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JUVRE MEADOW - AN ECONOMIC ANALYSIS

Line Block Christoffersen

Royal Danish Veterinary and Agricultural University Institute of Food and Resource Economics Environmental Economics and Rural Division Rolighedsvej 25, DK-1958 Copenhagen

October 2006

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TABLE OF CONTENTS 1 INTRODUCTION................................................................................................................................................... 3 2 OUTLINE OF QUESTIONNAIRE....................................................................................................................... 4

2.1 THE WTP QUESTION ........................................................................................................................................ 4 2.2 DESIGN............................................................................................................................................................. 6

3 REPRESENTATIVENESS OF THE SAMPLE................................................................................................... 7 4 SCREENING THE DATA ..................................................................................................................................... 9 5 MODEL ................................................................................................................................................................. 12 6 THE SURVEY....................................................................................................................................................... 17

6.1 PREPARATION OF DATA .................................................................................................................................. 17 6.2 RESULTS......................................................................................................................................................... 18

6.2.1 Result1: DBDC model .............................................................................................................................. 19 6.2.2 Result2: Extended model – DBDC and OE............................................................................................... 21 6.2.3 Result3: Extended model – positive WTP ................................................................................................. 23

6.3 SENSITIVITY ANALYSIS................................................................................................................................... 24 7 DISCUSSION AND CONCLUSION................................................................................................................... 28 8 REFERENCE LIST.............................................................................................................................................. 30 9 APPENDIX............................................................................................................................................................ 32

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1 Introduction In the EU-project COMCOAST it is discussed whether the dikes around the North Sea continually should be raised or alternatives should be considered. This is a part of the discussion on how to manage and administer the protection of the coast around the North Sea. The Danish Coastal Authority is part of a working group who are going to value the emergent recreational area when new alternative methods of coastal protection are applied. One project area is Juvre meadow. If the dike is moved further towards land, a new area of marshland arises. Through questionnaires sent out to people in the Rømø area, the value of the new marshland is estimated. The data is analysed by applying different types of models. Furthermore, different distribution functions are applied. We find that a double-bounded dichotomous choice model and an extended model, which added a follow-up open-ended question, describe data best. A mean willingness to pay is estimated in the range from DKK 34-52. A total of 5,094 men and women in the age group 18-75 are living in the Rømø area, covering the municipalities of Bredebro and Skærbæk. Based on the number of people living in the Rømø area it is possible to estimate the total WTP for the Juvre marshland area. The value of removing the dike in the Juvre meadow towards land and thereby re-establish the marshland, is estimated in a range of DKK 5.77 – 7.30 millions when using a discount rate of 3 %. The result covers the utility for people living in the Rømø area when valuing the benefit from now to infinity. In the following chapter, the structure of the questionnaire and the construction of the willingness-to-pay (WTP) questions is introduced. The respondents were asked to state their WTP for entry to the Juvre marshland area after the dike is moved. In chapter 3, a representativity analysis of the returned questionnaires is carried out. Different socioeconomic variables are compared to the Danish population in order to verify the ability of the sample to represent the target population. In chapter 4, the dataset is prepared for estimation. That is, returned questionnaires are screened and respondents are excluded due to insufficient responses, protest answers and inconsistencies. In chapter 5, we go through the econometric estimation technique in short. The choice of distribution function and the derived effect is discussed. Further, the defined ranges for each respondent’s WTP are discussed according to which consequences the ranges may have on the results. That is, how the data from the WTP questions is interpreted according to the ability of estimating the mean WTP. In chapter 6, the results are showed followed by sensitivity analyses.

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2 Outline of questionnaire The questionnaire consists of 26 questions about attitudes towards nature in general and the Juvre meadow, WTP questions and questions about socioeconomic characteristics. The respondent is at first introduced to the EU-project COMCOAST where it is discussed whether the dikes around the North Sea continually should be raised or alternatives should be considered. The Danish Coastal Authority is part of a working group who are valuing the upcoming recreational area when new alternative methods of coastal protection are taking into force. Juvre meadow is such a project area. If the dike is moved further towards land, a new area of marshland arises. The respondents are informed about the existing area of the Juvre meadow and about the consequences of moving the dike due to re-establishment of marshland, which is the original nature in the area. The scenario is further described in the questionnaire together with the WTP questions. The respondent’s affiliation to Rømø is verified. Afterwards, the respondents is asked about their attitudes toward nature in general; how often they visit recreational areas; memberships of different environmental organisations and their attitudes toward statements such as “Protection of the nature in marshland areas are more important than free access” and “Reduced agricultural production should be accepted in order to maintain a better protection of the nature in marshland areas”. These questions verify different types of respondents and help to explain respondents’ preferences for the new Juvre marshland area. In chapter 6 the different questions, which enter the model as explaining parameters, are further described and discussed according to the parameter estimates. After the introductory questions, the respondents are asked to state their WTP for entry to the Juvre marshland area, which is after the dike, has been moved. First, the scenario is explained. The area today and the emergent marshland area is described according to the potential for outdoor and recreational activities, flora and fauna and in relation to the agricultural environment. Respondents answering “no” to the first or/and second bid is furthermore asked to choose among different potential reasons for answering “no”. Based on the respondents’ answers, protest bidders are identified. We return to this phenomenon in chapter 4. Furthermore, all the respondents are asked to state the level of certainty in their choices. Finally, the respondents are asked about their socioeconomic relations. That is questions about gender, age, members in the family, education, employment and income. The questions enter together with other explaining variables the dataset as explaining parameters and help model the stated WTP as accurately as possible.

2.1 The WTP question In this survey, double bounded dichotomous choice (DBDC) questions are used for eliciting individuals’ WTP for a season ticket to the Juvre marshland area. Respondents are asked to state their WTP for access to the area after the dike has been moved further towards land. Hence, the respondents are not asked about their attitudes toward the scenario, but only about their preference in terms of WTP for the new recreational area – whether they will visit the area or not. Just as the respondents (landowners) are not asked to consider their own personal economic consequences, they are only asked about their preferences for the area in relation to recreational activities, flora, and fauna and so on.

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When using the DBDC-technique the respondents are presented with two dichotomous choice (DC) questions, where the specific bid amount in the second DC question depends on the respondents answer to the first DC question. The respondent is first asked whether she is willing to pay some specific amount for a season ticket to the Juvre marshland area. That could be DKK 40 for a season ticket. If the respondent answers ‘yes’, she is presented with a follow-up DC question and asked whether she is willing to pay twice as much (e.g. DKK 80) for access to the same area. If the respondent answers ‘no’ to the first DC question, she is asked about the WTP for the half amount (e.g. DKK 20). Due to the possibility of the respondents answering ‘yes’ or ‘no’ to each DC question, we face four possible response outcomes: yes-yes, yes-no, no-yes and no-no [Hanemann et al. 1994; Loureiro et al. 2006]. In the present survey, the respondent has also had the possibility of answering ’I don’t know’ to each of the DC questions. The reason for choosing this possibility in the questionnaire is due to the idea not to force any respondent to answer something one really does not know anything about. In order to increase the information about respondents answering ‘no-no’ to the DBDC questions, the DBDC questions is followed by an Open Ended (OE) question. Using a DBDC choice question in combination with an OE question makes it possible to specify the respondents WTP. Respondents answering ‘no’ to the first or/and the second DC question are given the opportunity to state a WTP which is not bounded. These respondents are then asked to state their maximum WTP for a season ticket to the Juvre marshland area or to tick of a box saying ‘I am not willing to pay anything for access to the area’. The overall WTP question is structured as illustrated in figure 2.1 below. Figure 2.1: Structure of the WTP question As it appears from figure 2.1, respondents answering ‘I don’t know’ are treated just the same way as respondents answering ‘no’. Respondents then answering ‘no’ or/and ‘I don’t know’ are going to answer both the DBDC question and the OE question. The reason for grouping respondents this way is due to a conservative choice.

Dichotomous Choice

Are you willing to pay DDK x for a season ticket

Are you willing to pay DKK 2x for a season ticket

Are you willing to pay DKK ½x for a season ticket

Yes No/I don’t know

Open Ended

I will maximum Pay ____DKK I will not pay at all

No/I don’t know

Yes No/I don’t know

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Several previous studies have used the combination of DBDC and OE questions, although they do not include the possibility for the respondents answering ‘I don’t know’. See for example Strazzera et al. (2003a) and Nunes & Van den Bergh (2004) where respondents answering ’no-no’ is presented with an OE question.

2.2 Design In order to estimate a mean WTP from the DBDC questions, variation in the bid values are compulsory. Different respondents are presented with different bid values. In table 2-1 the different splits are shown. Table 2-1: Bid design Split 1 Split 2 Split 3 Split 4 Split 5 Question 12 40 60 100 200 400 Question 13 80 120 200 400 800 Question 14 20 30 50 100 200 As it appears from table 2-1, the first bid is doubled in question two and halved in question tree. The different bid values are chosen from a preceding focus group meeting and in such a way that a choke price value is expected to be reached. The choke price is the price where no respondent are willing to pay more for the good in question.

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3 Representativeness of the sample In order to make a conclusion for the entire population on Rømø and in Bredebro and Skærbæk based on the results from the sample, it is necessary to clarify whether the sample is representative for the target population, the population on Rømø and in Bredebro and Skærbæk. Data on the socioeconomic variables in the target population are from Statistics Denmark1. Because Rømø belong to the municipality of Skærbæk, the socioeconomic data from Rømø are combined with the data from Skærbæk. The respondents are then divided into two subgroups to compare with corresponding groups from Statistic Denmark. In appendix 3, the sample is compared to the population in the two municipalities of Skærbæk and Bredebro respectively due to different socioeconomic variables. A chi-test (χ2) is applied based on the actual numbers from the sample and the expected numbers from Statistic Denmark. It is tested whether the distribution in the sample is significantly different from the population in the two municipalities. The sample is not entirely representative. However, for the population in the municipality of Bredebro, the sample is representative for gender, age group and family size. For the population in the municipality of Skærbæk, the sample is representative only for gender. Age The distribution of age groups is significantly different from the expected distribution in the municipality of Skærbæk. The number of people younger than 44 years is less than expected and the number of people above 44 years is higher than expected. The imbalance in the sample may be explained by a skewed age group distribution on Rømø, which then may explain a similar imbalance in the municipality of Skærbæk. Family size People with children are under-represented in the Skærbæk sample. However, the sample is only significant different on a 95 % level. Income In the Bredebro sample, the distribution on income is on a 95 % level significantly different from the distribution from Statistics Denmark. The middle-income group (200.000 – 399.999) are over-represented while the low-income group (below 100.000 – 199.999) is under-represented. According to economic theory it is expected, that higher income anchor a higher WTP than low income. It should then be expected that the WTP estimate in the present survey is overestimated due to the under-representation of the low-income group. Whether the income distribution has an effect on the WTP estimate, depend on whether the income parameter turns out to be significant in the parametric analysis. In the Skærbæk sample, people with a gross income below DKK 200.000 also are significantly under-represented while both the middle-income group and the high-income group are over-represented. As in the Bredebro sample, we expect the WTP estimate in the present survey to be overestimated.

1 Statistics from Statistics Denmark are available from www.statistikbanken.dk.

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Education People with an intermediate education/bachelor are significant over-represented in the Bredebro sample and respondents with a vocational education are under-represented. In the Skærbæk sample, people with lower education are significantly under-represented while people with a short, intermediate or higher education is significantly over-represented. This was expected according to the under-representation of the low-income group.

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4 Screening the data The bid design in the DBDC question consists of five splits, each with a different bid range. Five randomly selected respondent groups have received one of the splits. In order to facilitate robust WTP estimates it is necessary that each of the five respondent groups are represented by a reasonably large sample. Consequently, the five different questionnaires were sent to 107 respondents, adding up to 535 questionnaires in total. In table 4-1, the response rate is shown together with the effective sample. The effective sample is the number of respondents entering the WTP analysis after exclusion of blank questionnaires and respondents answering inconsistently on the WTP question or not answering it at all. Table 4-1: Response rate Number % Questionnaires sent out 535 100 Returned 405 75.7 Returned blank 7 1.3 WTP question not answered 3 0.2 WTP question answered inconsistently 5 0.9 Effective sample 390 72.9 Protest bidders 124 (31.8) Screened sample used for analysis 266 49.7 Out of 535 questionnaires, 405 were returned. However, not all the questionnaires were filled out completely: seven questionnaires were returned blank and three respondents did not answer the WTP questions. These ten respondents are eliminated from the dataset. Several other respondents did not complete the socioeconomic questions. In order to analyse the WTP estimate the socioeconomic questions are important. However, we do not yet know which socioeconomic variables will turn out to be significant in the models. Excluding respondents who have not answered the socioeconomic questions may leave respondents out of the analysis that otherwise would have been in the sample. It is therefore decided to keep the respondents in the sample. Some of the respondents answered the WTP questions inconsistently by answering ‘yes’ to the first or second DC question and subsequently in the OE question answered that they do not want to pay anything2. Five respondents are sorted out due to this inconsistency, leaving 390 respondents for further analysis, corresponding to an effective response rate of 72.9%. This response rate is quite good compared to other Danish surveys e.g. Bjørner et al. (2002), Hasler et al. (2005) and Olsen et al. (2005). Protesters Several of the respondents expressing zero WTP in the OE question (question 15) were identified as protest bidders – based on the reason indicated for a zero bid. Statements such as “I am not willing to pay because I already pay through taxes” are classified as protest answers. Such a statement reveals that the respondent is not actually answering the WTP question, i.e. the described scenario requiring a trade-off between the price (bid) and access to the recreational site. This means that the expressed zero bid does not reflect the respondents true preferences for access to the site. For the same reason, respondents answering, “I am against this type of surveys” are excluded. Statements 2 Two respondents answered ‘yes-no’ to the first and second DC question and subsequently in question 15 answered ‘I will not pay anything for access to the area’. Similarly three respondents has answered ‘no-yes’ and subsequently answered ‘I will not pay anything for access to the area’ in question 15.

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such as “I can not afford to pay for the access” or “The Juvre marshland has no value for me” indicate a genuine zero bid. In table 4-1 it appears, that 124 respondents or almost one third of the effective sample is classified as protest bidders. This is a rather large share of the effective sample compared to other surveys see for example Olsen et al. (2005). An explanation for the large share of protest bidders could be that people living on Rømø have an aversion against paying for recreational areas on ‘their own island’. Out of the 123 protest bidders, 48 are respondents living on Rømø corresponding to 40 % of the protest bidders. One explanation for the large number of protesters is that people generally express a positive WTP for recreational areas, but that the opposite is the case if the area in question is in their own backyard. Another explanation could be due to the general negative attitude from the inhabitants on Rømø during the collection of questionnaires. People seem to be afraid of negative economic consequences for their agricultural production, if the dike is being moved. If the protest bidders are included in the sample, the WTP estimate may be underestimated. Therefore, the respondents are eliminated. A sensitivity analysis is carried out in the end of the report in order to verify the effect of leaving out the protest bidders. For a discussion of protest answers see for example Bateman et al. (2002), Arrow et al. (1993) or Strazzera et al. (2003b). Certainty in the WTP answers The respondents are asked how certain they are in their WTP choices. This gives an opportunity to increase the statistic significance of the results by excluding respondents, who are very uncertain in their answers. On a six-point scale from ‘very certain’ to ‘very uncertain’ 148 (56 %) of the respondent answered ‘very certain’ and 78 (29 %) answered ‘certain’. Only 28 of the respondents answered ‘a little certain’ (6 %), ‘a little uncertain’ (2 %), ‘uncertain’ (1.1 %) or ‘very uncertain’ (1.1 %). Twelve of the respondents did not answer the question. Due to the very few respondents being uncertain we do not expect the uncertain respondents to have an influence on the significance of the results. In combination with the fact that only seven respondents returned the questionnaire blank and eight respondents answered the WTP question inconsistent or did not answer it at all, we expect the WTP estimates to appear with high validity. No respondents are excluded due to uncertainty in their WTP answers. Distribution of respondents on different DC splits As mentioned, the bid design in the DBDC question consists of five splits. Table 4-2 shows the response outcome distributed on the five splits. The results are based on the screened sample.

Table 4-2: Distribution of respondents on different DC splits Amount % Total First offer xi High offer 2xi Low offer ½xi Yes-yes Yes-no No-yes No-no

40 80 20 13 8 13 65 100 60 120 30 10 20 8 63 100 100 200 50 7 11 18 65 100 200 400 100 4 6 15 75 100 400 800 200 0 2 20 78 100

Note: Respondents answering ’yes-I don’t know’, ’I don’t know-yes’, ’I don’t know-no’, ’no-I don’t know’ or ’I don’t know-I don’t know’ are included in the four aggregated alternatives. In addition, respondents who failed to answer the two DBDC questions correctly, but did answer the OE question is included. It counts four respondents. As expected, the number of respondents answering ’yes-yes’ decrease as the first offer increases. No respondents have expressed their WTP to be higher than DKK 800 in the DBDC question and

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neither of the respondents has expressed a WTP higher than DKK 800 in the OE question. This indicates that the chosen bid-range from DKK 40 to DKK 800 is reasonable according to the respondent’s stated WTP. Thus, the chosen choke price has been adequate, which makes it possible to estimate the maximum WTP for access to the recreational area. The four different response outcomes are distributed among the 266 respondents as shown in figure 4.1. As it appears, 93 respondents expressed a positive WTP. In addition to the respondents answering ‘yes’ to one of the bid choices in the DBDC question, a few respondents have expressed their WTP in the OE question after having answered ‘no-no’ to the previous bid options. Further, a few respondents failed to answer question 15, and can therefore not be defined as zero-bidders. According to this, 93 (35%) respondents have expressed a positive WTP whereas 173 (65%) respondents are regular zero bidders. Figure 4.1: Distribution of respondents on response outcome.

The technical definitions of the respondents bid ranges are further discussed in chapter 6.

19 25

39

183

93

173

0

20

40

60

80

100

120

140

160

180

200

Yes-yes Yes-no No-yes No-no Positive responses Zero WTP

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5 Model A parametric approach is adopted in order to formulate a model for the respondents’ stated WTP. The respondents’ true WTP are assumed to follow a certain distribution for example a log-normal distribution. Assuming that the WTP is depending on individual explanatory variables, the model describing the WTP has the structure as shown in equation 5.1: logWTPi = βiXi + ei , where βi is the unknown individual characteristic parameter to be estimated in the model for individual i, Xi is the variables determining the WTP responses and ei the independent error variable accounting for unobservable characteristics and assumed to be normally distributed between respondents [Ritz 2002; Ritz 2004; Loureiro et al. 2006]. When using a DBDC questioning technique, the individual respondent’s true WTP is narrowed down to a certain range due to the size of the two bids in the DBDC question. If the first bid is defined as xi, the second bid is defined as 2xi if ‘yes’ and ½xi if ‘no’. The ranges defining the WTP for the individual respondent are then defined as follows:

1. Yes-yes: 2xi ; ∞ 2. Yes-no: xi ; 2xi 3. No-yes: ½xi ; xi 4. No-no: -∞ ; ½xi

If the response outcome is ’yes-yes’ or ’no-no’ the range is limited, whereas the response outcome ’yes-no’ or ’no-yes’ result in an unlimited range. The discrete outcome of the bidding process then, is observable and defined by the following equation 5.2 [Loureiro et al. 2006; Ritz 2004]:

1. Yes-yes: 2xi ≤ WTPi 2. Yes-no: xi ≤ WTPi < 2xi 3. No-yes: ½ xi ≤ WTPi < xi 4. No-no: WTPi < ½xi

where WTPi is the individual respondents’ WTP for a seasonal ticket to the Juvre marshland. The probability of the response outcome ’no’ to some given offer, can be expressed as Pi

n(offer) = F(offer; θ), where F( · ; θ) is a certain statistic distribution function with parameter vector θ = (µ, σ) and where µ is the mean and σ the scale parameter for the true willingness to pay. The probability of the response outcome ‘yes’ can similarly be expressed as Pi

y(offer) = 1 - F(offer; θ). Under the assumption of utility maximizing respondents and response consistency, the probability of the response outcome ‘yes-yes’, Pi

yy (xi, 2xi), is given by equation 5.3 [Hanemann et al. 1991; Patterson 1996; Nunes 1998; Strazzera et al. 2003b]: Pi

yy (xi, 2xi) = Pr{xi ≤ max WTP and 2xi ≤ max WTP} = Pr{2xi ≤ max WTP} Pr{xi ≤ max WTP | 2xi ≤ max WTP}

= Pr{2xi ≤ max WTP} = 1 – F(2xi;θ),

Equation 5.2

Equation 5.1

Equation 5.3

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The second line is the result of the likelihood for the respondent being presented for the high bid equals the likelihood for the respondent answering ’yes’ to the first bid. The third line follows from 2xi > xi and consequently Pr{xi ≤ max WTP | 2xi ≤ max WTP}≡ 1. Equally, the probabilities of the other response outcomes are given by the following equations: Pi

nn (xi, ½xi) = Pr{xi > max WTP and ½xi > max WTP} = F(½xi;θ) Pi

yn (xi, 2xi) = Pr{xi ≤ max WTP ≤ 2xi} = F(2xi ; θ) - F(xi;θ) Pi

ny (xi, ½xi) = Pr{xi ≥ max WTP ≥ ½xi} = F(xi ; θ) - F(½xi;θ) Given the discrete outcome of the DBDC bidding process the method of maximum likelihood is applicable in order to estimate the WTP for each respondent [Strazzera et al. 2003a; Loureiro et al. 2006]. Given a sample of N respondents, the log-likelihood function for the DBDC model can be defined as:

))];2(1ln(*));();2(ln(*));(½);(ln(*);(½ln*[)(ln1

θθθθθθθ ijj

iii

N

i

jniii

njii

nni

r xFrxFxFrxFxFrxFrL −+−+−+=∑=

Where r is binary variables with value 1 or 0 dependent on the response outcome (e.g. r i

nn = 1 if the respondent is answering ‘no-no’). The statistical analysis in the form of maximum likelihood estimation is conducted using the lifereg procedure in SAS, which allows interval based maximum likelihood estimation. This estimation method is prevalent in the literature, e.g. Ritz (2004), Barton (1998) and Nunes (1998). Using the lifereg procedure in SAS requires an assumption about response consistency. That is, the respondents’ answers to both of the DC questions are driven by one underlying WTP value. So the respondents are assumed to respond to the second bid in exactly the same way as they would if it was the first bid. This assumption is not necessarily correct. One hypothesis is, that the respondents might respond differently to the second offer (being DKK 80), if the first bid for example were DKK 40 instead of DKK 60. This is known as the anchoring effect, which cause a correlation on the WTP estimates. Another hypothesis is, that respondents answer ‘no’ to the second offer just because he/she already has answered ‘yes’ to the first offer [Mitchell and Carson 1989; Herriges and Shogren 1996; Saz-Salazar & Garcia-Menendez 1999]. These kinds of correlations can result in biased results. Different models could be used (e.g. the bivariate probit model) in order to take into account the possibility of the response outcome and the bids being correlated. However, in the literature there is no consensus about whether a correlation should be expected or not and which model to be preferred, see Strazzera et al. (2003a) and (2003b), Patterson (1996), Alberini (1995a) and Cameron & Quiggin (1994) for a discussion of the issue. In the following analysis, an assumption about response consistency is made and the correlation has not been tested. Distribution function When estimating the mean WTP by maximizing the log-likelihood function, it is necessary to make some assumptions about the distribution of the respondents’ true WTP. Because the respondents’

Equation 5.4

Equation 5.5

Equation 5.6

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true WTP is unobservable, the distribution function also is unobservable. The choice of distribution function may then be determining for the results [Nunes 1998]. There are several distribution functions to opt for, for example the normal distribution, the lognormal distribution, the logistic distribution, the log-logistic distribution, the exponential distribution and the Weibull distribution. Which distribution to choose depends on the data being analysed. The true WTP is unobservable, but we know how the respondents are distributed according to the different bid ranges. The distribution of respondents in the present survey appears figure 5.1. Figure 5.1: Distribution of respondents on the different bid ranges in percent.

13.0

12.2

14.514.9

13.7

3.1

1.5

3.8

5.3

1.9

3.8

4.6

0.4

3.1

1.91.5

0.8

0

2

4

6

8

10

12

14

16

infinity -20

infinity -30

infinity -50

infinity -100

infinity -200

20-40 30-60 50-100 100-200 40-80 60-120 200-400 400-800 80 -infinity

120 -infinity

200 -infinity

400 -infinity

No (I dont know) - No (I dont know) No (I dont know) - Yes Yes - No (I dont know) Yes - Yes

Note: The intervals are based on the DCDB ranges and do not include respondents expressing WTP in question 15. As can be seen from figure 5.1, the majority of the respondents answered ’no-no’ pulling the distribution towards the left side of the scale. This result was expected for different reasons. At first because of the number of protest bidders indicating that, the respondents are not willing to express a positive WTP. Secondly, because of the general experience in the literature, see for example Patterson (1996), Strazzera et al. (2003a) and Brouwer & Bateman (2000). Due to the skewed distribution of respondents, the respondents’ true WTP do not follow a logistic, exponential or the Weibull distribution function due to the increasing form of these functions. A group of functions not increasing in form is the lognormal, the log-logistic and the normal distribution function. The lognormal distribution and the log-logistic distribution are both skewed to the left, meaning that there are more observations in the low end of the bid scale than in the high end [Ritz 2002]. These two distribution functions consequently seem to have the best fit on data. However, the normal

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distribution also seems to fit data if we leave out the zero bidders. Due to the distribution of response outcomes on the different bid scales, none of the distribution functions then seems to be preferred to one another. Different statistic tests can be used to verify the best fitting distribution function. In the following, the Pseudo R2 value for each of the models and the estimates from the Akaike Information Criteria (AIC) is used to test the distribution functions. AIC calculates a value for each model based on the maximized log-likelihood value. AIC is calculated as shown in equation 5.7:

kLAIC 2log)2()( 1 +−=∧

θ where k is the degree of freedom (given by the number of significant explanatory variables in the model) and L1 the maximized log-likelihood value. The smallest AIC value indicates the best fitting model [Akaike 1974; Nunes 1998; Swait & Adamowicz 2001]. In addition, the Pseudo R2 is calculated from the log-likelihood values as follows from equation 5.8:

0102 /)( LLLPseodoR −= ,

where L0 is the log-likelihood for a model with only an intercept term included and L1 is the log-likelihood for a model with additional explanatory variables. The Pseudo R2 value say how good the model with explanatory variables fit data according to the model only with the intercept included. The model with the highest Pseudo R2 value and most significant explanatory variables should be the model best fitting data [Hanemann et al. 1991]. A Pseudo R2 greater than 0.1 indicate a good fit whereas a Pseudo R2 greater than 0.2 indicate an extremely good fit [Louviere et al. 2000]. In table 5-1 the statistical parameters with assumed normal distribution, lognormal distribution and log-logistic distribution respectively, are shown. Table 5-1: Statistic parameters Distribution function N Variable L0 L1 Pseudo R2 AICNormal 228 8 -254.848 -174.601 0.3149 367Log-normal 228 8 -252.386 -177.544 0.2965 373Log-logistic 228 8 -254.551 -176.270 0.3075 371

Note: Data used for the tests are based on the DBDC question. Due to the respondents’ avoidance of answering all questions in the questionnaire, the number of observations in the model is less than the full sample of 266 respondents. The three different distribution functions all seem to fit data very well. Even though the normal distribution seems to make the best fit on data, it is not the preferred distribution. This is because the normal distribution allows negative WTP estimates. Due to the scenario in the present survey, the WTP values are assumed to be non-negative. The advantage of the logarithmic models is that zero or negative WTP values are precluded. Further, generally it has been found that the skewed distributions fit data better than the symmetric ones [Patterson 1996; Strazzera et al. 2003a]. In the following analyses, it is assumed that the

Equation 5.7

Equation 5.8

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respondents’ true WTP is either log normally distributed or log-logistic distributed. Assumption of normal distribution is analysed as a sensitivity analysis. Other surveys assuming the distribution function to be lognormal distributed see for example Alberini (1995b), Strazzera et al. (2003a) and Strazzera et al. (2003b). Surveys assuming the distribution function to be log-logistic distributed see for example Hanemann et al. (1991), Patterson (1996) and Brouwer & Bateman (2000).

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6 The survey In chapter 6.1 the data is prepared for analyses. Subsequently three results are shown: 1) parameter and WTP estimates only based on the DBDC questions, 2) parameter and WTP estimates based on the extended model, the DBDC and OE questions, 3) parameter and WTP estimates only based on positive responses in the extended model.

6.1 Preparation of data In order to obtain a WTP estimate using the interval based maximum likelihood function, upper and lower limits for each respondents WTP has to be defined. The chosen way to define these limits depends on whether the estimates are based solely on the DBDC questions or on the OE question as well. Further, the chosen distribution function is dependent on the defined limits because logarithmic functions cannot be used when a limit is defined as zero. First part of the analysis is based on the DBDC question. Here the procedure to draw up the data and defining the limits is clear. How the limits are defined appears from equation 5.2 and table 6-1:

Table 6-1: Bid ranges in the DCDB questions First bid Second Lower limit Upper limit Yes Yes 2x + infinity Yes No X 2x Yes I don’t know X 2x No Yes ½x X No No - infinity ½x No I don’t know - infinity ½x I don’t know Yes ½x X I don’t know No - infinity ½x I don’t know I don’t know - infinity ½x

When the respondent answers ’yes-yes’ the upper limit is unknown. It could be anything from the lower limit to infinity. The upper limit then is defined as going to infinity. This might seem exaggerated. In a sensitivity analysis, we analyse the effect on the result when setting the upper limit to DKK 1000, which is just above the highest bid in the survey from both the DBCD questions and the OE question. Next, the model is extended to include the OE question. Respondents answering ‘no’ or ‘I don’t know’ to one of the DBDC questions is given the opportunity to express their own positive WTP or state a zero bid. Respondents stating a zero bid should be defined to have a WTP in the range from minus infinity to zero. However, when assuming the distribution function to be logarithmic, only positive response outcome would be included. Hence, the logarithm cannot be taken to zero or a negative number. A possibility is to avoid zero limits. Instead, the upper limits could be put close to zero, for example to DKK 0.001. This though creates another problem. By setting the range from minus infinity to 0.001, the interval is primarily negative. Due to the predominance of respondents expressing a zero WTP, rather high WTP estimates are calculated in order to make the data fit a logarithmic distribution function. A solution is to restrict the lower limit and consequently avoid the

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exaggerated negative interval. The lower limit then is put to 0.001 and the upper limit to 0.002 for respondents expressing a zero WTP. Defining the lower limit to be at minimum 0.001 also relies on the assumption that the utility cannot be negative; hence, the WTP for the new recreational area cannot be negative. However, plot owners enforced to change the utilization of their land and in doing so being economically influenced, may in fact have a negative utility. Despite their negative utility due to the economic deficit, these respondents might have a positive utility due to the creation of a recreational area. One might argue that these respondents should be excluded because they have not made the required tradeoffs between the price and the recreational site. However, we do not know whether this is the explanation for a zero bid and whether the respondents do have a negative utility. In table 6-2 the upper and lower limits in the extended model is illustrated. Table 6-2: Bid ranges in the extended model First bid Second bid Lower limit Upper limit Yes Yes 2x + infinity Yes No x OE bid or 2x Yes I don’t know x OE bid or 2x No Yes ½x X No No 0.001 OE bid or 0.002 No I don’t know 0.001 OE bid or 0.002 I don’t know Yes ½x X I don’t know No 0.001 OE bid or 0.002 I don’t know I don’t know 0.001 OE bid or 0.002 As can be seen from table 6-2, respondents expressing a WTP due to the OE question are defined to have a WTP in the range from 0.001 to the stated bid, their maximum WTP. Respondents being insecure expressing ‘I don’t know’ to the first or second bid are handled as if they were answering ‘no’.

6.2 Results As mentioned three different analyses are carried out: 1) The DBDC model, 2) the extended model with the OE questions included and 3) the extended model only based on positive response outcomes. The three analyses are all carried out assuming a lognormal and a log-logistic distribution of the true WTP. Result1 is based on bid ranges coded as illustrated in table 6-1. Result2 is based on bid ranges coded as illustrated in table 6-2. Finally, result3 is based on bid ranges coded as result1 e.g. as shown in table 6-1. Different variables are tested in order to find the model describing data best. In appendix 1, all variables tested in the models are described according to number of levels, coding and description. In appendix 2, variables not being socio economic variables are described and the distribution of answers among respondents showed. As mentioned, the socioeconomic variables are described in appendix 3.

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6.2.1 Result1: DBDC model Result1 is shown in table 6-3. Table 6-3: Parameter estimates in the DCDB model Model Lognormal distribution Log-logistic distribution Parameters Estimate Standard error p-value Estimate Standard error p-valueIntercept 4.188 0.594 <.0001 4.3449 0.5693 <.0001Visit 0.335 0.17 0.0487 0.2723 0.1624 0.0936Roemoe -0.6859 0.2294 0.0028 -0.6813 0.2248 0.0024Certain -0.835 0.2711 0.0021 -0.8521 0.2614 0.0011Children -0.3954 0.22 0.0723 -0.3792 0.2127 0.0746Nature_marsh1 -0.3788 0.1298 0.0035 -0.3546 0.1275 0.0054Nature_marsh2 -0.413 0.13 0.0015 -0.4534 0.1296 0.0005Danishnature1 0.7147 0.2131 0.0008 0.6865 0.2073 0.0009Firstbid 0.2612 0.0762 0.0006 0.287 0.075 0.0001Scale 1.0388 0.1157 0.5781 0.0681 N 228 228 Log likelihood L0 -252.386 -254.551 Log likelihood L1 -177.544 -176.270 Pseudo R2 0.2965 0.3075

Note: Explanatory variables are coded according to the sequence of categories in the questionnaire. Visit is coded 1-3 due to the frequency of visits in the nature in general where 3 is the highest frequency. Roemoe is dummy coded where 1 is respondents living at Rømø and 0 is respondents living in Skærbæk or Bredebro. Certain is dummy coded, where 1 is respondents being very certain or certain in their stated WTP and 0 is the remaining respondents being less certain. Children are dummy coded where 1 is respondents with children in the household and 0 is respondents without children. Nature_marsh1 is the responses to question 5a about protection of the nature in marshland areas and Nature_marsh2 is responses to question 5b about reduced agricultural production in marshland areas. The two variables is coded 1-3 for agree, neither/nor and disagree. Danishnature is dummy coded and represent responses to question 4 about increased financing of the Danish nature. 1 is respondents answering yes and 0 is respondents answering no or I don’t know. Firstbid is coded due to the five different splits where 1 indicate the first bid to be DKK 40 and 5 the first bid to be DKK 400. Respondents having answered the different questions entering the model are excluded. As it appears from table 6-3, regardless of the choice of models, we obtain equally significant variables. Six variables are significant at a 95 % level and two variables are significant at a 90 % level. Further, the Pseudo R2 values are almost equal and indicate that the models make a good fit. From the eight significant parameters, five is negative indicating a lower WTP than the average. Three parameters are positive indicating a higher WTP than the average. In the following, we briefly comment on the result. Visit turns out positive indicating that the frequency of visiting recreational areas influences the WTP for the new marshland area on Rømø positive. That is, respondents visiting recreational areas one to three times at week or more generally have higher preferences for the dike to be moved and the recreational marshland area to be established. This is reasonable, if the sum of utilities visiting the area often is greater than the utility of visiting the area one time. In addition, the price of the seasonal ticket for access to the Juvre marshland is cheaper per visit the more often the respondent do visit the area. Roemoe is negative. A respondent who lives at Rømø is less willing to pay for a seasonal ticket to the Juvre marshland area than the average. This was expected due to large part of the protest bidders being respondents living on Rømø. The explanation could be due to a rather pessimistic atmosphere

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among people during the preparation of the survey. Furthermore, some of the people living on Rømø are farmers and might fear that their land will loose in value. This, though, should not influence their utility of obtaining the recreational marshland area. If the farmers were asked about a recreational area another place than in their backyard, they might have expressed a positive WTP. One could then argue that these farmers should be excluded from the survey because they have not stated their WTP based on the scenario described (hence, the changes according to flora and fauna, recreational activities and so on) but based on their own economic situation. However, the respondents are kept in the survey, because other reasons could explain the result. Maybe people living on Rømø are satisfied with the area as it is and do not have preferences for a larger recreational area. Certain is also negative. Respondents being very certain or certain on their stated WTP have a lower WTP than the average. An explanation might be that respondents expressing a positive WTP are more uncertain due to their budget restriction, about the fact that they might not be able to pay the amount they have stated. It is easier to be sure on a zero bid than on a given amount. However, the bids expressed by the respondents are very small, for which reason this argument may not weight too much. As mentioned in chapter 4 only 10 % (28 respondents) of the respondents expressed uncertainty in their WTP answers. That is a rather small share, which means that one should not put too much effort in this variable. The variable Children is negative. Respondents with children in the household have a lower WTP than the average. This may be due to a lower disposable amount for recreational activities etc. Nature_marsh1 and Nature_marsh2 both turn out negative. Nature_marsh1 covers the statement in question 5a about ’Protecting nature in marshland areas is more important than free access’. Nature_marsh1 being negative indicate that respondents that disagree with the statement have less utility of a larger recreational area than respondents who agree. Nature_marsh2 covers the statement in question 5b about ‘A reduced agricultural production should be accepted in favour of a better protection of nature in marshland areas’. Nature_marsh2 being negative indicate that respondents who disagree with the statement are less willing to pay for a seasonal ticket for the Juvre marshland area. This sounds reasonable because both statements favour nature over agricultural production and free access. Danishnature1 turns out positive. As the two just mentioned parameters, respondents agreeing in the statement ‘More money should be spent in protecting the Danish nature’ express a higher WTP than respondents disagreeing. The last significant parameter is the technical variable firstbid. It is examined whether the size of the first bid has any influence on respondents’ WTP. The variable should turn out non-significant because the WTP should be independent of the first bid. However, the parameter turns out positive indicating that a higher first bid (xi), results in respondents expressing a higher WTP than the average. From table 4-2 it can be seen, that the frequency of ’no’ responses increases as the first bid is getting higher. This is also found in other studies where it is implied that the likelihood of respondents answering ‘no-no’ in DBDC questions is increasing with the size of the first bid [Loureiro et al. 2006]. An explanation is as mentioned in chapter 5 the anchoring effect. The effect is widespread in the literature and cover the effect that the respondents do not know their true WTP and think that the

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bid offered is the ‘correct’ WTP. This means, that the likelihood for a respondent answering ‘no-no’ is equal for all firstbids [Mitchell and Carson 1989; Herriges and Shogren 1996; Saz-Salazar & Garcia-Menendez 1999]. The results show that preferences for the recreational marshland area on Rømø are dependent on the individual respondent’s profile. Respondents visiting recreational areas often and agree to the statements about the Danish nature and marshland areas have stronger preferences for the dike being moved towards land than the average respondent. Additionally, other variables were tested in order to verify their influence on the WTP estimate. These did not turn out significant. The tested variables are, among others, gender, age, education and income. From table 6-4 the estimated mean WTP appear with confidence intervals and the median WTP.

Table 6-4: WTP for the DBDC model Model Median, DKK. Mean, DKK 95 % confidence interval (Mean) Log normal 26 43 37 - 50 Log logistic 27 45 38 - 52

The WTP estimates are statistically equal. We conclude that there in the DBDC model is no difference whether the distribution function is assumed lognormal or log-logistic. The mean WTP for a seasonal ticket to the marshland area after removing the dike is estimated to between DKK 37 and DKK 52.

6.2.2 Result2: Extended model – DBDC and OE The model is extended to include the OE question. By including a follow up OE question, it is possible to obtain more information about the respondents answering ‘no-no’ to the DBDC questions. The information helps verifying whether respondents answering ‘no-no’ are true zero bidders or whether they have a positive WTP just lower than the lowest bid offered. If the WTP estimate of the extended model is included in the confidence interval from the DBDC model, the extended model is according to Nunes & Van den Bergh (2004) assumed to be more valid. The results are shown in table 6-5. Table 6-5: Parameter estimates in the extended model

Model Log-normal distribution Log-logistic distribution Parameter Estimate Standard error p-value Estimate Standard error p-value

Intercept 5.5574 1.8455 0.0026 7.0675 1.857 0.0001Visit 0.9794 0.5199 0.0596 1.2183 0.4904 0.013 Roemoe -2.6777 0.6621 <.0001 -2.5885 0.6469 <.0001Certain -4.4003 0.9831 <.0001 -5.2919 1.0226 <.0001Children -1.1299 0.6868 0.0999 -1.1596 0.6919 0.0938Education 0.3406 0.2061 0.0985 …… …… …… Nature_marsh1 -1.1212 0.3967 0.0047 -1.1957 0.3872 0.002 Nature_marsh2 -1.5881 0.3938 <.0001 -1.8539 0.4038 <.0001Danishnature1 2.123 0.6639 0.0014 2.2872 0.6732 0.0007Firstbid -0.483 0.2139 0.0239 -0.4393 0.2093 0.0358Scale 4.3808 0.2186 2.5021 0.1437 N 227 231

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Log likelihood L0 -857.124 -865.152 Log likelihood L1 -684.417 -695.498 Pseudo R2 0.2015 0.1961

Note: In addition to the variables from result1 in table 6-3, the variable education is also significant. Education is coded due to the six different categories in the questionnaire. Respondents having answered the different questions entering the model are excluded. As it appears from table 6-5, the model assuming the true WTP’s to be log-normal distributed entail the largest number of significant explanatory variables. Here six variables are significant at a 95 % significance level and three is significant at a 90 % level. In the log-logistic model, seven variables are significant at a 95 % significance level while one variable is significant at a 90 % level. The Pseudo R2 value indicates that both models make a good fit on data, although the fit is better for the log-normal model. According to result1, more variables are included in the log-normal model, while the number of significant variables is the same for the log-logistic model. Both the Pseudo R2 values show a marked lower fit than in result1 indicating that the extended model do not fit data as well as the DBDC model. Whether the DBDC model or the extended model is preferred is not quite clear. Variables being significant in both results, except the variable firstbid, came out with the same sign. Firstbid is now negative indicating that a higher first bid (xi), results in respondents expressing a lower WTP than the average. The size of the first bid then does influence the response outcome. This is as before mentioned illustrated in table 4-2 where it appears that the frequency of ’no’ responses increases as the first bid is getting higher. The result indicates that the anchoring effect might be limited when the WTP question is extended from a DBDC question to a combination of DBDC and OE questions. The education parameter turns out positive indicating a higher WTP among higher educated respondents than the average. This could be due to a higher income and a surplus in the budget restriction, although the income parameter in itself did not turn out significant. The mean WTP estimates appear from table 6-6.

Table 6-6: WTP for the extended model - DCDB and OE Model Median, DKK. Mean, DKK. 95 % confidence interval (Mean) Log-normal 0 8 2-15 Log-logistic 0 20 2-38

According to result1 in table 6-4, the estimates from the extended model are different. In addition, the variance between the two extended models is much larger than in the previous results. The confidence interval in the log-logistic model covers values in the range from DKK 2 to DKK 38, which is much wider than before. This indicates a large difference between the respondent’s true WTP and the estimated model [Hanemann et al. 1991; Strazzera 2003b]. The log-normal model is much more precise. The WTP estimates obtained from the log-normal model, is lower than the WTP estimates obtained from the previous models whereas the WTP estimate from the log-logistic model is closer to the before obtained results. Both estimates are as expected lower than the results obtained from the DBDC model due to a larger amount of respondents defined to have a WTP in a narrower interval (upper limit on 0.002 instead of ½xi). However none of the WTP estimates is included in the

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confidence intervals obtained from the DBDC model as expected according to Nunes & Van den Bergh (2004), see table 6-4.

6.2.3 Result3: Extended model – positive WTP As before, the model is extended to include the OE question. Only respondents expressing a positive WTP is included in the estimation. The results appear from table 6-7. Table 6-7: Parameter estimates in the extended model – only respondents with positive WTP Model Log-normal distribution Log-logistic distribution Parameter Estimate Standard error p-value Estimate Standard error p-value Intercept 3.1349 0.2175 <.0001 3.1235 0.201 <.0001 Born -0.6396 0.3214 0.0466 -0.5976 0.3055 0.0505 Roemoe 0.4682 0.1835 0.0107 0.4232 0.1775 0.0171 Gender 0.2681 0.1571 0.0879 0.258 0.1492 0.0837 Danishnature1 0.3446 0.1578 0.029 0.3315 0.1501 0.0272 Firstbid 0.3674 0.056 <.0001 0.3819 0.0543 <.0001 Scale 0.6518 0.0661 0.3673 0.0417 N 90 90 Log likelihood L0 -135.166 -135.968 Log likelihood L1 -111.566 -110.065 Pseudo R2 0.1746 0.1905

Note: In addition to the variables in result1 and result2, the variables born and gender, turn out significant. Born is dummy coded reflecting the respondent’s native town, born on Rømø or not. Gender is dummy coded for men and women respectively. Respondents having not answered the different questions entering the model are excluded. Due to their positive WTP, 90 respondents are included in the data. The Pseudo R2 value indicate that the two different models make a good fit on data, though the fit is not as good as the fit obtained in result 1 and 2. The models describe respondents having a positive WTP. That is which groups are willing to pay more or less for a seasonal ticket to the Juvre marshland area. In both models five variables turns out significant. In the log-normal model four variables is significant at a 95 % significance level while only three is significant at a 95 % level in the log-logistic model. As in result1, the variable firstbid turns out positive. Again, this can be explained with the anchoring effect. Born is negative, indicating that respondents born on Rømø are willing to pay less for a seasonal ticket to the marshland area. This result was expected because the variable Roemoe in the other estimations turned out negative; hence, respondents living on Rømø have lower preference for an increased recreational area than respondents living outside Rømø have. However, Roemoe now turns out positive indicating that respondents living on Rømø are willing to pay more for a seasonal ticket than people not living on Rømø. An explanation for this result are, that most of the respondents having a positive WTP and live on Rømø are newcomers. Only 6 % of the respondents having a positive WTP are born on Rømø whereas 20 % are newcomers. The variable Gender is positive, indicating that the average woman willing to pay for a seasonal ticket to the Juvre marshland area, also are willing to pay more than the average. This result was

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expected because earlier Danish studies have shown that women have stronger preferences for environmental goods than men see e.g. Hasler et al. (2005) and Ladenburg et al. (2005). Table 6-8 shows that the two models produce almost identical WTP estimates. The mean WTP is between DKK 97 and DKK 124. Table 6-8: WTP for the extended model – only respondents with positive WTP Model Median, DKK. Mean, DKK. 95% confidence interval (Mean). Log-normal 98 110 97-123 Log-logistic 100 111 98-124 The mean WTP estimate is based on the 90 respondents having a positive WTP. That is, respondents willing to pay for a seasonal ticket to the new recreational marshland area, have stated a mean WTP in the range from DKK 97 to DKK 124. The estimate then do not reflect the mean WTP for respondents who filled out the questionnaire, it is only specifying the WTP for respondents expressing positive preferences for the scenario. The WTP must be adjusted to include respondents with a zero WTP in order to cover the average respondent’s preferences. Respondents having a positive WTP correspond to 35 %3 of the effective sample. The mean WTP is then adjusted to be only 35 % of the estimated WTP, see Carlsson & Kataria (2006) for an equivalent adjustment of estimates. In addition, the confidence intervals are adjusted to 35 % of the estimated.

• Log-normal distribution: DKK 38, confidence interval: 34-43 • Log-logistic distribution: DKK 39, confidence interval: 34-43

If we compare the results with the DBDC estimates, we find that the WTP estimates is (almost) included in the confidence intervals estimated in the DBDC model, see table 6-4. Though, pay attention to the lower end of the confidence interval, which is lower than then confidence interval from result1.

6.3 Sensitivity analysis In this chapter, three analyses are carried out in order to test the sensitivity of the results. The two first sensitivity analyses are based only on data from the DBDC question. The estimates are then compared to the parameter estimates and WTP estimates in result1. The last sensitivity analysis includes all three models (DBDC, extended model and the extended model only with positive WTP’s) under a normal distribution assumption. Estimates are compared to all three results in chapter 6.2. All respondents included, no protesters excluded When all respondents are included in the estimation, also the protesters are incorporated. These are for example respondents answering ‘no-no’ and in the following substantiate the answer with statements as ’I am already paying through taxes’. The hypothesis is that the WTP estimate becomes underestimated when including these respondents, because they enter the estimation with a zero WTP for the recreational area, for which in fact they might have positive preferences. We expect the estimate to be lower than the estimate in table 6-4. The results are shown in table 6-9. 3 The percent is calculated from 90/258 respondents where respondents failed to answer the questions included as variables in the model (result3) is excluded. Six respondents failed to answer the question about native town and two others failed to answer the question about gender.

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Table 6-9: Sensitivity analysis: Protesters included Model Log-normal distribution Log-logistic distributionParameter Estimate p-value Estimate p-value Intercept 3.8267 <.0001 3.8726 <.0001 Roemoe -0.4934 0.0302 -0.5399 0.0179 Certain -0.8002 0.0071 -0.8086 0.0046 Nature_marsh1 -0.338 0.0206 -0.3344 0.0222 Nature_marsh2 -0.3344 0.021 -0.3733 0.0113 Danishnature1 0.7161 0.0031 0.701 0.0036 Firstbid 0.2669 0.0016 0.3106 0.0002 Scale 1.3556 0.7448 N 347 347 Pseudo R2 0.2034 0.2104 Median WTP 16 17 Confidence interval (Mean) 20-25 22-28 Mean WTP 22 25 Variables being significant are (almost) the same as in the DBDC model. However, the variables visit and children are excluded. None of the parameters changes sign. In relation to the DBDC model, 119 respondents more are include in the estimation. That is 86 % more respondents with a stated WTP at zero DKK. As expected, the WTP estimates are considerably lower than in the DBDC model. The mean WTP for a seasonal ticket to the Juvre marshland area is between DKK 20 and DKK 28 where the WTP estimate in the DBDC model is between DKK 37 and DKK 52. Consequently, the mean WTP including protesters is halved. Upper limit narrowed to DKK 1000 instead of infinity Respondents answering ’yes-yes’ to the DBDC question is defined to have a WTP in the range from 2xi to infinity. This is because the true WTP is veiled and consequently the upper limit is unknown. This might seem unrealistic and one could expect the WTP to be overestimated. As a sensitivity analysis, the upper limit is assumed being DKK 1000. The result is shown in table 6-10. Table 6-10: Sensitivity analysis: Upper limit equal DKK 1000 Model Log-normal distribution Log-logistic distributionParameter Estimate p-value Estimate p-value Intercept 4.1635 <.0001 4.3138 <.0001 Visit 0.3278 0.0486 0.2654 0.0925 Roemoe -0.6732 0.0026 -0.6671 0.0022 Certain -0.8223 0.0019 -0.8345 0.001 Children -0.3844 0.0737 -0.3695 0.0735 Nature_marsh1 -0.3721 0.0033 -0.3473 0.005 Natyre_marsh2 -0.4051 0.0014 -0.4436 0.0004 Danishnature1 0.7039 0.0007 0.6737 0.0008 Firstbid 0.2654 0.0004 0.2924 <.0001 Scale 1.0216 0.5622

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N 228 218 Pseudo R2 0.3005 0.3143 Median WTP 27 28 Confidence interval (Mean) 37-50 39-52 Mean WTP 43 45 Variables being significant are the same as in the DBDC model from result1. The signs as well are identical. The WTP estimates are statistically identical to the results from table 6-4. According to these results, it does not matter whether SAS is allowed to estimate the WTP within a closed or open positive range. This is due to the small number of respondents answering ‘yes-yes’ (8 %) and most important according to the form of the logarithmic distribution where the likelihood of high bids is very small. Normal distribution As mentioned in chapter 5, the choice of distribution function is not quite clear. The normal distribution function was excluded because it allows negative WTP estimates. In the following, three analyses are carried out, all assuming the respondents true WTP to be normally distributed. The three analyses are due to the three different models analysed in chapter 6.2: The DBDC model, the extended model and the extended model only with positive WTP outcomes included. The results are shown in table 6-11. Table 6-11: Sensitivity analysis: normal distribution

DCDB1 Extended model2

Extended model only with positive response

outcomes3 No. of explanatory variables 8 8 4 N 228 231 92 Pseudo R2 0.3149 0.1644 0.1004 Median WTP 4 37 112 (40)4 Confidence interval -7-17 35-45 111 (39) -138 (49) Mean WTP 5 40 125 (44)

Note1: Significant variables: Visit, Romoe, Certain, Children, Nature_marsh1, Nature_marsh2, Danishnature1, Firstbid Note2: Significant variables: Visit, Roemoe, Certain, Children, Nature_marsh1, Nature_marsh2, Danishnature1, Firstbid Note3: Significant variables: Visit, Children, Danishnature1, Firstbid Note4: The mean WTP estimate in parenthesis is the calculated WTP when respondents stated a zero WTP is included. The percent used to fit the result to the full sample, is calculated from 92/260 respondents where respondents failed to answer the questions included as variables in the model is excluded. Four respondents failed to answer the question about frequency of visiting the area and two others failed to answer the question about children in the household. The WTP estimate from the DBDC model is significantly lower than the estimate in result1. Further, the lower confidence interval is negative. The same variables as in result1 are significant and appear with the same sign. The Pseudo R2 value shows a very good fit. The WTP estimate from the extended model is closer to the log-logistic model than the log-normal model in result 2, but significantly lower. The number of significant variables is almost appearing with the same sign, although firstbid turns out positive. The Pseudo R2 value shows a bad fit. The last model is the

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extended model only including positive response outcomes. Here the mean WTP is close to the estimates in result3. The number of significant variables is almost the same but the Pseudo R2 value shows a very bad fit. From the sensitivity analyses assuming the distribution function to be normally distributed, it appears that the results do change tremendously depending on the chosen distribution function.

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7 Discussion and conclusion In the preceding chapters, data from a DBDC survey are evaluated. Three different models are used in order to estimate the mean willingness-to-pay for access to the Juvre marshland area. This is a double-bounded dichotomous choice model, a model extended with an open-ended question, and the extended model only including respondents stating a positive WTP. For each model, two different distribution functions are applied. That is the log-normal distribution function and the log-logistic distribution function. As seen from chapter 6.2 the variables turning out significant in the three models have the same sign throughout all three models and are furthermore not depending on the chosen distribution function. Moreover, the number of significant variables does not change much. In table 7-1 the results from chapter 6.2 is summed up. As it appears, the WTP estimates change according to the chosen model and the applied distribution function.

Table 7-1: Results from chapter 6.2 Mean WTP, DKK Confidence interval,

DKK (Mean) Pseudo R2 Respondents included in the analyse

DBDC Log-normal 43 37-50 0.2965 228 Log-logistic 45 38-52 0.3075 228 Extended model Log-normal 8 2-15 0.2015 227 Log-logistic 20 2-38 0.1961 231 Extended model only with positive WTP’s Log-normal 38 34-43 0.1746 90 Log-logistic 39 34-43 0.1905 90

The results from the DBDC model and the extended model only including respondents with a positive WTP are very close to each other. As expected, the estimates from the extended model (only including positive WTPs) are below estimates from the DBDC model and the confidence interval is furthermore almost included in the DBDC confidence interval. This indicates that we obtain more information when we include an OE follow-up question than by the DBDC alone. When only respondents having a positive WTP is included, respondents expressing a zero bid in question 15 are excluded from the parameter analyses. After estimating the WTP, the WTP is adjusted in order to consider the zero-bidders as well. The advantage of estimating the WTP in this way compared to the extended model including all respondents is that data fit the logarithmic distributions better. As explained in chapter 5, the distribution of respondents on the different bid ranges is pulled to the left. This skewed distribution causes a better fit to the logarithmic distribution function compared to other distribution functions. However, when respondents expressing a zero bid in question 15 are included, the distribution is pulled too much towards the left side of the scale. Consequently, the data do not fit the logarithmic functions as well. This is seen from the pseudo R2 values in table 7-1. The DBDC model fits data best. The two extended models both provide a worse fit. However, the WTP estimates from the model only including respondents having a positive WTP is much closer to the estimates from the DBDC model and furthermore the variance between the to distribution functions is smaller and so is the range of the confidence interval. Based on the previous analysis it is concluded, that people

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living in the Rømø area as a mean are willing to pay between DKK 34-52 for a seasonal ticket to the Juvre marshland area. That is, the utility of moving the dike correspond to a positive value per person of DKK 34 - 52. In the Rømø area, covering the municipalities of Bredebro and Skærbæk, the amount of men and women in the age group 18-75 is 5,094. The total WTP for a seasonal ticket to the Juvre marshland area for people living in the Rømø area can then be calculated. From table 7-2 the result for the first year and the value when paying one time a year in all future appears. Table 7-2: Aggregated WTP for a seasonal ticket to the Juvre marshland area for people living in the Rømø area WTP for one year WTP future years *

DBDC Extended model only with positive WTP’s

Extended model only with positive WTP’s

Log-normal Log-logistic Log-normal Log-logistic 3% 5% 6% Mean WTP, DKK 219,042 229,230 193,572 198,666 6,452,400 3,871,440 3,226,200Confidence, lower limit 188,478 193,572 173,196 173,196 5,773,200 3,463,920 2,886,600Confidence, high limit 254,700 264,888 219,042 219,042 7,301,400 4,380,840 3,650,700

*As a conservative choice, the calculations are based on the lowest estimated WTP. That is the estimates from the extended model with a log-normal assumption for the distribution function It can be seen, that the value of removing the dike in the Juvre meadow towards land and thereby re-establishing the marshland, has a value of 3.226 million DKK when using a discount rate of 6 %. The discount rate says something about how much we value the future. The higher discount rate the less the future generations are valued. A 6 % discount rate is often the recommended and used rate in cost benefit analysis [Møller 2003; Finansministeriet 1999]. The result should be used with care. It is only a mean value meaning that it is based on what the mean respondent in the survey is willing to pay for a seasonal ticket to the Juvre marshland area. Some respondents expressed a much lower WTP and some a much higher according to their socioeconomic characteristics. Further, the mean WTP for a seasonal ticket is multiplied with the number of people living in the Rømø area, not only the respondents from the survey. According to the representativeness of the sample in chapter 3, the distribution among respondents is not fully representative for the distribution of people living in the Rømø area. This mean, that the mean WTP is not representative for the people living in the Rømø area why the results is not quite representative for the mean person in the Rømø area.

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8 Reference list Akaike, H. (1974): A new Look at the Statistical Model Identification. IEEE Transactions on Automatic Control, vol. AC-19(6), pp. 716-723. Alberini, A. (1995a): Efficiency vs. Bias of WTP Estimates: Bivariate and Interval-data Models. Journal of Environmental Economics and Management, vol. 29, pp. 169-180. Alberini, A. (1995b): Optimal Designs for Discrete Choice Contingent Valuation Surveys: Single-Bound, Double-Bound and Bivariate Models. Journal of Environmental Economics and Management, vol. 28, pp. 287-306. Arrow, K.; Solow, R.; Portney, P. R.; Leamer, E. E.; Radner, R. & H. Schuman (1993): Report of the NOAA Panel on Contingent Valuation. Washington, USA. The National Ocean and Atmospheric Associations Damage Assessment and Restoration Program (DARP). Bateman, I.; Carson, R. T.; Day, B.; Hanemann, M.; Hanley, N.; Hett, T.; Jones-Lee, M.; Loomes, G.; Mourato, S.; Özdemiroglu, E.; Pearce, D. W.; Sugden, R. & J. Swanson (2002): Economic Valuation with Stated Preference Techniques – A Manual. Edward Elgar, Cheltenham, UK. Bjørner, T. B.; Russell, C.; Dubgaard, A.; Damgaard, C. & L. M. Andersen (2002): Public and Private Preferences for Environmental Quality in Denmark. SØM Publication no. 39. AKF Forlaget, Copenhagen. Brouwer, R. & I. Bateman (2000): The temporal stability of contingent WTP values. CSERGE Working Paper GEC 20000-14. Cameron, T. A. & J. Quiggin (1994): estimation Using Contingent Valuation Data from a “Dichotomous Choice with Follow-Up” Questionnaire. K, vol. 27, pp. 218-234. Carlsson, F & M. Kataria (2006): Assessing management options for weed control with demanders and non-demanders in a choice experiment. Working Papers in Economics no. 208. May 2006. Department of Economics, School of Business, Economics and Law, Göteborg University. Finansministeriet (1999): Vejledning I udarbejdelse af samfundsøkonomiske konsekvensvurderinger. Finansministeriet. Available at: http://www.fm.dk/db/filarkiv/2950/hele.pdf. Hanemann, M.; Loomis, J. & B. Kanninen (1991): Statistical Efficiency of Double-Bounded Dichotomous Choice Contingent Valuation. American Journal of Agricultural Economics, vol. 73, pp. 1255-1263. Hasler, B.; Lundhede, T.; Martinsen, L.; Neye, S. & J. Schou (2005): Valuation of Groundwater Protection versus Water Treatment in Denmark by Choice Experiment and Contingent Valuation. National Environmental Research Institute, Denmark. NEI Technical Report no. 543. http://technical-reports.dmu.dk Herriges, J. A. & J. F. Shogren (1996): Starting Point Bias in Dichotomous Choice Valuation with Follow-Up Questioning. Journal of Environmental Economics and Management, vol. 30(1), pp. 112-131. Ladenburg, J.; Dubgaard, A.; Martinsen, L. & J. Tranberg (2005): Economic Valuation of the Visual Externalities of Offshore Wind farms. Report no. 179. Food and Resource Economics Institute, KVL, Frederiksberg, DK. Loureiro, M. L.; Gracia, A. & R. M. Nayga Jr. (2006): Do consumers value nutritional labels?. European Review of Agricultural Economics, vol. 33 (2), pp. 249-268.

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Louviere, J.; Hensher, D. A. & J. Swait (2000): Stated Choice Methods. Analysis and Applications. University Press, Cambridge, UK. Mitchell, R. C. & R. T. Carson (1989): Using Surveys to value Public Goods: The Contingent Valuation Method. Resources for the Future, Washington D. C., USA. Møller, F. (2003): Projektvurderinger over tid – aspekter af diskonteringsproblemstillingen. Danmarks Miljøundersøgelser. 170 p. – Arbejdsrapport fra DMU nr. 193. http://arvbejdsrapporter.dmu.dk. Nunes, P. A. (1998): Measuring the WTP for recreation and biodiversity protection programs. Discussion Paper. Public Economics. Centre for Economic Studies. Discussion Paper Series DPS 98.12. Nunes, P. A. L. D. & J. C. J. M. Van den Berg (2004): Can People Value Protection against Invasive Marine Species? Evidence from a Joint TC–CV Survey in the Netherlands. Environmental and Resource Economics, vol. 28(4), pp. 517-532 Olsen, S. B.; Ladenbug, J.; Petersen, M. L.; Lopdrup, U.; Hansen, A. S. & A. Dubgaard (2005): Motorways versus Nature. A Welfare Economic Valuation of Impacts. Environmental Assessment Institute, Copenhagen. Patterson, D. (1996): An extended model for double-bounded dichotomous choice data. University of Montana, Missoula, MT 59812. Paper presented at WNAR annual meeting, June 1993; updated June 1996. Ritz, C. (2002): An analysis of WTP in three Danish forests. Department of Economics and Natural Resources (FLEC). The Royal Veterinary and Agricultural University. Ritz, C. (2004): Estimation af betalingsvilje. En statistisk synsvinkel. Institut for matematik og Fysik. KVL. Strazzera, E.; Genius, M.; Scarpa, R. and G. Hutchinson (2003a): The Effect of Protest Votes on the Estimates of WTP for Use Values of Recreational Sites. Environmental and Resource Economics, vol. 25, pp. 461-476. Strazzera, E.; Scarpa, R.; Calia, P. & K. Willis (2003b): Modelling zero values in contingent valuation surveys. University of Newcastle Upon Tyne, CRE, Centre for Rural Economy. Department of Agricultural Economics and Food Marketing. Centre for Rural Economy Working Paper Series. Working Paper 47. Swait, J. & W. Adamowicz (2001): The Influence of Task Complexity on Consumer Choice: A Latent Class Model of Decision Strategy Switching. Journal of Consumer Research, vol. 28, pp. 135-148.

9 Appendix Appendix 1: Explanatory variables tested in the models Name Level Description

Age 6 1 = 0-24, 2 = 25-34, 3 = 35-44, 4 = 45-54, 5 = 55-64, 6 = 65 and above Romoe Dummy 1 = Live at Rømø, 0 = Do not live at Rømø Born Dummy 1 = Bor non Rømø, 0 = Not bor non Rømø

Visit1 3 1= Have visit the area within the last year two times at max, 2 = Visit the area at minimum one to three times every third month, 3 = Visit the area every other day

A_22 6 1= Primary and lower secondary school, 2 = Upper secondary level, 3 = Vocational education, 4 = Short education, 5 = Intermediate education/bachelor, 6 = Higher education

Edu 3 1=Primary and lower secondary school, 2 = Short education, 3 = Intermediate education or higher education Certain1 Dummy 1 = Very certain/certain, 0 = Other Gender1 Dummy 1 = Male, 0 = Female Child1 Dummy 1 = Children in the household, 0 = no children in the household Inc 3 1 = Low income (<200.000), 2 = Intermediate income (200.000-399.999), 3 = High income (>399.999) Nat1 3 Question 5a 1 = Agree, 2 = neither/nor, 3 = Disagree Nat2 3 Question 5b 1 = Agree, 2 = neither/nor, 3 = Disagree Nat3 3 Question 5c 1 = Agree, 2 = neither/nor, 3 = Disagree Dansk1 Dummy Question 4d. 1 = Yes, 0 = Other Dansk2 Dummy Question 4d. 1 = No, 0 = Other Dansk3 Dummy Question 4d. 1 = Don’t know, 0 = Other Firstbid1 Dummy 1: x=40, 0: x = Other Firstbid2 Dummy 1: x=60, 0: x = Other Firstbid3 Dummy 1: x=100, 0: x = Other Firstbid4 Dummy 1: x=200, 0: x = Other Firstbid5 Dummy 1: x=400, 0: x = Other Firstbid 5 1: x = 40, 2: x = 60, 3: x = 100, 4: x = 200, 5: x = 400

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Appendix 2: Distribution of respondents in the WTP sample on different variables tested in the models Distribution Aggregated distribution Live in/on (Romoe) Skærbæk 65 Bredebro 70 Rømø 131 Total 266 Born and grew op on/in (Born) Rømø 51 Other 209 Total 260 Visit in recreational areas Visit Every other day 65 138 1-3 times at week 73 101 1-3 times at month 78 23 Every other or third month 23 One or two times at year 20 Haven’t been in the area in the last 12 month 3 Total 262 262 Danishnature1: More money should be spent in protecting the Danish nature Yes 121 No/I don’t know 128 Total 249 Protecting the nature in marshland areas is more important than free access (Nature_marsh1) Agree 95 Neither/nor 78 Disagree 80 Total 253 A reduced agricultural production should be accepted in favour of a better protection of the nature in marshland areas (Nature_marsh2)

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Agree 88 Neither/nor 58 Disagree 106 Total 252 Restrictions in the agriculture for the sake of the nature in marshland areas should only take place when voluntary agreements with the plot owner have taken place (Nature_marsh3) Agree 171 Neither/nor 44 Disagree 40 Total 255

Appendix 3: Distribution of socio demographic variables WTP sample National sample Expected distribution Bredebro Skærbæk Rømø Skærbæk + Rømø Bredebro Skærbæk + Rømø Bredebro Skærbæk + RømøGender (Gender) ns ns Male 35 31 59 90 1267 2568 36 98 Female 35 34 70 104 1203 2508 34 96 Total 70 65 129 194 2470 5076 70 194 Age (Age group) ns * 0-24 2 4 8 12 225 512 6 19 25-34 9 7 14 21 358 675 10 26 35-44 14 14 19 33 553 1050 15 40 45-54 12 17 33 50 529 1131 15 43 55-64 24 15 36 51 511 966 14 37 65 and above 8 8 19 27 294 760 8 29 Total 69 65 129 194 2470 5094 69 194 Children in the household (Child) ns * Yes 27 26 28 54 966 1786 27 68 No 43 39 101 140 1504 3308 43 126 Total 70 65 129 194 2470 5094 70 194 Education ** *** Primary and lower secondary school 29 21 37 58 1157 2184 32 85 Upper secondary level 5 6 9 15 54 114 1 4 Vocational education 19 20 41 61 917 2045 25 80 Short education 2 8 9 17 82 152 2 6 Intermediate education/bachelor 12 9 20 29 194 351 5 14 Higher education 1 1 11 12 45 63 1 2 Total 68 65 127 192 2449 4909 68 192 Income * *** Below 100.000 – 199.999 26 24 40 64 1553 3239 36 98 200.000 – 399.999 36 32 66 98 1142 2293 26 70 400.000 and above 5 5 13 18 203 405 5 12 Total 67 61 119 180 2898 5937 67 180

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Note: Above each distribution, is indicated whether the distribution in the sample is significantly different from the distribution in Bredebro and Skærbæk + Rømø respectively due to data from Statistic Denmark. (ns) indicates no significant different between the WTP sample and the expected distribution, (*) indicates a significant difference on a 95% level, (**) indicates a significant difference on a 99% level and (***) a significant difference on a 99.99% level.

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