Conjoint Analysis: A Preference Based Approach for the Accounting of Conservation and Tourism Benefits in Choquequirao Management

Identification of attributes and levels

Before presenting the attributes and levels, let’s see the characterization of the study area in terms of its conservation and the development of tourist activity. The Choquequirao- ANCHOQ natural area has 103,814.39 hectares, it is located on the right bank of the Apurímac River, in the geography of the Santa Teresa and Vilcabamba districts, La Convencion Province and in the Limatambo and Mollepata districts. Anta Province of the department of Cusco. It is surrounded by mountain foothills on the western slope of the Salkantay mountain range and by the Qoriwayrachina, Sacsarayoc, Choquetarpo, Huamantay and Padreyoc mountains. The area is home to the Choquequirao Archaeological Park, located at 3,100 meters above sea level, in the middle of the mountainside that bears the same name. You can observe natural spaces with a variety of life zones related to dry, montane and sub-tropical forests, where there are extraordinary successions of bioclimatic zones and in which an important biodiversity develops. The NA-CHOQ is one of the 21 Regional Conservation Areas-RCA, established as such by D.S. N° 022-2010-MINAM [15]. Below you can see at a macro and micro location of the Choquequirao natural area (Figures 1 & 2).

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Fuente: tomado de https://www.google.com/search?q=mapa+de+choquequirao+cusco&tbm=isch&tbs=rimg:CUA2J- w7zhdxIji414xHNsbec

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Figure 2: Micro-location of RCA Choquequirao. Source: SNIP Investment Bank: public investment project with code 307376 Regarding the natural heritage of the RCA CHOQ, the Master Plan 2014-2018 GRRNGMA [16], indicates that it must conserve biological corridors and genetic refreshing areas for fauna species, mainly for the “spectacled bear”, Tremarctos ornatus, as well as many birds and mammals. In this way, the continuity of ecological processes in other nearby protected natural areas such as: Machu Picchu and Ampay would be ensured. On the other hand, high threats were identified, such as forest and grassland fires, contamination by solid waste generated by tourism and external geodynamics and as medium threats the expansion of the agricultural frontier, extraction of timber species for firewood among the most important and, finally, as low threats extraction of orchids and other ornamental plants.

The situation of the species in 2014, according to the classification and categorization of threatened species of wild fauna, determined by the Ministry of Agriculture, D.S. N ° 004-2014-MINAGRI, in the case of ACR Choquequirao, they are in danger. The Andean condor and the Andean cat are considered an endangered species (EN), and the colored puma in a near threatened situation (NT), being a total of three threatened species of wild fauna mammals and one endangered bird species (Andean condor), due to hunting and destruction of their hábitats (Figure 3).

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The Andean bear or spectacled bear, widely distributed in montane forests, needs large spaces to live, which is why the ACR serves as a biological corridor between Ampay and Machupicchu. The Andean bear is in the vulnerable situation in the category of VU.

Regarding Cultural Heritage, the Choquequirao-A°P° CHOQ Archaeological Park is located within the RCA-CHOQ, which is arranged in nine areas, built as small villages around a large square where all the coming roads are located. from each area [16]. It has been possible to locate the upper square (Hanan), the warehouses (Qolqa), the main square (Huaqaypata), the lower square (Hurin), the system of cultivation platforms close to the main square, La Llacta, (Chaqra Anden), the ceremonial platform (Ushno) and the dwelling of the priests at the bottom of the hill. The Park has multiple two-story buildings with niches inside, as well as some doors and niches made with adobe jamb and irrigation channels, see figure 4, which have been progressively intervened and others are abandoned. Minimal maintenance actions can be observed (replacement plasters and original plasters have been losing stability), few archaeological studies that allow archaeological excavations to have a better study of the original architecture and filtration of rainwater that is deposited at the base of the main walls affecting the stability of the most important sectors of A° P° CHOQ.

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Figure 4: The Archaeological Park of Choquequirao, shows multiple two-story buildings with niches inside, accompanied by hydraulic systems for the use of the houses and you can see a system of cultivation platforms near the main square. FUENTE: Tomado de: https://www.google.com/search?- q=choquequirao+cusco&source=lnms&tbm=isch&sa=X&v ed=2ahUKEwiZ2f2v97zmAhWeDrkGHY_XCY8Q_AUoAXoE CBAQAw&biw=1920&bih=920#imgrc=oDJ4qwheyLIZdM The A°P° of CHOQ also has a great system of platforms, a characteristic of the Inca settlements, which helped in the agricultural use on the slopes of the hills, and which currently, to the sight of tourists, seem floors carpeted by vegetation in the area, see Figures 4 & 5.

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One of the environmental goods and services that RCA CHOQ provides is scenic beauty, the most outstanding eco- systemic service for the development of tourism activity. In this sense, it has been implemented, for more than 10 years, as part of the tourism promotion policies deployed by the State visits to A°P° CHOQ, allowing this activity to take off. Thus, between 2005 and 2010, tourist activity grew at a rate of 3.16%, and as of 2011, due to problems of poor maintenance of accesses, insufficient and inadequate public tourist infrastructure and heavy rains registered in 2012, which caused Landslides and stones on the routes that lead to A°P° CHOQ contributed to the decrease in the flow of tourists at a rate of 0.66%, according to data from the Ministry of Foreign Trade and Tourism-MINCETUR, Table No. 01. Likewise, it can be observed that the greatest influx of tourists is registered between the months of June to August, a time when the level of rainfall decreases and is almost nil.

Currently, the tourist facilities in the RCA CHOQ are precarious, inadequate signage, pedestrian access to the park in critical safety and maintenance conditions, few spaces for tourists to rest and observe the landscape, lack of information centers, minimal conditions for the installation of camping areas and little presence of personnel to monitor and control along the access routes, see figure 6. On the access routes, tourists do not have adequate furniture, such as railings, garbage cans and toilets. These services can only be found when entering the park in the sector called Sunchupata and in this place is also located the ticket office administered by the Decentralized Directorate of Culture of Cusco-DDC, an entity that is in charge of collecting the entrance fees to the park, currently it is 18 dollars for tourists in general and 9 dollars for students.

Table 1: Flow of tourists to A°P° Choquequirao: 2005-2018. Source: Own elaboration according to data from MINCETUR. http://datosturismo.mincetur.gob.pe/appdatosTurismo/Content2.html The knowledge of the RCA-CHOQ, the research on conservation and tourism issues in natural areas, consultations with researchers, different work meetings with those responsible for the administration of the area and repeated previous interviews with small samples of visitors, allowed to have elements to identify the attributes and levels of the scenarios, associated with conservation and tourist activity in the RCA-CHOQ; allowing to identify four important attributes: “no intervention”, “improvement in conservation”, “improvement in tourism” and “improvement in conservation and tourism”. The selection alternatives are defined below, which were presented to the interviewees.

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Alternative 1: current situation of natural heritage and cultural heritage and tourism infrastructure ( 1 0 c q = , 1 0 tq = ) enario in which the area administration only develops maintenance actions, does not implement programs or restoration projects in deteriorated areas, nor scientific research activities on the ecosystems of the ACR, the snow- capped mountains, the local flora and fauna. Environmental education programs or conservation work would not be installed in the peasant communities that live in the park. Likewise, the archaeological park does not register improvements in the different enclosures, cultural conservation is not implemented or the enhancement of the nine areas of the park. With regard to tourism actions, routine and periodic maintenance activities are developed for tourist accesses and routes, tourist signage is scarce and inadequate, the service of the muleteers harms the transit of tourists and they do not provide services with their own standards in natural areas. Public tourist services, such as: camping areas, tourist viewpoints, access routes, hygienic services do not guarantee adequate enjoyment or safety for tourists, solid waste management is minimal, and management documents such as the Use Tourist Plan is not implemented.

Alternative 2: situation of no improvement in tourist infrastructure and improvement in conservation ( 2 0 tq = ,

2 1 c q = ). It consists of the implementation of projects aimed at the protection and conservation of natural resources, construction of control and surveillance posts, informational signage in the RCA, improving the capacities of technical operators in the management of natural resources, developing capacities in the population, in good agricultural practices, adequate management instruments, improve the organizational and participation capacities of Local Authorities and the population in the management of natural resources around the RCA. With regard to cultural heritage, actions are being developed to consolidate the enhancement of the complex of prioritized sectors of A°P° Choquequirao, archaeological research and preventive conservation.

The interventions would require the implementation of investment projects, which to date have not yet been executed, for the amount of S/. 49’294,749.00 and 14’288,333.00 in dollars, according to data from the Investment Bank of the National Public Investment System as of Decemberth 2017, with an exchange rate of 3.3 soles per dollar.

Alternative 3: the current state of the natural and cultural heritage is maintained, while if there are improvements in public tourism infrastructure, ( 3 1 tq = , 3 0 c q = ), which consists of the implementation of projects aimed at the “ Installation, improvement and expansion of public tourist services ”, which allow to have sufficient and adequate tourist infrastructure, with safe roads (protected with retaining walls, gabions, railings), installation of adequate bridges, improvement of works of art that allow an adequate management of rainwater in the enclosures and on the roads, installation of camping areas and tourist inns with their respective hygienic services and solid waste management, installation of a site museum and tourist viewpoints and installation of the signpost informative within the framework of international standards for natural areas. These interventions are identified in each of the investment programs of the respective entities, an investment that would demand in soles 31’650,399.00 and in dollars 9’591,030.00.

Alternative 4: joint actions in conservation and tourism are developed ( 4 1 c q = , 4 1 tq = ), projects and investment programs are implemented in both conservation and tourism, which demand in soles 80’945,148.00 and in dollars 24´528,833.00.

Levels were assigned to each of the alternatives described above, these being the characteristics of the choice of the respective attributes, for example the cost, which is an attribute of the scenarios, is described in four levels ($ 0, $ 3, $ 5 and $ 8), that represent the costs of each investment policy per visitor. The interviewees selected and ordered according to their preferences, according to the attributes of improvements in tourism and/or conservation. The attributes are independent of each other, that is, there should be no correlation between them, as indicated [17], you can see the following tables that summarize the scenarios, depending on their attributes and levels, see Table 2.

Specification of the Preference Model

The research is based on the theoretical model of Random Profit to calculate the willingness to pay, using as a methodology the Joint Analysis in its version of contingent management, which is a compensatory model and is linked to models Multi-attribute and start from the assumption that the different attribute levels can be offset against each other, making possible the existence of different products with a similar overall utility for consumers. The algorithm of the Conjoint Analysis Model is represented as follows:

( ) 1k jk U f u , u =

The utility will correspond to the value that the individual attributes to a product through the combination of factors (attributes), so that this value is the maximum for the choice made within the set of options. In other words, the level of utility obtained is an appropriate combination of attributes, weighted by the relative importance of each in the contribution of the total utility of a particular good [5, 18]. The conjoint-CJA analysis allows estimating the parameters or partial utilities associated with each attribute level, taking an interest in consumer preferences.

The structure of the CJA through the contingent ordering model is analyzed using the random utility model. The utility obtained by individual i from alternative j can be represented by ij U , J j ,..., 0 = , which can be expressed as the result of the aggregation of a deterministic and a stochastic component, so that:

ij ij ij V U ε + = . (1)

Where V_ij_ is the observable part of the total utility (deterministic component) that depends on the characteristics of the options and the person interviewed and €ij is the unobservable part (stochastic or random component).

The individual will choose alternative j if and only if ik ij U U > , j k ≠ ∀ .

Then, the probability that individual i chooses alternative j can be expressed as:

( ) ( ) ( )j k V V P j k U U P j Y P ik ij ij ik ik ij i ≠ ∀ − < − = ≠ ∀ > = = , , ε ε . The model is finally subject to the assumption that the error terms are distributed independently and identically with a distribution, which is assumed for the vector of disturbance terms ( ) iJ i ε ε ,..., 0 , of the extreme value type, Gumbel distribution [19], obtaining the so-called model conditional logit, whose expression is the following McFadden [20]:

V e j Y P ij

( ) , J j ,..., 0 = , (2)

= = J i ∑ =

V e ik

0 k It is known as McFadden’s Conditional Logit Model, where the term is the deterministic component of utility ij V that is expressed as a linear function of characteristics of individual i and option j.

On the other hand, for the estimation of the contingent ordering model, the recommendations of [21] were taken into account, who showed that any random utility model can approximate any degree of precision, through a mixed logit, with the specification appropriate mix and variables used. In Munizaga [18], it is indicated that the most interesting property of the Mixed Logit Model (MMNL) is that under certain conditions of regularity any random utility model has choice probabilities that can be approximated as closely as desired, by a Mixed Logit, by allowing the MMNL to model the presence of correlation between alternatives, it is capable of raising the assumption of independence of irrelevant alternatives typical of the multinomial logit model.

Likewise, to estimate discrete choice models from data obtained by contingent ordering, the correct relationship between the choice and ordering probabilities must first be identified. If Luce’s axiom Luce [22] holds, the ranking data can be transformed into choice data. That is, the ordering of m alternatives is equivalent to a sequence of m-1 independent choice problems of the most preferred alternative. If the ( ) iJ i ε ε ,..., 0 are independent and identically distributed with a distribution of the extreme value type (Gumbel distribution), and assuming the scalar parameter equal to 1, the probability that individual i performs the ordering where alternative 1 is preferred to alternative 2, the alternative 2 is preferred to 3, and so on, it is obtained from the product of m-1 ordinary logit likelihood functions, known as “Rank- ordered logit model”:

  = ∫∏∑ = ′

′ b e e P â Ω  

x T nit n  

dâ ) , â( ö . (3)

ni njt n

1 â x t j 

 To estimate well-being, starting from the indifference condition and following the developments made by Hanemann [23], the following mathematical expression is obtained for the individual compensatory variation:

       = −                ∑ ∑ (4)

m m i vk v k ij ij j j CV ln e ln e α β = =

( ) 0 0

1 .

1 1 1 Donde:

1 â Represents the marginal utility of income Represents the indirect utility before the change (status quo)

0 ij v Represents marginal utility after change in conservation and tourism ij k v Represents the compensatory variation for going from the initial state to the change of a level of improvement and environmental quality k.

( ) 0 i k CV α Equation (4) must be estimated econometrically using a discrete choice model [24]; for estimating indirect profits. This model assumes that the option that generates the most utility for the individual receives the highest score, then takes the first place in the “order”. Therefore, the probability that an individual assigns the highest rating to an option is a function of the indirect utility that each option generates in a particular way.

Choice of Data Collection Method and Measurement Scale

Once the attributes and levels of each of the RCA-CHOQ scenarios have been defined and the utility model specified, the third part of the experiment design focuses on the choice of alternative goods that will be evaluated by the interviewed visitors. It is important to consider that various techniques have been developed in order to reduce the multiple possible alternatives between attributes and their levels and to be able to continue to infer utilities from their combinations. For the investigation, the orthogonal design was chosen, which has resulted in the selection of four alternatives out of the eight possible ones.

The conjoint designs are orthogonal because the variation of each attribute is completely independent of the variation of all the other attributes, that is, the correlations between the levels of the different chosen attributes are null. The attributes used in CJA should be chosen carefully to include only those that are the most representative, which can influence consumer preference, [1, 2, 3, 7, 25]. In this way, the interviewees were presented with four alternatives of choice, I ordered them according to the preference assigned to each one of them and then it was expressly built following an orthogonal design. See the following Table 3.

Data collection was supported by surveys applied to 179 tourists at two RCA CHOQ departure points at different times in 2017. The maximum error made in the selection of the sample was 5% and the choice of the interviewees was random.

The questionnaire had three different parts, in the first one a series of data was obtained about the visit that the tourist makes to the RCA CHOQ, their prior knowledge and their attitude towards nature, towards the conservation of cultural heritage and towards tourism activities developed. In the second part, four differentiated choice scenarios were presented at the level of their attributes, in which the respondent responded by expressing their preferences for each of the alternatives and the third part was aimed at a group of socio-economic questions, which allow characterize the selected sample.

Regarding the alternatives presented to the interviewees, the most desired, with the greatest number of times selected as a favorite is 4, which contemplates the joint implementation of public policies for both conservation and tourism, 44.4% of the respondents have chosen this option. The Alternative that follows is 2, improvement of the levels of tourism without conservation, with an approval of 33.3% of the sample. Alternative 3, improved conservation and tourism status quo with 12.8%, and alternative 1, the initial situation without interventions, is also desired by 9.5% of those interviewed.

Estimation of the Utility Funtion

For the estimation of the CJA model, equation (3) was estimated using the rank-ordered logit Beggs [12] using the MMNL, taking into account that the utility function Vij is linear in the parameters and additively separable. The attributes described in Table 2 are included as explanatory variables. The indirect demand function (this does not depend on the “quantities” of the options but on their attributes) [26] with which the model is estimated is:

( ) ( ) 1 , , , = + − + j j ij c t i ij i j ij v v q q Z W â Y p e (5)

Equation five additionally assumes the separability of residual income from the effect of the other variables that intervene in the indirect utility function. For the estimation of well-being, starting from the indifference condition and following the developments made by Hanemann [23], the compensated variation that resembles the willingness to pay was estimated using equation (4).

Equation (4) must be estimated econometrically using a discrete choice model [24]. This model assumes that the alternative that generates the most utility for the individual receives the highest score, then takes the first place in the “order”. Therefore, the probability that an individual assigns the highest rating to an alternative is a function of the indirect utility that each alternative generates in a particular way [27, 28].

If one of the attributes is the price vector pj, the change from one level to another in any of the other attributes that define the good can be evaluated in terms of compensated variation Hanemann [23] in that sense this relationship provides the marginal utility value of income; therefore the WTP for a unit increase in the levels of other attributes other than price and this result can be obtained from the expression indicated in equation (4), in which β is the coefficient of the attribute being considered.