1

Friday, 13 June 2003 Draft, May not be referred.

Influence of logit model assumptions and survey method on

estimated willingness-to-pay for forest conservation in southern Finland

Emmi Lehtonen1, Jari Kuuluvainen1, Ville Ovaskainen2, Eija Pouta1, Mika Rekola1 and

Chuan-Zhong Li3

Abstract

The current policy process to develop forest conservation in southern Finland requires

information about Finnish citizens’ attitudes towards forest conservation. Dichotomous-

choice contingent valuation (CV) data were collected by both mail and Internet surveys

to provide monetary welfare estimates for policy planning and also to compare these

two data-collection methods. The willingness-to-pay (WTP) distribution, however, of

the commonly used logit model does not necessarily describe the respondents

sufficiently well and may produce unrealistic results. The model known as the spike

model describes better the respondents’ WTP distribution if the data include, in addition

to positive responses, also those of respondents who are indifferent or who have

negative attitudes towards the proposed project. Another problematic feature in the

logit-model, known as the “fat-tail” problem, arises if a large share of the respondents

would be willing to accept conservation even at the highest price levels. In this study,

we examined the spike model and methods solving the fat-tail problem and compared

welfare estimates of the models. Results indicated that the spike model, extended with a

term that pinched the probability to zero at the estimated maximum WTP, fitted the data

best. This result recommends, in CV analysis, the use of these kinds of theoretically

consistent models. Welfare estimates of the the mail and internet surveys differed

markedly. Despite its lower costs and greater flexibility in survey design, for the time

being the internet survey thus seems insufficient for obtaining a representative survey

sample by itself, but its use as an additional data source should be investigated further.

1Department of Forest Economics, University of Helsinki 2 Finnish Forest Research Institute 3 University of Dalarna, Sweden

Comments and suggestions are welcome, correspondence to emmi.lehtonen@helsinki.fi

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Introduction

The most widely used method of valuation of non-market benefits is contingent

valuation (CV) and especially its dichotomous choice form. This referendum-type

questionnaire was recommended, among other suggested features of reliable valuation

study, by NOAA panel (Arrow et al. 1995). Demand for valid and widely approved

valuation method has led to comparison of the properties of the methods for valuing

non-market goods and CV seems still to qualify the most reliable valuation method. CV

studies commonly use mail surveys but recently Internet surveys have been suggested

as a low cost alternative.

Among other desired features CV is argued to have, it is incentive compatible

(Carson et al. 2000) which, when the validity of the approach is assessed, is one of the

main concerns. Controversy, however, exists as to the correct willingness-to-pay (WTP)

distribution if the WTP observed seems to diverge from the most commonly used

distributions. Distribution to be used in estimation of the model parameters should lead

to a model that fits the data statistically as well as possible and the assumptions should

also be consistent with economic theory and random utility maximisation (RUM)

(Hanemann and Kanninen 1998).

In order to obtain a welfare measure, for example, for an environmental change,

the researcher first makes assumptions concerning the form of the utility function and

proper distribution of the error term in the sampled CV data, and then estimates the

model parameters. These parameters are in turn used to calculate the mean WTP

(Hanemann and Kanninen 1998; Haab and McConnell 1998). If the calculated results

seem unrealistic and the estimated cumulative density function (cdf) is unreasonable

regarding the data that was used, the researcher may attempt to improve the results with

arbitrary distributional assumptions when calculating welfare measures. This procedure

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is, however, unsatisfactory as the same distributional assumptions should be used both

in the estimation of the model and in the calculation of the welfare measures. Arbitrary

limits and ad hoc formulations in the calculation stage are thus incompetent methods to

obtain valid welfare measure (Haab and McConnell 1998).

One of the problems encountered in CV studies valuing public projects that aim

at improving the level of conservation is that the WTP distribution may not be smooth

as assumed by, e.g., the standard logit model. This is due to the fact that conservation

may not contribute to some people’s welfare, and some may actually dislike

preservation. Thus, some respondents may have zero or even negative WTP for

increased conservation. In the literature, alternative approaches for allowing for zero

and negative as well as positive WTP have been presented (Hanemann and Kanninen

1998; Kriström 1997; Huhtala 2000; Clinch and Murphy 2001; MacMillan et al. 2001).

On the other hand, Haab and McConnell (1997), argue that for most public goods

negative WTP is not plausible because respondents can simply ignore goods that

provide no utility.

Several recent studies, however, argue for the importance of explicitly allowing

for losers as well as gainers and also those who are indifferent concerning the matter.

Therefore, a ‘screening’ question to identify respondents with positive, zero and

negative WTP should be used and the valuation question formed appropriately for each

group. The spike model ( Kriström 1997; Saz-Salazar and Garcia-Mendez 2001)

basically allows for indifference (zero WTP), and negative WTPs in some model

specifications. Clinch and Murphy (2001) filter the responses by a question about the

perceived effects of the project. Using a model similar to the extended spike model, they

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estimate the distributions for positive and negative WTP separately and suggest that the

net of positive and negative WTP be used to measure the net benefits.1

Other feature often encountered in empirical CV studies is that the WTP

distribution is positively skewed, i.e., the right tail is fat. To certain extent this can be

accounted for by using skewed distributions, like log-logistic (Ready and Hu, 1995).

The design of the questionnaire, however, may be such that the amount of yes votes

with highest bid levels becomes overestimated. Some respondents want to support

nature conservation, but suspect that the bid they vote for will actually not be collected.

This property of the data is the so-called “fat tail” problem, which leads to

unrealistically high mean WTP estimates. In this situation, little information about the

shape of the right tail of the WTP distribution is available.

Furthermore, researchers often assume a linear utility function and an additive

symmetric error term so that WTP ranges from negative to positive infinity. If the

empirical data indicates a substantial share of indifferent respondents, a spike model

with a discontinuity at zero is a suitable alternative. However, as infinitely large WTPs

seem also implausible, it may be necessary to also constrain the positive side of the

distribution.

The non-parametric approach is one of the most straightforward methods when

the WTP distribution should be bounded from above (Haab and McConnell 1997). The

shortcoming of this method is the missing parameter estimates of the exogenous

variables of the probability function and the difficulties to do other inference except to

calculate at the means and medians (Haab and McConnell 1998). Moreover, the non-

parametric method, in which the bid curve is interpolated to cross the zero probability of

1 Keith et al. (1996) and MacMillan et al. (2001) suggest that ignoring negative WTP may result in serious overestimation of project benefits.

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choosing “yes” at some point of the bid axes ( Kriström 1990), does not really solve the

fat tail problem. If the proportion of “yes” answers is high at the highest bid levels,

there is not necessarily enough information to find the correct bid price for the

probability to become zero. This method is also very sensitive to the probability figures

for the highest bids.

One of the parametric methods to solve the fat tail problem has been censoring

of the distribution of WTP at some upper limit, usually at the largest bid (Bishop and

Heberlein 1979). When this is done, the WTP the distribution collapses at the truncation

point leading to a discrete jump in the distribution. This method can, however, be used

to give lower bound WTP estimate. In the truncated model (normalised truncated in

Ready and Hu, 1995), the density lies under the truncation limit and the distribution is

continuous (Duffield and Patterson 1991). This method underestimates the proportion of

“yes” answers for each bid and serves also as a lower bound estimate, even if the cdf

cannot fit the original data very well.

Ready and Hu (1995) introduced a pinched logit model to give a “best-guess”

estimate of the WTP. In the pinched logit model the WTP of each individual is

constrained by some maximum level that can be either estimated simultaneously with

the parameters or, e.g., the income of the respondent can be used as the highest possible

WTP. When theoretical WTP exceeds this maximum level, pinching term forces the cdf

to reach the zero probability of accepting the proposed bid level. Resulting WTP

distribution is continuous.

Internet has offered an interesting possibility to collect data via World Wide

Web. Data collection via Internet decreases the costs of the survey and makes it possible

to test the properties of the method with a sufficient number of different survey

versions. Institutions doing market research, psychological sciences (Birnbaum 2001)

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and social sciences (Dillman et al. 2001) have examined the internet as a survey media.

Presently, however, internet surveys seem liable to the most common sources of the

errors in survey studies which are coverage error, sampling error, measurement error

and non-response error (Groves 1989, ). The coverage error occurs when all the units

defined in the population do not have a non-zero probability to be in the drawn sample.

Sampling error affects the results if used sampling frame is, for example, a register of

Internet users who are willing to participate surveys instead of a representative sample

of population. Measurement errors should be prevented by careful pre-testing of the

questionnaires to make the questions as clear and unambiguous as possible. Non-

response error is the source of error that troubles especially the Internet surveys

compared to other survey methods (Dillmann et al. 2001 ). The used population must

also be considered very carefully to prevent coverage and sampling errors. As far as we

know, the only contingent valuation study exploiting Internet data was a study of

(Berrens et al. 2001 ). They compared the Internet and telephone data in the estimation

of WTP of the Americans for the ratifying of the Kyoto Protocol. They found some

differences in the data sets, but still the relational inferences were quite similar. Their

results indicated that, other things being equal, the Internet respondents were less likely

to vote yes than the telephone respondents. The use of the CV method with cheaper and

non-representative data sets has been studied by Harrison and Lesley (1996). In the

study they used students as a sample and calculated expected WTP measures at the

population means. These results were in accordance with the national study, in which

the data was argued to have been representative. The comparison showed that the WTP

measures did not differ markedly. The cheaper, non-representative data sets could

therefore be possibly used in the CV analysis.

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In this paper, we will use a pinched spike model in order to study the effect of

the fat tail problem when estimating the willingness to pay measures for increasing the

level of conservation of Forest in southern Finland. In addition, we compare the WTP

estimates obtained using a mail survey and an internet survey using exactly the same

questionnaire.

Theoretical framework

The spike model

To estimate the mean and median WTP, we use the spike model (Kriström 1997) that

allows for respondents with zero WTP (i.e., a probability mass at zero). Although the

number respondents with zero willingness to pay in the present data are not very large,

their effect on WTP estimates should be examined.

In our discrete-choice CV survey the respondent is asked to accept or reject a

preservation program that implies a given monetary cost (A) and provides an increase in

the provision of environmental goods (biodiversity). An individual’s WTP for a change

in from z0 to z1 can be defined by

(1) V(y – WTP, z1) = V(y, z0),

where V(y, z) the individual’s indirect utility function, y is income, z0 is the initial level

of environmental goods without the preservation program and z1 the final level with the

program (z0 < z1).2 For a continuum of individuals with different environmental

valuations, the probability that an individual’s WTP does not exceed a given bid A is

(2) Prob(WTP≤ A) = Fwtp(A).

In the spike model the WTP distribution is assumed to have the following form:

2 Because an improvement in environmental quality is considered, WTP for the change measures the compensating variation (e.g., Johansson 1987; 1993).

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(3) Fwtp(A) = 0 if A < 0

p if A = 0

Gwtp(A) if A > 0,

where p∈(0,1) and Gwtp(A) is a continuous and increasing function with Gwtp(0) = p and

lim A→ ∞ Gwtp(A) = 1.

The spike model requires information for two questions. First, we need to know

whether the respondent is willing to contribute at all to the project. To generate an

indicator of whether the respondent’s WTP is positive or zero, a follow-up question was

used. Those respondents who chose the alternative with increased conservation given

the proposed bid, are known to have positive WTP. Those who chose the status quo

(i.e., rejected increased conservation at the proposed bid) were asked about their reasons

and classified according to their answers. The answer “I support increased forest

conservation and I am prepared to pay some for that, but less than the suggested sum”

was interpreted as positive WTP as well. The responses “I am indifferent to increased

forest conservation, and I am not prepared to pay for that” and “I support increased

forest conservation, but I am not prepared to pay for that” were classified as zero WTP.

Finally, the response “I support a reduction in forest conservation” was taken to

represent negative WTP. Because the actual distribution of negative WTP remains

unknown, however, the cases representing negative WTP were merged with zero WTP.

Consequently, the indicator Si takes on the values 1 or 0 as follows:

(4a) Si = 1 if WTP > 0;

WTP > 0 if the respondent accepted the conservation program at the suggested bid, or

was prepared to pay some positive amount, even if less than the proposed sum;

(4b) Si = 0 if WTP = 0,

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including cases with WTP < 0; WTP = 0 if the respondent was indifferent to increased

conservation, supported increased conservation but was not prepared to pay anything,

or supported a reduction in forest conservation. While the last answer actually indicates

negative WTP, the cases were few (4.9 per cent of responses). Thus, coding these to

zero seems justified. The second choice, denoted Ti, is whether the respondent is willing

to accept a given bid A. That is,

(5) Ti = 1 if WTP > A (0 otherwise).

In our application Ti = 1 if the respondent chose the conservation alternative given the

proposed price, A.

The spike model can be estimated using parametric maximum likelihood

methods or the nonparametric approach. We use the parametric approach and the log-

likelihood function for the sample (Kriström 1997):

(6) [ ] [ ] [ ].)0(ln)1()0()(ln)1()(1lnln1

wtpiwtpwtpii

N

wtpii FSFAFTSAFTSL −+−−+−=∑

To estimate the parameters of the distribution, assume WTP to be distributed as the

logistic. The model then becomes:

(6) ( )[ ] 1exp1)( −−+= AAFwtp βα if A > 0

( )[ ] 1exp1)( −+= αAFwtp if A = 0

0)( =AFwtp if A < 0,

where α and β (α, β > 0) represent the marginal utility of environmental goods and the

marginal utility of income, respectively.

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Mean and median WTP

Generally, the mean is the area under (and above) the survival function, i.e.,

(7) .)()(1)(0

0∫∫∞−

∞

−−= dAAFdAAFWTPE wtpwtp

The latter part vanishes when negative WTP is not allowed, and the spike at zero has

zero contribution. As the distribution of WTP is the logistic, mean WTP for the spike

model is then obtained as ln[1 + exp(α)]/β (e.g., Kriström 1997; Hanemann and

Kanninen 1998). Median WTP equals α/β if [1 + exp(α)]–1 = Prob(WTP=0) < 0.5 and

zero otherwise.

Censoring the WTP distribution

Censoring the WTP distribution (Hanemann and Kanninen 1998, ) is used here to refer

to the same model that has also been called truncated model (Duffield and Patterson

1991; Ready and Hu 1995). Duffield and Paterson (1991) used correction to improve

the models suffering of “fat tail” –problem was censoring the distribution of WTP.

Usually WTP was assumed to be non-negative and the highest bid level was used as an

upper limit.

(8) ∫ ++−=

T

dAA

CVE0 ))ln(exp(1

11)(βα

,

Where the parameters α and β are the maximum likelihood estimates from the logit

model and T is the highest bid used in the study.

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Truncated model

This method has been referred also as a normalised model (Ready and Hu 1995; Boyle

et al. 1988). Similar model like the previous censored one is the base of this model. In

this method the estimated cumulative density function is adjusted by normalising it to

reflect censoring. Expected value of WTP is (Park et al. 1991):

(9) ∫

−=

T

dzTFzFWTPE

0 )()(1)( ,

where z is a normalised random variable and F(T) is the cumulative distribution

function evaluated at the maximum value of the close ended bid amount used in the

survey. This normalisation applied to logit cdf results in a cdf form (Ready and Hu

1995)

(10)

≤

≤<++++

>

=

.00

0))ln(exp(1))ln(exp(1

1

),,;(

ifb

TAifAT

TifA

TAFβαβαβα

This model has the property of an everywhere-continuous cdf and the WTP is

constrained to be positive, but otherwise it is not consistent with the criteria for a valid

WTP model which avoids ad hoc formulations due to arbitrary choice of the upper

limit.

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Pinched spike model

To be able to estimate a model that is consistent with the criteria for valid model of

WTP, a pinching term can be introduced into the spike model. This additional term

forces the probability of choosing the increased conservation to reach zero, when the

estimated WTP exceeds the income of the respondent (Ready and Hu 1995).

(11) [ ]

TifATA

ifAifA

TA

ATAF

>≤<=<

−

−+

−−

+=

−

000

1

1)exp(1

111

)exp(10

),,;(

1

βα

αβα ’

where A is the bid and T is the limit that forces the probability to support the project to

go to zero. We will estimate the pinched spike model both by using respondents’

income as the limit and by estimating an average upper limit in the sample used.

Although the income certainly is the upper limit that an individual is willing to sacrifice

for conserving nature, the actual upper limit is likely to be much lower. Therefore,

estimating the upper limit from the data seems on a priori ground a more justifiable

approach.

Data and empirical Methods

The data was collected using mailed questionnaires with three contacts and a

random sample of 1500 Finnish citizens. At the same time, the postcards with the

Internet address and password were sent to the 1000 randomly sampled Finnish citizens.

The questionnaire was designed during fall 2001 and spring 2002 using first-year

students as a test group. A pilot mail survey was carried out to test the questionnaire and

the difficulty of the choice tasks. A total of 300 respondents were sampled for the pilot

mail survey and the response rate was 52%.

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The actual mail survey data were collected in March 2002 with three contacts.

The sample contained 1500 Finnish citizens aged 15 to 74 years who had been selected

at random from the population register. The average response rate to the mail survey

was 51%. The respondents were compared to the general Finnish population on the

bases of distribution of age, gender and professional status, and were found to be

representative of the entire population. In addition to asking CV the questionnaire asked

questions about respondents’ forest conservation attitudes and beliefs and requested

them to give some specific background information. The attributes of the choice tasks

were chosen after consulting with experts and with the committee appointed to plan an

initiative for forest conservation in southern Finland. In the CV questionnaire, two

different projects of forest conservation were outlined, a limited project with a lower

level of conservation, and an extensive project with a higher level of conservation. The

attribute levels corresponding to limited and extensive projects are indicated in Table 1

with two and three asterisks respectively. (Lehtonen et al. 2003)

In the CV method, respondents are asked to evaluate a specific public project

and indicate their willingness to incur personal costs in order to carry out the project.

The CV method was used in this study in a dichotomous choice format, with the

respondent choosing between two alternatives. The alternatives were maintaining the

current state of forest conservation and increasing forest conservation with related costs

being passed on to the consumer. The sample was divided equally into a “limited”

programme and an “extensive” programme. Table 2 presents an example of a contingent

valuation choice situation, where the respondent chooses between the status quo and

increased conservation, in this case, and the extensive project. In both, the limited and

the extensive CV conservation projects, the bid levels varied between 5, 30, 100 and

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300 €. The willingness-to-pay measurements and their distributions were estimated

from the responses and offered bid levels using logit models.

Table 1 Attributes and their levels used in choice questions. Attributes Attribute levels

1 Information and education, % of forest owners reached annually - Information and education about environmental issues to forest owners would be increased. Costs would be funded by tax revenue.

30 * 40 **

50 60 ***

70

2 Conservation contracts, % of forested land - Forest owner would take an initiative of protection of his forest area. Forest owner would receive a government subsidy for a certain period of time.

0.4 * 2 **

4 6 ***

8

3 Conservation areas, % of forested land - Area of conservation areas could be expanded if government would buy or redeem environmentally valuable forest areas from private forest owners, companies or counties.

1.6* 2 **

3 4 ***

5

4 Biotopes at favourable levels of conservation - As an impact of conservation, these biotopes would reach favourable levels and currently endangered species would be better off.

1. 2. 3. 4.

Nothing* Broad-leaved forests, pastures, ridges**

1+ rich coniferous forests 2+ dry coniferous forests***

3+ marshes

5 Number of endangered species, after 50 years - Number of endangered species is fixed with biotopes in our questionnaire. If certain biotopes would reach their favourable level, then only endangered species living outside these biotopes would remain endangered.

650* 300**

200 100***

90

6 Increase in annual income tax 2003 – 2012, €/year

0 * 5

30 100 300

* Attribute levels in status quo are the same in all choice tasks. ** Attribute levels in contingent valuation limited project. *** Attribute levels in contingent valuation extensive project.

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Table 2 Example of contingent valuation choice task. Current state Alternative A

Information and education, % of the forest owners reached annually

30 60

Conservation contracts,

% of forested land

0.4 6

Policy means

Conservation areas, % of forested land

1 4

Biotopes at favourable levels of

conservation

Nothing Broad-leaved forests, pastures, ridges, rich and dry coniferous

forests

Impacts of conservation

Number of endangered species, after 50 years

650 100

Additional costs Increase in annual income tax of your household 2003 – 2012, €/year

0 300

I prefer

A follow-up question was used to classify the responses to positive, zero or

negative WTP. All respondents were presented with the same WTP question, because a

realistic question for respondents with negative preferences was difficult to formulate.3

This approach allows us to take explicitly into account positive and zero WTP. Because

the bid vector contained only positive values, however, the actual distribution of

negative WTP remains unknown. Therefore, the cases interpreted to represent negative

WTP were coded to zero WTP. Because responses indicating negative WTP were few

(4.9%), this should not affect the results markedly. With only positive and zero WTP

involved, the simple spike model ( Kriström 1997) applies to our data.

3 Technically, negative bids could be included to capture negative WTP. While interpretable as a tax decrease in compensation for potential development benefits forgone, this was not considered a feasible as regards comprehensibility and credibility. Negative bids would amount to using the WTA compensation format, the use of which is not recommended, one main reason being that people are not used to claiming such compensations. In particular, compensations for preservation programs beyond those accruing to the landowners would be unrealistic.

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Results

In table 3 we present the models estimated using the mail survey data. In all cases the

coefficient of the bid gets the expected negative sign and is statistically significant. The

marginal elasticity of income, however, was much higher in absolute terms in the

pinched spice model, where the upper limit is estimated from the data, than in the other

model specifications. The estimated WTPs differ significantly in absolute terms (Table

4). The highest WTP is obtained from the spike model, being almost one third higher

than the WTP of the standard logit model, which gives almost the same WTP as the

censored (at highest bid) WTP estimate. Both pinched spike specifications produce

lower WTP estimates than the models without pinching, which was expected. As can be

seen from the figure 1, pinched spice model with estimated upper limit seems to fit the

data well if the share of respondents voting for the project with the highest bid is to be

considered an outlier. Also the estimated average upper limit of 724 € per year during

the following ten year period seems realistic.

Table 3 Parameter estimates for logit-, spike-, censored and pinched spike –models. Logit

Model

Spike Model

Pinched Spike Model

(T=estimated)

Pinched Spike Model

(T=income)

Constant 0.662 (0.104)

0.503 (0.075)

0.527 (0.074)

0.503 (0.075)

Costs of conservation/1000 (Slope)

-0.422 (0.680)

-3.911 (0.384)

-10.898 (1.292)

-4.027 (0.389)

Truncation Point 0.723 (0.068)

Log likelihood (model) -490.356 718.303 701.9081 718.160

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Table 4 Willingness-to-pay measures calculated with different distributional assumptions (€/year/household).

Logit Spike Censored Pinched spike

(T=723€)

Pinched spike (T= respondents

net income)

E[WTP] 157€ 250€ 152€ 91€ 120€

Standard error 19.9€ 23.3€

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

bid/1000

prob

abili

ty

P(logit) P(spike)P(censored)P(Pinched T)P(Pinched Y)Real

Figure 1 Comparison of the estimated willingness-to-pay distributions

Table 5 presents the estimation results of standard logit model for internet

survey, mail survey and for the combined data using covariates. In both samples, the

coefficient of the bid is statistically significant and negative as expected. It is

interesting to note that the size of the program is closer to being statistically significant

in the internet data, while respondents income is not significant in the internet data but

is almost significant (at 5 percent risk) in mail survey. Further more, the marginal utility

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of income is smaller in absolute terms in the internet survey. While we have not

formally tested, whether the two samples can be considered to come from the same

population, these differences may indicate that this is not the case.

Table 5 Logistic regression model for support of increased conservation in contingent valuation. Model A included respondents of the mail survey, while model B included data from internet survey.

Mail survey Internet survey Combined data

Variable Coefficient p-value Coefficient p-value Coefficient p-value

Constant 2.808 0.000 -0.520 0.499 1.919 .0000

Size of programme 0.027 0.883 0.468 0.161 0.178 .2555

Costs of conservation -0.006 0.000 -0.004 0.016 -0.005 .0000

Attitude towards present conservation

-0.319 0.000 -0.417 0.001 -0.128 .0190

Forest owner -0.508 0.013 -0.799 0.033 -0.681 .0001

Income 0.073 0.066 0.084 0.222 0.063 .0568

Nature-related activities 0.089 0.003 0.099 0.089 0.105 .0000

Age -0.033 0.000 -0.031 0.015 -0.034 .0000

Southern Finland 0.464 0.015 0.333 0.331 0.399 .0137

www –dummy -0.116 .5241

N 620 204 824

Log likelihood (model) -355.1 -112.1 -484.8

Log likelihood (constant only)

-421.7 -131.8 -555.1

Chi-squared test 133.2 39.5 140.6

Significance 0.000 0.000004 0.000

The calculated WTP estimates (table 6) also point to the same direction, The

difference between the estimated WTP from the mail survey and from internet survey

calculated using population means for the covariates differ by 143 €. Although the

difference between mail survey and internet survey is much smaller when pinched logit

model is estimated, it seems that internet survey is not yet able to represent whole

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Finnish population. Compared to the population means, respondents of the Internet

survey were younger, had higher income and they lived more likely in southern Finland

Table 6. Expected willingness-to-pay measures for mail and internet surveys from the logit models. Population means were used as the respondent characteristics. Mail Survey Internet Survey E(WTP) - pinched spike model (T= estimated)

91 € (T = 723 €) 114 € (T = 680 €)

E(WTP) - only constant and bid

157 € 269 €

E(WTP)a

- characteristics included 200€ 343€

a WTP can have negative values when mean WTP is calculated from the formula: mean WTP = (b0+b2*mdcg+b3*minc+b4*msou+b5*msqa+b6*mnat+b7*mage+b8*mfow)/(-b1), where mdcg, minc… are the population means of each variable in the model and b0, b1,… are the coefficients of variables.

Discussion and Conclusions

According to the results of the present study, the model specification has a significant

effect on the estimated welfare measures. It seems that especially due to the fat-tail

problem a CV survey may produce overestimates on the effects of public projects

increasing the level of nature conservation. This calls for a careful survey design,

because in the optimal case, the willingness-to-pay question should be formulated in

such a way that the fat-tail problem does not arise in the first place. However, this may

not always be possible, as e.g., pilot surveys may not be able to detect a suitable range

for bids. If the fat-tail problem seems to be present in the data, it must be taken into

account at estimation stage. One question requiring further attention in the present data

set is the difference in the WTP estimates between models with and without the socio-

economic characteristics of the respondents. Finally, it must be concluded that the

internet survey cannot as yet replace mails surveys as the data collection media.

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