. 8
( 11)


The stage 2 input“biophysical environment relationship for each input in each sector
was speci¬ed as:
g pj (B1i j , B2i j , . . . , Bhi j , . . . , Bzi j , M1i j , M2i j , . . . , Mri j , . . . , Mvi j )
I pi j
1, . . . , z) on the ith farm in
Bhi j is the level of the hth biophysical variable (h
the jth sector
1, . . . , v) on
Mhi j is the level of the r th biophysical modi¬cation variable (r
the ith farm in the jth sector
The biophysical variables were stored on a grid cell (raster) basis within the GIS
for the entire extent of the study area (see the discussion of data below). Therefore,
by holding the modi¬cation variables at appropriate levels for the farm sector
under consideration, we could use the regression parameters of Equation (8.2) to
produce maps of predicted levels for all inputs for that sector. Subsequently a map
of predicted income for the study area could be derived by applying the regression
parameters of Equation (8.1) to the maps of predicted input levels.
The approach taken characterises farm decision-making as a process in which
the farmer ¬rst considers the institutional rules and constraints within which the
farm must operate,11 then assesses the physical environment of the farm and the
extent to which it may be modi¬ed (as described in Equation (8.2)), and ¬nally,
decides the type and level of inputs to use which in turn determine outputs and farm
pro¬tability (as per Equation (8.1)). We recognise and fully acknowledge the fact
that, from a sociological perspective, such a model remains na¨ve. In particular,
the writings of the Wageningen school (R¨ ling, 1993, 1994; van der Ploeg, 1993)
show that many economic models of farm decision-making omit consideration of
factors such as a farmer™s mind-set, intrinsic knowledge base, personal and social
experience, risk aversion (and its interaction with the former factors), access to and
quality of the local community knowledge base, etc. These are important in¬‚uences
which we do not deny and recognise as a limitation of our model.
11 One further fundamental constraint is the dif¬culty for the farmer of moving from one farm to another. Often
the farmer may face insurmountable problems in undertaking such a change.
Modelling opportunity cost: agricultural output values 231

The data
The models outlined above require individual farm-level data on both biophysical
characteristics and the variety of input, output and related variables which de¬ne a
farm. The Farm Business Survey of Wales (FBSW) provided the necessary farm-
level cost and revenue data, while biophysical characteristics were taken from the
LandIS database compiled by the Soil Survey and Land Research Centre (SSLRC,
Cran¬eld) and other sources. These data are brie¬‚y reviewed below.
During the 1989/90 study period the FBSW interviewed and obtained full ac-
counts data for a representative sample of 571 farms across Wales.12 Farms were
geographically referenced according to the location of the farmhouse and for the
purposes of this analysis these points were used to assign each farm to a 1 km
grid square. Access to the full FBSW dataset was permitted, although interviews
with surveyors, who had visited each of the farms concerned, showed that many of
the farms in the dataset were unsuitable for inclusion in the present study because
either the farmhouse was not located on the land managed or the farm itself covered
a diversity of environments, e.g. both lowland and upland areas affording winter
shelter and summer grazing. Retention of such farms within the sample risked
confounding the relation between farm performance and biophysical characteris-
tics, which would have negated the fundamental research objective of producing
models of the output value of a given area of land under a speci¬ed usage.13 Such
mixed environment farms were therefore excluded along with those with large non-
agricultural incomes, leaving a ¬nal sample of 240 farms. The FBSW dataset is
based upon full details of the annual accounts of the sample (which by law have to
be surrendered, on demand, to the FBSW). It is consequently a highly detailed and
rich dataset. Table 8.2 illustrates this by reproducing the annual record sheet for
one particular farm, in this case a typical dairy enterprise (to preserve anonymity
the grid reference has been changed, as have farm size details, and all ¬nancial
particulars have been erased). Individual farm details for each of the items listed in
Table 8.2 were made available. As can be seen, the level of information afforded
by the data is very considerable.
As discussed in Chapter 6, the SSLRC Land Information System (LandIS) was
compiled for the Ministry of Agriculture, Fisheries and Food to facilitate ˜land use
planning and national resource use™ (Rudeforth et al., 1984). It represents the most
comprehensive and detailed source of information on the biophysical characteristics
of land across England and Wales. LandIS includes long-term averages for a variety
of agroclimatic variables at a 5 km grid cell resolution. A summary of the variables
12 This is a routine, annual survey which typically interviews samples of this size. Farms are legally obliged to
join the sample when selected.
13 Note that the exclusion of such farms means that our models are not designed for predicting the incomes of
farms which straddle differing environments. However, as made clear here, our objective is to value differing
land uses in differing locations, rather than farms per se.
Table 8.2. FBSW annual farm account data: example of a typical farm record
Farm type: Specialist Dairy Business size group: 24“39.9 BSU Farm number: 12345
Location (OS grid ref.): Easting 2170; Northing 3010
Farm area (excluding common grazing):
actual hectares 69.78 Size of business (BSU) : 36.98
effective hectares 65.56 Year ending: 31 March 1990

r milk r purchased concentrates
Dairy Feed
r cattle r home-grown concentrates
r net milk quota3 r purchase bulk feed
r valuation change Tack and stock keep
r cattle
Other cattle Veterinary & medicines
r valuation change Other livestock costs4
r wool r purchased
Sheep Seeds
r sheep r home-grown
r valuation change Fertilisers
r pigs Other crop costs5
r valuation change r regular
Paid labour6
r eggs r casual
r poultry r contract work
r valuation change r repairs
r livestock r fuels
Other livestock
r valuation change General farm costs7
r main crops
Crops Land expenses
r by-products,
forage & cults

r cattle
Subsidies & grants Rent & rates
r sheep
r miscellaneous
FARM OUTPUT + Subsidies & grants

r bene¬t value
Notional outputs Notional inputs
r of farm houses
Machinery depreciation
+ Notional outputs + Machinery depreciation

Net farm income Milk yield per cow (litres)
less value of manual labour Milk sales per cow (by value)
of farmer & spouse Lambs reared per ewe (no.)
Modelling opportunity cost: agricultural output values 233

Table 8.2. (cont.)
Fat lamb sales per ewe (no.)10
Investment income
plus value of managerial Return on tenant™s capital (%)
Standard man-day availability11
input of paid managers
Standard man-day requirement11
Management & investment income
r cereals
Livestock Tillage
r roots & fodder
r hay
Crops Grassland
r silage
r pasture
Total tenant™s capital
Fallow & land let
r sole
Rough grazing
Woods, roads & buildings
Total area
r common
Rough grazing
Bare land and forage hired

Opening Closing Average
LIVESTOCK number value number

Dairy cattle
Other cattle
Other livestock
Total livestock

Outputs include any produce given to workers and consumed or used on the farm. Outputs of
livestock are given net of any purchases made. Output includes valuation changes which are detailed
in the section headed ˜Livestock™. Milk output includes quota transactions and any superlevies paid
have been deducted.
Inputs include stock changes as well as purchases made during the year.
Net milk quota comprises quota compensation payments, payments for quota ˜leased in™ and
˜leased out™, and superlevy payments where applicable.
Other livestock costs include purchased bedding materials and other costs incurred speci¬cally for
livestock enterprises.
Other crop costs include crop protection chemicals and other costs incurred speci¬cally for crop
enterprises and forage.
Labour costs include cash wages and salaries, other employer™s expenses and the value of
General farm costs include electricity, water and telephone charges, licences, insurances,
subscriptions, etc.
Miscellaneous output includes contract work, farm cottage rents and pro¬t on resale of purchased
agricultural produce.
Amount of which is BLSA also speci¬ed in FBSW records (BLSA = breeding livestock stock

appreciation, i.e. that part of livestock valuation changes relating to the breeding ˜stock on the farm™;
details are given in the section headed ˜Livestock™).
On some farms, fat lamb sales per ewe will include fat lambs from the previous year™s lamb crop.
Standard man-day availability is the number of eight-hour ˜man-days™ used on the farm during
the year. Standard man-day requirement is the number of eight-hour ˜man-days™ conventionally
regarded as necessary to maintain the farm™s enterprises during the year.
Source: FBSW (1990).
234 Applied Environmental Economics

Table 8.3. Agroclimatic variables obtained from LandIS

Variable name Label De¬nition
Accumulated Acctemp Average annual accumulated temperature
above 0o C (in o C)
Accumulated rainfall Rainfall Average annual accumulated rainfall (in mm)
Field capacity Fcapdays Average annual number of days where the soil
experiences a zero moisture de¬cit (in days)
Return to ¬eld capacity Retmed Median measure from a distribution of the
number of days between the date on which a
soil returns to ¬eld capacity and 31 Dec. of
that year (in days)
Retwet The upper quartile of the above distribution;
a measure of return to ¬eld capacity in wet
years (in days)
Retdry The lower quartile of the above distribution;
a measure of return to ¬eld capacity in dry
years (in days)
End of ¬eld capacity Endmed Median measure from a distribution of the
number of days between 31 Dec. and the
subsequent date on which ¬eld capacity ends
(in days)
Endwet The upper quartile of the above distribution; a
measure of the end of ¬eld capacity in wet
years (in days)
Enddry The lower quartile of the above distribution; a
measure of the end of ¬eld capacity in dry
years (in days)
Available water Avwatgra Soil water available for a grass crop after
allowing for gravity-induced drainage; the
difference between water content at ¬eld
capacity and at permanent wilting point
adjusted for grass rooting model (in mm)
Avwatcer As Avwatgra but adjusted for a cereal crop
(in mm)
Avwatpot As Avwatgra but adjusted for potatoes (in mm)
Avwatsb As Avwatgra but adjusted for sugarbeet (in mm)
Moisture de¬cit Mdefgra Difference between rainfall and the potential
evapotranspiration of a grass crop (in mm)
Mdefcer As Mdefgra but adjusted for a cereal crop
(in mm)
Mdefsbpt As Mdefgra but adjusted for a sugarbeet/potatoes
crop (in mm)
Workability Workabil A seven-point ordinal scale indicating the
suitability of the land for heavy machinery
work in spring and autumn (ordinal scale)
Spring machinery SprMWD Average number of days between 1 Jan. and
working days 30 Apr. when land can be worked by
machinery without soil damage (in days)
Modelling opportunity cost: agricultural output values 235

Table 8.3. (cont.)

Variable name Label De¬nition
Autumn machinery AutMWD The average number of days between 1 Sept. and
working days 31 Dec. when land can be worked by machinery
without soil damage (in days)
Lowland relief Lowrelif Lowland topographic relief denoted as regions 4, 5
region1 and 6 in Rudeforth et al. (1984) (dummy variable)
Soil type2 SoilX SSLRC soil type classi¬cation code (various
dummy variables for differing soils “ speci¬ed in
notes to regression models)

Note: All the variables listed are continuous unless speci¬ed otherwise. For further
information on de¬nitions and measurement, see Jones and Thomasson (1985) or Bateman
(1996), except for: 1 from Rudeforth et al. (1984: p.19); and 2 from Soil Survey of England
and Wales (1983) as recategorised by Bateman (1996) and Bateman and Lovett (1998).
Some variables were transformed (e.g. by taking natural logarithms) prior to regression
analysis; all such transformations are detailed in notes to regression models.

selected for use in this study is given in Table 8.3 (some of which were also discussed
in Chapter 6). Further details regarding the compilation of the agroclimatic database
and the geostatistical procedures used to interpolate measurements onto a 5 km
resolution grid are given by Jones and Thomasson (1985), Ragg et al. (1988),
Hallett et al. (1996) and at the SSLRC website.14
To supplement the characteristics extracted from LandIS, measures of elevation
and associated variables were generated from the Bartholomew 1:250,000 digital
map database for the UK. Contours and spot heights were processed within the GIS
to produce a digital elevation model (DEM) of Wales and estimates of elevation,
slope angle and aspect were then calculated at a 500 m resolution and subsequently
averaged to provide values for 1 km grid cells across the study area.
Integrating the farm and biophysical variables involved linking databases of
varying resolutions. The approach taken was akin to a point-in-polygon method
(Burrough and McDonnell, 1998) with the grid reference of each farmhouse being
used to select values from the 1 km resolution grids of topographic variables and
the 5 km cells of the LandIS agroclimatic measures. Characterisation of the bio-
physical environment facing each farm business was therefore a little generalised,
but thought to be appropriate given the nature of the data sources available and the
size of the study area. It also should be emphasised that the geographical matching
of farm and environmental variables in this study is considerably more mean-
ingful than in previous research reliant on agricultural census data aggregated to
14 See www.silsoe.cran¬eld.ac.uk/sslrc/services/dataproducts/landis.htm. Harrison et al. (1991) provide an early
examination of the use of GIS in the analysis of countryside data.
236 Applied Environmental Economics

Table 8.4. Farm cluster characteristics: average income and mean percentage of
total revenue from speci¬ed activities in each cluster of farms

Mean percentage of total annual revenue from each activity
No. of income Other
Cluster farms (£/ha p.a.) Milk Cattle Sheep livestock Crops Misc.
1 86 83 0.4 29.7 64.4 0.1 3.4 0.5
2 107 509 77.8 11.1 7.1 0.5 2.4 0.3
3 29 47 1.8 63.9 28.3 0.5 1.9 0.6
4 10 223 17.2 27.7 39.5 0.4 0.8 13.5
5 2 1,145 0.0 18.2 7.8 74.6 1.1 0.1
6 6 58 5.1 20.1 14.3 0.9 56.6 1.2
All 240 283 35.9 25.1 31.7 1.0 4.1 0.9

Farm sectors and farm income
Initial investigations revealed some substantial contrasts between different groups
of farms, most noticeably in terms of principal activity and resultant income levels
(Bateman and Lovett, 1992). Ignoring this issue could have led to the underes-
timation of standard errors and exaggeration of the degree of explanation of any
single model applied across all farms. Rather than adopt ad hoc rules for sectoral
de¬nition, a two-stage classi¬cation process was implemented. Firstly, a principal
components analysis (Norusis, 1985) was undertaken using farm-level data con-
cerning the proportion of total revenue derived from each of six groups of output
activities. Farms were subsequently grouped on the basis of their scores on the
six components using a hierarchical agglomerative technique based on the Ward
error sum of squares (ESS) statistic (Ward, 1963). Scrutiny of the output of this
analysis (particularly the ESS increments in the agglomeration schedule) suggested
that a six-cluster solution was the most appropriate.15 Table 8.4 lists activity and
income-level statistics for each cluster.
It was decided that sample sizes were insuf¬cient to justify further analysis of
clusters 3 to 6. This left the two principal agricultural sectors for Wales: farms in
cluster 1 specialised in sheep production with substantial production of beef cat-
tle (hereafter referred to as ˜sheep farms™); while farms in cluster 2 specialised
in dairying (hereafter referred to as ˜milk farms™). As a ¬nal test of sectoral
homogeneity, standard diagnostic tests for outliers were employed (Minitab, 1992).
This identi¬ed one outlier in cluster 1 and three in cluster 2 and these farms were
15 Note that these are reasonably similar to those de¬ned by the FBSW. However, unlike the latter, they do not
further subdivide farms according to their size as this may be (and subsequently proved to be) a signi¬cant
determinant of per hectare farm income.
Modelling opportunity cost: agricultural output values 237

omitted to leave a ¬nal sample of 85 sheep farms and 104 milk farms. The most
striking difference between these two clusters was a wide disparity in income lev-
els with mean net income per hectare on milk farms being nearly six times that on
sheep farms.
An issue which proved more complex than expected was the de¬nition of appro-
priate measures of what the farmer perceives as his/her annual net income (which
we term farm-gate income, FGI) and of the shadow value equivalent of this (note
that to permit comparability between farms of differing size all values referred to
subsequently are adjusted to a per effective hectare basis16 ). An immediately ap-
pealing measure in the FBSW dataset is the ˜net farm income™ (NFI) variable.17
However, following initial investigation (Bateman and Lovett, 1992) this variable
was found to be unsuitable for general modelling requirements because, while its
output value minus input value part (denoted ˜farm surplus™ in FBSW publications)
is, as expected, positively correlated with the quality of the biophysical farm envi-
ronment (the variables B1i j , B2i j , . . . , Bhi j , . . . , Bzi j in Equation (8.2)), for sheep
farms the opposite relationship occurs with respect to the ˜subsidies and grants™
constituent of NFI.18 This tends to suppress the link between environmental ad-
versity and overall income level which is a substantial focus of interest in this
The de¬nition of the correct measure of farm income is inherently problematic
and is itself the subject of research (Sturgess, 1996). Following conversations with
Tim Jenkins (FBSW Director, Aberystwyth) it was decided to base statistical in-
vestigations of agricultural value upon the farm surplus variable with subsequent
adjustments of predicted values to estimate FGI. An appropriate de¬nition was
agreed with FBSW:
farm surplus + (subsidies and grants ’ rent and rates ’ depreciation)
To obtain FGI requires an estimate of (.) in Equation (8.3). Actual observations on
(.) can be used to de¬ne an adjustment variable, ADJFGI, which is the absolute
difference (in £/ha) between FGI and farm surplus. This variable was de¬ned for
both the sheep and milk sectors (producing variables ADJFGIS and ADJFGIM
respectively). ADJFGIS was generally positive and found to vary according to the

16 This adjustment was at the individual farm level using FBSW data on effective farm area (the latter omits land
under roads, buildings, etc.). This applies to all regression models and results reported subsequently.
17 For precise de¬nition of this and subsequent FBSW terms, see FBSW (1990).
18 This is in itself interesting as it shows that, at least on sheep farms, subsidies and grants do compensate
for environmental adversity. Further complexity arises because the unpaid labour element of NFI is positively
correlated with such adversity, i.e. farmers attempt to combat poor physical environments by devoting relatively
more labour to the farm.
238 Applied Environmental Economics

biophysical environment (increasing with environmental adversity); accordingly a
simple regression model was used to predict its value.19 In contrast, a simple ¬‚at
rate of £95 was found to be adequate for ADJFGIM.
The farm-gate price received by farmers for their produce tells us the ¬nancial
value (to farmers) of that output but it does not necessarily correspond to the wider
social value of that output. In order to move closer to the latter we adjust for the
following ¬ve factors.
(i) Market price support. The Organisation for Economic Co-operation and De-
velopment produces annual estimates both of the value of output and the value of
market price support disaggregated for all major farm products in each member-
nation (OECD, 1992). Using this information, a rate of market price support can
be calculated and subtracted from the market price of the goods concerned.
(ii) Direct subsidies and grants. OECD (1992) also gives values for the amount of
direct subsidies and grants paid to farmers. However, unlike our market price support
calculation, such a rate of support cannot be said to be a reasonable approximation
of the direct payments received by each farm. Fortunately, the FBSW data supplied
for this research details individual farm direct subsidies and grants disaggregated
under three headings: cattle, sheep, and miscellaneous. Consequently, individual
payments can be directly subtracted from the total output value of each farm.
(iii) Input subsidies. Rates of input subsidy for each output heading were calcu-
lated from data given in OECD (1992). Ideally we would wish to allocate costs to
individual outputs and remove input subsidies from these different cost portions.
However, given that the same inputs are used on a variety of outputs, such an al-
location of costs was not possible. An alternative approach is to calculate input
subsidy values for each output by applying relevant input subsidy rates to the value
of each output. These can then be added to total input costs.
(iv) Levies. These are in effect negative market price supports and can be treated
in the same manner. Whereas adjusting for market price support will lower shadow
value (with respect to market price), adjusting for levies (where applicable) will
reverse the direction of movement (although the value of levies is invariably far
below that of market price support).
(v) Impacts of the above upon world price levels. The policy instruments above
have had a considerable and depressing impact upon world market prices for agri-
cultural produce which needs to be considered in our shadow pricing exercise
(Rosenblatt et al., 1988). Roningen and Dixit (1989) provide estimates of the rates
of world price increase of various farm products resulting from a general liberali-
sation of agricultural policy as implied by adjusting for the above instruments.20
19 See Bateman (1996) and subsequent discussion of Table 8.4.
20 Taken from Roningen and Dixit (1989: p. 16, table 5). The trade liberalisation adjustment attempts to remove
the distortions inherent in actual world prices stemming from policy intervention in the agricultural sectors of
the main developed countries in the late 1980s.
Modelling opportunity cost: agricultural output values 239

The resulting shadow value (SV) is not the full social value of agricultural output
as we ignore non-market externalities. However, such a value is more compati-
ble with cost-bene¬t analysis than are the farm-gate-based FGI values discussed
previously. The SV corresponding to farm surplus was calculated by adjusting the
recorded ¬nancial values of outputs and inputs to estimated world price equivalents
for the sample year. Two steps were involved in this calculation. First, output values
were adjusted for market price support and co-responsibility levies and input values
were adjusted for input subsidies.21 Second, the adjusted output value for each farm
product was multiplied by a trade liberalisation coef¬cient which attempted to cap-
ture the effect of multilateral agricultural trade liberalisation on the world price of
that product. For ease of computation a combined shadow value adjustment factor
for sheep and milk farms (SVadjs and SVadjm) allowing for all of these elements
was calculated. Results from this analysis indicate that the SV of output was around
55 per cent of farm surplus for the milk farms, a ¬gure that rose to about 60 per cent
for the sheep farms in our sample.
We have now established de¬nitions whereby we can identify both FGI and SV.
Both of these are derived from farm surplus which we now de¬ne as πi j in Equation
(8.1). One set of Equations (8.1) and (8.2) is estimated for each of the two farm
sectors under consideration.

Modelling farm surplus
Regression analysis proceeded in line with the principles described by Lewis-Beck
(1980), particular attention being paid to problems of multicollinearity. Referring
back to the modelling terminology de¬ned earlier, we ¬rst estimated the stage 1
value function (Equation (8.1)) which de¬nes the input“pro¬t relationship. This
identi¬ed the explanatory input variables which were best able to predict farm
surplus and which subsequently formed the dependent variables in the stage 2
equation set (Equation (8.2)) which de¬ned the input“biophysical environment
The dataset was extensively investigated with a variety of speci¬cations and
functional forms being tested. Table 8.5 reports the best-¬tting stage 1 model of
farm surplus per effective hectare for the sample of sheep farms and milk farms.
Given their cross-sectional nature, both models have a relatively high degree
of explanatory power.22 Examining the model for sheep farms we can see that
farm surplus increases with livestock intensity ($live/eh), with the ef¬ciency of that

21 All adjustments made were based on data from OECD (1992); further details are given in Bateman (1996).
22 There is debate as to what is an acceptable value for adj. R2 in cross-sectional studies. Hanley (1990) recommends
a value of 0.2 while Mitchell and Carson (1989) suggest 0.15. The current study relies primarily on the former,
more demanding, rule. Note also that the F ratio is signi¬cant in all cases and the null hypothesis of zero
coef¬cient of determination is rejected at 1 per cent signi¬cance for all our results.
240 Applied Environmental Economics

Table 8.5. Best-¬tting stage 1 models of farm surplus/ha on sheep
(cluster 1) and milk (cluster 2) farms

Farm surplus/ha for sheep farms Farm surplus/ha for milk farms
constant constant 4.80
(’3.35) (0.05)
lambs/ewe 180.87 $live/eh 0.467
(4.97) (7.38)
’3, 543.2
$live/eh 0.151 gShep%TO
(3.95) (’5.13)
$f&sLab/h 0.010 genC/h 1.680
(2.91) (2.75)
grants% $mlk/cow 0.241
(’2.15) (2.67)
R2 (adj.) 0.62 0.67
n 85 104

lambs/ewe = no. of lambs reared per ewe per annum (ef¬ciency measure)
$live/eh = value of livestock per effective hectare (input intensity)
$f&sLab/h = notional value of farmer and spouse labour input per hectare
(input measure)
grants% = total subsidies and grants (direct payments) expressed as a proportion
of total farm revenue (grant dependency measure)
gShep%TO = sheep grants expressed as a proportion of farm total output value
(grant dependency measure)
genC/h = general farm costs (electricity, water and telephone charges, licences,
insurances, subscriptions, etc.) per hectare (input intensity)
$mlk/cow = the value of milk produced per cow (ef¬ciency measure)
pLab/h = value of paid labour per hectare (ef¬ciency measure)
catt%FR = value of cattle output expressed as a proportion of total farm revenue
(enforced diversity measure)
Figures in brackets are t-statistics.

livestock (lamb/ewe) and with the amount of labour a farmer and/or spouse de-
votes to the farm ($f&sLab/h). However, increased revenue dependency upon
direct payments (grants%) is synonymous with relatively lower levels of farm
The stage 1 model for milk farms performs even better than that for sheep farms,
achieving a very satisfactory degree of explanation given that this is a cross-sectional
analysis. As before we ¬nd positive relationships between farm surplus and input
intensity ($live/eh, genC/h). Similarly, farm ef¬ciency is a clear determinant of farm
Modelling opportunity cost: agricultural output values 241

surplus, which increases with the value of milk produced per cow ($mlk/cow)23
and falls as more paid labour is required per hectare (pLab/h). Finally, we have
two variables showing that where milk farms have to rely increasingly upon lower
margin, non-core activities such as sheep and cattle (gShep%TO, catt%FR) so farm
surplus values tend to decline.
The second stage of the modelling process entails the estimation of predictive
models for each of the stage 1 explanatory variables for both types of farm. Thus,
stage 2 models are concerned with predicting the relationship between biophysical
characteristics and agricultural inputs. Table 8.6 presents the results of the stage 2
models for sheep farms.
Given their cross-sectional nature, the models have reasonable explanatory
power, with the possible exception of the model for labour inputs. Inspection of the
lamb/ewe model shows that the value of this input ef¬ciency measure is lower for
soils prone to waterlogging (lnFCdays), but improves where modi¬cation leads to
better forage availability (Silag%, $crop/h). Consideration of these variables raises
a problem regarding how they should be treated when using the model to predict
lamb/ewe for the entire study area. We have full coverage for all of the biophys-
ical variables (i.e. a raster layer for lnFCdays can readily be created within the
GIS) but the same is not true of the modi¬cation variables. A typical approach to
such problems is to hold such variables at defensible constant values.24 An analy-
sis of the distribution of both modi¬cation variables showed them to be somewhat
skewed and so, for the purposes of prediction, both were held at their median values
($crop/h = 19.50; Silag% = 0.145).
Livestock intensity ($live/eh) is well predicted by the next model, being neg-
atively related to increased susceptibility to waterlogging (lnFCdays) and posi-
tively related to improved access to the land (SprMWDSq) and forage availability
(Silag%), the latter being treated as before in generating predictions of $live/eh.
The third model shows farmer and spouse labour input rising in more waterlogged
areas (Endwet) and following a negative quadratic with respect to accessibility
(SprMWD, SprMWDSq), suggesting that as accessibility declines so does labour
input but at a declining rate indicative of some minimum level below which labour
input will not fall. However, the strongest relationship is with farm size, with small
farms exhibiting signi¬cantly higher levels of farmer and spouse labour input. Again
for predictive purposes this variable was held at its median value (<140eh = 1).
The ¬nal stage 2 equation for sheep farms predicts the proportion of total farm
revenue derived from subsidies and grants (grants%). Here the dependent vari-
able is purely predicted by biophysical variables which provide a good degree of
explanation. As discussed previously, sheep farm grants are a function of environ-
mental adversity, in this case modelled by increased waterlogging and slope.
23 This is analogous to the lamb/ewe variable in the stage 1 model for sheep farms.
24 See, for example, Garrod and Willis (1992a).
242 Applied Environmental Economics

Table 8.6. Best-¬tting stage 2 models for sheep farms

Dependent variable
Predictor lambs/ewe $live/eh $f&sLab/h grants%
’791.0 ’1.292
Constant 3.510 2, 711.9
(5.99) (4.38) (’0.29) (’4.94)
’0.452 ’410.0
lnFCdays ” 0.272
(’4.30) (’3.70) (5.70)
SprMWD ” ” ”
SprMWDSq ” 1.421 78.59 ”
(2.44) (3.27)
Endwet ” ” 37.86 ”
lnSlope ” ” ” 0.032
Silag% 0.59 1, 035.8 ” ”
(3.16) (6.14)
$crop/h 0.001 ” ” ”
<140eh ” ” 2, 191.4 ”

R2 (adj.) 0.37 0.45 0.25 0.39
n 85 85 85 85

Biophysical variables:
lnFCdays = natural log of the number of days per annum for which soil is at ¬eld capacity
SprMWD = number of spring machinery working days
SprMWDSq = square of number of spring machinery working days
Endwet = the end of ¬eld capacity period as measured in ˜wet™ years
lnSlope = natural log of mean farm slope angle
Modi¬cation variables:
Silag% = proportion of farm area put to silage
$crop/h = value of crops per hectare
<140eh = dummy for smaller farms (less than 140 effective hectares)
Figures in brackets are t-statistics.

Table 8.7 presents the stage 2 models for milk farms. The model for predict-
ing livestock intensity ($live/eh) on milk farms ¬ts the cross-sectional data well.
Livestock intensity declines in areas of higher waterlogging risk (lnEwet) and rises
in areas considered suitable for delicate crops (lnAWpot). There is also a positive
general association with lowland relief areas (Lowrelif). Farmers can also im-
prove the ability of the farm environment to support livestock both directly through
the fertilisers (Fert/h) and indirectly through inputs of concentrates (pConc/h). As
Modelling opportunity cost: agricultural output values 243

with our sheep models, for predictive purposes data on the biophysical variables
(here lnEwet, lnAWpot and Lowrelif) are available for the entire study area. How-
ever, as before, we hold the modi¬cation variables (here Fert/h and pConc/h) at
representative constant values. In the livestock intensity model both modi¬cation
variables exhibit a slightly skewed distribution and so are held at their median
values (pConc/h = 241.2; Fert/h = 88.36).
In the model predicting the proportion of farm total output value derived from
direct payments for sheep (gShep%TO), the dependent variable exhibits a quadratic
relationship with the waterlogging measure (Enddry), falling at a declining rate as
the end of ¬eld capacity period increases. This model is relatively weak compared
to previous stage 2 models. Nevertheless it does satisfy our theoretical validity
criteria (R2 (adj.) > 0.2). However, this is not true of the next model which predicts
the general farm costs per hectare input intensity measure (genC/h) and accordingly
we have grounds for doubting the validity of using such a model to predict the value
of this input in the stage 1 model for milk farms. However, inspection of genC/h
showed it to be reasonably normally distributed across farms and so it was decided
to hold it at its mean value (85.23) in the stage 1 equation.25 This is clearly not ideal
but it is a recognised and unbiased way of addressing such a problem.
The explanatory power of the best-¬tting model for the input ef¬ciency measure
$mlk/cow (the value of milk produced per cow) for our milk farm sample is rather
better, although a collinearity problem between the two variables AWcerSq and
SprMWD (both of which are related to soil moisture) makes their interpretation
problematic. Nevertheless, these variables were retained on the grounds that they
substantially improved prediction of the dependent variable, which is the prime
purpose of the stage 2 models. Other variables are more straightforward to interpret.
Soil classes 2 and 3 refer to some of the best (brown earth) soils found in the study
area26 while the variable Lowrelif indicates lowland areas. As expected both are
positively related to milk yields as is a higher level of concentrate usage (pConc/h).27
Interestingly, and in contrast to sheep farms, higher levels of labour input on milk
farms seem to be an indicator of inef¬ciency and consequent lower yields. This
seems reasonable and is backed up by the negative sign on paid labour input in
the stage 1 milk farm model. It seems that whereas low income levels mean that
sheep farmers have no option but to devote additional unpaid labour to their farms,
milk farms are generally operating at a much higher level of ef¬ciency where pro¬t
maximisation can often be enhanced through cost reductions.
As before, the modi¬cation variables are held as constants when the stage 2
models are used for predictive purposes. Here both f&sLab/h and pConc/h were
25 So in the stage 1 model we multiply the coef¬cient on genC/h by the mean value of the variable, i.e. 1.680 *
85.23 = 144.7.
26 27 Tests revealed no signi¬cant multicollinearity problem.
See Bateman (1996) for further details.
244 Applied Environmental Economics

Table 8.7. Best-¬tting stage 2 models for milk farms

Dependent variable
Predictor $live/eh gShep%TO genC/h $mlk/cow pLab/h catt%FR
Constant 468.0 0.1279 44.19 481.0 227.30 0.092
(0.28) (1.93) (3.47) (4.49) (2.65) (7.31)
lnEwet ” ” ” ” ”
lnAWpot 804.6 ” ” ” ” ”
Lowrelif 140.24 ” ” 84.10 ” ”
(2.05) (2.29)
Enddry ” ” ” ” ”
EnddrySq ” 0.00001 ” ” 0.032 ”
(3.06) (3.03)
AWgrSq ” ” 0.002 ” ” ”
AWcerSq ” ” ” 0.016 ” ”
SprMWD ” ” ” ” ”
soil2&3 ” ” ” 152.25 ” ”
RainSq ” ” ” ” ”
MdefCerl ” ” ” ” ”
Grazseas ” ” ” ” 1.0426 ”
ElevSq ” ” ” ” ”
lnSlope ” ” ” ” ”
sinAsp ” ” ” ” ”
pConc/h 0.743 ” ” 0.336 ” ”
(4.79) (4.03)
Fert/h 2.296 ” ” ” ” ”
’0.376 ’0.147
f&sLab/h ” ” 0.081 ”
(4.39) (’4.43) (’2.96)
Modelling opportunity cost: agricultural output values 245

Table 8.7. (cont.)

Dependent variable
Predictor $live/eh gShep%TO genC/h $mlk/cow pLab/h catt%FR
ehaHay ” ” ” ” ” 0.008
R2 (adj.) 0.44 0.24 0.20 0.29 0.27 0.16
n 104 104 104 104 104 104

Biophysical variables:
lnEwet = natural log of the end of ¬eld capacity period as measured in ˜wet™ years
lnAWpot = natural log of available water, measured for potato crop
Lowrelif = farm in SSLRC relief regions 4, 5 or 6 (lowland)
Enddry = end of ¬eld capacity period as measured in ˜dry™ years
EnddrySq = Enddry * Enddry
AWgrSq = square of water availability for grass crop
AWcerSq = square of water availability for cereals
SprMWD = spring machinery working days
soil2&3 = farm located on soil types 2 (brown earths) and/or 3 (podzols)
RainSq = square of the average rainfall (mm per annum) on farm
MdefCerl = soil moisture de¬cit for cereals
Grazseas = length of grazing season (days per annum)
ElevSq = square of farm elevation (m) above sea level
lnSlope = natural logarithm of average slope on farm
sinAsp = sine of aspect
Modi¬cation variables:
pConc/h = value of purchased concentrates per hectare.
Fert/h = value of fertiliser per hectare
f&sLab/h = notional value of farmer and spouse labour input per hectare
ehaHay = effective hectares of farm put to hay
Figures in brackets are t-statistics.

found to have somewhat skewed distributions and so were held at median values
of 135.6 and 241.2 respectively.
The next model considers another input ef¬ciency measure, namely the value of
paid labour per hectare on milk farms (pLab/h). Analysis of this model shows that
the level of paid labour employed on farms is lower in areas of relative environmental
adversity (indicated by high values of the RainSq, MdefCerl and ElevSq variables)
and higher in areas were the environment is more benign (high values for Grazseas
and EnddrySq). It is perhaps not surprising to ¬nd that the amount of paid labour
on farms is inversely related to the farmer and spouse labour input, suggesting that
as a farmer™s income increases so he/she substitutes paid labour for personal effort.
For predictive purposes f&sLab/h is again held at its median value.
246 Applied Environmental Economics

Finally the last stage 2 model is concerned with predicting catt%FR, an indicator
of a particular, lower margin, non-core activity on our milk farms. This model fails
our criterion of theoretical validity. However, catt%FR was approximately normally
distributed and was consequently set to its mean value (0.1107) for predictive
purposes within the stage 1 equation for milk farms.28
The various stage 1 and stage 2 models provide empirical estimates of the rela-
tionship between the biophysical environment, levels of inputs and resultant output
values on our sheep and milk farms. These estimates can now be applied to the
prediction of FGI and SV for both sectors across the entirety of the study area,
thereby yielding vital information concerning the potential for land use change and
policy impact within the area.

Mapping market and shadow values for farms
An initial attempt to implement our GIS-based methodology revealed that the range
of certain biophysical variables across the whole study area was somewhat greater
than that of the sample farms. This was most noticeable for the milk farm sample,
which lacked substantial upland observations. In general there was not a problem
across the vast majority of the study area, but it was at the extremes, particularly in
very mountainous areas, that models were effectively being used to predict outside
the range of available data.
In practice, there are two possible solutions to such a problem (Altman and
Gardner, 1989): either we can refrain from prediction in such areas or we can
truncate each biophysical variable to some level represented in our farm sample data.
The latter course of action was preferred as it was felt that having holes in the ¬nal
map of predicted values would be confusing. Affected cells were set to the upper or
lower limit of the farm sample data as appropriate. For our sheep farm models, over
90 per cent of the 20,563 1 km land cells constituting the entire surface of Wales
suffered no truncation of any variable, 8 per cent of cells had one variable truncated
and less than 2 per cent of cells suffered further truncation. However, for our milk
sample these proportions were 74, 10 and just over 15 per cent respectively. The
reason for this difference is simple, namely that there are relatively few milk farms
in extreme upland areas. Consequently we have to be circumspect about predictions
of milk farm values in such locations.
Farm surplus values were now estimated by running the various stage 2 models
(using truncated biophysical variable surfaces as appropriate) to predict the input
variables for the stage 1 models; from these, farm surplus values were then es-
timated. Table 8.8 details these values for both sectors, emphasising the highly
So in the stage 1 model we multiply the coef¬cient on catt%FR by the mean value of the variable, i.e. ’460.6
* 0.1107 = ’50.99.
Modelling opportunity cost: agricultural output values 247

Table 8.8. Predicted farm surplus values for sheep and milk farms

Sheep farms Milk farms

Farm surplus (£/ha)1 % of all cells2 % of all cells2
No. of cells No. of cells
0.00“49.99 2,483 12.1 7 0.1
50.00“99.99 6,346 30.9 37 0.2
100.00“149.99 9,492 46.2 248 1.2
150.00“199.99 1,728 8.4 463 2.3
200.00“249.99 323 1.6 825 4.0
250.00“299.99 191 0.9 261 1.3
300.00“349.99 ” ” 274 1.3
350.00“399.99 ” ” 317 1.5
400.00“449.99 ” ” 307 1.5
450.00“499.99 ” ” 500 2.4
500.00“549.99 ” ” 1,295 6.3
550.00“599.99 ” ” 2,342 11.4
600.00“649.99 ” ” 4,845 23.6
650.00“699.99 ” ” 5,067 24.6
700.00“749.99 ” ” 3,171 15.4
750.00“799.99 ” ” 543 2.6
800.00“849.99 ” ” 61 0.3

Notes: 1 Categories chosen to facilitate easy comparison with values reported in other
There are 20,563 1 km land cells in the study area.

signi¬cant difference in pro¬tability between the sectors. This difference becomes
more extreme if we recall that there are relatively few milk farms in areas of envi-
ronmental adversity, i.e. those cells at the lower end of the distribution of predicted
farm surplus probably refer to very few (if any) real-world milk farms.
By applying the adjustment factors (ADJFGIS and SVadjs for sheep farms and
ADJFGIM and SVadjm for milk farms) to the estimates of farm surplus the predicted
market and shadow values of output for each sector can be obtained. Considering
the sheep farm sector ¬rst, Plate 2a shows the resulting GIS-generated map for pre-
dicted farm-gate income (FGIs) while Plate 2b illustrates predicted shadow value
(SVs). The distribution of predicted values is similar across these maps and con-
forms strongly to prior expectations. Values are lowest in the Snowdonia, Cambrian
and Brecon mountains and increase with movement into lowland areas. Localised
variation due to soil quality and related impacts can also be detected. The somewhat
blocky nature of parts of these maps is primarily due to these latter effects, as the
LandIS variables are at a 5 km resolution whilst the other biophysical measures
are recorded on 1 km grid cells. Given this, the overall picture provided by these
results seems highly plausible.
248 Applied Environmental Economics

Table 8.9. Predicted farm-gate income and shadow values for sheep
and milk farms

Sheep farms Milk farms
No. of % of all No. of % of all No. of % of all No. of % of all
cells2 cells2 cells2 cells2
Value (£/ha) cells cells cells cells
’100.00“’50.01 ” ” ” ” 3 0.1 ” ”
’50.00“’0.01 ” ” ” ” 37 0.2 ” ”
0.00“49.99 ” ” 7,414 36.1 219 1.1 32 0.2
50.00“99.99 ” ” 12,389 60.3 418 2.0 364 1.8
100.00“149.99 8,296 40.4 728 3.5 887 4.3 1,184 5.8
150.00“199.99 11,506 56.0 32 0.2 264 1.3 452 2.2
200.00“249.99 527 2.6 ” ” 251 1.2 468 2.3
250.00“299.99 234 1.1 ” ” 336 1.6 734 3.6
300.00“349.99 ” ” ” ” 284 1.4 2,640 12.8
350.00“399.99 ” ” ” ” 479 2.3 7,510 36.5
400.00“449.99 ” ” ” ” 1,186 5.8 6,566 31.9
450.00“499.99 ” ” ” ” 2,231 10.9 613 3.0
500.00“549.99 ” ” ” ” 4,582 22.3 ” ”
550.00“599.99 ” ” ” ” 5,228 25.4 ” ”
600.00“649.99 ” ” ” ” 3,467 16.9 ” ”
650.00“699.99 ” ” ” ” 608 3.0 ” ”
700.00“749.99 ” ” ” ” 83 0.4 ” ”

Notes: 1 Categories chosen to facilitate easy comparison with values reported in other
There are 20,563 1 km land cells.

This analysis was repeated for milk farms and Plate 2c shows the map for pre-
dicted farm-gate income (FGIm) while Plate 2d details predicted shadow value
(SVm). As both the adjustment factors, ADJFGIM and SVadjm, are constants ap-
plied to predicted farm surplus values, these only differ in terms of absolute values.
For both we can see strong topographic and soil effects (see, for example, the band
of poorer soils extending down the centre of the Pembroke peninsula). As before,
the predicted values conform strongly to prior expectations.
Comparing Plates 2a“2d, it is clear that, for each sector, shadow values lie sub-
stantially below farm-gate income levels. However, the strongest contrast is between
sectors, with milk values very much higher than their sheep equivalents. Table 8.9
illustrates this contrast by summarising frequency distributions for all four vari-
ables. This table quanti¬es the very wide disparities in both farm-gate income and
shadow value levels between the sheep and milk sectors. As noted with respect
to farm surplus, this disparity becomes even sharper when we recognise that milk
Modelling opportunity cost: agricultural output values 249

farms tend to be concentrated upon better land, i.e. the lower, say, 10 per cent of
milk values will, in reality, contain very few actual milk farms.

Summary and conclusions
Any attempt to in¬‚uence patterns of land use requires an evaluation of the existing
usage of that land. This chapter has developed a GIS-based methodology for the
estimation of both the market and shadow values of agricultural output for our
study area. This methodology permits explicit incorporation of biophysical data
within the economic modelling of output values. The capacity to combine diverse
spatially referenced data afforded by the use of a GIS allows such modelling to be
undertaken at a highly disaggregated level, and yields readily interpretable maps of
predicted values as well as more conventional quantitative analyses. These valuation
maps are highly compatible not only with those estimated elsewhere in this study
but also with the decision-making approaches being developed and employed by
agencies such as the Countryside Commission, Forestry Commission and National
Assembly for Wales in their land use and planning roles (Countryside Commission
and Forestry Commission, 1996; Forestry Commission, 1998).
The application presented in this chapter provides models and mapped estimates
of both the market and shadow values of output of the two major farming sectors
in the study area: mainly sheep and mainly dairying farms. Results show that, for
both sectors, shadow values were considerably below corresponding market values.
Furthermore, sheep farm values were substantially lower than those enjoyed by the
dairy sector. Both sectors have suffered further losses in real incomes since our
study period, implying that our estimated rates of land use conversion are likely to
provide lower bounds on the actual potential for ef¬ciency gains from such changes.
The spatial detail of information provided by the resultant GIS-generated maps
permits analysts and policy-makers to assess issues such as the likely extent and
location of land use response to changes in policy parameters. They also permit
ready integration with the maps of woodland recreation, timber and carbon seques-
tration value estimated in previous chapters to allow us to evaluate the net bene¬ts
of transfers out of agriculture and into woodland, a task to which we now turn.
Cost-bene¬t analysis using GIS

In this chapter we assess the net bene¬ts of converting land out of agriculture and into
woodland. This appraisal is made from a number of standpoints. We have considered
two types of agricultural production (sheep and milk) each assessed in two ways
(farm-gate and social1 values), and two species of tree (conifer, represented by
Sitka spruce, and broadleaf, represented by beech). Furthermore, we have assessed a
variety of woodland bene¬ts (recreation, timber and carbon sequestration) allowing
us to consider a succession of de¬nitions of what, in economic terms, constitutes
a woodland. Finally, we have assessed the net bene¬ts of land conversion using a
variety of discount rates.
The results presented here consider various permutations of the factors discussed
above. In essence our approach starts with the present agricultural values of a
speci¬c farm type (say sheep farming) and subtracts various de¬nitions of woodland
bene¬ts (say, timber and carbon storage) assessed at a given discount rate (say
6 per cent). Thus a negative outcome would indicate that woodland bene¬ts outstrip
those of agriculture, and vice versa for positive sums. These various net bene¬t value
estimates are obtained by using the GIS to overlay the respective value maps and
adding or subtracting values as necessary.
A general caveat to our ¬ndings concerns the fact that our study data period is
the early 1990s rather than the present day. As discussed at some length in Chapter
8, the intervening years have seen a relative decline in the values of agriculture
both generally across the UK and in our study area of Wales. This means that
our ¬ndings will tend to overestimate the value of farming and hence somewhat
underestimate the potential for land use conversion into forestry. However, we are
1 In this chapter we refer to ˜social™ rather than ˜shadow™ values as we are attempting to examine a wider range
of internal and external bene¬ts and costs than that considered in the analysis of agriculture alone presented in
the previous chapter. We recognise that any de¬nition of ˜social™ value is open to the criticism that the ensuing
set of values is incomplete.

Cost-bene¬t analysis using GIS 251

not unduly perturbed by this state of affairs for, in any policy assessment, it is also
easy to underestimate the forces of inertia, tradition and risk aversion which can
induce lag to a decision which seems economically optimal. In short we are much
happier with a situation in which our ¬ndings are conservative than we would be if
intervening forces had moved against land use conversions.
A further caveat to our calculations concerns the extent to which the marginal
bene¬ts of woodland are constant or diminishing. The maps of timber value created
in Chapter 6 implicitly assume that the expansion of supply generated by any new
planting would have no net impact upon the price of timber. Given that the vast
majority of the timber consumed in the UK is imported, and that the price is in
effect ¬xed on the world market, this seems a reasonable assumption. Similarly the
maps of carbon sequestration value presented in Chapter 7 assume that the extra
carbon stored by any new planting would have a negligible effect upon the unit
value of carbon storage. Again, given the relatively minuscule proportion of excess
atmospheric carbon which would be removed by such afforestation, this seems a
very reasonable assumption. However, we cannot extend this line of reasoning to
the recreation value maps created in Chapter 4. Here any substantial increase in the
supply of recreational sites is liable to impact upon any excess demand2 such that the
value of any further sites is diminished. In effect, as the number of sites increases
so substitute availability rises and the marginal recreational value of woodland
To allow for this we have treated woodland bene¬ts in the following manner.
In the ¬rst of three stages agricultural values are assessed against timber values
alone. Results for the farm-gate perspective include the various forest grants and
subsidies available to farmers as well as incurred planting and maintenance costs
(as in Chapter 6). This analysis is in effect mimicking the actual decision faced by
farmers and provides a useful cross-check between our valuation estimates and the
real world. In order to provide social value assessments of the agriculture versus
timber trade-off we remove subsidies from both sides of the equation, a procedure
which shifts the balance in favour of forestry which has a lower level of subsidisation
than does conventional agriculture.
The second step adds carbon values to those derived from timber and reassesses
the net bene¬ts of conversion from agriculture.3 Again values are calculated from
both farm-gate and social perspectives.

2 The impact of substitutes is considered in Bateman et al. (1998) and Brainard et al. (1999). However, comparison
with the work of Willis and Benson (1989), as reviewed in Chapter 3, suggests that for any given individual
woodland our estimates are likely to be reasonable and may even be lower-bound values.
3 Dore et al. (2001) also compare agricultural values with timber and timber plus carbon sequestration values in
a study of marginal farming regions in northern Saskatchewan, concluding that the latter exceeds the former in
about twenty of the thirty years considered (the exception being the 1970s). However, the study is not spatially
disaggregated and estimates total annual values only.
252 Applied Environmental Economics

Finally, the third stage of analysis adds in recreational values and recalculates con-
version net bene¬ts. However, here we have to recognise the diminishing marginal
value of recreation as outlined above. Because of this we cannot have con¬dence
in the overall value sum created by such a calculation. Consequently we can only
use this stage to identify those areas which would generate the very highest net
bene¬ts from conversion. This in itself is a highly useful result given that, in reality,
resource limits mean that only a ¬nite, and probably relatively small, amount of
funds will be available to support conversion. Using the methodology outlined here
enables the identi¬cation of prime sites for such conversion.
From the perspective of the farmer, comparison of agriculture with the timber
plus carbon value (and with the timber, carbon and recreation value) does not have
any immediate resonance with the actual market situation as neither carbon nor
recreation values have any market or subsidy ˜price™. However, these calculations
do indicate the net bene¬ts which farmers could receive if they were compensated
for carbon and recreation values in the same manner in which timber values are
realised (i.e. via market prices and subsidies).
All three de¬nitions of woodland values (timber only; timber plus carbon; timber,
carbon and recreation) have direct relevance when viewed from the standpoint
of society which is interested in both the marketed and non-marketed values of

Results are categorised ¬rst by whether we take a farm-gate or social value per-
spective. Further disaggregation is by the de¬nition of woodland values discussed
above and then by the discount rate, woodland species and farm sector under con-
sideration. We begin by holding the discount rate and woodland species constant
and examine results by farm sector. We then vary the tree species and ¬nally change
discount rate to present a full sensitivity analysis.

Results for the 6 per cent discount rate
In this section we hold the discount rate at 6 per cent throughout. This is a useful
initial level to use for the calculation of social values as it is the current (at the time of
writing) government rate for socially bene¬cial projects both now and in our study
period. Our analyses of rates of return (Chapter 5) suggests that it is somewhat
higher than that commonly used on sheep farms although it may be representative
of rates used on some milk farms. We begin our discussion of results by considering
potential conversions to conifer woodland.
Cost-bene¬t analysis using GIS 253

Conversion from agriculture to conifer woodland
We begin this section by presenting results for conversion from sheep farms to
conifer woodland, subsequently turning our attention to the milk farm sector.

Sheep farms
Table 9.1 reports results from one full run of our cost-bene¬t model holding the
discount rate at 6 per cent and analysing the annual per hectare net bene¬t value
of conversion from sheep farming into conifer woodland. Our analysis uses data
recorded for (or interpolated to) a 1 km square basis and the entirety of Wales
comprises some 20,563 such squares. Each column presents the distribution of
values estimated for these squares.
The table is organised into two blocks each comprising four columns. The ¬rst
block details farm-gate values (columns (1) to (4)) while the second gives social
value equivalents (columns (5) to (8)). For both blocks the columns refer to suc-
cessively wider de¬nitions of woodland bene¬ts. The ¬rst columns of each block
(columns (1) and (5)) consider only the timber value while the next (columns (2)
and (6)) add in carbon sequestration values. Lastly, two columns in each block
add in woodland recreation values. Columns (3) and (7) use a lower-bound recre-
ation value (derived from the contingent valuation (CV) cross-study ˜meta-analysis™
discussed in Chapter 4), while columns (4) and (8) use an upper-bound value
(derived from our individual travel cost method (ITCM) analysis, also presented in
Chapter 4).4
Column (1) of the farm-gate values block of Table 9.1 indicates the net bene¬t to
farmers of converting from sheep farming to woodland under the present regime of
grants and subsidies (de¬ning woodland values as purely grants, subsidies and the
net bene¬ts of timber production). Remembering that negative sums show situations
where these woodland values outstrip the present sheep values, we can see that,
in the vast majority of cases (over 90 per cent of cells) the net bene¬ts to farmers
of staying in sheep production exceed those of converting into woodland. This
difference is relatively marginal with the net bene¬t of remaining in agriculture
being, in almost all cases, less than £100/ha and with almost 10 per cent of cells
showing a small net bene¬t from conversion.5 Nevertheless, the clear picture is
4 The CV cross-study meta-analysis and ITCM study derive mean recreation values of £1.82 and £3.59 per party
visit respectively. These values are somewhat lower than, although comparable to, those estimated for the study
area by Willis and Benson (1989). Site-based values were converted to per hectare equivalents by dividing
through by a mean site area of 4,000 hectares (Willis and Benson, 1989; Anna Chylack, Forestry Commission,
pers. comm. 1994). The resulting values are within the range quoted by Benson and Willis (1993).
5 Note that it is at the extremes that the truncation effect discussed in Chapter 8 will apply. These will tend to
mask the lowest agricultural values and so conversion could be bene¬cial in somewhat more than 10 per cent of
cases although this effect will be minor (particularly with respect to sheep farms where there is relatively little
Table 9.1. Distribution of the net bene¬ts of retaining sheep farming in Wales as opposed to conversion to conifer
(Sitka spruce) woodland:1 6% discount rate

Farm-gate values Social values
Lower limit Upper limit timber timber+ timber+carbon+ timber+carbon+ timber timber+ timber+carbon+ timber+carbon+
(£/ha/yr, (£/ha/yr, only carbon recreation (CVM) recreation (ITCM) only carbon recreation (CVM) recreation (ITCM)
1990) 1990) (1) (2) (3) (4) (5) (6) (7) (8)
’475.00 ’450.01
’450.00 ’425.01
’425.00 ’400.01
’400.00 ’375.01
25 274
’375.00 ’350.01
99 220
’350.00 ’325.01
90 117 610
’325.00 ’300.01
133 213 1,004
’300.00 ’275.01
232 474 1,472
’275.00 ’250.01
9 285 1,687 3,153
’250.00 ’225.01
153 737 284 5,121 6,478
’225.00 ’200.01
266 1,131 7,136 7,671 4,346
’200.00 ’175.01
599 1,582 8,292 3,446 1,639
’175.00 ’150.01
5 2,097 3,617 7 3,446 1,081 427
’150.00 ’125.01
899 5,852 6,153 771 757 208 111
’125.00 ’100.01
8,286 6,612 3,849 10,540 125 40 21
’100.00 ’75.01
6,895 3,005 1,459 7,438 27 15 6
’75.00 ’50.01
18 2,840 1,074 467 1,486 6 1
’50.00 ’25.01
1,978 809 272 164 296 1
’25.00 ’0.01
0.00 24.99 10,811 248 117 46 24
25.00 49.99 5,929 84 17 5 1
50.00 74.99 1,287 7 1 1
75.00 99.99 323 1
100.00 124.99 188
125.00 149.99 29
150.00 174.99
175.00 199.99
200.00 224.99
225.00 249.99 10
250.00 274.99 3 29 92
275.00 299.99 64 146 210
300.00 324.99 236 263 164
325.00 349.99 4 20 177 48 13
350.00 374.99 11 28 87 9 3
375.00 399.99 57 142 199
400.00 424.99 228 249 160
425.00 449.99 181 62 23
450.00 474.99 12 4

Notes: 1 Negative sums indicate areas where woodland values exceed agricultural values.
Blank cells indicate that no 1 km cells fall into this category. There are 20,563 1 km cells.
256 Applied Environmental Economics

that when we consider farmers™ perceptions of income, then, under the levels of
woodland grant and subsidy operating during our study period, our analysis predicts
very little conversion from sheep farming to woodland in the study area. This was
indeed the situation on the ground with sources at both MAFF (Fearn, 1990) and
the Forestry Commission (Adrian Whiteman, pers. comm., 1994) suggesting that
very few Welsh farms had entered forestry schemes at that time.
Does this result provide validation for our estimates? As indicated, the 6 per cent
discount rate used here is somewhat higher than the one we would expect sheep
farmers to use in their everyday decision-making, yet it produces a result which
is consistent with observed behaviour. There are a number of persuasive reasons
explaining this result. These centre around the common observation that decision-
makers in almost any ¬eld (and notably agriculture) demand a premium from risky
or unfamiliar investments. Such diversi¬cation brings inherent uncertainty for the
farmer regarding the levels of labour, capital, skill and entrepreneurship which will
be required, as well as uncertainty regarding the ultimate returns from such an
enterprise. This is particularly true of forestry which, for the farmer, is both very
different from the well-known patterns of sheep production and involves a time
scale which is an order of magnitude different from any of the decisions he/she
usually encounters.
Cobb (1993) reviews a number of studies of agricultural risk premiums and
reports on his own large-sample survey of UK farmers which revealed that they
required very substantial increases in gross margin before they would consider
conversion into low input extensi¬cation options such as that promoted under the
Countryside Stewardship Scheme. Cobb feels that this is primarily due to farmers™
preferences for familiar activities or agricultural techniques and to apprehension
about the unfamiliar.6 Our own research (see Chapter 3 and Bateman et al., 1996b)
found that this is also the case with respect to conversions out of conventional
agriculture and into woodland. Here substantial increases in pro¬t rates were
required before agreement to convert was forthcoming. As discussed in Chapter 5,
Lloyd et al. (1995) suggest that one reason for this may be a belief by farmers that
conversions to woodland may be irreversible, reducing future opportunities, and
may possibly lower land prices. Such perceptions are fostered by the long commit-
ment period of grant schemes and the requirement for replanting as a proviso in the
granting of felling orders.
The risk premiums associated with such conversions can be modelled in a number
of ways, one of which is to apply a higher discount rate than that normally used for

6 Another interesting possibility explaining negligible conversion rates is explored by Saarinen (1966). In a
study of US farmers who would, on purely ¬nancial grounds, have been better off giving up a speci¬c type of
farming, Saarinen found a consistent overoptimism about future performance, which persisted over long periods.
However, he did identify a subset of innovative farmers who were receptive to the possibility of diversi¬cation.
Cost-bene¬t analysis using GIS 257

standard investments. That is, in effect, what is being done in the farm-gate values
reported in Table 9.1 and we can see that our model produces a result which closely
resembles what is observed in the real world (as in column (1)). We return to this
theme subsequently (see discussion of Table 9.5 below).
Given that we now have support from the real world for the predictions of our
model, the ˜timber only™ farm-gate values (column (1)) also provide useful indi-
cations of the responsiveness of sheep farmers to increases in the level of timber
grants and subsidies. Our results suggest that even a modest increase in the real
level of such subsidies may produce signi¬cant increases in the ¬nancial viability
of conversion. Given that the higher discount rate used here implicitly takes into
account farmers™ risk aversion, then we might expect this to translate into actual
conversions. Some 10,811 cells (over 50 per cent of all cells) show an excess of
sheep values over timber woodland values of less than £25/ha/yr. This suggests that
while subsidies are currently too low to be effective, substantial conversions may
be induced from modest increases in these subsidies.
While the results shown in Table 9.1 are of interest, the GIS-generated maps from
which they are derived are more informative (although less easy to summarise).
Plate 3a shows the map which underpins our farm-gate valuation of the conversion
from sheep farming to woodland under present subsidy levels (column (1)). As
can be seen, the majority of areas produce positive differences between sheep
farming and timber, i.e. under present circumstances and if we only consider the
market-priced bene¬ts of forestry (timber and subsidies), then farm-gate income is
generally higher under sheep than woodland. The map shows that this difference is
smallest in mainly lowland, valley-¬‚oor areas, indicating that it is in these locations
that conversions might be most pro¬table.
The social value equivalent of the above analysis is given in the ¬rst column of
the second block of Table 9.1 (column (5)). The transfer savings created by a move
out of sheep and into the relatively less subsidised production of timber mean that
the social net bene¬ts of such conversion are signi¬cantly higher than their farm-
gate equivalents. This difference is very apparent in Table 9.1 because very nearly
100 per cent of cells record negative values, i.e. even when we only include timber
bene¬ts, the social value of woodland generally exceeds that of sheep production.
This result is all the more powerful when we recall that the 6 per cent discount rate
used here is the same as that used by the UK government for such calculations.
Comparison of columns (1) and (5) is revealing. While a conversion from sheep
to woodland is unattractive from the farm-gate perspective, it generates net bene¬ts
from society™s point of view. The potential clearly exists for a win/win bargain
in which society pays some of its subsidy savings back to farmers as compen-
sation for lost income, so that each side bene¬ts. Given that the magnitude of
social bene¬ts is similar to that of farm loss, such a compensation scheme would,
258 Applied Environmental Economics

on these ¬gures, need to be carefully constructed. However, once we widen our
de¬nition of woodland bene¬ts the case for compensation becomes much more
clear cut.
The second column of each block (columns (2) and (6)) adds in net carbon
sequestration values to the bene¬ts of woodland. In the case of the farm-gate values
we are in effect modelling the impact of assigning to farmers the net carbon ¬‚ux
value associated with planting trees on their land. In the general case where such
planting causes an increase in carbon storage we credit farmers with these values
as a hypothetical subsidy. In the more rare case of planting on peat soils, farmers
are now debited with a hypothetical charge against the farm account equivalent to
the value of carbon liberated.
The impact of this expanded de¬nition of woodland values is highly signi¬cant,
moving the vast majority of farms (over 95 per cent) to a situation where conversion
from sheep farming to woodland creates an increase in farm-gate income (column
(2)). However, the large carbon losses associated with planting on peat mean that
there are now a small number of farms which would generate strongly negative
values from such conversion. This bimodal distribution is echoed in the social
value equivalent of this analysis (column (6)). However, here the additional savings
of agricultural subsidies substantially improve the net bene¬ts of conversion to
In effect, then, we only have to expand our de¬nition of the social bene¬ts of
woodland to include net subsidy savings, timber production and carbon seques-
tration to justify very substantial conversion out of Welsh sheep farming and into
woodland. This conclusion is further reinforced if we now also consider the recre-
ation bene¬t values created by making that woodland open-access.7
Given our reservations regarding the accuracy of recreational bene¬t measures,
we have used two alternatives here. These are a lower-bound estimate obtained from
our cross-study analysis of CV estimates, and an upper-bound measure obtained
from our ITCM study. These are used to produce the third and fourth columns
of each block. As noted, substitution effects mean that wholesale conversion to
woodland would not attain the values shown in these columns. However, the results
do indicate that the conversion of just a few select sites (which would not induce
major substitution effects) would create woodlands of very high value in some
locations. This story is repeated in both blocks, with the social value columns ((7)
and (8)) exceeding farm-gate values (columns (3) and (4)) by a signi¬cant amount,
mainly attributable to subsidy savings.8

7 This statement hinges on the assumption, discussed in Chapter 4, that woodland recreational values are measures
of surplus over the values created by general agricultural land use.
8 Subsidy savings constitute the major difference between columns (1) and (5), a difference which is maintained
across subsequent pairs of comparable farm-gate and social values.
Cost-bene¬t analysis using GIS 259

Precise location of these prime conversion sites is facilitated by inspection of the
net bene¬t value maps underpinning these columns. Plate 3b illustrates the social
net bene¬t of conversion from sheep to woodland with the latter de¬ned as the
sum of timber, carbon storage and recreation values (measured using the lower-
bound CV estimate), i.e. column (7). From a policy-making perspective this map
illustrates the interpretative advantages of the methodology employed. Optimum
sites for conversion are easily identi¬ed and (remembering that negative sums
indicate areas where woodland values exceed those of agriculture) corresponding
estimates of the monetary net bene¬t of such conversion are given.
While Plate 3b is readily interpretable, its message throws a critical light over
past policy decisions. As the map clearly shows, the prime sites for conversion
are located in lowland areas (with high timber productivity and carbon storage)
and near to centres of high population and accessibility (yielding high recreation
values).9 This is particularly noticeable in South Wales where the urban centres of
Cardiff and Swansea, augmented by the infrastructure effect of the M4 motorway,
result in very high recreational values in addition to the excellent timber yields
and consequent carbon sequestration levels engendered by these lowland areas.
Conversely, conversion is least justi¬ed in upland areas, most noticeably upon
peat soils where our analysis shows that retention within agriculture is clearly
preferable. This result seems eminently sensible and accords with the sentiment
made popular in the 1980s that policy-makers should ˜bring forests down the hill™
(MacFarlane, 2000). However, as this slogan implies, actual planting decisions
have been almost completely at odds with such logic. The recreational needs of
the majority lowland urban populace have not been recognised, and forests have in
the main been planted in inaccessible upland areas “ quite the reverse of the action
suggested by Plate 3b. This policy seems to have been led by a desire to reduce the
land purchase costs of planting trees, in ignorance of the economic value of such a

Milk farms
A second set of comparisons is presented in Table 9.2 which maintains the woodland
species as conifer and holds the discount rate at 6 per cent but now examines
potential conversions out of milk production. To allow further comparison with
previous results, Plate 3c shows the net bene¬t map for the farm-gate value of
converting from milk production to conifer woodland when only timber values and
subsidies are considered (i.e. the present-day decision facing milk farmers; column

9 There is a fascinating comparison here with the prescriptions of von Thunen™s (1826) Isolierte Staat and
subsequent land use analysis. For example Haggett et al. (1977: p. 206) note (without the bene¬t of speci¬c
analysis) that although ¬nancially non-viable, ˜in highly urbanized areas the demand for “recreational” wooded
areas may sometimes lead to its persistence in areas of high accessibility™.
Table 9.2. Distribution of the net bene¬ts of retaining milk farming in Wales as opposed to conversion to conifer
(Sitka spruce) woodland:1 6% discount rate

Farm-gate values Social values
Lower limit Upper limit timber timber+ timber+carbon+ timber+carbon+ timber timber+ timber+carbon+ timber+carbon+
(£/ha/yr, (£/ha/yr, only carbon recreation (CVM) recreation (ITCM) only carbon recreation (CVM) recreation (ITCM)
1990) 1990) (1) (2) (3) (4) (5) (6) (7) (8)
’275.00 ’250.01
3 24 39
’250.00 ’225.01
29 32 75 3
’225.00 ’200.01
35 74 82 4 62
’200.00 ’175.01
70 77 128 11 55 122
’175.00 ’150.01
21 84 145 173 60 107 160
’150.00 ’125.01
29 175 197 191 105 191 270
’125.00 ’100.01
65 184 210 221 2 211 289 422
’100.00 ’75.01
94 227 250 258 37 308 297 568
’75.00 ’50.01
168 266 273 260 103 344 422 682
’50.00 ’25.01
203 290 209 208 188 423 413 737
’25.00 ’0.01
0.00 24.99 293 181 182 210 362 322 473 887
25.00 49.99 355 176 164 215 442 299 763 1,180
50.00 74.99 389 136 149 224 543 377 1,174 2,114
75.00 99.99 166 150 150 351 339 1,080 2,324 3,176
100.00 124.99 160 147 251 542 285 1,775 3,849 3,826
125.00 149.99 163 173 351 530 302 4,272 4,658 3,523
150.00 174.99 163 227 443 702 523 5,446 3,522 1,693
175.00 199.99 143 420 765 1,163 1,401 3,331 1,031 388
200.00 224.99 175 743 1,058 1,700 2,245 1,234 316 151
225.00 249.99 215 1,003 1,649 2,162 4,969 351 131 72
250.00 274.99 277 1,239 2,389 2,572 5,138 86 33 28


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