. 5
( 11)


The scheme had almost identical objectives to the FC™s WGS (and was payable
concurrently) with the additional goal of reducing surplus agricultural production.
As a consequence, higher rates of FWS were payable on better quality land. Al-
though these rates did not distinguish between conifer and broadleaf woodlands,
the period of annual support was longer for the latter.
Poor uptake of the FWS led to its replacement in 1992 by the Farm Woodland
Premium Scheme (FWPS) (MAFF, 1992a,b,c). Here farms ¬rst applied to the FC
for planting grants under the WGS (including BLS, WMG, CWS and the single
new woodland payments where appropriate). If approved the farm could then apply
to MAFF for FWPS payments as shown in Table 5.5.
For woodlands with less than 50 per cent broadleaves the FWPS is payable in
each of the ¬rst ten years after planting, a period which is extended to ¬fteen years
for mainly broadleaved woodlands.28 However, grant repayments with interest are
stipulated if land is returned to agriculture within twenty years for the former or
thirty years for the latter (MAFF, 1992b).29
With respect to our Welsh study area, the creation of the Cambrian Mountains and
Lleyn Peninsula Environmentally Sensitive Areas (ESAs) in 1986 and 1987, respec-
tively, seemed to offer the possibility of further grants for broadleaved woodland.30

26 In addition to this the FC also provides certain other grant payments for general and coppice management,
open spaces and grey squirrel control. Details are given in Johnson and Nicholls (1991).
27 The FWS also pays planting grants but, since its revision in 1992, these have been identical to those offered
under the WGS. Farmers may not collect both FWS and WGS planting grants.
28 This is considerably more front-loaded than the original FWS which provided lower annual sums but over a
longer period.
29 Farms may also convert land into forestry under the Common Agricultural Policy (CAP) set-aside scheme.
Set-aside woodland is not eligible for either FWPS or WGS BLS payments. Standard WGS payments may be
received concurrently with set-aside in high productivity areas but as this does not apply for most of our study
area we do not pursue this particular permutation any further.
30 Further grants towards the costs of promoting landscape or countryside conservation are occasionally paid by
the Countryside Commission and Nature Conservancy Council while the Agricultural Development Advisory
Service (ADAS) can provide certain technical support. However, the occasional nature of such support means
that it is not considered further in this study.
Timber valuation 127

Table 5.5. Payments under the Farm Woodland Premium Scheme1
(£/ha per annum)

Disadvantaged Disadvantaged
Present use Lowlands Area Area
Arable/improved grassland 250 190 130
Unimproved n/a 60 60

Notes: n/a = not available.
The following FWPS restrictions apply: (i) not more than 50 per cent
of farm eligible; (ii) not more than 40 ha of unimproved land per farm; (iii)
eligibility for arable/improved grassland restricted to land under such usage
within the previous three years; (iv) the FWPS as a whole is cash rather than
area limited. Further details are given in MAFF (1992b).
Source: MAFF (1992b).

The Welsh Of¬ce (1989a) stressed the importance of such features within the
Cambrian Mountains ESA while in a subsequent lea¬‚et (Welsh Of¬ce, 1989b) pay-
ments of £45/ha per annum became available for management of such woodlands.
These are clearly speci¬ed as additions to existing planting and management grants.
However, subsequent publications regarding the Lleyn Peninsula ESA offered lower
rates of grant (£15/ha per annum) restricted to existing broadleaf woodland alone
(Welsh Of¬ce, 1992a,b). Conversations with both ESA authorities in the late 1990s
indicated that those anomalies still persisted.
A policy and planning drive away from purely timber-orientated, monoculture
conifer plantations was signalled in 1988 when EC Directive 85/337 was imple-
mented via Environmental Assessment (Afforestation) Regulations which made
applicants for FC assistance submit an environmental assessment of the proposed
forest.31 In the same year the Department of the Environment, Transport and the
Regions (DETR), the ultimate national planning authority, indicated that planning
permission for such large conifer plantations would not normally be granted for
sites in England. As noted previously, this policy has since been reinforced in pol-
icy documents applying to both England (Forestry Commission, 1998) and, more
recently, our study area of Wales, with the National Assembly for Wales explicitly
promoting the concept of diverse, multipurpose woodland as opposed to conifer
monocultures (National Assembly for Wales, 2001a).

31 In practice such assessments became routine requirements for plantations of over 100 ha affecting National
Nature Reserves, National Parks, Sites of Special Scienti¬c Interest, etc.
128 Applied Environmental Economics

While the policy environment appears to be favourable to further woodland
expansions, the planning system may place a brake on this, particularly in the case
of farm woodlands. Lloyd et al. (1995) report study ¬ndings suggesting that some
farmers believe that conversions to woodland may be irreversible,32 a similar result
being reported by Crabtree et al. (1998). Indeed, our own informal contacts with
the Forestry Commission indicated that felling licences would only be granted on
condition that affected areas would be replanted.33 While future policy may change,
this means in effect that once farmers place land under trees they may well become
legally bound to maintain an equal area of woodland on the farm in perpetuity. This
irreversibility of land use may well slow the expansion of farm woodlands and we
consider the potential inertia of farmers in reacting to purely ¬nancial pressures in
the cost-bene¬t analysis presented at the end of this volume.

Grants: conclusions
Farmers considering diverting land into forestry are eligible for a variety of grants
and subsidies. These vary considerably according to which scheme they register
under and according to locational factors. In order to allow for this the timber
valuation model developed subsequently allows ¬‚exibility across the full gamut of
grant/subsidy opportunities existing in the early 1990s. Results for these various
permutations were identi¬ed using the following coding system:
S subsidy rate is (as follows)
I rate for planting on improved grassland or arable land
U rate for planting on unimproved land
nda rate for planting in a non-disadvantaged area
da rate for planting in a disadvantaged area
sda rate for planting in a severely disadvantaged area
+CW = rate for planting, given Community Woodland supplement
’CW = rate for planting, not given Community Woodland supplement

In the following section we incorporate these subsidies within the wider costs and
revenues arising from plantation management.

Plantation costs and revenues
Choice of species
Ideally one would wish to analyse all those species which are likely to be used
in a conversion from agriculture to forestry. The feasibility of such an analysis
32 See also Williams et al. (1994) which gives further details regarding this study.
33 This may also adversely affect land prices.
Timber valuation 129

was investigated with the FC™s Forestry Investment Appraisal Programme (FIAP).
However, while this is an excellent tool for the management of given stands, it was
not amenable to the type of modi¬cation required to answer the questions posed
by this research. Consequently it was decided that two representative species, one
conifer and one broadleaf, would be chosen for study.
Among the eight major species of conifer grown commercially in the UK,34 the
Sitka spruce stands out as by far the most dominant, constituting 28 per cent of total
forest area, more than double that of any other species (FICGB, 1992). Sitka spruce
is capable of producing an average annual yield in excess of 24 m3 /ha over an
optimal rotation, with typical UK productivity averaging 12“16 m3 /ha. The rapid
growth rate means that optimal felling ages can be very short, from sixty years
on poor ground to as little as forty-¬ve years on good sites.35 The choice of Sitka
spruce as a representative conifer therefore re¬‚ects a logical and often observed
timber-productivity decision. However, this species is not thought to be optimal in
terms of recreation value.
Interestingly there is little empirical evidence regarding a connection between
tree species and recreation value. In one of the few valuation studies to consider
this, Hanley and Ruffell (1992) failed to identify a signi¬cant relationship. This
may mean that all woodland recreation valuation studies are observing values for
outdoor, rather than speci¬cally woodland, activities. However, if we temporarily
lurch from the empirical to the anecdotal, it is the authors™ ¬rm belief that walkers
do recognise and appreciate the difference between the claustrophobic atmosphere
produced by a species like Sitka spruce (with its dense entanglement of lower
branches, tightly packed together to maximise timber yield, set in a bed of stultifying
acid pine needles) and, say, the much more airy and open feel of a Scots pine
woodland. An even clearer difference is evident when we then consider the gorgeous
spaciousness, beautiful trunks and foliage, and verdant undergrowth of an oak or
beech woodland.
To allow for this difference we decided to extend our appraisal to consider a
representative hardwood. Here the choice was more dif¬cult as the oak is the most
abundant broadleaf species but is relatively slow-growing and less productive than
the beech, which we selected for study as a more viable hardwood alternative.36

34 In descending order of total forest area, major conifers are: Sitka spruce (28%); Scots pine (13%); lodgepole
pine (7%); Japanese larch (6%); Norway spruce (6%); Corsican pine (2%); Douglas ¬r (2%); European larch
(2%). Major hardwoods are: oak (9%); ash (4%); beech (4%); birch (4%). The remaining area consists of a
range of species (FICGB, 1992).
35 As discussed subsequently, optimal felling age is a function in part of discount rate rather than just of growing
36 There are some ecological arguments in favour of the oak over the beech as the latter creates less understorey and
has a less penetrable canopy. However, data availability favoured the beech, which is, despite these drawbacks,
ecologically strongly preferable to the Sitka spruce.
130 Applied Environmental Economics

Sitka spruce costs and revenues
Irrespective of species, the majority of plantation costs occur at the start of the
rotation (planting, etc.) and at felling. Here we make the common FC assumption
that all cutting costs (both thinnings “ the extraction of undersized trees at set
points during the rotation so as to maximise long-run plantation yield “ and felling)
are either carried out by contractors or incur contractor-level implicit costs upon
the plantation operator. This allows us to use the standing timber price“size curve
discussed subsequently.
Estimates for these and other costs (maintenance, fertiliser, fencing, etc.) were
obtained from the FC and are detailed in Bateman (1996). Costs may vary some-
what depending upon infrastructure, distance to sawmills, local variation in input
supply prices (including labour), intensity of planting, etc. Typical values for such
parameters were incorporated within the data supplied by the FC.37

Four factors are key to the determination of timber revenues:
(i) the rate of growth
(ii) the price per m3
(iii) the discount rate (the rate at which forest managers or policy-makers progressively
reduce the present-day value of revenues that will be received further and further into
the future)
(iv) available grants and subsidies.

We will address each of these factors in turn.
Growth rate is typically de¬ned using the yield class (YC) measure, which is the
maximum average annual increment in volume which a stand of trees can deliver.
So, for example, a stand for which this value is 12 m3 /ha per annum is referred to
as being YC12.
Since its inception in 1919 the Forestry Commission has collected data quan-
tifying the characteristics of plantations growing in differing yield classes. These
˜yield models™ have been collated across varying species and management regimes
(Edwards and Christie, 1981) and show how, for each yield class, tree volume in-
creases over time. The yield models provide the basic data on tree growth used in
our subsequent analysis.
37 Note that costs were representative rather than being varied spatially. This is a potential weakness in the analysis,
and other commentators such as Thompson et al. (1997) have used spatially sensitive costs. However, the latter
study considers an area (British Columbia) forty-¬ve times larger than Wales and uses just three cost-level
zones. In effect, therefore, our own study performs well in comparison and we do feel it is reasonable to point
out that, while revenues vary very substantially across Wales (as shown in Chapter 6), costs are less variable.
Timber valuation 131

Figure 5.2. Price“size curve for conifers in England and Wales. (Source: Drawn from data
given in Whiteman, 1990.)

From the perspective of the timber producer, price is far from constant and is
instead a function of the mean volume per tree. Simply put, when trees are thin
they are of limited use and so their price/m3 is low. As trees increase in volume
so their usefulness, and therefore price/m3 , rises. This continues (at a diminishing
rate) to the point where a tree™s girth is such that it can be used for sawn wood,
telegraph poles and myriad other products. After this point the price/m3 remains
fairly constant and the value of a stand increases only as much as volume does.
Estimation of this ˜price“size curve™ has been the subject of repeated statistical
investigation by the FC (Mitlin, 1987; Whiteman, 1990; Sinclair and Whiteman,
1992). In this study we adopted the ¬ndings of Whiteman (1990), primarily because
this research uses the same base year as our wider study, but also because this
analysis recognises that prices are higher in England and Wales than in Scotland
and produces separate models which provide a substantially better ¬t to the data
(R2 = 87.5%) than the uni¬ed analysis for the whole of Britain reported by Sinclair
and Whiteman subsequently (R2 = 74.7%). Figure 5.2 illustrates the price“size
curve used in our analysis.
As a stand of trees grows, so thinner trees (known appropriately as thinnings) are
removed to help the remainder ¬‚ourish. The thinning process typically starts about
twenty years after planting and then occurs at regular intervals of, say, ¬ve years
132 Applied Environmental Economics

up to felling. The value of thinnings can be calculated via the price“size curve,
although for obvious reasons this value is substantially less than that of the main
crop. By relating the price“size curve to the timber volume information contained
in the yield model we can calculate the timber revenue generated each year from
planting to felling and compare this with per annum costs to obtain a value for
annual timber net bene¬t.
The optimal felling age therefore emerges as a key factor in determining the
overall value of a stand. As already mentioned this will vary according to the yield
class concerned, for, as the FC yield models show (Edwards and Christie, 1981),
the faster a tree grows the sooner it reaches its age of maximum annual average
product. Therefore, as yield class increases, optimal felling age falls. Early felling
is encouraged by the practice of discounting, which we now consider.
Discounting is the process by which revenues and costs occurring in the future
are converted into present-day values. By this process, different projects that have
returns occurring at different times can be compared on a common footing and
investment decisions made. The general result is that costs and bene¬ts arising
in the future are not valued as highly as those which occur in the present day.
This is for a variety of reasons including a simple preference for earlier rewards
(˜positive time preference™) and the fact that money invested in a project, such
as forestry, is no longer available for investment elsewhere, say in a bank, and
so there is a lost opportunity, in terms of the interest forgone, which increases
over time (the ˜opportunity cost of capital™). The further into the future that costs
and bene¬ts occur, the more they are discounted. By looking at how this effect
increases into the future we can observe the underlying ˜discount rate™ that is being
The factors determining discount rates are complex and while we return to con-
sider some of these in Chapter 7 we do not attempt to provide a full account of their
determinants in this volume.38 However, what is pertinent here is that changing the
discount rate can dramatically alter the present value of a given investment. This is
particularly true for forestry where (with the exception of felling expenditures) the
bulk of costs occur early in a rotation while felling revenues can be long delayed.
This impact can be demonstrated by examining the discount factor (DF) implied
by each discount rate. The DF shows the proportion (from 1 to 0) by which future
costs or bene¬ts should be multiplied to obtain their equivalent present-day value.
Figure 5.3 illustrates the DF for four discount rates (each of which has some rele-
vance for our analysis and which we discuss subsequently) as time progresses from
the present (year 0) into the future. As can be seen, for any discount rate, the further
into the future that a cost or bene¬t occurs, the lower is the DF and consequently the
38 Introductions are given in Pearce (1986), Hanley and Spash (1993) and Perman et al. (1999). Other useful
sources include Lind (1982a) and Markandya and Pearce (1994).
Timber valuation 133

Figure 5.3. Discount factor curves.

lower is the present value of that cost or bene¬t. Furthermore, we can also see that
changes in the discount rate imply very substantial alterations in the speed at which
the DF declines. For example, for net bene¬ts (bene¬ts minus costs) occurring ¬fty
years from planting we can see that at a 1.5 per cent discount rate we have DF =
0.5 (i.e. the present-day value is about half the net bene¬t received in year 50)
whereas with a 12 per cent discount rate, DF is virtually zero (i.e. the present value
of net bene¬ts received ¬fty years hence is almost nil).
We discuss the choice of discount rate subsequently, but for now the important
message is that discounting can very substantially affect the present-day value of
long-term investments like forestry, and the higher the discount rate the lower that
present-day value. As stated previously, this increases the impact of YC upon felling
date. Just as a higher growth rate results in an earlier optimal felling date, so does
a higher discount rate. Discounting makes it in the interest of forest managers to
obtain timber-felling revenues earlier rather than later, to the extent that they trade
off gains in timber volume against the discounting-induced reduction in the value
of that delayed timber volume.
The impact of varying yield class and discount rate upon optimal felling
age was calculated using the FIAP software mentioned previously. FIAP op-
erates by maximising the net present value of a stand subject to several user-
determined parameters. Results from this analysis are given in Table 5.6 which
shows the extent to which felling age declines as both yield class and discount rate
Application of the FIAP software indicated that it was insuf¬ciently ¬‚exible to
conduct our required analyses concerning variation of grant levels. Therefore, yield
134 Applied Environmental Economics

Table 5.6. Optimal felling age for various discount rates: Sitka spruce, YC6“24

Yield class
rate (%) 6 8 10 12 14 16 18 20 22 24
2 80 78 74 70 69 68 66 66 66 65
3 73 72 69 63 60 58 57 57 56 56
4 68 67 64 58 54 51 50 50 49 48
5 64 62 60 56 52 49 46 44 44 44
6 60 58 56 54 50 47 43 42 41 40
8 54 53 51 50 47 44 42 40 37 35
10 50 48 47 46 44 42 40 38 36 34
12 47 44 43 42 41 40 38 36 34 33

Notes: Optimal felling age (in years from planting) maximises NPV given the relevant
discount rate (r) and yield class combination. The above ¬gures treat the planting year
as year 0. The table was calculated using FIAP running at the Forestry Commission
headquarters at Edinburgh (except for the row for r = 3% which was interpolated). The
authors are obliged to Jane Sinclair and Roger Oakes at Edinburgh for assistance.
The table uses the following FIAP settings: spacing = 2.00 — 2.00; thinning = line,
MTT; delay on ¬rst thinning = none; stocking = 85%; successor crop NPV = 0;
price“size curve = GB conifer 1992; thinning price differential (£ 1992/93) = 0.30/m3 ;
charge per m3 (£ 1992/93) = 3.68/m3 .

models for YC6“24 Sitka spruce (from the tables given in Edwards and Christie,
1981) were transferred into a database for use in association with a statistical
package (Minitab, 1994) allowing the authors to write macros for repetitive data
analysis. In this manner, desired grant scenarios (discussed subsequently) could be
speci¬ed and their net present values (NPV) calculated.39 This model allows us to
convert yield class estimates into NPV equivalents taking into account any desired
grant scenario. Our yield class predictions and their estimated values are given in
Chapter 6.

Beech costs and revenues
Information on hardwood planting costs is far less readily available than for conifers.
Data were collected both from interviews with managers of broadleaf woodlands40
and from certain published sources (Lewis, pers. comm., 1988; Hart, 1987 and
pers. comm., 1990). However, the distributions of revenues and costs are similar to

39 Examples of the year-by-year revenue and cost streams derived from such models are detailed in Bateman
40 Notably Fred Lewis, Kerswell, Exminster and Cyril Hart, Chenies, Dean.
Timber valuation 135

Figure 5.4. Price“size curves for beech in Great Britain. (Source: Drawn from data given
in Whiteman et al., 1991.)

those for conifers, with high costs at planting and felling, mainly maintenance and
thinning costs at other times, and revenues at felling and to a minor degree from
thinnings (details are given in Bateman, 1996).

The factors affecting broadleaf timber revenues are the same as those relevant to
conifers, with price varying positively with tree volume. In their study of price“size
curves for broadleaves, Whiteman et al. (1991) show that, because thinnings have
relatively high extraction costs per m3 , standing prices for thinnings are on average
24 per cent below the price per m3 paid for clear fell timber. Consequently, two
price“size curves are estimated (with a third, average curve being reported for
ease of generalised account rather than for individual plantation assessment). As
hardwood timber values vary considerably among species, price“size curves are
estimated for individual species (unlike the generalised conifer relationship), with
those for beech being illustrated in Figure 5.4.
With timber volume and the price“size curve de¬ned, we can calculate annual
timber revenues, subtract costs per annum and derive the net timber bene¬t val-
ues for each year from planting to felling. As before, the optimal felling age de-
clines as the yield class and discount rate increase. This relationship was analysed
as described previously, results being given in Table 5.7.
Finally, hardwood yield class models and associated revenue and cost streams
were linked via spreadsheet to a statistical analysis package to allow them to be in-
tegrated with available grants and subsidies. Net present values for any user-de¬ned
136 Applied Environmental Economics

Table 5.7. Optimal felling age for various discount rates:
beech, YC4“10

Yield class
Discount rate (%) 4 6 8 10
2 125 120 119 118
3 105 99 95 93
4 91 85 80 78
5 81 75 71 69
6 75 69 65 62
8 65 59 56 53
10 58 52 48 47
12 53 47 43 42

Notes: Optimal felling age (in years from planting) maximises NPV
given the relevant discount rate (r) and yield class combination.
The above ¬gures treat the planting year as year 0. The table
was calculated using FIAP running at the Forestry Commission
headquarters at Edinburgh (except for the row for r = 3% which
was interpolated). The authors are obliged to Jane Sinclair and
Roger Oakes at Edinburgh for assistance.
The table uses the following FIAP settings: spacing = 1.20 —
1.20; thinning = broadleaved, intermediate thin; delay on ¬rst
thinning = none; stocking = 85%; successor crop NPV = 0;
price“size curve = broadleaves for 1989/90 T.R.; thinning price
differential (£ 1992/93) = 0.30/m3 ; charge per m3 (£ 1992/93) =
3.68/m3 .

yield class/discount rate/subsidy scenario could then be derived as detailed previ-
ously for the conifer models.

Discount rates
Any investment in forestry essentially trades off initial costs against delayed bene-
¬ts. This is conventionally achieved by calculating the NPV of the investment via
a discount rate (r) which is in¬‚uenced by positive time preference, the opportunity
cost of capital and other factors discussed subsequently. Now, this research sets out
to examine two perspectives on whether agricultural land should be converted to
forestry: that of the farmer; and that of society. However, there is good reason to
suppose that these two will have differing discount rates.41 Put at its simplest, if we
consider time preference, farmers are mortal while society is, at very least, much
41 For further discussion on the divergence of social from private discount rates see Baumol (1968), Goodin
(1982), Sen (1982), Sagoff (1988), Pearce and Turner (1990), Markandya and Pearce (1994) and Pearce and
Ulph (1998).
Timber valuation 137

longer lived (we hope!). Therefore, society is likely to place relatively more weight
on delayed returns than is an individual farmer. Accordingly we might expect soci-
ety to have a lower rate of positive time preference. A similar result is obtained when
we consider discounting based on the opportunity cost of capital. For a risk-averse
society this should imply a relatively low social discount rate dictated by the rate of
return on riskless investments (government bonds, etc.). However, for the private
individual the opportunity cost of capital should be relatively high on account of
the rates of return available from alternative investments.42 Both arguments suggest
that private (agricultural) discount rates might be higher than social discount rates.
In this section we examine evidence regarding agricultural and social real rates of
discount. However, before turning to this we need to address one further complica-
tion, the comparability of agricultural and forestry investments. Farmers commonly
make decisions on an annual cycle whereas the time horizon of a forester is usually
a full rotation of a stand, which typically varies from a minimum of four decades
for conifers to over a century for hardwoods. Comparison of annual gross margin
with rotation NPV is therefore problematic. Two approaches exist. First, agricul-
tural margins can be assessed and discounted over at least a rotation length. Second,
woodland NPV can be converted to an annual equivalent, i.e. the constant annual
return (or ˜annuity™) which, over the length of a rotation, would be valued equally
with the standard NPV sum. After discussion with relevant experts43 it was decided
that the former option lacked credibility as farmers (who are the relevant decision-
makers) are used to annual rather than rotational decision-making. Therefore, the
calculated NPVs for all our yield models (using the relevant agricultural or social
discount rate) were converted to annuity equivalents.44

Farmers™ discount rates
Literature review
A priori we would expect that the relatively lower rates of return exhibited by the
agricultural sector (compared to the industrial and commercial sectors) would re-
sult in somewhat lower real discount rates than those implied by the government™s
8 per cent average rate of return required of public sector agencies selling commer-
cially or the 6 per cent rate used for pure public good activities (H.M. Treasury,
1991; Pearce and Ulph, 1998).45 However, little explicit work has been published

42 This may be a less strong argument if re-investment is restricted to the agricultural sector where rates of return
are historically low.
43 Notably Colin Price and Rob Willis, University of Wales, Bangor.
44 The conversion process and related formulae are discussed in Bateman (1996).
45 The 8 per cent estimate is ˜based on average returns on assets achieved in the private sector for activities with
low cyclical year by year variability™ (H.M. Treasury, 1991). In 2002 H. M. Treasury published consultations
signalling a reduction of the pure public sector discount rate from 6 to 3.5 per cent.
138 Applied Environmental Economics

in this area, with most commentators examining real rates of return or agricultural
interest rates rather than discount rates per se.
The early work in this latter area is predominantly American, dating back to
Melichar (1979) who proposed that real rates of return were determined by expected
rents and actual and expected in¬‚ation rates. Feldstein (1980) modi¬ed this theory
by suggesting that such a mechanism may ultimately be driven by in¬‚ation acting
upon land prices, while Tanzi (1980) extended this by proposing a further link to
the business cycle. However, in an empirical test of these theories, Alston (1986)
failed to ¬nd a long-run link between in¬‚ation and land prices, and Burt (1986)
rejected such complex models in favour of a simple long-run equilibrium land price
approach which yields an estimate of the real rate of return of 4 per cent per annum.
Turning to the UK, similar results are reported by Cooper (1992) who uses a
real interest rate approach, based on the work of Brase and La Due (1989), to
estimate a mean value of 4.5 per cent for UK agriculture for the period 1964“90.
While agricultural interest rates are highly variable,46 such a result seems to be
roughly echoed by lending practice during our study period. In correspondence
with the authors, the National Westminster Agricultural Of¬ce (a major source of
farm ¬nance) quoted an average real agricultural interest rate of 4 per cent over
base rates.47
A lower interest rate, averaging 2.44 per cent above base rate, is reported by
Cunningham (1990) in a study of MAFF surveys, while MAFF itself employed an
agricultural interest rate risk premium of 2.78 per cent above base rate during our
study period.48 However, there are several problems with extrapolating from interest
rates to discount rates. First, if base rates change frequently, lags in the adjustment
system may confound the analyst. Second, interest rates vary signi¬cantly across
farms, projects and time.49 Third, the link between interest rates and discount rates
may be weak in that the former relate to returns on new investments rather than on
total assets (which are likely to be lower).
In addressing this latter point, Harrison and Tranter (1989) analysed the pe-
riod 1978/79 to 1986/87, reporting a mean real rate of return on all assets of
2.56 per cent.50 Positive time preference would suggest that the real discount rate
might be somewhat higher than this. Such an argument would support the ¬ndings
Annual averages range from ’13.01 per cent (1976) to +10.08 per cent (1990) in Cooper (1992).
47 Pers. comm. Sue Train, National Westminster Agricultural Of¬ce (NWAO), and letters from Brian Montgomery,
Senior Executive, NWAO, July 1993. However, this correspondence highlighted the variation in rates across
farms and projects. For example, a range of real rates of 0“5 per cent was given for differing projects and times
by Charles Morgan of Chris Grote Farms, Norfolk.
48 Pers. comm. Douglas Cooper, MAFF, 1993.
49 This point was made in correspondence with NWAO (see above) and Paul Hill (Wye College) who both stated
that while interest rates were roughly 2 per cent above base rates for good risks, they could be much higher for
risky investments.
50 Sample extends across Great Britain. Rates are quite consistent, only ranging from 1.87 per cent to 3.90
per cent.
Timber valuation 139

of Lloyd (1993) who uses a capital asset pricing model of agricultural land prices
in England and Wales for the period 1946“89 to empirically derive a long-run real
discount rate of 3.6 per cent.
These latter studies provide what we feel is the best evidence on agricultural real
discount rates. However, none of these studies is speci¬c to our Welsh study area
and so our own rate of return analysis was undertaken.

Empirical work
Two studies of agricultural rates of return in Wales were undertaken: a short time-
series analysis of the period 1987“92; and a cross-sectional study of the 1989/90
base year. In both cases data were provided by the Welsh division of the Farm
Business Survey (FBS, 1988, 1989, 1990, 1991, 1992) which de¬nes the nominal
return as farm income expressed as a percentage of tenants™ capital.51

Rates of return in Wales, 1987“92
Table 5.8 presents nominal rate of return (RoRn ) statistics for various categories
of farm identi¬ed during FBS surveys for the years 1987/88 to 1991/92. These
categories are further subdivided by farm size.
Statistical analysis was undertaken for all farm categories except pig, poultry
and cropping farms as these are minor activities in Wales and were not separately
classi¬ed after 1989. This showed that specialist or mainly dairy farms achieved
signi¬cantly higher RoRn than did other farms. Subsequent analysis also isolated a
quadratic relationship with size, measured in British stocking units (BSU), showing
that RoRn rose with size but at a diminishing marginal rate. RoRn also ¬‚uctuated
annually although only one year (1988/89) was found to be signi¬cantly different
from all others. A variety of further variables taken from the FBS database (see
discussion in Chapter 8) were also tested and found to be insigni¬cant in predicting
RoRn .
A model was constructed and tested across a variety of functional forms. Our best-
¬tting model is reported as Equation (5.1). Tests for interactions, multicollinearity,
autocorrelation and heteroscedasticity failed to isolate any signi¬cant problems
with this model.
’18.62 + 7.68 DAIRY + 9.57 HIYEAR + 1.13 BSUt ’ 0.0105 BSU2
RoRn t
(’9.06) (6.32) (6.53) (8.38) (’6.33)

51 The Farm Business Survey (FBS) was an arm of MAFF (operating in Wales under the auspices of the Welsh
Of¬ce) which conducted annual surveys of a representative sample of farms throughout the country. The sample
size averaged 734 farms per annum over our 1987“92 study period; however, many farms are retained in the
sample for about three years. The number of distinct farms in the time series is 2,867.
Table 5.8. Agricultural nominal rate of return (RoR) on tenants™ capital: Wales 1987/88“1991/92

1987/88 1988/89 1989/90 1990/91 1991/92 1987“92
mean mean mean mean mean mean
Farm type and size size size size size size
n n
size (BSU) (BSU) RoR (%) n (BSU) RoR (%) n (BSU) RoR (%) n (BSU) RoR (%) n (BSU) RoR (%) (BSU) RoR (%)

Specialist dairy
Up to 15.9 30 11.87 10.04 30 11.85 13.89 28 11.37 4.84 20 10.42 17 10.15 125 11.29 5.96
’0.13 ’6.25
16“23.9 26 19.57 10.21 26 19.32 13.02 18 19.98 14.29 14 19.27 4.27 20 19.48 9.27 104 19.52 10.64
24“39.9 35 30.82 13.76 35 31.23 26.52 38 30.95 17.81 34 31.63 13.30 28 31.13 15.24 170 31.15 17.44
40 and over 27 67.13 25.10 27 69.03 36.06 31 67.10 27.37 36 63.21 19.69 31 60.70 20.65 152 65.22 25.32
All sizes 118 31.83 18.11 118 32.33 27.77 115 34.21 21.16 104 36.82 15.56 96 34.54 16.25 551 33.85 20.01
Mainly dairy
Up to 23.9 14 14.14 6.65 14 14.14 4.78 14 15.38 0.01 25 16.31 15 14.15 82 15.02 1.06
’1.12 ’2.99
24“39.9 15 31.45 13.41 15 31.79 18.32 13 31.91 13.72 9 34.61 13.60 11 34.52 13.68 63 32.61 14.72
40 and over 18 56.08 15.55 18 54.48 19.36 18 59.89 16.08 15 73.32 10.05 16 72.21 13.70 85 62.63 15.15
All sizes 47 35.73 13.83 47 36.37 17.31 45 37.96 13.24 49 37.12 8.11 42 41.20 11.67 230 37.59 12.81
Hill sheep
Up to 15.9 24 10.13 24 10.55 1.34 25 22 11.36 116 10.33
’3.84 10.03 ’18.04 9.69 ’16.54 21 ’3.15 ’8.11
16 and over 27 32.57 13.96 27 31.67 20.06 24 33.68 6.14 32 34.28 11.14 142 32.65 9.78
31.14 ’1.04 32
All sizes 51 22.01 10.14 51 21.73 15.99 49 21.62 0.54 54 25.20 8.76 258 22.62 6.26
22.40 ’3.84 53
Hill cattle & sheep
Up to 15.9 39 10.30 3.91 39 10.64 9.49 35 10.87 10.44 172 10.75
’8.81 34 11.52 ’11.80 25 ’5.86 ’1.94
16“23.9 29 19.07 5.58 29 19.52 12.21 32 18.87 19.99 4.70 149 19.40 2.66
’2.55 36 19.65 ’4.06 23
24“39.9 26 30.14 12.87 26 30.33 17.70 28 29.82 5.72 29 31.37 2.57 25 31.41 8.29 134 30.61 9.23
40 and over 14 57.77 20.84 14 57.36 20.12 15 70.36 7.22 18 74.04 6.70 81 68.13 9.29
76.13 ’3.53 20
All sizes 108 23.59 12.11 108 23.82 15.85 110 26.13 2.38 117 32.12 5.37 536 26.79 6.43
28.88 ’2.85 93
Upland cattle & sheep
Up to 15.9 16 9.33 16 8.65 3.53 16 9.29 19 86 8.58
’3.66 ’7.42 8.29 ’17.65 19 7.56 ’15.09 ’8.64
16 and over 20 26.21 4.64 20 27.43 7.52 18 23.29 23 30.43 2.14 106 26.82 1.68
’2.07 25.66 ’3.53 25
All sizes 36 18.71 2.71 36 19.08 6.60 34 16.70 42 192 18.65
’3.57 17.80 ’6.57 44 20.55 ’0.81 ’0.51
Lowland cattle & sheep
All sizes 13 12.64 13 12.68 1.38 17 18.14 31 22.84 17.90 100 18.11
’1.50 ’5.05 ’1.59 26 ’0.06 ’1.38
Pig & poultry
All sizes 6 29.77 3.96 6 22.64 12.94 * * * * * * * * * 12 26.20 8.45
Cropping farms
All sizes 11 44.84 10.96 11 42.89 1.54 * * * * * * * * * 22 43.87 6.25
Summary statistics
Total no. of farms 390 390 370 394 353 1,897
Mean 28.07 9.54 27.81 14.06 28.45 4.91 29.91 0.61 30.16 5.40 29.23 7.07
Trimmed mean 27.11 9.43 26.75 13.61 27.26 4.93 28.61 0.57 29.04 5.67 28.37 6.95
Standard deviation 15.92 7.40 15.93 8.99 17.85 11.17 19.40 10.03 18.98 8.94 17.05 8.45
S.E. mean 3.32 1.54 3.32 1.87 3.90 2.44 4.23 2.19 4.14 1.95 3.56 1.76
Minimum 9.33 8.65 1.34 8.58
’3.84 9.29 ’18.04 8.29 ’17.65 7.56 ’15.09 ’8.64
Lower quartile 14.14 3.96 14.14 6.60 18.11 1.06
16.04 ’3.06 17.06 ’3.95 16.02 ’1.90
Upper quartile 32.57 13.83 32.33 19.36 33.94 14.01 35.72 9.08 34.53 12.68 33.85 12.81
Maximum 67.13 25.10 69.03 36.06 70.36 27.37 76.13 19.69 74.04 20.65 68.13 25.32

Notes: 1 The summary statistics are calculated by omitting the ˜All sizes™ category means (except where this is the only entry for the category).
2 The 1987“92 mean rate of return is weighted by annual numbers of farms as is the average BSU size.
3 * = not available.
4 n = number of farms in sample.
5 rate = nominal rate of net return on tenants™ capital, calculated as follows:
MII = Output ’ Inputs
and RoR = (MII/TC) * 100
(i) Output = All returns from an enterprise, plus the market value of any of its products transferred out to another enterprise, plus the market value of any production from
the enterprise given to workers or consumed on the farm. In the case of livestock enterprises, the value of purchased livestock and the market value of livestock transferred
in from another enterprise are deducted. All totals are adjusted for changes in valuation.
(ii) Inputs = Feeds (purchased concentrates, home-grown concentrates, purchased bulk) + tack and stock keep + veterinary and medicines + other livestock costs +
fertilisers + seeds (purchased and home-grown) + other crop costs + labour (farmer and spouse, paid, unpaid, casual) + machinery (contract, repairs, fuels, depreciation)
+ general farming costs + other land expenses + rent/rental value + rates. (Note that as a nominal farmer/spouse labour cost is included, we are calculating net rather than
gross returns.)
(iii) MII = Management and Investment Income; the MII represents the reward for the farmer™s (and spouse™s) management and interest on the tenants™ capital employed
on the farm.
(iv) TC = tenants™ capital: the value of livestock, machinery, crops (including cultivations) and stores. In the Farm Business Survey tables, tenants™ capital is expressed as
the average of the opening and closing valuations for these items.
Sources: Data taken from FBS (1988, 1989, 1990, 1991, 1992).
142 Applied Environmental Economics

RoRn = nominal net rate of return on tenants™ capital (per cent)
DAIRY = 1 for dairy farms (FBS specialist or mainly dairy categories);
0 otherwise
HIYEAR = 1 for 1988/89; 0 otherwise
BSUt = average size of farm type in year t
BSUt 2 = BSUt * BSUt

R2 = 77.9%; R2 (adj.) = 76.7%; F = 66.10; p < 0.001; ¬gures in brackets are

Average RoRn for dairy and non-dairy farms (denoted RoRD and RoRND re-
n n
spectively) over the study period can now be evaluated by substituting each
group™s mean values for explanatory variables into Equation (5.1).52 For dairy
farms this gives RoRD = 12.68 per cent, while for non-dairy farms this gives
RoRn = 1.62 per cent. This large difference between dairy and non-dairy farms

is highly signi¬cant and indicates the very considerable positive impact which
CAP milk quotas have had upon dairy farm incomes and the parlous state of the
non-dairy, agricultural sector within our study area. We return to this theme in
Chapter 8.
Conversion to real rates of return (RoRr ) was achieved using retail price indices
published by the Central Statistical Of¬ce (1993b).53 These show an average in¬‚a-
tion rate for the period 1987“92 of 5.81 per cent implying RoRD = 6.86 per cent
and RoRr = ’4.18 per cent.

Rates of return in Wales, 1989/90
We were particularly interested in RoRn during our study base year of 1989/90
and for the sample of farms that formed the basis of our analysis of agricultural
values (presented in Chapter 8). The ¬nding presented above suggests that this year
may be typical of a longer time period. Furthermore, the representative sample of
240 farms provided by FBS for our agricultural analysis included grid reference
locations which allowed us to consider a wider range of explanatory variables than
previously. These included data covering the environmental attributes of the farm
(soil type, altitude, etc.) obtained from the LandIS database discussed in Chapter 6.
However, while many such variables were signi¬cant predictors of RoRn they
proved to be collinear with the DAIRY and BSU variables considered previously,

52 The assumption of normality implicit in the use of means is relaxed in further testing reported in Bateman
(1996) and is shown not to have a signi¬cant impact upon ¬ndings.
53 Use of the RPI rather than some farm price index re¬‚ects the fact that, ultimately, investment funds could be
moved out of the agricultural sector.
Timber valuation 143

and these latter variables provided a superior degree of explanation. Following tests
of functional form, our best-¬tting model for these 240 farms was:
’39.37 + 12.12 DAIRY + 13.21 ln BSU
RoRn (5.2)
(“9.66) (6.50) (9.51)

RoRn = nominal rate of return, 1989/90
ln BSU = natural log of farm size in BSU
DAIRY = 1 if dairy farm; 0 if non-dairy farm54
R2 43.3%; R 2 (adj.) 42.8%; n 240; ¬gures in brackets are t-statistics.

Substituting variable means into Equation (5.2) allows us to calculate the RoRn for
dairy and non-dairy farms, RoRD = 15.27 per cent and RoRND = ’2.70 per cent
n n
respectively. Adjusting for in¬‚ation (which averaged over 9 per cent in 1989/90)
implies RoRD = 5.81 per cent and RoRND = ’12.2 per cent. These results reiterate
r r
our previous conclusion regarding the gulf between dairy and non-dairy farms in
Wales. Indeed, here we see the latter group making negative nominal and real rates
of return, a situation which is clearly unsustainable in the long run and has been
evident in disastrously low income levels in the Welsh non-dairy sector during the
1990s (see Chapter 8).

Farm discount rates: summary
While data are scarce, available information suggests that discount rates for agri-
culture will be low relative to those in other sectors of the economy. Our survey
suggests that estimates of general rates as low as 3 per cent in real terms are quite
defensible. However, our analysis of rates of return highlights the great variability
which exists in the performance of different sections of the agricultural community
and in particular, with reference to Wales, the disparity between dairy and non-
dairy farms. As Table 5.8 indicates, during our study period the elite of dairy farms
consistently recorded nominal (and sometimes real) rates of return in double ¬g-
ures, while, as subsequent analyses have shown, Welsh non-dairy farms regularly
showed negative real rates of return. These latter rates were clearly unsustainable
and the exodus from Welsh hill-farming throughout the years of our study period
has continued up to the present day.
The link between rates of return and discount rates is not simple, involving as
it does consideration of time preference. This may raise discount rates above rates

˜Non-dairy™ is de¬ned as less than 20 per cent of farm output being milk (n (non-dairy) = 126 of which 124
had zero milk revenue, 1 had 3 per cent milk revenue and 1 had 7 per cent milk revenue (the next farm had 24
per cent milk revenue)).
144 Applied Environmental Economics

of return, although studies such as Lloyd (1993) suggest that this will not be by
a particularly large amount. In the case of dairy farms, rates of 12 per cent and 6
per cent were selected to provide, respectively, an upper-bound and majority best
estimate of real discount rates for Welsh dairy farms during our study period. A
6 per cent rate is also the government™s speci¬ed discount rate (H.M. Treasury, 1991)
for ˜returns accruing to the public sector from projects in the public sector™ (Pearce
and Ulph, 1998: p. 268), a rate which has applied from 1989 to the present. For
non-dairy farms, rates were clearly signi¬cantly lower, with negative rates of return
being the reality for many farms in the sector. However, given the unsustainability
of negative rates, we felt that a real discount rate sensitivity range from 1.5 per cent
to 3 per cent would both embrace the majority of such farms and provide results
which were of more relevance to those non-dairy Welsh farms which have survived
the traumas of the 1990s.

Social discount rates
We can now formalise and extend our analysis of the factors in¬‚uencing discount
rates as per Equation (5.3) which draws upon the notation of Pearce and Ulph

δ + µg (5.3)


= discount rate
δ rate of time preference (the rate at which utility is discounted)
µ elasticity of the marginal utility of consumption schedule
= expected growth rate of average consumption per capita

Economic commentators have long acknowledged that the values of the variables
identi¬ed in Equation (5.3) which are appropriate to decisions affecting just the
individual investor may differ from those values appropriate to decisions affecting
the whole of society. The of¬cial UK social rate is derived from empirical data aver-
aged over a wide variety of sectors giving values of about 2 for each of the elements
of the basic discount rate formula detailed in Equation (5.3), i.e. r = δ + µg = 2 +
(2 * 2) = 6 per cent. However, a wide variety of views exists regarding the value
of each of these elements.
Perhaps most controversial is the value of δ, the pure rate of time preference
in the social discount rate (rs ). If society is immortal (or aspires to be) then, as
very many eminent commentators have pointed out, δ should be very low or zero
(Ramsey, 1928; Pigou, 1932; Solow, 1974b, 1992; Broome, 1992; Cline, 1992a,
Timber valuation 145

1993; Fankhauser, 1993, 1995; Price, 1993; Arrow et al., 1996; Pearce and Ulph,
1998). Such arguments have been reinforced by the debate surrounding sustain-
able development. This has centred upon notions of Rawlsian equity (Rawls, 1972)
wherein, to be truly equitable, decisions regarding the use of resources (be they
involving man-made, human or natural capital)55 should be made behind a ˜veil of
ignorance™ with respect to their temporal impact. Such a view is fundamental to
the often quoted Brundtland Commission de¬nition of sustainable development as
˜development that meets the needs of the present without compromising the ability
of future generations to meet their own needs™ (World Commission on Environ-
ment and Development, 1987). Price (1993) sees this as only interpretable as an
abandonment of discounting for global-level social decision-making.
A more ˜conventional™ view is given by Fankhauser (1993) who sees the require-
ments of sustainable development as implying that δ = 0, but not necessarily that
rs = 0. Pearce and Ulph (1998) review an extensive literature on social δ, reporting
a range from 0“1.7 per cent but favouring (for empirical reasons) a relatively high
best estimate of δ = 1.4 per cent.
Turning to consider the elasticity of the marginal utility of consumption (µ),
Price (1993) reports a wide spread of private sector rates, generally ranging from 0.5
(Squire and van der Tak, 1975) to 3 (Little and Mirlees, 1974).56 Stern (1977) ¬nds
many values in the region of 2.57 However, we would expect the social preference
value of µ to be somewhat lower than that found in the market. This is borne out by
Pearce and Ulph (1998) who report a best estimate of social µ of 0.8 with a range
of 0.7“1.5.
The social value of g (the expected rate of growth of average consumption per
capita) is typically taken as being the real rate of growth of national income. Fol-
lowing such an approach, Lind (1982b, 1982c) argues for a maximum rate of
g = 2 per cent.58 However, the sustainable development debate has highlighted the
problem that accounting measures such as GDP often ignore changes (frequently
losses) in the natural and other non-market capital base of the economy (Repetto
et al., 1989).59 Taking account of these, Pearce and Ulph (1998) suggest a best
estimate for g in the UK of 1.3 per cent with a range of 1.3“2.2 per cent.
Taking best estimates from Pearce and Ulph (1998) gives a central estimate of
rs for the UK of about 2.4 per cent (= 1.4 + (0.8 * 1.3)). While this may seem

55 For an introduction to the role of capital types in notions of sustainability, see Turner and Pearce (1993) or
Pearce and Barbier (2000). While radical from a neoclassical perspective, more extreme (but very interesting)
views are given in the work of Herman Daly (Daly, 1977; Daly and Cobb, 1990; Daly, 1995).
µ is negative but we report modulus values following the convention of Pearce and Ulph (1995).
Stern (1977) reports one extreme value of µ = 10.
58 Turner et al. (1994) point out that real growth in GDP in less developed countries is often much lower or even
59 Repetto puts forward an adjusted, sustainable national income measure. See also Pearce et al. (1989), Pearce
and Warford (1993) and Pearce (1993).
146 Applied Environmental Economics

low with respect to the Treasury™s rate,60 it is higher than that put forward by
certain other commentators, particularly with respect to the discounting of global
warming damages (perhaps the most potent challenge to intergenerational equity
in the history of man). While not stating any particular rate, Arrow et al. (1996)
make explicit reference to the range of 0“2 per cent used by Cline (1992a) in his
economic analysis of long-run climate change models. Similarly, in his evaluation
of the social costs of greenhouse gas emissions, Fankhauser (1993) uses a central
(mode) estimate of rs = 0.5 per cent with a range of 0“3 per cent (the upper end
being mainly for comparison with other studies).
A further complication arises from the issue of multiple discount rates: the no-
tion that social preferences may diverge radically between projects to the extent
that a single discount rate is something of an oversimpli¬cation. As Arrow et al.
(1996) and many earlier commentators have pointed out, the key factor here is
substitutability, i.e. the extent to which development bene¬ts (often in terms of
man-made capital, K m ) can be traded off against costs (generally in terms of natu-
ral capital, K n ). Assuming that sustainability is socially desirable and that both sets
of capital can be measured in some comparable numeraire (presumably money),
then perfect substitutability would mean that any project would simply have to
pass a standard Hicks“Kaldor hypothetical compensation test to be sanctioned.61
In the literature of sustainable development this has been termed the ˜very weak
sustainability™ rule (Turner and Pearce, 1993), which states that, provided total net
bene¬ts (total capital) are non-declining, a project may be sanctioned. This perfect
substitutability assumption may be more acceptable for some K m /K n swaps (e.g.
Sitka spruce plantations into paper, thence into money and so back to new planta-
tions) than for others (e.g. the destruction of SSSIs to make way for motorways62 ),
i.e. some K n destruction is irreversible.
Pearce and Turner (1990) de¬ne a continuum of capital types from money (the
purest form of K m ), through various types of K n (trees, land, etc.) to ˜critical natural
capital™ (K c ),63 the last being those services of the planet vital to life support (climate
and atmosphere control, ozone layer, etc.). As we move away from money along
this continuum, the potential for substitution, rather than staying constant, falls until
it reaches zero with K c . n
Such a view causes problems for cost-bene¬t analysis if we feel that the accumu-
lation of K m does not adequately compensate for the loss of K n . This is the view of
the ˜weak sustainability™ rule (Turner and Pearce, 1993) which argues that stocks of
K c should be inviolate, while K n should be subject to some safe minimum standard

60 Pearce and Ulph (1998) suggest that for policy purposes the Treasury should use a range of 2“4 per cent.
61 See almost any cost-bene¬t text, for example Pearce (1986).
62 As in the case of the M3 Twyford Down extension in southern England.
63 The term is borrowed from Pearce and Turner (1990).
Timber valuation 147

(SMS) below which use should be prohibited.64 A further interpretation, the ˜strong
sustainability™ rule, in effect argues that such an SMS has already been breached
and that any further use of K n should be offset by actual physical compensation
in terms of shadow projects restoring, transplanting or recreating levels of any K n
used in future projects.65
The divergence between best estimates of rs given by Pearce and Ulph
(2.4 per cent) and Fankhauser (0.5 per cent) or Arrow et al. (implicitly 0“2 per
cent) can therefore be viewed as comparing a general rate of K m /K n substitutability
with that of a non-substitutable good: global climate. The implication of such an
analysis is that, because of the various rates of substitutability and irreversibility
inherent in the differing capital bases of each project, society will have different
discount rates for different projects. Furthermore, we could extend this line of rea-
soning to the individual costs and bene¬ts of a single project so that, in our forestry
case study, UK timber (for which losses are reasonably reversible) might attract a
higher rs than recreation bene¬ts (which arguably belong to a more depleted set of
K n ), which in turn is more discounted than carbon storage (which contributes to
the K c stock of global climate services). Following this argument we examine the
impact of using differing discount rates in our forestry case study.
In practice, the variance of rs within a project is clearly a decision-making night-
mare and opens up the potential for discount rate ˜management™ abuses. Indeed,
the avoidance of abuse may be the most cogent argument for adopting a single rate
policy. Henderson and Bateman (1995) report numerous examples from around
the world of both inter- and intraproject multiple discount rates.66 However, these
appeared to be almost exclusively motivated by policy objectives rather than em-
pirical evidence regarding underlying preferences. Unfortunately, the manipulation
of discount rates to give policy-favoured projects a spurious sheen of ¬nancial re-
spectability is widespread if invalid.
The desirability of a single rate is therefore clear. The Pearce and Ulph (1998)
results (central estimate rs = 2.4 per cent; range = 2“4 per cent) are useful here but
we have to recognise that probably the recreation bene¬ts, and almost certainly the
carbon sequestration bene¬ts, of woodland would attract a lower than average rate
of public pure time preference. Accordingly, we have chosen a sensitivity analysis
64 Under weak sustainability, further use of K n up to the SMS must still be compensated for by re-investment
(savings) of the appropriate level of K m proceeds from each project (Turner and Pearce, 1993).
65 Under strong sustainability an individual project must compensate K n both in terms of K m savings and by
appropriate contributions to an offset physical compensation, shadow project fund. Such physical compensation
must be actual rather than hypothetical (rejecting the Hicks“Kaldor rule). A still stronger view (very strong
sustainability) states that each project must have its own actual physical K n compensation shadow project (see
Turner and Pearce, 1993).
66 Henderson and Bateman (1995) examine theoretical and empirical arguments in favour of hyperbolic dis-
count rates. Bateman (1996) reassesses all of the analyses presented in this volume using a hyperbolic dis-
count rate and shows that this further increases the potential for transfers from agriculture to multipurpose
148 Applied Environmental Economics

for rs which includes one rate (1.5 per cent) below the Pearce and Ulph range67 and
another at the centre of that range (3 per cent). For comparative purposes we have
also employed the Treasury™s 6 per cent public sector discount rate throughout,
although we echo the sentiments of Pearce and Ulph that this seems ˜very dif¬cult
to justify™.

Discount rates: conclusions
Given the major impact which variations in the discount rate will have upon long-
delayed forestry returns, we feel that our discussion highlights the need to adopt a
sensitivity analysis approach. We feel that real social discount rates of 1.5 per cent
and 3 per cent are well justi¬ed as a reasonable range here. The Treasury™s 6 per
cent rate is also included for comparative purposes. Turning to consider farmers™
real private discount rates, the 1.5 per cent and 3 per cent rates are useful for
assessing decisions in the Welsh non-dairy agricultural sector.68 Conversely, rates of
6 per cent and 12 per cent roughly describe reasonable limits to apply to dairy farms
in Wales.69

The private value of timber production
The discussions in this chapter show that the private value of a productive planta-
tion is determined by a variety of factors including species, plantation costs, timber
yield, timber price (where both the price“size curve and assumptions regarding
future real prices are important), grants and subsidies, and the discount rate. All
these factors were brought together by integrating data from the FC yield models
(Edwards and Christie, 1981) for Sitka spruce (YC6“24) and beech (YC4“10)
within a series of spreadsheets. This allowed easy manipulation of all assumptions
(e.g. grant schemes, discount rates, optimal felling age,70 etc.) to produce a full
range of private NPV and annuity equivalent values. Results from this exercise
are reported in full in Bateman (1996) which details a variety of permutations,
ranging across all species, yield class, discount rate and subsidy scheme scenar-
ios. Results are also calculated for a single, optimal rotation of trees and for a
scenario of perpetual replanting after each felling. As this produces a plethora of
permutations, we reproduce results for just one scenario here. Figure 5.5 graphs

67 This also re¬‚ects the lower-range estimates of Fankhauser (1993) and Arrow et al. (1996).
68 We recognise that a number of these farms may not be attaining rates of return of even 1.5 per cent. However,
such farms are unlikely to keep operating in the long term. The 3 per cent rate also provides an assessment under
conditions similar to those likely to apply if discount rates are cut as recently proposed by H. M. Treasury.
69 Discussion of results obtained using hyperbolic discount rates is given in Bateman (1996).
70 Set as per Tables 5.6 (for conifers) and 5.7 (for broadleaves).
Timber valuation 149

Figure 5.5. Farmers™ private timber values for Sitka spruce (annualised equivalents of
a perpetual series of optimal rotations: r = 3%). Various yield classes and subsidy

annuity equivalents for the full range of Sitka spruce yield classes and all feasible
grant scheme registrations (using the abbreviations developed at the end of the
earlier section on grants (p. 128) assuming that a system of perpetual replanting is
used and a 3 per cent discount rate is applied. Figure 5.6 repeats the analysis for
For both Sitka spruce and beech we see that, as expected, annual equivalent
values rise with yield class (just as they fall with discount rate; see subsequent
results). As subsidy schemes are not linked to timber productivity the difference
between scheme payments is constant across yield classes. Comparison between
Sitka spruce and beech is interesting as it shows that, holding yield class constant
(i.e. YC 6, 8 or 10), returns from broadleaves are higher than for conifers. This is
due to higher prices and subsidy levels for broadleaves and occurs despite the lower
felling age of conifers. However, because conifers are capable of much higher yield
classes than broadleaves on almost any given site and, more importantly, because
such high-yield plantations have much lower felling ages (thus avoiding the severe
discounting that occurs with long-rotation broadleaves), they provide much higher
annual equivalents than broadleaves.
An overview of discounting impacts is given in Table 5.9 (full details for all
yield class/species combinations are presented in Bateman, 1996). Here annualised
150 Applied Environmental Economics

Table 5.9. Farmers™ private timber values for high-output Sitka spruce and
beech across various discount rates (annualised equivalents of a perpetual
series of optimal rotations)

Farmers™ private value (annualised equivalent, £/ha)
Discount rate
(%) Sitka spruce (YC24) Beech (YC10)
1.5 496.30 103.54
3 388.46 80.68
6 219.36 31.21
12 19.45 9.59

Note: Subsidy option for all cases is SUnda’CW = subsidy for previously unim-
proved grassland, not in a disadvantaged area and without Community Woodland

Figure 5.6. Farmers™ private timber values for beech (annualised equivalents of a perpetual
series of optimal rotations: r = 3%). Various yield classes and subsidy types.

equivalents for highest output Sitka spruce (YC24) and beech (YC10) under one
subsidy permutation are given for all the discount rates considered.
In subsequent chapters we examine how forest timber values compare with agri-
cultural returns under a variety of scenarios. However, we now turn to consider the
other, non-market, bene¬ts of woodlands.
Timber valuation 151

The social value of woodlands
In moving from the private to the social value of timber production a number of
issues need to be addressed. The basic plantation costs and timber (thinnings and
maincrop) bene¬ts can defensibly be used in an unaltered form as, unlike the prices
of agricultural produce, UK timber prices are not the subject of intervention or
otherwise controlled. However, we do have to subtract all grants and subsidies, as
these are simply transfer payments, to obtain our baseline social value for timber
net bene¬ts (see Bateman, 1996, for further details).
As discussed in our opening chapter, the social value of a woodland is more
than just the value of timber therein. In earlier work (Bateman, 1992) we identi-
¬ed and discussed a detailed set of environmental and non-environmental non-
market costs and bene¬ts which may arise from afforestation. Here we sum-
marise that discussion by brie¬‚y considering the major non-market items which
may need to be examined when moving from a private to a social assessment of

Non-environmental non-market social costs and bene¬ts
Here we discuss four major issues: national security; economic security; import
substitution; and employment.

National security
While national security formed the impetus for the creation of the Forestry Com-
mission just after the First World War, and was an important spur to planting after
the Second World War, the prospect of the UK being blockaded from receiving
timber supplies for any extended period seems rather unlikely. We therefore con-
clude that there are no signi¬cant national security bene¬ts to be derived from the
expansion of a domestic supply capability.

Economic security
While not of strategic importance, uninterrupted security of supply does bring
avoided-cost bene¬ts. In a study of this issue, Pearce (1991) states that ˜an evaluation
of the chances of embargoes and other supply interruptions suggests that a small in-
crement in prices of 0.2 to 0.8 per cent to re¬‚ect the shadow value of economic secu-
rity would be justi¬ed™. Accordingly, timber bene¬ts were increased by 0.5 per cent
in our social evaluation models.71

71 Note that this is an across-the-board single increase, not a compounding of an annual real price increase.
Consequently the net effect is very small.
152 Applied Environmental Economics

Import substitution
As mentioned earlier in this chapter, timber is one of the UK™s major import items.
In 1999 the UK imported over 21 million m3 of wood and panels and over 25
million m3 of pulp and paper (FC, 2001c). Despite this dependence on imports,
the basic theory of comparative advantage has long shown that this does not nec-
essarily imply that the UK should strive to change this situation (see, for example,
S¨ derstern, 1980). This theory shows that a given amount of resources should only
be invested into reducing timber imports if those same resources cannot be invested
more productively in some other manner. Repeated studies of precisely this issue
have consistently shown that this is not the case (H.M. Treasury, 1972; Bowers,
1985; National Audit Of¬ce (NAO), 1986; Pearce, 1991) and so the import-saving
argument is rejected.

It has been argued that creating jobs in forestry is a good way to stem the ongoing
trend of rural depopulation and combat the psychological and other economic costs
of rural unemployment. However, numerous studies have suggested that forestry is
a relatively expensive and inef¬cient method of providing rural employment, par-
ticularly when compared to agriculture (H.M. Treasury, 1972; Laxton and Whitby,
1986; NAO, 1986; Evans, 1987; Johnson and Price, 1987). Forestry expansion could
therefore be seen as creating shadow costs.
Such conclusions were tentatively disputed by studies in the early 1990s which
argued that, as Forestry Commission employment was falling and productivity
rising, an economic bene¬t of rural employment might occur over the course of the
decade (Thompson, 1990; FICGB, 1992). However, in the event, the steady increase
in private woodlands meant that employment in British forestry (excluding primary
processing) rose from about 17,000 in the mid 1980s to over 27,000 a decade later
(FC, 1985b, 1997). The low-employment/high-productivity argument may be due
for a revival in coming years as employment levels have recently fallen to just over
18,000 (FC, 2001c) and it is interesting to note that rural employment has again
moved to centre stage as a policy argument for increased forestry (FC, 1998). Our
view is that a more likely promoter of the economic case for forestry employment
bene¬ts is the parlous state of UK agriculture (discussed in Chapter 8). However,
in the absence of a speci¬c and contemporary study these are mere speculations
and a cautious approach is to assume that the case for the employment bene¬ts of
forestry is unproven.
In conclusion the only clearly valid non-environmental, non-market social bene¬t
we can isolate is a small bene¬t due to increased economic security of supply and
we adjust social values marginally (as indicated above) to re¬‚ect this.
Timber valuation 153

Environmental non-market social costs and bene¬ts
Woodlands create a number of social bene¬ts and costs of which we discuss the
following major issues: recreation; carbon storage; acidi¬cation impacts; landscape
amenity; biodiversity effects; and other non-use (bequest and existence) values.

Recreation use and option value
Recreation use value is the major focus of our valuation research as discussed in
Chapters 2“4. Because of the potentially signi¬cant problems of declining marginal
utility,72 we have decided not to incorporate such bene¬ts within the plantation
value models presented in this chapter. Instead these models deal primarily with
timber values to which recreation bene¬ts are added in subsequent chapters.73
One potential de¬ciency in our research is that travel cost estimates of recreation
value ignore option values. These are in theory addressed through our contingent
valuation studies; however, we recognise that option value is not a principal aim of
these studies.

Carbon sequestration
As with recreation, we deal with carbon sequestration separately (in chapter 7). This
is not because of diminishing marginal utility, for (as explained in later chapters)
the likely levels of sequestration will not have a signi¬cant impact upon the global
CO2 budget, but rather because of the complexities of this issue which we feel
deserve separate attention.

Forests are cited as both the victims and perpetrators of acidi¬cation damage.
Although research into the impact of acidic deposition upon trees is abundant
(European Commission and the United Nations Economic Commission for Europe,
1994; Marques et al., 2001; Takahashi et al., 2001), relatively little ongoing work
concerns the contribution, if any, which trees make to acidic impacts upon soil
and watercourses (Hornung and Adamson, 1991). Indeed, some dispute what they
term ˜the myth of soil acidi¬cation™, asserting that ˜Within its lifetime, a spruce
cannot signi¬cantly acidify the soil below it™ (Baldwin, 1996: p. 1). The Forestry
Commission suggests that forests tend to act as a catalytic ¬xing medium for
industrially emitted atmospheric acid (Innes, 1987); others argue that this is only
part of the story and that conifers, in particular, directly contribute to a lowering
72 As the area of woodland expands we would expect the increase in recreation opportunities to result in an
observable decline in per hectare recreation values. Given supply and demand conditions we would not expect
this to be a problem for timber production.
73 As discussed elsewhere, this implicitly assumes that the monetary evaluations of woodland recreation are
surpluses to the amenity value of the present agricultural landscape.
154 Applied Environmental Economics

of pH levels (see Harriman and Morrison, 1982; Batterbee, 1984; Edwards et al.,
1990;74 Nisbet, 1990; Grieve, 2001). We take the position that whether or not forests
actually generate the acids concerned, they are signi¬cantly linked to increased
acidi¬cation of soils and aquifers in non-buffered areas and therefore do generate
costs. Our research in this area has not progressed beyond the stage of a literature
survey, although this has shown that the acidi¬cation problem is eminently amenable
to GIS analysis, which we intend to conduct in future research.75

Landscape amenity
The remit of this study excludes the landscape amenity values of forestry. Although
the contingent valuation method has been applied to general landscape valuation
(see, for example, Willis and Garrod, 1993), these studies have not looked specif-
ically at the impact of woodland. However, a number of hedonic pricing studies
have demonstrated that forests do generate signi¬cant amenity values, as re¬‚ected
in property prices (Garrod and Willis, 1992a,b,c; Powe et al., 1997; Peterson and
Boyle, forthcoming). Taken together, these studies indicate that while broadleaves
generate landscape amenity bene¬ts, certain conifers, including Sitka spruce, can
result in amenity losses. Such results therefore constitute a caveat to our own
¬ndings. However, our recent research shows that GIS techniques are particularly
appropriate to the estimation of landscape values via the hedonic pricing method
(Lake et al., 1998, 2000a,b; Bateman et al., 2001a). The GIS allows the de¬nition
of ˜viewsheds™ quantifying what can and cannot be seen from any given location.
Derived variables have been shown to be powerful predictors of amenity values
(ibid.) and we intend to apply such an approach to valuing woodland landscape in
future research.

Biodiversity impacts
Work, in collaboration with ecological scientists, is currently ongoing in an attempt
to incorporate biodiversity impacts into our model of woodland values. Early ¬nd-
ings indicated that afforestation of agricultural areas by conifers such as Sitka spruce
is liable to change the balance of bird species to the detriment of some of the most
endangered birds in Wales (Bateman et al., 1997c). More recently we combined
GIS techniques with data provided by the British Trust for Ornithology to gener-
ate algorithms for selecting priority areas for conservation in Wales (Woodhouse
et al., 2000).76 In ongoing extensions to this work we are linking these ¬ndings
with land use change data to model the relationships between agriculture, forestry

74 This collection of papers focuses exclusively upon acidi¬cation in Wales.
75 Such research would also allow consideration of related issues such as the impact of afforestation upon hydro-
electric potential (see Barrow et al., 1986).
76 See also the GIS-based approaches of Swetnam et al. (1998) and Cowling and Heijnis (2001).
Timber valuation 155

and species diversity. This research should provide a mechanism for investigating
the biodiversity consequences of policy decisions and consequent land use change
in a manner which will link to the CBA assessments presented in this volume.
While there exist substantial (and possibly insurmountable) practical, economic
and philosophical problems in the valuation of biodiversity impacts (Garrod and
Willis, 1994; Kahn, 1995; Carson, 1998; Shogren et al., 1999), it seems likely that
afforestation with non-native species such as Sitka spruce would induce a loss of
unknown and potentially substantial magnitude which should be set against the
values reported in subsequent chapters. The biodiversity impacts of planting beech
woodland are generally (although not exclusively) considered to be positive and
should similarly be set against the other values presented subsequently.

Other non-use values
Biodiversity values may arguably provide a proxy for wider existence values
(although this is debatable). However, other non-use issues such as bequest val-
ues do not feature explicitly in our study (although potentially they may in¬‚uence
our contingent valuation ¬ndings) and this provides a further caveat to the accuracy
of our results.

Non-market social costs and bene¬ts: summary
We are left with having to acknowledge a number of de¬ciencies in the extent of
our study. While we feel that our analysis is relatively sophisticated and useful
in a policy-making context, it remains far from perfect. Nevertheless, those items
which we feel to be of major signi¬cance (recreation and carbon sequestration) are
dealt with outside our rotation model in other chapters. Of the remaining social
costs and bene¬ts, economic security arguments seem to justify a minor upward
revision of social bene¬t values which is quanti¬ed and incorporated within the
rotation values model. Of the remaining issues, acidi¬cation, biodiversity and non-
use values remain insuf¬ciently addressed but the subject of ongoing research.
If we accept that this must remain a partial analysis until that work is complete,
we would defend the present study both as a signi¬cant improvement on existing
CBA assessments of forestry values and, more importantly, as demonstrating an
improved methodology for conducting such studies.

Annual equivalent social timber values
Given the above caveats, we can now calculate social net bene¬t timber values
for our plantation models. These include timber values and the value of economic
security of supply but exclude recreation and carbon sequestration values which
156 Applied Environmental Economics

Figure 5.7. Social value for Sitka spruce (annualised equivalent of a perpetual series of
optimal rotations). Various yield classes and discount rates.

Figure 5.8. Social value for beech (annualised equivalent of a perpetual series of optimal
rotations). Various yield classes and discount rates.

are dealt with subsequently. As there is no subsidy dimension to these calculations
(remember that we have removed all transfer payments) we can illustrate results
across all yield classes and discount rates on a single graph as shown in Figure 5.7
for conifers, and Figure 5.8 for broadleaves.
Comparison of Figures 5.7 and 5.8 shows relationships similar to those observed
in the private sector evaluations. Again we see (on this restricted range of value
types) that conifers are able to outperform broadleaves (interestingly values for
broadleaves are negative for most low yield class/high discount rate combinations,
illustrating the impact of discounting on the long rotation periods of such trees).
Given that we have excluded recreation and non-user values, such a result is not
Timber valuation 157

We have constructed rotation models which, across the full range of yields for
our two representative tree species, take into account plantation costs and bene¬ts,
real prices, grants and subsidies. We have also considered the difference between
private and social perspectives both in terms of differential discount rates and with
regard to the differing range of values which the two assessments should appraise.
In subsequent chapters the private and social values derived from this analysis
are aggregated with our estimates of recreation and carbon sequestration values
to provide our overall assessment of the values generated by farm forestry. These
values are then compared with those for existing agricultural activities so as to
estimate likely conversion rates under a variety of scenarios.
Modelling and mapping timber yield and its value

In this chapter we present various models of timber production for the two species
under consideration: Sitka spruce and beech. In the next section we present a
brief review of previous studies. These have exclusively been based upon rela-
tively small-scale surveys of tree growth; furthermore, they have also generally
been con¬ned to comparatively small areas and often to one topographic region,
e.g. upland areas. Our study differs from these previous models in that it employs a
GIS to utilise large-scale existing databases covering a very large and diverse study
area: the whole of Wales. The subsequent section presents details regarding the
various datasets used in this study and discusses how these data were transformed
for the purposes of subsequent regression analysis. Subsequently, results from our
models of Sitka spruce and beech growth rates are presented, while the following
section presents and analyses GIS-created map images of predicted yield class.
The ¬nal section applies the ¬ndings of the previous chapter to produce monetised
equivalents of these results.

Literature review and methodological overview
Literature review
It is clear that tree growth rates depend upon a variety of species, environmental
and silvicultural factors. Early work in this ¬eld relied on simple rules of thumb
based upon relatively little supporting data (Busby, 1974) or analyses of single
factors. Reviews across this literature provide a number of clues regarding the
speci¬cation of a yield class model. An early focus of interest was the impact
of elevation upon productivity (Malcolm, 1970; Mayhead, 1973; Blyth, 1974).
Subsequent papers considered the various routes by which elevation affected YC
including windiness (Grace, 1977), slope and aspect (Tranquillini, 1979). Other

Modelling and mapping timber yield and its value 159

work examined the impact of factors such as soil type, soil moisture transport and
droughtiness (Page, 1970; Blyth and MacLeod, 1981; Jarvis and Mullins, 1987)
and crop age (Kilpatrick and Savill, 1981). However, the estimation of statistical
models across the full range of likely explanatory variables is a relatively recent
innovation. Amongst such investigations we could ¬nd no examples concerning the
productivity of beech and believe the model presented subsequently to be the ¬rst
such investigation of this species. However, there has been more attention paid to
the other species under analysis, Sitka spruce, which has been separately studied by
both Richard Worrell (then of the University of Edinburgh) and Douglas Macmillan
(then of Macauley Land Use Research Institute, MLURI).1
While there had been a number of earlier considerations of factors affect-
ing the growth of Sitka spruce (Malcolm, 1970; Malcolm and Studholme, 1972;
Mayhead, 1973; Blyth, 1974; Busby, 1974; Gale and Anderson, 1984), the work
of Worrell (1987a,b) and Worrell and Malcolm (1990a,b) is notable as being the
¬rst to adopt a multiple regression approach across a wide range of explanatory
variables. These were: elevation (including separate dummy variables for hilltop
and valley bottom sites); windiness; temperature; aspect (measured as sine and
cosine); and a full range of soil dummy variables. However, while they provide
vital pointers for our own modelling exercise, Worrell™s results are not transfer-
able to our Welsh case study. This is partly due to the upland Scottish location of
Worrell™s experiment but primarily as a result of the focus of his study. Worrell
was mainly interested in detecting the in¬‚uence of elevation upon yield class in
upland areas.2 To this end he selected eighteen principal sample sites,3 all of which
had relatively steep slopes, and took measurements along a vertical transect at each
site. By locating samples at sites ranging from 50 m to 600 m above sea level
a very strong, central tendency relationship with elevation could be established.
However, such a model is only applicable to similar, steeply sloping sites (strictly
speaking, only the subset of those found within Scotland), and is not readily gen-
eralisable to the plethora of environmental conditions found in an area the size of
A similar, though less extreme, consideration prevents us applying the ¬ndings
of Macmillan (1991). Here again the study is geographically con¬ned, this time
to lowland Scotland, although the 121 sites used are not selected to emphasise
the in¬‚uence of any particular explanatory variable and are therefore somewhat
more generalisable within lowland areas. However, while in many cases this would
be adequate, with respect to our study area the topographic variability of Wales
means that a model based purely upon lowland data is insuf¬cient for our needs.
1 We are grateful to both Richard Worrell and Douglas Macmillan for extensive discussions of their work.
2 An important question given that this is the location of much of the existing stock of Sitka spruce.
3 The number of individual tree measurements is not reported.
160 Applied Environmental Economics

Nevertheless, the Macmillan paper is interesting both because it uses multiple re-
gression with a prior principal components analysis (PCA) of explanatory variables
(reporting a ¬nal degree of explanation of R2 = 36.8 per cent) and because the data
collected have been more recently re-analysed using GIS techniques (Elston et al.,
1997) to produce a somewhat improved model (R2 = 43.9 per cent)4 , a result
which underlines the potential advantages of applying GIS methods within this
A short note regarding model ¬t is justi¬ed here. As discussed in the previous
chapter yield class (YC) is the average annual growth rate of a plantation assessed
over an optimal rotation. YC is therefore given in m3 /ha/yr. However, YC values
are rounded to the nearest even number so that while we have stands with YC
6 or 8 we do not have sites with YC 7. While this does not invalidate statistical
analysis, as YC is the dependent variable, this approach to measurement does induce
variance into the dataset and therefore makes high degrees of explanation dif¬cult
to attain. As such the absolute value of ¬t statistics such as R2 should be treated
with some caution and instead we should consider, where possible, relative degrees
of ¬t compared to those attained in other studies.

Overview of modelling approach
These prior studies provide very useful indications regarding the likely explanatory
variables which should be considered in our analysis. The differences in modelling
approach are also of interest and we consequently decided to investigate both a
PCA and standard multiple regression methodology. However, subsequent analysis
showed that PCA models were narrowly outperformed by those obtained using
standard regression techniques. Given their relatively straightforward interpreta-
tion, here standard regression models are reported in preference to those obtained


. 5
( 11)