. 3
( 11)


Recreation: predicting values 57

The Wantage CV study: households™ WTP and farmers™ WTA compensation
for a community woodland
This project consisted of two CV surveys examining issues related to the provision
of open-access, recreational woodlands on land currently used for farming.18 Two
speci¬c aims were to determine:
(i) the willingness of the local community to pay for the provision of such a woodland
(ii) the willingness of local farmers on whose land the proposed woodland could feasibly
be located to accept compensation.

The study was motivated by the introduction of the Forestry Commission™s (FC)
Community Woodland Scheme (CWS), a policy intended to promote open-access
woodlands ˜within 5 miles of the edge of a town or city and in [areas] where the
opportunities for woodland recreation are limited™ (Forestry Commission, 1991).
Results from the research permitted cost-bene¬t assessment of the CWS. The study
examined valuations of a proposed (hypothetical) community woodland scheme
near Wantage, Oxfordshire. Full details of this study are presented in Bateman et
al. (1996b).

Household WTP survey
Study design
Bene¬ts from the proposed community woodland were assessed through a face-
to-face CV survey of 325 randomly selected households in and around Wantage.
A number of questions were designed to elicit information which might explain
differences in valuations, although the main focus of the survey concerned WTP
issues. The survey interview opened with a ˜constant information statement™ which
informed households about the size (100 acres) and facilities (recreational walks
and car parking) of the proposed wood and its open-access nature. Respondents
were then asked whether or not they would be prepared to pay towards provision
of the wood. Such a ˜payment principle™ question was included mainly as a way
of validating zero bids as it was felt that directly presenting respondents with a
WTP question might intimidate those who held zero values (Harris et al., 1989).
Respondents who answered ˜no™ to this question were asked to state their reasons
for such a response whilst those who answered positively were asked the WTP
Two WTP questions were used in the study. First, respondents were asked how
much they were WTP per household per annum in extra taxes (referred to subse-
quently as the ˜per annum question™). Second, respondents were asked how much
18 Further details regarding this study are given in Bateman et al. (1996b).
58 Applied Environmental Economics

Table 3.6. Summary WTP results: per annum (WTPpa) and
per visit (WTPfee) formats

Truncated Median Lower Upper
1 2
Format n Mean (£) 95% C.I. mean (£) (£) quartile (£) quartile (£)
WTPpa 325 9.94 8.92“11.14 8.85 10.00 2.00 15.00
WTPfee 325 0.82 0.75“0.89 0.68 0.75 0.05 1.00

Notes: 1 Bootstrapped con¬dence intervals calculated by the BCa percentile method
(Efron and Tibshirani, 1993). See text for de¬nition.
Omits potential warm-glow bids. See text for de¬nition.
All values in 1991 prices.
Minimum bid is zero for both formats (included in calculation of mean, median, etc.).

they would be WTP per adult per visit as a car parking fee (referred to subsequently
as the ˜per visit question™). Therefore all respondents who were WTP some amount
were presented with, in turn, both the per annum and per visit format questions.19
In all cases an OE elicitation format was used in line with our previous ¬ndings
(and a desire to produce defensible, lower-bound values) and the entire design was
successfully tested using a pilot sample of thirty respondents.

WTP results
Considering ¬rst the payment principle question, just under 25 per cent of respon-
dents stated that they were unwilling in principle to pay for the proposed recreational
woodland. This rate is very similar to that obtained for almost identical services
in the Thetford 2 study discussed subsequently, and somewhat higher than that
recorded for larger, high-pro¬le environmental resources such as National Parks
(Willis and Garrod, 1993; Bateman et al., 1994). When asked, well over three-
quarters of those refusing the payment principle cited income or related economic
constraints as the main factor underlying their answers and none said that they were
objecting to the principle of valuation per se. Such responses give us no cause for
rejecting the application of CV techniques to this issue.
Table 3.6 gives summary WTP statistics for responses to the two formats used in
this study. To guard against the potential non-normality of the response distributions
we report bootstrapped 95 per cent con¬dence intervals, calculated via the BCa
percentile method (Efron and Tibshirani, 1993) using 999 simulations. This method
is based on a re¬ned normal approximation which corrects for bias and skewness
in the distribution of mean WTP and is hence an improvement over the basic

19 Ideally we would want to either use separate samples for each format or vary the order in which questions are
presented so that any ordering or anchoring effects might be assessed. Such an analysis is undertaken as part
of our second Thetford CV study, reported subsequently.
Recreation: predicting values 59

non-parametric bootstrap. This is of importance with the samples of WTP values
considered, which are skewed and truncated at zero.
A within-format comparison with over thirty on-site (user) CV studies of a vari-
ety of outdoor recreation resources (ranging across woodlands, wetlands, National
Parks, etc.) using per annum WTP measures (Bateman et al., 1994) showed that
estimates obtained from the Wantage survey were logically related to the charac-
teristics, substitutability, uniqueness and provision-change factors inherent in the
contingent market presented to respondents. Given this result it is interesting to
note that the Wantage WTP per annum (WTPpa) measure lies considerably above
that estimated for the Thetford 1 samples, suggesting that the inclusion of infor-
mation on average annual tax support for the Forestry Commission (£2.60) in the
latter study had downwardly biased WTP bids. Similarly, while the Wantage WTP
per visit (WTPfee) amount falls within one standard deviation of the mean of all
other comparable UK studies (as reviewed at the start of this chapter), it lies well
below the per visit measures recorded in the Thetford 1 study (Table 3.4), indicating
that the latter were upwardly biased by the use of payment cards. On both these
counts therefore, results from the Wantage study appear more valid and generally
applicable than those from the Thetford 1 study.
The Wantage WTP responses were investigated for evidence of a number of the
biases identi¬ed in Chapter 2 including warm-glow bids, free-riding and strategic
overbidding (see Bateman et al., 1996b, for details). No conclusive evidence of
free-riding or strategic overbidding was found; however, limited indications of
warm-glow effects were detected. Warm-glow giving (Kahneman and Knetsch,
1992) occurs where respondents purchase moral satisfaction rather than the good
on offer in the contingent market (i.e. they see the CV market as a donation to
a good cause and offer some, typically small, amount which is not related to the
speci¬c characteristics of the good and therefore contravenes the assumptions of
the CV method). In order to investigate the sensitivity of welfare measures to such a
bias the distributions of bids under both formats were examined for evidence of any
appropriate amounts which respondents might choose to give under warm-glow
bidding. For the annual format, a strong assumption was made that the relevant
bid threshold was £5 per annum whilst for the per visit question, a threshold of
£0.50 was assumed. Mean WTP was then recalculated by setting all bids up to and
including these thresholds to zero to yield the truncated means listed in Table 3.6.
Inspection of these truncated means indicates that, for both formats, even under
such strong assumptions, warm-glow bidding makes relatively little difference to
the estimated mean, which declines 11 per cent for the annual payment format and
17 per cent for the per visit format (medians remain constant throughout). We would
suggest that such assumptions are too strong as they omit some genuine, low-value
bids. We conclude then that although warm-glow bidding may be a feature of this
60 Applied Environmental Economics

Table 3.7. Stepwise regression of lnWTPpa on signi¬cant predictors

Step 1 2 3 4 5 6
’5.397 ’5.335 ’5.096 ’4.418 ’4.214 ’4.374
lnINCOME 0.755 0.726 0.683 0.683 0.647 0.630
(9.79) (9.56) (9.06) (9.16) (8.54) (8.33)
lnRURVIS 0.165 0.160 0.140 0.156 0.131
(3.78) (3.74) (3.25) (3.61) (2.98)
lnPKVIS 0.246 0.227 0.239 0.235
(3.69) (3.43) (3.62) (3.59)
’0.590 ’0.560 ’0.520
(’2.90) (’2.75) (’2.58)
AGE17“25 0.167 0.173
(2.32) (2.42)
lnVISWOOD 0.140
R2 0.288 0.261 0.292 0.310 0.321 0.333

lnWTPpa = natural logarithm of household™s annual WTP (£)
lnINCOME = natural logarithm of household™s gross annual income. Income was
recorded on an eight-point scale (see Bateman et al., 1996b, for details).
lnRURVIS = natural logarithm of number of visits made by household to rural sites per
lnPKVIS = natural logarithm of number of visits made to parks
PREFTOWN = 1 if prefers town-based recreation; = 0 otherwise
AGE17“25 = number of persons in household aged 17“25 years
lnVISWOOD = natural logarithm of household™s predicted visits to proposed wood per
Figures in brackets are t-statistics.

and other CV surveys, with regard to this study the impact of any such tendency is
not severe.

Validation: bid curve analysis
Responses to both WTP formats were subjected to theoretical validity testing via
bid curve analysis. For the WTPpa bids, analysis showed that a log-linear functional
form provided the best ¬t to the data. Table 3.7 reports results from a forward-entry
stepwise regression analysis relating the log-linear dependent variable, lnWTPpa,
to signi¬cant explanatory variables. These models provide a good degree of expla-
nation (easily satisfying the ¬t criteria discussed in Chapter 2) with bids being linked
in the expected manner to a number of explanatory variables. In essence the models
show that higher WTP bids were associated with richer households, containing
young people, which enjoyed outdoor rather than urban-based recreation. Tests for
multicollinearity suggested that the variables lnRURVIS and lnVISWOOD should
Recreation: predicting values 61

probably not be included in the same model and so we identify the model given at
step 5 of Table 3.7 as providing the best explanation of per annum WTP responses.
Unlike the per annum bids, analysis of responses to the per visit WTP ques-
tion showed them to be much less ¬rmly linked to standard explanatory variables.
While a log-linear dependent variable provided the best ¬t of the data, the resulting
bid curve model, detailed in Equation (3.2), achieved only a low degree of over-
all explanatory power (R2 = 5%) and failed to satisfy the ¬t criteria discussed
0.595 ’ 0.135 PENSION ’ 0.00175 VISWOOD (3.2)
(25.33) (’3.94) (’2.26)
lnWTPfee = natural logarithm of stated WTP per visit
PENSION = number in household aged 65 years or over
VISWOOD = predicted number of household visits to the proposed wood
per annum
Figures in brackets are t-statistics.
Comparison of Equation (3.2) with those obtained from the Thetford 1 per visit
format (detailed in Bateman, 1996) showed that all were dominated by the intercept
term. This observation, we suggest, may be re¬‚ecting the ˜social norm™ concept
discussed with respect to our cross-study analysis of the UK CV literature.

The procedure used to calculate aggregate WTP varied according to the question
format used. The per annum format question elicited a mean WTP (including those
who refused to pay as zeros) of £9.94 per household. At the time of the study the
town of Wantage had an adult population of about 11,500. Therefore, even if we
take an extreme upper-bound estimate on household size (so as to derive a lower-
bound estimate on household WTP) of 2.57 (Central Statistical Of¬ce, 1991)20 this
would give an estimate of some 4,473 households in Wantage which would, in turn,
imply an aggregate WTP of £44,450 per annum for the woodland.
For the per visit measure we elicited a WTP of £0.82 per adult visit (again
including those who refused to pay as zeros). The mean estimated number of visits
(including those who would not visit) was just under ¬fteen per annum, implying
a total annual entrance fee expenditure of £12.29 per adult. Grossing up across
all adults21 implies a total annual willingness to pay entrance fees of £141,252.
20 This ¬gure refers to average UK total household size (including adults and children) rather than the average
number of adults per household. If the latter were used this would increase our estimate of household WTP,
i.e. we have employed a conservative, lower-bound assumption.
21 Note that we have already accounted for non-visitors in the annual per adult visit rate.
Table 3.8. Farm characteristics and farmers™ willingness to accept compensation for transferring from present output to

Pro¬t/acre WTA/acre Allocation
Farm Land use Tenure (£) (£) (acres) Reason for non-allocation
1 Mainly arable Owned 100 250 0 Land should be used to produce food
2 Mainly arable Owned ” 20,000 0 Does not like government policy
3 Mainly arable Owned 125 300 0 Does not want public access to the farm
4 Arable Owned 30 200 5 ”
5 Arable Owned 105 250 30 ”
6 Arable Owned 45 150 2 ”
7 Mainly arable Owned 130 ” 0 Does not want public access to the farm
8 Arable Owned ” ” 0 Land not suitable to grow trees upon
9 Dairy Rented 85 ” 0 Does not want public access to the farm
10 Arable Owned 116 300 0 Farm too small for the scheme
11 Mainly arable Owned 100 ” 0 Does not want public access to the farm
12 Mainly arable Owned 186 100 125 ”
13 Mainly arable Owned 186 200 100 ”
14 Mainly arable Owned 163 250 20 ”
15 Mainly arable Rented 150 250 0 Does not want public access to the farm
16 Arable Owned 280 600 3 ”
17 Arable Owned 145 150 0 Farm too small for scheme
18 Mainly arable Owned 140 ” 0 Farmer too old to undertake long-term project
19 Set-aside Owned ” 250 0 Unwilling to undertake alternative to set-aside
Mean1 ” ” 130 250 15 ”

Note: 1 Excludes Farm 2.
Recreation: predicting values 63

However, we are sceptical that respondents would actually visit as often as stated
(stated visitation rates considerably exceed the actual rates which we have observed
at other woodland sites; see Bateman, et al., 1999c and Chapter 4) and so regard
this as an overestimate of the likely annual value of such a site. Further comment
on these ¬ndings is given in our conclusions to this study.

Farmers™ WTA survey
Farmers around Wantage were interviewed in order to obtain information concern-
ing likely participation in the Community Woodland Scheme (CWS) and associated
compensation requirements. Data on a variety of factors which might determine
WTA levels were collected. Table 3.8 lists several of these factors, together with
stated WTA sums and the amount of land farmers were willing to allocate to the
CWS, for the nineteen survey participants.

WTA results
Twelve farmers (63 per cent) initially stated that they were unwilling to allocate
land for public access recreational woodland.22 Amongst these the most commonly
stated reason for refusal was that the farmer did not want to allow public access to the
farm (¬ve farms, or 42 per cent of those refusing to enter the scheme). Such concerns
may be well founded, as repeated public use of footpaths within a wood may lead to
their classi¬cation as public rights of way. Furthermore, subsequent interviews with
senior Forestry Commission staff revealed that land-owners would not be granted
felling licences unless equivalent areas of replanting were agreed.23 In other words,
the decision to allocate a certain area of agricultural land to recreational forestry
may, in practice, be dif¬cult to reverse. Such irreversibility may, perversely, prove
to be a considerable block to the extension of farm-forestry although the small
sample size precludes any ¬rm conclusion being drawn.
Seven farmers (37 per cent) were initially willing to allocate land to the recre-
ational woodland scheme, the mean allocation being just over 40 acres per par-
ticipating farm. Uptake among participating farms appeared to be bimodally dis-
tributed, with two farms willing to allocate 100 acres or more to woodland and
the remainder only willing to undertake small-scale afforestation projects. Whilst
grant aid is available for small-scale schemes, if the objective is to provide a viable,
discrete recreational area then such small pockets (unless they can be combined)
may not be suitable. Nevertheless the willingness to undertake large-scale planting

22 This general unwillingness to participate in such schemes is also reported in a similar study in France by Noel
et al. (2000).
23 Interview with Chief Forester, Santon Downham, Thetford Forest. See also Chapter 5, this volume.
64 Applied Environmental Economics

by two farmers is encouraging, particularly where the objective (as under the CWS)
is simply to ensure that the local community has access to a nearby woodland recre-
ation site.
The majority of interviewees (fourteen farms; 74 per cent) stated a sum which
they would be willing to accept in annual compensation for allocating land out of
agriculture and into public access woodland (WTApa). This included seven (58 per
cent) of the farmers who initially rejected the principle of such allocation. This
latter result seems to indicate that, if the price was right, such farms would consider
a move out of conventional agriculture. However, there was one very noticeable
˜protest bid™24 amongst this subsample which, at £20,000/acre, was not only more
than 150 standard deviations above the mean of the remaining sample and more
than thirty times larger than the next highest bid, but also of approximately equal
magnitude to the entire annual net farm income. It is possible that this respondent
had in mind a discounted total net present value sum for the entirety of the project,
in which case such a response would be reasonable. However, given that no other
respondent gave an answer within the same order of magnitude, we feel that such
an explanation is unlikely and a protest strategy seems much more probable.
Excluding this one outlier, the mean stated WTApa was £250/acre. Almost
all farms required higher annual subsidy compensation rates than they currently
achieved under agriculture. This seems reasonable given that woodland is an un-
known quantity to most farmers, who consequently require a risk premium com-
pared to standard activities.
Validation: bid curve analysis
Analysis of responses showed that stated compensation levels were strongly related
to both existing pro¬t levels and the overall size of the farm. No further signi¬-
cant explanatory variables were identi¬ed and the best-¬tting regression model for
WTApa is:25
WTApa 94.04 + 1.48 PROFIT ’ 1.93 ACRES (3.3)
(1.81) (4.04) (’3.37)
WTApa = Farmers™ required compensation (£/acre) for
entering the woodland scheme
PROFIT = Level of pro¬t under existing agriculture (£/acre)
ACRES = Area in acres which the farm is prepared to allocate
into the woodland scheme
Figures in brackets are t-statistics.

24 The authors dislike the general application of this term to anyone who does not give an expected answer to a
bidding (WTP or WTA) question. However, this particular respondent seemed to satisfy all relevant requirements
of an archetypal ˜protester™.
25 The previously identi¬ed outlier was excluded from this analysis.
Recreation: predicting values 65

The model presented in Equation (3.3) ¬ts the data well (although sample size
is clearly a problem), satisfying ¬t criteria (R2 = 70%) and indicating logical re-
lationships between the dependent and explanatory variables. Farmers with higher
pro¬t levels from existing activities demanded higher levels of compensation for en-
tering the woodland scheme. Furthermore, those who were only willing to consider
small-scale planting required higher per acre payments. This implies, logically, that
large-scale plantations, which presumably will bene¬t from economies of scale, are
considered viable alternatives at relatively lower per acre subsidy rates than small-
scale woodlands.
To allow comparability with our household WTP survey, aggregate farm WTA
needed to be calculated for a similar 100 acre site. Using the mean stated WTApa
of £250/acre produced a total compensation requirement for such a woodland of
£25,000 per annum.

Comparison of household WTP and farm WTA measures
Both measures of aggregate household WTP exceeded our estimate of aggregate
farm WTA to a considerable degree. In the case of the annual format we have
a simple26 bene¬t/cost ratio of 1.78 whilst the entrance fee format yields a ratio
of 5.65. Such results point strongly in favour of the establishment of Community
Woodland Schemes. However, we prefer to retain a cautious approach to the WTP
sums. Another way of examining these is to consider the minimum number of
payments needed to meet the required aggregate compensation level. Using the per
annum format and our estimated household size implies that some 2,515 households
(i.e. 56 per cent of all those in Wantage) would need to pay the £9.94 mean WTPpa
for the scheme to break even. Alternatively, all the households in Wantage would
have to pay £5.59 per annum for the scheme to again break even.27 Using the per
visit mean WTP of £0.82 implies that 30,487 individual visits per annum would be
required to pay for the forest, i.e. each individual in Wantage would need to make
2.65 paying visits per annum for the site to break even.

The Wantage study: conclusions
The Wantage study provides a number of ¬ndings which are of use to our overall
research objectives. First, it gives a number of recreation bene¬t estimates which,
compared to our earlier Thetford 1 study, appear relatively unbiased. Second, the

26 The term ˜simple™ refers here to the fact that this study represents only a partial cost-bene¬t analysis of such a
27 Note that this is considerably less than the mean WTP excluding suspected strategic overbidders detailed in
Table 3.6.
66 Applied Environmental Economics

WTA experiment suggests that, given appropriate compensation, suf¬cient farmers
are prepared to countenance entry into the CWS to make the scheme viable. The
strong bid function estimated from WTA responses implies that familiarity with the
concept of compensation makes farmers adept at determining appropriate threshold
compensation levels, these levels being linked to current pro¬tability and postulated
involvement with the scheme. Third, aggregate bene¬t sums considerably exceed
estimates of farmers™ compensation requirements suggesting that the implementa-
tion of such projects could result in the creation of substantial net public bene¬ts.
The magnitude of the implicit bene¬t-cost ratio is also suf¬cient to overcome any
residual concerns regarding the precise value of estimated welfare measures.

The second Thetford CV/TC study
This study consisted of a joint CV/TC on-site survey of recreational visitors to
Lynford Stag, the site previously used in the Thetford 1 study. The overarching
objective was to examine how responsive bene¬t estimates were to changes in
study design and analytic methods. We will discuss the CV study ¬rst (further
details can be found in Bateman and Langford, 1997a).

The Thetford 2 CV study: budget constraint and question-order effects
The CV study used a split-sample design to address two principal issues arising
from the literature review presented in Chapter 2:

(i) the impact of explicitly asking respondents to consider their budget constraints prior to
stating WTP
(ii) question-ordering effects.

In addition to these effects, payment vehicle impacts were again investigated
through use of both per annum taxes and per visit entrance fees.

Study design
The study objective required a split-sample design in which respondents were
divided into two groups, each of which was further divided into two subgroups as
Group B: Prior to any WTP question, respondents were asked to calculate
and state their annual recreational budget.
Group NB: No budget question was asked prior to any WTP response.
Subgroup 1: WTP per annum (tax payment vehicle) was asked prior to WTP
per visit (entrance fee payment vehicle) question.
Subgroup 2: WTP per visit (fee) was asked prior to WTP per annum (tax)
Recreation: predicting values 67

The above design gave us four subsamples (B1, B2, NB1 and NB2), each of
which provided both per annum (tax) and per visit (fee) WTP responses for which
we de¬ned a series of testable hypotheses concerning the effects under investiga-
tion. Testing used various approaches. Simple comparisons of means and standard
(normal) con¬dence intervals were undertaken. However, while of interest, such
statistics are potentially biased by necessary distributional assumptions. To com-
bat this, non-parametric con¬dence intervals for mean WTP were calculated via
the BCa percentile bootstrap method (Efron and Tibshirani, 1993) as discussed
In line with preceding studies an OE elicitation format was used throughout.
In addition to the valuation responses the survey also elicited information regard-
ing relevant visit, socio-economic and interview condition variables necessary for
subsequent validity analyses. The questionnaire was tested with a pilot survey
of thirty-two respondents. This resulted in marginal changes to the questionnaire
which was then applied to the main survey from which a sample of 351 respondents
was collected.
WTP results
As in previous designs, prior to the budget and WTP questions, respondents were
asked a ˜payment principle™ question enquiring whether or not they were willing to
pay anything at all. Some 96 respondents (27.6 per cent of all respondents;28 a rate
in line with previous results)29 stated that they were not prepared to pay at least some
amount for the recreational facilities provided at the site, leaving 255 respondents
to answer the budget and WTP questions. To prevent overstating sample WTP (and
avoid problems caused by somewhat uneven numbers in each subsample accepting
the payment principle), in later calculations these refusals were allocated evenly
between the four subsamples and treated as zeros.30
Those who agreed to the payment principle were (unbeknown to themselves)
then randomly allocated to one of the four groups de¬ned above and asked the
relevant WTP questions, results from which are described below.

WTP per annum (tax) responses
Table 3.9 presents mean WTP per annum (via taxes) for each of our four subsamples.
For notational simplicity we can refer to the subsamples described in the upper row
as NB1a and NB2a (left- and right-hand cells respectively; subscript a indicates per
annum (tax) response) and those on the lower row as B1a and B2a . Below each
mean (in rounded brackets) we report 95 per cent con¬dence intervals calculated
28 Reasons for refusing to pay were mainly related to economic factors and are analysed further in Bateman and
Langford (1997a). At most only 2 per cent of the sample gave refusal reasons which can be interpreted as in
some way protesting against the valuation process.
29 See, for example, Bateman et al. (1995a).
30 The inclusion of such zeros reinforces the need to conduct non-parametric testing.
68 Applied Environmental Economics

Table 3.9. Mean WTP (tax) per annum and 95 per
cent con¬dence intervals for each subsample
(including payment principle refusals as zeros)

Payment ordering scenario

1 (tax then fee) 2 (fee then tax)
Budget question (£) (£)
NB (not asked) 12.55 7.62
(8.94“18.47) (4.36“15.77)
[8.11“16.99] [2.87“12.37]
B (asked) 32.60 16.37
(23.18“45.89) (11.78“22.12)
[21.76“43.43] [11.19“21.55]

Note: Figures in round brackets are 95% C.I.s calculated by
the BCa percentile method, as discussed previously, while
¬gures in square brackets are conventional 95% C.I.s.

via the BCa percentile bootstrap method, while below these (in square brackets)
we report standard normal 95 per cent con¬dence intervals for comparison.
Table 3.9 indicates that the inclusion or exclusion of the recreational budget
question, and/or changes in the ordering of payment vehicle presentation, results in
apparently consistent and major impacts upon stated WTP. For ordering scenario 1
(tax then fee), the inclusion of the budget question (i.e. moving from cell NB1a to cell
B1a ) raised mean annual WTP (tax) by a factor of 2.60, while for ordering scenario
2 (fee then tax) inclusion of the budget question (i.e. moving from cell NB2a to
cell B2a ) raised mean annual WTP (tax) by a factor of 2.15. However, examination
of BCa con¬dence intervals shows that only the ¬rst of these differences is clearly
signi¬cant (i.e. the 95 per cent BCa con¬dence intervals do not overlap).
Considering the impact of changing the order of payment questions upon per
annum responses, in those subsamples not given the prior budget question, asking
for per visit WTP before the per annum question (cell NB2a ) lowered the latter to
just 60.7 per cent of stated annual WTP when not preceded by a per visit question
(cell NB1a ). For those subsamples which were given a prior budget question, this
disparity increased so that annual WTP preceded by a per visit question (cell B2a )
was just 50.2 per cent of the annual WTP otherwise (cell B1a ). Again, the BCa
con¬dence intervals indicate that only one of these differences (the latter) is signif-
icant, suggesting in this case that the prior per visit question substantially reduced
the subsequent stated per annum WTP.
Consideration of the diagonals in Table 3.9 shows that where the apparently
negative effect of including a prior per visit WTP question is combined with the
Recreation: predicting values 69

Table 3.10. Mean WTP (fee) per visit and 95 per cent
con¬dence intervals for each subsample (including
payment principle refusals as zeros)

Payment ordering scenario

1 (tax then fee) 2 (fee then tax)
Budget question (£) (£)
NB (not asked) 0.45 0.20
(0.35“0.57) (0.12“0.32)
[0.35“0.55] [0.11“0.29]
B (asked) 0.78 0.46
(0.57“1.09) (0.33“0.66)
[0.53“1.03] [0.30“0.62]

Note: Figures in round brackets are 95% C.I.s calculated by
the BCa percentile method, as discussed previously, while
¬gures in square brackets are conventional 95% C.I.s.

positive impact of a prior budget question (cell B2a ), then the resultant per annum
WTP statement is not signi¬cantly different from that elicited in the absence of
both preceding questions (cell NB1a ). However, comparison of stated per annum
WTP when preceded solely by the apparently negative effect of a prior per visit
question (cell NB2a ) with annual WTP preceded solely by the positive impact of
a prior budget question (cell B1a ) shows a highly signi¬cant difference in WTP
Comparison of the BCa and standard (normal) con¬dence intervals is also inter-
esting. The distributional assumption underlying the latter does not prevent negative
WTP values and the presence of signi¬cant numbers of zeros (payment principle
refusals), alongside a distribution of non-zero responses containing some relatively
high values, results in unreliable con¬dence intervals. These problems are corrected
for in the BCa approach by using empirically derived estimates of bias and skew-
ness which are calculated for each subsample. Upper and lower percentile points
are then calculated accordingly. Here we can see that reliance upon conventional
(normal) con¬dence intervals would overemphasise the signi¬cance of differences
between subsamples.

WTP per visit (fee) responses
Table 3.10 presents mean WTP per visit (via fees) for each subsample and 95 per
cent con¬dence intervals (as previously described). In the subsequent discussion,
subsample notation is similar to that used above, with the subscript v indicating per
visit (fee) responses.
70 Applied Environmental Economics

Considering Table 3.10 we can see that the design effects detected in the per
annum experiments have been repeated in the per visit studies. Again the inclu-
sion of a prior question regarding recreation budgets seems to lead to increases
in subsequent per visit WTP responses which are signi¬cant in both cases. Table
3.10 also shows that the pre¬xing of per visit WTP questions by per annum ques-
tions apparently increases per visit WTP bids. However, examination of the BCa
con¬dence intervals indicates that only one of these two differences is statistically
Consideration of the diagonals in Table 3.10 again tells a consistent story regard-
ing the interplay of budget and ordering effects. Where these tend to shift responses
in the same direction (i.e. comparing in¬‚uences which are both negative in cell
NB2v with in¬‚uences which are both positive in cell B1v ), con¬dence intervals
indicate highly signi¬cant differences, but where they work in opposition (com-
paring cell NB1v with cell B2v ), equality cannot be rejected. Finally, as before,
reliance upon normal con¬dence intervals would generally lead us to overestimate
the signi¬cance of these results.

Validation of survey results was carried out in accordance with the criteria set
by Mitchell and Carson (1989). A central notion here is the concept of construct
validity which is in turn composed of convergent and theoretical validation. In prac-
tice, convergent validity testing has generally been achieved by comparing bene¬ts
with those of other studies, while theoretical validity has been examined through
the estimation of bid functions and analysis of their consistency with theoretical
Two types of convergent validity test were undertaken. In the ¬rst, results from
the NB subgroups of this study were compared with the other estimates of UK
woodland recreation value discussed earlier in this chapter (there were no studies
comparable with the B format subgroups). Tests showed that the results obtained in
the present study strongly conformed to expectations from prior research (details
are given in Bateman and Langford, 1997a). A second test compared results from
the NB subgroups with those from a selection of studies in a similar format of
different resources (e.g. wetlands, reservoirs, etc.). It was found that results across
these studies were logically related to both substitute availability and the change
in provision presented in the contingent market and that the ¬ndings of the present
study were consistent with these expectations (details are given in Bateman and
Langford, 1997b).
Theoretical validation of our results was carried out via statistical investigation
of the bid functions underlying WTP responses. A semi-log (dependent) functional
Recreation: predicting values 71

form provided the best ¬t for the per annum data:
1.20 + 1.50 BUDGET ’ 0.633 ORDER
(10.6) (11.17) (4.76)
+ 0.390 GREEN + 1.08 NONCAR + 0.574 SUPERB (3.4)
(1.66) (3.35) (2.88)
lnWTPtax = natural logarithm of WTP per annum (tax vehicle)
BUDGET = 1 if respondent had been asked to state annual recreational
budget prior to WTP questions; = 0 otherwise
ORDER = 1 if respondent faced a prior per visit WTP question (ordering
scenario 2); = 0 otherwise
GREEN = 1 if respondent was a member of at least one of various
countryside/wildlife organisations; = 0 otherwise
NONCAR = 1 if the respondent did not travel to the site by car; = 0
SUPERB = 1 if the respondent rated scenery at the site on the top of a
four-point scale; = 0 otherwise.
Figures in brackets are t-statistics.
Equation (3.4) ¬ts the data well (adjusted R2 = 33.7%), easily satisfying the
criteria for theoretical validity discussed previously. The model again indicates
the signi¬cant in¬‚uence of budget constraint and question ordering on per annum
responses. This ¬nding is repeated in the per visit bid function shown in Equation
(3.5), which again satis¬es the Mitchell and Carson (1989) criteria regarding the
degree of explanation (adjusted R2 = 26.4%) although the strength of the constant
in this model recalls our earlier comments regarding the in¬‚uence of social norms
upon entrance fee WTP responses. Here a linear form ¬tted the data best, re¬‚ecting
the clumping of bids around two round-¬gure amounts (50p and £1).
0.618 + 0.167 BUDGET ’ 0.167 ORDER
(8.12) (2.48) (1.94)
’ 0.299 GREEN + 0.397 CAMP (3.5)
(3.05) (3.16)
WTPfee = WTP per visit (entrance fee vehicle)
CAMP = 1 if the respondent often camps in the area; = 0 otherwise
Other variables as de¬ned above.
Figures in brackets are t-statistics.
72 Applied Environmental Economics

In general the above ¬ndings are unremarkable with one exception: the dramatic
change in the in¬‚uence of the explanatory variable GREEN which is positively
related to per annum bids (although only signi¬cant at the 10 per cent level), but
negatively associated with per visit bids (signi¬cant at the 1 per cent level). We
consider this and other ¬ndings below.

Budget constraint effects
In both our per visit and per annum responses the inclusion of a prior budget
constraint question resulted in a very substantial increase in subsequent stated
WTP. Three of the four comparisons which make up this analysis indicated that
this difference was statistically signi¬cant, a result of some importance for CV
The direction of impact is also interesting. Most commentators (Mitchell and
Carson, 1989; Willis and Garrod, 1993) discuss cases in which, a priori, we would
expect that respondents™ consideration of annual expenditure upon recreation and
consequent budget constraints would lead to a reduction in stated WTP compared to
statements made without such consideration. However, here we observed a strong
opposite effect whereby respondents who were asked to calculate their present
annual expenditure stated signi¬cantly higher WTP sums than those not asked the
prior budget question.
Why has this effect occurred? It seems to us that two interpretations are possi-
ble, one generally supportive of CV and the other critical. The former argues that
respondents forced to overtly consider their annual recreational budget ¬nd that,
on average, this accounts for a signi¬cant portion of their total annual expendi-
ture, perhaps more than they realised without such consideration. Certainly, stated
annual recreational budgets were not insigni¬cant. The mean budget (£227.30)
was considerably affected by the skewed nature of this distribution. Nevertheless,
the median value of £120 shows that most respondents had considerable annual
recreation budgets. Following this argument then, after considering the apparent
importance of recreation in their preference sets, such respondents gave higher
WTP sums than would otherwise have been stated. If we accept such a line of
reasoning then a supplementary question arises as to which WTP measure (with, or
without, the prior budget question) is correct. The argument would seem to suggest
that answers formulated following the consideration of available budgets will be
less susceptible to mental accounting problems and therefore preferable.
A more critical interpretation of our ¬ndings, however, argues that the calculation
of the annual budget (which is relatively high compared to WTP) acts as an anchor
for subsequent WTP statements. Kahneman et al. (1982) suggest that such an effect
is most likely to occur where individuals are inexperienced and face considerable
Recreation: predicting values 73

uncertainty in forming their response. Here, then, our use of an open-ended WTP
elicitation approach may have exacerbated such an effect, as individuals do not
have as much experience of setting prices as reacting to them.
Clearly such ¬ndings give us pause for thought regarding the degree to which
WTP responses may be manipulated by small and apparently defensible changes
in questionnaire design. The responsiveness of stated WTP to the inclusion of
the budget question is remarkable and a matter of signi¬cant concern for CV

Ordering effects
Irrespective of whether or not a budget constraint question was asked, stated WTP
per annum amounts were higher when given as an individual™s ¬rst WTP response
than when given after a response to the per visit WTP question (although this effect
is only signi¬cant in one treatment). A ¬rst point to note regarding such ordering
effects is that, as indicated in our literature review, these results are not necessarily
inconsistent with economic theory. Indeed the work of Carson et al. (1992, 1998)
and Randall and Hoehn (1992) would lead to such an expectation. However, there
are further (although not necessarily contradictory) explanations of these results. A
somewhat simplistic interpretation of such ¬ndings might be that such respondents
were taking prior per visit payments and extrapolating them to produce a per annum
sum.31 However, this would imply that per annum responses made prior to per visit
bids were in error.
An alternative explanation of the apparent ordering effect is suggested by our
observation that membership of ˜green™ groups was positively correlated with WTP
per annum but negatively related to WTP per visit. We suggest that this apparent
disparity arises from a change, induced by the switch in payment vehicle, in the
perceived nature of the good under evaluation. When presented with a non-preceded
WTP per annum question (ordering scenario 1), respondents recognise a typical
payment mechanism for funding public goods in the UK. Individuals understand
the redistributive nature of most UK taxes and that such a payment would preserve
the common-property, public-good, nature of recreation within Forestry Commis-
sion woodlands. Here, then, payments ensure provision for both the payee and other
members of society, both types of provision being likely to be valued by the respon-
dent. However, respondents facing ordering scenario 2 are initially presented with
a WTP per visit (entrance fee) question. Such payments only ensure access for the
payee and imply the exclusion of non-payers. The payment vehicle thus describes
a private, rather than a public, good. This perception is liable to be retained when,
subsequently, respondents are presented with the per annum WTP question. We
31 Factors such as discounting, uncertainty and risk mean that we would not expect a simple relationship between
per visit and per annum WTP.
74 Applied Environmental Economics

can therefore view the apparent ordering effect in per annum responses as arising
out of a category shift in perceptions, induced by the payment vehicle, regarding
the nature of the good under evaluation. The observed relationship of responses
conforms to the perceived loss of services between ordering scenarios 1 (recreation
seen as a public good) and 2 (recreation seen as a private good).
If the difference in WTP statements is derived purely from the additional value
aspects which respondents feel they obtain from woodland as a public good
(bequest, altruism, etc.) rather than as a private good, then, while complicating
the matter, this may be viewed as simply re¬‚ecting preferences. However, a num-
ber of commentators have argued that the evaluation of the same asset as either a
public or private good may alter the underlying motivations upon which individual
preferences lie. Schkade and Payne (1994) and Blamey (1998) note that evaluations
of public goods appear in part to re¬‚ect norms regarding civic duty and fairness.
Furthermore, Brennan and Buchanan (1984) argue that such valuations may also be
in¬‚uenced by a self-image or expressive value, derived from contributions towards
goods which bene¬t not just the individual but also others in society.
In support of such an argument it is important to emphasise that the study was
conducted midway through a high-pro¬le, year-long public debate concerning (and
generally opposing) proposals by the then UK government to privatise the Forestry
Commission estate, a resource which provides the largest area of open-access recre-
ational land in the UK. Countryside groups and their members were vociferous in
their opposition to privatisation, as evidenced in the remarkable swing from posi-
tive to negative correlations with WTP as payment vehicles switch from those of
a public to a private good. If normative and expressive values do underpin these
differences, then, as Sugden (1999b) argues, CV estimates must be considered as
being context-speci¬c rather than as absolute valuations of the assets concerned.
A contrary and more critical explanation of the observed ordering effect follows
Kahneman et al. (1982) in arguing that relatively small prior per visit WTP re-
sponses have here downwardly anchored subsequent per annum bids. In the context
of our particular experiment, with one WTP response directly preceding another,
such an effect is similar to the widely observed phenomenon of starting point bias
(Boyle et al., 1985). However, the remarkable and highly signi¬cant reversal in
WTP correlation signs for members of green groups described above, makes us
feel that the public/private goods argument cannot be ignored here. This does not
preclude the possibility that the observed ordering effect has been heightened by
anchoring/starting point bias, with consequent questions being raised regarding the
validity of such results.
Each of the theoretical expectation, public/private goods and anchoring argu-
ments can also be applied as explanations of the observed ordering effects in per
Recreation: predicting values 75

visit WTP responses. Here the direction of causation is reversed in that the introduc-
tion of a prior per annum WTP question raises per visit WTP (although again only
one of these effects is statistically signi¬cant). This could be following theoretical
expectations, perhaps enhanced by the per annum approach inducing respondents
to think of this as being a public as opposed to a private good. Alternatively it may
be that the relatively high prior per annum response upwardly anchors subsequent
per visit responses, or a mixture of both.

The analysis applied a split-sample approach to the investigation of budget con-
straint, temporal and ordering effects in CV studies. In three out of four tests
signi¬cant budget constraint effects were detected. Interpretation of such results
is not straightforward as they may be viewed either as the expected consequence
of respondents revising bids in the light of further re¬‚ection, or as evidence of an
anchoring bias. While both explanations may have some validity their implications
for future studies are in direct con¬‚ict. If budget constraint questions induce re-
spondents to consider more fully their personal circumstances, then, following the
recommendations of Arrow et al. (1993), some variant of these questions should
be included prior to WTP questions. Conversely, if the responses to budget con-
straint questions anchor subsequent WTP bids, then this suggests that they should
be avoided.
Two of the four tests of ordering effects indicated that signi¬cant differences
were observed. Again, at least two explanations of these results can be proposed.
Following Carson et al. (1992, 1998), economic theory allows for divergence be-
tween measures of the same good elicited at different points in a valuation sequence.
Such differences are likely to be exacerbated if the sequence itself induces differ-
ing subsamples to view the resource under evaluation as either a public or a private
good. Following such an explanation, the divergence in valuations can be seen
either as re¬‚ecting the differing attributes of such goods, or as arising from a con-
sequent change in the motivations underlying the preferences expressed. However,
as with our budget constraint experiment, these divergences can also be interpreted
as evidence of prior responses anchoring subsequent bids.
In conclusion, these ¬ndings can be viewed either as demonstrating the suscep-
tibility of CV results to design effects or as quantifying the limits of such effects.
For the purposes of our subsequent work we adopt the latter position, stressing that
the valuation of environmental preferences remains more of an art than a science,
but that such values, if treated with due caution, can improve decision-making sub-
stantially when compared with standard approaches in which such preferences are
implicitly ignored.
76 Applied Environmental Economics

The Thetford 2 TC study: a GIS-based investigation of measurement
and estimation effects32
The analysis of revealed visitation behaviour derived from the TC data gathered
in the Thetford 2 survey involved the ¬rst application of geographical information
system (GIS) techniques to be presented in this volume. The GIS was used to provide
estimates of travel time and distance from outset locations to the site. The spatial
analytic capabilities of the GIS were then used to perform a sensitivity analysis of
common measurement assumptions in TC studies. As we shall see in Chapter 4, the
GIS was also used to manipulate TC data so as to generate a transferable arrivals
function, capable of estimating the number of visitors both to this surveyed site and
to other unsurveyed sites in our wider study area of Wales.
The Thetford 2 TC study was also used to conduct a full sensitivity analysis across
a range of unit-value assumptions regarding travel expenditure and time cost and to
assess how effects vary between differing estimation procedures, namely ordinary
least squares (OLS) and maximum likelihood (ML) techniques. Survey details are
as for the Thetford 2 CV study (the questionnaire was designed to facilitate both CV
and TC analysis), although here we stress the importance of questions concerning
the recreational trip. Respondents were asked to state:
(i) home address, and trip origin if different to this (e.g. if on holiday away from home)
(ii) how they travelled to the site
(iii) the perceived travel time and cost
(iv) the number of other sites visited during the day™s trip
(v) the proportions of the whole day™s enjoyment attributable to time spent travelling, time
spent at the survey site and time spent at other sites.

Applying GIS to the TC method
One of the most obvious advantages of using GIS techniques in TC studies is
to standardise and improve the accuracy in the derivation of travel distance and
duration variables. Given that these are the basic elements underpinning estimates
of individuals™ travel expenditure, travel time and hence travel cost, the potential
bene¬ts are clearly considerable. This section describes the procedure by which the
GIS was used to calculate travel times and distances.
Using the data collected from the visitor survey, the 1km National Grid ref-
erence of trip origin was located by consulting the Ordnance Survey™s Gazetteer
of Great Britain (Ordnance Survey, 1987). Digital road network details were ex-
tracted from the Bartholomew 1:250,000-scale database for the UK. This source
provides information on road classes, distinguishing ¬fteen separate categories
from minor, single-track country lanes to motorways. Computing constraints made
32 Further details of this study are given in Bateman (1996) and Bateman et al. (1996a)
Recreation: predicting values 77

Table 3.11. Average road speed estimates

DoT estimates Adjusted speeds

Rural (1) Urban (2) Rural (3) Urban (4)
Road type (m.p.h.) (m.p.h.) (m.p.h.) (m.p.h.)
Motorway 70 50 63 35
A-road primary, dual carriageway 60 40 54 28
A-road other, dual carriageway 55 35 50 25
A-road primary, single carriageway 50 35 45 25
A-road other, single carriageway 40 25 32 18
B-road, dual carriageway 40 25 36 18
B-road, single carriageway 30 17 24 12
Minor road 20 15 14 11

Source: Columns (1) and (2) from Department of Transport (1992, 1993).

it impractical to assemble a detailed road network for the entire area covering
origins of Thetford visitors (this ranged from near Newcastle upon Tyne in the
north to Hampshire in the south). We therefore de¬ned a study area to include
the counties of Norfolk, Suffolk and Cambridgeshire, together with adjoining dis-
tricts in Lincolnshire and Essex. This encompassed over 92 per cent of the visitor
Typical speeds can be assigned to the different classes of road de¬ned in the
Bartholomew™s database so enabling travel times to be calculated for discrete sec-
tions of road. From these, travel times can be calculated for routes across the whole
network. Data on average travel speeds for differing categories of road were ob-
tained from a variety of sources. This exercise revealed both the paucity of such
data and some signi¬cant differences in estimates. An initial investigation was un-
dertaken using road speeds given in Department of Transport (DoT) sources as
detailed in columns (1) and (2) of Table 3.11.
Travel times from each road segment in the network were calculated as:
length of road segment (in miles)
travel time (3.6)
speed (miles per hour)
Minimum travel time can be calculated by specifying the time from Equation
(3.6) as the impedance associated with a particular road segment in the digital
network. An algorithm is then used to identify the route between the trip origin
and forest site which minimises the cumulative impedance, thereby also deriving
the minimum travel time (see Lupien et al., 1987). Utilising the DoT road speeds
in Table 3.11, a series of travel times were calculated for a variety of routes be-
tween a sample of towns and villages in the area. These were then compared with
those generated using the alternative road speeds given in Gatrell and Naumann
78 Applied Environmental Economics

(1992) and the Automobile Association™s Autoroute route planning software pack-
age. Further calibration was achieved by calculation of travel times for a number
of routes well known to the authors and their colleagues. These assessments con-
sistently pointed to the conclusion that the DoT road speeds given in Table 3.11
were overestimates of those realistically attainable in the study area. Such a ¬nd-
ing re¬‚ects the fact that these of¬cial road speed estimates are based on limited
information regarding the impact of road junctions and other sources of traf¬c con-
gestion. Although it was feasible to consult Ordnance Survey maps regarding the
topology of motorway junctions it was not practicable to conduct a systematic as-
sessment of all junctions (or other traf¬c constraints) throughout the road network.
Accordingly, a sensitivity analysis was undertaken to obtain appropriate adjust-
ment factors by comparing calculated travel times with those regarded as more
realistic.33 Best-¬t adjusted road speeds are presented in columns (3) and (4) of
Table 3.11.
The calculation of individuals™ travel times and distances using the GIS involved
three steps. First, the survey site was identi¬ed on the road network and an al-
gorithm in the GIS software (Arc/Info) was used to calculate the minimum sum
impedance34 between the destination and each unique segment of road. This pro-
duces the minimum cumulative time (in minutes) that it takes to reach the start-point
and end-point of each road segment. These times are then stored in an output table
(Environmental Systems Research Institute, 1994).
The second step involved ¬nding the nearest point on the road network for
each individual visit origin. Travel times from this point to the site were then
extracted using both the prepared output table and interpolation between the two
end-points of each road segment. Finally, the distance travelled by each visitor
along these minimum impedance routes was calculated using further GIS facilities
As a test of the validity of these GIS-de¬ned measures, respondents™ estimated
travel times and distances were compared with their GIS equivalents.35 Travel time
distributions were found to be very similar (a two-sample t-test for difference gave
a t-statistic of 0.09 for which p = 0.88). A similar result was obtained regarding
travel distances. However, the values highlighted some potential advantages of the
GIS approach. These are illustrated in Figure 3.1 which graphs the ratio of stated
to GIS-calculated distance against the absolute value of the latter.
Examining Figure 3.1 shows that, on average, the distance measures coincide
reasonably well. Most observations have a ratio value of about 1 (i.e. stated =

33 Further details are given in Bateman et al. (1999c).
34 The algorithm used works recursively through the entire road network, keeping information about the minimum
impedance route found so far, until all possible route permutations are exhausted.
35 A similar analysis is reported by Liston-Heyes (1999).
Recreation: predicting values 79

Figure 3.1. Graph of the ratio of stated to GIS-calculated distance against calculated dis-
tance. (Source: Adapted from Bateman et al., 1996b.)

GIS-calculated values) and there are approximately as many observations below 1
as above. However, given that the GIS distance is based on a minimum impedance
algorithm (minimum possible travel time), those respondent estimates below the
unity line are likely to be subject to some form of error, a situation which we
suspect is due to respondents rounding their stated travel time estimates, e.g. a true
travel time of twelve minutes is reported as being ten minutes. Support for such
an argument comes from noting that, with a few exceptions (discussed below), a
similar distribution of upward rounding errors can be seen lying above the unity
line, e.g. a true travel time of eight minutes being reported as ten minutes.
Such results indicate that GIS measures are, for the majority of visitors, good
estimates of true travel distance and duration. However, Figure 3.1 shows that
for a small minority such a conclusion does not hold. Six respondents (i.e. about
2 per cent of the sample) lie above the upper 95 per cent con¬dence interval around
the unity line. Cross-checking against responses from these parties shows them
to be ˜meanderers™ (see Chapter 2), whose main objective is enjoyment of the
journey rather than time spent on site. The relatively low importance of the on-
site recreational experience to such respondents will be re¬‚ected in their responses
to question (v) above which are used as utility weights on travel costs in the TC
model. Such a procedure ensures that we only use that portion of travel costs which
is due to the on-site recreational experience in calculating the bene¬t values of that
site. Coincidentally, this same procedure drastically reduces the in¬‚uence of any
error due to the use of GIS-based measures for such meanderers. Given this, and
80 Applied Environmental Economics

the advantages of such measures with respect to rounding errors, we consider that
GIS-calculated travel distance and duration provide a good basis for TC studies, an
assumption which we test subsequently in this study.

Sensitivity analysis 1: unit-value assumptions and estimation techniques
In Chapter 2 we discussed the various de¬nitions of travel expenditure and time cost
which underpin travel costs. Here we test various combinations of each, de¬ning
travel expenditure as marginal (petrol only) or total running costs (8p and 23p
per mile respectively)36 and time costs at the following wage rates: 100 per cent
(assuming that leisure time is valued at the full wage rate); 43 per cent (the DoT
appraisal rate); 0 per cent (assuming that there is no opportunity cost of non-work
time); and a best-¬t rate (that rate which maximises the model™s ¬t to the data).37
These combinations de¬ned a series of alternative travel cost (expenditure plus
time) variables which were then used as the basis of a number of models to predict
visits to the site at Thetford Forest. Other explanatory variables were derived from
survey data and are discussed subsequently.
A further issue which our theoretical appraisal highlighted was the impact of
varying the estimation procedure employed. In particular, it was noted that the
use of ordinary least squares (OLS) techniques failed to allow for the truncation
of non-positive visits (i.e. it does not take into account the fact that any on-site
survey respondents cannot make less than one visit to the site). This issue can be
addressed by the use of maximum likelihood (ML) methods where the underlying
likelihood function can be de¬ned to allow for this truncation (for details regarding
the present study, see Bateman et al., 1996b). For comparative purposes both OLS
and ML estimation methods were applied to the various unit-value permutations
described above. Goodness-of-¬t measures were given by R2 statistics for OLS
regressions and log likelihood values for ML analyses.

Tests across a variety of functional forms indicated that in all cases the natural
log of the number of visits made by a party to the site (lnVISIT) gave the best
de¬nition of the dependent variable. To enhance comparability across models a
consistent set of explanatory variables was used in all sensitivity analysis models as

36 Automobile Association estimates given in Benson and Willis (1992).
37 Further permutations, including the use of measures based on respondents™ perceived travel costs, are presented
in Bateman (1996) and Bateman et al. (1996a).
38 Other variables considered but rejected from the comparative models include: party size; age<25; age>65;
membership of any environmental organisation; membership of separate organisations; other main activity
Recreation: predicting values 81

TC = travel cost (travel expenditure + travel time); various
permutations as discussed previously
HSIZE = household size
HOLS = 1 if respondent was on holiday at time of interview; = 0
WORK = 1 if respondent was working at time of interview; = 0
LIVE = 1 if respondent lives near site; = 0 otherwise
RATING = respondent™s rating of scenery at the site (from 1 = poor to
4 = superb)
NT = 1 if respondent was a member of the National Trust; = 0
TAX = 1 if respondent was a taxpayer; = 0 otherwise
MDOG = 1 if respondent™s main reason for visit was dog walking; = 0

Table 3.12 presents the travel cost coef¬cient (full functions given in Bateman,
1996) and three consumer surplus (CS) values from ML-estimated models for the
various de¬nitions of travel cost considered in the sensitivity analysis.
Given the strong correlations among the various de¬nitions of travel cost, and that
the set of other predictors remains constant across models, goodness-of-¬t statistics
were similar for all the models detailed in Table 3.12 (see details in Bateman, 1996).
However, the marginal cost (8p per mile) travel expenditure model using a best-¬t
(2.5 per cent) travel time assumption provided an overall optimal ¬t to the data
and is therefore our preferred model from the ML analyses (shown in italics in
Table 3.12). This is an interesting result as it suggests that time costs, although highly
signi¬cant in determining trips (see Chapter 4), can be substantially overstated in
absolute terms, resulting in large overestimates of consumer surplus (e.g. bene¬t
estimates are nearly 2.5 times higher if the DoT wage rate is used rather than our
best-¬t rate). A similar degree of bene¬t overestimation occurs where the poorer-
¬tting full travel expenditure assumption is employed.
Comparison of bene¬t estimates from our preferred model with those obtained
from the other studies considered in this chapter strongly reinforces the ¬ndings of
our review of previous research, in that the values obtained from our TC studies
are consistently above those derived from CV analyses, the magnitude of this dif-
ference being similar across studies. Reasons for this disparity are discussed in the
conclusions to this chapter.
In the TC method as shown in Chapter 2, welfare estimates are obtained by
integration under the demand curve which is in turn derived from the trip generation
Table 3.12. Sensitivity analysis: ML models (best-¬tting model shown in italics)

Travel cost CS per household CS per household CS per person
Travel Travel time coef¬cient per annum per visit per visit
expenditure cost cost (wage rate) (t-statistic) (£)1 (£)1,2 (£)1,3
Marginal Zero (0%) 140.39 3.62 1.21
(8p/mile) (’3.32) (127.55) (3.29) (1.10)
Marginal DoT (43%) 374.10 9.65 3.22
(8p/mile) (’2.92) (339.87) (8.77) (2.92)
Marginal Full (100%) 743.61 19.18 6.39
(8p/mile) (’2.72) (675.57) (17.42) (5.81)
Marginal Best ¬t (2.5%) 153.23 3.95 1.32
(8p/mile) (’3.24) (139.21) (3.59) (1.20)
Full Zero (0%) 381.31 9.83 3.28
(23p/mile) (’3.32) (346.42) (8.93) (2.98)
Full DoT (43%) 570.56 14.71 4.90
(23p/mile) (’3.02) (518.36) (13.36) (4.45)
Full Full (100%) 898.02 23.16 7.72
(23p/mile) (’3.00) (815.85) (21.04) (7.01)
Full Best ¬t (6%) 402.83 10.39 3.46
(23p/mile) (’3.32) (365.97) (9.44) (3.15)

Notes: 1 values in each cell are at 1993 prices; lower values (in brackets) are at 1990 prices (for comparison with subsequent chapters).
De¬‚ator from Central Statistical Of¬ce (1993a).
On average, households visited Thetford Forest nearly ¬fteen times per annum.
Calculated using median party composition ¬gures of three persons (two of whom were >16 years). Mean party size was considerably
skewed by a few large parties and was not thought to provide an appropriate measure. Note that this assumption treats adults and children
Recreation: predicting values 83

function. This function itself also provides a degree of theoretical validation of
the study through inspection of the various relationships found to be statistically
signi¬cant predictors of visits. Equation (3.7) details the trip generation function
for our best-¬tting ML model.
’0.4853 ’ 0.0776 TC + 0.0718 HSIZE ’ 1.4728 HOLS
(’0.819) (’3.235) (1.326) (’2.762)
+ 1.7408 WORK + 2.2770 LIVE + 0.5050 RATING ’ 0.4629 NT
(3.840) (5.771) (3.198) (’1.915)
+ 0.4416 TAX + 0.6066 MDOG (3.7)
(1.863) (2.461)
’ 454.59
Log likelihood value Sigma 1.18 (16.79)
Variables as previously de¬ned. Figures in brackets are t-statistics.
The model given in Equation (3.7) has expected signs and signi¬cance on all ex-
planatory variables (of our standard set of predictors only HSIZE proved to be
statistically insigni¬cant). The travel cost variable is highly signi¬cant, easily pass-
ing a 1 per cent test, and indicating that visits are inversely related to the sum of
journey and time costs. More visits are made by those who live or work near the
site, who rate the scenery highly, use the location for dog walking (these respon-
dents made a relatively large number of visits) and were taxpayers. Those making
less frequent visits included respondents who were on holiday at the time of the
survey (most of whom did not live locally) and those who were members of the
National Trust, a factor which may either be linked to a wider recreational op-
portunity set or to an interesting inverse link with income (which we explore in
Chapter 4).
Given the ¬ndings of our ML analyses, only zero and 43 per cent wage rate time
costs were used in the OLS sensitivity analysis, the results of which are presented in
Table 3.13. These results con¬rm our prior ML ¬ndings that models using marginal
journey costs (8p/mile) and very low (here zero) time costs ¬t the data best. However,
in other respects our OLS-based models do not compare favourably with their
ML counterparts. Although comparison of overall goodness-of-¬t statistics (log
likelihood values versus R2 ) is problematic, explanatory variable t-values in directly
comparable models were generally higher in ML than OLS models, and invariably
so with regard to the travel cost variable. Perhaps more importantly from a practical
point of view, these results fail both convergent validity (Mitchell and Carson, 1989)
and plausibility tests, in that the bene¬t estimates derived are over ¬ve times larger
than those obtained from our ML models (which were themselves in line with
results elsewhere in the literature). Given this, we can conclude that the theoretical
problems inherent in the application of OLS techniques to individual TC valuations
Table 3.13. Sensitivity analysis: OLS models (best-¬tting model shown in italics)

Travel cost CS per household CS per household CS per person
Travel Travel time cost coef¬cient per annum per visit per visit
expenditure cost (wage rate) (t-statistic) (£)1 (£)1,2 (£)1,3
Marginal (8p/mile) Zero (0%) 313.19 21.38 7.13
(’2.93) (284.53) (19.42) (6.47)
Marginal (8p/mile) DoT (43%) 1271.82 86.81 28.94
(’2.12) (1155.45) (78.87) (26.29)
Full (23p/mile) Zero (0%) 871.97 59.52 19.84
(’2.90) (792.19) (54.07) (18.02)
Full (23p/mile) DoT (43%) 1645.33 112.13 37.38
(’2.51) (1494.78) (101.87) (33.96)

Notes: 1 values in each cell are at 1993 prices, lower values (in brackets) are at 1990 prices (for comparison with subsequent chapters).
De¬‚ator from Central Statistical Of¬ce (1993a).
On average households visited Thetford Forest nearly ¬fteen times per annum.
Calculated using median party composition ¬gures of three persons (two of whom were >16 years). Mean party size was considerably
skewed by a few large parties and was not thought to provide an appropriate measure. Note that this assumption treats adults and children
Recreation: predicting values 85

are matched by empirical problems, and that consequently results obtained from
such analyses should not be used for decision-making purposes.

Sensitivity analysis 2: measurement issues39
In Chapter 2 we noted that certain common simplifying assumptions regarding the
measurement of travel time and distance might have the potential to produce biased
estimates of consumer surplus. In particular we highlighted the use of centroid
rather than actual outset origins and various simplifying assumptions regarding
journey routing, notably the use of straight-line distance or constant travel speeds.
The use of a GIS allows us to investigate the potential impact of these measurement
assumptions by permitting the analyst the following types of ¬‚exibility:

(i) Relatively precise journey origins (accurate, in this study, to 1 km) may be speci¬ed;
(ii) Alternatively, centroid journey origins may be de¬ned using a variety of administrative
(iii) Travel distance and travel time may be calculated either using straight lines or by
reference to a digital road network. Where the latter approach is used, information
on road quality and corresponding speeds can also be incorporated to provide more
accurate measures of travel distance and time.

In order to investigate the centroid issue, three types of outset origin were spec-
i¬ed: (i) the 1 km resolution outset location used previously; (ii) the geographical
centroid de¬ned by UK district boundaries; and (iii) the geographical centroid de-
¬ned by UK county boundaries.40 In order to ensure suf¬cient variation at the
county level, the road network had to be extended to cover the entire sample of
survey respondents. This was achieved by de¬ning a simpler skeleton digital road
network beyond the previously de¬ned area, concentrating upon the main roads.
This simpli¬cation was considered reasonable given that visitors travelling from a
considerable distance were unlikely to make much use of minor roads until they
were near to the site.
For each origin at the three resolutions the travel distance and duration measures
underpinning travel costs were calculated ¬rst by using the minimum impedance
algorithm in conjunction with the digital road network (i.e. routing visitors along
the least-cost path as described previously) and secondly by using straight-line
The various travel cost measures obtained from all these permutations were then
entered into a series of trip generation functions. Statistical tests again indicated

39 Further details of this analysis are given in Bateman et al. (1999a).
40 UK districts and counties roughly correspond to the smallest and largest US counties used as centroids in the
TC-based study by Loomis et al. (1995).
86 Applied Environmental Economics

Figure 3.2. Comparison of 1 km grid reference with county centroid trip origins. (Source:
Bateman et al., 1999a.)
that a semi-log (dependent) functional form provided the best ¬t to the data. Given
our previous ¬ndings, ML estimation techniques were employed throughout.

Figure 3.2 illustrates some of the graphical output which can be produced by a
GIS and demonstrates the impact of adopting large catchment areas. Here the 1 km
outset origins derived from visitors™ responses are compared to the county cen-
troids. Inspection of those counties in the vicinity of the site clearly shows that
the majority of visitors set out from origins which are closer to the site than the
centroids for their corresponding areas. This is likely to be the case irrespective
of the size or location of the area. However, the relative error caused by this ef-
fect is much greater for areas close to the site than for more distant ones. This
Recreation: predicting values 87

Table 3.14. Sensitivity analysis: effects of varying outset origin on
TC bene¬t estimates

Source of distance CS per CS per CS per
and duration household per household per person per
Outset origin measures annum (£) visit (£) visit (£)
1 km grid Digital road network 173.25 4.47 1.49
reference Straight line 141.97 3.66 1.22
District Digital road network 206.40 5.32 1.78
centroid Straight line 173.71 4.48 1.49
County Digital road network 364.73 9.40 3.14
centroid Straight line 338.29 8.72 2.91

systematic bias will result in an overestimate of consumer surplus as discussed
Full results from our analysis are presented in Table 3.14. Here, following the
¬ndings of our previous sensitivity analysis, marginal travel expenditure (8p/mile)
and best-¬t travel time costs (2.5 per cent of wage rate) are used throughout to
de¬ne travel costs.
Examining Table 3.14 reveals that using straight-line as opposed to road-based
measures of travel cost consistently produces lower estimates of consumer surplus.
This is as expected and re¬‚ects the underestimate of true travel cost produced
by straight-line approximations. The resultant underestimation ranges up to 20
per cent; however, this is small compared to the error induced by using large-
area centroids as opposed to more accurate estimates of outset origin. While the
increase induced by moving from 1 km origins to district centroids is similar to that
of changing from road network to straight-line measures, a very substantial impact
occurs where we move from 1 km to county centroid origins with bene¬t estimates
more than doubling.
These ¬ndings lead us to conclude that the bene¬t estimates produced by studies
adopting large-area centroid origins and/or straight-line-based measures of travel
cost should be treated with caution. By contrast, the GIS-based measures derived
from the higher resolution origins utilised in the present study seem to offer a
substantial improvement in the robustness of bene¬t estimates.

Thetford 2 TC study: conclusions
Perhaps the primary objective of the Thetford 2 TC study was to show how GIS
techniques can enhance the application and validity of the method. These techniques
were applied to the fundamental tasks of calculating the travel distance and duration
data and have been shown to have a number of advantages over more conventional
88 Applied Environmental Economics

Table 3.15. Valuing recreational visits to woodland: a synthesis of studies

£ per party per visit2

Upper 95% Lower 95%
£ per person Mean party C.I. party C.I. party
Study Method per visit size (3.05) size (3.27) size (2.85)
Cross-study analysis CV 0.60 1.82 1.95 1.69
(OE WTP use value)
Wantage CV 0.82 2.50 2.68 2.33
(OE WTP/visit study)
Thetford 2 ITC 1.20 3.59 3.85 3.35
(ML model)

Notes: 1 Figures are best-estimate means (1990 prices). Bateman (1996) also reports 95%
C.I.s and alternative estimates based on WTP per annum studies.
The sensitivity analysis on party size treats adults and children equally as party members.
Note that the per person per visit value used is kept constant within each row.

approaches. The advantages are perhaps best demonstrated in our second sensitivity
analysis which uses the ¬‚exibility of GIS to indicate how a number of common
measurement assumptions can lead to substantial biases within bene¬t estimates
and, more importantly, how they can be avoided.
The study has also revisited a number of areas of controversy in the existing
literature by conducting a sensitivity analysis across a number of common unit-value
assumptions and estimation techniques. This analysis quanti¬ed the magnitude of
potential welfare measure variance as well as yielding some defensible values for
use in our subsequent research.

Summary and conclusions
This chapter has presented a considerable number of results regarding the valuation
of woodland recreation bene¬ts. From our review of the existing literature we
identi¬ed a number of CV analyses which provided the basis for a cross-study
meta-analysis of values. This work showed that WTP responses were logically
linked to the values individuals were asked to assess and to the elicitation method
employed. From the various values which can be derived from our cross-study
model we emphasise the estimate of use value derived using an OE elicitation
method, the latter being conducive to the estimation of the lower-bound values we
have emphasised throughout. This result is reproduced in the top row of Table 3.15
which summarises the more robust valuations presented here.
The remaining rows of Table 3.15 summarise selected results from our own
valuation work. Reviewing the various research objectives we set ourselves in
Recreation: predicting values 89

Chapter 2 with respect to the CV method, we have seen through the Thetford 1
study the substantial variation in WTP values reported by woodland users as op-
posed to non-users of woodland recreation, while the Wantage study has contrasted
these with the WTA compensation levels demanded by farmers for providing wood-
land recreation opportunities on their land. Taken together, the three CV studies
presented in this chapter also provide evidence of the considerable variation in
values induced by choice of elicitation method and payment vehicle. While these
effects are, arguably, consistent with theoretical expectations, of greater concern
are the substantial impacts induced by adding budget constraint questions and test-
ing question ordering in the Thetford 2 CV study. While we would not contend
that these studies are beyond criticism, such ¬ndings suggest that values should be
treated with some caution and that the conservative approach advocated by H.M.
Treasury may be justi¬ed.
Turning to consider the objectives for our TC studies set out at the end of
Chapter 2, in the Thetford 2 study we have used GIS techniques to investigate
the impact of different strategies for measuring travel time and travel distance
upon resultant consumer surplus estimates. The GIS has permitted a substantial
improvement in de¬ning the journey outset location, modelling journey routing
and conducting sensitivity analyses on consumer surplus estimates. We have also
examined the impact of various statistical modelling procedures and functional
forms upon those estimates. Again we have seen that bene¬t estimates are highly
sensitive to a range of methodological issues, reinforcing the need to exercise care
when incorporating bene¬t estimates in CBAs.
Given these concerns we have omitted the Thetford 1 studies from Table 3.15
as these were principally methodological tests and the values produced have to
be treated with considerable caution. We have fewer reservations regarding the
validity of CV estimates obtained from the Wantage study. However, as the ben-
e¬t transfer methods employed in the following chapter require per visit val-
ues we do not make any further use of the WTP per annum results obtained
from this or the Thetford 2 CV study. The per visit estimates obtained from the
latter study are also dif¬cult to apply to a wider context as they are strongly
in¬‚uenced by the various designs used in each sample (and the one readily
comparable estimate is included within our cross-study meta-analysis). How-
ever, the value obtained from our preferred model in the Thetford 2 ITC study
does appear to have reasonable claims to validity and forms the ¬nal row of
Table 3.15.
Examination of the various values presented in Table 3.15 indicates that they
conform well to prior theoretical and empirical expectations in that per party per
visit values obtained from our CV studies are similar to, but somewhat smaller
than, our TC estimates. Such a ¬nding conforms to the large-sample cross-study
90 Applied Environmental Economics

comparison of TC and CV studies reported by Carson et al. (1996) as well as
satisfying a plausibility test.
Given that conservative measures have been emphasised throughout, we use the
lower of the two CV values shown (i.e. £1.82 per party per visit) for our subsequent
bene¬t transfer work, both because it gives a more defensible estimate of recreation
values and because it is based on a large number of studies. This claim cannot be
made for our ITC value. However, the study underpinning this particular value
appears robust and has considerable advantages over others in the literature. Given
this outcome we also use this value as an upper-bound contrast with the cross-study
CV measure within the bene¬t transfer work discussed in the following chapter.
Finally, although all of the values discussed above have been adjusted in real
terms to our 1990 study period, is there any evidence that these values may have
changed over time up to the present day? This question is considered in a recent re-
examination and extension of our meta-analysis work presented in Bateman et al.
(2001d). Here, we combine the various CV and TC estimates of woodland per person
per visit recreational values into one meta-model. This study utilises multilevel
modelling techniques (Goldstein, 1995) to control for intra-unit correlation (IUC)
between value estimates produced by each study author and within each forest
(i.e. the possibility that estimates produced by a given author are more similar
than those produced by taking a random sample from all estimates). The study
¬nds no signi¬cant evidence of IUC effects either within authors or within forests.
Furthermore, conclusions regarding valuation estimates remain broadly the same as
reported here and so are not repeated. However, the expansion of estimates permitted
by combining results from all CV and TC studies permitted investigation of whether,
controlling for all other signi¬cant factors, any time trend in the real value of
woodland recreation could be observed. Findings suggest that a small increase in
real values was statistically signi¬cant across the time series (of seventeen years)
considered. While we consider a number of possible reasons for this result we
cannot reject the hypothesis that this re¬‚ects an underlying real increase in the
perceived recreational value of woodland over time. This result is reminiscent of
that postulated by Krutilla and Fisher (1975) in their discussion of the value of
natural environments over time. Certainly, there seems little reason to suppose
that recreation values will decline in real terms over time; rather they should be
stable or increase. In Chapter 9 we consider the implications of such trends for our
cost-bene¬t results.
Recreation: predicting visits

In this chapter we utilise a geographical information system (GIS) to model the
predicted number of visitors to a particular woodland site and test the ef¬ciency of
the resultant arrivals function in estimating visits to other sites. This is achieved
through a zonal model which estimates visitor arrival rates from areas around a
given site, and which is then applied to other sites through the de¬nition of similar
zones around them. Findings from our studies of the value of open-access woodland
recreation (discussed in Chapter 3) are then applied to our predicted visits surface
to obtain valuations of potential demand.1

Estimating an arrivals function
Previous studies
We are concerned with estimating overall visit rates which are applicable across
populations, rather than being speci¬c to individuals. By de¬nition, conventional
ITC valuation studies refer only to site visitors and say little about non-visitors.


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