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Modelling Strategies for Discontinuous Distance Decay in Willingness to Pay for Ecosystem Services

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Abstract

Distance decay is a well-known phenomenon affecting welfare measures of localized improvements in environmental quality. We focus on an often overlooked issue in the distance decay literature, namely the modeling of jump discontinuities, i.e. when the willingness to pay distance decay function makes a vertical jump up or down. In an empirical stated choice experiment concerning localized water quality improvements where a toll bridge presents a barrier in the landscape that causes a sudden jump in travel costs, we first estimate individual-specific willingness to pay. We then investigate distance decay in these obtained estimates. We find that the degree of distance decay depends on which type of ecosystem services respondents are primarily motivated by. Besides modelling distance decay with a range of commonly used parametric functional forms, we also test a nonparametric generalized additive model specification. We find only minor differences between the different distance decay specifications, with no generally superior model specification. The nonparametric approach tends to capture distance decay in WTP just as well as any of the parametric specifications, but without requiring the analyst to make assumptions concerning the functional form of the distance decay relationship.

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Notes

  1. We did run a model with a lognormal specification for the price parameter which indeed confirmed the existence of a fat tail issue causing the individual specific WTP estimates to become much more dispersed and with a substantial number of severely inflated and improbable WTP estimates.

  2. As will be outlined in Sect. 4, the dummy parameter estimate may however also potentially be affected by other differences between Zealand and Funen.

  3. We use a subset of a bigger dataset that was first used in Jensen et al. (2019). The survey and data description provided in the current paper thus focuses mainly on data collection aspects of particular relevance for the research questions addressed here. For full details of the data collection, the reader is referred to Jensen et al. (2019).

  4. Protesters were identified as those always choosing the zero-cost status quo option and subsequently reasoning this with one of the following statements: “I’m against increases in my income tax”, “The polluter should pay” or “The government should pay”.

  5. The entire dataset as well as full documentation of the original dNmark valuation study that generated the data is available in the ERDA repository at https://sid.erda.dk/cgi-sid/ls.py?share_id=dbvRvqoRrg.

  6. As very few respondents were classified as being particularly motivated by provisioning services, for modelling purposes we decided to merge this segment with the segment that did not appear to be motivated by any single particular ecosystem service.

  7. We note that this could be a result of type II error even though with 553 and 1292 respondents in the two compared segments the sample sizes would not be considered small.

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Acknowledgements

We are thankful to Anne Kejser Jensen for making the dataset available. This work was supported by the Danish Council for Strategic Research under the project: “Danish Nitrogen Mitigation assessment: Research and Know-how for a sustainable low-nitrogen food production” (DNMARK).

Author information

Authors and Affiliations

  1. Department of Food and Resource Economics, University of Copenhagen, Rolighedsvej 23, 1958, Frederiksberg C, Denmark

    Søren B. Olsen

  2. Banedanmark, Copenhagen, Denmark

    Cathrine U. Jensen

  3. Department of Environmental Science, Aarhus University, Aarhus, Denmark

    Toke E. Panduro

Authors
  1. Søren B. Olsen
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  2. Cathrine U. Jensen
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  3. Toke E. Panduro
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Correspondence to Søren B. Olsen.

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Appendices

Appendix 1: Statements and Questions used for Classifying Respondents According to Their Main Ecosystem Service Motivation

Motivation (ecosystem service)

Significant distinguishing statements

Biotic conditions (regulating)

The conditions in and around coastal waters must ensure biodiversity conservation in terms of diversity of animal and plant species

The conditions in and around coastal waters must support nutrient recycling

The conditions in and around coastal waters must ensure good living conditions for animals and plants

Conditions for recreation and lifestyle (cultural)

The conditions in and around coastal waters must provide physical and mental well-being

The conditions in and around coastal waters must preserve livelihood and lifestyle in the area

The conditions in and around coastal waters must support recreational activities such as hiking, beach trips and picnicking

Conditions for the fishing industry (provisioning)

The conditions in and around coastal waters must secure commercial fisheries

The conditions in and around coastal waters must ensure industrial production in the area

The conditions in and around coastal waters must ensure water based production of e.g. mussels

figure a

Appendix 2: Graphical Illustrations of Estimated Distance Decay Relationships when a Priori Knowledge Concerning the Presence of a Jump Discontinuity is Utilized

See Figs. 3, 4 and 5.

Fig. 3
figure 3

Distance decay in WTP (GAM, Linear and Linear with dummy specifications)

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Fig. 4
figure 4

Distance decay in WTP (Log, Log with dummy and Inverse specifications)

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Fig. 5
figure 5

Distance decay in WTP (Inverse with dummy, squared and squared with dummy specifications)

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Appendix 3: Model Estimates and Graphical Illustrations of Estimated Distance Decay Relationships Assuming the Jump Discontinuity is not Known a Priori

See Tables 8, 9, 10 and Figs. 6, 7, 8.

Table 8 Distance decay models for cultural services segment
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Table 9 Distance decay models for regulating services segment
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Table 10 Distance decay models for segment covering remaining respondents
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Fig. 6
figure 6

Distance decay in WTP (GAM, linear and linear with dummy specifications)

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Fig. 7
figure 7

Distance decay in WTP (Log, Log with dummy and inverse specifications)

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Fig. 8
figure 8

Distance decay in WTP (inverse with dummy, squared and squared with dummy specifications)

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Olsen, S.B., Jensen, C.U. & Panduro, T.E. Modelling Strategies for Discontinuous Distance Decay in Willingness to Pay for Ecosystem Services. Environ Resource Econ 75, 351–386 (2020). https://doi.org/10.1007/s10640-019-00370-7

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