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Parametric and Non-parametric Models To Estimate Households’
Willingness To Pay For Improved Management of Watershed
Myrna G. Carandang, Margare t M. Calderon, Leni D. C a macho and
Josefina T. Dizon
68 Journal of Environmental Science and Management 11(2): 68-78 (December 2008 )
ISSN 0119-1144
ABSTRACT
This paper explores the applicability of parametric and nonparametric models to estimate
households’ willingness to pay (WTP) for improved watershed management. The parametric
models used are spike and logit models, while the Turnbull estimator and the lower bound
estimation approach were used for the nonparametric estimation. .
The analyses made use of data obtained from a survey carried out in 2004 of 2,232 Metro
Manila households. The WTP estimates of the spike and logit models are PhP 24.00 and PhP
29.00 per household per month, respectively, which are lower than the nonparametric WTP
estimates. This can be attributed to the fact that parametric models consider the effects of the
independent variables on WTP. While the nonparametric estimation is characterized by its
simplicity, the sample mean WTP was calculated only from the raw data or actual response data
without any distributional assumptions for the unobserved component of preferences. The
mean WTP estimates generated by the study can be a basis in setting the price of raw water
for Metro Manila households on the premise that the revenues that will be generated will be
used for the improvement of the Angat, Ipo, Umiray and La Mesa watersheds.
Key Words: willingness to pay, spike model, logit model, non-parametric methods
INTRODUCTION
The contingent valuation is a method using
survey questions which reveal whether the
respondents are willing to pay a given bid
amount for a particular public good. The response
elicited from the respondents is either “yes” or
‘no”. Thus, the contingent valuation responses
are binary or discrete choice variables. Discrete
choice contingent valuation data can be analyzed
using different parametric models such as logit
and spike models. Another way of estimating the
willingness to pay of the discrete choice contingent
valuation methods is through the nonparametric
approach. It is one of the most straightforward
methods in estimating the willingness to pay for
a particular public good.
Estimating the willingness to pay of the
Metro Manila households for the improved
management of the Angat, Ipo, Umiray and La
Mesa watersheds is very important. It will help
generate empirical evidence that could inform
decisions about pricing the raw water provided
by the watersheds that supply Metro Manila.
The government is presently intensifying its
thrust in improving watershed management. This
is evidenced by many policies and guidelines that
are geared towards the improvement of watershed
management in the country. The 2003 Revised
Master Plan for Forestry Development (RMPFD)
program enumerated the current initiatives of the
government regarding watershed management in
terms of policy, technology and research and
development.
As in many government undertakings, watershed
management requires resources to sustain its
development as well as sustain the participation
of several concerned sectors. One of the potential
tools to generate sustained funding for watershed
management is the watershed user’s fee concept.
This concept intends to generate funds by setting
aside or capturing portions of benefits from
watersheds. These funds can, in turn, be used to
protect and develop the source of such benefits
through a plow-back mechanism. In addition, this
will help perpet uate the cycle of watershe d
Journal of Environmental Science and Management Vol. 11. No. 2 (December 2008) 69
the response will either be “yes” or “no”. Thus, if
the respondent answered “YES” to this question,
it is assumed that his WTP is positive, otherwise,
if his answer is “NO”, his WTP is assumed to be
zero. However, zero WTP may mean differently
to var ious respondents. It might be that an
individual may find that a program does not
contribute to his utility or there are other reasons
why a person is not voting for a program. The
spike model can be used to further analyze the
zero willingness to pay in referendum-style
contingent valuation studies where other standard
statistical tools cannot do.
Zero responses are very common in contingent
valuation studies (Kristöm 1997). Consequently,
when the level of zero responses is so high, the
spike model is more suitable in analyzing CV
data as compared to other models. This is because
the spike model allows a non-zero probability of
zero willingness to pay or to zero responses in
referendum-style CV studies (Kristöm 1997, Saz-
Salazar and Menendez 1999).
This model can also solve the so called “fat-
tail” problem which arises when a large share of
the respondents would be willing to support a
project even at the highest price levels. However,
some respondents support the pr ogram but
suspected that the bid they vote for will actually
not be collected. This type of data caused the “fat
-tail” problem which leads to unrealistically high
mean WTP estimates (Lehtonen et al. 2003).
Mathematical Model and Estimation
In the case of improving the management of
watersheds in Metro Manila, a respondent was
asked whether or not he or she is willing to
contribute to a trust fund that will be used for the
improved management of the watersheds supplying
water to Metro Manila. This will result in more
relia ble water supp ly and pr oduce other
environmental services or there will be change in
environmental quality z0→z1. The willingness to
pay for this change in environmental quality can
be expressed as:
(1) V(y-WTP, z1) = V(y, z0)
Where: V(y, z) is the individual’s indirect
utility function,
development, protection, provision of economic
goods and environmental services, and the integrity
and health of watersheds. The main idea for this
concept is the institutionalization of a system of
determining an acceptable payment scheme for
watershed users to be collected based on the users
willingn ess to pay ( WTP ). T he rev enu es
generated from fees can be used to further develop
and maintain the watersheds’ productive and
protective functions. This only shows that
estimation of realistic WTP is very necessary.
This paper compares the WTP estimates of
Metro Manila households for improved watershed
management using parametric and non-
parametric models.
MATERIALS AND METHODS
The data used in the estimation of WTP came
from the contingent valuation study that looked
into Metro Manila households’ WTP for the
improved management of four watersheds in Luzon
(Calderon et al. 2005). The watersheds where the
water supply of Metro Manila comes from are
Angat, Ipo, Umiray and La Mesa. The factors
identified to significantly affect their willingness
to pay were: bid amount, occupation, additional
water expenses, water distributor serving the
household, and income. The contingent valuation
scenario was presented to the respondents using
the dichotomous or discrete choice referendum
format.
Models to Estimate Households’ WTP for
Improved Watershed Management
a. Spike Model
The spike model is a parametric model that
can be used to estimate the willingness to pay
(WTP) and it allows a number of the respondents
to have zero WTP. This model recognizes distinct
groups of answers- those who have a positive
willingness to pay and those who have a zero
wil lingness to pay. It also deals with thos e
responses that have negative willingness to pay
values (Jacobsson and Dragun 1996).
In contingent valuation studies using the
discrete or dichotomous choice question format,
Parametric and Non-parametric Models To Estimate Households’ Willingness To
Pay For Improved Management Of Watershed
70
(4b) Ei = 0 if WTP = 0
This implies either of the following: the
respondent was indifferent to the program;
or, the respondent supported the program
but was not prepared to pay anything; or,
the respondent supported a reduction in
the program which indicates negative
WTP (WTP <0). However, these latter
cases were few, thus, coding these to zero
seems justified (Lehtonen, et. al 2003).
On the other hand, the variable Di will be
used to indicate the respondent’s willingness to
pay the suggested bid amount, that is,
(5) Di = 1 if WTP > A (0 otherwise)
The spike model (Kristom 1997, Hanemann
and Kanninen 1998) can be estimated using the
parametric maximum likelihood function for the
sample as follows:
N
(6) L = ∑{EiDi ln[1-Fwtp(A)]+Ei (1-Di )
1
ln [Fwtp(A)–Fwtp (0)]+(1–Ei) ln[Fwtp (0)]}
After estimating the maximum likelihood
function, the mean WTP is calculated by
solving this integral:
(7) ∫
where: α and β are the coefficients obtained
fr om the esti mat ed ma ximu m
likelihood function and represent the
marginal utility of environmental goods
and the marginal utility of income,
respectively.
However, if the value of β is positive, then
the mean WTP is determined by the following
equation:
(8) mean WTP =
Likewise, the spike value is defined as the
value where Fwtp(A)= 0 which is the probability
of WTP equals to zero. Kristom showed that
y is income,
z0 is the initial level of environmental quality
without the program,
z1 is the final level with the program (z0 < z1)
If there exists a continuum of individuals
who associate different values to the project, the
probability that an individual’s WTP does not
exceed an amount A ( or the probability that a
respondent will say no to a specified amount A)
is given by:
(2) Prob (WTP ≤ A) = Fwtp (A)
where: Fwtp (A) is a right continuous non-
decreasing function
The spike model assumes that the distribution
function of WTP has the following form:
(3) Fwtp (A) = 0 if A < 0
Fwtp (A) = p if A = 0
Fwtp (A) = Gwtp(A) if A >0
where: p belongs to (0,1) and Gwtp(A) is
a continuous and increasing function such
that Gwtp(0) = p and limA →∞ Gwtp(A) =1.
This creates a spike at zero.
The spike model uses two valuation questions:
1. Whether the respondent is willing to contribute
at all to the project/program; and
2. Whether the respondent is willing to contribute
a specific price or the given bid amount A.
The first question is used to determine
whether the respondent is in the market or not
while the second question suggests a specific
price A. If the answer to the first question is no,
the second is not needed.
For each respondent i, an indicator Ei which
takes on the values of 0 or 1 will be defined to
determine whether the respondent is “in-the-
market” or not.
(4a) Ei = 1 if WTP > 0
This implies that the respondent is “in-the-
market” and the respondent either accepted
the program at the suggested bid amount or
was prepared to pay some positive amount,
even if it is less than the proposed sum.
[ ]
)exp(1ln
1
α
β
+
)exp(1
)exp(
A
A
βα
β
α
−+
−
Journal of Environmental Science and Management Vol. 11. No. 2 (December 2008) 71
the spike value can be calculated using
the following formula:
(9) Spike Value =
The median WTP for spike model is then
obtained by:
(10) Median WTP =
if the spike value < 0.5 and 0 otherwise.
The Maximum Likelihood Approach
The method of maximum likelihood approach
(Hanemann and Kanninen 1999) seeks the values
of the unknown parameters based on the data that
were observed. The data consist of “yes” or “no”
responses from survey participants. In this case,
Di represents the willingness to pay responses of
the individuals, i.e., Di = 1 if yes (the respondent is
willing to pay the given bid amount) and Di = 0,
if no response. The discrete choice or binary
dependent variable is represented by Di..
In addition, diff erent ind epen dent or
explanatory variables (denoted by Xi) have been
observed for each respondent that includes the
bid amount (A) presented to him, and other variables
such income, socio-economic variables, etc.
The response probability formula, Fwtp (A),
is the likelihood function for the ith respondent.
It expressed the likelihood or probability of observing
the response that was observed, Di, given the
explanatory variables Xi and the unknown
parameters denoted by α and β. This can be
expressed as:
(11) Fwtp(A) = Pr (Di│Xi, β)
Since the distribution of the willingness to
pay is assumed to be logistic, equation no.
11 becomes:
(12) Fwtp(A) = if A > 0
Fwtp(A) = if A = 0
Fwtp(A) = 0
if A < 0
β
α
[ ]
)exp(1
1
α
+
[
]
1
)exp(1 −
−+ A
βα
[
]
1
)exp(1 −
+
α
0
),Pr(ln
)( =
∂
∑=
∂
∂
β
β
β
β
XiDi
L
However, the formula for the response prob-
ability function depends on what the analyst/
researcher has selected.
The likelihood function for the overall set of
responses (D1, D2, …Dn) representing the discrete
choice dependent variable given the corresponding
set of explanatory variables (X1, X2, …, Xn) and
the true but unknown parameters, α and β, is simply
the product of the individual likelihood functions
for each observation in the sample. So, taking the
logarithm, the log-likelihood function for the
sample is the sum of individual likelihoods as
given in Equation No. 6.
Maximization of the log-likelihood function
yields the first-order conditions:
(also with respect to α)
These first order conditions are set of non-
linear equations that require iterative numerical
solution techniques. The solution to this will
yield the coefficients of α and β.
B. Logit Model
In many disciplines , especia lly in th e
behavioral, social and related sciences, measurement
is still a real problem. Frequently, the researcher
has no meaningful alternative but to settle to
categorical dichotomies or imprecise qualities.
Hence, the obtained data are characterized as being
discrete or qualitative. In the context of contingent
valuation studies, the use of discrete classification/
choice models is very important.
The logit model is also a parametric approach
that can analyze this kind of data. It is a special
regression model which allows the dependent
variable in class variable form. The logit model
can be expressed as a binomial/binary or multi-
nomial model.
The binomial logit model was also used to
determine the WTP of respondents using the
dichotomous or discrete choice valuation format.
In this case, a respondent was asked whether or not
nonparam et r ic approac h i s one of the most
straightforward methods when the WTP distribution
should be bounded from above.
Two nonparametric estimation approaches
were used in this study to estimate the WTP for
the improved watershed management. These are
the Turnbull Estimator and the Lower Bound
Estimation of WTP methods.
These methods essentially use the sequence
of proportions of “yes” or “no” responses for
each bid, by beginning with the lowest bid.
Jacobsson and Dragun (1996) reported that
“Ayer et al. (1955) show that if the sequence of
proportions forms monotonic non-increasing
sequence of proportions, then this sequence
provides a distribution free maximum likelihood
estimator of the probability of acceptance”.
Further, when samples are large and as the
given bid amount increases, the proportion of
“no” responses to each bid is expected to increase
or the proportion of “yes” bids would be expected
to be strictly decreasing as the size of the bid
increased. If the initial sequence is not monotonic,
an algorithm is used to transform the sequence
into a monotonic one.
The non parametric estimation of WTP was
adapted from the procedures described by Haab
and McConnell (2002) for the Turnbull estimate
and procedures described by Bateman et al.
(2002) for lower bound estimate.
a) The Turnbull Estimator
The parameter definition and relation used in
deriving the Turnbull distribution-free estimator
are as follows:
Parameter Definition Relation
Bj Bid Amount
M Number of Bid Amounts
Nj Number of no responses
(WTP=0) to bid Bj
Yj Number of yes responses
(WTP=1) to bid Bj
Tj Total number offered Tj=Nj+Yj
bid Bj
Fj Pr(WTP≤0) Fj=Nj/Tj
he or she would be willing to contribute a specific
amount to a trust fund that would be used for the
improved management of the four watersheds
supplying water to Metro Manila. The dependent
variable in this study is the “yes” or ‘no” response
of the respondent to the question. The independent
variables are the different factors affecting their
willingness to pay.
Mathematical Model and Estimation
Based on Hanemann’s formula, as cited by
Jacobsson and Dragun (1996), the willingness to
pay for a change in environmental quality can be
expressed as:
Log Pr (WTP=1)
---------------------- = α + β1X1 +
1 - Pr(WTP=1)
β2X2 + … + βmXm + βnA
where: WTP = 1 is equivalent to the “yes”
response,
X1,X2, …,Xn are the independent
variables, and A is the bid amount.
The equation can also be expressed as:
1
Pr(WTP = 1) = -----------------------------------
1+ exp(-β0-β1X1 - β2X2 -…- βmXm)
From the model, the mean WTP was determined
using the formula:
Mean = α/β
where: α is the constant plus the coefficients
of the other variables multiplied by
their respective mean values; β is the
coefficient of the bid amount variable
C. Non-Parametric Approach
The nonparametric approach is another way
of estimating the willingness to pay of the discrete
choice contingent valuation methods. This approach
removes the need to make any distributional
assumptions. The method relates to utility theory
as the probabilities of a yes or no answer will
dep e nd o n ly o n t h e s i ze o f t h e bi d. T he
Parametric and Non-parametric Models To Estimate Households’ Willingness To
Pay For Improved Management Of Watershed
72
equivalent sub-sample. The distribution of the
respondents as well as their willingness to pay
the given bid amount is given in Table 1. Out of
the total respondents, 1,288 or 58.2% were found
to be “in-the-market”. This implies that 58.2% of
the respondents were willing to vote for a legislation
that will create a trust fund for the improved
management of watersheds even if its passage
will require them to contribute X pesos/
household/month to this trust fund. However,
only 40% of those “in- the-market” are willing to
pay the offered bid amount. Of these, more than
50% of the respondents who were offered the bid
amounts: 5, 10, and 30 pesos are willing to pay
and more than 47% for PhP 20.00 and PhP 25.00.
As the bid amount increases, the percentage of
the respondents who are willing to pay decreases.
When asked about their WTP for the bid amount,
the percentage of WTP = 0 responses received
was 60 %.
Figure 1 presents a graph of the distribution
of WTP among respondents to the discrete choice
valuation question asked in the survey. It can be
that no r espondent has declared a WTP less than
zero, i.e., no one believed they should be paid
money to have the management of the four
watersheds be improved. However, 1,341 respondents
are clearly not willing to pay the offered bid
amount for improved management of watersheds
and account for a large spike in the distribution
at zero. For the respondents expressing a positive
WTP, majority of them (66%) were willing to
pay the lowest value, in this case, the bid amount
of PhP 5.00, while a decreasing number of
households a r e pr epar ed to pay la r ger
amou nts. T he distribution of those with positive
WTP appears to be skewed to the right.
The maximu m likelihood function was
estimated giving values of α =-0.4353039 and β
= 0.02020969. These two parameter estimates
were used to calculate the mean WTP and the
spike value. Table 2 shows the values of the
coefficients for the spike model, mean WTP,
median WTP and the spike values.
The spike is defined as the value of Fwtp (0),
that is, the probability that WTP is equal to zero.
From its formula, the computed spike value is
approximately equal to 0.60. This is close to the
Procedure to Calculate the Turnbull Distribution-
Free Estimator
1. For bids (Bj) indexed j = 1, …, M, calculate
Fj = Nj/(Nj + Yj) where Nj is the number of
“no” responses to Bj and Yj is the number
of “yes” responses to the same bid, and Tj
= Nj + Yj .
2. Beginning with j = 1, compare Fj and Fj+1.
3. If F j+1 > Fj then continue.
4. If F j+1 < Fj then pool cells j and j+1 into one
cell with boundaries (Bj, Bj+2), and calculate
F*j ={Nj + N j+1}/{Tj +T j+1} = N*j/T*j.
That is, eli minate bi d B j+ 1 and po ol
responses to bid B j+1 with responses to bid
Bj.
5. Continue until cells are pooled sufficiently
to allow for a monotonically increasing
sequence.
6. Set F* M+1 = 1.
b) A Lower Bound Estimate for the Willingness
to Pay
1. Calculate the proportion of “yes” responses
to each given bid amount by dividing the
number of “yes” responses by the total
number of respondents offered each bid
amount.
2. If the monotonic sequence of the probabilities
is not satisfied, the pooling should be done
using an algorithm similar to the Turnbull
estimation.
3. Calculate the estimates of the probabilities
of the WTP that falls between bid amount
Bj and B j+1.
4. Multiply each given bid amount (Bj) by the
probability that WTP falls between it and
the next highest price (B j+1) from step 3.
5. Sum the quantities from step 3 over all bid
amounts to get the estimate of the lower
bound on willingness to pay, that is, the
mean WTP.
RESULTS AND DISCUSSION
A. The Spike Model
The contingent valuation study was conducted
among 2,232 respondents. Each bid was randomly
assigned to the respondent s representin g an
Journal of Environmental Science and Management Vol. 11. No. 2 (December 2008) 73
Bid
Amount
(Pesos)
No. of respondents
offered
No. of respondents
who are in-the-
market
(E = 1)
No. of
“Yes”
responses
(WTP=1)
%
No. of “No”
responses
(WTP=0)
%
5 220 152 145 66 75 34
10 224 141 129 58 95 42
20 218 122 106 49 112 51
25 210 121 97 46 113 54
30 213 132 108 51 105 49
50 216 122 84 39 132 61
75 244 139 79 32 165 68
100 215 128 58 27 157 73
150 239 116 50 21 189 79
200 233 115 35 15 198 85
TOTAL 2232 1288 (58.2%) 891 40% 1341 60%
Table 1. Respondents Distribution, Number of Respondents who are In-the-Market and Number of Yes
No Responses by Bid Amount.
0
200
400
600
800
1000
1200
1400
0 5 10 20 25 30 50 75 100 150 200
Bid Amount (P)
No . o f H ou seho ld s e xp ressi ng th is W TP
Figure 1. Distribution of WTP among Respondents.
Model α β Mean WTP Median
WTP
Spike
Value
Spike
Model
-0.4353039 0.02020969 24.69 0 0.607
Table 2. Results of Spike Model.
Parametric and Non-parametric Models To Estimate Households’ Willingness To
Pay For Improved Management Of Watershed
74
observed fraction of respondents rejecting to pay
which is 60%. The mean WTP obtained from the
spike model was PhP 24.69 per household per
month. The median, on the other hand, was zero
since more than half of those interviewed said
they were not willing to pay anything.
B. The Logit Model
The binomial logit model developed for this
study where 58% of the respondents expressed
willingness to pay was able to determine the
significant factors affecting the WTP of the
Metro Manila water users for the improved
management of the four watersheds. These are
the bid amount (BA), water distributor (WDist),
water expenditures (WExp), type of occupation
(Occ) and family income (Inc) (Table 3). The
model is significant at 0.24 level of significance
with chi-square value of 1990.51 and was able to
correctly classified 65.4% of the total responses.
The r esu lting mean WTP is PhP 29.11 per
household per month (Table 4).
The signs of the coefficients of the variables
included in the model are all in the expected
directions except for water expenditures. The
probability of a “yes” response decreases as the
bid amount the respondents are asked to pay
increases. Respondents who have higher income
have a higher probability of saying “yes” to the
WTP question since they have greater capacity to
pay than those who have low income. Although
unexpected, the results a lso show that people
with higher water expenditures due to more volume
of water consumed are more likely to say “yes”
to the WTP question than those who consumed
less volume of water. This could imply that
respondents give a high level of importance to
water.
C. The Non-Parametric Methods
Turnbull Estimates
Following the procedures cited above and
with the Turnbull estimates in Table 5, the mean
WTP using the Turnbull Estimator was estimated
as 56.84. The Turnbull also provided an estimate
of the range in which median WTP falls. The
median represents the price for which the
probability of a no response equals 0.5. From the
same table, the probability of no response, {Fj =
Prob (WTP=0)}, which is equal to 0.5 lies between
bid amounts PhP 20.00 and PhP 25.00, hence, the
median WTP is the range 20-25.
Lower Bound Estimates
In the same manner, Table 6 provides the
lower bound estimates after following the
procedures described above and the algorithm of
maintaining the monotonic sequence of the
probabilities. The mean WTP was estimated to
be equal to PhP 57.34 (Table 7) which is almost
equal to the Turnbull estimate. The midpoint
WTP was computed to be equal to PhP 64.55.
Significant Variable Coefficient Probability Value
BA -0.0117403 0.000
Wdist -0.2052112 0.025
Wexp 0.0002374 0.027
Occ1 0.1735257 0.088
Occ3 0.3637454 0.004
Inc 0.0000038 0.101
Model Chi-Square Value = 1990.51 with 0.2411 level of significance and 65.41% correctly classified responses.
Table 3. Significant Variables Affecting WTP.
Model α β Mean WTP Median WTP
Logit 0.341710610 -0.0117403 29.11 29.11
Table 4. WTP Estimates Using Logit Model .
Journal of Environmental Science and Management Vol. 11. No. 2 (December 2008) 75
Parametric and Non-parametric Models To Estimate Households’ Willingness To
Pay For Improved Management Of Watershed
76
Bid Amount
(tj)
Number of No's
(Nj)
Total Number of
Respondents (Tj) Fj (=Nj/Tj) Fj* fj*
5 74 220 0.06757 0.33636 0.33636
10 93 224 0.10753 0.41518 0.07882
20 110 218 0.18182 0.50458 0.08941
25 112 210 0.22321 0.50827 0.00369
30 103 213 0.29126
50 130 216 0.38462 0.60185 0.09358
75 165 244 0.45455 0.67623 0.07438
100 157 215 0.63694 0.73023 0.05400
150 188 239 0.79787 0.78661 0.05638
200 197 233 1.01523 0.84549 0.05888
200+ 1 0.15451
Mean WTP = Σtj (f*j+1) = 56.84915
Median WTP = 20- 25
Table 5. Turnbull Estimates for Improved Watershed Management.
Bid Amount
(Bj)
Number of Yes
(Yj)
Number of No's
(Nj)
Total Number
of Respondents (Tj)
Lj
Pr (WTP=1)
Lj*
5 146 74 220 0.66363636 0.66363636
10 131 93 224 0.58482143 0.58482143
20 108 110 218 0.49541284 0.49541284
25 98 112 210 0.46666667 0.49154930
30 110 103 213 0.51643192
50 86 130 216 0.39814815 0.39814815
75 79 165 244 0.32377049 0.32377049
100 58 157 215 0.26976744 0.26976744
150 51 188 239 0.21338912 0.21338912
200 36 197 233 0.15450644 0.15450644
Table 6. Lower Bound Estimates for the Improved Watershed Management.
BID RANGE (Lj* - Lj+1*) LOWERBOUND (tjlb) tjlb(Lj* - Lj+1*)
<5 0.33636364 0 0
5-10 0.07881494 5 0.394074675
10-20 0.08940858 10 0.894085845
20-25 0.02874618 20 0.574923547
25-50 0.09340115 25 2.335028691
50-75 0.07437766 50 3.718882817
75-100 0.05400305 75 4.050228746
100-150 0.05637832 100 5.637832052
150-200 0.05888268 150 8.832402536
>200 0.15450644 200 30.90128755
Mean WTP
Midpoint WTP
57.33874646
64.55
Table 7. Lower Bound Estimate for Willingness to Pay.
Journal of Environmental Science and Management Vol. 11. No. 2 (December 2008) 77
Comparison of the Models
The different models used in estimating the
willingness to pay for the improved management
of watersheds in Luzon yielded different mean
WTP estimates (Table 8). Parametric models
(spike and logit) provided lower mean WTP
estimates than the nonparametric models. This may
be because the parametric models considered
different factors affecting WTP. As Lehtonen et
al. (2003) pointed out, the shortcoming of the
nonparametric estimation is the missing parameter
estimates of the independent variables of the utility
function and the difficulties to do other inferences.
The mean and median WTP estimates were
calculated using only the actual response data.
Further, the results can also be attributed to
the strengths and weaknesses of the different
models used in handling the common problems
in contingent valuation such as large number of
zero responses and large number of respondents
willing to support a program even with the
highest bid levels. The data used in the spike
model have shown 60% zero responses. As
Kristom (1997) and Saz-Salazar and Menendez
(1999) found out, when the level of zero responses
is high, the spike model is more suitable in
analyzing contingent valuation data as compared
to other models. Although 36% of the respondents
were willing to pay the highest bid amounts (PhP
150.00 and Php 200.00), this will still contribute
to unrealistically high mean WTP estimates.
According to Lehtonen et al. (2003), this problem
can be better handled by the parametric models.
CONCLUSION AND RECOMMENDATION
The st u dy used t h e parame t r i c a nd
nonparametric models in estimating the mean
willingness to pay of the Metro Manila residents
for the improved management of watershed.
The parametric models give lower mean WTP
estimates than the non-parametric methods. The
mean willingness to pay as estimated from the
spike and logit models, amounts to PhP 24.00 per
household per month and PhP 29.00 per house-
hold per month, respectively. The nonparametric
Turnbull and lower bound met hods both
yielded a mean willingness to pay of PhP 57.00
per household per month. This can be explained
by the fact that the independent variables or
factors affecting the willingness to pay wer e
considered in the parametric model estimation
wh i l e the nonparametric estimates were based
only on the actual response data. The results are
consistent with the analyses of the contingent
valuation data of Kristom (1997), Saz-Salazar
and Menendez (1999) and Lehtonen et al. (2003).
The WTP estimates derived from this study
can be used as a basis for pricing the raw water
provided by the Angat, Ipo, Umiray and La Mesa
watersheds on the premise that the revenues that
will be generated will be used for the improvement
of these watersheds. The parametric estimates are
mor e conservative than the nonparametric
estimates, and may be more acceptable to water
users given that the situation will be from one
where raw water is free to one where raw water
is priced.
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Parametric Spike
Logit
24.69
29.11
0
29.11
Non Parametric Turnbull Estimator
Lower Bound Estimates
56.85
57.34
20-25
64.55
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Table 8. WTP Estimates of the Different Models.
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Pay For Improved Management Of Watershed
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