An Analysis of Congestion Effects Across and Within Multiple Recreation Activities

An Analysis of Congestion Effects Acrossand Within Multiple Recreation Activities

Kimberly Rollins,1 Diana Dumitras2 and Anita Castledine3

1Department of Resource Economics, University of Nevada, Reno, NV(phone: 775-784-1677; fax: 775-784-1342; e-mail: [email protected]).

2Department of Management and Economic Engineering in Agriculture, Universityof Agricultural Sciences and Veterinary Medicine, Cluj-Napoca, Romania.

3Department of Resource Economics, University of Nevada, Reno, NV.

This paper uses stated and revealed preference data to quantify differential welfare impacts fromchanges in congestion at outdoor recreation sites that support multiple activities. The results indicatethat welfare impacts from congestion vary by congestion point, site, and activity within a given site.Estimating willingness to pay (WTP) for multiple sites and activities allows for parametric testingof whether WTP varies among sites and activities. The most general implication of this study is thatif one has the ability to discriminate by activity, doing so is preferable purely in terms of overallmodel performance. This approach is especially useful for circumstances in which visitor flows in asystem of multiple use areas can be managed so as to increase net benefits associated with publiclands.

Dans la presente etude, nous avons utilise des donnees sur les preferences declarees et revelees pourquantifier l’impact differentiel que des variations de congestion dans les aires d’activites recreativesmultiples ont sur le bien-etre. Les resultats ont montre que l’impact differentiel de la congestion sur lebien-etre varie selon le point de congestion, l’aire et l’activite au sein d’une aire donnee. L’estimationde la volonte de payer (VDP) pour des aires et des activites multiples permet de verifier, a l’aided’un test parametrique, si la VDP varie ou non entre les aires et les activites. L’implication la plusgenerale de cette etude est que si quelqu’un a la possibilite de discriminer selon l’activite, le fait de lefaire est preferable purement si l’on considere la performance globale du modele. Cette methode estparticulierement utile dans les cas ou l’affluence des visiteurs dans un systeme d’aires polyvalentes peutetre geree de sorte a accroıtre les avantages nets lies aux terres publiques.

INTRODUCTION

Jakus and Shaw (1997) provide an “economist’s definition” of congestion during recre-ation as occurring “when either the utility of one person diminishes due to the presenceor behavior of other persons (i.e. an externality), or when the costs of doing an activityincrease due to the presence of other persons (costs can be in loss of time, or in actualout-of-pocket monetary loss).” In practice, congestion is often measured as the numberof encounters with other groups. The change in utility or costs associated with an activityis the welfare change induced by a change in the number of encounters. Estimates ofwelfare effects from congestion can, in theory, be used to calibrate permit and quotasystems to encourage optimal use of recreation areas. This literature spans over 30 yearsand includes contributions from Fisher and Krutilla (1972), Cicchetti and Smith (1973,1976), McConnell (1988), Richer and Christensen (1999), and Kerkvliet and Nowell

Canadian Journal of Agricultural Economics 56 (2008) 95–116

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96 CANADIAN JOURNAL OF AGRICULTURAL ECONOMICS

(2000). However, issues encountered in empirical modeling to estimate welfare costs fromcongestion have in some cases limited the applicability of results.

While using number of groups encountered as a measurement unit appears straight-forward, welfare estimates depend on the context in which encounters are defined andmeasured, and in how preferences relate to these contexts. A review of the empiricalliterature reveals that measuring welfare effects from congestion has been problem-atic throughout the same 30 years, as demonstrated by Freeman and Haveman (1977),Dorfman (1984), McConnell (1988), Jakus and Shaw (1997), Michael and Reiling (1997),and Boxall et al (2003). A common thread in these studies is that welfare effects perencounter vary depending on the type of activity, characteristics of the recreation site,individuals’ ex ante expectations, actual congestion experienced, mitigating actions avail-able to the individual, and the point during a trip where congestion is encountered.Omitting context-specific heterogeneity in preferences regarding how congestion is en-countered limits applicability of results, especially when recreation managers have theability to manage encounters within these contexts. Boxall et al (2003) show that thisomission can result in inefficient estimation.

Boxall et al (2003) developed a model that includes both revealed and stated prefer-ence data in a panel to measure variation in congestion effects due to differences in pref-erences for congestion by site and congestion point. Prior to this approach, past effortsbased on revealed preferences alone to estimate congestion effects were not successful.Other authors have also used models based on combined, revealed, and stated preferencedata, but not specifically for measuring welfare effects of congestion. Whitehead et al(2000), Hanley et al (2003), and Loomis (1997) ask people how many trips they wouldtake under hypothetical conditions and combine these data with actual trips under cur-rent conditions to value recreational site visits. Alberini et al (2006) set out to test thevalidity of pooling actual and hypothetical trip data in a travel cost model to estimate thevalue of sports fishing. They conclude that actual and contingent behaviors are drivenby the same demand function, and that pooling can be done for estimation purposes.Azevedo et al (2003) could not reject the hypothesis that the underlying demands are in-consistent between stated preference and revealed preference methods applied to wetlandrecreation in Iowa. However, they suggest that the analysts’ initial beliefs can affect theinterpretation of inconsistency tests. They point out that when there is no a priori ratio-nale to believe that either method dominates, “different interpretations of inconsistencytests can be used to ‘reject’ either approach,” so that it may not be possible to fall back oneither source of data as “the ‘correct’ source of values.” They conclude that approachescombining data may effectively treat strengths and weaknesses of both sources, therebyresulting in more accurate valuation estimates. In estimating the value of improvementsin recreational site quality, Whitehead (2005) notes that unobserved preferences may becorrelated with both observed behavior and stated preferences. He uses stated preferencedata—the additional annual number of trips people state they would take to a site ifwater quality was improved—with revealed preference data to account for endogeneityin the demand change. Whitehead (2005) points out that in using combined data, his ap-proach corrects for what would have been biased valuation measures. He concludes thatfuture contingent valuation work should continue to develop methods of incorporatingobserved preference data to improve the efficiency and reliability of resulting valuationestimates.

CONGESTION EFFECTS IN MULTIPLE RECREATION ACTIVITIES 97

Boxall et al (2003) incorporate observed preference data in a contingent valuationmodel to estimate welfare effects from changes in congestion. They note that many authorswho were not successful in using stated preference data alone have indicated that ex anteexpectations about congestion and mitigating behavior onsite may confound efforts toestimate welfare effects from congestion. Their model exploits natural variation in actualnumbers of encounters with other groups experienced among individuals in the sample,basing the hypothetical changes in encounters as increases or decreases from observednumbers. Responses to these hypothetical changes are observations in a panel. The actualnumber of groups encountered and a zero change in trip costs are also included in thepanel with a “yes” response to indicate actual conditions. This paper uses this model,extended to treat multiple activities, and applies it to three sites where congestion pointsare shared by recreational users engaged in different activities.

A congestion point is defined here to be a specific situation during a recreation tripwhere (or when) encounters with other groups may be particularly welfare detracting orenhancing, such as at campsites, while portaging, along trails, or at access points. Mea-surements that distinguish differences in how encounters impact trip values by congestionpoint as well as by activity provide information for decisions regarding strategic reorgani-zation of routes and trails, campsite spacing, locations of portages, and placement of siteaccess points, allowing for optimal dispersal of users to reduce congestion costs withoutreducing an overall site visitation quota (or to increase a site visitation quota withoutincreasing the congestion costs).

Welfare effects from congestion are often estimated by including the number ofencounters experienced during a recreation trip as a covariate in models that estimate thewillingness to pay (WTP) for a trip, such as in Kerkvliet and Nowell (2000). This providesa general estimate of the welfare effects of congestion. Boxall et al (2003) use multiplecongestion variables; each represents the number of encounters at each congestion point.Interaction terms in the econometric model allow for testing of independence betweencongestion point and site. Their data support rejecting the hypothesis that the congestioncosts are the same for all congestion points. They also show that including multiplecongestion variables results in better overall model performance. Extending their modelto include multiple activities would similarly involve creating interaction terms to allowfor testing of independence between congestion point, site, and activity, and testinghypotheses that congestion point-specific congestion costs are the same for all activitiesand sites.

This paper presents a model to estimate activity-specific and congestion point-specific congestion costs across a number of sites, and allows for parametric testingto determine whether congestion costs vary by congestion point, activity, and site. Interms of management implications, if there is no detectable statistical difference in wel-fare effects from congestion by activity or congestion point, then there may be little togain from the effort of routing to separate users engaging in different activities (unlessrouting is done for environmental purposes). We are unaware of published work that esti-mates welfare measures of congestion to accommodate hypothesis testing across multipleactivities and congestion points. The combination of revealed and stated preference datawith multiple observations per individual measures congestion as both the actual and theexpected numbers of encounters. Resulting regression coefficients are used to calculateWTP for visits and for changes in congestion by site, activity, and congestion levels. The


model is applied to data collected at three recreation sites in Ontario, Canada during the2003 season, where activities include canoeing, fishing, car-camping, kayaking, hunting,rest and relaxation, and hiking.

EMPIRICAL MODEL

Individual preferences for congestion experienced at multiple congestion points duringa recreational site visit are represented as a random utility model where utility, U , isexpressed as the sum of a systematic component V , and a random component ε. Income,y, and other observable individual characteristics, s, are included in V . Congestion, c, is ak × m vector of the number of groups encountered at congestion point k during activitym:

U = V(c, y, s) + ε (1)

Preferences for congestion are captured by modeling an individual’s response to a choicebetween observed levels of congestion experienced during an actual trip and a proposedchange in congestion with an accompanying change in the trip cost, P. The correspondingchange at an individual congestion point ckm is indicated by superscript t. When t = 0,ct

km represents the actual congestion level observed by the respondent at congestion pointk and activity m. When t = 1, ct

km represents a hypothetical change from the observedcongestion level. For example, Equation (2) indicates that an individual engaged in activity3 (here, all other m-1 activities are suppressed, and k = 5 congestion points) will be willingto pay additional cost P for a change in congestion at congestion point 2 if the value ofthe change is at least as great as the income change:

V 0 (c0

13, c023, c0

33, c043, c0

53, y, s) + ε0 ≥ V1 (

c013, c1

23, c033, c0

43, c053, y − P, s

) + ε23 (2)

Individual preferences for congestion at all k congestion points and all m activities arecaptured by repeating Equation (2) for changes in P and ct

km for each km combination.This results in a total of k × m equations, with a separate error term, εkm, for each uniquecongestion point and activity combination. The model is applied to data in which eachequation is represented by multiple observations providing variation in the values of Pand (c1–c◦) for each km combination. The dependent variable is the individual’s “yes” or“no” response to the specified change. Following Equation (2), the probability of a “yes”response is a random variable with probability:

Pr(yes) = Pr[V1

(c0

13, c123, c0

33, c043, c0

53, y − P, s)

− V 0(c0

13, c023, c0

33, c043, c0

53, y, s) ≥ ε0 − ε23

] = Fη (�V) (3)

where η = ε0 − εkm and F η(·) is the cumulative density function of η, and Pr(No) = 1 –Pr(Yes). Maximum WTP is found by setting �V equal to zero and solving for P. Theprobability of a “yes” response corresponds to a standard probit model if the cumulativedensity function is assumed to be standard normal, as described in Hanemann et al(1999).


Each observation could represent a unique individual respondent. Alternatively,each respondent could provide multiple observations in a panel, with each observationrepresenting a response to a different km combination. Use of multiple observations perindividual implies assuming that responses are independent among congestion pointswithin the individual’s set of responses. A random effects probit specification allows forcorrelation between multiple responses of the same individual in a panel. In this casea respondent-specific disturbance is included in addition to the disturbance associatedwith the model. The general expression for the random effects model is given by Greene(2003).

Individual WTP is calculated using data and resulting parameter estimates as inEquation (4),

WT Pi = 1β f ee

∗(

N∑i=1

α + β Xi

)(4)

where α is the intercept, β fee is the coefficient estimated for trip cost (and as Cameron(1988) shows, (1/.β f ee

)2 is the variance of WTP), and β X is the vector of cross products

of remaining coefficients and independent variables. WTPi is calculated for each sampleobservation i. WTPs for specific combinations of congestion point, activity and otherindependent variables (such as site) are calculated by averaging over the associated kmcombinations.

Multiple Observations Per Respondent and Other Empirical ConsiderationsIt is unlikely that a representative sample of all activities at a given site could be generatedin which all individuals in the sample engage in every activity for a total of k × mobservations per individual. More realistically, each individual in a sample may representa single activity (where the unit of observation for each individual in the panel is a singletrip, with one main activity). This is sufficient for estimation as long as all activities arerepresented in a random sample of respondents in proportions that are representative forthe sites included in the sample.

Each observation for a given individual within a sample represents the individual’sresponse to a unique combination of congestion point, congestion level, and trip costvalues. If all k congestion points are experienced at all m activities, then the model wouldinclude k × m congestion variables and each individual would be represented by no lessthan k observations, one for each congestion point. However, it is possible that someactivities may not include all congestion points (hiking is not likely to include portages asa congestion point), resulting in an unbalanced panel, where the number of observationsper individual varies according to the activity and the number of congestion pointsencountered.

The number of observations per individual is determined only in part by the num-ber of congestion points associated with an activity. “Yes” or “No” responses to othercombinations of varying trip costs and congestion levels can also be included in themodel. Additional observations are associated with holding the congestion levels for all


congestion points constant at observed levels while varying trip costs, as in Equation (5),

Pr(yes) = Pr[V1(c0, y − P1, s) − V0(c0, y, s) ≥ ε0 − ε1

]Pr(yes) = Pr

[V1(c0, y − P2, s) − V0(c0, y, s) ≥ ε0 − ε1

] (5)

and setting the response to “yes” for the observed levels of congestion with no change inactual trip costs, as in Equation (6).

Pr(yes) = Pr[V0(c0, y, s) + ε0 ≥ 0

] = 1 (6)

Observations of the former type are typical of standard contingent valuation formatsthat use multiple bid amounts, while observations of the latter type incorporate revealedpreference data into the model.

SITE CHARACTERISTICS, ACTIVITIES, AND DATA

Data were generated via onsite sampling at three different sites in Ontario, Canadabetween May and October over the 2003 season. The three sites, Killarney ProvincialPark, Kawartha Highlands, and Spanish River Valley, were chosen in part because theyrepresent activities and ranges of qualitative differences in these activities that would beapplicable to other sites throughout Ontario. Each site is briefly described below.

Site CharacteristicsKillarney Provincial Park (48,500 ha) and the adjacent public lands lie on the northshore of Georgian Bay. The region contains numerous lakes, rugged terrain with whitequartzite ridges and hills providing spectacular views, and forests of pine and hardwoods.The relatively calm waters are especially accessible to the beginner and the intermediatecanoeists and families with children. Killarney Provincial Park is a wilderness park withgroup numbers and sizes limited by quota. Boats with motors are not permitted. The parkincludes a system of hiking trails with 33 hike-in backcountry camp sites, 140 canoe-inbackcountry camp sites, and one campground accessible by car. Adjacent public landsproviding additional hiking trails, kayaking, and camping opportunities are included inthe Killarney study site. Visitation rates and activities were previously not well documentedon these public lands. One of the study goals was to document the uses of these lands fordeveloping a comprehensive management strategy.

Kawartha Highlands is a 37,587 ha natural environment park within the OntarioParks system. It contains no developed park services and few public facilities. Existingfacilities are limited to access points with boat launches, some backcountry campsites, andlimited parking (there are no campgrounds, washrooms, showers, nor designated hikingtrails). It has neither user quotas nor restrictions on motor boat use. The public landsare interspersed with private lands with cottages, recreation camps, trapping cabins, andhunt camps. Two roads bisect the park, providing vehicular access, and entry points foroffroad vehicles. The terrain is flat with interconnected lakes, calm waterways, and severalrelatively undisturbed areas with environmental heritage value. Kawartha Highlands iswithin a 2-hour drive of major urban centers; its location and natural amenities make ita popular weekend getaway for people from these centers. Recreational activities include


fishing, swimming, boating and canoeing, small and large game hunting, offroad vehicleuse, and nature viewing and photography.

A unique aspect of the Kawartha Highlands is the number of private cottages ownedby weekend or seasonal residents with long-established family roots in the area. A numberof private hunting camps associated with long-term leased hunting rights also exist inthe Kawartha Highlands. These leases are no longer available, but existing leases arehonored until they expire. These camps are family-owned and are not used for commercialpurposes. Groups of big game hunters have been using these camps for generations, andlikely have come to build social ties over the years, both within and among hunting groups.There are relatively few newcomers who are not associated with these private camps in theKawartha Highlands area. As Table 1 indicates, the average length of a big game huntingtrip in Kawartha is over 10 days.

The 98,634 ha Spanish River Valley site includes two provincial parks and adjacentpublic lands with interspersed private lands. This is a rugged area with numerous inter-connected lakes, rapids, small waterfalls, and river runs that offer novice to intermediatewhite water canoeing during most of the year and advanced white water canoeing in thespring. A number of private companies provide canoes and arrange transportation upriver. Canoeists typically put in up river with an average trip progressing over 5 daysthrough a varied landscape. Table 1 indicates that respondents in the sample whose mainactivity was canoeing at the Spanish River reported trip lengths of 5.9 days, which wouldbe expected for a typical river run. The area is considered semiwilderness, with outstand-ing natural features and no extensive development. The area provides remote tourismopportunities and is home to a number of commercial outfitters. Cottages located onnearby private lands are available for rental and accommodate extended visits. The re-moteness of the area would imply that typical cottage visits would be for longer thanweekend visits. Table 1 appears to confirm this: an average “rest and relaxation” visitis for almost 12 days. The area also offers camping, hunting, and fishing opportunities.

Table 1. Numbers of respondents and trip lengths by activity and site

Kawartha highlands Killarney park Spanish riverresponse rate – 56% response rate – 69% response rate – 62%

Average Average Averagetrip trip trip

Number of length Number of length Number of lengthActivity responses (days) responses (days) responses (days)

Canoeing 233 3.6 554 4.4 66 5.9Kayaking 15 1.9 39 3.9 3 3.7Hunting 47 10.6 0 —– 3 5.0Fishing 56 3.9 6 5.2 14 6.1Rest and relaxation 160 12.1 102 3.4 22 11.8Hiking 7 3.7 258 3.6 0 —–Car camping 1 2.0 97 4.1 0 —–Total: 519 6.8 1,056 4.1 108 7.0


Day and weekend trips are also accommodated at the lakes of the region. There are nocar-camping areas nor designated hiking trails.

Valuation QuestionsRespondents are asked to indicate the main activity they engaged in during their tripby choosing one activity from a list, or by selecting “other” and filling in an activity.Participants are asked a series of questions to determine their total trip costs by expendi-ture category. The valuation question format follows that of Boxall et al (2003), with theexception that the previous study did not repeat the question corresponding to Equation(5). This question asks whether respondents would take the same trip at a higher cost, P1

(i.e., with no change in the number of encounters with other groups anywhere during thetrip). The question is repeated with a second cost, P2, drawn from the same distributionas the first.

Prior to a second set of valuation questions about changes in congestion, respondentsare asked to recall the numbers of encounters with other groups they experienced, onaverage, during their trip at different congestion points. These data are used to constructan observation for each respondent as in Equation (6), where the probability of a “yes”is set to 100% for the observed numbers of encounters with no change in trip cost.

The next valuation question asks whether they would take the same trip if twochanges were made:

• the dollar cost of the trip is $Pi higher than what they actually paid, and• the number of groups they would encounter at one of the congestion points is doubled

(or halved) relative to the observed number of encounters.

This question is repeated for each of the congestion points. Respondents are askedto consider each of the congestion questions independently, thereby assuming that con-gestion changes occur at a single congestion point with conditions at others held con-stant. Overall visitation numbers at these three sites are low enough such that the as-sumption of congestion at each congestion point being independent of the others is notunreasonable.

The range of changes in the number of encounters in the resulting data is a functionof the variation in the numbers of groups actually encountered at each congestion point—that is,one encounter per day is doubled to two, three doubled to six, four halved to two,two halved to one, and so on. The two versions of the changes in encounters (doublingor halving) are randomly assigned, but are consistent within a given questionnaire. Thecongestion changes questions make up the remaining k Equations (3), for a total of k +3 equations per respondent.

The distribution of responses to the pilot questionnaire tested in the previous seasonwas used to determine starting values for the distribution of WTP for the stated preferencequestions. During the pilot, distributions from which bid amounts were generated wereiteratively updated to improve efficiency of the design, as described in Rollins et al (1997).The final survey was conducted from June through October, 2003.

SamplingSince it is possible that some activities or user types might be more or less abundantduring different parts of the recreational season, sampling over the entire season ensured


a representative sample of activities and user characteristics. Reliable estimates of visi-tation by activity for each site did not exist prior to this study. Sampling was thereforedesigned to provide reliable estimates of user numbers by site and proportions of usersby activity. Preliminary estimates were established from visitor counts conducted by theOntario Ministry of Natural Resources and information provided by local guide servicesand visitor lodges. These were further refined during a pilot survey run during the monthof August in 2002. The resulting estimates were the basis of a sampling scheme that ran-domized over entry points, weekdays, weekends, and month to collect data representativeof different recreational activities and user groups for each site.

The different activities are represented in unequal proportions of the total visitswithin and among sites (the distribution of visits by activity is summarized in Table 1for the final sample). While it would have been ideal for empirical modeling to stratifysampling to obtain similar numbers of observations for each activity, this was not done.Researchers did not necessarily know which visitors participated in which activities at thetime they were intercepted. Sampling by activity would have implied a very large numberof onsite interviews in order to capture adequate subsamples by activity for all activities.In this case, sampling solely by proportion of overall visits by site would be expected toresult in large variation in the numbers of observations by activity, possibly excluding theoption of running separate empirical models for specific activity/site combinations. Theimplications of this are described below with the empirical results.

During the onsite visits, the total numbers of groups entering each site as well asthe proportion of groups sampled were recorded. A research assistant approached eachgroup, explained the nature of the study, and requested that the adult with the nextbirthday take the survey home to fill out and return in its postage-paid envelope afterhaving completed the trip. The name and address of each person receiving a survey wasrecorded and a reminder postcard was sent to each survey recipient within the week. Thereminder postcard included a URL for a survey webpage with an access code and a uniquepassword. The web version was designed to appear visually as close as possible to thepaper version. Survey respondents were offered the choice of returning their completedpaper survey or to complete their survey via the internet option. After 3 weeks, surveyparticipants who had not completed their surveys were contacted with a second reminderpostcard, and after another 3 weeks, nonrespondents were mailed a second survey withthe URL, an access code and a password.

DataTable 1 summarizes responses and average trip lengths by activity for the three sites.Response rates varied from 56% at Kawartha to 69% at Killarney. Approximately 15%of the total respondents chose to use the internet option. Tests to determine system-atic differences between those who chose the internet option versus the paper optionreveal no differences in respondent characteristics or in WTP for visits and changesin congestion. However, we suspect that the web option may have enhanced the re-sponse rate by allowing participants to self-select their preferred means to respond.Similar results are also reported by other authors; for example, Lewis et al (2006),Stringfellow and Roman (2006), and Roberts et al (2006) who report finding similaritem-missing rates, frequencies, and correlations in data between mail and web versions ofquestionnaires.


Table 1 lists the seven activities included in the analysis: canoeing, kayaking, hunting,fishing, rest and relaxation, hiking, and car camping. The results of pilot and pretestversions indicated the need for a category to accommodate trips made primarily for thepurpose of relaxing with family and friends while enjoying site amenities and possibly,but not necessarily, participating in multiple activities.

The two most popular activities at Kawartha are canoeing and rest and relaxationwith about 45% and 31% of respondents indicating these as their main activities. It isnot surprising that rest and relaxation accounts for a third of the respondents, giventhe proximity to the metropolitan areas and the number of private cottages in the area.Hunting and fishing together make up almost 20% of Kawartha responses. A numberof private hunt camps at Kawartha had been built on public lands under leases thathave since been grandfathered into current land-use regulations. This accounts for theproportion of hunting as a main activity at this site, relative to the other sites. Averagetrip lengths for hunting and rest and relaxation at Kawartha are longer than for the otheractivities—consistent with the fact that these activities are also associated with stays atprivate cottages and hunt camps.

Trip lengths at Killarney are less variable over the different activities than atKawartha, in part due to the lack of private cottages and camps. Hunting is not per-mitted at Killarney and fishing is of fairly low quality. More than half, 52%, of the groupsat Killarney list canoeing as the main activity and almost 25% list hiking, not surprisingsince Killarney is noted as a high quality destination for these two particular activities.The majority of Spanish River respondents are canoeists with trip lengths that correspondwith the numbers of days that are required to run the river. Fishing is of good quality,with about 13% listing this as a main activity. Many of the 20% of the groups at SpanishRiver listing rest and relaxation as a main activity stayed in private cottages and camps inthe area, with an average trip length of almost 12 days. The data summarized in Table 1thus provide information that is consistent with what is known about these areas and thekinds of recreational opportunities that they offer.

Table 2 summarizes travel times, distances, and the expenditures reported by surveyrespondents. As would be expected, Kawartha respondents indicated an average traveldistance of 186 km, and the average travel time of 2 hours. This is consistent with themajority of these trips being made from the nearby metropolitan areas. Even though theaverage trip length is longer at Kawartha than at Killarney and only slightly less than atthe Spanish River, Kawartha visitors report much lower trip expenditures. This is in partdue to shorter travel distances to Kawartha, and is also indicative of a larger proportionof visitors staying in private cottages and camps, bringing foods from home, and fewerusing professional guide services. Expenditures as a per day average are $20/day atKawartha, $64/day at Spanish River Valley, and $89/day at Killarney. Table 3 summarizesencounters per day with other groups by congestion point. Because there are no designatedhiking trails at Kawartha Highlands or Spanish River Valley, “while on trails” is not acongestion point for these sites.

The data are structured as a panel in which each respondent is represented by up toeight observations as described above. Variables include individual and trip characteristicsthat do not change among the set of observations for an individual respondent, and bidamounts and congestion levels by congestion point that do change within a respondent’sobservations. Site-specific variables allow for constants to vary among the three sites;


Table 2. Mean travel times, distances, and expenditures by site

Kawartha highlands Killarney Spanish river valley

Mean trip length (days) [SD] 6.7 [12.01] 4.0 [2.34] 7.2 [7.35]Mean total trip expenditure (CAN$) $135 $356 $464Average travel distance (km) 186 477 407Average travel time (hours) 2.1 5.1 5.7

the variable KL = 1 when the site is Killarney, and zero otherwise, and similarly for thevariables KA and SP for Kawartha and Spanish River.

The variable Incr_cong_dummy indicates whether the respondent was presented withincreases (doubling) or decreases (halving) in congestion levels for each of the congestionpoint. The dummy is set to 1 for increases, and 0 for decreases. This does not change withinan individual respondent’s set of observations; respondents received questions aboutdoubling or halving existing congestion levels, but not both. Income is the respondent’sannual income. The variable Children_KL indicates the presence of children under the ageof 14 years for trips to Killarney. Preliminary modeling indicated this to be a significantinfluence on WTP at that park. This variable is constructed as a cross-term that takes ona value of 1 for Killarney respondents who indicate having children on their trip, and is 0otherwise.

The variable Ln(days on site) is the log of the trip length. Rollins et al (1997)estimate WTP for wilderness canoe trips of varying lengths while allowing constantand bid coefficients to vary by trip length. Their model is improved significantly byallowing the parameters to vary by trip length, with resulting WTP estimates indicatingthe expected declining marginal value per trip day. Using this approach, we estimatedseveral augmented models that allowed constant and bid coefficients to vary with triplength categories. For this application, however, a single variable, the log of the trip length,provides the best fit; other specifications for trip length show no improvement. We suspectthat the inclusion of other substantive variables—activity, site, income, children, and theinteraction terms for site and activity—pick up much of the variation that ultimatelyexplains differences in preferences beyond the single trip length variable.

The variable Fee is the hypothetical increase in the cost of the trip over what eachrespondent reported to have paid. Fee varies within an individual’s set of observations.

Table 3. Mean number of encounters per day

Congestion point/site Kawartha highlands Killarney park Spanish river

At access and departure points 2.7 (3.0) [457] 3.4 (4.0) [976] 2.3 (2.7) [97]While on trails N/A 3.4 (3.2) [818] N/AWhile on water 5.0 (6.8) [424] 4.6 (4.6) [744] 1.7 (1.4) [91]While camping 2.0 (3.2) [281] 3.1 (5.6) [593] 1.1 (1.3) [66]While portaging 1.8 (2.4) [267] 2.6 (3.1) [874] 0.1 (0.8) [79]

Standard errors in parentheses; Numbers of observations in square brackets.


For observations associated with Equation (6) in which the cost is unchanged, Fee is setto 0. Otherwise Fee is the dollar amount indicated in the specific valuation question.Interaction terms constructed by multiplying Fee with individual site dummies allow thecoefficients Fee_KL, Fee_KA and Fee_SP to vary over sites. Additional interaction termsallow Fee_site to vary by activity.

Each observation includes the variable Congestion, a scalar corresponding to ctkm

in Equations (2) and (3). Thus, for Equation (6) Congestion is the actual number of en-counters, and for Equation (3) Congestion is the hypothetical doubling (or halving) ofthe actual number of encounters for the given congestion point. A series of interactionterms account for changes in congestion-by-congestion point, site, and activity. Inter-action terms for congestion by activity are denoted as Cong_activity (i.e., Cong_canoe,Cong_kayak, Cong_hunt). Interaction terms for congestion-by-congestion point, activity,and site are denoted as Cong_activity_site_congestion point.

The variables mentioned above, Fee_KL, Fee_KA, Fee_SP, Incr_cong_dummyKL, KA, SP, Ln(Days on Site), and Children_KL,are included in the three mod-els that represent increasingly refined specifications for congestion. These are pre-sented in Table 4. Model 3 includes a single variable, Congestion, calculated as theaverage number of group encounters at all congestion points for each observation.Model 2 uses interaction terms to account for changes in average congestion by ac-tivity, denoted as Cong_activity (i.e.,Cong_canoe, Cong_kayak, Cong_hunt). Finally,Model 1 uses selected interaction terms for congestion-by-congestion point, activity,and site denoted as Cong_activity_site_congestion point (i.e., Cong_canoe_KL_water,Cong_hunt_KA_access). The differences in the number of observations between Model1 and Models 2 and 3 arise because not all respondents answered all congestion ques-tions at all of the congestion points, and Model 1 includes the congestion point-specificinteraction terms. Table 5 presents Models 2 and 3 with the reduced set of observationsfrom Model 1, so that direct comparisons are more easily interpreted. This is discussedbelow.

EMPIRICAL CHALLENGES

Since there is no theoretical reason to assume that underlying preferences for trips withdifferent activity, congestion point, and site combinations should be the same, in the idealsituation we would have run a full-pooled model. This would have facilitated parametrictesting for differences in preferences for congestion across the different trip types. How-ever, the full unrestricted model, which included all relevant interaction terms, failed toconverge because subsets of interaction terms comprise small numbers of observationsand lack sufficient variation. We therefore proceeded to construct a pooled model thatwould limit restrictions on preferences to those that are supported by the data and to in-clude as many interaction terms as was estimable for combinations of sites, activities, andbid variables. For example, interaction terms were initially set up to allow Fee to vary withall activity/site combinations. Attempts to include subsets of Fee_activity_site interactionterms resulted in unstable models, which appeared to be affected by collinearity with theother interaction terms. A specification that omitted the separate site constants, KA, KL,and SP, but included interaction terms for Fee_activity_site combinations converged, butwas outperformed by the models in which Fee varies with site but not with activity.


Table 4. Congestion models: Estimation results

Dep. variable: Model 1 Model 2 Model 3Yes/no response Coeff. (std. error) Coeff. (std. error) Coeff. (std. error)

Fee_KL −0.0241 (0.0009)∗∗∗ −0.0239 (0.0006)∗∗∗ −0.0240 (0.0006)∗∗∗

Fee_KA −0.0272 (0.0010)∗∗∗ −0.0242 (0.0009)∗∗∗ −0.0233 (0.0009)∗∗∗

Fee_SP −0.0170 (0.0016)∗∗∗ −0.0159 (0.0013)∗∗∗ −0.0159 (0.0013)∗∗∗

Incr_cong_dummy −0.5177 (0.1314)∗∗∗ −0.5058 (0.0992)∗∗∗ −0.4986 (0.0998)∗∗∗

KL 1.6865 (0.2531)∗∗∗ 1.6970 (0.1705)∗∗∗ 1.5324 (0.1662)∗∗∗

KA 1.0729 (0.2117)∗∗∗ 0.9793 (0.1603)∗∗∗ 0.8912 (0.1571)∗∗∗

SP 1.4838 (0.4376)∗∗∗ 1.5539 (0.3452)∗∗∗ 1.3960 (0.3447)∗∗∗

Ln(Days on Site) 1.0418 (0.1071)∗∗∗ 0.9305 (0.0767)∗∗∗ 1.0052 (0.0753)∗∗∗

Income 0.0124 (0.0027)∗∗∗ 0.0133 (0.0020)∗∗∗ 0.0138 (0.0020)∗∗∗

Children_KL 0.4615 (0.2466)∗∗ 0.5829 (0.1600)∗∗∗ 0.5715 (0.1591)∗∗∗

Congestion −0.0998 (0.0125)∗∗∗

Cong_canoe −0.1358 (0.0196)∗∗∗

Cong_kayak −0.1350 (0.0595)∗∗

Cong_hunt 0.6229 (0.1057)∗∗∗

Cong_fishing −0.1248 (0.0556)∗∗

Cong_R&R −0.0591 (0.0264)∗∗

Cong_hiking −0.1177 (0.0241)∗∗∗

Cong_carcamping −0.0833 (0.0212)∗∗∗

Cong_other −0.1504 (0.0812)∗∗

Cong_canoe_KA −0.1618 (0.0414)∗∗∗

Cong_canoe_KL_water −0.0554 (0.0222)∗∗∗

Cong_canoe_KL_camp −0.0602 (0.0177)∗∗∗

Cong_canoe_SP_camp −0.2715 (0.1427)∗∗

Cong_kayak_access −0.1228 (0.0669)∗∗

Cong_hunt_KA_access 1.5311 (0.2916)∗∗∗

(Cong_hunt_KA_access) 2 −0.1614 (0.0467)∗∗∗

Cong_fishing_water −0.0875 (0.0385)∗∗

Cong_ R&R_KA −0.0883 (0.0488)∗∗

Cong_hiking_KL_access −0.1085 (0.0406)∗∗∗

Cong_hiking_KL_trail −0.0877 (0.0458)∗∗

Cong_campg_KL_camp −0.1161 (0.0307)∗∗∗

Cong_cmpg_KL_trail 0.1540 (0.1154)(Cong_cmpg_KL_trail)2 −0.0103 (0.0057)∗∗

No. of observations 6,280 10,180 10,180N of groups 875 1,479 1,479Rho 0.7535 (0.0139) 0.7403 (0.0116) 0.7443 (0.0114)Log-likelihood −2536.32 −4213.86 −4235.14% Correct predictions 72.4% 71.6% 71.3%

Levels of significance are indicated as: ∗∗∗ = 1%, ∗∗ = 5%, ∗ = 10%.

The interaction terms used in Model 1 were the results of successively adding com-binations of site/activity/congestion point interaction terms to the model. Interactionterms with parameters that were not significantly different from zero at the 10% levelwere dropped. Parameters were restricted to be the same when we could not reject the


null hypothesis that parameters were not different at the 10% level. For example, therewas not a detectable difference among congestion points for canoeing at Kawartha, thusthe variable Cong_canoe_KA includes all congestion points for canoeing at Kawartha.Moreover, when colinearity was an issue, we used a less restrictive interaction term.

We suspect that these problems are caused in part by the relatively small numbersof observations comprising some site/activity combinations due to the variation of theproportion of total trips in each activity category. Observations distributed more evenlyover activities may have resulted in a larger number of interaction terms for the con-gestion point/activity/site combinations as well. Because of the difficulties encounteredin the pooled model, one might suggest running separate models for each activity/sitecombination. However, we were unable to do this because the numbers of observationsin many subsets of site/activity combinations are simply too low to support estimationof separate models. As it is, we are able to show that allowing measures of congestionto vary by activity and congestion point improves overall fit of the models, as describedbelow.

ESTIMATION RESULTS AND WELFARE MEASURES

All three models presented in Table 4 predict the probability of a “yes” response to agiven level of congestion and change in trip cost. The models are robust over the 10shared variables. As would be expected, encounters generally have a negative influenceon WTP per trip. Model 2, with eight activity-specific congestion variables, is a better fitthan Model 3 and provides recreation managers with the additional information that theimpact on WTP varies considerably by activity. The quadratic specification for Cong_huntsuggests that WTP for hunting trips increases with encounters with other groups up toa point, and then decreases thereafter. Forty-seven of the 50 hunting responses are fromthe Kawartha Highlands site, where hunting is predominantly characterized by privateparties who may have strong social links during this time of the year. In addition, thepresence of other groups may serve to move game optimally, increasing the success of thehunt. That the model suggests an optimal number of five encounters with other groupscould support both explanations.

While Models 2 and 3 each have the same number of observations, Model 1 hasfewer observations since not all activities include all congestion points (i.e., no portagingwith hiking or car camping). Thus, while a likelihood ratio test confirms that Model 2is superior to Model 3, Model 1 cannot be compared to Model 2 using formal tests.However, we can use pseudo R-squares to indicate the relative performance of Model1 versus Model 2. The percent correct predictions for Models 3 and 2 are 71.3% and71.6%. The percent correct predictions for Model 1 is 72.4%, an increase of 0.8% overModel 2. So there is support for the notion that Model 1 is performing at least as wellas Model 2. As an additional informal test of the relative performance of these models,Models 2 and 3 are run with the reduced set of 6,280 observations from Model 1 topermit Log-likelihood ratio testing. As Table 5 shows, the reduced sample versions ofModels 2 and 3 are robust in comparison with the results from Models 2 and 3 in Table4, but with expectedly larger standard errors. The Log-likelihood for the reduced sampleversion of Model 2 is −2551.52 and −2571.27 for Model 3, indicating that Model 1,with Log-likelihood of −2536.32, is superior to the reduced sample Models 2 and 3. Chi


Table 5. Reduced sample sized models 2 and 3 for comparison with model 1

Dep. variable: Reduced sample model 2 Reduced sample model 3Yes/no response Coeff. (std. error) Coeff. (std. error)

Fee_KL −0.0240 (0.0009)∗∗∗ −0.0240 (0.0009)∗∗∗

Fee_KA −0.0269 (0.0010)∗∗∗ −0.0259 (0.0009)∗∗∗

Fee_SP −0.0170 (0.0016)∗∗∗ −0.0171 (0.0015)∗∗∗

Incr_cong_dummy −0.5126 (0.1315)∗∗∗ −0.4906 (0.1321)∗∗∗

KL 1.6970 (0.1705)∗∗∗ 1.5609 (0.2356)∗∗∗

KA 0.9793 (0.1603)∗∗∗ 1.0012 (0.1917)∗∗∗

SP 1.5539 (0.3452)∗∗∗ 1.2037 (0.4137)∗∗∗

Ln(Days on Site) 1.0444 (0.1050)∗∗∗ 1.1617 (0.0989)∗∗∗

Income 0.0124 (0.0027)∗∗∗ 0.0127 (0.0027)∗∗∗

Children_KL 0.5643 (0.2461)∗∗ 0.4846 (0.2466)∗∗

Congestion −0.1392 (0.0207)∗∗∗

Cong_canoe −0.1738 (0.0269)∗∗∗

Cong_kayak −0.1491 (0.0783)∗

Cong_hunt 0.6330 (0.1094)∗∗

Cong_fishing 0.1474 (0.0656)∗∗

Cong_R&R −0.0697 (0.0416)∗

Cong_hiking −0.1583 (0.0564)∗∗∗

Cong_carcamping −0.2100 (0.0564)∗∗∗

Cong_other −0.0474 (0.2955)No. of observations 6,280 6,280N of groups 875 875Rho 7,537 (0.0139) 0.7587 (0.0135)Log- likelihood −2551.52 −2571.27Correct predictions(%) 71.9% 71.6%

Levels of significance are indicated as: ∗∗∗ = 1%, ∗∗ = 5%, ∗ = 10%.

square tests indicating improvement between each of the models are significant at or abovethe 1% level.1

The revealed preference data are included in two ways: first as the base for thehypothetical changes in encounters presented to respondents thereby providing a va-riety of levels over which congestion changes, and second as a separate observation,Equation (6), which indicates the actual average level of congestion during the trip, a0 increase in trip costs, and a “yes” response. When Model 1 was estimated excludingEquation (6) there was no appreciable difference in coefficients there was an overallslight loss in efficiency, as given by the Log-likelihood. We conclude that much of theinformation from Equation (6) is also embedded in the other observations for eachrespondent.

Parameter estimates from Model 1 were used to calculate WTP for different con-gestion levels using Equation (4). Figures 1, 2, and 3 illustrate changes in WTP (overand above the actual expenses—i.e., surplus benefits) over different levels of congestionfor combinations of congestion points, sites, and activities. Thus the slopes of the curvesin Figure 1 indicate how WTP can be expected to change with congestion. For hunters,


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150.00

200.00

250.00

1 2 3 4 5 6 7 8 9 10

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WT

P (

$)

canoeing relaxing fishing at water hunting at access

Figure 1. Variation in WTP from congestion at Kawartha

moving from one to two encounters with other groups increases WTP by roughly $40(calculated as $210–$170). Increases from 2 to 5 encounters would increase WTP by$43 ($253–$210). Changes to WTP decline beyond 5 encounters; moving from 5 to 8encounters decreases WTP by $68 ($253–$185).

Visitors to Kawartha who engage in canoeing, rest and relaxation, and fishing arelikely to share congestion points. It appears that rest and relaxation visitors are moretolerant of congestion, averaging WTPs of about $45 higher for all congestion levels than

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P (

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hiking on trails car camping on trails

Figure 2. Variation in WTP from congestion while using trails at Killarney


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25.00

50.00

75.00

100.00

1 2 3 4 5 6 7 8 9 10

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WT

P (

$)

canoeing kayaking

Figure 3. Variation in WTP from congestion while canoeing and kayaking at Kawartha

those of visitors whose main activity is fishing. However, this may simply be an artifactof this group having larger surplus benefits (as measured by WTP over and above theactual expenses) in general. The key is that the two groups have similarly sloped curvesindicating that they are affected similarly at the margin. As indicated by their more steeplysloped curve, however, canoeists are more negatively affected by each additional unit ofcongestion.

Graphs like Figure 1 show the differences in WTP for given congestion levels at aglance. At the existing average level of congestion of approximately 5 encounters “onthe water” at Kawartha (Table 3), the difference in surplus benefits between canoeistsand fishing visitors is about $15 and is $50 between canoeists and people who engagein rest and relaxation. While differences in this case between canoeists, fishing, and restand relaxation visitors are not great, site mangers who are in the process of adding basicinfrastructure (parking areas, picnic tables and fire pits, outhouses) might want to doso in a way to entice rest and relaxation visitors to specific areas that are less likely tocreate conflicts with canoeing visitors. On the other hand, while there appear to be largedifferences among hunters’ and other visitors’ tolerance for congestion, these groups areless likely to be sharing congestion points, since the hunting season is concentrated in theautumn.

Figure 2 illustrates the differences in congestion costs on hiking trails at Killarneybetween people who consider their main activity to be hiking versus car camping. Carcampers are more tolerant of congestion throughout all congestion levels and with agradual increase in the value of a trip with increasing congestion up to about nineencounters. Hikers’ WTP is strictly decreasing in congestion, however. Table 3 shows theexisting average level of congestion is about three to four encounters while on trails atKillarney. At this level, the difference in per trip WTP between the two groups is about$50, but the difference attributable strictly to congestion is small, given the differences in


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Kawartha Killarney Spanish River

Figure 4. Median WTP per trip by signature site and activity with 99% confidence intervals(calculations based on Model 1 results, aggregated by site and activity)

slopes. Figure 3 illustrates a case in which the costs of congestion on the water for canoeistsare increasing faster than for kayakers at Kawartha. Both groups use the same areas, butchanges in congestion impact them differently. Managers might consider advertisingcertain areas as canoe areas and others as kayak areas to provide a signal to users thatwould allow some self-selection to help reduce some congestion costs for canoeists.

To isolate the effect of congestion on WTP, Figures 2, 3, and 4 show WTP over andabove the actual trip costs. In contrast, Figure 4 presents total WTP per trip by activityand site. Since WTP is estimated as the amount people are willing to pay over and abovethe actual trip costs, actual trip cost is added to predicted WTP to arrive at total per tripWTP for each observation. Point estimates and confidence intervals for WTP by activityand site are constructed from the mean and standard deviations of the predicted WTPsfor each subcategory in the data set. We included Figure 4 to provide a reference forthe value of reducing congestion costs relative to total per trip WTP for each site andactivity. For example, average congestion levels on the water are about five for Kawartha(Table 3). Figure 4 indicates that the average Canoe trip is valued at about %150. Anincrease in congestion from five to seven encounters would induce approximately a $15decrease in WTP, or about 10% of the overall trip value.

Iterative updating conducted during the final survey did not improve estimationresults when tested as described by Rollins et al (1997). Using simulated data, Kanninen(1993) show that iterative updating with a known underlying distribution improves the


mean square error of WTP estimates substantially for the first and second iterations, butimprovements are nominal beyond two iterations. Rollins et al (1997) arrive at similarfindings using actual data. We suspect that in this situation, the underlying distributionsfor WTP did not change appreciably over the season or between years, so that the iterativeupdating conducted during the pilot phase was sufficient.

IMPLICATIONS, SHORTCOMINGS, AND FURTHER RESEARCH

This paper demonstrates an effective method to quantify differential welfare impacts fromminor changes in congestion at outdoor recreation sites that support multiple activities.The results indicate that welfare impacts from congestion vary by congestion point, site,and activity within a given site. Estimating WTP for multiple sites and activities allowsfor parametric testing of whether WTP varies among sites and activities. These methodsare useful for circumstances in which land managers are engaged in managing visitorflows in multiple use areas so as to increase net benefits associated with public lands. Themethod is easily generalized to other cases in which mail-back surveys can be conductedover multiple sites and recreational activities.

The most general implication of this study is that if one has the ability to discriminateby activity, doing so is preferable purely in terms of overall model performance. Addi-tionally, a model that can distinguish differences in how encounters impact trip values byactivity and congestion point provides even more precise welfare measures. Testing fordifferences in congestion costs by congestion points can help to target management ef-forts to those circumstances where welfare impacts will be the greatest. Since it is commonfor systems of recreation sites to be managed to support multiple activities, an empiricalmodel that allows congestion costs to vary across activities, congestion points, and siteswould accommodate permit and quota designs for systems of recreation sites managedfor multiple uses. Such results would be useful in determining whether it is worthwhileto design routes that segregate users by activities and to identify which sites in a systemare most suited for specialized activities that are more highly valued when quotas arerestrictive.

In terms of applicability to management, observing differences in the impacts ofadditional encounters on different activity groups could affect decision making as toplacement of infrastructure and route planning. In this application empirical results showthat over certain ranges, trip values can increase with congestion over certain ranges ofcongestion for some activities (i.e., hunters at Kawartha and car campers using the trailsat Killarney) and at specific points in a trip. Thus allowing a few more encounters onan average can actually enhance welfare for recreational users engaged in these activities,even while detracting from the welfare of recreational users engaged in other activities(i.e., canoeists and fishers on the water at Kawartha and hikers using the same trailsat Killarney). A model that can separate out differences, such as positive and negativewelfare impacts, provides more precise welfare measures associated with congestion.

Our review of the literature on congestion indicates relatively few published empiricalworks that measure activity and congestion point-specific congestion welfare effects.There is room for more empirical research that could improve upon the approach used inthis paper. This application suffered from the unequal distribution of activities representedin the data. A full model with all relevant activity/site/congestion point combinations


could not be estimated because several of the interaction variables included too fewobservations and variation. This was a result of the sampling strategy in which samplingwas conducted by proportion of visits over sites as a whole. The proportions of visitsby activity at these sites varied considerably. The resulting model would not suffer frombias, but the variances could be suspect. It is likely that we could not reject the nullthat congestion parameters for in site/congestion point/activity combinations are notdifferent more often than we would have had we used a data set that was more balancedin terms of the numbers of observations for each activity. In future work, it would beadvisable to stratify in order to achieve a minimum number of observations for eachactivity/site combination.

One advantage of a stated preference approach is the option to investigate a widerange of behavioral models. Some of these could include modeling recreationists’ be-havioral responses to mitigate congestion in a repeated trip context. This might involveasking about past trips, congestion experienced, and whether the level of congestion af-fected decisions that affected subsequent trips, such as selection of site, activity, or thetime of the year. Another behavior that may have impact on the recreational users inthis study is the tendency to make repeat visits to the same site. People who are avidusers tend to make repeat visits more often than would otherwise be expected, and thosewho have the opposite tendency seek out different experiences more often than wouldbe expected. Avidity bias can be an issue in revealed preference models that are basedon onsite sampling because those who go more often have a higher probability of beingsurveyed. A method of controlling for avidity bias is to parameterize and thus control forthe avidity tendency (positive or negative) in users. In this study, a subset of the peoplewho visit Kawartha Highlands may have a higher avidity for that site than do other users,given the number of private cottages and given the social networks that appear to havedeveloped among frequent visitors to that area. Do those people who are avid users havea higher tolerance for congestion at Kawartha because of this? If so, how would control-ling for avidity among these users affect the overall results? A model that identified andcontrolled for avid users might be used to measure congestion effects that are mitigatedby avidity. The data in this study were collected over an entire season, but we captured avery small number of repeat within-season visitors. However, we did ask respondents toindicate how many times over the previous 5 years they had visited the same sites and allof the substitute sites identified in the pilot survey. This data may provide for a means totest whether avidity mitigates congestion costs in the context of a multiple year aviditymodel.

The congestion literature includes references to a number of other behavioral re-sponses, such as altering plans, which can mitigate unexpected congestion costs (see, forexample, Shelby et al (1989)). But we are not aware of published empirical work that mea-sures the marginal value of these actions. This is not surprising since empirical studiesusing stated preference approaches have in the past been unsuccessful. This would be afruitful area for further research using the methods described in this paper.

NOTE1While most of the coefficients are quite robust for Models 2 and 3 in moving from the full data setto the reduced data set (Tables 4 and 5), there are some notable differences. Congestion for “other"


activities goes from being significant to not significant; and the probability of a “yes" decreasesmore notably in the reduced data set for car camping and decreases by a less notable amount forthe overall congestion coefficient. Given that the observations omitted from Table 5 results werethose that did not include all of the interaction terms needed for Model 1, we suspect that thedifferences a function of the types of activities that respondents who were less likely to respond tothe congestion point- specific congestion questions were engaged in.

ACKNOWLEDGMENTS

The authors wish to acknowledge support from the Ontario Ministry of Natural Resources and theUniversity of Nevada Agricultural Experiment Station.

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An Analysis of Congestion Effects Across and Within Multiple Recreation Activities

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