Using Contingent Valuation to Estimate Prices for Non-Market Amenities Provided by Protected ...

25 Pages·2002·0.09 MB·English

Using Contingent Valuation to Estimate Prices for Non-Market Amenities
Provided 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 to
estimate 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. In
contrast to other articles, which estimate WTP (median) by following a single bounded
approach, and which in most of cases use only one ad-hoc model, this paper shows alternative
measures of WTP (mean and median) following a double bounded approach. The estimations
are made using a sample of 2245 park visitors and four models: three of them consistent with
indirect utility functions, and an ad-hoc model which has been widely used in the contingent
valuation literature. Because the answer to the second bid is endogenous a bivariate probit
model is used in the four models estimated.
The econometric estimation of the compensating surplus derived by both nationals and
foreigners when entering the park shows a low level of sensibility to model specification and to
the estimated WTP (mean or median). WTP is estimated at approximately $12 for foreigners
and $5 for nationals. The estimation of WTP in the four models is not sensitive to specific
nationality of foreigners. The estimated correlation of answers and their significance changes
with the estimated model. Furthermore, the goodness of fit tests (χ2) are statistically
significant. This paper shows that CVM can be used to design policies that improve pricing
schemes for protected areas, and that such pricing schemes can lead to a more sustainable
management 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 Rica
for their comments. All remaining errors are responsibility of the authors.
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, tropical
countries as Costa Rica are receiving important economic benefits coming from tourism, as
result of an important investment in conservation of natural resources through National
Parks and other kinds of conservation. This country has invested an important amount of
resources in conservation that has permitted to keep more than 25% of its territory under
protection (Adamson, 1994). This tourism is particularly intensive in amenities which these
conservation areas provide.3
In spite of profits those protected areas provide, incapacity to capture profits derived from
goods and services provided by them is threatening their existence and development.4 Two
factors explain this paradox. First, most of services provided are not directly traded in a
market but they appear to be positive external effects, then, administration of those areas is
not able to appropriate directly over those benefits. This case includes local and global
external 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 the
government, independently of supply conditions --costs of each area-- and demand
conditions --visitors willingness to pay.
The entrance fee to National Parks is one of the collect instruments --price-- for one of the
services that is nearer to market. As there are limitations to capture profits, entrance fee
should 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 extracts
consumer's surplus. In those cases, is important to determine economic valuation derived
by consumers from enjoying tourism. This paper shows the way to apply Contingent
Valuation Method (CVM) in a close ended format (referendum) of two questions with
discrete 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 used
CVM; in some of them unclear results are found, and/or have applied valuation theory in a
wrong 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 beyond
borders, 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 National
Parks territories. In 1991 Constitutional Court of this country pronounced and determined that the government
has to pay for those territories or give them back to their original owners. So, territories located in national
parks, like in Santa Elena, have also generated international judgements. In that situation, theme of economic
valuation of those natural assets has been object of discussion and the results of this research project were
acquired for those targets.
2
Different from those articles, this paper follows CVM of two offers, through the
introduction of a second offered threshold in a "follow-up" dichotomous-choice CV
question that elicits a second discrete response. If the respondent says he/she is willing to
pay 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 those
other papers, so it let to compare WTP to get in MANP from national and foreigners
visitors. 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 their
asymptotic properties.
Finally, this work goes forward from others, as it uses four alternative models, three
consistent 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 to
strengthen conservation areas sustainability, particularly contributing to define an entrance
fee structure.
II. Description of the experiment location
MANP is located in the province of Puntarenas at the Pacific coast of Costa Rica, 157 km
south from San José by road, and 7 km south from Quepos town. It was declared National
Park in 1972. It is 779 terrestrial hectares long and it has 55.000 marine hectares too. It
belongs to Central Pacific Conservation Area.
The park is a little biological island located in an area that receives different use of soil
pressures, like agriculture, raising cattle and an intensive touristic development. MANP is
catalogued as one of the most beautiful schemes and joint to Poas Volcano National Park
are the most visited by tourists.
It is located in the lifezone “very humid tropical forest” in a region of great rain
precipitation (3.875 mm/year) and of high temperatures. Some parts of the forest are in
regeneration because they were object of selected wood extraction in the past. The place
called Punta Catedral, is the result of a geomorphologic phenomenon, due to its past as an
island and sediment accumulation that joined to continental land, making a sandy belt
denominated “tómbolo”. In addition, this park includes twelve islands located near of its
beaches. Most of them present vegetation and are natural home for birds.
This park protects zones of primary forest, secondary forest, mangrove trees, vegetation of
beach and marine environments, where live some of flora and fauna species in danger of
extinction.

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.).
3
Some species of flora that characterize forest are: “guácimo colorado”, “pilón”, “cedro
maría”, “guapinol”, “surá”, “guapinol negro” (timber – yielding tree in danger of
extinction); “lechoso”, “madroño”, “cenízaro” and “ceiba”. In the secondary forest (old
agricultural and raising cattle areas), are important: “balsa”, “peine de mico”, “guarumo”,
“guácimo”, “capulín blanco” and “garocho”. The mangrove tree zone that covers 18
hectares, approximately, is composed by three species: “colorado” mangrove, “botoncillo”
and “mariquita”. In the vegetation of beach outstand “manzanillo” (a tree that has a milky
substance and poisonous fruits), “almendro”, “roble sabana” and coconut groves.
Talking about terrestrial fauna, 109 species of mammals and 184 of birds have been
distinguished. In the first group outstand “mapache”, “pizote”, “guatusa”, “perezosos de
dos y tres dedos”, “carablanca” monkey, congo monkey and “tití” monkey (this endemic
sub-specie is in danger of extinction, due to destruction of its environment and because it is
captured 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 de
agua”. 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 19
species of corals, 24 species of crustaceans, 17 of alga y 78 species of fish have been
identified (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, q >
1
q means a good improvement or in the ambient quality of interested, in this case it is
0,
supposed the visit to MANP is a good that gives utility to individuals); y, income; and s
consumer characteristics vector.
Following the random utility model U can be written as (assuming the vector prices to be
constant)
U(q, y ;s) = V(q, y; s) + ε (1)
The utility change due to an increase in q, to q > q is given by:
1 0
∆U = U(q ,y;s) - U(q ,y;s) = V(q ,y;s) - V(q ,y;s) + ε - ε (2)
1 0 1 0 1 2
Variable εεεε is assume independent and identically distributed with E(εεεε) = 0.
On the visitor scheme, a change in q to q >>>> q is ensured. It is supposed that individual
0 1 0
understands he/she will get a welfare improvement, in the way that V(q ,y;s) + ε ≥
1 1
V(q ,y;s) + ε . Individuals are informed that change will cost T colones, so the questions is
0 0
if he/she is willing to pay that price. Following to Hanemann and Kaninenn (1996), we
have:
4
Pr ( Si ) = H (T; y; s; γ)= Pr (V(q ,y - T; s) + ε ≥ V(q ,y; s) + ε ) (3)
1 1 0 0
Pr ( No ) = 1 - P( Si ) (4)
Con H (T; y; s; γ) = 1 - G (L (T; y; s; γ )) (5)
"Si";siL(T;y;s; γ)−η≥0 (5.1)
answer=
 "No";otherway
Where T is the offered price (“bid”), and γ the joint of estimated parameters associated to
covariance vector (y; s). To define ηηηη = εεεε1 - εεεε0, where Fη (•) as function of ηηηη accumulative
distribution, 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(q ,y - C; s) + ε = V(q ,y; s) + ε (7)
1 1 0 0
From where C can be generated, C = C(q , q ,y; s, η), equal to its Maximum Willingness to
0 1
Pay (MWTP) to an increase in q. From the last mention it is concluded, that if the
individual 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(q , q , y; s, η) ≥ T) (8)
0 1
Although, C(q , q , y; s, η) is a random variable. Once supposed a distribution function to
0 1
the random variable ηηηη, and the model, in any way, equation (3) and (8), will not be just an
economic behavioral model, will be a statistic model too. In this case this variable has a
normal standard distribution that results in a probit model (where the distribution function
is given by F . In this case:
η
Pr(Si)=P(Y =1) = F (∆V) (9)
η
The Likelihood Functions to maximize is:
logL = ∑n[y log F (∆V) + (1− y ) log(1− F (∆V))] (9.1)
i i η i η
Wide amount of studies that use CVM estimate a function for ∆∆∆∆V, which are not consistent
or inferable from a utility function (McConnell, 1995; Freeman (1993); Hanemann, 1984,
entre otros). Jakobbson y Dragun, (1996) report studies with consistent estimations with an
utility model, that show up econometric results less desirable than the reported en ad hoc
models. In many cases, the estimated coefficients are not significant, signs are not
5
consistent with theory, or goodness of fit from the estimated models are less with respect to
the ad hoc estimated models.
This paper presents four models of ∆V (equation 11). Models I to III are consistent with
utility 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 Rica
Echeverría et al. 1995), whom have work this ad hoc model.
The ∆V four models are:
Modelo I : α −β bid +η
ModeloII :α −β log (bid) +η
ModeloIII.:α +β log(1−bid /y) + η (10)(10)
ModeloIV : α −β log(bid) +γ log(y) + η
α =α−α
 1 2
Conβ φ 0

η = ε−ε

1 2
During the estimations of this models additional consumer variables or characteristics can
be introduced, which are summarize in vector s. These variables, characteristics of an
individual like age, sex, environmental interests (belong or not to an environmental group),
etc. can be included aggregating the next term of these equations:
∑j γ
x ; i = 1, 2,....j. (11)
i i
i=1
Measures of Willingness to Pay
The estimating way of compensating surplus (in this case, associated to MANP), comes
from 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 (expected
value)
∞( )
C+ ≡E{C}= ∫ 1−G (T) dT (13)
c
0
When the marginal utility of income is constant (model I) measures of C+ y C* are the
same. Next, measures of C* y C+ are presented for model.
6
α
Modelo I : C*= C+= (14)
β
 ( )α
C* = e β
Modelo II :  ( )α ( )η  (15)
C+ = e β E e β
  
  α 
 C*= y e β −1
 

  α ( )η  
Modelo III : C+ = y e β E e β −1 (16)
    



Conα=α−α
1 0
η= ε−ε
1 0
( )η  ( )
Finally, E e β = e (1/2β2); siηes probit. (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 their
maximum willingness to pay for improvement -given by C = C(q , q ,y; s, η)- is greater
0 1
than the fee or offered price –bid or T--, and remembering that C comes from de V(q , y -
1
C; s) -V (q , y; s) = 0, where the state “1” pay and get in the park and “0” do not pay but do
0
not 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 a
hypothetical improvement, because that amount means the consumers MWTP to enjoy
from that improvement. In this case are used for the four models different measures given
by C* y C’, and some of the cases, as example of susceptibility results of C+, given for the
last equation.
Follow-up dichotomous-choice valuation questions
The last explained methodology is called "single-bounded", because only a price or bid is
offered. It has been mentioned that a way to gain precision in estimations, to use better a
given sample and to make CVM estimations more efficient, is to include a “follow-up
dichotomous-choice valuation questions” after the first question . In practice, it means that
if the surveyed person says he/she would be willing to pay $T, then he/she has to answer
for a higher price or bid. If he/she says no to the first question, in the second a lower price
7
or bid is offered. This method is called Contingent Valuation Method with follow-up
questions.6 The NOAA panel recommended this double bounded method, because it lets to
obtain information about biases that could be introduced into valuation (mentioned by
Cameron and Quiggin, 1994).
When double bounded format is used, is important to consider that the answer for the
second bid is endogenous to first. In this format of valuation, while it is randomly assigned
the first bid to surveyed person, the follow-up bid to be offered will take one of two
determined values (higher or lower) depending on his/her first answer. Then, the
probability that he/she receives a higher second bid (assigned by a determined rule, not
randomly) is equal to probability to say "yes" in the first answer. Analogously, the
probability that he/she receives a second bid lower than first is equal to the probability to
say “no” in the first answer. However, the quantity that is offered to the surveyed person as
a second bid depends on the first answer (in other words, it is not random), so, as Cameron
y Quiggins (1994) say, it is technically inadequate to use only the answers to second
question and try to estimate MWTP as in a single-bounded method (forgetting the first
question), due to endogenous condition of the second bid.
Let ∆V(1) = Y , y ∆V(2) = Y (18)
1 2
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 the
survey. 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:
Y = X’ *B + η y Y = X’ * B+ η (19)
1 1 1 2 2 2
Notice that X’ does not have to be the same as X’ . So, the fact that there is a correlation
1 2
between errors must be included in the model.
A model of joint distribution function (Y y Y ) is required. Like Cameron y Quiggin
1 2
(1994), in this paper the selected model is the Bivariate Standard Normal (BSN), it means
the media of each η is equal to zero and the variance is equal to one, where ρ indicates
correlation between the differences of errors, so: corr. (η , η ) = ρ. The last model is
1 2
written as NBV(0, 0, 1, 1, ρ).
The vector of answers to both valuation questions can assume four possible results: "yes" to
first bid and "yes" to second bid; "yes" and "no"; "no" and "yes"; "no"and "no". This is
indicated as: (I , I )= (1,1); (1,0), (0,1), (0,0). Let g(Y ,Y ) be the density function BSN,
1 2 1 2
hence:

6 In general, the second bid doubles first if the surveyed person says “yes” to first question and is half of it if
he/she says “no”. this practice is generalized, but there is no theory to justify this (see Cameron & Quiggins
(1994) and Hanemann & Kaninenn, (1996).
8
( ( ) [ ])
g(y , y ) = 1( ) (e) ( −1/ 2−2ρ2 ) y12−2ρ y1y2 + y22 (20)
1 2  2π(1− ρ)1/2 
the likelihood function of the model is:
  
 ∞ ∞
LogL= ∑  (I I ) log ∫ ∫ g(y ,y ) d y d y 
i  1 2  1 2 2 1
 y y 
1 2
y 
∞
+ (1−I ) I log ∫1 ∫ g(y ,y ) d y d y 
1 2  1 2 2 1
−∞ y 
2
y y 
+ (1−I ) (1−I ) log ∫1 ∫2 g(y ,y ) d y d y  (21)
1 2  1 2 2 1 
−∞ −∞ 
 y  
+I (1−I ) log ∞∫ ∫2 g(y ,y ) d y d y  
1 2  1 2 2 1 

y −∞  
1
Notice that if residual is modeled standard normal, parameters to estimate using maximum
likelihood are in the limits of the integral. The difference in the double bounded model is
because the two questions are correlated, in this case appears a double integral, if a standard
normal is used, only appears one integral instead of Fη). The format of double bounded was
also 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% of
visitors to MANP during the period of the survey was applied. Survey was applied from
June 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 less
frequent were: Swiss, Dutch, Argentineans, Spanish and Italian. More than eighty per cent
of foreign tourists (84%) visited Costa Rica for the first time, and more than 40% visited
MANP first instead of going to another park.
Thirty seven percent of national visitors completed college. In case of foreigners it was
seventy seven percent. Talking about scholarship, 11.5% of nationals have more than 19
years of formal education. In the case of foreigners, it was 23.6%. other difference between
9
nationals and foreigners is referred to level of income . Net annual income media for
foreigners was $42.700. For nationals it was about ¢162.300, it means about $8.000 per
year.7 From the total of foreign visitors, 34% declared to have an annual income between
$30.000-$60.000.
Table 1. Sample (N) Distribution
Question of Availability of Paying to Entries to MANP
Foreigners Total Nationals Total
N total 1442 N total 803
Not interested 92 Not interested 85
Not know (NK)/ Not 64 NK/ NA 27
answer (NA)
Protest 5 Protest 2
N Final* 1283 N Final 692
(NK/ NA) / N total 0,04 (NK/ NA) / N total 0,03
Protest/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 necessary
corresponds 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", so
they were excluded from sample; in the same case, those surveys that identified respondent
as 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 Contingent
Valuation Method in two levels, in case of the estimation of variation in the indirect utility
in the first level (Y , equation 25 and 26) do not have explicit at the right side as explicative
1
variable the bid (implicitly is evaluating at US$6 and taking it out the constant parameter).
In the case of Y equation, bid does appear as explicative variable.
2
First Specification
Different specifications were estimated from defined models in equation 11, following
estimation at two levels. The next specifications include (ing), education level (number of
education years), a dichotomous variable that measures environmental preferences, in this
case belonging to an ecological group (ecol), and indicator of the enjoying from the visit
through a qualification variable (calif) of the park enjoying.
With the objective to identify the different specifications will be used a consecutive number
next 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 with
care, given existing problems to compare nominal data of income between countries.
10