The Travel Cost Demand Model as an Environmental Policy

The Travel Cost Demand Model as anEnvironmental Policy AssessmentTool: A Review of Literature

Frank A. Ward and John B. Loomis

Estimates of the benefits of environmental improvement, usually a nonmarketcommodity, can be a valuable part of the information base for economically efficientenvironmental decision making. The objective of this paper is to review the literatureof one class of nonmarket valuation methodologies based on observed consumptionbehavior subsumed under the term "travel cost demand models." Relative to travelcost demand models, we examine policy issues and underlying concepts focusing onchoice theory and welfare evaluation. In addition, we identify major related empiricalissues including demand specification, data problems, demand estimation, and welfaremeasurement. Unanswered questions may contribute to a research agenda.

Key words: environmental policy, recreation benefits, travel cost model.

The continued demand for environmentalquality as manifested by outdoor recreationparticipation coupled with reductions in fund-ing for resource management increases the im-portance of obtaining defensible measures ofrelative economic value by public resourcemanagers. To allocate resources efficiently inthe economic sense, managers require infor-mation on relative values and costs of recre-ational outputs and resource inputs, respec-tively. Outdoor recreation resources values arenot directly observable in the marketplace.

Some economists (Freeman; Smith 1984;Feenberg and Mills) prefer the resource val-uation methodology used for nonmarket goodsbe based on observed consumption behavior.One such class of nonmarket valuation meth-

Frank A. Ward is an associate professor, Department of Agricul-tural Economics and Agricultural Business, New Mexico StateUniversity, Las Cruces; John B. Loomis is an assistant professor,Division of Environmental Studies and Department of Agricul-tural Economics, University of California, Davis. New MexicoState University Agricultural Experiment Station Journal ArticleNo. 1286.

This paper draws on the exchange of ideas among participantsin the W- 33 State Agricultural Experiment Station Regional Proj-ect, "Outdoor Recreation and the Public Interest." Any omissionsand errors are the sole responsibility of the authors.

The authors wish to thank the former editors, Richard Johnstonand Darrell Hueth, for their encouragement and direction in de-veloping this paper. They also extend thanks to two anonymousreviewers whose suggestions improved the manuscript.

odologies has been subsumed under the gen-eral term travel cost demand models (TCM),in which a recreationist is viewed as choosingone or more sites, site qualities, and site visitrates based in part on relative travel costs fromhome to each site.

Federal agency planning standards continueto assign importance to economic efficiency asa natural resources policy objective. With thepublication of the U.S. Water ResourcesCouncil's "Economic and EnvironmentalPrinciples and Guidelines for Water and LandRelated Resources" (1983), economic efficien-cy became the sole objective. TCM is one oftwo officially sanctioned approaches (the otherbeing contingent valuation methods, reviewedin Schulze, d'Arge, and Brookshire; and inCummings, Brookshire, and Schulze) for mea-suring efficiency benefits for federally financedoutdoor recreation investments. Thus, agencyeconomists, planners, and researchers whoneed to keep up with the recreation demandtechnology may wish access to the fundamen-tal concepts, procedures, and terminology as-sociated with the rapidly proliferating TCMliterature.

The objective of this paper is to review theliterature on the travel cost methodology. Tomeet that objective, the paper is divided intofive parts, including this section. In the second

Western Journal of Agricultural Economics, 11(2): 164-178Copyright 1986 Western Agricultural Economics Association

Travel Cost Literature Review 165

section, we identify a range of policy issueswhich have been or could be addressed throughuse of TCM models. Third, we examine con-cepts which underlie TCM models with a focuson choice theory and welfare measurement.Fourth, we examine some major empirical is-sues which have been confronted by TCM re-searchers, with a special focus on demandspecification, data problems, demand esti-mation, and welfare measurement. Finally,conclusions are presented. Throughout the pa-per it is hoped that unanswered questions willcontribute to a research agenda.

We do not pretend to quote and summarizeall contributions of the last fifteen years. Forexample, we leave largely untouched impor-tant recent developments in "household pro-duction models" (Bockstael and McConnell1981) and "hedonic travel cost models" (Men-delsohn and Brown). Furthermore, the scopeof our review is limited to conceptual andmethodological developments with less em-phasis on measured recreational values per se(Sorg and Loomis).

Policy Issues

Management Choices

There are a variety of resource managementissues for which TCM has been applied. Threesuch classes of policy issues have emerged. Firstis the existing value of recreation from theavailability of a particular single recreation site.This value is often needed to identify the rec-reation benefits lost if project X or land usepolicy Y is adopted (Clawson and Knetsch).Second is the benefit (benefit foregone) if asingle site's environmental quality is improved(reduced). With the reduction of federal andstate resource management budgets, this sec-ond policy issue is likely to be more importantthan in the past, which commonly saw theopening up of entirely new sites (Mendelsohnand Brown; Vaughan and Russell). Third isthe benefit gained (lost) from a wide range ofpricing or environmental quality policies di-rected at systems of multiple sites. This lastclass probably has always been the most im-portant to policy makers, but because of thehigh costs of data gathering and analysis, it hasreceived the least attention from TCM prac-titioners (Burt and Brewer; Cicchetti, Fisher,and Smith).

Economic Criteria for EnvironmentalManagement

In examining the TCM literature, one mightcome to the conclusion that the major eco-nomic criterion used by government agencydecision makers when evaluating recreation siteimprovement is that which is measured by theTCM, namely the direct on-site recreationbenefit which accrues to the site user. Not so.Even if one accepts the value judgment thatthe relevant objective function is national (orregional) economic efficiency, four compo-nents could be included in that efficiency: (a)direct on-site recreationist benefit, (b) benefitsaccruing to off-site users such as option or ex-istence values, (c) revenues accruing to themanaging agency from entrance fees, and (d)the net gain in regional income derived fromon-site visitor expenditure. Although this pa-per will follow traditional TCM lines by fo-cusing exclusively on the first component; infact, a state agency may care very little aboutany of the first three but have great interest inthe last, particularly where a recreation sitecontributes materially to a region's export base.

Concepts: Choice Theory andWelfare Measurement

The earliest conceptual basis of the TCM isfound in Hotelling (1949). It was later refinedby Clawson; Clawson and Knetsch, and manyothers. These authors point out that, while alack of (variation in) site fees precludes directestimation of a demand schedule for a site, thetypically large variation in travel costs acrossvisitors to a site does permit one to trace outa demand schedule if consumers would reactto higher entrance fees the same way they doto higher travel cost (Dwyer, Kelly, and Bowes).

Following Bishop and Heberlein, we takethe focal point of analysis to be the recreationparticipation rate (r) of the ith consumer (i =1, .. , n) at thejth site (i = 1, ... , m), sym-bolized by ri, measured as recreational tripsper year. For any given jth site, visits to alter-native sites are taken to be imperfect substi-tutes.

Demand functions for ordinary priced goodscan be derived from neoclassical utility theory(e.g., Henderson and Quandt). Similarly, a de-mand function for each site in a system of"m"multiple recreation sites can be identified. De-

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Western Journal of Agricultural Economics

fine minimum dollar cost per trip (includingonly expenses which would be avoided with-out the trip) as di, and total time required fora trip to site j as ti. Assume that all trips tothe jth site are for the sole purpose of visitingthat site. Let yik be the quantity of the kthnonrecreation-related good consumed by theith consumer, priced at pi, typically assumedequal across all consumers. Furthermore, letwi be the hourly wage rate and Ti work timefor the ith consumer if all available time werespent working. The product wiTi measures whatBecker has termed full income. This may bespent either for recreation, the prices of whichinclude both money costs and income foregoneor for other nonrecreational goods and ser-vices.

Given these definitions, the ith consumer'sbudget constraint can be defined as

(1) Y= pyY + rr,

where

Y= wT,rj = dj + wtj, and

where the i index is suppressed here andthroughout the remainder of the paper unlessotherwise noted; bars over a symbol indicatea vector, while symbols without bars are sca-lars; Y is full income, and prj is total moneyplus time equivalent cost per trip to the jthsite for the ith consumer. Thus, Pr, the siteprices, are treated in the same manner as or-dinary prices in the ith consumer's decisionmaking. Typically, Prj will be different for dif-ferent consumers, since travel distances (mon-ey plus time costs) and opportunity costs oftime will vary by individual.

Suppose for each jth site, a measurable en-vironmental quality index, qj, constant overindividuals can be assigned. Assume a utilityfunction for the ith representative recreationistof the following form:

(2) U = U(y, ,),

where utility depends on the consumption ofthe y goods, site participation rates, and sitequalities, respectively. Maximizing utility (2)subject to the budget constraint (1) leads to aset of ordinary demand functions for both they goods and r. For the jth site, the ith consum-er's ordinary demand is

(3) ri = ri(py, Pr Y, q).

An alternative formulation of the empirical

valuation problem starts with the objective ofminimizing expenditures in (1) subject to autility constraint. Specifically, the minimumexpenditure for the ith consumer to reach util-ity (U°) associated with the status quo siteprices, environmental quality levels, and in-come is

(4) E(py, P q, U°) = min py + Pr,subject to U - U°,

where nonrecreational related goods prices areassumed fixed.

In addition to yielding the expenditure func-tion defined by (2), the solution to (4) yields aHicksian compensated demand function foreach jth site. For the ith consumer, each jthsite's compensated demand function equals thepartial derivative of the consumer's expendi-ture function with respect to that site's price,i.e.,

(5) r*j p, Pr' q, U°) = dE(.)aPrj,

where r* indicates the ith consumer's com-pensated demand function for the jth site.

Given the efficiency objective of greatesteconomic value of watershed-related manage-ment decisions, two questions of majr po-icysignificance arise. First is the consumersurmpluslost (gained) when one or more of thie jsitesare closed (made available for use). Second isthe consumer surplus lost (gained) when a siteundergoes a change in environmental qguaity.Both will be discussed.

Regarding site closure, observe that closinga site is a special case of site pricing. Definethat vector of closed sites as CL. The CL vec-tor could include any combination of elementsin the j index from the empty vector (no sitesclosed) to all elements in the j index (all sitesclosed).

The consumer surplus is an approximationto the two exact welfare change measures,compensating variation (CV) and equivalentvariation (EV). For a given vector of initialsite environmental qualities qo the ith consum-er's CV measure of benefits lost (gained) whenthe CL vector of sites is closed (made availablefor use) is defined in terms of the expenditurefunction as

(6) CVi = E(P, y° , U° ) - E(py° , Pr°, ° q° U°)

where os (Is) indicate initial (terminal) values.This CVis exactly equal to the areas to the leftof the individual's (compensated) demandfunction and above the current site price

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summed across all sites. Here, CVi can be in-terpreted as the compensation that would berequired to keep the ith consumer at utilitylevel UO, given closure of all sites in the CLvector.

Aggregate CV across all existing site de-manders is given by

(7) cv= I Cv i .i

As to the second policy issue, valuing qualitychange, the expenditure function is again thestarting place. Following Freeman, the partialderivative of (4) with respect to the jth sitequality qj gives the Hicksian-compensated in-verse demand function, a marginal willing-ness-to-pay function for qj,

(8) wq* = -dE(.)/aqj= E,(py, pr, t, U°).

The compensating variation to the ith con-sumer for a nonmarginal change in the vectorof all site quality indices is

(9) CV, = E(py, Pr, q UO) - E(py, Pr, q, U°)

where for anyjth site not undergoing a qualitychange, qj = qj.

Aggregating these quality-dependent bene-fits across all consumers is found by summing(9) over the i index.

Since the TCM typically uses observationson price and quantity, the demand curve de-rived is an ordinary, or Marshallian, demandcurve. When one integrates under this curvebetween any two prices, the result is the Mar-shallian consumer surplus rather than the de-sired Hicksian CV or EV. Under conditionsdescribed by Willig the differences between theMarshallian and exact welfare measures, suchas in (6) may be small. For large price changesand/or when the income elasticity of the rec-reation site is large, formulas provided byHausman may in principle be applied to or-dinary demand curves to estimate the exactwelfare measures.

The assumption that the individual faces aconstant and exogenously determined price pertrip to the site is often quite reasonable andhas been an implicit assumption of most em-pirical TCM studies. Brown et al., Ward (1984),and others have shown that a portion of travelcosts (and travel time) could be a choice vari-able for the recreationist. That is, some of thedivergence between reported travel cost andminimum travel cost related solely to distance

such as described by Brown et al. may be at-tributable to differences in household charac-teristics such as income, recreational tastes,and family size.

Another major assumption made in theabove choice-theoretic framework is that thequality of the recreation experience (e.g., sitequality) must be taken as given by the recre-ationist. This is plausible in several recreation-al settings. Having a better kayak does not im-prove the river for rafting, which is determinedby nature or government agency release pat-terns. However, in some cases the householdcan significantly influence its own site quality,within limits. It can improve its chances toharvest fish or game animals by buying betterscopes or hiring a guide to compensate partlyfor below-optimum provision of game animalsor habitat by public agencies.

The upshot of this discussion is that mea-surement of recreation benefits under condi-tions of exogenous quality and constant mar-ginal costs of ,tra vel. can r ut sinTCM,. Ifeither of the.e.se it.ins.otho.ld,the analyst may wish to employ a more generalapproach, such as the household .produ.. tio.(HP) method (Bockstael and McConnell 1981).

Empirical Issues

Thissecton examines several empiricl issuesrelatead to TCM studies iencluing (a) demandfunction specification, (b) data problems, (c)demand estimation, and (d) benefit measure-ment.

Demand Function Specification

Econometric and theoretical questions relatingto the proper specification of demand equa-tions are not unique to TCM studies. Excellentreviews are found in Deaton and Muellbauer;Johnson, Hassan, and Green; and Barton forgeneral commodity systems. For TCM studiesin particular three issues to be discuseddefinition/measurement of critical v ,ariabletheole of ubstituteb s n nci lfsp.cified e utins.

Defintion/m ri-ables. Much attention in TCM studies has fo-cused on definition/measurement of two crit-ical variables: (a) quantity and (b) price.Quantity, or some measure of use, such as rjin (3) is the dependent variable. Price acts both

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as a policy variable (by simulating fees and/orclosure) and a basis for measuring benefits.

(a) Quantity. Empirically measuring thequantity or use rate variable, rj in (3), is notas straightforward as it may seem. In fact, sev-eral measures of quantity consumed have beenused in TCM studies. Two include visitor tripsand visitor days. McConnell (1975) suggeststhat the utility maximization process impliedin the TCM requires each round trip to reflectone unit of consumption. Alternatively stated,the most defensible price measure is not priceper visitor day but rather price per visitor trip.To the extent that a wide array of travel andon-site days can be associated with one trip,costs can be most meaningfully parcelled outon a trip basis.

Aside from the trip/day controversy, evenif one agrees that the trip is the fundamentalindividual decision unit, the correct statisticalspecification of quantity is not obvious. Threeapproaches to specifying quantity that havebeen employed in TCM studies will be dis-cussed: zonal methods, individual methods,and hybrids.

An approach which has become known asthe zonal or aggregate method was employedby Clawson and Clawson and Knetsch. Thezonal name has been coined because recrea-tionists living at similar distances from a siteare grouped into zones (e.g., one or more con-tiguous counties). To adjust for differences inpopulation sizes of the zones or counties aroundthe site, visits are divided by population yield-ing visits per capita. This adjustment providesone way to account for the effect of populationdensity on observed participation at a site. Theassumption associated with this zonal group-ing is that tastes and preferences should besimilar, on average, across all the distancezones.

An advantage of the zonal method is thatwhen dividing by population, the reduced rateof participation at higher travel costs is auto-matically accounted for. Specifically, observedvisits per capita is a product of two separateindividual decisions, namely the decision toparticipate (observed as a probability of par-ticipation) and the number of on-site visitstaken by participants. While using visits percapita as the dependent variable accounts forboth of these effects, it does so by estimatingonly one coefficient for each explanatory vari-able (price, income, etc.) to account for bothdecision processes. Recently, maximum like-

lihood techniques, such as probit, tobit, andlogit techniques, have been developed to mod-el these two decisions independently (Mc-Connell and Bockstael). There is still consid-erable uncertainty about the outcome of thesedevelopments.

One statistical problem often associated withany sort of per capita specification occurs whenthe units of aggregation (zones) have radicallydifferent sizes of aggregation. In the TCM,zones of origin can have populations rangingfrom a few thousand to several million. Thiscan introduce non-constant error variance(heteroscedasticity) into estimated demandcurves. Suggested corrections range from spec-ifying population as an independent variable(Knetsch, Brown, and Hansen), weighting ob-servations by square root of population (Bowesand Loomis), to selection of functional formto minimize the effect of heteroscedasticity(Vaughn, Russell, and Hazilla; Strong).

Two limitations of the zonal TCM relatesto loss of information efficiency from usinghighly aggregated data and the inability to sep-arate out the influence of travel time from trav-el cost. In the first case, by aggregating infor-mation on income, price of substitutes, tastes,and preferences, much useful information thatwould serve as demand shifters is often lost.As Brown and Nawas point out, estimates ofthe travel cost coefficient from zonal modelsare often statistically inefficient and thereforereduce precision on the crucial price variablerelative to use of disaggregated data.

As will be discussed in more detail, it isimportant to account for the influence of traveltime in estimating the effects of price on use.In the zonal TCM this is difficult to do becauseaggregating recreationists by similar distancestends to create a high correlation (i.e., multi-collinearity) between travel cost and traveltime.

The individual observation TCM approachwas developed in the early 1970s, partly inresponse to the above-mentioned multicollin-earity, inability to specify shifter variables, andloss of precision in estimators. Brown and Na-was, and Gum and Martin developed an in-dividual observations TCM in which quantityconsumed is defined as the number of tripstaken per year or season by each sampled in-dividual or household. This quantity is re-gressed on the individual's or household'sunique travel cost, travel time (or distance),and socioeconomic characteristics. Because no

168 December 1986


aggregation occurs, multicollinearity is re-duced and precision of estimators is increased.

There are two difficulties with the individualobservations approach. First, when a typicalrecreationist only takes one trip a year or isconstrained to one trip a year (as in the caseof hunting unique species), it is often difficultto estimate an individual observation TCMdemand curve because visits per season arealmost all equal to one (Freeman, p. 203). Thesecond difficulty is that probability of partic-ipation as a function of distance is ignored.The individual observation approach is amodel of the current participant's demand fortrips but will underestimate how aggregate vis-itation would increase if a closer similar sitewere added because potential recreators havebeen excluded. Brown et al. have shown thatwhen the proportion of nonparticipants in-creases with distance from the site, the indi-vidual observation TCM can overstate theconsumer surplus estimates.

More recently, hybrid approaches have beenemployed to combine the best features of zonaland individual observations. Brown et al. de-veloped a method for defining quantity whichmaintains the individual observations but di-vides each individual's trips by his share ofhis zone's population. Thus, a single observedtrip from a zone of origin of 50,000 populationrepresents twice the effective participation asfrom a zone with 100,000.

Another hybrid approach is to estimate sep-arate functions for probability-of-participa-tion and individual trip rates. In this approach,the consumer is viewed as making the recre-ation decision at a given site in the sequentialstages "will I go at all?" and then "given thatI go, at what rate will I visit?" These two func-tions can then be used jointly to calculate aconsumer surplus as described by Hanemann.One way in which this may be accomplishedis by constructing a multinominal logit in whichone views probability of participation andnumber of trips to take as a nested decisionprocess (Peterson, Anderson, and Lime).

(b Price. Defining the price variable formarket commodities is fairly straightforward.For an individual consumer, price is the draw-down on income from one extra unit boughtin the marketplace. This price is externally im-posed on the consumer's decision processthrough the market forces of supply and de-mand. However, for TCMstudies the properdefinition for price per trip made to the jth

recreation site, prj in (3), is less clear. Followingthe spirit of Bishop and Heberlein, two relatedissues will be discussed: () determination ofwhich monetary expenditures should be in-cluded in estimates of a recreation site's price,and b) measurement of time values.

In evaluating which expenditures to includein per trip travel costs, it should be remem-bered that a major purpose of TCM models isto measure the recreational value (consumersurplus) of one or more recreation sites or pol-icies which change opportunities at those sites,given the absence of actual site pricing policieswhich would permit direct site demand esti-mation. Given that purpose, the travel costvariable should be defined so that site con-sumers respond to variations in travel cost ina similar manner as they would respond tovarying site entry fees. Thus, a criterion fordefining the travel cost variable is its abilityto mimic the effect of site entry fees on visits.The decision of which expenses to include ismade more difficult by the fact that recrea-tionists' behavior depends largely on how theyperceive costs. For example, how well do theyrecognize the costs of wear and tear on equip-ment, such as vehicles and specialized recre-ation equipment? Generally speaking, only thevariable costs of transportation have been usedwhen calculating this component of price.

Incorpprating travel time (as distinct fromout-of-pocket expenses) continues to receivewide attention. Early applications of TCM usedonly round-trip variable monetary transpor-tation cost as the price variable. However,Knetsch; and Cesario and Knetsch (1970) rec-ognized the reason that more distant recrea-tionists visit a site less frequently than recre-ationists living closer is the joint effect oftransportation cost and travel time. The op-portunity cost of scarce time acts as a separatedeterrent at the margin to visiting more distantsites. Failure to account for the separate effectof travel time results in the appearance thatvisitation is quite sensitive to the money pricebecause all of the observed decrease in visita-tion is falsely ascribed to transportation cost(distance). This is a special case of the classicomitted variable, which, given the positivecorrelation between the two costs, causes anestimate of the all-important price coefficientwhich is too price-sensitive. Consumer surplusis understated, relative to alternative uses ofthe resource.

Correction for this source of bias has taken

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several forms. Cesario and Knetsch (1970)propose introducing an explicit money cost tobe imputed to scarce travel time which is thenadded to the transportation cost to arrive atwhat might be called total travel cost. Al-though ingenious, the resulting benefit esti-mates are obviously dependent on the specificvalue of travel time chosen. Since Cesario andKnetsch's suggestion, a great deal of effort hasgone into estimating recreationists' perceivedopportunity cost of travel time (Cesario;McConnell and Strand; Ward 1983a, b; Smith,Desvousges, and McGivney). Currently, manyanalysts rely on the travel time values fromcommuting studies summarized by Cesario anduse a value of one-third to one-half the wagerate as the value of travel time when using thezonal methodology. Attempts to measure ex-plicitly the imputed value of travel time in arecreational setting can be found in McConnelland Strand; and Ward (1983a, b). Both haveobserved the willingness of visitors to trade offtravel cost for travel time, using the result asa shadow price of travel time. Applying thatmethodology to their respective samples, theydemonstrate that one-third the wage rate is aconservative measure of travel time value.

Should one choose to construct a TCM basedon individual data, travel time could be in-cluded as a separate visit predictor. This elim-inates the need to value travel time exoge-nously, as time and money costs as separatevisit determinants would already be isolated.The issue of how one should handle travel time(particularly in zonal TCMs) continues to re-ceive a great deal of attention from TCM re-searchers.

There is continued controversy in the lit-erature about whether the opportunity costs ofon-site time need be included in the price vari-able or otherwise incorporated into the de-mand equation(s). According to McConnell(1975), the opportunity cost of on-site timeshould be included in the price variable, andfailure to do so will bias benefit estimatesdownward. Cesario and Knetsch (1976) feelsuch on-site costs should be excluded. Wil-man; and Knetsch, Brown, and Hansen feelsuch on-site costs should be excluded. Wilmanhas developed a model showing the necessityof including on-site time under certain circum-stances. The framework of Smith, Desvousges,and McGivney is more general but also sug-gests the importance of including on-site time.Recent work by Ward (1984) demonstrates that

on-site time can be an endogenous variableand should not be included as part of priceunless adjustments are made.

As a final thought on the on-site time ques-tion, we might add that while there clearly isan opportunity cost to on-site time, it is pre-cisely this time on site that produces the utilitydesired by the recreationist. Perhaps one wayto account for the role of on-site time in rec-reation decision making is to estimate differentdemand equations for trips a function of lengthof trip (Miller and Hay).

Substitutes and jej a f.idspecication. Eco-nomic theory suggests that price and avail-ability of substitutes is an important deter-minant of demand. If the travel cost to a givensite and the travel cost to a substitute site arepositively correlated, then omission of priceof substitutes as a demand shifter will resultin estimation of a more inelastic demand curvethan the true demand curve (Caulkins, Bishop,and Bouwes). In principle, the solution to thismodel specification problem is to include pricesof all important substitute activities as site de-mand determinants.

Much effort has gone into incorporation ofsubstitutes into TCM demand curves. Burt andBrewer; and Cicchetti, Fisher and Smith spec-ify a system of demand equations. Here, sitesare classified into types and a demand curveis estimated for each type. The price of theown-type and cross-price effects of other sitesare included in each demand equation. A pol-icy which introduces or deletes a site is treatedas a price change to recreationists for consum-ing that type of site.

Often a system of demand equations suffersfrom high multicollinearity between own priceand cross price. If one lives a long way fromone type of recreation site he or she may livea great distance from all types of recreationsites. Knetsch, Brown, and Hansen have ad-dressed this problem and incorporated bothquality of substitutes and price of substitutesby using an index value as a measure of sub-stitutes. In particular, they use the ratio of sitequality of the substitute site (e.g., surface acres,harvest, etc.) divided by distance from the or-igin to the substitute site. If this ratio for agiven origin-substitute site combination isgreater than the ratio for the given origin-studycombination, then the substitute site is said tobe competitive to the study site for that origin.Details of index construction are given inKnetsch, Brown, and Hansen; and Sorg,

170 December 1986


Loomis, and Donnelly. Work continues on de-veloping a better understanding of the natureand extent of substitutes into consumer deci-sion making and the related improved speci-fication of substitutes into TCM demandcurves.

Functojaorm. One of the few systematicattempts to evaluate the effects of functionalforms of the TCM demand curve on consumersurplus is provided by Ziemer, Musser, andHill. Compared with the linear and double log,the semilog of the quantity variable was de-termined to be the most appropriate for theirsample of Georgia anglers. Support from sta-tistical test for the semilog of the quantity termcan be found in both Vaughan, Russell, andHazilla; and Strong. Both of these studies sug-gest that the semilog helps to minimize theheteroscedasticity in zonal models as well.

More work needs to be done in specifyingutility functions which are consistent with rec-reationist decision-making behavior and theresultant ordinary demand functions consis-tent with underlying preferences. Particular at-tention needs to focus on the way in whichown- and cross-site price and quality enterseach site's ordinary demand functions. Cross-price effects would normally be expected to bepositive (sites are substitutes for one another),but there is less a priori expectation on signsof cross-quality effects. Hanemann demon-strates that where site quality is a perfect sub-stitute for quantity in the utility function, in-creases in quality increase welfare but greatersite quality will reduce site demands, e.g., moredeer density at a given site will substitute forsite trips and actually reduce participation.

.Da~ta!Issues

TCM can be performed with a wide variety ofdata sources. However, inattention to the de-tails of data collection can lead to biased es-timates of benefits.

Sampling can be conducted on site, in whichcase the analyst observes only current recrea-tionists (i.e., visits > 0). If the analyst uses thisdata with OLS regression to estimate an in-dividual model without accounting for thetruncated and censored nature ofthe data, mis-specification can result (McConnell and Bock-stael). Using the zonal method of dividing anorigin's visits by origin population reduces thisproblem but at a loss in efficiency of parameterestimates.

If data are collected via a household surveycontaining visitors to the site of interest as wellas current nonvisitors, the sample selection biasencountered above with on-site survey isavoided. However, incorporation of nonvisi-tors in the estimation of an individual obser-vation TCM model poses two problems. Thefirst is difficulty in collecting or determiningprice data from these respondents because theydid not visit any sites. This can be overcomepartly by calculating such distance from a roadmap. The second difficulty relates to econo-metric problems associated with use of ordi-nary least squares (OLS) regression when thedependent variable takes on discrete units in-cluding zero. This has been addressed by useof the tobit approach to estimation (Mc-Connell and Bockstael).

One advantage of TCM in general, and zonalTCM in particular, is that demand schedulescan often be estimated using secondary datasuch as wilderness permits (Smith and Kopp),rafting permits (Bowes and Loomis), and biggame hunting applications (Loomis). TCM canalso take advantage of origin-destination in-formation collected as part of recreation sur-veys designed largely (sometimes exclusively)for other purposes (Desvousges, Smith, andMcGivney; Miller and Hay).

Demand Estin aon

In addition to the above-mentioned sources ofestimation ndifficuiclte.which.plagueall .T CMstudies, three specal demand estimation prob-lems will be discussed: parameter restrictions,too little variation in important variables, andthe congestion issue.

Parameter restrictions. Hanemann demon-strated that most single-site demand modelspecifications with no parameter restrictionswhatsoever can be shown to be consistent withsome underlying utility function. Thus, we dis-cuss parameter restrictions in the context ofmultiple-site models.

Estimating systems of multiple-site de-mands poses special estimation problems.Johnson, Hassan, and Green observe that ademand system with parameter restrictions re-sults in a reduction of the number of coeffi-cients in the system of demand functions, mak-ing joint estimation of the parameters morefeasible. In addition, the resulting demand sys-tems are attractive because they can be spec-ified to satisfy basic restrictions from under-

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lying utility theory. Furthermore, empiricallytestable restrictions on the demand system aredesirable because they allow one to test thehypothesis that the system is consistent withbehavioral theory.

Cicchetti, Fisher, and Smith specified a sys-tem of site demand equations as linear in pricesto facilitate imposing and testing the symmetryrestrictions on cross-price coefficients requiredfor path independence of total consumer sur-plus. Since the restrictions implied by sym-metrical cross-price terms extend across thesystem of site demand equations, impositionof symmetry requires joint estimation. Seem-ingly unrelated regressions (Zellner) were usedwith the symmetry restriction imposed. Theauthors' findings suggested rejection of thesymmetry hypothesis. Two alternatives aregenerally available in such a case: (a) reesti-mate without the restrictions, paying the priceof a resulting path-dependent (not unique)multisite benefit measure; or (b) keep the re-strictions, which may be consistent with econ-omy theory but not with the data. As theoret-ical work advances, we can expect to seeparameter restrictions which can allow testingof a wide range of behavioral hypotheses.

Too little variation in important variables.In the case of single-site models in which sitequality explicitly enters as a determinant, theabove problems are compounded by the dif-ficulty of finding circumstances where sitequality varies enough to permit efficient esti-mation of quality coefficient(s). Most TCMmodels have been constructed with cross-sec-tion data gathered over such a short period oftime that site quality is essentially fixed. Con-sequently, even if one had a testable site de-mand model consistent with utility theory, onecannot statistically isolate the role of changesin actual quality as it affects visits.

Where primary data surveys are involved,one alternative to insufficient actual quality/visit variation typically has been to posit hy-pothetical questions to respondents, such as"how would your current participation rate tothis site change if your hourly fishing catch ratedoubled?" (Ribaudo and Epp). This approachyields the desirable quality/visit variation, butit too suffers. First, it is based on hypotheticalresponses to unobserved and/or unknown con-ditions. Second, for on-site samples taken inrelatively poor site quality conditions, even ifone believes the hypothetical responses, oneexcludes from the sample the population of

prospective site visitors who do not currentlyparticipate because of poor quality.

Two approaches to incorporating both priceand quality variation in site demand functionsmay have promise. The first approach is pool-ing of time-series and cross-section data, longused in agricultural commodity demand anal-ysis. TCM data sets typically have lots of vari-ation in price (due to distance) but not in qual-ity. Conversely, with data sets often availablefrom agency record keeping, one can observetime-series variation in quality (e.g., waterlevels, vegetation, fish populations) and its ef-fect on total participation, but there is nobreakdown on participation by distance zone,i.e., no price variation. The pooling solutionwould combine independent parameter esti-mates from both data sets to estimate the fullyspecified visit equation (3). To our knowledgethere are no published accounts of this meth-od. If this method were used, the researcherwould have to reconcile the individual visitsmeasure in the cross-section data set (per cap-ita for zonal studies) with the aggregate visitsmeasure for the time-series data.

A second approach with promise is poolingobservations of sites, each of which has vary-ing levels of site quality. Instead of estimatingsingle-site models in which site quality doesnot vary, multisite single-equations modelshave been estimated and are sometimes re-ferred to as varying parameter models(Vaughan and Russell). Multisite models in-corporate the influence of quality as both in-tercept and slope shifters (Cesario and Knetsch1976; Vaughan and Russell; Donnelly et al.).Alternatively, Mendelsohn and Brown's he-donic TCM rearranges the entire TCM prob-lem from "many origins to a single site" to "asingle origin selecting among many sites." Theirapproach uses travel cost to estimate willing-ness to pay for characteristics of a site such asscenery and fish harvest in the first stage. Inthe second stage, a demand curve for the char-acteristic is estimated using each origin's priceof a characteristic and quantity of character-istics consumed. The hedonic TCM approachis said to be a compromise between a fullhousehold production approach and the sim-ple TCM (Mendelsohn and Brown).

Coggesti During the late 1960s, crowdingat recreation areas became such a problem thateconomists developed methods to employ theTCM to correctly estimate demand and ben-efits of a recreation site under congestion. Smith

172 December 1986


(1975) discussed the difficulty with respect towilderness areas where the level of congestion,and hence quality recreation experience, var-ied over a season or period of data collection.

McConnell (1980) and Anderson demon-strate how the TCM can be used to constructa congestion "constant" demand curve. Theseauthors observe that it is from this demandcurve that the benefits of the site under currentlevel of congestion are correctly measured.Their argument is that if one wants to find thenet willingness to pay for the current condi-tions, congestion must be held constant at thecurrent level when calculating the area underthe demand curve. To estimate such a conges-tion constant demand curve when congestionvaries over the season or sample period, it willoften be necessary to include a shifter variableto account for these differences in congestion.Alternatively, it may be possible to estimatedemand curves for weekdays, weekends, andholidays if congestion is homogenous withincategories but varies from category to category.The role of income in influencing forecasts ofcongestion-adjusted demand curves is dis-cussed in Stevens and Allen. Congestion is butone of many factors influencing site quality.Other factors include harvest success in fishingor hunting (Mendelsohn and Brown; Donnellyet al. 1985), water quality (Smith, Desvousges,and McGivney), and size of recreation site(Knetsch, Brown, and Hansen), to name a few.

Measuring Benefits

TCM researchers have commonly used theMarshallian consumer surplus as the relevantwelfare measure. This section assumes that amultiple-site model is the focal point of anal-ysis, for which interest is in (a) benefits fromthe existing system, (b) benefits from pricingpolicies, and (c) benefits from site quality pol-icies.

Computing the area under the ordinary de-mand system (3) gives the Marshallian mul-tiple-site consumer surplus for the ith individ-ual. This benefit measure is not unique unlessthe price effects matrix is symmetrical. Onemethod which assures unique benefits mea-sured has been to specify the demands as alinear system in prices and (possibly) qualitiesusing a restricted least squares procedure inwhich cross-price effect parameters are re-stricted to be a symmetric matrix. Use of thelinear system with the stated restrictions on

the price coefficients greatly simplifies thecomputation of the Marshallian surplus, whichwe discuss next.

Benefits from the existing system. Compu-tation of a single site's benefits requires a sim-ple integral of the demand curve. To computesystem benefits, removal of the entire site sys-tem from the opportunity set can be simulatedby raising all site prices to the point at whichthe participation vector is zero. The Marshall-ian benefit to the ith sampling unit (e.g., in-dividual) is computed in the following steps:(a) predict trips, (b) compute reservation prices,and (c) calculate benefits.

Based on the individual's observed trips tothe vector of sites, ro one needs to compute thereservation price vector which would reduceparticipation to zero at all sites. First considerthe linear trip predictor associated with vari-ations in (not absolute levels) prices and qual-ities:

(10) r = P, + Br(r- Pro) + Bq(q- qo)

where "o" subscripts refer to baseline values;Br the estimated square symmetric matrix ofown- and cross-site price effect parameters as-sumed applicable to all individuals, and Bq isan estimated square matrix of own- and cross-site quality effect parameters. Defining visitsby (10) generalizes the single-site benefit com-putation method proposed by Gum and Mar-tin in which observed rather than predictedvisits are used to define demand, i.e., whereeach individual's demand function intersectsthe observed 7o and Pro.

The vector of maximum or reservation pricesinclusive of travel costs, Pr* is found by solving(10) for the Pr which would reduce P to zero.

(11) Pr* = Pro + (-Br)-lFo

where -1 is the matrix inverse operator. Forthe special case of a single site, (11) shows thereservation price to be the sum of existing trav-el cost plus the ratio of observed trips to thenegative of the own-site price coefficient. Someresearchers have found that the computed re-servation price vector defined by (11) is toohigh to be believable. Given this difficulty, onemethod which has been used (Gum and Mar-tin) has been to truncate the site demand func-tion at a "critical" price equal to the maximumobserved travel cost from sampled visitors. Incomputing benefits, as soon as this "critical"price is reached, participation is assumed tofall to zero.

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Based on the maximum price vector (11),Cicchetti, Fisher, and Smith show that theMarshallian consumer surplus for the ith in-dividual due to the existence of all sites atcurrent travel costs for the linear system (10) is

(12) S = .5(r. - Pro)T(Br)(Pr - Pro)Tr

where T is the matrix transpose operator, S isthe summed areas beneath the individual's sitedemand functions.

If the ith sampling unit is defined by zonalaverages, then (10) becomes a per capita vis-itation function with one observation per zoneof origin, (11) the price vector such that percapita participation is zero at all sites, and (12)per capita benefits. The latter term needs to bemultiplied by ith zone population to measureabsolute ith zone benefits due to the system ofsites. Aggregate benefits are found by summingover the zone index.

Note that the reservation prices do not re-flect entry fees per se but are merely a mea-suring device for defining the upper limit ofthe demand function area to be counted asbenefits.

Benefits under site- riciz fr/e. Al-thoughlittle TCM research has been directedat evaluating site-pricing policies, TCMs arewell-suited for that purpose. We discuss (a) thegeneral case of entry fees, and (b) the specialcase of closing down the site(s).

Suppose an agency wishes to estimate theimpact on user benefits and/or agency reve-nues associated with imposing a vector of sitefees, F, not all zero. For the ith individual, theeffect of F is to raise travel costs to a higherlevel, Pr from the current level, Pro, i.e.,

(13) Pr = -+ Pro,

in which F is assumed constant across indi-viduals. This equation can be used to predictindividual visits, r, associated with any givenfee vector, F.

Total use-related benefits can be defined asthe sum of agency revenues received from Fplus remaining unpriced benefits accruing tothe site user. Agency revenues received fromthe ith individual, Ri is the sum of fees chargedper trip times trips consumed, aggregated oversites, i.e.,

(14) Ri= pr,

where trips r are computed from (10) and totalsite price inclusive of fee is defined by (13).

The residual unpriced benefits which re-

main, given the entry fees F, are measured byan equation structurally identical to (12) withtwo changes. First the fee-dependent trip vec-tor is inserted into the position currently oc-cupied by ro in (12). Second, insert Pr inclusiveof fees from (13) into the position occupied byPro in (12). Total benefits under conditions ofa zero entry fee will always exceed total benefitswhen a fee is imposed for uncongested sites.The difference is the well-known "dead-weight" efficiency loss.

Site closure, an important policy issue, is aspecial case of entry fees. Suppose that theagency decides to close the subset of sites, CL.If the closed sites were first, fourth, and sev-enth, the set CL would contain the elements(1, 4, 7). One can simulate closure as raisingprices at CL until all visits in CL equal zero.Denote the open site set as OP.

Simulating closure of the CL sites in a sys-tem of"m" sites requires finding the vector ofreservation prices which would simultaneous-ly reduce visits in CL to the zero vector. Tocompute the (unknown) CL reservation pricesand OP site participation rates requires par-titioning the visit predictor (10) as follows, as-suming q = qo:

(15) [ r(OP) F + Br(OP, OP) Br(OP CL)) O(CL)J ° LBr(CL, OP) Br(CL, CL)]

- Pr Pro(OP)Pr - Pr(CL)]

in which the CL/OP status is in parentheses.The knowns in (15) are the zero trip vector atthe CL sites, 0, the entry fees at the open sites,(Pr - Pro) and the price effects matrix Br, par-titioned into four parts. For example, the (OP,CL) index refers to a submatrix of Br, withrows OP and columns CL.

The object is to solve for the unknowns of(15), i.e., the trip vector at the open sites, P(OP),and the reservation price vector which wouldsimulate closing the CL sites, p,. (CL). Al-though not shown here, the solution involvesmoving all unknown terms to the left side andthen solving for them through standard matrixinversion procedures, similar to (11). Giventhe solution for the OP trip vector and CLreservation price vector an equation structur-ally identical to (12) can be used to computetotal benefits for the system of remaining opensites (not shown). Thus the loss in benefits fromclosing the CL sites equals the full system ben-

174 December 1986


efits minus the benefits from the remaining OPsites.

Benefits rom chaning qualit. Suppose thata system of site demand equations as in (3)has been estimated econometrically and onewishes to sue the information contained in theestimates to measure welfare changes frompolicies which change quality.

To use quality-induced changed areas under(3) to value those quality improvements, onemust invoke the additional assumption of"weak complementarity." This occurs if, whenthe quantity r0 demanded is zero, the marginalutility of qj is zero (Maler). In such cases, whenqj increases, the demand for rj shifts out, andthe exact welfare value of qj' - qj is approx-imated by the integral between rj(, P, Prq , Y)and rj(p, r, q°, Y), to the extent that the in-tegral between Marshallian demand curves ap-proximates the integral between Hicksiancompensated demand curves (Willig). Theweak complementarity condition may applyto a number of situations. For example, themarginal utility of lake level or fish density ata particular waterbody could be assumed to bezero for those people who did not use thewaterbody for recreation (Freeman).

Suppose that one is willing to make the ma-jor assumption that (3) represents a linear ap-proximation to a true system of demand func-tions consistent with utility theory and that sitequality and quantity are "weak complements"as discussed above. The goal is to approximatethe system benefits associated with a new qual-ity vector, q, not equal to original quality, qo.

Using (3), one would follow essentially thesame procedure as was employed for measur-ing benefits under fixed original site qualities.The only difference is that one would begin bydefining the new level of q and then using theestimated Bq matrix in (10) to predict F as-sociated with the new q.

In much the same way as computed for con-stant quality, maximum site prices under avariable quality vector in (10) would be solvedfor as

(16) P.(q) = Pro + (-Br)- 1[r + B,(q- o)]

where (16) is the "variable quality" generali-zation of (11). As shown in (16) increases inquality which increase participation at a siteincrease the maximum price at that site. Notethat (16) requires the price effects matrix B, tobe inverted but not the quality effects matrix,Bq.

Finally, an equation similar to (12) is usedto compute variable-site-quality benefits forthe ith individual. Instead of inserting "exist-ing quality" trips into the benefits measure, FO,as was done in (12), one would use trips aspredicted by (10) in which quality is allowedto vary.

As an alternative to the Marshallian ap-proximation to benefits from varying qualitydescribed above, four steps could be followedto recover the exact quality dependent welfaremeasures described by (9). First, one wouldspecify one or more alternative algebraic formsfor the quality-dependent utility function, eachfunction being defined by both an algebraicstructure and general parameters to be esti-mated. Second, analytically derive the corre-sponding Marshallian demand system (3) andexpenditure function (4) for each utility func-tional form considered. Third, use data onprice, quality, incomes, and other demandshifters to estimate each candidate Marshall-ian demand system (3), picking the one whichbest fits the data. Fourth, based on the esti-mated coefficients for the best fit Marshalliandemand system and the known relationshipsfound in step two, recover the exact welfarechange measure (4) for any price/quality policydesired. This approach has not generally beenfollowed in past TCM studies but offers prom-ise. Barriers to application include specifyingutility functions which yield realistic demandsystems yet which can be estimated with readi-ly available regression packages. Especiallywhere multiple sites are involved, specifying autility function in which all sites' qualities arearguments will likely yield highly nonlinear or-dinary site demands.

Conclusions

The TCM is limited to measun th terecreation benefits royvidd b a naturare-source. The benefits estimated from TCM donot include any opt y e e e(Bishop) nor any existence values (Randall andStoll). For many types of commonly availablerecreation sites, this omission of off-site userbenefits is probably not significant. For des-ignated wilderness areas, wild and scenic rivers,unique wildlife species (e.g., bighorn sheep orwhooping cranes) these off-site benefits maybe equal to or greater than the on-site recre-ation benefits (Walsh, Loomis, and Gillman;

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Brookshire, Eubanks, and Randall; Stoll andJohnson).

In terms of policy issues to which TCMmodels could be applied, we are far behind ourlinear programming colleagues who use theircomputed benefit measures as objective func-tions in which optimal resource allocation de-cisions can be found. There has been far toolittle emphasis on optimization of natural re-source systems based on computed TCM wel-fare measures (Hof and Loomis provide a no-table exception).

Although the acceptability of the TCM isincreasing, several issues remain less than sat-isfactorily resolved. These include valuationof travel time in zonal TCM, treatment of on-site time and incorporation of substitutes andsite quality into TCM demand curves.

Continued research is necessary to developa consensus on issues such as on-site time anddefinition of the dependent visitation variablein TCM. Ultimately, several variations of theTCM likely will be available for estimating asite's demand schedule. Thoughtful matchingof the particular variant of the TCM approachto the management issue to be addressed willalways be necessary.

[Received June 1982; final revisionreceived July 1986.]

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