber. Even in these
cases, measurement of depreciation is problematic, mainly on account of
difficulties with unit valuation.
SEEA does not envisage treating defensive expenditures as part of EC. It does
recommend identifying and reporting environmental defensive expenditures
within the accounting system.
The depreciation of non-renewable resources
The correct measure of the depreciation of a stock of a non-renewable resource is
D = THR = (P – c)(R – N)
(19.25)
where
D is depreciation
THR is total Hotelling rent
P is the price of the extracted resource
c is the marginal cost of extraction
R is the amount extracted
N is new discoveries
In a fully competitive economy would have:
THR = CIV
with CIV for Change in (market) value of the resource stock.
Generally, CIV is not observable. Nor is marginal cost, c.
Methods used for measuring the depreciation of nonrenewable resources
Net Price II
D = (P – C)(R – N)
(19.26)
C for average cost, c>C
Net Price I
D = (P – C)R
Change in Net Present Value
T
T
t
t

D   [(Pt C t )R t /(1 r) ] [(Pt C t )R t /(1 r) ]
0
1
t 0
t 1
Given C rather than c, an estimate of CIV.
El Serafy’s (user cost) rule
D = R(P – C)/(1+r)T
(19.28)
In (19.27) and (19.28), r is the interest rate, and T is deposit lifetime
(19.27)
Measuring non-renewable depreciation - applying four
methods to the same data
Table 19.3 Alternative estimates of minerals depreciation for
Australia 1988/9 to 1991/2, ASS$ x 106
Year
El Serafy rule
Net price I
Net price II
ABS NPV
change
1988/89
952
8511
1989/90
1228
9872
–19321
– 6500
1990/91
1922
12023
–147035
–19900
1991/92
2328
13624
299075
–9700
Total of depreciations calculated for 33 minerals, using data
from ABS (1995). r = 7.5%.
UK asset values
Table 19.4 UK asset values 1999 - 2007
£billion end year
Oil
Gas
Oil+Gas
Non-financial
Assets
Residential
Buildings
1999
46.964
30.495
77.459
3877.5
1848.9
2000
53.611
43.011
96.622
4245.1
2106.5
2001
51.812
50.451
102.263
4484.8
2267.8
2002
50.883
46.566
97.449
5076.8
2737.1
2003
53.045
44.250
97.295
5522.2
3054.9
2004
78.536
50.754
129.29
6069.0
3427.0
2005
100.192
65.402
165.594
6283.0
3555.0
2006
120.921
69.439
190.36
6863.1
3915.3
2007
177.891
68.340
246.231
7380.0
4313.6
Source: Office of National Statistics 2008a
2007 - oil and gas less than 5% of Non-financial Assets, less than 10% of Residential
Buildings
Oil and gas deprecation in the UK
10000
0
-10000
-20000
-30000
-40000
oil
gas
total
-50000
-60000
-70000
Figure 19.2 Oil and gas depreciation
for the UK 2000-2007
Derived from data on year end asset
value – ONS 2008a
Australian asset values
Table 19.5 Australian asset values 2002 - 2006
$billion 30th June
2002
2003
2004
2005
2006
4004
4435.9
5014.8
5391.4
5876.7
2150.0
2291.5
2482.5
2702.1
2932.9
346.9
352.3
361.2
382.6
409.3
812.4
892.5
991.6
1086.2
1172.1
1854.7
2144.3
2532.3
2689.3
2943.8
Land
1639.8
1920.4
2284.0
2417.7
2633.3
Subsoil
204.9
213.6
237.2
260.2
298.8
1.9
2.0
2.1
2.2
2.2
Total NFA
Produced
Machinery and
equipment
Dwellings
Non-produced
Forest
Source: ABS 2008.
NFA – non-financial assets
Subsoil – all economically significant non-renewable and mineral
resources, valued using the present value method – about 5% of
NFA, less than Machinery and equipment, Dwellings
Forests are native forests, plantations get counted as produced
assets. Both valued at commercial value of standing wood.
Environmentally adjusted national income - Indonesia
Year
EDP
Index
1
EDP/GDP
1971
GDP
Index
1
1972
1.09
0.90
0.99
1973
1.22
0.97
0.96
1974
1.32
1.48
1.36
1975
1.38
0.98
0.85
1976
1.47
1.12
0.92
1977
1.60
1.08
0.81
1978
1.73
1.19
0.78
1979
1.83
1.19
0.78
1980
2.01
1.28
0.76
1981
2.17
1.48
0.82
1982
2.22
1.58
0.86
1983
2.32
1.49
0.78
1984
2.44
1.68
0.83
1.20
Source: Based on Repetto et al (1989)
The first attempt to do this? By the
World Resources Institute, using their
estimates with official GDP estimates.
Depreciation for:
Oil – Net Price II
Timber – Net Price II allowing for
growth
Soil – physical loss valued using loss of
agricultural output
The results are dominated by changes in
the price of oil, and new discoveries of
oil – EDP rose by 51% 1973 to 1974
Environmentally adjusted national income - UK
Table 19.7 UK GDP, NDP and NDP adjusted for oil and gas depreciation
2001
2002
2003
2004
2005
2006
2007
GDP
1021828
1075564
1139746
1200595
1252505
1321860
1401042
-FCC
115796
121914
125603
135184
138520
147858
158143
=NDP
906032
953650
1014143
1065411
1113985
1174002
1242899
-5641
4814
154
-31995
-36304
-24766
-55871
911673
948836
1013989
1097406
1150289
1198768
1298770
GDP growth
5.3%
6.0%
5.3%
4.3%
5.5%
6.0%
NDP growth
5.3%
6.3%
5.1%
4.6%
5.4%
5.9%
EDP growth
4.1%
6.9%
8.2%
4.8%
4.2%
8.3%
-DEPCTN
=EDP
Source: derived from ONS 2008b.
FCC – Fixed Capital Consumption, depreciation of reproducible capital
DEPCTN – end year to end year balance sheet changes for Oil+Gas
These are current value figures – no adjustment for inflation
Environmentally adjusted national income - Australia
Table 19.8 Australian GDP, NDP and NDP
after net depletion adjustment
2001/2
2002/3
2003/4
2004/5
2005/6
GDP
735714
781675
840285
896568
965969
-FCC
115259
121526
127754
134523
145476
=NDP
620455
660149
712531
762045
820493
-ADJSTMNT
1317
865
894
87
234
=EDP
619138
659284
711637
761958
820259
While the Australian statistical agency,
ABS, does not adjust the national income
estimates in its main publications, it did
do that in Year Book Australia 2008.
Units are millions of current AUS$.
FCC – Fixed Capital Consumption
ADJSTMNT – the ‘net depletion
adjustment’ which is
Growth rates
GDP
6.7%
6.2%
7.5%
6.7%
7.7%
NDP
6.6%
6.4%
7.9%
6.9%
7.7%
EDP
6.5%
6.5%
7.9%
7.1%
7.7%
5.0%
5.6%
6.0%
6.3%
subsoil (fossil fuels and
minerals) extraction
plus
GDP pc
land degradation
less
Source: ABS 2008.
subsoil additions
Wealth and genuine saving 1
EDPt = Ct + IRt + DNt
(19.29)
So
EDPt > Ct for (IRt + DNt) > 0
EDPt = Ct for (IRt + DNt) = 0
EDPt < Ct for (IRt + DNt) < 0
so that maximum consumption consistent with not running down the capital
stock is Ct = EDPt, so that EDPt is sustainable income
Sustainable development requires
Ct ≤ EDPt
(19.30)
Ct = EDPt implies that IRt and DNt are equal and of opposite sign so that (IRt +
DNt) = 0.
Wealth and genuine saving 2
With KRt for reproducible capital and KNt for natural capital we can write
Wt = KRt + KNt
(19.31)
where W stands for wealth as the aggregate capital stock. For Wt+1 we can write
Wt+1 = (KRt + IRt) + (KNt + DNt)
so that
Wt+1 - Wt = IRt + DNt
which by equation 19.29 is
Wt+1 - Wt = EDPt - Ct
(19.32)
so that Wt+1 - Wt ≥ 0 if Ct ≤ EDPt.
Hence,
Wt+1 - Wt ≥ 0
(19.33)
is equivalent to the expression 19.30 as a test for sustainable development. Wt+1 - Wt
is what is now widely known as 'genuine saving' or 'genuine investment' for period t.
Theory for an imperfect economy 1
The earlier theory supporting EDP as the proper measure of national income was
derived for an optimising economy. Dasgupta (2001),for example, argues that nonnegative genuine saving/investment is a test for sustainable development that does not
require the optimising assumption.
For constant population, social well-being at is

V   U (C )e

t
  ( t )
t
t
dt
(19.35)
A consumption stream beginning at t = 0 is said to to correspond to a sustainable
development path if at t
dV
0
dt
t
Vt+1 ≥ Vt, see Appendix 19.3, is equivalent to
N
I p
G
t
I
i 1
G
t
Is
Genuine
saving
dA
 0
dt
it
it
(19.36)
where
dA
dt
it
Is
Change
in asset i
and pit is the accounting price for
asset i
Theory for an imperfect economy 2
The accounting price for asset i is the change in Vt consequent on an
infinitesimally small change in the size of i at t, other things equal.
Accounting prices depend upon four related factors:
(a) the conception of social well-being,
(b) the size and composition of existing stocks of assets,
(c) production and substitution possibilities among goods and services, and
(d) the way resources are allocated in the economy. ( Dasgupta 2001 p 123)
The price of getting away from results based on the assumption of optimisation
is the assumption that the accountant can forecast all of the utility
consequences of small perturbations in all relevant asset stock sizes through
to the distant future.
And, no differences in the conception of social well-being?
Problems with genuine saving as a sustainability test 1
Clearly, no accountant could could have the information for a comprehensive
measure of genuine saving.
The implicit claim must be that aggregating over a wider range of assets
using estimates of accounting prices will produce a better guide to policy
than looking just at investment in reproducible capital.
While plausible, this is not generally true – looking at an extended but
incomplete range of assets may produce a result further from the truth.
Genuine savings/investment results need to be treated with caution as tests
for sustainable development and guides to policy.
Problems with genuine saving as a sustainability test 2
Table 19.9 Numerical example for incomplete genuine saving accounting
Time
KR
K1N
K1S
K1H
K0N
K0S
K0H
W
0
100
1000
100
100
500
100
100
2000
1
102
950
101
101
550
110
120
2034
Change
2
-50
1
1
50
10
20
34
KR
KeN
KeS
KeH
We
0
100
1100
50
50
1300
1
102
1000
51
51
1204
Change
2
-100
1
1
-96
Actual genuine saving is 34
Looking just at reproducible capital says 2
Measured genuine saving is –96 - opposite sign to actual.
World Bank estimates of genuine saving
In World Bank (2006), for each country
Genuine saving = Gross Saving (GNI less private and public consumption, plus foreign transfers)
- Depreciation of reproducible capital (replacement value)
+ Educational expenses (public sector operating expenses)
- Depletion of natural resources (energy, minerals and forest depletion using Net
Price I)
- Pollution damages (CO2 damages at $20 per tonne carbon emission)
It is noted that ‘we should be cautious in interpreting a positive genuine saving rate’
as ‘There are some important assets omitted from the analysis’. A negative genuine
saving rate should also be interpreted cautiously.
World Bank - Genuine saving and income
%
25
20
Vertical axis is % of GNI
15
Low
10
Middle
High
5
0
-5
1970 1975
1985
1995
Figure 19.3 Genuine saving by
income group
2004
World Bank - Genuine saving in world regions
%
30
Vertical axis is % of GNI
20
For the world, genuine saving is
around 10% over 1974-2004
World
10
Middle East and
Africa
0
East Asia
-10
-20
-30
1974
1980
1990
2004
Figure 19.4 Genuine saving for
selected regions and the world
Middle East and Africa strongly
influenced by oil and gas
extraction, and price changes for
such. Results here consistent with
rents being consumed, rather than
invested in reproducible capital.
World Bank – total wealth and its components
Table 19.11 Asset values for income groups and the world, $ per capita
Income
group
Produced
capital
Natural capital
Subsoil
Timber
NTFR
Cropland
Pastureland
Protected
areas
Total
Low
1174
325
109
48
1143
189
111
1925
Middle
5347
1089
169
120
1583
407
129
3496
High OECD
76193
3825
747
183
2008
1552
1215
9531
World
16850
1302
252
104
1496
536
322
4011
Source: World Bank 2006
Per capita asset values increase with income
Ratio of produced to natural capital value increases with income
Share of natural capital as agricultural land decreases with income
Share of subsoil assets in natural capital increases with income
Accounting for international trade 1
Consider 2 trading economies, 1 and 2. Let x12 be exports from 1 to 2, and x21 be exports from 2
to 1. Let y represent total output, and f represent final demand, comprising c for consumption and
s for saving/investment. We can then write:
y1 = x12 + c1 + s1 = x12 + f1
(19.37)
y2 = x21 + c2 + s2 = x21 + f2
If we define coefficients q12 = x12/y2 and q21 = x21/y1, equations 19.37 can be written as
y1 = 0 + q12y2 + f1
y2 = q21y1 + 0 + f2
which in matrix notation, using upper case letters for matrices and lower case for column vectors,
is
y = Qy + f
with the solution
y = (I - Q)-1 f = Lf
where I is the identity matrix.
(19.38)
Now, let
Accounting for international trade 2
D1 = DM1 + DN1 = dm1y1 + dn1y1 = z1y1
D2 = DM2 + DN2 = dm2y2 + dn2y2 = z2y2
where M and m subscripts refer to human made capital and N and n subscripts refer to natural capital, so that we can write
for total global depreciation
D = z1y1 + z2y2
or, in matrix notation
D = z’y
(19.39)
where z’ is [z1 z2]. Substituting for y in Equation 19.39 from Equation 19.38 gives
D = z’Lf
or
T = ZLF
(19.40)
where Z and F are matrices with the elements of z and f along the diagonals, and zeroes elsewhere. For the two country case,
Equation 19.40 is:
t 11 t 12  z 1 l 11 f1 z 1 l 12 f 2 
t t   z l f z l f 
 21 22   2 21 1 2 22 2 
Accounting for international trade 3
T = ZLF
where Z and F are matrices with the elements of z and f along the
diagonals, and zeroes elsewhere. For the two country case
 t t  z l f z l f 
 t t   z l f z l f 

 

11
12
1 11
21
22
2
21
1
1
1 12
2
22
2
2
In the matrix T the row elements give depreciation in a country arising by virtue of final demand
in that and other countries, while column elements give depreciation in all countries by virtue of
final demand in one country. So, row sums, DiIN , give depreciation in i, and column sums, DiATT,
give depreciation attributable to i. Thus, in the two-country case here t11 + t12 is the depreciation
of total capital actually taking place in country 1, while t11 + t21 is the depreciation of capital in
the global economy that is on account of, attributable to, final demand in country 1.
Accounting for international trade 4
A slight extension of the method of Proops and Atkinson allows for consideration of these issues
on a per capita basis. Let P be the matrix with the reciprocals of population sizes along the
diagonal and zeroes elsewhere. Then, for the two-country case,
A = TP = ZLFP
(19.41)
is
a 11 a 12  z1 l 11 (f1 / p 1 ) z1 l 12 (f 2 / p 2 )
a a   z l (f / p ) z l (f / p 
 21 22   2 21 1 1 2 22 2 2 
so that column sums from A, diATT, give depreciation in all countries attributable to per capita
final demand in country i. And,
B = PT = PZLF
(19.42)
is
b 11 b 12  (z1 / p 1 )l 11 f1 (z1 / p 1 )l 12 f 2 
b b   (z / p )l f (z / p )l f 
 21 22   2 2 21 1 2 2 22 2 
so that row sums from B, diIN, give per capita depreciation in country i on account of global final
demand. These depreciation measures can be compared with si, per capita saving in i.
Per capita saving and depreciation by region
Some entries from Table 19.11 Excesses of per capita saving over depreciation – difference
from global excess
(si-diIN) - (s-d)
US$
In natural capital only nonrenewables
accounted for here.
1980
1982
1984
1986
1988
W.Europe
570
341
344
522
764
USA
153
-200
38
-429
-401
Africa
-102
-68
-113
-140
-238
Middle East
-578
853
-1024
-1135
-978
Looking at things on the attributable
basis does not much alter the general
picture
s-d
173
76
106
109
220
Africa’s contribution always negative
For the world as a whole, genuine
saving positive
Mid East usually negative
(si-diATT) -(s-d)
US$
1980
1982
1984
1986
1988
W.Europe
440
249
306
528
754
USA
48
-271
-141
-613
579
Africa
-102
-79
-119
-146
-246
Middle East
238
-273
-708
-950
-779
Takes no account of ability to save –
income levels.
Sustainable development indicators 1
Sustainable development indicators – efforts by official agencies, and others, to
provide data on the natural environment and the economy relevant to sustainable
development, other than via modified national income or wealth accounting.
1994 – UK government adopted strategy for sustainable development
1996 – began publication of indicators to monitor progress
Sustainable development indicators in your pocket (DEFRA) is organised around
four ‘priority areas’ ( see also DEFRA website )
Sustainable consumption and production
Climate change and energy
Protecting natural resources and enhancing the environment
Creating sustainable communities and a fairer world
Aggregation to produce a single ‘bottom-line’ indicator is explicitly rejected –
it is not practicable or meaningful to combine all 126 disparate indicator measures
into a single index of sustainable development. Aside from the technical difficulties
involved, some indicator measures are more important than others and key messages
would be lost (DEFRA 2008b)
Sustainable development indicators 2 – ISEW/GPI
ISEW – Index of sustainable economic welfare
GPI – Genuine progress indicator
Daly and Cobb 1989 version
ISEW  {(C/D) + (E + F+ G + H)– (I + J + K + L + M + N + O + P + Q
+ R + S + T + U) + (V + W)}/Pop
C is personal consumption expenditure
D is an index of distributional inequality
E is an imputed value for extra-market labour services
F is an estimate of the flow of services from consumer durables
G is an estimate of the value of streets and highway services
H is an estimate of the value of publicly provided health and education services
I is expenditure on consumer durables
J is an estimate of private defensive spending on health and education
K is expenditure on advertising at the national level
L is an estimate of commuting cost
M is an estimate of the costs of urbanisation
N is an estimate of the costs of automobile accidents
O is an estimate of water pollution costs
P is an estimate of air pollution costs
Q is an estimate of noise pollution costs
R is an estimate of the costs of wetlands loss
S is an estimate of the costs of farmland loss
T is an estimate of the cost of non-renewable-resource depletion
U is an estimate of the cost of long-term environmental damage
V is an estimate of net additions to the stock of reproducible capital
W is the change in net overseas indebtedness
(19.43)
GDP and GPI compared
Despite differences in the adjustments
GDPpc made to personal consumption across
ISEW/GPI exercises, results generally
similar:
40000
35000
30000
25000
20000
15000
GPIpc
10000
5000
0
1950
1974
2004
Figure 19.5 GPI per capita and GDP per
capita for the USA 1950-2004
Source: Talberth et al 2007
For every society there seems to be a period in
which economic growth brings about an
improvement in the quality of life, but only up
to a point – the threshold point – beyond which
if there is more economic growth, quality of life
may begin to deteriorate. (Max-Neef 1995)
Sensitivity analysis (Neumayer 2000)
suggests that if here is a threshold, it is not
due to movements in the environmental
components of the index.
Results do appear to be sensitive to
assumptions about unpaid labour.
The economy and the environment again: what the economy
does
Environment
Extractions
Insertions
Economy
Satisfactions
Figure 19.6 What the economy does
The economy extracts materials and
energy from the environment, using them
along with capital and labour to produce
the means to the satisfaction of human
needs and wants, and inserts back into the
environment an equal mass of waste
(Chapter 2)
Common (2007a) suggests that a natural
measure of economic performance would
be
E = S/I
with
E for efficiency
S for satisfaction
I for (environmental) input
Aggregation without prices
E = S/I
For S use
HLY = H x LY
where HLY is Happy Lifetime Years
H is the average score for self-assessed happiness/satisfaction (Chapter 3)
LY average life expectancy at birth
For I there is no uniquely correct measure. Use as proxies
Energy use – a measure of work done, which is what impacts on the
environment
Ecological footprint – the area of land and water to provide environmental
inputs and absorb wastes
Greenhouse gas emissions – the source of the major environmental problem
now facing the world
Performance converting environmental impact into
satisfaction
Table 19.15 Highest and lowest E scores
ECE
ETE
EF
EG1
EG2
Country
HLY
per toe1
Country
HLY
per toe1
Country
HLY
per ha
Country
HLY
per ton Carbon2
Country
HLY
per ton Carbon2
Bangladesh
336.00
Bangladesh
181.44
Bangladesh
56.00
Uruguay
501.00
Jordan
512.86
Senegal
104.33
Morocco
91.20
Vietnam
54.00
Bangladesh
168.00
Albania
113.00
Morocco
95.00
Philippines
64.77
Peru
45.89
Vietnam
144.00
Bangladesh
112.00
Honduras
94.2
Albania
62.85
India
42.63
Albania
84.75
Vietnam
108.00
Philippines
88.60
Peru
62.28
Morocco
42.22
El Salvador
71.86
El Salvador
100.60
Canada
7.41
USA
6.87
Latvia
7.55
Canada
9.23
Australia
8.81
USA
7.14
S Africa
6.77
Ukraine
7.48
Australia
8.69
USA
8.78
Luxembourg
7.00
Russia
6.68
Russia
6.43
Russia
7.65
Ukraine
8.52
Russia
6.74
Ivory Coast
6.04
USA
6.01
Estonia
7.35
Estonia
8.18
Iceland
5.39
Tanzania
3.50
Estonia
5.22
Zimbabwe
7.18
Russia
7.86
ECE – commercial energy. ETE – total energy. EF – ecological footprint.
EG1 – greenhouse gas emissions including land use changes
EG2 – greenhouse gas emissions excluding land use changes
1 toe for tonnes oil equivalent. 2 all ghgs converted to heating equivalent CO 2
Efficiency based sustainable development indicators
1. Each nation’s ghg emission allowance to be its population size multiplied by an
equal per capita share of the set global emissions total. For the ith nation
GHG  sP
*
i
i
where
GHG
s
P
*
Country i experienced sustainable development if
Ei,t+1>Ei,t and GHGi,t≤GHG*i and GHGi,t+1 ≤GHG*i.
If, that is, E increased and emissions stayed within equitable
allowance.
2. For F*i as a nation’s share of the world’s available productive
land and water(per capita share of global times population size),
country i experienced sustainable development if
Ei,t+1>Ei,t and Fit ≤F*i and Fi,t+1 ≤F*i
If, that is, E increased and footprint stayed within equitable
allowance.