Environmental & Resource Economics (2006) 34: 189–209 DOI 10.1007/s10640-005-6205-1
Springer 2006
Modeling Multiple-Objective Recreation Trips with Choices over Trip Duration and Alternative Sites CHIA-YU YEH1, TIMOTHY C. HAAB2 and BRENT L. SOHNGEN2,* 1
Economics Department, National Chi Nan University, Taiwan; 2Agricultural, Environmental, and Development Economics, Ohio State University, Columbus, OH, USA; *Author for correspondence (E-mail:
[email protected]) Accepted 2 December 2005 Abstract. Traditionally, recreation demand studies have focused on single-day, single-activity trips, despite anecdotal and empirical evidence that many recreational trips involve overnight stays and multiple purposes. This paper develops a random utility model that explores how visitors choose alternative sites and trip durations for multiple-objective trips. We focus on a recreational activity, beach visits, that appear to have significant proportions of the population taking single and multiple-day trips, and many of the multiple day trips involve multiple objectives. Multiple-duration and multiple-objective issues are incorporated in pricing trip costs. The results of the research suggest that the accepted method for incorporating travel costs into random utility models can lead to biased estimates of the structural utility parameters and, consequently, biased measures of welfare in a multiple-objective trip setting for single- and multiple-day users. Key words: beaches, multiple durations, multiple objectives, random utility model, recreation demand
1. Introduction Recreational demand studies tend to focus on single-day, single-activity trips, despite anecdotal and empirical evidence that many recreational trips involve overnight stays and multiple activities. When multiple-day trips clearly have a single objective (i.e., to visit a single recreational site, or to participate in a particular recreational activity), trip duration can be treated as a separate choice, as suggested by Shaw and Ozog (1999), and it is feasible to attribute the entire cost of a trip to the main recreational activity. In many recreational situations, however, visitors have multiple objectives for a given trip. For example, visitors may visit different types of recreation sites, such as beaches or parks without beaches, or they may engage in a range of activities like visiting family, going to amusement parks, etc. In this circumstance, it is
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more difficult to properly value the welfare effects of changes in the levels of amenities at recreational sites. This paper develops a random utility model (RUM) to estimate welfare from changes in site quality on multiple-day trips, when those trips involve more than one purpose. Estimating a RUM model that includes multiple-day trips invites a host of theoretical and empirical issues. First, non-linearity in income effects makes it difficult to estimate compensating variation from small changes in attributes (Small and Rosen 1981; Morey et al. 1993; Shaw and Ozog 1999; Morey and Rossman 2000). Second, there is endogeneity among the number of trips taken in a season, travel costs, and trip durations, but most RUM applications assign arbitrary sets of choice occasions, or blocks of time for each trip (McConnell and Strand 1999). Third, individuals may value on-site time differently from travel time (i.e., Wilman 1980; Smith et al. 1983; McConnell 1992), which could have important implications for longer duration trips, which often involve more travel time in general. Finally, multiple-day recreational trips often have a number of objectives other than the primary recreational activity of interest to the researcher (Smith and Kopp 1980; Bell and Leeworthy 1990; Shaw and Ozog 1999; McConnell and Strand 1999). This paper focuses on the question of relating trip costs to a specific recreation resource when visitors have multiple objectives for their trips.1 To date, no uniform method has been established in the literature for pricing recreational trips. However, it is likely that whatever methods are chosen for a given recreational activity, prices should vary by trip duration, recreational activity, and trip objective. If trips are varied in duration, pricing trips with only travel costs causes visitors from the same origin who travel to the same site to have similar values for the trip, even though they may have different trip durations. Longer trips, in this case, would be valued less per day for multiple-day trips, even though their actual marginal costs of taking the trip are likely to be higher due to onsite costs such as staying the night. Incorporating onsite costs could help to explain differences in trip value; however, individuals who visit the same site but have multiple objectives likely value the resources, and consequently, the amenities at sites, very differently. For example, activities such as boating or fishing trips may be capital intensive with high fixed costs, so that individuals on these trips mainly focus on the recreational activity of interest. Other activities, such as day-hikes or beach visits, have smaller fixed costs if they do not involve transporting equipment. For trips with small additional costs, individuals who are on a different type of trip altogether, such as visiting family, can engage in the activity for relatively little additional money. Simply using full travel or trip costs to value a trip could bias welfare estimates. Accounting for the importance of different objectives within a trip can provide useful information for valuing welfare associated with site amenities or changes in these
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amenities. If visitors undertake a trip mainly for recreational activities onsite, modelers should attribute most of the trip costs to the recreation resources, while individuals who are observed to visit a recreational site during some other kind of trip should get less value. To account for multiple objectives inherent in certain types of trips, this study proposes using the proportion of time spent on each objective to identify the importance of these different objectives in a trip. The value of each trip objective is assumed to be proportional to the time visitors spend on different activities during their trips. A budget-constrained random utility model (RUM) is proposed to estimate the values of beach amenities under different assumptions about how trips are priced. Visitors are first assumed to choose trip duration and then form a set of alternative sites for multiple-objective trips. Our empirical example is developed with a dataset on visitation to 15 Lake Erie beaches (see Murray et al. 2001). Lake Erie beaches are of interest because they frequently experience adverse water quality conditions, and there are few studies examining beaches in the Great Lakes region. For the empirical example, four alternative assumptions are used to generate trip prices, and the resulting models are estimated with either nested or unnested RUM models. The results indicate, not surprisingly, substantial differences in estimates between the traditional methods of valuing trips, i.e., using full travel or trip costs, and the weighted methods. Using full trip or travel costs induces correlation across site choices for single- and multipleday beach users, suggesting that individuals can substitute across not only sites but also duration of trip. When travel or trip costs are weighted by the proportion of trip time spent on the beach, the estimated inclusive values reject the consistency of the proposed nested structure, indicating that site choices are not correlated across duration decisions. As expected, if individuals cannot substitute across trip duration, welfare measures for both types of trips are larger than under the unweighted, nested models. Simply using full travel or trip costs may seriously bias estimates of the structural utility parameters and, consequently, welfare estimates. By weighting trip costs, welfare measures avoid the downward bias from ignoring the importance of multiple-day trips, as well as the upward bias from attributing all trip costs to the specific recreation resource. 2. Modeling Single- and Multiple-Day Trips To construct a model of single and multiple day visits to Lake Erie beach sites, we begin by assuming that individuals have choices over trip duration and site. Individuals who decide to take a multiple-day trip that includes a visit to the recreational resource in question (in this case, Lake Erie beaches) spend more aggregate time and income than individuals taking single-day trips. Total trip time is time spent on traveling and time spent on different
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activities at the destination site. If a multiple-day trip is taken, the travel time and the time spent on recreational activities takes more than 1 day: tm ¼ tt þ to > ts
where to ¼
n X
toi
ð1Þ
i¼1
where tm is the time spent in a multiple-day trip which includes tt, the time spent on traveling, and to, the aggregated time spent on a number of recreation activities (n), and ts is the maximum amount of time available for individuals on a single-day trip. Not only is more time needed for a multipleday trip, but monetary expenditures are also greater: em ¼ et þ eo > es
ð2Þ
where em is the money spent in a multiple day trip which includes et, the monetary expense of traveling, and eo, the money spent on an overnight stay, and es is the maximum expense for taking a single-day trip to the same site (i.e., the out of pocket expenses associated with driving to the site). The total trip budget then determines the individuals’ decision on whether to take a single- or multiple-day trip. The trip budget can be estimated using opportunity costs of time to value the time spent traveling and the time on-site. First, travel time is estimated by dividing travel distance (d) with the speed of traveling (s) and valued by the trade-off rate of an hour of work to travel time, kt. The monetary costs of travel are estimated by multiplying the distance with the given travel expenses per mile (cd). For a round trip, the travel costs (ct) are the sum of the opportunity costs of travel time (in the first term) and the monetary travel costs (in the second term): ct ¼ kt tt þ et ¼ 2 kt d=s þ 2 cd d
ð3Þ
Longer trips cost more, and usually involve more objectives, as well as onsite costs (i.e., lodging, additional food expenses associated with eating out). To control for the fact that visitors spend different amounts of their trip time on different objectives, the objective time costs are estimated with the opportunity costs of onsite time valued as a ratio of hourly income to leisure onsite time, ko.2 Lodging costs are also included for overnight trips. Thus, onsite costs (co) contain onsite time costs (in the first term) and lodging costs (cl) (in the second term): co ¼ ko to þ eo ¼ ko
n X
toi þ cl
ð4Þ
i¼1
The sum of travel costs and onsite costs is a representative value of trip costs (denoted by c below). An individual who takes a multiple-day trip to a
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specific site should spend more than the maximum trip costs of a single-day trip (cs): ! n X toi þ cl > cs ð5Þ c ¼ ct þ co > cs ) ð2 kt d=s þ 2 cd dÞ þ ko i¼1
This inequality shows how the trip budget determines the decision of trip duration. If an individual who drives less in terms of time and distance to a site or has fewer objectives that do not cost her more than the threshold, she would take a single-day trip to this area. Otherwise, she would take a multiple-day trip. For individuals considering taking a single- or multiple-day trip, we assume that they make the following utility comparison. Visitor i chooses to take a trip of duration k to site j if her utility of this decision (mijk) is higher than of the other alternatives: mijk > milm
for l 6¼ j and m 6¼ k
ð6Þ
The utility comparison pattern is represented by a random utility model (RUM). Hanemann (1982) proposes the budget-constrained utility function for these qualitative discrete choice models. Individual i is assumed to maximize a utility function, u(xj, z) for visiting beach j with quality attributes xj and the nume´raire z with price normalized to one. The utility maximization framework is subject to the budget constraint: yi=cjk +z where yi is the income and cjk is the trip costs for k type of trip to site j. The indirect utility function conditional on this decision becomes: mijk ¼ fðyi cjk ; xj ; eijk Þ
ð7Þ
The error term (e) represents the stochastic term. To estimate the indirect utility function, a two-level decision RUM is adopted. A RUM is plausible for characterizing substitutability among alternatives, because the probability of choosing a site changes as the quality characteristics at other sites change. The two-level decision allows for substitution between single- and multiple-day trips, as well as among alternative sites. Following Shaw and Ozog (1999) and Kaoru (1995) who suggest that visitors tend to decide duration first and then location section, we assume that visitors first choose whether to take a single- or multiple-day trip, and then choose the destination among 15 alternative beach sites (Figure 1). Each site is observed to attract both single- and multiple-day visitors, and consequently, each subgroup of trip duration decisions contains all 15 alternative sites. Although some particular beaches tend to be more popular for overnight visitors and some are more attractive for a single-day trip, several alternative nesting structures explored do not provide meaningful results.3 With the assumption that the error term in the utility function follows a
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Beach Trip
Single-Day
Multiple-Day
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Beach Sites
Beach Sites
Figure 1. Two-level decision tree of beach recreation trip.
generalized extreme value (GEV) distribution, the nested multinomial logit (NMNL) model, developed by McFadden (1974), can be expressed as a probability function associated with visitors taking k type of trip to site j: J ðrk 1Þ k P mjk =rk mlk =rk ak e e l¼1 ð8aÞ Pjk ¼ J rm K m P P m =r ak e lm m m¼1
l¼1
where a ‡ 0 and 0 £ r
