Tourism Economics, 2008, 14 (2), 263–282

Hiking in the Alps: exploring substitution patterns of hiking destinations MARA THIENE

Dipartimento Territorio e Sistemi Agro-forestali, University of Padua, Viale dell’Università 16, 35020 Legnaro (PD), Italy. Tel: +49 8272760. Fax: +49 8272703. E-mail: [email protected]. RICCARDO SCARPA

Department of Economics, Waikato Management School, University of Waikato, Private Bag 3105, Hamilton, New Zealand. Tel: 64 7 838 48 48. Fax: +64 7 838 43 31. E-mail: [email protected]. Tourism in the Alps used to rely on a network of facilities maintained in part by the military Alpine Corps. Hiking has been growing in popularity, while the national draft is no longer compulsory. This situation calls for a renewed approach to management of the maintenance of alpine facilities. The authors explore the use of destination choice models which allow for various substitution hypotheses and highlight how single mountain sites can be substitutes for others, although located in a different geographical area. The results supply helpful information for local policy decision makers as they provide insights about the redistribution of visits following the implementation of different policy scenarios. The authors investigate such redistributions following the variation of availability to hikers in terms of alpine shelters, length of trails, site access and the application of access fees. They also estimate changes in welfare for selected variations of alpine facilities and availability of destinations. The findings highlight the sensitivity of results to the use of different specifications of demand models to guide local policy strategies. Keywords: outdoor recreation; hiking; random utility models; travel cost; substitution patterns

The Alps are a famous destination for various outdoor recreational activities. Among these, hiking is considered one of the most popular, as it is cheap, does not require complicated skills and can be performed at a variety of levels across The authors wish to thank all those who made this empirical study possible, Prof Tiziano Tempesta for support and the valuable comments of the reviewers for Tourism Economics.

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the dense network of hiking tracks that criss-cross the alpine territory. Yet, alpine hiking has been the subject of relatively little research work from the viewpoint of environmental and resource economic valuation (Romano et al, 2000; Simma et al, 2001; Scarpa et al, 2003). This paper aims to fill this gap and it focuses in particular on the issue of the correct specification of substitution patterns in destination choice modelling for the purpose of policy analysis. Information about visitor redistribution and changes of consumer surplus is a key ingredient for evaluating local policies affecting the tourist attractiveness of mountain sites. Travel cost methods have been applied to study tourism economics (ChavezComparan and Fischer, 2001; Stoeckl, 2003; Herath and Kennedy, 2004). In this study, we focus on travel cost random utility (RU) models that have been applied to numerous outdoor recreation activities (McConnell, 1992, 1995; Kling and Thompson, 1996) and used to model site choice destination for various mountain outdoor activities, such as – for example – rock climbing (Jakus and Shaw, 1996, 2003; Hanley et al, 2001, 2002; Grijalva et al, 2002; Scarpa and Thiene, 2005). RU models have been favoured because of their ability to deal with responses to qualitative changes in destinations and their ability to represent alternative patterns of substitution between destination sites (Parsons and Kealy, 1992; Morey et al, 1993; Kaoru et al, 1995). In this study, we explore the role of substitution as we find it of particular importance in the case of alpine hiking, where the individual is faced with many alternative mountain destinations. The selection of efficient management policies of hiking resources can be guided by the outcome of RU models. In this context, we illustrate RU analysis first, focusing on its conceptual advantages. Then we compare three RU models: (a) the multinomial logit, (b) the two-stage nested logit and (c) the error component (mixed logit). These three models are used to analyse destination choices of a sample of hiker members of the Italian Alpine Club (CAI) from Veneto, whose decision making is assumed to be driven by the attributes of the hiking destinations in the Veneto mountains. Econometric estimates of the RU parameters and a comparison between the three approaches are then presented. We derive and contrast relevant welfare measure estimates to illustrate the implications of differing hypotheses about substitution patterns. Finally, we forecast the effects of implementing some selected environmental policies. In doing so, we emphasize the information value provided by such models in simulating outcomes of policy scenarios. These illustrations provide useful information for policymakers who are involved in the management of mountain areas.

Random utility models A general framework In travel cost modelling, RU discrete choice models are employed to derive structural estimates of the individual probability of site selection. When the determinants of site selection are site attributes that may be impacted by policy actions, such structural estimates can be used to infer the welfare changes per

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trip occasion. Early theoretical references to RU discrete choice models were made by Thurstone (1927), while the first applied studies were in the 60s (Marshack, 1960). McFadden is credited with the complete formal derivation of the commonly employed conditional logit model from well-behaved economic preferences (McFadden, 1974) and the development of the nested logit model and the conditions of its consistency with random utility (McFadden, 1978). In these categories of models, differences in taste, as well as the partial ignorance of the researcher about the individual, are captured by an error component (or unobserved utility) distributed stochastically; hence, the term random utility model (RUM) (McFadden, 1974). A modern treatment of RUMs and their estimation can be found in Train (2003).

The conventional multinomial logit Discrete choice models based on the quality of alternatives are derived by assuming that the decision maker chooses the utility maximizing alternative from the available choice set (Thurstone, 1927; Marschak, 1960). Let n indicate the individual decision maker choosing from J alternatives. The utility n derives from alternative j is Unj, j = 1, …, J. Utility maximization implies that i is chosen if Uni > Unj, given that j ≠ i. For each respondent n, the researcher observes a destination choice yi and a vector of socio-economic characteristics sn, while for each destination j, a vector of attributes xj is observed as reputed to be of relevance in determining the perceived utility of a visit to the site. The researcher then uses these to compute a representative or indirect utility function for each destination j, denoted as Vnj = V(xni, sn) + εnj, where εnj represents the unobservable component of the overall utility of visiting such destination. The probability of selection of the ith alternative from the choice set including 1,2,3, …, J alternatives is defined on the basis of the following inequality: Pni = Pr(εnj – εni < Vni – Vnj∀j ≠ i).

(1)

Assuming that εnj is an independent identically distributed Gumbel1 variable, the probability of observing a difference among the unobservable components of utility such that alternative i is selected can be written, using the logistic cumulative formula, as: e λVni Pni = ––––– , Σj e λVnj

(2)

where the scale parameter λ remains unidentified in estimation and, hence, is often normalized to 1 and will be ignored in the following notation. In what follows, we will assume that indirect utility is linear in the parameters. Parameter estimation is commonly achieved by maximum likelihood, by assuming independence among choices. The log-likelihood function of a sample with N choices and J(n) alternatives for each individual to maximize is: N

J(n)

n=1

i

ln L(β) = Σ Σ yni ln(Prni) where yni is the indicator of observed choice.

(3)

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In many applications in the literature, the objective of the RUM analysis is the derivation of welfare measures associated with some changes in the attributes of choice. Variations of surplus due to changes of attributes in the destination set can be measured by difference from ex ante and ex post scenarios, as follows (Train, 2003): 1 

J 1



 J0



∆E(CSn) = –– ln ΣeV nj – ln ΣeV nj   , αn  j=1  j=1   1

0

(4)

where αn is the travel cost parameter (the marginal utility of income), V1 indicates the deterministic component of the indirect utility function after the proposed change and V0 that relative to the initial state. Given the assumed zero income effect (implied by linearity in income), the surplus change coincides with path-independent welfare measures, such as equivalent and compensating variations.

From generalized extreme value (GEV) models to mixed logit models Conventional conditional logit models are quite restrictive in many respects. For example, this specification implies proportional substitution patterns among alternatives. This is evident if one observes that the ratios of any two selection probability Pi /Pj = eVi/eVj is independent of the values of indirect utilities of other alternatives Vq , q ≠ i,j. This gives rise to the undesirable independence of irrelevant alternatives (IIA) property. More flexible substitution patterns can be accommodated by other specifications at an affordable computational cost. Such is the case in the family of models with unobservable error component distributed generalized extreme value (GEV). In particular, it is convenient to think in terms of correlation among alternatives2 (Bockstael et al, 1986). When correlation is zero, then the GEV returns the conditional logit model as a special case (Train, 2003). Among the GEV specifications, the most frequently employed are those of the nested logit form (Train et al, 1987; Morey et al, 1993; Lee, 1999; Karlstrom and Morey, 2004). These are particularly appealing when the destinations can be divided naturally into groups, with higher substitutability within each group than across groups. Each group can also contain subgroups, thereby creating a ‘nested’ structure, and hence the name of this specification. In nested logit, the following properties must hold: (1) For any two alternatives in the same nest, the probability ratio is independent of the attributes or existence of other alternatives. The IIA property holds within nests; that is, substitution among sites is allowed. (2) For any two alternatives in different nests, the probability ratio is dependent of the attributes or existence of alternatives in other nests; that is, the IIA property does not hold across nests, suggesting that there is no substitution among sites. The probability that alternative i is chosen given that nest Bk is selected is: Pni = PniBkPnBk ,

(5)

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eWnk+λkInk PnBk = ––––––––– , ΣKl=1eWnl+λlInl

(6)

eYni/λk PniBk = ––––––– , Σ eYnj/λk

(7)

j∈Bk

where PniBk is the conditional probability of selection of alternative i, given that nest Bk is chosen, and PnBk is the marginal probability of choice for one alternative in nest Bk.; Wnk depends on variables that describe nest k; these variables differ among nests, but do not differ among alternatives in the same nest k; Ynj depends on variables that describe alternative j; these vary within nest k. λk is the parameter of the GEV distribution and reveals which nest contains the higher correlation in unobserved factors: the nest with the lower λ has the higher correlation. Finally: Ink = ln Σ eYnj/λk . j∈Bk

(8)

The term Ink is called the inclusive value (IV) and it represents a measure of expected utility associated with a given nest. For consistency of the model with RU theory, the value of the parameter associated with the inclusive value must not be outside the interval 0–1 (McFadden, 1978; Borsch-Supan, 1990), as discussed in depth in the literature (Herriges and Kling, 1995). Hence, we obtain: I1nk – I0nk

∆E(CSn) = ––––––– . αn

(9)

In empirical applications concerning outdoor recreation, we do not find studies with more than three stages (Morey et al, 1993), while two-level nested logit models are quite common (Hausman et al, 1995; Kling and Thompson, 1996). Mixed logit models (MXL) are more flexible than nested logit models because they may allow for unrestricted substitution patterns, correlation in unobserved factors over time and random taste variation. Choice probabilities are the integral of standard logit models over a density of parameters (Train, 2003):  eβ′xni  Pni = ∫ ––––– f(β)dβ .  Σjeβ′xnj 

(10)

The mixed logit probability is a weighted average of the logit formula evaluated at different values of β, with the weights given by density f(β). That is, the β vector of coefficients of variables is assumed to vary randomly over decision makers in the population, representing individual taste variation or additional error components. The density function, which can take different specifications (i.e. normal, uniform, triangular) will be described by a mean b and a covariance

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W, although, for error components, the mean is assumed to be zero. Such models are estimated by simulation by averaging a large number of probabilities computed at random draws. When a mixed logit model is specified as an error component model (EC), it allows one to account for correlations among utilities for different alternatives (Train, 2003). In these models, utility is specified as: Uni = α′xnj + ηnj = α′xnj + µn′ znj + εnj ,

(11)

where xnj and znj are vectors of observed variables relating to alternatives j; α is a vector of fixed coefficients; µ is a vector of random terms with zero mean; and εnj is distributed iid extreme value. The terms in znj are error components, defined along with εnj, representing the stochastic portion of utility. Hence, this unobserved portion of utility can be correlated over alternatives: Cov(ηni,ηnj) = E[(µn′ zni + εni)(µn′ znj + εnj)] = zni′ Wznj ,

(12)

where W is the covariance of µn. Depending on the choice of variables to enter as error components, various correlation patterns and substitution patterns can be determined. Crucially for this application, EC models may be specified so as to allow the utility from one destination to be correlated simultaneously with those of other destinations belonging to more than one nest. This issue is of obvious importance in the context of the north-eastern Alps because it is clear that some mountain destinations may be perceived as substitutes for many other sites outside a specific nest. Belonging to a given substitution set becomes a testable hypothesis. The destinations with correlated utility can be modelled as sharing an error component. This is just a normally distributed random variable with zero mean. In estimation, such correlation will be revealed by a significant estimate of the standard deviation of such error component. The test is based on the null that the error component (and hence the correlation) is not there. Hence, the implied restriction is for the standard deviation to be equal to zero, which is a value at the boundary of the admissible range for a standard deviation (range is the positive orthant). As a consequence, for restrictions at the boundary of the range, the typical test statistics have an undefined distribution and other information criteria can be used for model selection (Akaike, Bayesian). However, when the improvement on the log-likelihood value at a maximum is substantial, and considering that most fitting criteria are derived from such value, it is safe to assume that the null is rejected.

The data The sampling frame is based on the Veneto chapter of CAI members because a great number of the Veneto hikers belong to the CAI.3 This membership is quite popular across regular mountain users as the club provides a great deal of locally relevant services, such as training courses, activity maps, guides, rescue services, etc. The data for our study were collected with a survey from a sample of 904 excursionist members of the local chapter of the CAI, who

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Table 1. Descriptive statistics of excursions per head by destination. Mountain groups

Mean

St dev

Median

90th percentile

Visitors

1. Vette Feltrine. M. Sole 2. P. Dolomiti Pasubio 3. Cansiglio–Alpago 4. Altipiano Asiago 5. M. Grappa 6. Lessino–M. Baldo 7. Antelao 8. Pelmo 9. Tofane–Cristallo 10. Duranno–Cima Preti 11. Sorapiss 12. Agner–Pale San Lucano 13. Tamer–S. Sebastiano 14. Marmarole 15. Tre Cime–Cadini 16. Civetta–Moiazza 17. Pale di S. Martino 18. Marmolada

2.59 4.91 2.18 3.64 2.7 5.03 1.39 1.35 1.86 1.45 1.35 1.31 1.64 1.7 1.8 1.86 2.05 1.61

3.53 5.64 3.02 4.22 2.99 8.68 0.94 0.69 1.42 0.72 0.82 0.72 1.06 1.66 1.29 1.7 1.63 1.22

2 3 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1

5 11 4 10 5 13 2 2 3 2 2 2 3 3 3 3 4 3

304 421 197 418 321 255 178 186 130 31 100 89 127 104 396 322 299 154

reported on their mountain visits for the year 1999. The total number of trips reported to each destination (10,391)4 and some descriptive statistics are listed in Table 1. The interviewer would meet the CAI members at club meetings taking place in the municipalities of the Veneto region. Since Veneto is a region located in the north-east of Italy, with plains, hills and mountains, the sampling method ensured that people living in all parts of the region were recruited into the sample. Typically, various parts of the questionnaire were explained to a group of respondents and then each member of the group would fill out the questionnaire on their own. Respondents were asked questions about their mountain abilities and experience (that is, how long they had been going to the mountains) and whether they attended mountaineering training courses. They were also asked whether they climbed regularly on cliffs and indoor climbing walls and if they practised other activities like ski-mountaineering. They were also asked the total number of excursions to each of the 18 sites in the past 12 months. Finally, they provided socio-economic information about their households. Round-trip distance from own residence to each of the destinations in the choice set was calculated using the software package ‘Strade d’Italia e d’Europa’. These data were used to estimate the individual travel cost for each trip. Distance costs were converted into monetary values using a figure of €0.35 per km, which was the fuel cost at the time. We assumed that each reported trip was a ‘one day out’ trip, as customary for this form of local outdoor recreation. In Italy, there usually is no cost attributed to travel time, mainly because the opportunity to produce extra income during spare time is very limited. The 18 mountain destinations differ substantially, from both a morphological and mountaineering point of view, but they can provide non-specialist outdoor

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recreation and so are all destinations for local excursionists. Two broad, geographically determined groups can be distinguished. Destinations 1–6 (Table 1) belong to the pre-Alps, which are mountains with gentler slopes and lower peaks separating the plain from the proper Alps. Because of their closeness to the main urban centres and the presence of relatively high hiking difficulty, even though the length of the paths is limited, the pre-Alps are the final destination of many local excursions. Destinations 7–18 are in the north-eastern Alps, in the mountain chain of the Dolomites, which is an extended rocky area made mostly of dolomite rocks. This rare and distinguished rock type is geologically well defined as it originates from coral reefs. Mountains made of this rock are scenically quite attractive as they tend to show orange-pink reflections at sunset. This creates the dramatic colouring of the landscape for which the Dolomites are well known worldwide.

Empirical analysis Estimated models Because of its ability to accommodate flexible substitution patterns, the nested logit model is suitable to model destination choices by hikers across the 18 major alpine destinations. The use of the nested logit model allowed us to model the recreational behaviour of the sample by decomposing the decision making in two sequential stages and by including as explanatory variables the attributes of the single destinations. Two separate substitutability hypotheses across sites have been examined. The first nesting hypothesis (NL1) divides the destinations into two sets, on the basis of their degree of wilderness. In this hypothesis, the hiker first would decide whether to visit wild and large sites or less wild and more ‘friendly’ (easier to hike) sites. In the former set, hikes are generally longer and in a harsher alpine environment. Once this decision between degree of wilderness has been made, then he or she would decide which destination to visit within each of these two sets. The second nesting hypothesis (NL2) considers substitutability to be a function of both geographical proximity and hike difficulty. Destinations that are closer to the place of residence and show mainly easy hikes are more substitutable between themselves than those that are further apart or contain a more challenging environment. In this hypothesis, a hiker first would decide whether to visit closer sites in the pre-Alps, or more distant ones in the Dolomites. Then he or she would decide which destination to visit within each of these two sets, on the basis of the recreational attributes. We illustrate the nesting associated with each of the two hypotheses in Figure 1. Each hypothesis warrants a different selection of destination attributes and is tested empirically using the conditional logit model as a baseline. Finally, we investigate more in-depth substitution patterns of mountain sites by using EC models, which are more flexible mixed logit specifications that allow the situation in which one or more destinations may belong to more than one substitution set simultaneously. By an adequate use of error components, one can create a correlation pattern across utilities of alternative sites similar to the one implicit in both models NL1 and NL2. The innovative aspect, which

Exploring substitution patterns of hiking destinations MODEL 1 Hikes in wild and wide sites I Nest

271

Hikes in more friendly sites

II Nest Marmolada Tre Cime Civetta

Vette Feltrine Piccole Dolomiti Consiglio–Alpago Grappa Lessini Baldo Antelao Pelmo Tofane

MODEL 2 I Nest Moderate to difficult hikes in close and far sites

Duranno C. Preti Sorapiss Agner Tamer Marmarole Pale S. Martino Asiago

Easy hikes in close sites

II Nest Pelmo Tofane Marmolada Antelao Tre Cime Civetta Vette Feltrine

Duranno C. Preti Sorapiss Agner Tamer Maramarole Pale S. Martino Piccole Dolomiti

Cansiglio–Alpago Grappa Lessini Baldo Asiago

Figure 1. Nesting of Model 1 (‘wilderness of sites’) and Model 2 (‘proximity and difficulty of hikes’).

cannot be modelled by nested logit, is the presence of both error components in the utility of Piccole Dolomiti–Pasubio, because this destination shares features in common to both groups under the nesting hypothesis NL1. With this in mind, a first set of mountain sites – the ‘wilder sites’ – share a common error component and include: Marmolada, Tre Cime, Civetta and Piccole Dolomiti–Pasubio. The other set – the ‘friendlier sites’ – includes the remaining 14 mountains, and again Piccole Dolomiti–Pasubio, and they share a second error component.

Results In Table 2, we present the estimated coefficients for the following models: conditional logit (MNL), nested logit under the two nesting hypotheses (NL1 and NL2)5 and the EC model. Nested logit estimates always dominate statistically, in terms of log likelihood, the respective conditional logit, but show an estimate for the inclusive value parameters coherent with random

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Table 2. Maximum likelihood estimates. MNL1 and NL1 ‘wilderness of sites’; MNL2 and NL2 ‘geographical proximity and difficulty of hikes’ and EC. Variables MNL1

MNL2 –0.1369 (0.0019) 0.0003 (0.0000) 0.0554 (0.0017) –

VEGETA

–0.1378 (0.0021) 0.0004 (0.0000) 0.0474 (0.0020) 0.0264 (0.0005) 0.0001 (0.0000) –0.0112 (0.0304) –

STORIA

–

COST SENTK RIFU FERR BOS_C PEND

Log likelihood Inclusive value

–24,572.09

Inclusive value EC Wild sites (st d) EC friendly sites (st d)

– – 0.1400 (0.0249) 0.1161 (0.0172) –24,583.89

Models NL1 –0.1622 (0.0025) 0.0003 (0.0001) 0.0326 (0.0021) 0.0557 (0.0037) 0.0001 (0.0000) –0.0309 (0.0033) –

–24,291.53 0.8168♠ (0.0346) 0.5701♦ (0.0191)

NL2

EC

–0.1565 (0.0022) 0.0001 (0.0000) 0.0545 (0.0017) –

–0.1675 (0.0026) –0.0001 (0.0000) 0.0327 (0.0022) 0.0497 (0.0038) –0.0001 (0.0000) –0.0525 (0.0034)

– – 0.1858 (0.0251) 0.3002 (0.0203) –24,402.89 0.9050* (0.0540) 1.1511♣ (0.0531)

–23,849.18

4.1185 (0.1581) 0.3768 (0.0365)

Note: Standard errors in brackets. Legend: COST = travel cost (€); SENTK = paths (km); RIFU = alpine shelters (number); FERR = challenging vie ferrate (number); BOS_C = area covered by conifers woods (ha); PEND = average steepness of sites (degree); VEGETA = presence of wild flowers (dummy); STORIA = presence of First World War historic items (dummy); * inclusive value easy hikes in close sites; ♣ inclusive value moderate to difficult hikes in close and far sites; ♦ inclusive value wild and wide sites; ♠ inclusive value more ‘friendly’ sites; EC wild sites = standard deviation of error component in wild sites (Marmolada, Tre Cime, Civetta and Piccole Dolomiti–Pasubio); EC friendly sites = standard deviation of error component in friendly sites (remaining 14 sites and Piccole Dolomiti–Pasubio).

utility theory in NL1 only. We conclude that the sample at hand provides evidence against the nesting hypothesis NL2; in other words, visitors do not seem to decide their destinations on the basis of geographical proximity. The EC model performs statistically much better than the others since it shows a gain of more than 700 points in terms of log-likelihood value. The estimated standard deviation associated with error component of ‘wild sites’ is much higher than the one with EC of ‘friendly sites’, and both estimates are statistically significant. Hence, results show a strong correlation among utilities of wilder and large mountains. Piccole Dolomiti–Pasubio, a pre-Alps site, turns out to be a good substitute for all the sites, recalling its particular attitudes

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and geographical peculiarities which allow an outdoor activity similar to that which can be practised in the more famous and much larger Dolomites. In all models, the single coefficient estimates are statistically significant and show prevalently expected signs in the MNL and NL models. In these models, the choice probability is influenced positively by a dense network of marked trails (SENTK) and the presence of alpine shelters (RIFU). This is consistent with appreciation of recreational facilities that allow hikers to reach their destinations with ease and that offer them protection should there be a sudden weather change. The presence of conifer forests (BOS_C) is positive, while hikers seem to prefer paths that are not excessively steep (PEND). Some hikers also seem to appreciate more challenging trails, such as ‘ferrate’ (FERR), which are technically difficult trails equipped with a wire rope that allows hikers to reach the top of the mountain without necessarily climbing. The strong significance of the inclusive value parameter estimate, along with the observed improvement in the log-likelihood value at a maximum, indicate that this hypothesis is consistent with the data. The second nested logit model, which implements the hypothesis that destination choices take place on the basis of geographical proximity and difficulty of hikes, shows a slightly different structure in the indirect utility estimates. Hikers seem to appreciate sites with attributes such as wild flowers (VEGETA) and the presence of historic items from the First World War (STORIA). The error component model shows parameter estimates that have some unexpected signs for the extension of the network of trails and for the area covered in woodland.

Elasticity estimates The effects of small changes in the attributes of one destination on the selection probability of this destination (own elasticity) or any other destination (cross elasticities) are important quantities in the evaluation of the predictive performance of the model, especially in capturing the effects of substitution patterns. In RUMs, these quantities are a complex non-linear function of parameter estimates (Herriges and Phaneuf, 2002). We focused on the effect of changing alpine shelters and on extending the network of trails, not only because we believed these two attributes to be important in site selection, but also because such variables could be affected directly by management policies on the side of the local authorities in charge. In Table 3, we report own elasticity and cross elasticity estimates (the variation in the relative selection probability of one site following the relative change of value of an attribute at another site) for all models so as to evaluate their plausibility. Let us consider the effect of an increase in alpine shelters. The destination site enjoying the highest own effect is Tofane (MNL = 1.186 and NL = 0.817). This is justified, as this destination is located in an area with an intense flow of visitors all year round (Da Pozzo et al, 2003). The destination instead that would induce the highest response from other sites is Asiago, according to MNL1, and Marmolada, according to NL1, the latter with an effect of –0.143 at the own nest and of –0.02 at the cross nest. We note that there is more effect on the sites of Civetta and Marmolada, which are located in the same nest (shaded area), as they are closer substitutes and have more challenging hikes

Note:

0.363 0.186 1.186 0.411 0.833 0.870 0.203 0.829 0.375 0.375 0.094 0.794 0.590 0.281 0.417 0.824 1.100 0.421

–0.065 –0.004 –0.048 –0.016 –0.069 –0.127 –0.035 –0.120 –0.005 –0.005 –0.001 –0.061 –0.027 –0.004 –0.010 –0.030 –0.039 –0.006

Tinted entries belong to one nest.

Piccole Dolomiti Pelmo Tofane Consiglio–Alpago Pale S. Martino Asiago Grappa Baldo–Lessini Marmarole Sorapiss Duranno Vette Feltrine Tamer Antelao Agner Civetta Marmolada Tre Cime

0.251 0.128 0.817 0.280 0.570 0.595 0.136 0.578 0.257 0.258 0.064 0.546 0.409 0.193 0.287 0.447 0.639 0.268

–0.042 –0.002 –0.029 –0.013 –0.048 –0.089 –0.027 –0.073 –0.003 –0.003 –0.001 –0.040 –0.014 –0.002 –0.006 –0.139 –0.143 –0.025

–0.034 –0.002 –0.023 –0.010 –0.038 –0.071 –0.021 –0.058 –0.002 –0.002 –0.001 –0.032 –0.011 –0.002 –0.005 –0.021 –0.020 –0.004

Elasticities to alpine shelters MNL NL Own % Variation Own % Variation elasticity induced elasticity induced to in other own other sites nest nest 1.157 0.637 0.585 0.257 0.373 0.332 0.902 0.678 0.297 0.417 0.214 0.322 0.487 0.210 0.479 0.490 0.870 0.607

–0.206 –0.013 –0.024 –0.010 –0.031 –0.048 –0.155 –0.098 –0.004 –0.005 –0.003 –0.025 –0.022 –0.003 –0.012 –0.018 –0.031 –0.009

0.983 0.537 0.495 0.215 0.313 0.279 0.745 0.580 0.251 0.351 0.180 0.272 0.414 0.177 0.405 0.326 0.620 0.474

–0.165 –0.010 –0.018 –0.010 –0.027 –0.042 –0.146 –0.073 –0.003 –0.004 –0.002 –0.020 –0.014 –0.002 –0.008 –0.101 –0.139 –0.044

–0.133 –0.008 –0.014 –0.008 –0.021 –0.043 –0.116 –0.058 –0.002 –0.003 –0.002 –0.016 –0.012 –0.002 –0.006 –0.015 –0.020 –0.007

Elasticities to extension of trails MNL NL Own % Variation Own % Variation elasticity induced elasticity induced to in other own other sites nest nest

Table 3. Elasticity to alpine shelters and to extension of trails hypothesis ‘wilderness of sites’.

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than the other sites. A similar set of considerations can be made for the elasticity to the extension of the network of trails. The two pre-Alps sites, Piccole Dolomiti–Pasubio and Monte Grappa, show the largest own elasticity and cross elasticities. These are both very frequently visited (Tempesta and Thiene, 2004) because they are within easy reach of urban centres. Interestingly, the NL1 model (‘wilderness of sites’) also shows a strong response in the probability of visit of sites in the cross nest.

Policy scenarios for simulations Despite the observed improvement in the log-likelihood value, the EC estimates of coefficients for some key variables have different signs from those obtained with MNL and NL models. The length of trails and the presence of conifer woods are expected to influence the probability of selecting a given mountain site for a recreational visit. In fact, both variables show a positive sign in both specification estimates. Hence, we considered EC estimates to be less consistent with our theoretical expectations and, for the purpose of illustrating the policy simulations, we decided to restrict ourselves to the use of MNL and NL models. The maintenance of facilities for alpine recreation can be very costly and user fees are often advocated as a way of fund-raising. It is therefore instructive to examine the implications in terms of probability of selection of other sites for policies increasing the travel cost to a given site by a given amount of user fee. In the first two columns of Table 4, we report the probabilities for a 50% cost increase at two sites (Tamer and Civetta), chosen because of their location in the pre-Alps and Dolomites, respectively. Under the hypothesis of ‘wilderness of sites’, a 50% increase in travel cost is predicted to reduce by 2% the own probability of visit, with a redistribution which favours first Grappa and Asiago (0.36% and 0.25%, respectively) and Piccole Dolomiti and Baldo–Lessini as pre-Alps sites. This is followed by Pale (0.17) and Civetta (0.11), as Dolomites sites. When, instead, the same cost increase is brought about at Civetta, the decrease in probability of selection is twice as strong (4.13%), with a redistribution that favours other sites in the Dolomites, such as Marmolada (1.02%) and Tre Cime (0.58%) and then some sites closer to the plain, such as Grappa and Asiago. It should be emphasized that this substitution pattern is quite realistic. In fact, Tamer, despite belonging to the Dolomites, is not particularly attractive as compared to the other famous Dolomites sites; therefore, it is plausible that visitors facing increasing cost would choose pre-Alps sites first. In the second case, a cost increase at Civetta would switch the probability of selection towards other similar sites instead, since this is one of the most famous mountain sites of the Dolomites. Marmolada and Tre Cime, both famous areas of the Dolomites, represent a plausible cheaper substitute than others in the case of cost increase. In the second two columns of Table 4, we report the results of a simulation elaborated under the assumption that alpine shelters are reduced by 20%. A decrease of shelters can be very problematic for hikers, especially in the case of sudden weather changes, which is a frequent event in alpine sites. On the other hand, alpine shelters are, in some areas, very numerous and it might be of some interest to explore the impact of their decrease on the choice probability of site selection, which produces results similar to those described

Vette Feltrine Piccole Dolomiti–P. Consiglio–Alpago Asiago Grappa Baldo–Lessini Antelao Pelmo Tofane Duranno Sorapiss Agner Tamer Marmarole Tre Cime Civetta Pale S. Martino Marmolada

0.169 0.230 0.121 0.253 0.358 0.176 0.030 0.044 0.081 0.028 0.026 0.046 –2.000 0.029 0.048 0.117 0.173 0.072

0.220 0.342 0.157 0.354 0.486 0.264 0.038 0.055 0.102 0.035 0.033 0.060 0.106 0.036 0.588 –4.132 0.231 1.025

0.174 0.202 0.123 0.237 0.333 0.149 0.032 0.047 0.088 0.030 0.028 0.052 –1.944 0.031 0.048 0.121 0.176 0.072

0.226 0.309 0.161 0.334 0.455 0.233 0.042 0.062 0.116 0.039 0.038 0.067 0.112 0.041 0.581 –4.033 0.231 0.985

Hypothetical scenarios nesting strategy ‘wilderness of sites’ Increase travel cost Decrease alpine shelters by 50% by 20% Tamer Civetta Tamer Civetta

Table 4. Percentage changes in the probability of selection.

0.073 0.064 0.061 0.087 0.119 0.058 –0.783 0.023 0.044 0.014 0.010 0.024 0.047 0.047 0.012 0.019 0.065 0.028

0.283 0.236 0.236 0.318 0.426 0.218 0.068 0.113 –2.971 0.064 0.048 0.100 0.183 0.060 0.102 0.143 0.243 0.131

0.061 0.042 0.050 0.061 0.083 0.037 –0.670 0.029 0.057 0.016 0.013 0.023 0.040 0.016 0.027 0.033 0.051 0.032

0.373 0.263 0.310 0.371 0.497 0.240 0.121 0.202 –4.046 0.102 0.092 0.146 0.248 0.109 0.208 0.218 0.309 0.234

Hypothetical scenarios nesting strategy ‘geographical proximity and difficulty of hikes’ Increase travel cost Decrease alpine shelters by 50% by 20% Antelao Tofane Antelao Tofane

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before in terms of redistribution. When the estimates obtained under the hypothesis of ‘geographical proximity and difficulty of hikes’ are used to evaluate the consequences of a 20% decrease in alpine shelters, it is interesting how the predicted redistribution is also quite plausible. The destination site Tofane, another famous Dolomites site, is predicted to undergo a decrease by 4.04%, with a redistribution directed to both the pre-Alps and the Dolomites.

Welfare measure estimates from select policies Table 5 reports the point estimates of the expected changes in surplus over the entire summer period, referred to the whole sample, the single visitor and per choice opportunity. In the table, we report these estimates for a number of policies that could be coded by changes in the attribute values. The same policies were evaluated with the nested logit and the conditional logit models for both nesting hypotheses. The simulated policies involve changes in the availability of mountain facilities such as alpine shelters, site closure for conservation purposes, closure of the most challenging vie ferrate and, finally, extension of the network of trails. These policies are implemented at either all or selected sites, the latter to allow for comparison of impact among different areas. Estimated welfare changes are quite different across the two hypotheses when the NL models are employed, while they are similar when the MNL models are employed. The study of how these estimates and their plausibility vary across specifications allows one to evaluate the two contrasting substitutability hypotheses. We first focused on the increase of alpine shelters in all sites, which gave an average consumer surplus (CS) in the sample of €8.14 per visitor. We noticed that there was more variability captured by nested logit models, in particular by the one specified on the basis of geographical proximity and difficulty of hikes (NL2). We then moved to evaluate the loss in welfare due to the entire closure of all alpine shelters at selected destinations (Marmolada, Tofane, Piccole Dolomiti). The presence of alpine shelter is very important in destinations where hiking can be more risky because of exposure to sudden weather changes. The welfare loss differed depending on the site and again NL2 provided higher values. Site closure to hiking sometimes can be the consequence of environmental policies aimed at conservation. We explored the welfare consequences of site closures in our model to evaluate further the substitutability hypotheses. We simulated the closure of one pre-Alps destination (Piccole Dolomiti) and two Dolomites destinations (Civetta and Tofane). In each nest, we selected destinations with a high number of good hiking trails because we wanted to see whether the predicted welfare estimates were sufficiently and plausibly high, as one would expect in this case. We hypothesized that, although Piccole Dolomiti belonged to the pre-Alps, hikers might prefer it compared not only to the other pre-Alpine destinations, but also to the Dolomites because of its proximity to the plain. While all models supported welfare estimates consistent with our expectations, we observed how sensitivity was highest in NL2. Despite its utility inconsistent estimate for the inclusive value, this model seemed to capture reality best, as it predicted a much higher estimate (€38 per visitor) for the closure of hikes in Piccole Dolomiti.

One more alpine shelter in all destinations Closure of all alpine shelters in Marmolada Closure of all alpine shelters in Tofane Closure of all alpine shelters in Piccole D. No more hikes at Piccole Dolomiti No more hikes at Civetta No more hikes at Tofane Closure vie ferrate in Tofane Closure vie ferrate in Pale S. Martino 2% increase of trails in all sites 5% increase of trails in all sites 2,395.60 5,993.52

1,082.37

2,712.89

–12,925.40 –16,371.44 –3,070.19 –6,427.44

–6,807.12

–2,754.24 –3,1169.92

–1,467.26

–12,231.54 –2,946.88

–7,114.48

–4,121.19

–3,552.72

–2,664.30

–3,579.84

–2,147.07

–973.04

–4,455.67

–6,056.80

–1,785.51

1,980.45

790.73

–2,226.43

–2,201.06

6,454.56

4,208.48

CS for the sample NL1 MNL2

3,578.49

MNL1

4,248.80

1,699.52

–14,048.16 –27,734.72

–35,192.72

–12,891.04

–10,920.32

–7,448.96

20,195.36

NL2

3.00

1.19

–1.62

–1.08

–14.29 –3.39

–3.05

–4.56

–2.37

–1.97

3.95

MNL1

–2.95

–4.93

–2.46

–2.43

4.65

6.63

2.65

–7.53

–3.93

2.19

0.87

–18.11 –13.53 –7.11 –3.26

–34.48

–7.87

–3.96

–6.70

7.14

CS per visitor NL1 MNL2

4.70

1.88

–15.54 –30.68

–38.93

–14.26

–12.08

–8.24

22.34

NL2

0.26

0.10

–0.14

–0.09

–1.24 –0.29

–0.26

–0.39

–0.21

–0.17

0.34

MNL1

0.58

0.23

–0.65

–0.34

–1.57 –0.62

–3.00

–0.68

–0.34

–0.58

0.62

0.19

0.76

–1.18 –0.28

–0.26

–0.43

–0.21

–0.21

0.40

CS per choice NL1 MNL2

0.41

0.16

–1.35 –2.68

–3.39

–1.24

–1.05

–0.72

1.94

NL2

Table 5. Comparing welfare change estimates (in €). MNL1 and NL1 ‘wilderness of sites’; MNL2 and NL2 ‘geographical proximity and difficulty of hikes’.

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To complete the evaluation of the models, we also computed the implied welfare changes for the closure of the most challenging vie ferrate at some selected destinations (Tofane and Pale di S. Martino) and a 2% and 5% extension of the network of trails at all sites. The loss of welfare for vie ferrate in Pale di S. Martino was twice as large as that in Tofane, indicating the vie ferrate are probably more appealing. Finally, extending the network of trails is assessed as producing a welfare gain of about €2–6.5 per visitor consistently across all models. The fact that welfare estimates obtained with the MNL and NL models are different is quite relevant, because it underlines the importance of taking into account different specifications. Generally, conventional logit models seem to underestimate the changes in welfare measures, whereas nested logit models turn out to be more accurate.

Conclusions There is a well-recognized need for economic information to manage natural resources efficiently. The availability of information linked directly to the economic effects of attribute changes in natural resource-based activities is important in the context of public decision making. From this study, it clearly emerges that the increasing demand for hiking is connected directly to the nuances of each destination and its recreationally relevant attributes. Hence, random utility models represent an appealing tool to address demand analysis when this is dependent on the attributes of the destination site. In this case, we have modelled the probability of choice of destination by visitors to the 18 main alpine destinations in Veneto (Italy) using an approach that allows for more flexible substitution patterns among sites than the conventional multinomial logit model. Such an approach produces better quality and more realistic implications of visitor behaviour. In the comparison between the two implemented hypotheses, the implied predictions seem to support the nesting according to the ‘geographical proximity and difficulty of hikes’ rather than the alternative nesting hypothesis according to ‘wilderness of the sites’. However, the statistical fit demonstrated by the error component model suggests that the real substitution pattern may include sites which belong to more than one substitution set simultaneously. Yet, the parameter estimates of this betterfitting model show unexpected signs. The jury is still out on what represents an adequate substitution pattern in these alpine destinations; however, the modelling methods employed here seem suitable to resolve this issue, which may well require more adequate data collection for more conclusive evidence in favour or against any of the competing hypotheses. Despite the inevitable uncertainty with respect to model specification, it seems appropriate to highlight the policy implications of these forecasts. Many of the investigated mountain sites belong to protected areas at regional or national level and land managers are usually very interested in obtaining information on how visitors might value changes in management. One of the typical problems that policymakers face is the need for closure of selected areas to protect endangered wildlife. It is difficult to understand what will be the impact of such policies on tourism flow and how visitors will value it. Tools

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providing information about the loss of welfare due to such closures can be very useful. Alpine huts in mountain sites are often highly valued by hikers because of the facilities and services they can offer, but they also play a leading role in channelling hiker flow and thereby inducing trail congestion. Hence, one of the possible strategies to decrease congestion would be the closure of some alpine huts. On the other hand, an increase in the network of trails could be a useful tool for land managers, both to increase visitors and channel them towards selected areas. Policymakers who are involved in the management of protected, or even environmentally sensitive, areas need information about visitation demand. That is, they look for data predicting how a certain policy would change the visit flow and its redistribution to selected sites and the magnitude of welfare estimates that visitors attribute to a specific modification. Finally, we note that model specification seems to be more relevant for consumer surplus, while price elasticity estimates are relatively robust across models, the implication being that further research should focus on better methods to distinguish across-model specifications in empirical applications when these are carried out to derive recommendations predicated on estimates of welfare changes. Endnotes 1. The Gumbel distribution is also known as extreme value type I. 2. Consider, for example, the choice of destination among the following: sea, lake, mountains and hills. It is apparent that in this choice context, the substitutability between sea and lake is quite different than that between lake and hills. The nested logit model can capture this type of difference in substitution. 3. Tempesta and Thiene (2004) highlighted that about 25% of the excursions in the studied area were completed by CAI members. 4. 10,391 is the total number of visits to all 18 sites of the sample; instead, the table reports the total visitors to each site. 5. Models have been estimated by using NLOGIT3 and GAUSS software.

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