Using Contingent Valuation to Estimate Prices for Non-Market AmenitiesProvided by Protected Areas

Marcos Adamson-Badilla and Federico Castillo1,2

Abstract

This article uses a Contingent Valuation Method (CVM) in its closed-ended format in order toestimate willingness-to-pay (WTP) for an entrance fee to the Manuel Antonio National Park(MANP) in Costa Rica. MANP is one the two most visited protected areas in the country. Incontrast to other articles, which estimate WTP (median) by following a single boundedapproach, and which in most of cases use only one ad-hoc model, this paper shows alternativemeasures of WTP (mean and median) following a double bounded approach. The estimationsare made using a sample of 2245 park visitors and four models: three of them consistent withindirect utility functions, and an ad-hoc model which has been widely used in the contingentvaluation literature. Because the answer to the second bid is endogenous a bivariate probitmodel is used in the four models estimated.

The econometric estimation of the compensating surplus derived by both nationals andforeigners when entering the park shows a low level of sensibility to model specification and tothe estimated WTP (mean or median). WTP is estimated at approximately $12 for foreignersand $5 for nationals. The estimation of WTP in the four models is not sensitive to specificnationality of foreigners. The estimated correlation of answers and their significance changeswith the estimated model. Furthermore, the goodness of fit tests (χ2) are statisticallysignificant. This paper shows that CVM can be used to design policies that improve pricingschemes for protected areas, and that such pricing schemes can lead to a more sustainablemanagement and financial stability resulting in welfare improvement for society.

JEL: Q26

Key words: Contingent valuation, bivariate probit, compensating surplus, double-bounded.

1 Marcos Adamson: Researcher and Professor Faculty of Economics, University of Costa Rica.Federico Castillo: Post Doctoral Fellow, Department of Environmental Science, Policy and Management.University of California, Berkeley.2 Research was funded by the Costa Rica-Holland Bilateral Agreement for Sustainable Development (CBDS;project #75-P-96). We would like to thank members of the Faculty of Economics, University of Costa Ricafor their comments. All remaining errors are responsibility of the authors.

2

I. Introduction

National Parks offer a wide variety of services to society. They are reserves of biodiversity,perform hydric and climatic regulation functions, protect soil quality, etc. Recently, tropicalcountries as Costa Rica are receiving important economic benefits coming from tourism, asresult of an important investment in conservation of natural resources through NationalParks and other kinds of conservation. This country has invested an important amount ofresources in conservation that has permitted to keep more than 25% of its territory underprotection (Adamson, 1994). This tourism is particularly intensive in amenities which theseconservation areas provide.3

In spite of profits those protected areas provide, incapacity to capture profits derived fromgoods and services provided by them is threatening their existence and development.4 Twofactors explain this paradox. First, most of services provided are not directly traded in amarket but they appear to be positive external effects, then, administration of those areas isnot able to appropriate directly over those benefits. This case includes local and globalexternal effects; some of them are pecuniary; for example, as perceived by nearer tourism;and other no pecuniary. In the second case, in spite of those services could trade in markets,like direct entrance to parks, most of these areas depends on collected fees given by thegovernment, independently of supply conditions --costs of each area-- and demandconditions --visitors willingness to pay.

The entrance fee to National Parks is one of the collect instruments --price-- for one of theservices that is nearer to market. As there are limitations to capture profits, entrance feeshould be administrated in an efficient way, looking to maximize received income.

An alternative to achieve this objective is to design a strategy of collecting that extractsconsumer's surplus. In those cases, is important to determine economic valuation derivedby consumers from enjoying tourism. This paper shows the way to apply ContingentValuation Method (CVM) in a close ended format (referendum) of two questions withdiscrete response, in order to estimate compensated surplus (Hanemman, 1984 y Freeman,1993), or willingness to pay (WTP) to get in Costa Rica's Manuel Antonio National Park(MANP).

This paper is relevant because of scarcity of related articles in Latin America that have usedCVM; in some of them unclear results are found, and/or have applied valuation theory in awrong way, or have limited to follow a single bounded method.

3Benefits or positive external effects from these areas take place in an internal level and they affect beyondborders, for example, carbon fixing and with this contribute to avoid global warming.4 For example, in Costa Rica, government has not already paid to original owners more than 12% of NationalParks territories. In 1991 Constitutional Court of this country pronounced and determined that the governmenthas to pay for those territories or give them back to their original owners. So, territories located in nationalparks, like in Santa Elena, have also generated international judgements. In that situation, theme of economicvaluation of those natural assets has been object of discussion and the results of this research project wereacquired for those targets.

3

Different from those articles, this paper follows CVM of two offers, through theintroduction of a second offered threshold in a "follow-up" dichotomous-choice CVquestion that elicits a second discrete response. If the respondent says he/she is willing topay the first offered amount (1st bid) to get in MANP, then a second higher amount (2nd bid)is offered, if not, a second lower bid is offered.5

Besides, estimations presented in this paper come from a sample bigger than used in thoseother papers, so it let to compare WTP to get in MANP from national and foreignersvisitors. This model of two offers lets get more efficient estimations (Cameron y Quiggin,1993), and a big sample lets that maximum likelihood estimators effectively present theirasymptotic properties.

Finally, this work goes forward from others, as it uses four alternative models, threeconsistent with indirect utility functions and one ad-hoc, widely used in previous works.This job offers an example of how can be used CVM in development countries tostrengthen conservation areas sustainability, particularly contributing to define an entrancefee structure.

II. Description of the experiment location

MANP is located in the province of Puntarenas at the Pacific coast of Costa Rica, 157 kmsouth from San José by road, and 7 km south from Quepos town. It was declared NationalPark in 1972. It is 779 terrestrial hectares long and it has 55.000 marine hectares too. Itbelongs to Central Pacific Conservation Area.

The park is a little biological island located in an area that receives different use of soilpressures, like agriculture, raising cattle and an intensive touristic development. MANP iscatalogued as one of the most beautiful schemes and joint to Poas Volcano National Parkare the most visited by tourists.

It is located in the lifezone “very humid tropical forest” in a region of great rainprecipitation (3.875 mm/year) and of high temperatures. Some parts of the forest are inregeneration because they were object of selected wood extraction in the past. The placecalled Punta Catedral, is the result of a geomorphologic phenomenon, due to its past as anisland and sediment accumulation that joined to continental land, making a sandy beltdenominated “tómbolo”. In addition, this park includes twelve islands located near of itsbeaches. Most of them present vegetation and are natural home for birds.

This park protects zones of primary forest, secondary forest, mangrove trees, vegetation ofbeach and marine environments, where live some of flora and fauna species in danger ofextinction.

5 When says “yes” to first answer and the second amount is about the double the first one and when says “no”to first and the second is reduced to about half the initial amount, this methodology is called a "double-bounded referendum" approach. (Cameron y Quiggin, op cit.).

4

Some species of flora that characterize forest are: “guácimo colorado”, “pilón”, “cedromaría”, “guapinol”, “surá”, “guapinol negro” (timber – yielding tree in danger ofextinction); “lechoso”, “madroño”, “cenízaro” and “ceiba”. In the secondary forest (oldagricultural and raising cattle areas), are important: “balsa”, “peine de mico”, “guarumo”,“guácimo”, “capulín blanco” and “garocho”. The mangrove tree zone that covers 18hectares, approximately, is composed by three species: “colorado” mangrove, “botoncillo”and “mariquita”. In the vegetation of beach outstand “manzanillo” (a tree that has a milkysubstance and poisonous fruits), “almendro”, “roble sabana” and coconut groves.

Talking about terrestrial fauna, 109 species of mammals and 184 of birds have beendistinguished. In the first group outstand “mapache”, “pizote”, “guatusa”, “perezosos dedos y tres dedos”, “carablanca” monkey, congo monkey and “tití” monkey (this endemicsub-specie is in danger of extinction, due to destruction of its environment and because it iscaptured to use it as a mascot). In the group of birds is common to see “tucancillo”,“pelícano o buchón”, “guaco”, “gavilán pescador”, “martín pescador verde” and “gallito deagua”. Besides, “iguanas”, “garrobos”, snakes and infinity of insects can be watched too.In the ocean, dolphins are widely seen and some people have seen whales. It also have 19species of corals, 24 species of crustaceans, 17 of alga y 78 species of fish have beenidentified (Adamson, 1998).

III. Theoretical framework

Following to Hanemann (1984) it is supposed that visitors have indirect utility functions,U(p, q, y, s), where p, price vector; q variable (vector) of state of nature (for example, q1 >q0, means a good improvement or in the ambient quality of interested, in this case it issupposed the visit to MANP is a good that gives utility to individuals); y, income; and sconsumer characteristics vector.

Following the random utility model U can be written as (assuming the vector prices to beconstant)

U(q, y ;s) = V(q, y; s) + ε (1)

The utility change due to an increase in q, to q1 > q0 is given by:

∆U = U(q1,y;s) - U(q0,y;s) = V(q1,y;s) - V(q0,y;s) + ε1 - ε2 (2)

Variable εεεε is assume independent and identically distributed with E(εεεε) = 0.

On the visitor scheme, a change in q0 to q1 >>>> q0 is ensured. It is supposed that individualunderstands he/she will get a welfare improvement, in the way that V(q1,y;s) + ε1 ≥V(q0,y;s) + ε0. Individuals are informed that change will cost T colones, so the questions isif he/she is willing to pay that price. Following to Hanemann and Kaninenn (1996), wehave:

5

Pr ( Si ) = H (T; y; s; γ)= Pr (V(q1,y - T; s) + ε1 ≥ V(q0,y; s) + ε0) (3)

Pr ( No ) = 1 - P( Si ) (4)

Con H (T; y; s; γ) = 1 - G (L (T; y; s; γ )) (5)

≥−

=otherwayNo

syTLsiSianswer

;""0);;;(;"" ηγ (5.1)

Where T is the offered price (“bid”), and γ the joint of estimated parameters associated tocovariance vector (y; s). To define ηηηη = εεεε1 - εεεε0, where Fη (• ) as function of ηηηη accumulativedistribution, so it can lead to define the probability of pay dispersion as::

Pr (Si) = P( Y = 1) = Fη (∆V); con ∆V = V(q1, y - T; s) -V (q0, y; s) (6)

Where Y is the answer: Y=1, if the person says “yes” and Y=0 if the individual says “no”.An equivalent way to express this result is by compensating variation (C) , that satisfies:

V(q1,y - C; s) + ε1 = V(q0 ,y; s) + ε0 (7)

From where C can be generated, C = C(q0, q1,y; s, η), equal to its Maximum Willingness toPay (MWTP) to an increase in q. From the last mention it is concluded, that if theindividual answer “yes” to the valuation question, the price offered is less than MWTP and“no” is greater. An equivalent condition to (5) is:

Pr (Si) = Pr(C(q0, q1, y; s, η) ≥ T) (8)

Although, C(q0, q1, y; s, η) is a random variable. Once supposed a distribution function tothe random variable ηηηη, and the model, in any way, equation (3) and (8), will not be just aneconomic behavioral model, will be a statistic model too. In this case this variable has anormal standard distribution that results in a probit model (where the distribution functionis given by Fη . In this case:

)()1()Pr( VYPSi F ∆=== η (9)

The Likelihood Functions to maximize is:

[ ]∑ ∆−−+∆= n

i ii VFyVFyL ))(1(log)1()(loglog ηη (9.1)

Wide amount of studies that use CVM estimate a function for ∆∆∆∆V, which are not consistentor inferable from a utility function (McConnell, 1995; Freeman (1993); Hanemann, 1984,entre otros). Jakobbson y Dragun, (1996) report studies with consistent estimations with anutility model, that show up econometric results less desirable than the reported en ad hocmodels. In many cases, the estimated coefficients are not significant, signs are not

6

consistent with theory, or goodness of fit from the estimated models are less with respect tothe ad hoc estimated models.

This paper presents four models of ∆V (equation 11). Models I to III are consistent withutility function (Hanemann y Kaninenn, 1996), and model IV is ad hoc. The last of them,will lead to compare with another results coming from estudies developed in Costa RicaEcheverría et al. 1995), whom have work this ad hoc model.

The ∆V four models are:

−=

−=++−

+−++−

+−

εεη

βααα

ηγβαηβα

ηβαηβα

21

21

0

)log()(log:)/1log(:.

)(log::

φCon

ybidIVModeloybidIIIModelo

bidIIModelobidIModelo

(10)(10)

During the estimations of this models additional consumer variables or characteristics canbe introduced, which are summarize in vector s. These variables, characteristics of anindividual like age, sex, environmental interests (belong or not to an environmental group),etc. can be included aggregating the next term of these equations:

ii

j

ix i jγ=∑ =

11 2; , , .... . (11)

Measures of Willingness to Pay

The estimating way of compensating surplus (in this case, associated to MANP), comesfrom Hanemann (1984):

C*, which is the median MWTP, it means: Fηηηη (∆∆∆∆V(C*)) = 0.5. (12)This means that if there is a probability 50:50 to pay less than C*; the mean (expectedvalue)

{ } ( )+∞

≡ = −∫C GE C T dTc10

( ) (13)

When the marginal utility of income is constant (model I) measures of C+ y C* are thesame. Next, measures of C* y C+ are presented for model.

7

( )( ) ( )

( )

εεηααα

βα

βη

βα

βα

βη

βα

βα

01

01

*

*

*

)16(1

1

:

)15(:

)14(:

−=−=

−

=

−=

=

=

==

+

+

+

Con

Ey

y

IIIModelo

EIIModelo

IModelo

eeC

eC

eeCeC

CC

Finally, ( ) ( ) .;)2/1( 2

probitessiE ee ηββ

η

=

(17))

Methodology

The used question is of the kind “would you be willing to pay $T for an improvement?” o“would you pay $T to entry the park?” where it is assume they will say yes, when theirmaximum willingness to pay for improvement -given by C = C(q0, q1,y; s, η)- is greaterthan the fee or offered price –bid or T--, and remembering that C comes from de V(q1, y -C; s) -V (q0, y; s) = 0, where the state “1” pay and get in the park and “0” do not pay but donot enjoy the park.

In cases when is asked for an improvement, compensating measures are used, it means,how much the entry from consumers has to be compensated (decrease) to enjoy ahypothetical improvement, because that amount means the consumers MWTP to enjoyfrom that improvement. In this case are used for the four models different measures givenby C* y C’, and some of the cases, as example of susceptibility results of C+, given for thelast equation.

Follow-up dichotomous-choice valuation questions

The last explained methodology is called "single-bounded", because only a price or bid isoffered. It has been mentioned that a way to gain precision in estimations, to use better agiven sample and to make CVM estimations more efficient, is to include a “follow-updichotomous-choice valuation questions” after the first question . In practice, it means thatif the surveyed person says he/she would be willing to pay $T, then he/she has to answerfor a higher price or bid. If he/she says no to the first question, in the second a lower price

8

or bid is offered. This method is called Contingent Valuation Method with follow-upquestions.6 The NOAA panel recommended this double bounded method, because it lets toobtain information about biases that could be introduced into valuation (mentioned byCameron and Quiggin, 1994).

When double bounded format is used, is important to consider that the answer for thesecond bid is endogenous to first. In this format of valuation, while it is randomly assignedthe first bid to surveyed person, the follow-up bid to be offered will take one of twodetermined values (higher or lower) depending on his/her first answer. Then, theprobability that he/she receives a higher second bid (assigned by a determined rule, notrandomly) is equal to probability to say "yes" in the first answer. Analogously, theprobability that he/she receives a second bid lower than first is equal to the probability tosay “no” in the first answer. However, the quantity that is offered to the surveyed person asa second bid depends on the first answer (in other words, it is not random), so, as Camerony Quiggins (1994) say, it is technically inadequate to use only the answers to secondquestion and try to estimate MWTP as in a single-bounded method (forgetting the firstquestion), due to endogenous condition of the second bid.

Let ∆V(1) = Y1 , y ∆V(2) = Y2 (18)

The difference in the indirect utility function, based on the first answer to first offered bid,and the second answer to second offered bid, respectively. Y1 could be different from Y2,either by a strategic behavior or by acquired experience by the surveyed person during thesurvey. I2 is an indicator that equals one if T2 is higher than WTP and zero in other case.Equals to RUM, a systematic and a random components are assumed, so:

Y1 = X’1*B + η1 y Y2= X’2 * B+ η2 (19)

Notice that X’1 does not have to be the same as X’2. So, the fact that there is a correlationbetween errors must be included in the model.

A model of joint distribution function (Y1 y Y2) is required. Like Cameron y Quiggin(1994), in this paper the selected model is the Bivariate Standard Normal (BSN), it meansthe media of each η is equal to zero and the variance is equal to one, where ρ indicatescorrelation between the differences of errors, so: corr. (η1, η2) = ρ. The last model iswritten as NBV(0, 0, 1, 1, ρ).

The vector of answers to both valuation questions can assume four possible results: "yes" tofirst bid and "yes" to second bid; "yes" and "no"; "no" and "yes"; "no"and "no". This isindicated as: (I1, I2)= (1,1); (1,0), (0,1), (0,0). Let g(Y1,Y2) be the density function BSN,hence:

6 In general, the second bid doubles first if the surveyed person says “yes” to first question and is half of it ifhe/she says “no”. this practice is generalized, but there is no theory to justify this (see Cameron & Quiggins(1994) and Hanemann & Kaninenn, (1996).

9

( )( )( ) [ ]( )( )e yyyyyyg

2221

21

2

2/1212)22/1(

121),( +−−−

−= ρρ

ρπ(20)

the likelihood function of the model is:

−+

−−+

−+

=

∫∫

∫∫

∫∫

∫∫∑

∞−

∞

∞−∞−

∞

∞−

∞∞

ydydyygy

yII

yydydyyg

yII

yydydyyg

yII

yydydyyg

yIILLog

i

122121

122121

122121

122121

),(log)1(

),(log)1()1(

),(log)1(

),(log)(

2

1

21

2

1

21

(21)

Notice that if residual is modeled standard normal, parameters to estimate using maximumlikelihood are in the limits of the integral. The difference in the double bounded model isbecause the two questions are correlated, in this case appears a double integral, if a standardnormal is used, only appears one integral instead of Fη). The format of double bounded wasalso used in this project particularly in the section of fee.

IV. Sample

Two thousand two hundred forty five complete surveys were done, that is about 20% ofvisitors to MANP during the period of the survey was applied. Survey was applied fromJune 1997 to February 1998. Assignation of bids was completely random.

Seventy eight percent of visitors were groped in four categories of nationality: Costaricans,(34%), Americans (29%), Canadians (8%) and Germans (6%). Other nationalities lessfrequent were: Swiss, Dutch, Argentineans, Spanish and Italian. More than eighty per centof foreign tourists (84%) visited Costa Rica for the first time, and more than 40% visitedMANP first instead of going to another park.

Thirty seven percent of national visitors completed college. In case of foreigners it wasseventy seven percent. Talking about scholarship, 11.5% of nationals have more than 19years of formal education. In the case of foreigners, it was 23.6%. other difference between

10

nationals and foreigners is referred to level of income . Net annual income media forforeigners was $42.700. For nationals it was about ¢162.300, it means about $8.000 peryear.7 From the total of foreign visitors, 34% declared to have an annual income between$30.000-$60.000.

Table 1. Sample (N) DistributionQuestion of Availability of Paying to Entries to MANP

Foreigners Total Nationals TotalN total 1442 N total 803Not interested 92 Not interested 85Not know (NK)/ Notanswer (NA)

64 NK/ NA 27

Protest 5 Protest 2N Final* 1283 N Final 692(NK/ NA) / N total 0,04 (NK/ NA) / N total 0,03Protest/N total 0,00 Protest/N total 0,00*/ If deduced from the total of each item in a separated way, the sum of this does not necessarycorresponds to the final sample, because some of surveys could present some of these characteristics.Source: Elaborated by the author based on the surveys data.

Table 1 shows a not significant amount of zero protests and of "not know or not answer", sothey were excluded from sample; in the same case, those surveys that identified respondentas not interested.

V. Models Estimation

The valuation question in the strict sense is not a closed-ended with follow up questions,because in first level is always asked for the same bid, that is the same actual entry fee(US$6 for foreigners and ¢200 for residents and nationals). According to the ContingentValuation Method in two levels, in case of the estimation of variation in the indirect utilityin the first level (Y1, equation 25 and 26) do not have explicit at the right side as explicativevariable the bid (implicitly is evaluating at US$6 and taking it out the constant parameter).In the case of Y2 equation, bid does appear as explicative variable.

First Specification

Different specifications were estimated from defined models in equation 11, followingestimation at two levels. The next specifications include (ing), education level (number ofeducation years), a dichotomous variable that measures environmental preferences, in thiscase belonging to an ecological group (ecol), and indicator of the enjoying from the visitthrough a qualification variable (calif) of the park enjoying.

With the objective to identify the different specifications will be used a consecutive numbernext from the roman number. So, for the first specification of models will be used model

7 Change rate at the beginning of field work was ¢142.28/$. The comparison of those data has to be done withcare, given existing problems to compare nominal data of income between countries.

11

I.1 to indicate what is the first specification about for model I, Model II.1, to indicate firstspecification of model II, etc.

Model I.1

First answer or level (for all models but model IV)

εαααα 143201 +∗+∗+∗+= califecoleducYSecond answer or level

εβββββ 2432102 +∗+∗+∗+∗+= califecoledubidY

Model II.1

First answer or level (for all models but model IV)

Second answer or level

( ) εβββββ 2432102 log +∗+∗+∗+∗+= califecoledubidY

Model III.1

First answer or level (for all models but model IV)

Second answer or level

εβββββ 2432102 1log +∗+∗+∗+

−∗+= califecoledu

ingbidY

Model IV.1

First answer or level (for all models but model IV)

Second answer or level

( ) ( ) εββββββ 2loglog 5432102+∗+∗+∗+∗+∗+= ingcalifecoledubidY

Where correlation between answers is corr(εεεε1,εεεε2) = ρρρρ

12

The estimation results from the last models presents in table 2 for foreigners and in table 3for nationals. In case of foreigners is observed that for all models in the first answer, thereis just one significant variable at 5% (the statistics –t. are present in the parenthesis underthe estimated parameter) is qualification variable given for the visitors to MANP. Thisvariable can be considered as a proxy of enjoy quality from the visit, it is positivelyassociated with the probability to obtain “yes” in the question if visitants feel that $6 areworth it to get in the MANP. Only in the ad hoc model IV.1 appears another variablesignificant (income).

In the second answer, for foreigners case, in all models the most significant variable wasthe bid or supply (significant even at 1%). The first two models, appears as significantvariable the education years, but not in models III, IV for this specifications. The proxyvariable (global qualification from the visit) is significant en model II, and in IV (ad hoc),in which the new entry is siginificative in that second answer too.

Except for the first model, a significant correlation presence is found between the answersto the first and second questions. The proof of goodness to fit of the model (Chi squarewith seven degrees of freedom (χ2; 7 d. f.) indicate that rejects the null hypothesis ofslopes equals to zero. Variables together explained pretty good the answers. This could bechecked with the significant value, indicated in the immediately inferior row of the Chi-square value and gives zero values even at fourth digit

Finally, a more refined test of goodness like the pseudo R2 (or Maddala´s R2 ) shows levelsbetween 0.02 to 0.08.8

In the national visitors (table 3), for the first answer the only significant variable in the fourmodels was the “qualification”. In the second answer the offer or bid is significant in all themodels, and the income in the ad hoc model. Is important to remember that models I and II,even though income is present in the indirect utility function, in the variation of the utilityit is not present because it was eliminated. It results in WTP neutral to income. In themodel III the income is present, and the WTP presents a unitary income elasticity. At thesame form that foreigners, in its first specification, we find that the sign of the correlationis not stable between the models neither significantly different of zero. When evaluating themodels with the χ2 test, the null hypothesis is rejected, which means the variables in jointlyare significant. In an interesting form, in all cases, the pseudo R2 in the nationals models ishigher than the foreigners case.

8 For example, Hanemann, Loomis y Kanninen (1991), in a study that too use dichotomous choice withfollow-up questions, show level of pseudo R2 between 0.01. to 0.28 in the best fit.

13

Table 2. Basic Models Estimation of Availability of Paying to Entries to MANP forForeigners.

ModelModel I.1

ecoledubid ∗+∗+∗+∗+ 43210 βββββModel II.1

( ) ecoledubid ∗+∗+∗+∗+ 43210 log βββββ

Model III.1ecoledu

ingbid +∗+∗+

−∗+ 43210 1log βββββ

Model IV.1( ) califecoledubidlog 543210 +∗+∗+∗+∗+ ββββββ

Parameter EP(n= 1283)

EP(n= 1283)

EP(n= 1283)

EP(n= 1283)

FIRST ANSWER

αααα0000

(T.Stat)

-0.0495(-0.153)

-0.0625(-0.194)

-0.0105(-0.033)

-1.5307(-2.764)

αααα2222

(T.Stat)

0.0090(0.538)

0.0099(0.597)

0.0069(0.414)

0.0024(0.139)

αααα3333

(T.Stat)

0.1250(1.181)

0.1327(1.253)

0.1064(1.016)

0.1052(0.973)

αααα4444

(T.Stat)

1.1499(5.731)

1.1449(5.672)

1.1499(5.730)

1.1246(5.297)

αααα5555

(T.Stat)

0.1604(3.586)

SECOND ANSWER

ββββ0000

(T.Stat)

0.9401(3.240)

2.6678(7.786)

0.1300(0.490)

1.5634(3.436)

ββββ1

(T.Stat)

-0.1198(-11.269)

-1.4575(-14.925)

93.8294(4.236)

-1.4809(-15.246)

ββββ2222

(T.Stat)

0.0259(2.277)

0.0274(2.401)

0.0128(1.140)

0.0204(1.754)

ββββ3

(T.Stat)

0.0797(0.994)

0.0942(1.175)

0.0781(1.008)

0.0713(0.877)

ββββ4

(T.Stat)

0.1540(0.734)

0.4355(2.064)

-0.2371(-1.183)

0.4361(2.104)

ββββ5

(T.Stat)

0.1255(3.508)

ρ (1,2)ρ (1,2)ρ (1,2)ρ (1,2)(T.Stat)

-0.1206(-1.272)

0.3097(2.338)

-0.6033(-12.244)

0.3118(2.365)

χχχχ2222

(d.f)179.583

(7)191.131

(7)60.046

(7)214.569

(9)

Signif. 0.0000 0.0000 0.0000 0.0000

R2

Maddala 0.0702 0.0747 0.0235 0.0839

Source: Elaborated by the author based on the surveys data.

14

Table 3. Basic Models Estimation of Availability of Paying to Entries to MANP forNationals

ModelModel I.1

cecoledubid ∗+∗+∗+∗+ 43210 βββββModel II.1

( ) cecoledubid ∗+∗+∗+∗+ 43210 log βββββ

Model III.1ecoledu

ingbid ∗+∗+∗+

−∗+ 43210 1log βββββ

Model IV.1( ) califecoledubid llog 543210 ∗+∗+∗+∗+∗+ ββββββ

Parameter EP(n= 692)

EP(n= 692)

EP(n= 692)

EP(n= 692)

FIRST ANSWER

αααα0000

(T-Stat)

1.2525(1.466)

1.3966(1.528)

1.1432(1.295)

1.9853(0.608)

αααα2222

(T-Stat)

-0.0097(-0.189)

-0.0155(-0.303)

-0.0048(-0.089)

-0.0105(-0.123)

αααα3333

(T-Stat)

-0.0235(-0.058)

-0.0304(-0.076)

-0.0089(-0.022)

-0.0273(-0.060)

αααα4444

(T-Stat)

1.2569(2.225)

1.1857(2.105)

1.3027(2.444)

1.1803(1.992)

αααα5555

(T-Stat)

-0.0556(-0.164)

SECOND ANSWER

ββββ0000

(T-Stat)

0.7912(1.466)

6.5305(9.299)

0.4214(1.081)

5.0477(4.842)

ββββ1

(T-Stat)

-0.0011(-11.499)

-1.0692(-11.871)

35.3485(8.294)

-1.0664(-11.783)

ββββ2222

(T-Stat)

0.0182(1.581)

0.0200(1.691)

-0.0168(-1.504)

0.0097(0.746)

ββββ3

(T-Stat)

-0.0727(-0.453)

-0.0633(-0.393)

-0.0554(-0.376)

-0.0639(-0.395)

ββββ4

(T-Stat)

0.0914(0.218)

0.4258(1.052)

0.2373(0.678)

0.4385(1.063)

ββββ5

(T-Stat)

0.1363(1.967)

ρ (1,2)ρ (1,2)ρ (1,2)ρ (1,2)(T-Stat)

-0.0015(-0.003)

0.3731(1.052)

-0.3952(-0.912)

0.3718(0.727)

χχχχ2222

(d.f)146.505

(7)164.255

(7)77.020

(7)168.581

(9)

Signif. 0.0000 0.0000 0.0000 0.0000

R2

Maddala 0.1407 0.1577 0.0739 0.1619

Source: Elaborated by the author based on the surveys data.

15

Second specification

This specification of the four models is interested in identify differences statisticallysignificant in estimators related to nationality of foreign visitors, so WTP to get in MANPwould change depending on the nationality of visitors. In this case, the group of foreignersis divided in four categories: Americans, Germans, Canadians and one denominated"others". This separation of nationalities in the group of foreigners is made based in therelative participation of them in visiting the park. Hypothesis is that variable nationalityreflects social and economics differences between groups, which are not incorporated inother variables (for example, social differences that affect willingness to pay, costumes,etc.).

The variable nationality is introduced to model through dummies variables. They aresimultaneously introduced in two ways: a. studying if intercept or estimated constantchanges, and b. affecting bid estimated coefficient. Last mentioned is in order to captureany effect that nationality can have in both parameters. Immediate to suppose is thatnationality could have an effect on the parameter associated to bid. Nevertheless, in thewillingness to pay there are other factors involved that are different from price, so, eventhough is not obvious, is fare to introduce a dichotomous variable that can also affectintercept..

This specification is similar to last, but in this case dummies variables are aggregated inequation of Y2, as it follows:

Let:d1 = {1 nationality = american; 0 other way.d2 = {1 nationality =german; 0 other way.d3 = {1 nationality = canadian; 0, other way.d1 = d2 = d3 = 0 nationality = other nationalities.

Model I.2: is equal to bivariate model I.1. The first answer (Y1) is specified in the sameway and now Y2 is equal to:

( ) ( ) ( ) εγγγϕϕϕβββββ

23322113322

11432102

+++++

++++++=

biddbiddbidddddcalifecoledubidY

Model II.2: is similar to II.1, with dummies by nationality in Y2 (introduced over interceptand the log(bid)).

Model III.2: is similar III.1, with dummies by nationality in Y2 (over intercept and log (1-bid/ing)).

Model IV.2: is similar to IV.1 with dummies by nationality in Y2 (introduced over interceptand the log(bid)).

16

Results of estimations are shown in table 4. In the first level estimations are fundamentallythe same as in the case without nationalities.

In case of introducing differences by nationality, in the group of foreigners, captured inestimations of second answer, education is a significant variable only in the same modelsbefore incorporate nationality were, it means in models I.2 y II.2. with the variablequalification and correlation happens the same, staying the first as significant only in II.2model, and second in all models except I.2.

None of the dummies introduced is individually significant in all models. By itself, χ12 (or

likelihood ratio, associated degrees of freedom are indicated in parentheses below the valueof χ1

2) indicates that all models explain good the answers (this is corroborated by theprobability value of finding a likelihood ratio higher in the rejection area, indicated in thetable as Signif, that shows a probability of zero even in the fourth digit). In fact, thisimproves even more related with the presented results in table 2.

Nevertheless, when the second likelihood ratio is done (χ22, subindex indicates that is a

second ratio) to prove null hypothesis that joined coefficients or parameters associated todummies by nationality are equal to zero, this is not rejected at 5% of significance (asshown by Signif.). This low explicative power of the variables is reflected by R2 ofMaddala, which, for all models, are almost the same as shown in table 2.

In this case, empiric evidence indicates that in WTP to get in MANP, into the group offoreigners, WTP is not affected by nationals.

17

Table 4. Basic Models Estimation of Availability of Paying to Entries to MANP withdummies by nationality

Model Model I.2 Model II.2 Model III.2 Model IV.2Parameter EP

(n= 1283)EP

(n= 1283)EP

(n= 1283)EP

(n= 1283)

FIRST ANSWERαααα0000

(T-Stat)

-0.0496(-0.153)

-0.0629(-0.195)

-0.0080(-0.025)

-1.5290(-2.742)

αααα2222

(T-Stat)

0.0089(0.533)

0.0099(0.595)

0.0067(0.398)

0.0024(0.138)

αααα3333

(T-Stat)

0.1246(1.172)

0.1330(1.248)

0.1069(1.019)

0.1056(0.971)

αααα4444

(T-Stat)

1.1511(5.694)

1.1455(5.630)

1.1514(5.718)

1.1248(5.249)

αααα5555

(T-Stat)

0.1603(3.566)

SECOND ANSWERββββ0000

(T-Stat)

0.97771(3.006)

2.3562(6.104)

0.2114(0.775)

1.2902(2.642)

ββββ1

(T-Stat)

-0.1179(-1.320)

-1.3012(-10.555)

117.3501(3.605)

-1.3223(-10.951)

ββββ2222

(T-Stat)

0.0246(0.2.146)

0.0260(2.263)

0.0112(0.995)

0.0199(1.697)

ββββ3

(T-Stat)

0.0626(0.769)

0.0756(0.928)

0.0700(0.896)

0.0583(0.706)

ββββ4

(T-Stat)

0.1161(0.545)

0.3803(1.767)

-0.2574(-1.275)

0.3854(1.827)

ββββ5

(T-Stat)

0.1218(3.322)

ϕϕϕϕ1111

(T-Stat)

0.1042(0.374)

0.7437(1.432)

-0.0212(-0.232)

0.7086(1.372)

ϕϕϕϕ2222

(T-Stat)

0.3119(0.587)

1.5357(1.247)

-0.0624(-0.393)

1.5064(1.220)

ϕϕϕϕ3333

(T-Stat)

-0.3217(-0.905)

0.0979(0.138)

-0.1483(-1.132)

0.0722(0.103)

γγγγ1111

(T-Stat)

-0.0034(-0.168)

-0.2684(-1.307)

-58.3246(-1.199)

-0.2746(-1.345)

γγγγ2222

(T-Stat)

-0.0291(-0.801)

-0.6374(-1.360)

61.2376(0.605)

-0.6354(-1.354)

γγγγ3333

(T-Stat)

0.0157(0.582)

-0.0894(-0.312)

-50.2076(-0.725)

-0.0870(-0.305)

ρ (1,2)ρ (1,2)ρ (1,2)ρ (1,2)(T-Stat)

-0.1376(-1.412)

0.2804(2.070)

-0.6059(-12.148)

0.2883(2.126)

χχχχ22221111

(d. f)184.165

(13)198.212

(13)64.346

(13)220.769

(15)

18

Signif. 0.0000 0.0000 0.0000 0.0000

R2

Maddala

0.0720 0.0775 0.0251 0.0863

χχχχ22222222

(g. l)4.582

(6)7.082

(6)4.299

(6)6.651

(6)

Signif. 0.5984 0.3133 0.6362 0.3543

Source: Elaborated by the author based on the surveys data.

Willingness To Pay to get in MANP

Third specification

Models were estimated using statistically significant variables and WTP to get in MANPwere re-estimated

First answer for models I.3, II.3 y III.3

εαα 1401 +∗+= califYSecond answer

Model I.3

εβββ 22102 +∗+∗+= edubidYModel II.3

( ) εββββ 242102 log +∗+∗+∗+= califedubidYModel III.3

εββ 21log102+

−∗+=

ingbidY

Model IV.3

Thus aggregate α5 * log (ing) to the first

Second answer( ) ( ) εββββ 2loglog 54102 +∗+∗+∗+= ingcalifbidY

19

Here: Correlation between levels = corr(εεεε1,εεεε2) = ρρρρ

Results show that variables are highly significant (as shown by t-statistics, in table5).empirically is found that the second answer is associated to first, as shown bysignificance of correlation estimate (except in model. I.3). As hoped, the prove orlikelihood ratio, that measures the goodness of fit, indicates that null hypothesis is rejected,it means that slopes are equal to zero, so variables explicate answers.WTP to get in MANP, in case of foreigners, measured by C* (median) is about $12 for allmodels, except for III.3 , where WTP is close to $60, been five times higher than othermodels.

When using C’ to measure WTP, in all models estimation is about $11 y $12 again. By theother side, empiric evidence tells that C’ has more stability to specification of the model(even in models with theoretical fundament (I, II y III.) and in ad hoc (IV). In this last casemeasuring of WTP is similar to reported by indirect utility functions. This result is likereported by Browher y Stoll (1988) but they find it in an estimation of a single-bounded.

Now that C’ gives an excellent measure of consumer’s surplus, if consider C’ as measure ofWTP, and knowing that MANP fee is $6, in average is affirmative to say that each foreignvisitor is getting as consumer’s surplus, of 50% of the benefits derived from enjoyinggetting in MANP. In this case, System of National Conservation Areas (SINAC) uses anentrance fee that just covers 50% of the aggregate value generated by visitation to that park.Indeed, making a re-distribution of benefits generated by this active through foreign visitorsin approximately 50%.

20

Table 5. Selected Models of Availability of Paying to Entries to MANP for Foreigners

Model Model I.3 Model II.3 Model III.3 Model IV.3

Parameter EP(n= 1287)

EP(n= 1287)

EP(n= 1287)

EP(n= 1287)

FIRST ANSWERαααα0000

(T-Stat)

0.1372(0.719)

0.1488(0.769)

0.2359(1.335)

-1.4924(-3.043)

αααα4444

(T-Stat)

1.1511(5.843)

1.1384(5.697)

1.0494(5.747)

1.1160(5.286)

αααα5555

(T-Stat)

0.1647(3.702)

SECOND ANSWERββββ0000

(T-Stat)

1.0673(4.668)

2.6981(7.926)

0.1484(3.682)

1.7611(4.044)

ββββ1

(T-Stat)

-0.1189(-11.374)

-1.4598(-15.147)

103.604(4.746)

-1.4802(-15.250)

ββββ2222

(T-Stat)

0.0283(2.523)

0.0283(2.531)

ββββ4

(T-Stat)

0.4293(2.044)

0.4398(2.170)

ββββ5

(T-Stat)

0.1413(4.039)

ρ (1,2)ρ (1,2)ρ (1,2)ρ (1,2)(T-Stat)

-0.1260(-1.248)

0.3122(2.362)

-0.6013(-12.119)

0.3102(2.350)

% ofprediction 88.97 89.51 88.97 90.05

χχχχ2222

(d.f)176.882

(3)188.604

(4)54.096

(2)210.429

(5)

Signif. 0.0000 0.0000 0.0000 0.0000R2

Maddala

0.0690 0.0735 0.0211 0.0820

C* 12.916 11.627 61.304 12.124C1 12.205 12.261 10.988 12.600

Source: Elaborated by the author based on the surveys data.

21

As similar in the case of foreigners, (it means, identification of variables in each of the fourdifferent models used) is the result of identified statistic significance of variables. Giventhat those variables are not the same as in case of foreigners, in third specification modelsfor nationals and foreigners are not equal each other. In the case of nationals, the firstanswer is specified as:

εαα 1401 +∗+= califY

Second answer is given by

Model I.3

εββ 2102 +∗+= bidYModel II.3.

( ) εββ 2log102 +∗+= bidYModel III.3

εββ 21log102+

−∗+=

ingbidY

Model IV.3

( ) ( ) εβββ 2loglog 5102 +∗+∗+= ingbidYAdjustments to selected models for nationals are presented in table 6. For the first question(in a summarized way: do you consider your visit worth ¢200 you paid?) that associatedparameter to indicator of quality of enjoyment derived from visits is significant. This meansthat there is a positive association between quality of enjoyment of MANP perceived bytourists and the probability to say “yes” to mentioned question. In the case of secondquestion, variables that explain probability of answer are fundamentally bid and income inthe case of the two models where they appear (models III.3 y IV.3).The R2 of Maddala(higher than foreigner’s case) are between 0.13 – 0.16.

Talking about WTP to get in MANP for nationals, models place it in the case of medianWTP (C*), between ¢847 a ¢1000 ($5.7 to $6.8), except in model III.3 that is located closeto ¢2000 ($13) (interestingly the same structure of model used in foreigner’s case) Whenusing C’ as measure of WTP, notice that it has more stability to model specification,because WTP is between ¢1000 y ¢1158 for all models ($6.8 to $7.8.

Making an analogous case for foreigners is possible to say that profits captured by nationalsas consumer’s surplus are about ¢800 ($5.4) per visit. In percentage terms, it represents

22

about 400% of the actual fee. The amount is lower than $6 (converted to colones) that arecaptured by foreigners in each visit

An indirect comparison of WTP for foreigners and nationals indicates that the first group isalmost the double of second. This is consistent with the higher level of annual income formthat group and with higher levels of education. in the results obtained to Monte VerdePreserve by Echeverría et al (1995) in order to estimate the value of the reserve reports thatWTP for foreigners is lower than nationals.

This result appears to be a paradox if consider that the foreign group has a higher income(in that case nationals income is 34% of foreigners income). Trying to explain that result,those authors argued that nationals give high value to their national resources thanforeigners do. But they do not present empirical evidence that supports their affirmation.

By the other side, there are not reported a focus-groups work, and they use a little sample(351 observations).The unique model they estimated is ad-hoc, with a specification of thetype IV, and their results present t-statistics low significant, particularly when separatesample in order to compare WTP for nationals and foreigners. Those paradoxical resultsshould be due to the reduced size of the sample. Estimation for nationals they used 42observations and 309 for foreigners.

Estimating both models with theoretical fundament, and the model ad-hoc itself, thisresearch found that using bigger samples is able to conclude that enjoyment of nationalparks behaves as a normal good, and so its consumption and WTP tend to raise withincome. So, rare results those authors obtained are due to necessity of big samples to get themaximum likelihood estimation. In other way, is not possible to be sure of the asymptoticproperties of estimators.

23

Table 6.Selected Models of Availability of Paying to Entries to MANP for Nationals.

Model Model XIII Model XIV Model XV Model XVI

Parameter

EP(n= 694)

EP(n= 694)

EP(n= 694)

EP(n= 694)

FIRST ANSWER

αααα0000

(T-Stat)

1.1108(2.340)

1.2309(2.380)

1.0080(2.152)

1.2356(2.383)

αααα4444

(T-Stat)

1.2616(2.206)

1.1306(1.991)

1.3722(2.584)

1.1259(1.976)

SECOND ANSWER

ββββ0000

(T-Stat)

1.1105(9.870)

7.0598(11.762)

0.3983(5.746)

5.2774(5.704)

ββββ1

(T-Stat)

-0.0011(-11.604)

-1.0463(-11.811)

33.3914(7.987)

-1.0532(-11.829)

ββββ5

(T-Stat)

0.1566(2.498)

ρ (1,2)ρ (1,2)ρ (1,2)ρ (1,2)(T-Stat)

0.0029(-0.007)

0.3294(0.814)

-0.4124(-1.074)

0.3378(0.817)

% ofpredictio

n91.35 90.06 81.56 95.96

χχχχ2222

(d.f)144.840

(2)160.605

(2)74.256

(2)167.298

(3)Signif. 0.0000 0.0000 0.0000 0.0000

R2

Maddala 0.1387 0.1538 0.0711 0.1602

C* 1002.72 851.87 2007.00 898.76

C1 1001.99 1010.72 1157.69 1044.72

Source: Elaborated by the author based on the surveys data.

24

VI. Conclusions

When the foreigner group is divided, we find empirical evidence that WTP inside of it isnot statistically different between nationalities.

The results show that WTP of foreigners visitors is about the double of the nationalsvisitors ($12 and $6 respectively) . This results are consistent with the presumption thatenjoyment of the existence and visits to National Parks are normal goods. So, since thatforeigner visitors have a higher income, their WTP is higher than nationals visitors. Theopposite results, reported by Echeverría et al. may come from the very small sample used.

When this WTP are compared with the entrance fee ($6 for foreigner and about $2 fornationals) we can conclude that this country losses about 50% of the amenity economicvalue derived from the visits to MANP.

This situation represent a good opportunity in order to increase the entrances fees closer to"demand prices" and to capture much more economics resources from this natural areas.

Finally, this paper shows that CVM can be use in developing countries and that thismethodologies can be useful in order to strengthen the use of natural resources in thiscountries.

25

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