Download - Perceptions versus Objective Measures of Environmental Quality in Combined Revealed and Stated Preference Models of Environmental Valuation

Ž .JOURNAL OF ENVIRONMENTAL ECONOMICS AND MANAGEMENT 32, 65]84 1997ARTICLE NO. EE960957

Perceptions versus Objective Measures of EnvironmentalQuality in Combined Revealed and Stated Preference

Models of Environmental Valuation*

WIKTOR ADAMOWICZ

Department of Rural Economy, Uni ersity of Alberta, Edmonton, Alberta T6G 2HI, Canada

JOFFRE SWAIT

Department of Marketing, Uni ersity of Florida, Gaines ille, Florida

PETER BOXALL

Northern Forestry Centre, Canadian Forest Ser¨ice, Edmonton, Alberta, Canada

JORDAN LOUVIERE

Department of Marketing, Uni ersity of Sydney, Sydney, Australia

AND

MICHAEL WILLIAMS

Intelligent Marketing Systems, Edmonton, Alberta, Canada

Received December 15, 1994; revised December 18, 1995

This study examines perceptions and objective attribute measures in discrete choicemodels of recreation site choice behavior. These forms of attribute measurement areexamined in individual and combined revealed preferencerstated preference models. Ourresults suggest that the model based on perceptions slightly outperforms the models based onobjective attribute measures. However, issues such as the definition of the choice set and themeasurement of welfare present significant challenges when using perceptions data. Q 1997

Academic Press

INTRODUCTION

Ž . Ž .Interest in combining revealed preference RP and stated preference SP dataw x w xhas risen in transportation 3 and marketing 19, 20 . There are few studies in

environmental economics, however, that have combined these data sources tow xexamine effects of environmental quality change 1, 4, 10 . The advantages of

* The authors thank three anonymous reviewers, the participants of the Fourth Annual Meeting ofthe Canadian Resource and Environmental Economics Study Goup and Forestry and the Environment:Economic Perspectives II for comments on this paper. The research assistance of Kristy McLeod andBonnie McFarlane is also gratefully acknowledged. Funding was provided by the Science and Technol-ogy Opportunities fund of the Canadian Forest Service, the Canada]Alberta Partnership Agreement inForestry, and the NCE program in Sustainable Forest Management.

650095-0696r97 $25.00

Copyright Q 1997 by Academic PressAll rights of reproduction in any form reserved.

ADAMOWICZ ET AL.66

combining RP and SP data include an increase in the amount of informationŽavailable, the possibility of modeling ‘‘new goods’’ or goods with attribute levels

.outside the range of current levels , and reduction in the collinearity offered by thew xSP statistical designs 1 . While these features represent significant advantages in

modeling the effects of environmental quality changes on recreation demands, anumber of important issues remain to be examined. One of the major issues is theuse of objective versus perceptual measures of environmental quality.

In this paper we examine a set of RP, SP, and combined models of recreationalsite choice in a random utility framework. In these models the choices are assumedto be independent and are based on the respective utilities an individual receives

Ž .from sites in a set of available alternatives the choice set . The utility associatedwith alternative i is

U s V q e , 1Ž .i i i

where V is the deterministic component and e is an error component. While mosti i

economic analysis employing this structure relies on the use of objective measuresŽ .of attributes prices, environmental quality, etc. to form V , there are actuallyi

many ways to ‘‘generate’’ the deterministic component. Table I provides anoverview of three possible dimensions that describe data that could generate V .iThe first is the form of attribute data. These include objective measures ofattributes, respondent perceptions of attributes, and descriptions of sites con-structed by combinations of researcher-generated attributes. A second dimension isthe manner in which choice data are generated by the respondent. These include

Ž .choices that an individual reveals in her or his actual behavior RP and responsesto a designed stated preference task. Finally, the RP choices may be based on achoice set defined by the researcher or on a choice set defined by the individual.1, 2

These alternate structures generate five possible models representing choice. Itis also possible to combine the various models. In this paper we focus on a subsetof the possible choice structures and examine the elements of the diagonal inTable I and combinations of these three structures. This provides us with a crosssection of the possible models, and allows us to focus on the issue of using

1 ŽAn important aspect of modeling recreation site choice is the determination of the choice set e.g.,w x.8, 17 . In the case of attributes measured by an agency, the choice set can be defined as all availablesites if attribute data are available for these sites. When using perceptions data, the individuals mayreport that they are unaware of certain sites or they do not have any information on which to base

Žperceptions. These missing perceptions observations could be replaced with some other values e.g.,.means or model responses from other recreationists , or individuals who do not complete the entire set

of questions could be deleted from the analysis. The latter is probably unwise since considerableinformation would be lost; however, this approach is often used in applied analysis. As an alternative,one could adjust the choice set of the individual to reflect the fact that if the individual is not aware ofthe attributes of a site, it is unlikely that the site is part of the individual’s choice set. Note that in SPexperiments, the choice set is based on site descriptions constructed from the set of site attributes andbecomes part of the design of the experiment under researcher control.

2 Note also that RP models are ex post in nature since the model is constructed on trips alreadytaken, whereas SP models are based on ex ante information since the individual is indicating which sitehe or she will choose on the next choice occasion.

COMBINED RP]SP VALUATION MODELS 67

TABLE IData Structures for Examining Choice Behavior

Choice data

Revealed choices Stated choices

Choice set definition Choice set definition

Attribute data Researcher defined Respondent defined Researcher defined

aŽ .Objective 1 RPo 2 XŽ .Perceived 3 4 RPp X

Ž .Constructed X X 5 SP

a RPo, RPp, and SP are acronyms for revealed preference objective data, revealed preferenceperceptions data, and stated preference, respectively.

perceptions versus objective measures in site choice models.3 These alternateŽ . Ž . Žstructures are labeled RPo RP objective , RPp RP perceptions , and SP stated

.preference .In our examination of the attribute data structures in site choice models we used

two new features in the estimation of the joint RP]SP models. These joint modelsare meaningful only if the null hypothesis of parameter equality, after accounting

w xfor relative scale differences, is accepted 19 . We examine these relative scalefactors and test hypotheses of parameter equality for RP and SP models using bothobjective and perceived data. In doing this we employ a FIML approach to theestimation of the relative scale parameter rather than grid search procedures which

Ž w x.were used by previous researchers e.g., 1 . The likelihood function we use is alsodifferent than those used in previous studies in that it examines the weighting ofchoices versus choice sets. This issue arises in joint RP]SP models because in theRP data an individual provides information on the number of choices of eachalternative from a specified choice set, whereas in the SP data an individualprovides one choice from a series of difference choice sets. The likelihood functionemployed here addresses this problem through the weighting and transformation ofthe two types of choice data.4

This paper employs data collected from recreational moose hunters in Alberta,Canada. These individuals were questioned about their hunting trips and theirperceptions of hunting site attributes and they were asked a series of statedpreference questions about hunting site choice. The perceptions data were meas-ured in the same units as the objective measures and the attributes presented in

3 While we use researcher-defined choice sets in the objective measures models and respondent-defined choice sets in the perceptions models, it is worth noting that these two forms of choice set

w xdefinition made relatively little difference in terms of predictive ability, at least for these data 14 .4 An additional issue that arises in models of this type is the existence of non-participation as part of

the choice set. RP applications tend not to include non-participation because data on this ‘‘choice’’ aregenerally not collected and because modelling non-participation generally requires some form of time

Ž .series or panel data structure i.e., one must observe non-participation choice occasions . As Morey etw xal. 15 point out, excluding non-participation can result in significantly biased welfare measures. In our

application, the SP component includes non-participation as one of three options available to theindividual. Thus, non-participation is built directly into the choice set and the issue of hunters leavingthe activity can be examined. Of course, since the sample was based on hunters, the situation ofindividuals becoming active as hunters is still problematic as data on the non-hunting public arerequired.

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the stated preference design, allowing a direct comparison between the measuresŽ . Ž .and models. The results show that the RP objective and RP perceptions models

appear to suffer from collinearity and missing attribute levels. The joint modelresults show that RP models can be combined with SP data, and, after accountingfor variance effects, there is no significant difference between the parameters ofthese two data structures. However, it is difficult to choose between the specificjoint RP]SP models using measures to fit and other descriptive model perfor-mance indicators. We examine various methods of model selection to determinethe ‘‘best’’ model and find that the joint RP]SP model based on perceptionsmoderately outperforms the other models. However, welfare measurement withmodels based on perceptions of quality attribute can be problematic. Can welfare

Ž .be affected by altering perceptions and not actual ‘‘objective’’ conditions? Willperceptions converge towards objective attribute values? We conclude the paperwith a discussion of these issues.

MODELING AND DESIGN ISSUES

Random Utility Model

As described above, we examine models of recreational site choice in which theindividual chooses one site from a set of available alternatives. Selection of one

Ž .alternative over another implies that the utility U of that object is greater thaniŽ .the utility of another U . Since overall utility is random one can only analyze thej

probability of choice of one alternative over another, or

� 4Pr i s Pr V q e ) V q e ; ; g C , 2� 4 Ž .i i j j j n

where C is the choice set of individual n. Assuming a type I extreme value errornŽ .distribution with scale parameter m, 2 produces the conditional logit specification

w xof the probability of choice 12 :

e mVi

� 4Pr i s . 3Ž .mVjÝ ejg Cn

In a single data set identification of m is not possible; however, in cases where twoor more data sets are being combined, estimation of the relative scale parameterŽ . w xcapturing the ratio of the variances between the various data sets is possible 19 .

DATA COLLECTION AND EXPERIMENTAL DESIGN

The particular form of recreation we investigate is moose hunting in Alberta,Canada. Moose hunting is a popular form of recreational activity in the province.These is also considerable concern that changes in habitat caused by forestryactivity and other industrial uses of wildlands will have a significant effect onrecreational hunting values. Thus, this research is focused on the effects of changesin wildland habitats as a result of forestry activity.

Ž .The study area consists of 14 Wildlife Management Units WMUs in west-centralAlberta. This region is also a center for forestry activity in the province. A survey


designed to collect SP choices, RP information, attribute perceptions, and demo-Ž w xgraphic information was constructed see 13 for a more detailed description of the

.survey approach . The survey also included a contingent valuation question about amanagement change at a particular WMU. Focus groups were held to aid inquestionnaire design and issue definition. A sample of 422 moose hunters fromrural towns in the study area and one nearby major urban center were drawn fromthe set of provincial moose hunting license holders.

An important data collection issue was to obtain SP, RP, and attribute percep-tion, and demographic information from each respondent. Since the survey wasconsiderably long and complex, telephone and mail surveys were ruled out asoptions. Instead, in-person interviews in group meetings were used. Our surveystrategy involved attracting respondents to meetings at one of five towns or citieswithin the study region. Each potential respondent was sent a letter explaining theproject. The respondent was then telephoned and asked to attend one of themeetings in her or his local area. After accepting an invitation to attend a session,the respondent was then telephoned again the day before the meeting. Of the 422

Ž .hunters in the sample, 312 74% agreed to participate in a meeting. Of these 312,Ž .271 64% of the entire sample and 87% of those who agreed to participate

actually attended one of the meetings. The meetings ranged in size from 20 to 60respondents. The meetings were structured such that the initial portion of thesession involved the completion of the questionnaire and the final portion was adiscussion on wildlife management issues. Each individual completed a question-naire within the group setting. The order of the sections of the questionnaire wasrandomized across respondents to avoid ordering effects.

Stated Preference Design

The particular design strategy we employed involved initially determining a set ofŽdecision attributes and levels to represent recreational hunting site choice in this

case, choice of a particular WMU, described as a generic bundle of attribute levels;.thus, there is no association of these alternatives with actual WMUs . We concep-

tualized the hunters’ decision problem as one in which we would offer them achoice between pairs of competing WMU descriptions and give them the option ofchoosing to hunt in one of the described WMUs or not to go moose hunting at all.Each WMU description was based on attributes and levels that were determinedfrom focus group discussions with hunters and from previous research on sitechoice. These attributes are displayed in Table II. The design problem involvesselecting a sample of WMU profile pairs from the universe of pairs given by aŽ 2 4. Ž 2 4. Ž .2 = 4 = 2 = 4 = 2 versions factorial, in other words, treating left- andright-hand pairs as a composite set of attributes and levels. As discussed by

w xLouviere and Woodworth 9 , the necessary and sufficient conditions to estimatethe parameters of a broad class of multinomial logit models can be satisfied byselecting the smallest orthogonal main effects design from this larger factorial tocreate the WMU profiles and pairs simultaneously. The smallest orthogonal maineffects design consists of 32 pairs, which were blocked into two sets of 16 pairs eachusing a two-level blocking factor.

This design strategy produced a survey in which hunters were shown 16 pairs ofWMU profiles and asked what they would most likely do if their choices wererestricted to only the left- and right-hand WMUs and the choice of not moose

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TABLE IIAttributes Used in the Stated Preference Experiment

Attribute Level

Moose populations Evidence of -1 moose per dayEvidence of 1 or 2 moose per dayEvidence of 3 or 4 moose per dayEvidence of more than 4 moose per day

Hunter congestion Encounters with no other huntersEncounters with other hunters on footEncounters with other hunters on ATVsEncounters with other hunters on trucks

Hunter access No trails, cutlines, or seismic linesOld trails, passable with ATVNewer trails, passable with four-wheel-drive vehicleNewer trails, passable with two-wheel-drive vehicle

Forestry activity Evidence of recent forestry activityNo evidence of recent forestry activity

Road quality Mostly paved, some gravel or dirtMostly gravel or dirt, some paved

Distance to site 50 km150 km250 km350 km

Ž . 5hunting in the region at all see Fig. 1 for an example of the choice question .Logical reasons why such choice restrictions might occur were suggested, such asfloods, wildlife management decisions to close areas to hunting, and blocking ofaccess by timber companies. Such occurrences are realistic and had occasionallyhappened in the past; hence, they provide hunters with rational reasons whychoices might be restricted. Thus, the data for analysis consists of the single choicefrom a trinary set of options observed in each of the 16 sets for each hunterin the sample.

Re¨ealed Preference Data

In contrast to the SP approach, RP models arise from information on actualhunting trips. Each hunter was asked to complete a ‘‘trip log’’ that elicitedinformation on the hunting trips for the 1992 season. Information collected

Ž .included destination WMU , distance, dates of trip, party size, length of trip,and harvest.

Objecti e Quality Attributes

Objective measures of site attributes were collected from Alberta Fish andWildlife managers who were familiar with the study area. The attributes weremoose population levels, access levels, congestion levels, road quality, and presence

5 This stated preference structure has been examined in terms of its performance and consistencywith other stated preference protocols. It appears to be a very reliable structure, at least within the

w xcontext of marketing and transportation research. See 5 and 10 .


FIG. 1. Example of the instrument used to gather stated preference data.

of forestry activity. Attributes were collected using exactly the same categories asŽ .the attributes in the SP task see Table II . This provides a direct correspondence

between the SP task and objective RP measures. Objective distance measures wereŽcalculated by measuring using a rotary planimeter and a 1 : 250,000 map of

.roadways to the areas the distance between each hunter’s residence and a pointnearest the center of each WMU that could be reached by road or truck trail. Thisdistance measure was translated into travel cost using an estimated out-of-pocketcost of $0.27rkm plus the value of travel time. Travel time value estimates werebased on individually reported full wage rates for those individuals who indicatedthat they could have been working during the time they were hunting and a zero

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value for those who indicated that they could not have been working duringthis period.

Perceptions of Quality Attributes

Individuals were asked to provide their perceptions of quality attributes in eachWMU in the study region. The respondents were asked to check off the level ofeach attribute they felt best represented the conditions in each hunting zone. Theywere also allowed to choose ‘‘I don’t know’’ for each zone. These attributes wereexactly the same as those used in the SP task and the RP objective measuresŽ .Table II .

ŽIn summary, we model three different characterizations of choice SP, RPo, and.RPp , which are illustrated by the equations

RPo: U s X b q e ; C s 1, 14 researcher defined ,Ž .i o RPo i n

RPp: U s X b q e ;i p RPp i4Ž .

C s set defined by respondents, maximum size s 14 ,Ž .n

SP: U s X b q e ; C s 1, 3 site A, site B, neither ,Ž .i sp SP i n

where X indicates the use of objective measures of the attributes, X indicateso puse of individual specific perceptions measures, X indicates the use of attributesspdefined in the stated preference task, and C is the choice set. These three modelsnform the basis for the econometric analysis in which we examine the modelsseparately and in combination.

MODEL ESTIMATION

Stated Preference Model

A stated preference model was estimated using maximum likelihood. All at-tributes were included in the model as were two alternative specific constantsŽ . Ž . 6 ŽASCs one for each hunting alternative . The alternative of not hunting non-

.participation is the third alternative and attribute levels are assumed to be zeroŽ .for this choice. Attributes except travel cost are effects coded rather than dummy

coded because dummy coding incorporates the base category into the interceptwhile effects coding avoids this by making the parameter value for the base equalto the negative sum of the parameter values for the other three categories.7 In

6 To save space, the table reports the coefficient estimates for the direct effects of attributes only.Ž .Coefficients on alternative specific constants ASCs and interactions between attribute levels and the

‘‘urban’’ characteristics of individuals are not reported but are available from the authors upon request.7 Categorical attributes are commonly structured in models as sets of dummy variables where one

category is designated as the ‘‘base’’ and its effect is captured in the model intercept. Thus, a four-levelcategorical variable would have three columns in the matrix of explanatory variables that are eitherŽ . Ž . Ž . Ž .1, 0, 0 , 0, 1, 0 , 0, 0, 1 , or 0, 0, 0 corresponding to the first, second, third, and fourth categories. Thefourth category in this case is captured in the intercept. Effects coding avoids incorporating the basecategory in the intercept by making the parameter value for the base equal to the negative sum of the

Ž . Ž .parameter values for the other three categories. The columns in the design matrix are 1, 0, 0 , 0, 1, 0 ,Ž . Ž .0, 0, 1 , and y1, y1, y1 corresponding to first, second, third, and fourth categories. Adamowicz et al.w x1 discuss the rationale for using effects codes rather than dummy codes in discrete choice models.


TABLE IIIParameters of Site Choice Models

RP objective RP perceived SP RPo]SP RPp]SP RPo]RPp RPo]RPp]SP

Travel cost y0.0098 y0.0053 y0.0047 y0.0127 y0.0043 y0.0096 y0.0058Ž . Ž . Ž . Ž . Ž . Ž . Ž .y5.4 y2.8 y17.8 y6.4 y4.7 y4.6 y6.1

Road quality 0.1303 y0.0295 y0.0494 y0.0627 y0.0295 y0.0180 y0.0115Ž . Ž . Ž . Ž . Ž . Ž . Ž .Unpaved 0.6 y0.1 y1.5 y0.8 y1.0 y0.1 y0.3

AccessNo trail } } y0.1082 y0.2913 y0.1005 } y0.1348

Ž . Ž . Ž . Ž .y1.8 y1.7 y1.7 y1.8Old trails 1.4911 0.1037 0.3301 0.7078 0.2808 0.4095 0.3341

Ž . Ž . Ž . Ž . Ž . Ž . Ž .1.5 0.5 5.3 3.7 3.7 2.4 4.14WD trail } 0.1540 0.0624 0.2055 0.0628 y0.1257 0.0609

Ž . Ž . Ž . Ž . Ž . Ž .0.9 1.1 1.5 1.3 y0.7 1.1Congestion

No hunters y2.8610 0.3206 0.5967 1.6297 0.5327 } 0.6750Ž . Ž . Ž . Ž . Ž . Ž .y2.5 0.7 10.6 5.2 4.4 5.4

On foot } y0.6137 0.0044 y0.0048 y0.0380 y0.6074 y0.526Ž . Ž . Ž . Ž . Ž . Ž .y2.1 0.1 y0.0 y0.7 y1.7 y0.7

On ATV } 0.1948 y0.2677 y0.7550 y0.2290 0.1582 y0.3026Ž . Ž . Ž . Ž . Ž . Ž .0.8 y4.5 y4.1 y3.3 0.7 y4.0

Logging 0.0726 0.1483 0.0370 0.0316 0.0329 0.0807 0.0357Ž . Ž . Ž . Ž . Ž . Ž . Ž .0.1 1.0 1.1 0.4 1.1 0.5 1.0

Moose populationMoose 1 0.0023 y1.0378 y1.2218 y3.2069 y1.0388 y0.8539 y1.2470

Ž . Ž . Ž . Ž . Ž . Ž . Ž .0.0 y3.9 y18.5 y5.6 y4.9 y3.1 y6.1Moose 2 y0.900 0.1956 0.0040 y0.2534 y0.0064 0.1239 y0.0672

Ž . Ž . Ž . Ž . Ž . Ž . Ž .y0.2 1.0 0.1 y1.9 y0.1 0.6 y1.2Moose 3 y1.3721 0.0530 0.4447 1.2469 0.3577 y0.0087 0.4277

Ž . Ž . Ž . Ž . Ž . Ž . Ž .y1.5 y0.2 7.8 5.1 4.1 y0.0 5.0u s ln t y0.9840 0.1247 y0.2744 y0.12801 1

Ž . Ž . Ž . Ž .y5.8 0.6 y1.5 y0.8u s ln t y0.06782 2

Ž .y0.32r 0.2437 0.1834 0.2581 0.2566 0.2740 0.2143 0.2445

Number ofchoice sets 199 190 4,256 4,455 4,446 389 4,645

Number of 2,786 1,315 12,768 15,554 14,083 4,101 16,869observationsŽchoice sets =alternatives per

.choice set

Note. Asymptotic t statistics are in parentheses. For variable definitions see Table II. SP, stated preference;RPo, revealed preference, objective attribute measures; RPp, revealed preference, perceived attribute mea-

Ž .sures. Coefficients on alternative specific constants ASCs and interactions of attributes with ‘‘urban’’characteristics are not included in this table but are available from the authors on request.

testing specifications it became clear that there were two distinct groups in thesample: hunters residing in rural areas and hunters residing in the major city in the

Ž . Žregion Edmonton . Therefore, interactions between urban residence urban s 1,.non-urban s y1 and all attributes were included in the model.

The model is highly significant and most of the main parameters are significantŽ .Table III . Travel cost is negative and significant as expected. Respondents fromurban areas have a significantly different travel cost parameter, reflecting theirwillingness to travel further for hunting experiences. The ASCs8 associated

8 Alternative specific constants capture the ‘‘utility’’ of an alternative that is not captured by theattributes in the model. For example, the utility of site i may be modeled as a function of an attribute Xand an ASC as V s a q bX , where a is the ASC. However, since ASCs are not related to specifici i i iattributes, they do not explain choice in terms of observable attributes. Thus, ASCs improve modelperformance, but they cannot easily be used in predicting the effect of changes due to attribute changes.Ideally, one would want to use attributes to thoroughly explain choice.

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Ž .with each site site A and site B are significant and reflect the higher utility,all else held constant, associated with hunting. The use of ASCs to model non-participation is relatively crude as it does not include any attributes for thenon-participation alternative; however, it is a simple and useful approach that

w x 9should reduce bias associated with models that force participation 15 .An access level with Old Trails is the most appealing to the hunters as is hunting

Ž .in areas with low congestion No Hunters . Somewhat surprisingly, forestry activityis not a significant factor in predicting site choice. We surmise that once factorssuch as access and congestion are accounted for, forestry activity does little toexplain choice. In other words, forestry activity is correlated with access, conges-tion, and probably moose population because the activity provides access and oftenimproves habitat for moose. Moose population levels, as expected, are highlysignificant, with the lowest level of moose population having a strong negativecoefficient. Many of the interaction effects are not significant but are retained inthe model to maintain a consistent specification between model structures.

Re¨ealed Preference Models

Objecti e measures model. A revealed preference model employing the objectivemeasures of the attributes was estimated using the actual choices made by the

Ž .hunters RPo, Table III . The rural]urban interaction effects were also estimatedŽ . Žbut not reported in Table III , as was a set of ASCs eight total ASCs, six unique

.ASCs to account for characteristics not included in the set of attributes. A full setof ASCs could not be included in the model because of poor conditioning of thedesign matrix. The four ASCs reflect the maximum number that could be esti-mated after incorporating equality restrictions for sites assumed to have similarcharacteristics.10

The parameters for several attribute levels could not be estimated in this model,either because the level did not exist in reality or because of collinearity between

Ž .attributes. For example, only one of the three parameters for access Old TrailŽ .and for congestion No Other Hunters could be estimated. This problem arises

because of lack of variation in the data of these attributes.Using these objective measures of attributes, utility is significantly affected by

Žtravel costs and encountering no other hunters relative to encountering other.hunters in trucks . Interacting the attributes with a dummy variable representing

urban residence suggests that urbanites are significantly less affected by thedisutility of travel and have significantly different preferences over access levelsŽ .Old Trails and moose populations. Some of the signs of these parameters aresomewhat counter-intuitive. For example, encountering no other hunters hassignificantly lower utility than encountering other hunters in trucks.

9 ŽIn a case were the choice set involves distinct groups sets of sites and non-participation for.example it is necessary to test for violations of the IIA property of the logit model. We examined a

nested logit model in which the individual first chooses to participate or not, and then chooses one ofthe two available sites. We found that the nested model was not significantly different from the simpleconditional logit model for our data set. Therefore, we use conditional logit estimators throughout theremainder of the paper.

10 For example, WMUs 338 and 348 are assumed to have the same ASC since both do not have alottery-rationed bull moose hunt during the rut.


Ž .Perceptions model. A second revealed preference model RPp employing theperceptions of the attributes by each respondent was estimated using the actual

Ž .site choices made by the hunters RPp, Table III . Perceptual information was usedfor the access, forestry, moose population, and congestion attributes, while objec-tive measures of distance and road quality were used. The rural]urban interactioneffects were also included in this model, as were the ASCs.

An issue that arises here is the treatment of missing perceptions information.Missing perceptions could be replaced with the modal response from the sampleŽ .since the attributes are categorical the modal response seems most appropriate .Alternatively, if an individual stated that he or she did not know anything about aparticular site, it could be removed from the choice set. In this case a site wasexcluded from an individual’s choice set if the individual responded ‘‘I don’t know’’

Žto all of the attribute perception categories for that site except distance and road.quality . If she or he responded ‘‘I don’t know’’ to any individual attribute

perception, the response was replaced with the modal response of the samplepoints from the same town of residence as the respondent. Thus, the resulting datacontain individual specific choice sets where the choice sets comprise sites that theindividual reported at least some perception of quality attributes.

The results from the perceptions model are different from the objective meas-2 w Ž . Ž .xures RP model. First, the r value 1 y log-likelihood 0 rlog-likelihood b for

Ž .the RPp model is lower than the RPo 0.1834 versus 0.2437 . Second, moreattribute parameters could be estimated because there was more variation in theperception attribute data than in the objective data. Two levels of the accessattribute and all three levels of the congestion attribute could be estimated. Sitechoice is significantly affected by travel cost, one level of the congestion attribute,and moose populations. As expected, low moose populations reduce utility. Urban

Ž .hunters experience less disutility from travel as in the RPo model ; however, thecongestion results still appear to be counter-intuitive, with low congestion levelshaving high disutility.11 A final difference between the RPp model and the RPomodel is that in the former a larger set of ASCs could be identified without placingrestrictions on them. In the RPp model, 12 ASCs were identified, whereas in theRPo model only 6 unique ASCs were estimable.

Joint Models

Joint models were estimated using either the RP objective measures dataandror the RP perceptions data andror the SP data. These models were estimated

Ž .by ‘‘stacking’’ the data matrices from the individual models RP andror SP andestimating a single set of parameters. We estimated four models: SP in combina-tion with RPp, SP with RPo, SP with RPp and RPo, and RPp with RPo. Tests of

Žsignificance of parameter equality between the individual components SP, RPo,.RPp and accompanying tests of scale parameter differences were accomplished

w xusing the methods outlined by Swait and Louviere 19 . The design matrix of onedata set is multiplied by a relative scale factor. This scale factor is estimated as aparameter using FIML methods. The resulting joint model incorporates the differ-

11 Modeling congestion as an attribute is often a troublesome task. Sites are often congested becausethey are attractive; thus, congestion variables may be confounded with other attributes. Congestion maybe associated with good access, high moose populations, or other attributes.

ADAMOWICZ ET AL.76

Ž .ence in scale variance between the data series. Hypothesis tests of parameterequality, conditional on different scale, are carried out using a likelihood ratio test

Ž .of the restricted joint and unrestricted models.An important element in this joint model estimation was the appropriate

weighting of the likelihoods from model components. For example, consider thecase of combining SP and RP data. In the SP task, each trio of alternatives is

Ž .considered a choice set and each person provides one response choice in this set.In the RP data sets, however, the choice set is fixed for the individual and eachindividual may make several trips to each of the sites. The RP data can be modeled

Ž .on a trip frequency basis each trip comprises a choice within the choice set or itcan be modeled in terms of proportions of trips to each of the sites.12 Thisequivalence is premised on the total number of trips being fixed for each individ-ual, which is the case here since the trips were made in the past and cannotbe altered.

Assuming that the SP and RP data are independent, and that there isindependence among the SP replications of an individual respondent, thelikelihood function for the joint conditional logit model can be written as

N RP N SP

RP SP� 4 � 4L b , t s f ln Pr i N b q f ln Pr i N b , t , 5Ž . Ž .Ý Ý Ý Ýin inns1 igC ns1 igCn n

where n indexes individuals from the RP and SP samples; i indexes alternativesŽ . RP SPsites ; f , f are the frequencies of choice in the RP and SP observations,in in

� 4 � 4respectively; Pr i N b and Pr i N b , t are the probabilities of an individual nw Ž .xchoosing alternative i as in Eq. 3 in the RP and SP samples, respectively; b is

the parameter vector for a linear-in-parameters deterministic component of theutility function and is assumed to be the same in both the RP and SP models; and tis the ratio of the scale parameter of the SP data to the scale parameter of the RP

Ždata or, equivalently, t can be thought of as the ratio of the square root of the. RPvariances of the RP and SP error terms . In the RP data, f will weight thein

observations according to their frequency; hence, if some individuals took manytrips, that observation will receive considerably more weight than other observa-tions. In the SP choices, f SP will be either 1 or 0 and will sum to 1 over allinalternatives in each choice set. Therefore, we specify f RP as proportions so thatinthese also add up to 1 over each RP choice set. The use of proportions rather thanfrequencies for the RP data eliminates overweighting of each RP observation morethan any individual SP observation. Thus, by making the total of the dependentvariables sum to 1 within each choice set, whether of RP or SP origin, we havegiven each RP and SP observation equal weight.

The parameter estimates from the joint models are presented in Table III. Theresults of hypothesis tests of parameter equality and scale variability are presentedin Table IV. At a 5% level of significance, the hypothesis of parameter equalitybetween SP and RPo must be accepted. This means that these two models sharethe same preference structures, after allowing for error variance heterogeneity. At

12 In a data set where each individual has the same total number of choices, either approach willproduce identical coefficients; however, the standard errors in the latter approach must be adjusted by

Žthe square root of the number of trips to be consistent with the former approach assuming that the.total number of trips is constant across observations .


TABLE IVTests of Scaling and Parameter Equality

2Log No. of x Degrees of PModel likelihood parameters value freedom value

RP objective y397.2 21RP perceived y261.4 33SP y3468.7 28RP objective q SP y3871.7 41 11.6 8 0.170RP perceived q SP y3745.7 41 31.2 20 0.052RP objective q RP perceived y664.1 33 11.0 21 0.963RP objective q RP perceived q SP y4171.0 42 87.4 40 0.000

a 5% level this hypothesis is also not rejected for the RPp]SP model. The RPmodel with perceptions of attributes is not significantly different from the statedpreference model; however, the model combining all three sets of data stronglyrejects parameter equality. Finally, the RPo and RPp models are not significantly

Ždifferent in terms of parameter values, once difference in scale is accounted for as.evidenced by the acceptance of the null hypothesis .

The scale parameter estimates are actually for the exponential of the relativeŽ .scale factor, i.e., t s exp u , where u is the parameter shown in Table III. In the

RPp]SP model, u is estimated as 0.1247 with a t-statistic of 0.6. This suggests thatŽ .the actual scale factor not the exponential of the scale factor is not significantly

different from unity, implying that not only are the parameters in these two modelsnot different but, in addition, the variances are not different. In the RPo]SP

Ž .model, however, u is 0.984, and is significantly different from zero t statistic s 5.8 .This implies that the variances of RPo and SP are significantly different and thatthat variance in the RPo model is higher than the variance in the SP model.

The parameters of the RPo]RPp]SP model should be interpreted with cautionsince they involve restrictions that are not supported by the hypothesis test;however, the joint models, RPo]SP and RPp]SP, can be interpreted as typicalconditional logit models. Note that in this case the elements that were missing in

Ž . Žthe two RP models coefficients on some of the attributes are estimable Table. ŽIII . There are more significant attributes in the joint model relative to the RPo

.model and most of the signs are as expected. In contrast to the RPo model, themoose population coefficients in the RPo]SP model reflect increasing preferenceas moose populations rise; a factor expected in this type of activity. It is interestingto note that this pattern is observed in all models except the RPo model, which isthe type of model most commonly estimated by researchers. Finally, it is possible inthe joint models to estimate a larger set of ASCs. This was not possible using theRP data alone.

Given these results, which model is preferred? Based on the tests of scalingŽ .Table IV , the RPo]RPp]SP models can be rejected. We reject three other model

Ž .based on examination of estimated parameters Table III : the RPo model isrejected based on missing attribute levels and the counter-intuitive results withsome attributes such as moose populations; and the RPp and RPo]RPp modelsare rejected due to missing attribute levels and similar counter-intuitive results.

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Although the moose population parameters perform as expected in these lattermodels, the congestion parameters do not conform with our expectations.13 Theyalso have the lowest r 2 of all of the models.

ŽSince our version of the SP model is based on generic sites rather than specific.WMUs it does not contain ASCs for actual moose hunting sites. Therefore, the

performance of this model is also relatively poor using the criteria described above.However, since we are interested in evaluating SP methods by themselves as well asin joint models, we continue to consider this model.

We are left with the two joint models, RPo]SP and RPp]SP, and the SP model.The parameters for the moose populations, congestion, and access attributesperform as expected; their r 2 values are similar; and all attributes and WMUASCs are estimable where possible. To choose between these models, we examinetheir performance in simulations of actual site choices. We do not have a holdoutsample, but the models we are interested in have been estimated on either jointRP]SP data or SP data alone. Thus, none of them have been examined in terms oftheir power in predicting RP choices only. Furthermore, we examine how well the

Ž .model based on objective measures RPo]SP performs when perception data arethe basis of the simulation and vice versa. More specifically, we examine predic-

Ž .tions using objective data X ,o

U s X bi o ŽSP .

U s X b 6Ž .i o ŽRPo ] SP.

U s X b ,i o ŽRPp ] SP.

Ž .and using perceptions data X ,p

U s X bi p ŽSP .

U s X b 7Ž .i p ŽRPo ] SP.

U s X b .i p ŽRPp ] SP.

The simulation exercises produce three measures of model performance: asimulated r 2, a Pearson ratio test, and comparisons of predicted versus actualfrequencies of choice. The r 2 comparison is based on the notion that in models of

Ž . 2this size a small )0.01 improvement in the r can be interpreted as a superiorw x 14model in a non-nested test sense 7 . The Pearson ratio examines the standard-

ized residuals from the models and, in well-specified models, approaches 1 asymp-totically. The difference between simulated and observed frequencies of choice areexamined using both a sum of absolute errors and a sum of squared errors.

The results of our simulation exercises are presented in Table V. In theŽ 2simulations using objective data, the RPo]SP model performs best highest r ,

.lowest sum of squared errors . This is not surprising given that the objective modelŽ .is based on objective and stated data. However, the RPp]SP model performs

13 Ž w x.Congestion effects are quite complex and are often non-linear in nature see 18 . That is,encounters with a few people may be desirable whereas encounters with many may be very undesirable.Our categorization of the congestion variable may not be able to capture all of the complexity of thisissue.

14 w xThis ‘‘test’’ is discussed in Ben-Akiva and Lerman 2, p. 172 .


TABLE VResults of Tests of Model Performance

Data used Objective data Perceptions data

Coefficient set used SP RPo]SP RPp]SP SP RPo]SP RPp]SP

a 2Simulated r 0.071 0.246 0.157 0.106 0.083 0.178bPearson ratio 0.71 0.973 0.672 0.66 0.65 0.626

Sum of absolute errors in choice 3.31 2.49 2.43 2.61 3.30 2.56cprediction

Sum of squared errors in 457.46 290.84 293.64 379.59 434.65 315.01dchoice prediction

a Using the RP objective data and the RP perception data, and the parameter vectors from the SP,RPo]SP, and RPo]SP models, likelihood values are simulated and r 2 calculated.

b The Pearson ratio is the ratio of the Pearson residual and the degrees of freedom in the model. In aw xwell-specified model the Pearson ratio should asymptotically approach 1 16 . This ratio is calculated

using the simulation process described in footnote a.c For both RP objective data and RP perceptions data, choice frequencies are simulated using the

parameters from the three models. The sums of absolute values of differences between actual andpredicted choice frequencies are presented here.

d For both RP objective data and RP perceptions data, choice frequencies are simulated using theparameters from the three models. The sums of squared differences between actual and predictedchoice frequencies are presented here.

quite well also, with sum of squared errors results comparable to the RPo]SPmodel and much lower errors than the SP model exhibits. The simulations usingthe perceptions data are different. The RPp]SP model performs best while theRPo]SP model is very poor in predicting choice in this case. The r 2 is smallŽ . Ž .0.083 and the errors absolute and squared are very high. Based on thisinformation we feel that the RPp]SP model is the most robust and can predictchoice well using either objective or perception information. We conclude that inour empirical example the RPp]SP model is the superior model.

IMPLICATIONS OF USING PERCEPTIONS DATA

Researchers have claimed that choices are made on the basis of perceptionsŽ w x.e.g., 11 ; however, there has been relatively little use of perceptions of qualityattributes in applied economic modeling probably because the variation in the datamay be reduced when perceptions are employed andror the high level of effortinvolved in collecting individual level perceptions information. Our results suggestthat collection of such data may be useful in modeling choice and estimating jointmodels.

While useful on the surface, however, some problems arise in using perceptionsinformation in modeling recreation site choice. First, when attempting to simulatechoices for individuals not in the sample it is not clear what form of attributesshould be used in the model unless perceptions have also been collected fromthese individuals. Second, even if sampled individuals are being used to predictchoice or measure welfare impacts, the use of perceptions may be problematic. Forexample, if an agency wishes to improve the quality of a particular site byimproving one attribute, it may believe there is a base level and a particular target

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level of quality. In a model based on objective measures, the welfare impacts wouldsimply be measured by examining the difference in utility between the base leveland target level. When using perceptions information, however, individuals willhave their own perceptions of base quality levels and the agency’s target level ofquality may be different than the individual’s base level perceptions.

One approach to measuring the value of quality changes is to measure theŽimpact of changing each individual’s perceived quality level by a fixed amount a

.percentage for continuous attribute or a level of categorical attributes . Analternative approach is to change perceptions to the agency’s objective measure forthose individuals who have perceptions that are lower than the target level, andassign zero changes for individuals who have perceptions greater than or equal tothe target. This approach assumes that the individual’s perception converges to the

Žagency target level over time or that the agency is essentially ‘‘correct’’ and.individuals converge to these estimates .

We use the second of the two approaches described above to examine theŽwelfare implications of changing moose populations from level 1 lowest popula-

.tion to level 2 for WMU 344. This is a site that has been the focus of considerableresearch on forestry]wildlife interactions and exhibits the lowest populations anddensity of moose in our study area. We examine a second change which involvesclosing this WMU to hunters. This involves deleting it as one of the alternativesites in a choice set and is not affected by the use of perceptions data in the samemanner as the moose population change, since the site is unavailable regardless ofthe potential differences between agency and individual attribute perceptions.Three models are used to examine these impacts, SP, RPo]SP, and RPp]SP, usingthe two different data sources, objective and perceptual. The measures are ex-pected to differ because of parameter differences between the models and because

w xthe sources of data are different. We use Hanemann’s 6 estimate of compensatingvariation per trip.

Ž .Results of welfare changes averages over the sample are shown in Table VI.Ž .The lowest welfare measure $8.93rtrip is for the moose population change

results using the SP model. The RPp]SP model provides a welfare measure that is

TABLE VIPer Trip Estimates of Welfare Change Associated with Some

Attribute Changes for Moose Hunters in Alberta

Environmental quality change

Data Change perceptiona bsource Model to agency target Close recreation site

Objective SP $8.93 y$5.81RPo]SP $56.35 y$7.73RPp]SP $16.11 y$10.71

Perceptual SP $3.63 y$9.61RPo]SP $1.34 y$7.33RPp]SP $7.44 y$20.16

a Ž .Increase moose population in WMU 344 from level 1 to level 2 agency target .In perceptions data, attribute perceptions are increased to the agency target level ifthe perception by the individual is below that level.

b Close WMU 344.


nearly twice as large as the SP measure and the RPo]SP measure is more than sixtimes the size of the SP measure. Clearly, the choice of model significantly affectsthe welfare estimate.

A somewhat different picture emerges using the same models with the percep-tual data. First, the welfare measures are smaller when using the perceptions data.This is probably due to the fact that individuals are assumed to experience awelfare gain only when their perception of the site quality is below the agencytarget. If they perceive the moose population to currently be greater than or equalto the agency target, they have no welfare gain. Second, the measures from thethree models are more similar using the perceptions data. In this case, the RPo]SPmodel produces the lowest measure and the RPp]SP is highest.

The site closure welfare measures are less variable than the results presentedabove; however, unlike the moose population change, the welfare changes using

Ž .the perceptual data are higher in absolute value in each model than those usingthe objective data. The largest welfare changes for closing the site are provided bythe SP and RPp]SP models using perceptual data.

In comparing the RPo]SP and RPp]SP models, the model based on perceptionsproduces higher welfare measures in all cases except the moose populationincrease using objective data. It seems that individuals in the sample perceivemoose populations to be better than the agency does, and this results in a relativelysmall welfare measure in response to the population improvement. The fact thatindividuals perceive moose populations to be higher than the agency probably leadsto higher ‘‘marginal utility’’ coefficients in the objective model than the perceptionsmodel. The fact that WMU 344 was not visited very frequently is not explained bymoose populations in the perceptions model, whereas it may be in the objectivemeasures model.

DISCUSSION ON THE DIFFERENCE BETWEEN PERCEIVED ANDOBJECTIVE MEASURES

An issue that arises from the estimation results and welfare measures is how thedifference in data source leads to a difference in results. How does the differencebetween perceived and objective measures of attributes lead to strikingly differentparameters and welfare measures? A first response is that the perceptions andactual measures are not always strongly correlated. There is a significant positivecorrelation between moose population perceptions and objective measures. Exam-ining the objective assessment versus the modal perceived response by huntersprovides a correlation of 0.64; however, similar correlations for access and conges-tion variables are 0.30 and 0.11, respectively, and the latter correlation is notstatistically significant. The underlying reason for these divergences between per-ceptions and objective measures is itself an interesting topic for further research.The impact of such divergences on statistical models is also worthy of further study.However, at a minimum, this correlation information suggests that the agency andthe hunters differ significantly in their views of access to the sites. Thus, it is notsurprising that coefficients, at least for these factors, will be different between themodels.

In terms of the difference in welfare measures, hunters generally perceived sitesŽ .to have higher on average moose populations than were suggested by the

ADAMOWICZ ET AL.82

objective measures. Thus, using the perceptions data in the manner we have, thewelfare measures for a population increase are expected to be smaller whenperceptions are used. When closing a site, however, the fact that perceptions aregenerally higher for moose populations suggests that the welfare losses underperceptions will be larger than those under objective measures. These generaltrends are illustrated in Table VI, except that the loss associated with closing site344 is slightly larger in the objective case than in the perceptions case when theRPo]SP parameters are employed. This may be a result of the relatively large ASC

Žfor site 344 in the RPo]SP model which may result from the smaller amountof individual specific variation and lower explanatory power associated with

.attributes .There is also very little variation across sites in the objective measures of access

and congestion, suggesting that parameter estimation using these data will bedifficult. In the objective data there is also no variation in the attributes betweenhunters. In the perceptions data there is considerably more variation across sitesand variation between hunters. This difference in variation can be interpreted asthe reason for the differences in scale effects between the models. For example, inthe RPo]SP model, the RPo variance is significantly higher than the SP variance,whereas in the RPp]SP model, the RPp and SP variances are not significantlydifferent. The variation in the attributes in the perceptions data may capture moreof the variation in the observed component of the random utility model rather thanthe error term. Thus, the lack of variation in the objective data may lead to thehigher error variance in the RPo data. This is also supported by the fact that thescale parameter in the RPo]RPp model shows a higher variance in the RPo

Ž .component Table III .

CONCLUSIONS

What does our paper contribute to the methodology of environmental valuation?w xFirst it replicates Adamowicz and co-workers’ 1 finding of RP]SP parameter

equality, once variance heterogeneity is accounted for, and shows that joint RP]SPmodels are superior to RP models alone. Even combining objective and perceivedmeasures within a RP model appears to improve the model performance, at leastrelative to using an objective measures model alone. Our study also presents anattempt to scale three data sets. Although the null hypothesis for equal parameterswas not accepted in this case, the attempt illustrates the possibility of combiningmore than two data sources and accounting for variance heterogeneity.

Ž .Second, our study is the first to our knowledge to examine both perceptionsand objective attribute measures within the same general model in a nonmarketvaluation context. Researchers have been claiming that choices are made on thebasis of perceptions of attributes. Our results on this matter suggest that this is thecase, but in our empirical example this result was not overwhelming. The percep-tual models performed slightly better than those based on objective data; however,welfare analysis using perceptions data remains a significant challenge. The diver-gence between objective and perceived measures suggests that a dynamic androrstochastic model is required. This model should incorporate a mechanism for themovement of perceptions toward objective measures as quality signals are observed


by the individual. The model should also consider the impact of attribute uncer-tainty on decisions and welfare. Clearly, the treatment of perceptions is an issuethat requires further investigation.

The one case where a ‘‘fair’’ comparison between perceptual and objectivewelfare measures can be made is a change involving recreational site closure. Herethere is no question about which quality levels to choose for the base and alteredsituations; the site is simply removed from the choice set. Table VI provides

Ž .welfare measures for the closure of one of the sites WMU 344 . Other siteclosures can be examined but we expect the results to be qualitatively similar. Inthis case the perceptual welfare measures were larger than the objective ones. Thisresult is in part due to the fact that the perceptions of site quality at the site weclosed are, in general, higher than the objective measures. It is tempting to suggestthat previous attempts to model environmental changes using objective data mayhave underestimated the value of those changes. However, further comparativestudies must be conducted before this result can be considered general.

Although our model selection tests support the use of a joint SP]RPp model onemust question whether the benefits of employing perceptions data outweigh thecosts. In our empirical example, the benefits of perceptions information seem to be

Ž .modest, whereas the costs survey time, explanation, etc. were significant. Also,given the difficulty in measuring changes in welfare with perceptions data, onewould need to find significant benefits associated with this type of data to outweighthe costs. While in our sample the gains from using perceptions are modest, itcould be that gains in other samples are significant. Our case involves relativelyactive, intense recreationists. In a less intense activity such gains may besignificant.

ŽThird, given the development of new techniques in the literature discrete choice.models and multi-model estimation with scaling it is important to determine what

constitutes the best model. In our study, we used a variety of in-sample tests tosupport the selection of the joint RPp]SP model as the preferred one. Bettertechniques, such as out-of-sample tests and approaches where each type of model

w xis used to predict the choices from the other models 20 , should be examined.Finally, the issue of choice set determination is a key topic for further research.

The size of the choice sets may differ dramatically depending on the assumptionsused to construct these sets. Our use of perceptual data to develop individual

Žspecific choice sets produced choice sets that were approximately half the size on.average of the overall choice set. Other methods have also been used to determine

Ž w x.choice sets e.g., 8, 17 . We believe this is a critical issue in environmentalvaluation that has received relatively little attention in the literature.

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