33
AN INDIVIDUAL TRAVEL-COST METHOD OF EVALUATING FOREST RECREATION
K. G. Willis and G. D. Garrod*
Consumer surplus for outdoor recreation has traditionally been estimated by a Clawson-Knetsch travel-cost method. This paper presents zonal consumer-surplus estimates for visitors to a number of forests and compares these estimates to those derived from individual visitor observations. Both travel-cost procedures are used to assess the magnitude of recreational benefits and are found to produce widely different consumer-surplus estimates. This raises questions about research methodology and has implications for the value of recreation associated with forestry and its contribution to the rate of return on forest investment.
1. Introduction
Traditionally, consumer surplus for non-priced outdoor recrzation has been estimated by a Clawson-Knetsch (1966) travel-cost model. This approach aggregates individual visitors to a recreation site into their zones of origin, and then seeks to explain the variation between visitor rates from each zone by travel cost, the income and socio-economic characteristics of the residents of each zone, and the characteristics of any alternative sites. From the resulting demand curve, consumer surplus per zone can be calculated. This ty e of model is still widely used (Loomis et al., 1986; Willis and Benson, 19887 and continues to be developed to value different kinds of recreational activities.
Recently, however, attention has been focused on deriving consumer- surplus estimates from the travel cost incurred by individual visitors to a site, i.e. the observations used are those of individuals themselves rather than zonal aggregates of individuals. This approach has arisen as the result of a number of factors. First, there is often a desire to analyse data on individual willingness- to-pay (WTP), for example for licences to hunt wildlife (in the USA). Second, in many studies the number of observations is small in relation to areas and population, thus rendering the Clawson-Knetsch (C-K) approach infeasible.
Third, situations occur where a number of individuals start from a common origin (e.g. from a college) but disperse in small numbers to numerous destinations (e.g. nearby ski-resorts) (Morey, 1985). Fourth, the purpose ma be to value the attributes of goods such as recreation, in the Lancaster (19661 sense: individuals d o not simply wish to purchase recreation but desire combinations of views, wildlife, streams, and other site attributes. What is
* Dr Ken Willis and Mr Guy Garrod are members of the Countryside Change Unit, Department of A 'cultural Economics and Food Marketing, University of Newcastle upon Tyne NE17RU.
AKesponsibility for errors and omissions rests with the authors.
34 K. G. WILLIS AND G. D. GARROD
required to estimate such attribute values, are samples of individuals spread across many sites in order to permit variability in attributes. The C-K travel- cost method may be inappropriate when analysing data like this, especially in cases where it is necessary to aggregate large sample numbers of observations into zones for one or two sites.
The urposes of this paper are: to compare the consumer-surplus estimates derivefby the zonal C-K travel-cost method (ZTCM) and by the individual travel-cost method (ITCM) for a common data set; and to discuss the relative robustness of the estimates produced by each technique. The anal sis uses a survey of the recreational use of forests, which was undertaken in 1
B
88 for theForestry Commission (Willis and Benson, 1989).
2. The Clawson-Knetsch Method The C-K model has the general form:
where Vhj = number of trips from zone h to forest j Ph = population of zone h
Chj = travel cost from zone h to forest j (f)
sh
= socio-economic characteristics of the PO ulation of zone h (e.g.A,, = recreation attributes of forest j in relation to other substitute e,, = errorterm
income, car ownership, club membership7 recreational facilities k
Table 1 Alternative Functional Forms for Clawson-KnetPch Zonal Travel-Cost Method Funcfional Forms
Semi-Log
Foresf Linear (Dependent) Log- Log
Brecon
ran
N e w Forest
-177.1 -5.7 - 12.6
0.17 0.54 0.27
138.8 +13.3 +47.1
-0.13 0.75 0.47
-873.8 0.17
-3.2
0.99 +45.8 0.86
-27308.2 +35.3 +432.6
0.12 0.92 0.76
-8633.6 0.90
-3.7
0.97 +4.7
0.82 Ruthin
I1 \ -3% 2 -4.1 +6.7
lil
0.20 0.96 0.63f2] 1 Correlation coefacient between actual and predicted Overall percenta e error = [(predicted visits- actual vkits)/actual visits] number ofvisits. '100.
)i( n 0.96 . 0.63 ~ _ _
\-I
1 Overall percenta e error = [(predicted visits- actual vkits)/actual visits] '100.
f2] Correlation coefacient between actual and predicted number ofvisits.
AN INDIVIDUAL TRAVELCOST METHOD OF EVALUATING FOREST RECREATION 35 Leaving aside the familiar discussion of the issues concerned with the choice of functional form until the next section, it is sufficient to say that, after comparing several models (see Table l), the semi-log (dependent) form was chosen; the results for the travel-cost coefficients are presented in Table 2 (all of the travel-cost coefficients are significant at the 5 per cent level). Integrating over the semi-log equations produced a set of consumer-surplus estimates ranging from f 1.43 per visitor at the New Forest to f2.60 at Brecon (see Table 3, Column 2).
Table 2 Clawson-Knetsch Zonal Travel-Cost Method Regression Coerticients (Semi-bg (Dependent) Form)
% Households % Householh in Travel with a Social Classes
Forest Constant Cost Car I & 2 R2
Brecon -9.9515 -0.3837 4.5087 0.8033
( 1.6266) (0.0392) (2.4549)
Buchan -4.2843 -0.4442 0.8033
(0.6820) (0.0634)
Cheshire -9.8929 -0.5252 4.4685 0.9908
Lome -4.9182 -0.6937 6.0074 0.9505
New Forest -6.9496 -0.7021 11.5027 0.9657
(1.0529) (0.0 189) ( 1.4985) (2.078 1) (0.057) (2.8288)
(1.1438) (0.0408) (3.9138)
Ruthin -6.5265 -0.3963 0.9040
(0.3363) (0.0333) Standard error in parentheses
All results significant at 5% level N=21 in allcases
Table 3 Consumer-Surplus Estimates and Distance-Cost Coefncients for Forest Recreation from Semi-Loe (DeDendent) Form of the Clawson-Knetsch Zonal Travel-Cost Model
4. Travel- 5. Consumer Cost Sur lusper 2. Consumer 3. Travel- Coefficient $kitor
1. Travel- Sur lusper Cost With all Other (Price= 6. A n n u l Forest Cost &itor Jackknife Variables Petrol Cost) Number of District Coefficient (f) Coefficient Excluded (4 Visitors
Brecon -0.3837 2.60 -0.3973 -0.3519 0.81 150,000
Buchan -0.4442 2.26 -0.4905 - 0.71 121,500
Cheshire 4.5252 1.91 -0.4886 4.5386 0.51 224,229
Lome -0.6937 1.44 -0.7452 -0.7308 0.42 385 ,000
New Forest -0.7021 1.43 -0.7082 -0.7072 0.44 8,000,000
Ruthin -0.3963 2.52 -0.4040 - 0.77 90,000
There remains the question of the stability and robustness of the estimates.
Two main methods were used to examine these. First, Column 3 of Table 3 reports the results of a jackknife regression, where for each observation the onginal regression equation is compared to the e uation generated when that observation is omitted (Mosteller and Tukey, 197%. In almost all cases there is an extremely close corres ondence between the ordinary-least-squares (OLS) coefficients and the jack
E
nife coefficients. Divergencies in estimates occur:first, where there were few visitors (e.g. Buchan), so that, for some zones no
36 K. G . WILLIS AND G . D. GARROD
visitors were recorded in the sample; and second, where most visitors to a forest came from relatively nearby (e.g. Cheshire), so that the more distant zones again recorded zero visits. All of the jackknife regression travel-cost coefficients were significant at the 5 % level, suggesting that this coefficient is extremely stable and that omitting one observation will not greatly affect the results. Second, the problem of mis-specification was investigated by examining how the value of consumer surplus changed when all variables apart from travel cost were omitted from the model (see Column 4 of Table 3).
Exclusion of all such variables causes on average an acceptable 10% variation in the value of the consumer surplus.
It has been suggested that a travel-cost valuation of a site may be subject to bias if substitute sites are not included in the analysis, and various approaches have been devised to deal with this problem (Knetsch, 1963; Burt and Brewer, 1971; Cicchetti et al., 1976; Seller et al., 1985). Rosenthal (1987) argued that omitting substitute prices from a ZTCM model caused significant bias in consumer-surplus estimates: including substitutes more than halved consumer surplus per person per trip from $7.10 to $2.81 over his eleven cases. In the 1988 survey of forest visitors, respondents were asked about substitute forest sites and also about other substitute recreation sites; but a majority either failed to answer these questions or found it extremely difficult to res ond. The res onses, by performing an OLS regression with the respondents’ ex ressed was regressed against several other variables, including a 0-1 variable which recorded whether individuals specified a substitute forest which they would visit instead of the named forest. The results (Table 4) suggest that the length of a forest visit positively, and significantly, influences WTP; and that if visitors believe that a substitute site is available, their WTP is reduced. The presence of a substitute non-forest recreation site does not appear to be significant.
substitute site question was explored in more detail on the basis o
P
individual wil,P
’ngness-to-pay to visit the forest site used as the dependent variabP
e. ThisTable 4 The Effect of Including Substitute Sites on ResDondents’ Willingness-to-Pay Dependent variable = willingness-to-pay per capita as an entrance charge
OLS Regression
R2 = 0.0880
Independent Variables Estimate Standard Error t-ratio
Site visit length 0.05556 0.01864 2.9802
Other substitute 0.19122 0.11820 1.6177
Jackknife Regression RZ = 0.0875
IndeDendent Variables Estimnte Srandard Error t-ratio
Substitute forest 4.17612 0.08367 -2.1050
_. ~
Site visit length 0.05 86 1 0.06179 0.9485
Substitute forest -0.18476 0.17853 -1.0348
Other substitute 0.2oooo 0.14367 1.3924
3. The Individual Travel-Cost Method
The individual observations which comprise the data for the ZTCM model can be used to estimate the consumer surplus that individuals derive from the recreational benefits of each forest. The ZTCM uses a zonal average for costs, assuming that the cost per individual per trip is the same for all individuals from
AN INDIVIDUAL TRAVEL-COST METHOD OF EVALUATING FOREST RECREATION 37 a given zone, whereas the ITCM allows travel cost to vary across all individuals.
The choice of zonal or individual data has been discussed by Brown and Nawas (1973), Brown etaf. (1983), and McConnell(l985). The general model is:
where V,, = number of visits made per year by individual i to forest j C,, = travel cost faced by individual i to visit forest j (f)
MI = 0-1 variable: whether individual i is a member of an outdoor or environmental organisation
F, = 0-1 variable: whether an alternative forest was named by individual i
GI = 0-1 variable: whether an alternative non-forest recreation site was named by individual i
N, = size of individual i’s party
PI, = 0-1 variable: whether the visit to forest j was the sole purpose of the trip by individual i
El, = individual i’s estimate of the proportion of the day’s enjoyment which was contributed by the visit to forest j
L,, = number of hours spent by individual i in forest j A, = age of individual i
Y, = income index for individual i el, = errorterm
Since it was reasonable to assume that the time spent travelling to and from a forest had some opportunity cost, either in terms of wages or some alternative leisure activity foregone, it was decided that time costs should be included in the travel cost. Thus, travel cost was estimated as the sum of full car running costs (95% of visits were made by car) plus time costs. In an appraisal of the value of non-working time, the Department of Transport (1987) advocated a (standard average) value of 43% of earnings, and this ‘official’ value was adopted as the cost of travel time. Full car running costs (cost of petrol plus standing charges such as: insurance; depreciation; road tax; and service costs) were derived from Royal Automobile Club estimates, based on 1300-16OOcc engine sizes with petrol at f 1.65 per gallon. These costs were adopted on the basis that they are the real costs that road users face. The validity of this position was confirmed in the forest surveys when respondents were asked to estimate what their trip to the site had cost per mile. This produced an average estimate three times as great as the petrol cost of travel and only slightly lower than full running-cost estimates.
The variable M, stood as a proxy for preference for outdoor recreation, and the variables F, and
GI
were introduced to show whether the respondent had specified some local recreational alternative (be it another forest (F,) or some other facility (G,)). The variable N, was used as a proxy for the non-financial organisation costs involved in the visit, and two further variables, P,, and El,, were specified because the forest visit may have formed part of a larger itinerary, including travelling and other visits en route.38 K. G. WlLLlS AND G. D. GARROD
The next step was to fit an OLS regression model to the above data. Of the five functional forms investigated, previous research (e.g. Strong, 1983) has shown that models based on two forms, the quadratic and semi-log (independent), often suffer from heteroskedastic disturbances, making them unsuitable candidates for
OLS
regression. A Breusch-Pagan test confirmed the presence of heteroskedasticity in the data, so these models were rejected. The double-log and semi-log (dependent) forms avoid the problems associated with heteroskedasticity, but were still unsuitable. The double-log form was rejected because it implies infinite visits per individual at zero cost and generates infinite consumer surplus whenever demand is inelastic, whereas the semi-log (dependent) form, though implying finite visits at zero cost, was abandoned after providing estimates of consumer surplus which were far higher than those yielded by other travel-cost studies at UK forest sites (e.g. Hanley, 1989; Willis and Benson, 1989). Although the linear form of the model has theoretical defects (Christensen and Price, 1982), it was more suitable for the estimation of consumer surplus than the other functional forms investigated, and was used to estimate the regression parameters.Rearranging the resulting linear e uations, and then integrating, gave a set of consumer-surplus estimates for in
3
ividual visitors to each of the SIX forests.These figures, shown in Table 5 , ranged from €0.40 per visitor at Cheshire to f2.32 per visitor in the New Forest. Values were greatly reduced when petrol costs only were considered (see Table 6).
Table 5 Individual Travel-Cost Method Estimates, Based on Full Running Costs Truncated-Maximum
0 LS Likelihood
Consumer Consumer
Travel-Cost Surplus Travel-Cost Surplus
Forest Coefficient (4 Coefficient (4
Brecon -0.358 1.40 -0.757 0.66
Buchan -0.996 0.50 -2.515 0.20
Cheshire -1.259 0.40 -8.408 0.06
Lome -0.327 1.53 -0.522 0.96
New Forest -0.215 2.32 -4.280 0.12
Ruthin -0.386 1.29 -0.566 0.88
Table 6 Individual Travel-Cost Method Estimates, Based on Petrol Costs
Truncated-Maximum
0 LS Likelihood
Consumer Consumer
Petrol-Cost Surplus Petrol-Cost Surplus
Forest Coefficient (4 Coefficient (4
Brecon -1.973 0.26 -3.484 0.14
Buchan -5.530 0.09 -13.390 0.04
Cheshire -6.480 0.08 44.966 0.01
Lome -2.767 0.18 -3.822 0.13
New Forest -1.082 0.46 -15.800 0.03
Ruthin -1.658 0.30 -2.166 0.23
4. The Truncated-Maximum Likelihood Method
Several authors (e.g. Balkan and Kahn, 1988) have stated that it is inappropriate to use the method of OLS to estimate the regression parameters of survey-based recreation models. Their studies have shown that the estimates
AN INDIVIDUAL TRAVEL-COST METHOD OF EVALUATING FOREST RECREATION 39 described above are likely to be over-estimates of the true magnitude of consumer surplus. This is a consequence of the truncation bias associated with data collection, which arises because the demand model is estimated on the basis of surveys conducted at each of the recreation sites. Although such surveys are commonly used in recreation demand studies, they provide no information on individuals who choose not to use a site. OLS neglects the truncation bias, and in order to overcome it a maximum-likelihood estimator was employed to estimate the regression coefficients.
The model for forest recreation is:
where: i indexes individuals; j indexes forests; Xji is a vector of independent
variables with coefficient vector
p.,
such that Xji =(Cji,M,,Fi,Gi,Ni,Pji,Lji,Ai,Yi)
and eji are disturbances assumed to be independent, identically distributed N(0,az). Given this model, the maximum-likelihood estimator is based on the density function of Vji which is truncated normal:
( l/a)O[(vji-pjXji)/u] if Vji>O
(1 - @[-pjXji/a]) (4)
0 otherwise
f(V,J =
where 0 ( , ) and @(.) are respectively the density function and the distribution function for the standard normal distribution.
Newton’s method was employed to com ute maximum-likelihood estimates, and new values of the travel-cost coe
8
icient for each forest were derived. These are shown in Table 5, along with the associated values for the consumer-surplus estimates which range from f0.96 per visit at Lorne to just f0.06 per visit at Cheshire. Estimates based on petrol costs are shown in Table 6.It may be argued that the true functional relationship between individual visits and travel cost is non-linear, and perhaps convex. If, in practice, a convex functional form provides a better approximation of the data, the estimates in Table 5 could be shown to be the lower bounds of actual consumer surplus per visitor. Figure 1 shows that the linear specification implies an under-estimate of consumer su lus for those visitors who make only one trip to a forest. In addition, for
1:
t ose individuals who visit a forest more than once, the estimated consumer surplus of a single visit clearly under-estimates their total consumer surplus. Thus, in this case, the use of single visit estimates to approximate total consumer surplus per visitor, regardless of the number of visits made, ensures that the linear functional form always gives lower-bound estimates.The estimates derived from the TML model provided consumer-surplus estimates which are lower than those obtained by
OLS,
suggesting that in this case the OLS regression coefficients are biased towards zero, resulting in over- estimates of the consumer surplus. Consequently, the ITCM consumer-surplus estimates derived using the TML method were preferred. These results compare favourably with those from similar studies such as Smith and Desvousges’ (1985) examination of visitor demand for water-quality benefits.40 K. G. WILLIS AND G. D. GARROD Figure I Consumer Surplus and Frequency of Visits
msed true visit rate (Vji)
Travel cost per visit
(Cji)
1 -
1 - -
Estimate of consumer surplusFrequency of visits per period (Vji)
5. Discussion and Conclusions
The travel-cost approach is an attractive methodology for valuing recreational benefits because it is based on observed behaviour and not, as in expressed preference studies, on how recreationalists say they would behave. However, from the empirical results in this study, it is apparent that differences between the ZTCM and ITCM consumer-surplus estimates exist.
In order to obtain some empirical evidence as to which of the above estimates was closest to the actual consumer su lus, the results were compared with the answers to a contingent valuation (
! i
V) question, which was included in the survey in order to elicit an entry charge for access to the forests.The estimates derived from the CV question are included in Table 7, along with the comparable results for both the ZTCM and the ITCM. The question was framed as an equivalence measure, by first assuming that the individual was entitled to some alternative level of utrlit
,
or alternatively to a set of propert rights different from those currently he1dy
; and then by determining how muc that individual would pay to ac uire the current set. In theory, this measure of benefit should be less than thekarshallian consumer surplus estimated using both the ZTCM and the ITCM. However, while the CV estimates are always much lower than the ZTCM estimates, they are sometimes higher than the ITCM estimates. Even so, the ITCM estimates are always much nearer to the CV estimates than those derived using the ZTCM, suggesting that, in this case, the ITCM provides the closest travel-cost approximation of the true consumerz
surplus.
A N INDIVIDUAL TRAVEL-COST METHOD OF EVALUATING FOREST RECREATION 41
Table 7 A Comparison of Some Benefit Estimates for Informal Forest Recreation
Consumer Surplus Consumer Sur lus Willingness- To- Based on ZTCM Based on ITEM pay
( O W ( T M U (CV)
(4
(f) (4Brecon 2.60 0.66 0.46
Buchan 2.26 0.20 0.57
Cheshire 1.91 0.06 0.47
Lome 1.44 0.96 0.72
New Forest 1.43 0.12 0.43
Ruthin 2.52 0.88 0.44
(per person pervisit, 1988prices)
These results raise questions concerning the recreational-use benefit of the Forestry Commission estate, and about the extent to which these positive external effects add to the internal rate of return on timber production. The ZTCM consumer-surplus estimates im ly a recreational value of f53.0 million per annum (Benson and Willis, 19907 for the whole Forestry Commission estate. A presumption towards consumer surplus based on the ITCM greatly reduces this figure. Each of the six forests used in this study represents one particular group of forests sharing similar characteristics in terms of tree variety, maturity and recreational use (Willis, 1990). Multiplying the ITCM consumer surplus per visit for each forest by the total number of visits made to all forests in the group it represents, gives an aggre ate consumer-surplus estimate of f3.354 million. This compares with the ZT8M estimate of f20.515 million for the six groups (Willis, 1990). Thus the ITCM produces an aggre ate Extrapolating this result over the whole Forestry Commission estate suggests a total consumer surplus of f8.665 million per annum, which is close to the figure o f f 10 million hypothesised by the National Audit Office (1986).
estimate equivalent to only 16.35% of that suggested by the ZT
8
M.Acknowledgement
Financial support from the Economic and Social Research Council under their Countryside Chan e Programme, which funds the Countryside Change Unit at Newcastle University, is grateally acknowledged. The views expressed in this paper are those of the authors alone.
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