. 7
( 11)


Product (™000 m ) % of total (from felling) (years from felling) (™000 m ) % of total (from felling) (years from felling)
Sawn logs 2,925 49.292 70 150 558 49.512 150 300
Board 1,154 19.447 15 401 87 7.720 15 40
Paper 936 15.774 1 5 138 12.245 1 5
Mining 23 0.004 40 200 40 200
<1 <0.001
Fuel2 142 2.393 1 5 114 10.115 1 5
Other2 142 2.393 15 30 114 10.115 40 80
Bark 612 10.313 1 5 116 10.292 1 5
Total 5,934 100.000 ” ” 1,127 100.000 ” ”

Notes: 1 Based on this being almost exclusively particleboard as per statistics given in Forestry Commission (1992).
Based on assumption that roughly 50 per cent of ˜Other Industrial Wood™ (FICGB, 1992) is fuel-wood, as per statistics given in Forestry
Commission (1992).
Sources: Carbon liberation dates from Cannell and Cape (1991) and Thompson and Matthews (1989a,b). Production data from FICGB
(1992) and Forestry Commission (1992); Adrian Whiteman, pers. comm., 1993.
194 Applied Environmental Economics

5 per cent) is held as soil organisms (Jenkinson, 1988). On uncultivated soils a
number of natural factors in¬‚uence soil carbon content. These include soil tex-
ture, moisture, temperature and the lignin content of the natural plant cover (Parton
et al., 1987). In lowland areas the quantity and type of organic material returned
to the soil as dead plant tissue is, in the long run, balanced by the decomposition
of SOM and release of CO2 and water (Jenkinson, 1988). Such soils are therefore
in carbon balance. However, soils which are poorly drained and frequently water-
logged (typically in upland areas) exhibit very slow decomposition rates.17 Where
organic deposition exceeds decomposition, peat is formed (Askew et al., 1985).
Such soils have no predetermined upper limit for SOM levels (although average
levels can be calculated) and consequently may have very high carbon contents
(Adger et al., 1992).
On cultivated soils a variety of additional factors may in¬‚uence soil carbon
levels, including tillage regime, crop selection, addition of fertiliser and organic
matter, irrigation and residue treatments18 (Parton et al., 1987). The transition from
uncultivated to intensive arable land, particularly where bare fallow rotation systems
are used, is commonly associated with very signi¬cant losses in SOM (Klimowicz
and Uziak, 2001). The majority of a soil™s carbon is held near the surface and
repeated tillage exposes the SOM to the atmosphere, increasing decomposition
rates signi¬cantly above natural levels (Jenkinson, 1988). Tiessen et al. (1982)
reports a 35 per cent fall in carbon levels over a seventy-year period as a result of
switching grassland into cropping.19 Jenkinson (1988) reports a similar loss over
roughly thirty years for an area of old established grassland switched into various
arable crops, the loss being greatest where land was regularly ploughed with no
crop cover being sown.
The growth of intensive agriculture world-wide during the twentieth century has
led to massive depletions in soil carbon levels.20 These depletions have provided a
major source of global CO2 emissions (Bridges and Batjes, 1996) which is ˜second
only to fossil fuel combustion in contributing to historical increases of global carbon
dioxide concentrations™ (Post et al., 1990).

Afforestation and soil carbon
The potential for forest soils to store carbon is well known (Kaiser et al., 2001;
Neff and Asner, 2001; Rasse et al., 2001); indeed, the majority of a forest™s stored

17 Harrison et al. (1995) report a strong negative relation between soil moisture de¬cit and carbon content. See
also Edwards (1975).
18 For example, whether or not stubble is burned.
19 Clay and silt loam soils. Use of leguminous crops reduced losses from 35 per cent to 18 per cent (Tiessen
et al., 1982).
20 Although there is evidence that cultivated soils may outperform forests in consumption of carbon monoxide
(King, 2000).
Modelling and valuing carbon sequestration 195

carbon is held in its soils rather than its vegetation (Brown, 1998; UNDP et al.,
2000). However, until recently, relatively little work had been done on the long-
term effects of afforestation upon soil carbon levels in the UK. An important early
exception was provided by the work of Jenkinson (1971, 1988) who examined two
areas which had been arable for many years before being abandoned and allowed
to revert to woodland for some eighty years. This natural afforestation resulted in
very considerable increases in soil carbon.
R. Matthews (1993), in his model of Sitka spruce forest carbon budgets, combines
the work of Jenkinson with that of Whitehead et al. (1975) and Wilson (1991)
in formulating his soil carbon ¬‚ux predictions.21 Here soil is assumed to have
previously been under intensive cropping resulting in an initial, pre-afforestation,
soil carbon content of 30 tC/ha. This is assumed to rise to approximately 70 tC/ha
some 200 years after planting and reach a subsequent maximum of 100 tC/ha.
Similar results are reported by Sampson (1992) in a study of two US sites which
exhibit long-term soil carbon equilibrium increases of about 50 tC/ha arising from
In a study using similar soil and management conditions, Dewar and Cannell
(1992) report soil carbon storage curves for hardwoods which are similar to those
of R. Matthews (1993) suggesting that there is not a particularly signi¬cant species
effect here. More recent research provides some, although mixed, evidence on
whether or not different tree species induce different rates of soil carbon storage
(Priha et al., 2001). Given this uncertainty, we do not differentiate between species
in this respect. However, other factors can have very substantial impacts upon soil
carbon ¬‚ux.
The major determinants of soil carbon change under afforestation are soil type and
prior usage, from which we can estimate present carbon levels and predict long-term
equilibrium levels under afforestation.22 Adger et al. (1992) report equilibrium soil
carbon levels for a variety of soils and land uses. This work was combined with in-
formation gathered in conversations with Professor David Jenkinson (Rothamsted),
Dr Robert Sheil (University of Newcastle upon Tyne) and Professor Steven
McGrath (Rothamsted), to whom we are grateful, to produce estimates of the full

21 A further assumption, that clear felling will not reduce soil carbon providing replanting occurs within one year,
is also made by R. Matthews (1993) with reference to the work of Edwards and Ross-Todd (1983). However,
recent work by Harrison et al. (1995) suggests that SOM may decline during the ¬rst ¬fteen years following
replanting after which it begins to rise again slowly, taking anything up to sixty years to return to equilibrium.
See also Adger and Brown (1994).
22 The SSLRC LandIS system provides the best source of soil type data for England and Wales. Land cover data
may be obtained from the ITE/NERC database. Furthermore, 5 km soil property, nutrient and elements maps
are provided in McGrath and Loveland (1992) although the data supporting these maps were not available for
this study. Alternative approaches include use of the CORINE land cover database (European Union, 1992) as
employed by Cruikshank et al. (1995). Milne and Brown (1997) use the ITE land cover data to produce 1 km
resolution maps of carbon storage in vegetation and soils for the whole of Great Britain. Our own work examines
potential changes rather than current storage levels.
196 Applied Environmental Economics

Table 7.3. Post-afforestation changes in equilibrium soil carbon storage levels for
various soils previously under grass (tC/ha): upland and lowland sites1

Upland sites Lowland sites
Soil type Under grass Under trees Change Under grass Under trees Change
Peat 1,200 450 (750) n/a n/a n/a
Humic gley 180“400 250“450 50“70 180“350 180“450 0“100
Podzol 200“400 250“450 50 100“200 100“450 0“250
Brown earths n/a n/a n/a 100“120 100“250 0“130
Humic stagno 180“400 250“450 50“70 120“350 120“450 0“100
Stagnogley 170“400 170“450 0“50 100“120 100“450 0“330

Notes: 1 Use prior to afforestation is assumed to be long-established agricultural pasture
(dairy, cattle or sheep).
n/a = not applicable; soil type not common at this altitude.
Brackets indicate negative amounts.
Source: See text.

range of changes which could occur through afforestation of various soil types. This
analysis was extended to consider both lowland and upland areas which, because of
varying rainfall and land use, may exhibit signi¬cantly different rates of soil carbon
accumulation. Table 7.3 presents results from this analysis.
Inspection of Table 7.3 shows that afforestation is generally synonymous with
long-term increases in soil carbon storage levels and that these increases are liable
to be somewhat larger in lowland sites because of the prevalence of more intensive
prior agricultural land uses.23 The one clear exception to this trend arises where
planting occurs on previously unplanted peat soils. Here the extremely high prior
levels of soil carbon are substantially reduced by the planting and tree growth
processes (Cannell et al., 1993; Davidson and Grieve, 1995; Harrison et al., 1995).24
Although UK forests are at present net absorbers of atmospheric carbon,25 in an
analysis of the carbon dynamics of land use in Great Britain during the period
1947“80, Adger et al. (1992) calculate that the planting of coniferous trees on
peatlands, combined with the widespread substitution elsewhere of old-growth

23 Feedback links between global warming and changes in forest soil carbon sequestration are investigated by
Dalias et al. (2001).
24 Cannell et al. (1993) examine the direct carbon ¬‚ux impact of planting on peatbogs and suggest that there is
a threshold depth of disturbance or ploughing of peat above which the net impact of afforestation is increased
emission over one rotation, but below which there was net sequestration of carbon (although this study, like
our own, ignores the effect upon other greenhouse gases such as methane). Updegraff et al. (2001) examine
the relationship between changes in temperature and water table and emission of carbon dioxide and methane
from peatlands. See also Steinkamp et al. (2001).
25 Cannell and Dewar (1995) estimate current sequestration due to the total UK forest estate at 2.5 million tC per
annum. Adger and Subak (1996) provide estimates for agricultural land.
Modelling and valuing carbon sequestration 197

broadleaf forest, with high carbon storage, by new conifer plantations, has resulted
in the forestry sector being a net contributor to carbon emissions, a result which
reinforces the need to incorporate soil carbon ¬‚ux within our analysis.
Given the impact of discounting upon our subsequent valuations of carbon ¬‚ows,
the shape of the soil carbon ¬‚ux function is clearly important. The general con-
sensus is that marginal soil carbon ¬‚ux is relatively high in the years following
initial planting and declines smoothly to reach equilibrium over some extended
period (Cannell and Milne, 1995a,b). Robert Shiel (pers. comm., 1994) suggests
that roughly 95 per cent of the net change in soil carbon will occur within 200 years
of planting. Both R. Matthews (1993) and Dewar and Cannell (1992) illustrate to-
tal soil carbon storage curves which have negative exponential shapes. Combining
these pieces of information allows us to model both total and marginal soil carbon
storage curves.

Functional relationships are estimated for our three model elements:
(i) carbon storage in live wood
(ii) carbon emission from thinnings and wood products
(iii) carbon storage or release (as appropriate) from afforested soils.
Functions for both Sitka spruce and beech were estimated on a per hectare per
annum basis.
A number of factors were relevant to selecting the period for the analysis. These
were the long time periods involved in these various functions (e.g. rotations of
more than 100 years); the overlapping of functions (e.g. the wood product liberation
curve from an initial rotation will not have run to zero before the second rotation is
felled and a second such curve commences); and the impact of discounting (e.g. low
discount rates will produce signi¬cant non-zero discount factors far into the future).
In the light of these factors, it was decided that the analysis should be extended to
cover a 1,000-year time period with replanting assumed to follow within a year of
felling throughout this period. This allows the calculation of equilibrium carbon
¬‚ux effects (although the subsequent process of discounting exponentially favours
short-term impacts).
Once functions have been estimated we can readily calculate the per hectare net
carbon storage (or emissions) for a selected species in any given year as follows:
(i) The carbon storage function for live trees of a given species and yield class is taken and
run from planting to felling date (F). This function is restarted after each F to simulate
(ii) Emissions from thinnings and products deriving from prior rotations are summed and
subtracted from (i). Note that the emissions functions from any given rotation will
198 Applied Environmental Economics

extend beyond the lifespan of the next rotation, i.e., such functions overlap such that in
any given year there may be emissions from more than one previous rotation. However,
there are no emissions prior to ¬rst thinning of the initial rotation;26
(iii) The net soil carbon ¬‚ux function is applied from the date of ¬rst planting. Predicted
sequestration (or emission) is added (subtracted) from the sum of (i) and (ii) to yield
the marginal net annual change in carbon storage.

The above calculations are performed for each year in our 1,000-year analysis.
The process is then repeated using the other YCs considered in stage (i) above.
Finally the entire calculation is repeated using functions for the other species under
Valuation of the marginal net annual change in carbon storage is achieved by
reference to the relevant unit values for each year given in Fankhauser (1994b) as
discussed previously. We thereby derive a stream of marginal carbon storage values
for each species, and within each YC, under consideration. These are undiscounted
values to which any desired discount rate may be applied to calculate net present
value or annuity equivalents as required.
As a ¬nal step we use our GIS to apply these various valuations to the maps of
predicted YC for the two species under consideration presented in Chapter 6. In so
doing we produce maps of live wood carbon storage value. The GIS is also used
to relate our soil carbon values to the LandIS soil type data layer and produce a
map of soil carbon ¬‚ux values.27 By superimposing these maps and adding their
values we obtain a joint live wood and soil carbon sequestration value map. Finally,
by subtracting the thinnings and wood product emissions levels for the relevant
species, we obtain a map of the overall net carbon ¬‚ux value for a given species for
all locations in our case study area. Such a map allows us to readily identify those
areas which, if afforested, would yield optimal carbon storage values.28

Modelling carbon storage in trees
Carbon storage in Sitka spruce live wood
As discussed previously, carbon sequestration in an unthinned standing crop follows
an approximately S-shaped time trend. Figure 7.1 showed that in thinned crops the
total carbon storage curve is non-linear, following the unthinned S-shaped growth
curve up to TD1 after which a signi¬cantly shallower path is followed until the
rotation ends at F (as the majority of UK plantations are subject to thinning we
shall concentrate upon such stands for the remainder of this analysis). However,
as we showed in Chapter 5, within each species both TD1 and F can be shown to
26 Note that we ignore emissions from vehicles and machinery involved in planting and felling.
27 Skidmore et al. (1991) use an expert systems approach to map forest soils from a GIS.
28 Cieszewski et al. (1996) provide an analysis of error propagation within carbon ¬‚ux assessments.
Modelling and valuing carbon sequestration 199

be functions of yield class and discount rate.29 Carbon storage modelling therefore
needs to re¬‚ect this complex interaction of diverse factors.
While a simple approach to this problem would be to use long-term equilibrium
storage levels (such as those reported by Dewar and Cannell, 1992), this would
ignore the low levels of carbon storage occurring in the early years after initial
planting. Given that we wish to discount storage values, this overstatement of early
sequestration could result in a substantial upward bias in bene¬t estimates. A supe-
rior approach is suggested by Pearce (1991, 1994) who, in the ¬rst major UK study
of this issue, adopts a negative exponential total carbon storage function. While
clearly better than a simple average, this approach still results in some overstate-
ment of early storage rates as the marginal storage curve implied by the differential
of a negative exponential shows annual net storage being highest during the initial
planting year and declining thereafter.
To avoid these problems we start the modelling process by explicitly considering
the S-shaped curve which is total carbon storage in unthinned live wood (uTWCS).
The Bureau of Transport and Communications Economics (BTCE, 1996a) dis-
cusses a number of functional forms for modelling this curve; however, for sim-
plicity we adopt the cubic given in Equation (7.1):
β1iYC + β2iYC t + β3iYC t 2 + β4iYC t 3
uTWCSi,YC,t (7.1)
i = species (for Sitka spruce, i = SS; for beech, i = BE)
YC = 4, 6, 8, . . . 26 (for i = SS)
t = years from planting (t = 0, 1, 2, . . . F)

A priori we would expect β 1 = 0, β 2 > 0, β 3 > 0 and β 4 < 0.30 In order to estimate
Equation (7.1), data for Sitka spruce YC12 were taken from R. Matthews (1992,
1993).31 Initial investigations con¬rmed that an optimal statistical model based on
Equation (7.1) gave estimates of β 1 which were not signi¬cantly different from
zero (as expected) and so this element was dropped from our ¬nal model which is
reported as Equation (7.2).
0.43727t + 0.10747t 2 ’ 0.0010267t 3
uTWCSSS,12,t (7.2)
(4.40) (28.09) (“29.21)

R2 = 99.9%; n = 81. Figures in brackets are t-statistics.

29 Recall that discount rate is held constant in Figure 7.1 such that only the yield-class effect is illustrated.
The β 4 term provides a potential advantage over non-declining functional forms such as the logit, which cannot
capture a possible reduction in the volume of a stand if left unmanaged with natural regeneration permitted.
31 These data are based upon a superior total/merchantable volume function to that used in Matthews (1991) upon
which the estimates of Pearce (1991) are based.
200 Applied Environmental Economics

Not surprisingly, given the predictability of tree growth patterns, Equation (7.2)
¬ts the data extremely well. All estimated coef¬cients are very highly signi¬cant
(p < 0.001 in all cases) and have expected signs and magnitudes.
We now need to generalise across yield classes. The work of Cannell and Cape
(1991) shows that, within a given species, carbon storage varies linearly across
YC. We can therefore derive a species-speci¬c YC adjustment factor, which we
denote AiYC , to permit us to adjust from the YC of our baseline data (YC12) to
any other Sitka spruce YC. Cannell and Cape (1991) report curves linking timber
volume, biomass, carbon storage and stand age for a variety of Sitka spruce YCs.
Using this information we can estimate an adjustment factor for Sitka spruce of
ASS,YC = 0.08333 YC (note that when YC = 12 then ASS,12 = 1.0).32 A gener-
alised function for uTWCSi,YC for i = SS and any YC can then be derived as in
Equation (7.3):

uTWCSSS,YC,t (7.3)

These functions will continue to rise until t = F. However, as noted, F is a
complex function of both the discount rate (r) and YC. This relationship was in-
vestigated using the YC/discount rate analysis of optimal felling dates reported in
Chapter 5. Our resultant best-¬t model is shown in Equation (7.4):

114.43 ’ 997.3r + 7167r 2 ’ 2.8657YC + 0.05919YC2
FSS,YC (7.4)
(32.67) (“6.25) (3.62) (“9.21) (5.79)


FSS,YC = optimal felling date for a given yield class (YC) of a speci¬ed
tree species (here Sitka spruce, SS)
r = discount rate (expressed as a decimal)
R2 = 96.6%; n = 39. Figures in brackets are t-statistics.

Equation (7.4) ¬ts the data extremely well for the range of observed F with all
parameters signi¬cant at p < 0.001. It shows, as noted previously, that F declines
with both r and YC, although the clear signi¬cance of the square terms in Equation
(7.4) indicates that this is not a simple, straight-line relationship.
We now consider thinned crops. To do this we ¬rst need to estimate TD1. Ex-
amination of the yield models given in Edwards and Christie (1981) shows a clear
relationship between TD1, F and YC as demonstrated in Table 7.4 for their Sitka
spruce yield models.

32 For derivation, see Bateman (1996).
Modelling and valuing carbon sequestration 201

Table 7.4. Date of ¬rst thinning (TD1) for Sitka spruce yield models
(r = 0.05 throughout)

Optimal felling year (F)1 Year of ¬rst thinning (TD1)2
YC Ratio (TD1/F)
6 68 33 0.485
8 67 29 0.433
10 64 26 0.406
12 58 24 0.414
14 54 22 0.407
16 51 21 0.412
18 50 20 0.400
20 50 19 0.380
22 49 18 0.367
24 48 18 0.375

Sources: 1 From Chapter 5, this volume.
From Edwards and Christie (1981); models for 2m spaced planting with no delay in

Inspecting Table 7.4 shows that, as YC rises and F falls, so TD1 declines. One
simple method of capturing this relationship is to ¬rst model the ratio TD1:F as a
function of YC as shown in Equation (7.5):
0.48149 ’ 0.0049061YC
(32.21) (“5.27)

RATIOTD1SS,YC = ratio of TD1 to F across YC for Sitka spruce
R2 = 77.7%; n = 10. Figures in brackets are t-statistics.

While the small sample size used in Equation (7.5) is not ideal, individual
t-statistics are highly signi¬cant and, as no further data are available, this seems a
reasonable approach. TD1 can now be calculated for any given YC by multiplying
the corresponding felling date by Equation (7.5) as shown in Equation (7.6):

(0.48149 ’ 0.0049061YC) — FSS,YC
TD1SS,YC (7.6)

As shown in Figure 7.1, once thinning commences total tree carbon storage
falls progressively below that predicted by our uTWCS function. Using data from
R. Matthews (1991, 1992, 1993) we can measure this proportion as the thinning
factor (TF) detailed in the ¬nal column of Table 7.5.
Statistical investigation showed that TFSS,t (the thinning factor for Sitka spruce
in year t) could be well predicted by the natural log of the number of years since
202 Applied Environmental Economics

Table 7.5. Thinning factor for Sitka spruce (TFSS,t ): YC12

Reduction in
total potential
Total unthinned Total thinned tree carbon Thinning factor
Years after date tree carbon tree carbon storage arising
TFSS,t =
of ¬rst thinning storage (tC/ha) storage (tC/ha) from thinning
(t* = t ’ TD1) uTWCSt
(uTWCSt ) (tTWCSt ) (tC/ha)
0 50 50 0 1.00
5 67 55 12 0.83
10 84 61 23 0.73
15 109 71 38 0.65
20 133 82 51 0.62
30 169 95 74 0.56
40 192 107 86 0.56
50 206 116 90 0.56
60 211 120 91 0.56

Source: Based on data in R. Matthews (1991, 1992, 1993).

thinning had commenced in a given plantation (denoted t* where t* = t ’ TD1
for all t ≥ TD1; note that where t < TD1 (i.e. before thinning commences) we
constrain TF to equal 1). Equation (7.7) details our best-¬tting model of TFSS,t .

1.000 ’ 0.1158 ln t —
TFSS,t (7.7)
(37.90) (“13.41)
R2 = 96.3%; n = 9. Figures in brackets are t-statistics.

We are now able to calculate total live wood tree carbon storage for thinned
stands of Sitka spruce in any year t (tTWCSSS,YC,t ):

tTWCSSS,YC,t (7.8)

The function shown in Equation (7.8) increases in each year from planting until
felling after which replanting is assumed to follow within one year and the function
returns to zero and restarts its growth path. Given that this model is discontinuous
it cannot readily be differentiated. Consequently, marginal carbon storage was cal-
culated by solving equation (7.8) iteratively for each year in our time series and
calculating the annual change.33

33 Care was taken to ensure that restarting of the growth path following felling was not recorded as a fall in
tree carbon storage. All carbon liberation is captured by the function relating to felling waste and timber
Modelling and valuing carbon sequestration 203

Carbon storage in beech live wood
The modelling of carbon storage in beech live wood followed the methodology used
for Sitka spruce and therefore will be only brie¬‚y described. Information regard-
ing sequestration in beech is somewhat sparser than for its widespread coniferous
counterpart, so much so that our analysis is based upon the estimates for oak (YC4)
given in Dewar and Cannell (1992), adjusted by consulting the YC4 model for
beech given in Edwards and Christie (1981). This exercise relies on the ¬ndings
of G. Matthews (1993), who suggests that, within YC bands, carbon storage for
oak and beech will be similar. Using this approach, observations on the S-shaped
unthinned carbon storage curve uTWCSBE,4,t were built up for use in the estimated

0.2414t + 0.030752t 2 ’ 0.00014252t 3
uTWCSBE,4,t (7.9)
(2.17) (13.73) (“13.24)
R2 = 99.9%; n = 26. Figures in brackets are t-statistics.

As with Sitka spruce, the model of total carbon storage in unthinned beech
live wood ¬ts the data very well. All parameter estimates are highly signi¬cant
(p < 0.05 for t and p < 0.000 for t2 and t3 ) and coef¬cients have expected
signs and magnitudes (the latter differing logically from those of our Sitka spruce
An adjustment factor for beech (ABE,YC ) was calculated as before to allow com-
parison across YC, the data given in Dewar and Cannell (1992) implying that
ABE,YC = 0.25 YC (note that when YC = 4, then ABE,4 = 1.0). A generalised
function for uTWCSi,YC for i = BE and any YC can then be derived as:

uTWCSBE,YC,t (7.10)

We can now estimate F for beech as a function of r and YC using the data reported
in Chapter 5. Our best-¬t model is:

173.86 ’ 1901.4r + 8870.8r2 ’ 5.387YC + 0.2500YC2
FBE,YC (7.11)
(20.78) (“18.07) (11.99) (“2.25) (1.47)
R2 = 97.8%; n = 32. Figures in brackets are t-statistics.

Equation (7.11) ¬ts the data very well and recon¬rms the relationships noted
regarding Sitka spruce. All estimates are signi¬cant at p < 0.05 or better with the
exception of the YC2 term which has p = 0.152. While this is in itself insigni¬cant
the term is retained both for comparison with our previous model and because it
yields a slight improvement in adjusted model ¬t.
204 Applied Environmental Economics

Table 7.6. Date of ¬rst thinning (TD1) for beech yield models
(r = 0.05 throughout)

Year of ¬rst thinning (TD1)1 Optimal felling year (F)2
YC Ratio (TD1/F)
4 35 81 0.432
6 30 75 0.400
8 25 71 0.352
10 25 69 0.362

Sources: 1 From Edwards and Christie (1981); models for 1.2m spaced planting with no
delay in thinning.
From Chapter 5, this volume.

The year of ¬rst thinning (TD1) is also estimated as before. Table 7.6 presents
the data for this analysis. As can be seen, the lack of variation in YC for British
beech considerably reduces the number of observations available.
As before we now estimate RATIOTD1BE,YC , as shown in Equation (7.12):

0.47666 ’ 0.012861YC
(15.29) (“3.03)

R2 = 82.1%; n = 4. Figures in brackets are t-statistics.

The very low number of observations underpinning Equation (7.12) is problem-
atic although it is not clear how further data could readily be generated. Neverthe-
less, relationships are as expected and this seems acceptable as a methodological
exercise. TD1 can now be calculated for any given YC as:

(0.47666 ’ 0.012861YC) — FSS,YC
TD1BE,YC (7.13)

Dewar and Cannell (1992) do not report any information from which a thinning
factor (TFBE ) might be derived. However, we can obtain an estimate for this by
examining the beech yield models of Edwards and Christie (1981). Figure 7.3
illustrates implicit TFBE from data given in the latter.
Inspection of Figure 7.3 shows that TFBE,t is very similar to TFSS,t as detailed in
Table 7.5. In both cases TF follows a roughly logarithmic pattern, falling rapidly
once thinning commences and becoming fairly stable after about thirty years.
We can therefore assume an approximate equality between these relationships
and use Equation (7.7) to de¬ne TFBE,t . Given this, we are now able to calcu-
late total live wood tree carbon storage for thinned stands of beech in any year
Modelling and valuing carbon sequestration 205

Figure 7.3. Thinning factor for beech. (Source: From data given in Edwards and Christie,

t (tTWCSBE,YC,t ) as:

tTWCSBE,YC,t (7.14)

Modelling carbon liberation from felling waste and timber products
The methodology adopted for modelling carbon liberation from felling waste and
timber products was common to both Sitka spruce and beech. Earlier in this chapter
it was shown that end use has a major impact upon overall carbon ¬‚ux. Examining
Table 7.2 indicates that, for all but the shortest lifespan products, carbon libera-
tion appears to follow a roughly normal distribution. Short lifetime products (those
from which virtually all carbon is liberated within ¬ve years of felling) have modal
liberation during the year of felling after which liberation rates fall swiftly over
time. Assuming an approximately straight-line, downward-sloping liberation dis-
tribution for the latter and a normal distribution centred upon the modes listed in
Table 7.2 for all other products, we obtain the product-speci¬c carbon liberation
schedules illustrated in Figure 7.4 for Sitka spruce and Figure 7.5 for beech. These
are expressed as a proportion of the total amount of carbon stored by one hectare
of live wood (i.e. excluding soil ¬‚ux) during the course of a full rotation.
In Figure 7.4, panels (a) to (e) show carbon liberation distributions for Sitka
spruce products and waste categorised according to longevity. So, for example,
from panel (a) we can see that nearly 10 per cent of the total carbon stored in
live wood by a rotation of Sitka spruce is liberated in the year of felling (t = 0)
via short lifetime (¬ve year maximum) products (e.g. paper and fuel) and waste
(including felling waste). Conversely, panel (c) shows that in the same year only
Figure 7.4. Annual carbon liberation distributions for products and waste expressed as a
proportion of total carbon sequestration in wood from one rotation of Sitka spruce.
Modelling and valuing carbon sequestration 207

Figure 7.5. Annual carbon liberation distributions for products and waste expressed as a
proportion of total carbon sequestration in wood from one rotation of beech.

0.1 per cent of total live wood stored carbon is liberated via medium lifespan
(forty year maximum) products (e.g. board). Panel (f) sums all these distributions
to produce an overall carbon liberation distribution. This shows that liberation is
highest in the felling year and then falls rapidly to some low positive amount which
208 Applied Environmental Economics

then gradually declines over an extended period. A number of statistical models
were ¬tted to these data, the optimal model being reported in equation (7.15) with
predictions being illustrated in panel (g) of Figure 7.4.

0.0017146 + 0.110363 ETRENDSS,t
LIB%SS,t (7.15)
(6.30) (36.53)


LIB%SS,t = annual carbon liberation from all products and waste as a
proportion of the total carbon stored in live wood by one
rotation of Sitka spruce
ETRENDSS,t = 1/(1+t ) where t = 0 at felling (F) and maximum t = 200
R2 = 87.0%; n = 201. Figures in brackets are t-statistics.

The ETRENDSS,t variable provides a good ¬t to the carbon liberation data as
illustrated by the similarity between actual and predicted liberation distributions
shown in panels (f) and (g), respectively, of Figure 7.4. Equation (7.15) implies
that all carbon stored in live wood by a rotation of Sitka spruce will be liberated by
t = 200, after which we constrain LIB%SS,t to equal zero.
Turning to Figure 7.5, panels (a) to (d) detail carbon liberation proportion distri-
butions by product category for beech, while panel (e) illustrates their sum. Again
this was modelled using a variety of approaches and functional forms with the best
model being:

0.0007818 + 0.121461 ETRENDBE,t
LIB%BE,t (7.16)
(4.01) (45.97)


LIB%BE,t = annual carbon liberation from all products and waste as a
proportion of the total carbon stored in live wood by one
rotation of beech
ETRENDBE,t = 1/(1+t ) where t = 0 at felling and maximum t = 300
R2 = 87.6%; n = 301. Figures in brackets are t-statistics.

Equation (7.16) for beech has the same form and explanatory variable as for
Sitka spruce in equation (7.15). A similar high degree of ¬t is achieved, as illus-
trated by comparing actual and predicted liberation in panels (e) and (f), respec-
tively, of Figure 7.5. Equation (7.16) implies that all carbon stored by a rotation of
beech will be liberated by t = 300 after which we constrain LIB%BE,t to equal
Modelling and valuing carbon sequestration 209

Modelling carbon storage and loss from soils
Examining Table 7.3 it is tempting to conclude that we should model individual
soil category carbon changes, including some element for altitude. Indeed the in-
tegrative and analytical capabilities provided by a GIS invite such an approach.
However, we are painfully aware of the paucity of data that underpins Table 7.3 and
of the numerous complications (such as the implications of replanting) which have
yet to be quanti¬ed. We therefore adopt a simpli¬ed and conservative approach to
modelling soil carbon ¬‚ux along the lines of Dewar and Cannell (1992), Sampson
(1992) and R. Matthews (1993), all of whom assume a constant, smooth and
marginally diminishing carbon ¬‚ux path for all soils.
Erring on the conservative side, Table 7.3 supports a net long-term increase in
soil carbon equilibrium levels for non-peaty soils at a range of altitudes of about
50 tC/ha. For peat soils a net long-term loss of some 750 tC/ha seems defensible.
Following our literature review we know that for both peat and non-peat soils the
rate of carbon ¬‚ux will be highest immediately after felling and decline such that
95 per cent of soil carbon change will have been achieved after about 200 years.
Equation (7.17) calculates the proportion of the total change in soil carbon
(PROPT SCt ) which will have been achieved in any year t, where t = 0 at plant-
ing. Notice that PROPT SCt = 1.00 when t = 263 (based on the assumption
that 95 per cent of total soil carbon change occurs by t = 199) after which it is
constrained to equal 1.00 throughout the remainder of the period under analysis.
PROPT SCt 0.1793022 ln TIME1t (7.17)
TIME1t = t + 1 and t = 0 at planting.
Equation (7.17) implies a diminishing marginal proportion of soil carbon change
over the period 0 ¤ t ¤ 263 (i.e. annual carbon changes are highest in the year in
which the ¬rst rotation is planted and decline thereafter). These marginal values
can be obtained by simple, one-period differencing. Multiplying these annual pro-
portions by the total change (50 tC/ha for non-peat soils and ’750 tC/ha for peat
soils) gives the annual soil carbon gains and losses (in tC/ha).

Net carbon storage in live wood, products and waste
Setting aside soil carbon impacts (discussed subsequently), the carbon storage and
liberation equations reported above for Sitka spruce and beech were operationalised
through a custom-written Fortran program.34 This program yielded estimates of
carbon sequestration value by species for a range of YC and discount rates. For
34 This program is listed, with sample output, in Bateman (1996).
Table 7.7. NPV of net carbon ¬‚ux (sequestration in live wood and liberation from products and waste) for an optimal rotation
of Sitka spruce: various yield classes and discount rates (£, 1990)

Discount rate
(%) YC4 YC6 YC8 YC10 YC12 YC14 YC16 YC18 YC20 YC22 YC24 YC26
1.5 811 1,166 1,491 1,815 2,122 2,415 2,692 3,002 3,308 3,609 3,902 4,228
2 699 1,007 1,290 1,570 1,837 2,089 2,364 2,634 2,897 3,151 3,404 3,652
3 536 774 1,005 1,208 1,415 1,629 1,816 2,015 2,199 2,391 2,567 2,781
5 342 496 643 785 916 1,035 1,160 1,278 1,393 1,503 1,626 1,761
6 284 411 535 653 761 859 963 1,060 1,156 1,253 1,367 1,466
Modelling and valuing carbon sequestration 211

each discount rate/YC combination, three net carbon sequestration values were
(i) the net present value (NPV) of the initial optimal rotation
(ii) the NPV of a perpetual series of optimal rotations (to t = 1,000, assuming replanting
after felling), and
(iii) the annuity equivalent of the latter.

Bateman (1996) reports full results of all these analyses for all three measures. For
brevity, here we report just the ¬rst of these measures for Sitka spruce (Table 7.7)
and beech (Table 7.8).
Considering Tables 7.7 and 7.8 we can see that both yield class and discount
rate have highly signi¬cant impacts upon net carbon sequestration values. The data
reported in these tables allow us to estimate, for each tree species, a series of linear
regression equations where, for each speci¬ed discount rate, the net present value of
sequestration is related to yield class.35 The resultant regression models are reported
in Table 7.9.
As can be seen, the models reported in Table 7.9 ¬t the data well. These models
can now be applied to our maps of predicted timber YC, as derived in Chapter 6,
to produce maps of the net carbon sequestration value derived from consideration
of storage in live wood and emissions from thinnings and wood products (but
not soil carbon impacts) for the entire Welsh study area. Discounting effects can
be analysed by simply selecting the equation from Table 7.9 which refers to the
desired species/discount rate combination. As examples, Figure 7.6 illustrates the
resultant NPV map for an optimal ¬rst rotation of Sitka spruce using a 3 per cent
discount rate,36 while Figure 7.7 illustrates the respective value for beech.
The images detailed in Figures 7.6 and 7.7 strongly re¬‚ect the underlying pattern
of timber yield and consequently echo the environmental determinants of such
growth rates. Notice that the pattern of net carbon ¬‚ux values is similar for the two
species, re¬‚ecting lower growth rates in the upland areas running down the centre
of the country and higher yields in bisecting valleys and on superior lowland soils.
However, carbon ¬‚ux NPV sums are consistently higher for Sitka spruce than for
beech. This arises because the superior growth rate of Sitka spruce directly ¬xes
more carbon, more quickly, than beech does. As a consequence the former is far
less affected by the process of discounting, and resultant NPV levels are higher.
Figures 7.6 and 7.7 are calculated holding the discount rate constant at 3 per cent.
Table 7.10 relaxes this restriction and, for both of the species under consideration,
compares the NPV of net carbon ¬‚ux for live wood, waste and products across a

35 Bateman (1996) also reports equations predicting the NPV in perpetuity and the annuity equivalent carbon
storage values.
36 This rate is chosen here to re¬‚ect recent debate concerning an appropriate social discount rate (Pearce and
Ulph, 1998); see Chapter 5.
212 Applied Environmental Economics

Table 7.8. NPV of net carbon ¬‚ux (sequestration in live wood and liberation
from products and waste) for an optimal rotation of beech: various yield
classes and discount rates (£, 1990)

Discount rate
(%) YC2 YC4 YC6 YC8 YC10 YC12
1.5 886 1,673 2,401 3,059 3,690 4,326
2 706 1,332 1,889 2,421 2,941 3,437
3 466 875 1,246 1,607 1,924 2,262
5 242 454 649 830 1,003 1,178
6 186 349 497 638 775 907

Table 7.9. NPV of carbon in live wood, waste and products from an optimal
rotation of Sitka spruce and beech: linear predictive equations with yield class
as the single explanatory variable: various discount rates

Discount rate
R2 (adj.)
Species (%) Intercept (t-value) Slope (t-value)
Sitka spruce 1.5 254.32 (14.62) 152.83 (145.11) 99.9
Sitka spruce 3 187.70 (9.90) 100.46 (87.48) 99.9
Sitka spruce 6 106.77 (9.06) 52.71 (73.89) 99.8
Beech 1.5 281.86 (4.68) 341.52 (44.20) 99.7
Beech 3 148.14 (4.92) 178.34 (46.18) 99.8
Beech 6 56.18 (5.54) 71.80 (55.19) 99.8

range of discount rates.37 The table gives frequency counts and percentages for the
number of 1 km cells within each value band.
Analysis of Table 7.10 shows that both the choice of discount rate and the choice
of species have substantial impacts upon net carbon storage values. As before we
¬nd that the slower timber growth rate of beech results in lower discounted values
of carbon sequestration than those for Sitka spruce. However, as expected, this
divergence of values between species declines as the discount rate falls.

Extending the analysis to include soil carbon ¬‚ux
Equation (7.17) de¬ned the total proportion of soil carbon ¬‚ux (sequestration or lib-
eration) achieved in any year (t) for any tree species. This equation was differenced
to calculate the marginal proportion change in any year t. The actual marginal
change in soil carbon was then obtained by multiplying the total change over the
full period under analysis (50 tC/ha for non-peaty soils; ’750 tC/ha for peaty soils)
by the marginal proportion change in each year. This annual soil carbon gain or
37 Annuity equivalents are reported in Bateman (1996).
Modelling and valuing carbon sequestration 213

< 1,250
1,500 “1,749 Motorway
1,750 “1,999 Dual carriageway
2,000“2,249 Single carriageway
0 10 20 30 40 50

Figure 7.6. NPV of net carbon storage in live wood, products and waste from an optimal
¬rst rotation of Sitka spruce: 3% discount rate.

loss was subsequently valued using the Fankhauser values as discussed previously.
These values were then discounted at various rates, and net present value perpetuity
sums calculated as shown in Table 7.11.38

38 Given that soil carbon change is a slow process (Milne and Brown, 1997), taking many rotations to complete,
calculation of ¬rst rotation NPV sums is of less interest here than in our analysis of tree carbon ¬xing values.
Annuity equivalents are reported in Bateman (1996).
214 Applied Environmental Economics

1,000 “1,199
1,200 “1,399
1,400 “1,599 Motorway
1,600 “1,799 Dual carriageway
Urban Single carriageway

0 10 20 30 40 50

Figure 7.7. NPV of net carbon storage in live wood, products and waste from an optimal
¬rst rotation of beech: 3% discount rate.

Maps of soil carbon ¬‚ux values were created by applying the values given in
Table 7.11 to a soil map derived from the LandIS database (see the discussion in
Chapter 6). Given the lack of detailed information concerning soil ¬‚ux impacts, the
resultant maps (reproduced in Bateman, 1996) contain only two values, representing
the presence or absence of peaty soils, the latter being generally con¬ned to extreme
upland areas where carbon storage is already low due to depressed tree growth rates.
Table 7.10. NPV of Sitka spruce and beech carbon ¬‚ux for live wood, waste and products: various discount rates (r)

Sitka spruce Beech
r = 1% r = 3% r = 6% r = 1% r = 3% r = 6%
NPV (£/ha) Freq.1 % Freq.1 % Freq.1 % Freq.1 % Freq.1 % Freq.1 %
250“499 ” ” ” ” 1 0.005 ” ” ” ” 161 0.783
500“749 ” ” ” ” 228 1.109 ” ” ” ” 20,402 99.217
750“999 ” ” 5 0.024 8,042 39.109 ” ” ” ” ” ”
1,000“1,249 ” ” 50 0.243 12,292 59.777 ” ” 159 0.773 ” ”
1,250“1,499 5 0.024 624 3.035 ” ” ” ” 7,809 37.976 ” ”
1,500“1,749 27 0.131 3,621 17.609 ” ” ” ” 12,595 61.251 ” ”
1,750“1,999 71 0.345 8,648 42.056 ” ” 1 0.005 ” ” ” ”
2,000“2,249 571 2.777 7,615 37.033 ” ” 41 0.200 ” ” ” ”
2,250“2,449 2,036 9.901 ” ” ” ” 387 1.882 ” ” ” ”
2,500“2,749 3,561 17.318 ” ” ” ” 4,057 19.730 ” ” ” ”
2,750“2,999 6,371 30.983 ” ” ” ” 8,457 41.127 ” ” ” ”
3,000“3,249 7,643 37.169 ” ” ” ” 7,620 37.057 ” ” ” ”
3,250“3,499 278 1.352 ” ” ” ” ” ” ” ” ” ”
Mean 2,859.75 1,900.39 1,005.36 2,907.06 1,518.99 608.08
s.d. 384.82 319.28 266.81 320.42 273.61 236.07

Note: 1 From a total of 20,563 1 km land cells.
216 Applied Environmental Economics

Table 7.11. NPV perpetuity sums1 for soil carbon
¬‚ux: all tree species (£/ha)

Discount rate (%)
Soil type 1.5 3 6
Non-peaty 743 601 476
’11,144 ’9,018 ’7,141

Notes: 1 Calculated for t = 0 to 999.

Table 7.12. Number of 1 km land cells1 at differing levels of NPV for net carbon
¬‚ux (live wood, waste, products and soils): Sitka spruce, various discount rates (r)

r = 1% r = 3% r = 6%
Soil type NPV (£/ha, 1990)
Peaty 33 ” ”
’9,000:’8,501 438 ” ”
’8,500:’8,001 5 ” ”
’8,000:’7,501 13 117 ”
’7,500:’7,001 ” 298 ”
’7,000:’6,501 ” 14 ”
’6,500:’6,001 ” ” 489
Non-peaty 500:999 ” ” 3
1,000:1,499 ” 1 9,650
1,500:1,999 ” 181 10,421
2,000:2,499 32 7,907 ”
2,500:2,999 538 11,985 ”
3,000:3,499 5,349 ” ”
3,500:3,999 13,933 ” ”
4,000:4,499 222 ” ”

Note: 1 From a total of 20,563 1 km land cells.

In order to assess the full impact of tree planting upon carbon ¬‚ux, the undis-
counted marginal soil carbon storage values were added to the undiscounted annual
net carbon ¬‚ux values for live wood, products and waste calculated previously. The
resultant total annual carbon ¬‚ux values were then discounted at various rates to
yield the net present value for any desired period. Table 7.12 lists the NPV of total
net carbon storage for Sitka spruce across various discount rates (values for beech
are similar but re¬‚ect our comparison in Table 7.10 by being consistently below
those for Sitka spruce; as such they are not reproduced here).
The most striking feature of Table 7.12 is the highly bipolar distribution of results.
Planting on peat soils causes very large soil carbon losses which overwhelm any
Modelling and valuing carbon sequestration 217

’8,000” ’7,501
’7,500” ’6,501
1,000”1,999 Motorway
2,000”2,499 Dual carriageway
>= 2,500 Single carriageway
0 10 20 30 40 50 km

Figure 7.8. NPV of net carbon ¬‚ux (live wood, products, waste and soils), Sitka spruce:
3% discount rate.

values generated by storage in live wood. Elsewhere, however, the value of carbon
storage is both positive and substantial. Given the nature of this distribution, mean
values and variance measures are somewhat inappropriate; however, the spatial
distribution of values is well illustrated in Figure 7.8 which shows the NPV values
for net carbon ¬‚ux generated by Sitka spruce when assessed using a 3 per cent
discount rate.
218 Applied Environmental Economics

Consideration of Figure 7.8 shows that, with respect to carbon storage values,
planting on peat soils is clearly to be avoided, a result which underpins the ¬ndings
of Adger et al. (1992) discussed previously. However, elsewhere such planting is
creating substantial public-good bene¬ts which have not commonly ¬gured in CBA
appraisals of forestry proposals.

Summary and conclusions
The objective of this chapter was both generally to advance the methodology for
modelling carbon sequestration and, speci¬cally, to produce maps of the value
of net carbon ¬‚ux induced by planting trees in locations across Wales. This was
achieved by ¬rst reviewing the existing literature regarding the value of carbon
sequestration or liberation per se. Here we concluded that the work of Fankhauser
represents the current state of the art and duly adopted his valuations for use later
in the chapter. Our second and principal objective was to construct, for both of the
tree species under investigation, models of the quantity of carbon sequestered, or
liberated, from three sources: the growth of live wood; changes in the carbon content
of woodland soils; and carbon liberation from felling waste and timber products.
To allow for the long-term nature of these processes, these models were run over a
highly extended period. Valuation of the various carbon storage and emission ¬‚ows
was then achieved by reference to unit values reported in the literature. A GIS
was used to apply the live wood carbon sequestration and waste/product emission
analyses to existing models of predicted tree growth rates for a large study area.
Similarly our soil carbon ¬‚ux model was related to data on soil type distribution.
The GIS was then used to overlay results from these various analyses to permit
the construction of a net carbon ¬‚ux valuation map for both of the species under
Such maps are directly compatible with those estimated in previous chapters
for woodland recreation and timber production values. In Chapter 9 we combine
all of these maps to derive the total value generated by woodland in a given area.
However, before that, in Chapter 8, we examine the value of agricultural output in
those areas, which would constitute the major opportunity cost of conversion of
land use from farming into woodland.
Modelling opportunity cost: agricultural output values

Having concluded our assessment of the monetary value of land under forestry we
now turn to consider the prime opportunity cost of such a decision, namely the value
of the major land use in Wales: agriculture. This chapter presents models of net
agricultural income1 received by farmers (referred to as the ˜farm-gate™ value) and
its social or ˜shadow price™ equivalent which adjusts for the various subsidies and
other transfer payments which characterise UK agriculture.2 As before, a GIS-based
approach is used to generate maps of such values for the entire study area. This
permits subsequent comparison of total woodland values with those for agriculture
(see Chapter 9).
The following section presents the necessary policy background. This establishes
the broad and progressively strengthening economic case for the transfer of at
least some land out of conventional agriculture and into alternative land uses and
overviews the theoretical and methodological basis of our analysis. An overview
of developments since our 1990 study period is also presented, showing that there
has been a clear worsening of the economic situation for farmers in our study area,
which means that our analysis will provide a conservative estimate of the potential
for land use change from farming to forestry.
The following two sections outline the GIS-based methodology employed and
discuss the data. For modelling purposes, farms in the sample were clustered into
distinct groups as explained in the next section, which also reviews de¬nitions of
farm-gate and shadow value of production. Thereafter, the results of the modelling

This chapter is an extension of the analysis presented in Bateman et al. (1999d)
1 An alternative approach to valuation might be to examine land prices. However, these have been distorted
through subsidised over-use of agricultural land (North, 1990). Furthermore, in debating land purchase as a
route towards reducing agricultural output, Colman (1991) argues that, at best, such land purchase schemes will
be on a minor scale.
2 Note that, just as for the case of woodland, certain agricultural externalities are not assessed, for example
landscape amenity (see Fleischer and Tsur, 2000).

220 Applied Environmental Economics

exercise for both sheep and dairy farming are discussed and the consequent GIS
maps are presented. The ¬nal section provides a summary and conclusions.

Policy background in the UK
Government intervention within the British agricultural sector can be traced back
to at least the Middle Ages (Ernle, 1919) and so it would be wrong to characterise
farms as being purely subject to market forces prior to the UK™s entry into the
EEC in 1973.3 Nevertheless, the simultaneous entry into the Common Agricultural
Policy (CAP) heralded one of the most fundamental changes in the organisation of
agriculture in Britain™s peacetime history.

The initial CAP support system
The policy principles of the CAP were laid down in 1957 as Article 39 of the foun-
dation document of the EEC, the Treaty of Rome (European Economic Community,
1962). This advocated a basically expansionist ideology enshrined in various po-
tentially con¬‚icting intentions to ensure (i) producer ef¬ciency (ii) market stability
(iii) consumer equity, and (iv) a ˜fair™ standard of living for farmers.4 In considering
the subsequent interpretation and implementation of these aims, commentators have
highlighted both the post-war demand for greater food security and the fact that the
CAP is a product of the Treaty of Rome and was therefore seen as a cornerstone of
the underlying desire, particularly by the Commission of the European Community
(CEC), for greater political union among member states (Bowler, 1985; McInerney,
1986; Fennell, 1987; Gilg, 1996).
In practice, a special section of the Community budget, the European Agricultural
Guidance and Guarantee Fund (usually known by its French acronym FEOGA), was
created to ¬nance the expansion of EEC agriculture. Rather than assistance being
paid directly to farmers it was decided that each year the Council of Ministers would
set a ˜target price™ for each commodity, usually signi¬cantly above the prevalent
world price. This internal EEC target price was principally maintained by imposing
an import levy upon non-EEC produce. However, while this was adequate for most
goods where the EEC was a net importer, if domestic supply exceeded demand,
then the possibility of surpluses depressing internal prices arose. To combat this a
system of export subsidies was introduced, payable where internal EEC prices fell
below an ˜intervention price™ level set somewhere below the target price but above
world price. Figure 8.1 illustrates the essentials of the support system.
3 Market restrictions and intervention prior to 1973 are discussed in Bowers and Cheshire (1983), Blunden and
Curry (1985), Robinson (1990), Smith (1990), Ritson (1991a) and Cobb (1993).
4 Discussion of these aims is presented in Blunden and Curry (1985), Franklin (1988), Fearne (1991), Ritson
(1991b) and Gilg (1996).
Modelling opportunity cost: agricultural output values 221

Figure 8.1. Model of a typical CAP price support system. (Source: Adapted from Ritson,

A further complexity arose from the internal operation of the CAP prior to mone-
tary union. Support prices were ¬xed in European Currency Units (ECU) and so had
to be translated into actual payments via national currencies. However, ¬‚uctuations
in exchange rates could lead to substantial and quickly transmitted instability in
producer prices. Therefore, for agricultural goods alone, EEC member states were
allowed to maintain prior exchange rates (known as ˜green™ currency) for convert-
ing CAP support prices into domestic prices. This system caused differences in re-
alised support prices for the same commodity across countries and if left unchecked
would have led to goods moving from low-price to high-price countries prior to
their sale into intervention. Consequently, an interim system of border taxes and
subsidies (known as Monetary Compensation Amounts, MCA) on intra-EEC trade
was also introduced (Fennell, 1987; Ritson, 1991a). The advent of the European
Union (EU) Single Market on 1 January 1993 swept away internal borders, making
MCAs unworkable. While a strong exchange rate mechanism (ERM) would have
reduced many problems, the exit of the UK from the ERM on 16 September 1992
precluded this option and necessitated a compromise solution wherein green cur-
rencies effectively ˜¬‚oat™, with devaluation in the ˜green pound™ occurring regularly
(Neville and Mordaunt, 1993). This complication persists for the UK following its
222 Applied Environmental Economics

decision in 1999 not to join the ¬rst wave of EU monetary union and ¬‚uctuations
in the green pound remain a source of problems for UK farmers.

Operation of the CAP in the UK: 1973 to the early 1990s
The UK™s entry into the EEC and the CAP in 1973 coincided with the world
commodity price boom which was primarily responsible for a substantial increase
in agricultural prices, but for which the CAP got much of the blame (Britton, 1990;
Hodge, 1990a; Robinson, 1990; Ritson, 1991b). UK food prices rose by 18 per cent
in 1974 and 24 per cent the following year (Capstick, 1991). Indeed the retail food
price index kept above that of other items for the remainder of the 1970s and the
¬rst half of the 1980s (ibid.), a trend echoed in the growth of land prices during
the period (Harvey, 1991a). During the mid 1970s the price guarantee system and
world-wide price buoyancy resulted in increased agricultural stability and incomes
(Blunden and Curry, 1985; Hill, 1990; Moyer and Josling, 1990) although this
was bought at the cost of welfare losses to consumers and taxpayers (Morris,
1980; Australian Bureau of Agricultural Economics, 1985). However, the natural
consequence of increased price subsidies was over-use of land for agricultural
purposes (North, 1990), increased food production, and with it higher support costs,
which with sluggish growth in domestic demand (Harrison and Tranter, 1989) could
only result in higher export subsidies and intervention storage costs (Blunden and
Curry, 1985; Buckwell, 1989; Smith, 1990; Cobb, 1993). During the late 1970s and
early 1980s the total budget costs of the CAP rose by around 25 per cent per annum
(Cobb, 1993) with FEOGA guarantee expenditure increasing from about ECU 2.5
billion in 1970 to nearly ECU 30 billion in 1988 (Moyer and Josling, 1990).
The price pressure of this level of support led to an increased misallocation of
resources (Marsh and Swanney, 1980; Tarrant, 1980; Body, 1982; Buckwell et al.,
1982; Hill, 1984)5 and resultant inef¬ciencies, which meant that as producer subsidy
equivalents rose from about 30 per cent to peak at over 60 per cent in 1987, so the
net economic loss (sum of producer and consumer welfare effects) of the CAP rose
to exceed ECU 9 billion in 1986 (Josling, 1993). Despite widespread criticism,
little was done in practical terms to alleviate a rapidly worsening situation. Many
commentators both then and since have identi¬ed the decision-making framework
as the principal cause of this policy response lag, with particular criticism being
aimed at the willingness of the Council of Ministers to avoid dif¬cult decisions
and put the short-term concerns of their national agricultural constituencies before
the long-term need for budgetary prudence (Marsh and Swanney, 1980; Hill, 1984;
5 EEC subsidies and consequent increase in exports and depression of world prices also had major impacts upon
non-EEC countries and in particular the less-developed world (Anderson and Tyers, 1991). The economic
consequences of this effect are considered subsequently in this chapter.
Modelling opportunity cost: agricultural output values 223

Bowler, 1985; Fennel, 1987; Hodge, 1990b; Smith, 1990; Fearn, 1991; Josling,
1993; Winters, 1993; Gilg,1996; Billing, 1998). The UK was by no means innocent
of such prevarication; for example, the green pound was frequently devalued during
this period, thus raising MCA payments to UK farmers (Harris et al., 1983). In
essence, then, the CAP exhibited all the signs of a classic intervention failure
(Burrell, 1987; Tyers and Anderson, 1987; Rosenblatt et al., 1988; Anderson and
Tyers, 1991).
Eventually the EEC was forced to acknowledge that something had to be done
about the spiralling CAP budget (CEC, 1985a). While thresholds upon guarantees
had been introduced in 1982 (Cobb, 1993), the ¬rst substantial response came with
the introduction of milk quotas (CEC, 1985b). While the Council of Ministers still
provided a brake upon reform (CEC, 1989, 1990), nevertheless gradual reductions
in support for milk (European Economic Community, 1987) and cereals were in-
troduced (CEC, 1987) and in real terms prices began to fall throughout the late
1980s (Moyer and Josling, 1990; Hubbard and Ritson, 1991). This coincided with
a reduction in non-price support; for example, UK grants dropped from almost
£200 million in 1983/84 to about £23 million in 1988/89 with capital allowances
being cut in 1986 (Cobb, 1993).
The severity of these real-price decreases meant that by 1990 the food price
index had fallen below that of general prices (Capstick, 1991) and agricultural in-
comes were in decline (Howarth, 1985; Organisation for Economic Cooperation
and Development (OECD), 1987; Hill, 1990; Moyer and Josling, 1990). However,
continued increases in productivity and falls in demand (Capstick, 1991; CEC,
1992a) meant that the budgetary costs of the CAP were persistently high and the
system remained one of intervention failure (Anderson and Tyers, 1991; Josling,
1993). One of the consequences of this situation was that more land was being used
for agriculture than was economically ef¬cient, with estimates of surplus agricul-
tural land in the UK ranging from 0.7 million to 5 million hectares (North, 1990;
Harvey, 1991b; Potter et al., 1991).
Our study period of 1990 was therefore set within a period when market interven-
tion was unable to reverse long-term agricultural decline, characterised by falling
real prices and incomes and over-use of land for farming. We now turn to consider
the extent to which these trends have altered or intensi¬ed up to the present day.

Operation of the CAP in the UK: the early 1990s to 2001
The early 1990s saw a fusion of concerns regarding the ¬nancing of the CAP with
long-standing but ongoing concerns regarding the negative environmental impacts
of present land use (Nature Conservancy Council, 1977; Shoard, 1980; Body, 1982;
Hodge, 1990a,c; MacKenzie, 1990; Whitby, 1991a,b; Turner et al., 1994). These
224 Applied Environmental Economics

dual pressures of increasing subsidy cost and environmental degradation led many
commentators to consider the possibility of reorienting support away from conven-
tional production measures and towards a more holistic agri-environmental system
where both food and amenity become recognised and remunerative farm outputs
(Baldock and Conder, 1987; Bowers, 1987; Blunden and Curry, 1988; Department
of the Environment, 1988; Potter, 1988, 1990; Royal Society for the Protection of
Birds, 1988; Hodge, 1990d; Neville-Rolfe, 1990; Cobb, 1993; Colman, 1993).
At the national level a number of UK national policies attempted to address
these joint aims including the Alternative Land Use and Rural Economy (ALURE)
package (Ministry of Agriculture, Fisheries and Food (MAFF), 1987b) which in-
troduced Environmentally Sensitive Area (ESA) payments, the Premium Scheme
(MAFF, 1990), and the Countryside Stewardship Scheme (MAFF, 1992d) which
arose from the Government White Paper Our Common Inheritance (H.M. Govern-
ment, 1990). However, while some saw these as a signi¬cant reorientation of UK
agricultural policy and recognition of the symbiosis of land use and the environment
(Blunden and Curry, 1988; Department of the Environment, 1988; Neville-Rolfe,
1990; Colman, 1991, 1993) others criticised the limited funding for such schemes
(Robinson, 1990; House of Lords, 1992; National Farmers Union (NFU), 1992).
A more fundamental response, at the EU level, to pressures for agri-environmental
reform was embodied in the Fifth Action Programme on the Environment
(CEC, 1992b), commonly known as the MacSharry Reforms after the then European
Commissioner for Agriculture, Ray MacSharry. These proposed a substantial re-
duction in price support compensated by direct payments to farmers which would be
conditional upon placing land into non-productive ˜set-aside™ with further require-
ments to reduce negative environmental impacts. Although subsequently watered
down, the principle of such reforms was accepted (CEC, 1992c,d; Neville and
Mordaunt, 1993).
The MacSharry Reforms have been complemented by a variety of agri-
environmental policies (AEPs) including further ESA schemes, Countryside
Stewardship, Nitrate Sensitive Areas, Countryside Access, etc. (Evans and Morris,
1997; Hanley et al., 1999; MacFarlane, 2000). However, funding for AEPs has
always been relatively modest, with annual spending amounting to about 2.5 per
cent of the total of £2,857 million of CAP funds spent in the UK in 1996/97 (Hanley
et al., 1999).6
The small-scale increases of AEP payments during the 1990s pale in comparison
to the substantial falls in real agricultural prices which occurred over the decade.
With the exception of a brief period of substantial growth between about 1993
and 1995, the decade was a period of unprecedented decline in farm incomes.

6 Norman et al. (1994) provide an early treatise on the application of GIS techniques to target AEPs.
Modelling opportunity cost: agricultural output values 225

By 1998, total income from farming (TIFF)7 in the UK fell to £2.51 billion, its
lowest level for twenty-¬ve years. After a small rise in 1999, estimates for 2000
showed a further fall to £1.88 billion (DEFRA, 2002). At the farm level, incomes
fell across all sectors to levels which were lower than those of our study period
at the start of the decade (Countryside Agency, 2001). As the Rural White Paper
concluded, ˜Farming is going through its most dif¬cult period since before the
Second World War. Farm incomes have fallen by around 60% over the past ¬ve
years. No sector of farming has been unaffected™ (Department for the Environment,
Transport and the Regions, 2000: p. 89). Similarly a Cabinet Of¬ce report to the
Prime Minister stated that ˜Any assessment of rural areas must begin with the
acknowledgement that agriculture, the countryside™s most visible and most typical
activity, is facing major problems, and that many sectors and people within it
are facing real crisis™ (Cabinet Of¬ce, 2000: p. 4). This was particularly true in
Wales where the 1990s proved a desperate time for agriculture, as quanti¬ed in
Table 8.1.
Table 8.1 shows that all sectors of Welsh farming have experienced sharp declines
in agricultural prices and incomes. These have triggered a fall in the number of farms
as both farms and herds/¬‚ocks increase in size. Declining prices mean that Welsh
farmers are now heavily reliant upon subsidies, as recognised in the recent National
Assembly for Wales draft policy for the future of agriculture:
Farmers are overwhelmingly reliant on subsidy for this income. Direct CAP subsidies now
account for 420% of the net farm income of the average farmer in Wales: this ¬gure would
be far higher if indirect support was taken into account. (National Assembly for Wales,
2001b: section 1.1)

Welsh farmers have attempted to bolster falling incomes through increasing the
number of beef cattle and sheep. In part this has been facilitated by the increase in
permanent grassland and reduction in rough grazing noted in Table 8.1. However,
this has also been attempted through increases in stocking density, extending a
trend which dates from at least the UK™s entry into the CAP. Figure 8.2 illustrates
this trend, showing the relationship between altitude and stocking intensity for four
periods ranging from the early 1970s to the late 1990s. This shows that in each
period stocking densities increase with height above sea level, but that densities
have consistently increased at all altitudes over the past thirty years.
Wales now has one of the highest sheep stocking densities in the EU (Fuller, 1996)
leading to considerable problems of overgrazing and consequent adverse impacts
upon biodiversity (Fuller et al., 1995; Dobson, 1997; Woodhouse et al., 2000). In
particular, large increases in the number of sheep over successive decades have
been blamed for a signi¬cant fall in the density and variety of wildlife observed in
7 The preferred and internationally agreed measure of aggregate agricultural income.
226 Applied Environmental Economics

Table 8.1. Change in Welsh agriculture 1990 to 2000

Measure 1990 2000 Change (%)
Number of dairy cows (™000) 326.8 268.6
Number of farms 6,374 4,307
Average herd size 51 62
Number of beef cows (™000) 202.4 223.3
Number of farms 11,332 9,326
Average herd size 18 24
Average market price (per kilo)1 £1.04 £0.84
Number of sheep & lambs (™000) 10,866.6 11,148.0
Number of farms 17,587 15,088
Average ¬‚ock size 618 739
Average market price (per kilo)1 £1.56 £0.84
Dairy index2 100 36
Cattle and sheep (Less Favoured 100 24
Areas) index2
’6 ’106.0
Cattle and sheep (non Less 100
Favoured Areas) index2
Land use
Permanent grass (™000 ha) 904 933
Rough grazing (™000 ha) 516 442
Woodland etc. (™000 ha)3 50 58

Notes: 1 Pounds (sterling) per kilo liveweight.
Incomes index includes subsidies and holds 1989/90 to 1991/92 = 100.
Includes set-aside land; excludes arable land.
Sources: National Assembly for Wales (2000, 2001c).

Wales (National Assembly for Wales, 2001b). For example, the number of breeding
pairs of lapwings in Wales has fallen from about 14,000 in 1970, to 7,500 in 1987
and to just 1,700 in 1998 (ibid.).
Examination of Welsh agricultural statistics (National Assembly for Wales, 2000,
2001b,c) shows that our 1990 study period was ¬rmly on a declining trend line ex-
tending from the late 1970s to the present. Although the present state of farming
is indeed parlous, inspection of trends in farm income shows that, if anything, the
increase in real agricultural incomes seen in the period from about 1993 to 1995 was
against the general decline seen over the past two decades. Looking into the future
we see no signs of any impending change in these trends either in Wales or across
the UK in general. The most recent CAP reform proposals, known as Agenda 2000,
Modelling opportunity cost: agricultural output values 227

Figure 8.2. Sheep stocking intensity in Wales, 1972 to 1997. (Source: Woodhouse, 2002.)
The ¬gure shows the mean number (thicker lines; 95% C.I.s shown either side of each line)
of breeding ewes per hectare of farmland for 2 km cells in Wales relative to height above
sea level.

extend recent policy trends through a continuation of reductions in output-related
price support and increased reliance upon area-based measures (Billing, 1998;
Hanley et al., 1999; Brouwer and Lowe, 2000a,b; Lowe and Baldock, 2000). In-
creased measures for agri-environmental support are complemented by further
movement away from paying subsidies on a per animal (headage) basis, moves
which are speci¬cally designed to discourage excessive stocking in ecologically
fragile environments such as the Less Favoured Area designation which embraces
most of Wales. Such policies are backed at the UK national level in strategy docu-
ments such as the Rural White Paper (Department for the Environment, Transport
and the Regions, 2000).
This policy and economic environment means that if Welsh farmers try to
compete on price alone they will continue to perform badly. This situation is explic-
itly recognised by the National Assembly for Wales (2001b), whose agricultural
policy recognises farming as a sector in rapid decline which needs to rapidly diver-
sify out of sole reliance upon food production into other activities including, among
others, farm woodlands. Although farmers have long been recognised as being
resistant to diversi¬cation there is recent evidence to suggest that the persistent
228 Applied Environmental Economics

nature of agricultural decline, compounded by unforeseen and highly damaging
shocks such as the BSE crisis and the more recent foot and mouth epidemic, has
made farmers more receptive to ideas of diversifying their activities out of tradi-
tional food production and into other enterprises. A survey of farmers in England
and Wales conducted in 2000 found that 59% of farmers said they would either
de¬nitely (26%) or possibly (33%) seek new income from outside their farming
businesses (Countryside Agency, 2001). Similarly 48% of farmers said they would
either de¬nitely (19%) or possibly (29%) seek to diversify into non-farming use of
land, resources or buildings (ibid.). This suggests a con¬‚uence of economic, policy
and psychological factors which together make more viable the type of land use
change considered in this study.

Conclusions: the potential for change
This policy review clearly shows the potential for economic gains (both in the sphere
of market ef¬ciency and the provision of environmental bene¬ts) from the reform
of agricultural policy. In particular there is the possibility of welfare improvements
by inducing conversions out of conventional agriculture and into alternative land
use such as the woodland option considered in this study. Furthermore, our review
of events since our study period shows that declining agricultural values mean
that our ¬ndings are likely to underestimate the true potential for ef¬ciency gains
from such land use change. However, while the possibility of creating positive
social net bene¬ts clearly exists, such transfers are unlikely to occur unless we
also consider the consequent market value to producers. In subsequent sections
we discuss approaches to the modelling of both the shadow and market values of
agriculture so that such a comparative analysis can be undertaken.

Developing a GIS-based modelling methodology
Despite the considerable potential of utilising the spatial analytic capabilities of a
GIS for modelling in agricultural economics, until recently such systems have only
been used to a limited extent (Moxey, 1996). However, whenever there are economic
issues with a spatial dimension (e.g. changing patterns of land use, policy measures
which are area-sensitive), then the ability to overlay and integrate spatial data
(relating, say, to land characteristics) with economic data (which might relate to the
farm business), means that a GIS provides the opportunity for much greater realism,
comprehensiveness and relevance in modelling. The present analysis adopts such
an approach in order to generate estimates of farm-gate and shadow values of
agricultural output which could then be used, inter alia, to model changing patterns
of land use.
Modelling opportunity cost: agricultural output values 229

Following a review of the literature (Bateman, 1996), it was decided to make
an analysis of farm pro¬tability the basis of our modelling methodology. This
is a common approach (e.g. Chambers and Pope, 1994) and accords with that
adopted by the UK study which most closely resembles the present research, namely
the NERC/ESRC Land Use Modelling Programme (NELUP) at the University of
Newcastle upon Tyne (O™Callaghan, 1995, 1996).8 Both the present and NELUP
studies use a GIS to integrate the physical environment into an analysis of farm
pro¬tability (Moxey and Allanson, 1994; Watson and Wadsworth, 1996; Moxey
and White, 1998). However, unlike our own study, the NELUP model did not have
access to individual farm-level data (discussed below) but instead depended upon
aggregated, parish-level, agricultural census information collected by the Farm
Business Survey (Allanson et al., 1992).9 This is a substantial drawback as it limits
the scope for using the capabilities of a GIS to relate the input-output situation of
a particular farm to the characteristics of its biophysical environment.
The analytical framework which we present in this chapter was developed it-
eratively as a result of empirical investigation. An initial single model attempting
to relate farm income measures to a variety of input intensity measures (e.g. live-
stock per hectare), environmental factors (e.g. soil type) and what we refer to as
modi¬cation variables (e.g. fertiliser per hectare), proved to be overly simplistic
for two reasons.10 First, farm output decisions, and hence incomes, are subject to
institutional rules (most noticeably, in the study area, whether or not a given farm
holds a milk quota) to the extent that farms cannot be considered a homogeneous
group. Second, investigations indicated that, even within a homogeneous subgroup
of farms, a single model did not adequately describe a farmer™s decision process with
regard to how the farm environment in¬‚uences input and output decision-making
and hence income (Bateman and Lovett, 1992).
In order to address the ¬rst of these issues, farms were classi¬ed into broadly
homogeneous groups or sectors (using a cluster analysis described subsequently)
within which policy constraints were similar. The second issue was tackled through
a two-stage modelling procedure: in stage 1, income values were determined
by the array and intensity of inputs utilised; while in stage 2, the inputs em-
ployed were dependent on the prevailing biophysical characteristics and possi-
ble modi¬cations of those characteristics. Cross-section regression analysis was
then used to estimate the parameters of the stage 1 and stage two relationships
within each sector. The stage 1 pro¬t“input relationship within each sector was

8 An alternative, linear programming approach is the Land Use Allocation Model described by Jones et al.
9 Note, however, that a small farm-level study of ten farms has been conducted under the NELUP programme
(Oglethorpe and O™Callaghan, 1995).
10 The single equation approach was also hampered by multicollinearity between input and biophysical variables
(Bateman and Lovett, 1992). Our multistage approach to addressing multicollinearity owes much to Smith and
Desvousges (1986).
230 Applied Environmental Economics

speci¬ed as:
πi j f j (I1i j , I2i j , . . . , I pi j , . . . , Iki j ) (8.1)
πi j is the pro¬t level of the ith farm (i 1, . . . , n) in the jth sector ( j 1, . . . , m)
1, . . . , k) on the ith farm in the jth
I pi j is the intensity of use of the pth input ( p


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