Introduction

Motivation

Research Contribution

  • Develop and apply spatially explicit valuation approach accounting for endowment with natural capital using a discrete choice experiment

  • Improve understanding of heterogeneity of natural capital values across space and groups

  • Map distribution of willingness to pay for natural capital (protected areas and high nature value farmland) across Germany

Research Questions

  1. How do people value changes in the stock of natural capital, in the form of protected areas and high nature value farmland, across space?

  2. How can we aggregate willingness to pay (WTP) values to provide spatially explicit natural capital values?

Spoiler

Hypotheses

🌱 H1: Natural Capital has Value

People place significant value on natural capital

📊 H2: Diminishing Marginal Utility

The marginal value of natural capital decreases as endowment increases

🏕️ H3: Use vs. Non-Use

Use-related values are higher than non-use-related values

📍 H4: Distance Decay

The marginal value decreases as distance increases

Survey Structure

Survey Structure

Spatially Explicit Choice Experiment

Good to be valued

  • Changes in the area of protected areas and high nature value farmland

  • Local changes near the respondent’s home

  • Binary referendum choice; repeated 10 times

Features of the experiment

  • Individualized maps of the land-use change

  • Generated from CORINE land cover data with an R algorithm

  • Full factorial design; alternatives and attributes randomised

The Referendum

  • Referendum on proposed regional program by local municipalities
  • Natural capital related attributes: protected areas & high nature value farmland
  • Changes relative to status quo endowment around place of residence

The Referendum

Payment Vehicle

  • Program financed by a mandatory annual payment per household

  • Half is paid by European Union

  • Payment duration varied with split samples

Split samples

Figure 1: Split-samples used in survey

Attributes and levels

Attribute Levels Description
Size of protected areas Vector A: status quo, +100, +200, +300, +500, +800 hectares
Vector B: status quo, +200, +400, +600, +1000, +1600 hectares		 The total area designated as protected area. Levels indicate the expansion in hectares from the current status.
High nature value farmland The total area of high nature value farmland. Levels indicate the expansion in hectares from the current status.
Accessibility of new protected areas Not accessible, Half accessible, Fully accessible The extent to which the public can access newly designated protected areas, ranging from no access to full access.
Visibility of new high nature value farmland Barely visible, Clearly visible Indicates how visible the new areas of high nature value farmland are from public roads or paths.
Annual payment into a nature conservation fund 5, 10, 20, 40, 60, 80, 120, 150, 200, 250 euros The amount each household contributes annually to a fund dedicated to nature conservation efforts.

Note: Each respondent is assigned either Vector A or Vector B; the assignment applies to both size attributes (protected areas and high nature value farmland).

Example Choice Card

Example Choice Card

Example Choice Card

Sample

Endowment Natural Capital

Methods and Estimation Results

Methodology: Functional Form

Utility is a function of natural capital and cost, and a status quo effects (ASC):

\[U_i = -\beta_c \left[ \alpha\,\text{ASC} + \sum_{NC} f(NC,\Phi) - C \right] + \epsilon_i\]

  • \(U_i\): utility of choice option \(i\); \(\epsilon_i\): random error
  • \(\text{ASC}\): status-quo indicator (\(=1\) for the status-quo option)
  • \(\alpha\): status-quo parameter vector: base effect and its shift with income, distance & scope, \(\alpha = (\alpha_0, \alpha_{\text{Inc}}, \alpha_{\text{Dist}}, \alpha_{\text{Scope}})\)
  • \(f(NC,\Phi)\): value of a change in natural capital, one of five types \(NC \in \{\text{PA}_{\text{no}}, \text{PA}_{\text{half}}, \text{PA}_{\text{full}}, \text{HNV}_{\text{hidden}}, \text{HNV}_{\text{visible}}\}\) (Protected Areas by access, High Nature Value farmland by visibility); \(\Phi\) set of parameters
  • \(C\): annual payment; \(\beta_c\): price coefficient

Functional Forms

Different shapes for the value function \(f(NC,\Phi)\):

Function Type Function \(f(\text{NC},\Phi)\) Parameters (‘\(\Phi\)‘)
Linear \(\beta_{\text{NC}} \cdot \text{NC}\) \(\{\beta_{\text{NC}}\}\)
Quadratic Utility \(\beta_{\text{NC}} \cdot \text{NC} + \beta_{\text{NC}_{\text{sq}}} \cdot \text{NC}^2\) \(\{\beta_{\text{NC}}, \beta_{\text{NC}_{\text{sq}}}\}\)
Logarithmic \(\beta_{\text{NC}} \cdot \log(\text{NC})\) \(\{\beta_{\text{NC}}\}\)
Box-Cox \(\beta_{\text{NC}} \cdot \frac{\text{NC}^\lambda - 1}{\lambda}\) \(\{\beta_{\text{NC}}, \lambda\}\)
Log-Linear \(\beta_{\text{NC}} \cdot \text{NC} + \beta_{\text{NC}_{\text{log}}} \cdot \log(\text{NC})\) \(\{\beta_{\text{NC}}, \beta_{\text{NC}_{\text{log}}}\}\)

Results Functional Forms

Model Fit of Mixed logit models

Model AIC BIC LLout
Quadratic Utility Function 128533.25 128809.48 -64238.63
Log Utility Function 128773.39 128950.97 -64368.7
Linear Utility Function 128574.99 128752.57 -64269.5
Box Cox Utility Function 128548.7 128775.6 -64251.35
Log-Linear Utility Function 128554.29 128830.52 -64249.15
Cubic Utility Function 128565.43 128940.32 -64244.72

Marginal WTP for High Nature Value (visible)

Estimated WTP Functions: Quadratic

Methodology Distance

The value declines with distance \(D\) to it:

\[U_i = -\beta_c \left[ \alpha\,\text{ASC} + \sum_{NC} \left(1 + \delta_{NC}\,\log D\right) f(NC,\Phi) - C \right] + \epsilon_i\]

  • \(U_i\): utility of choice option \(i\); \(\epsilon_i\): random error

  • \(\text{ASC}\): status-quo indicator (\(=1\) for the status-quo option)

  • \(\alpha\): status-quo parameter vector: base effect and its shift with income, distance & scope, \(\alpha = (\alpha_0, \alpha_{\text{Inc}}, \alpha_{\text{Dist}}, \alpha_{\text{Scope}})\)

  • \(f(NC,\Phi)\): value of a change in natural capital, one of five types \(NC \in \{\text{PA}_{\text{no}}, \text{PA}_{\text{half}}, \text{PA}_{\text{full}}, \text{HNV}_{\text{hidden}}, \text{HNV}_{\text{visible}}\}\) (Protected Areas by access, High Nature Value farmland by visibility); \(\Phi\) set of parameters

  • \(C\): annual payment; \(\beta_c\): price coefficient

  • \(D\): distance from home to the change; \(\delta_{NC}\): distance-decay parameter

Estimated WTP Functions: Distance

  • Use split sample variation in maximum distance of new areas

  • \(\text{WTP}_{PA_i} = (1 + \delta_{PA_i} \cdot log(\text{D}))\left(\beta_{\text{PA}_i} + 2 \cdot \beta_{\text{PA}_{i,sq}} \cdot \text{PA}_i\right)\)

Methodology Income

Utility scales with household income \(I\):

\[U_i = -\beta_c \left[ \alpha\,\text{ASC} + \sum_{NC} \left(1 + \delta_{NC}\,\log D + \gamma\,\log I\right) f(NC,\Phi) - C \right] + \epsilon_i\]

  • \(U_i\): utility of choice option \(i\); \(\epsilon_i\): random error

  • \(\text{ASC}\): status-quo indicator (\(=1\) for the status-quo option)

  • \(\alpha\): status-quo parameter vector: base effect and its shift with income, distance & scope, \(\alpha = (\alpha_0, \alpha_{\text{Inc}}, \alpha_{\text{Dist}}, \alpha_{\text{Scope}})\)

  • \(f(NC,\Phi)\): value of a change in natural capital, one of five types \(NC \in \{\text{PA}_{\text{no}}, \text{PA}_{\text{half}}, \text{PA}_{\text{full}}, \text{HNV}_{\text{hidden}}, \text{HNV}_{\text{visible}}\}\) (Protected Areas by access, High Nature Value farmland by visibility); \(\Phi\) set of parameters

  • \(C\): annual payment; \(\beta_c\): price coefficient

  • \(D\): distance from home to the change; \(\delta_{NC}\): distance-decay parameter

  • \(I\): local income; \(\gamma\): common income-scaling parameter

Estimated WTP Functions: Income

  • Use GIS data on available income to incorporate differences in income

  • \(\text{WTP}_{PA} = (1 + \delta_{PA} \cdot log(\text{D}) + \gamma \cdot log(\text{I}))\left(\beta_{\text{PA}} + 2 \cdot \beta_{\text{PA}_{sq}} \cdot \text{PA}\right)\)

Mixed Logit Model (Parameter estimates)

Mean SD Distance
Protected Areas NA 11.34 (1.03)*** -8.51 (0.78)*** -0.37 (0.22)*
Protected Areas NA Squared -0.08 (0.03)*** 0.07 (0.03)**
Protected Areas HA 16.99 (0.80)*** -1.22 (0.24)*** -0.28 (0.14)**
Protected Areas HA Squared 0.03 (0.03) -0.18 (0.02)***
Protected Areas FA 21.76 (0.74)*** -4.82 (0.40)*** -0.29 (0.10)***
Protected Areas FA Squared -0.09 (0.02)*** 0.30 (0.01)***
High Nature Value NV 12.21 (0.44)*** -8.46 (0.28)*** -0.36 (0.07)***
High Nature Value NV Squared -0.09 (0.01)*** -0.07 (0.01)***
High Nature Value V 15.60 (0.68)*** -4.31 (0.27)*** -0.25 (0.12)**
High Nature Value V Squared -0.10 (0.01)*** -0.02 (0.01)**
Annual Payment -3.25 (0.03)*** -1.97 (0.04)***
Scope high 6.46 (0.89)*** -79.50 (0.26)***
ASC SQ -50.57 (0.63)*** 121.13 (0.40)***
ASC Distance Interaction 14.85 (2.10)***
ASC Income Interaction -21.22 (0.36)***
Income Scale Factor 0.24 (0.02)***
No Observations 131,440
No Respondents 13,144
Log Likelihood (Null) -91,107.27
Log Likelihood (Converged) -59,821.95
*** p < 0.005; ** p < 0.025; * p < 0.05. Robust standard errors in parentheses.

Aggregation

Aggregation of willingness to pay values

  • Results are useful if aggregated to spatial scales

  • Each raster cell has a unique value

  • Value depends on status quo endowment, the number and characteristics of beneficiaries, and distance

A stylized example

Focus on one cell

People and extent of the market

WTP of one Person

WTP of more persons

WTP of more persons

WTP of more persons

WTP of more persons

Steps to Aggregate WTP

  1. Calculate the status quo endowment

  2. Compute estimated marginal WTP per person

  3. Multiply with the population in the cell

  4. For each cell: compute all other cells where people would benefit from the change

  5. Aggregate WTP by summing up associated cells

Cell WTP Protected Areas

WTP for Protected Areas

WTP High Nature Value Farmland

Conclusion

Results

🌱 H1: Natural Capital has Value

Willingness to pay for protected areas and high nature value farmland is positive and significant

📊 H2: Diminishing Marginal Utility

Marginal willingness to pay falls as the endowment rises, magnitute depends on functional form choosen

🏕️ H3: Use vs. Non-Use

Accessible protected areas and visible farmland are valued more

📍 H4: Distance Decay

Marginal willingness to pay declines with distance to the change

Policy Implications

  • Implementation of biodiversity policies should incorporate spatial heterogeneities

  • Endowment, income and number of beneficiaries are important drivers of aggregated values

Thanks for Listening

  • Joint work within the ValuGaps Team since 2020

  • Several institutions and collaborators involved

  • Visit https://valugaps.de/en/ for more information

  • Pre-registration, questionnaire, data, code and estimated models and intermediate data available on Open Science Framework (link on request)

References

Addicott, Ethan T, and Eli P Fenichel. 2019. “Spatial Aggregation and the Value of Natural Capital.” Journal of Environmental Economics and Management 95: 118–32.
Brandon, Carter, Katrina Brandon, Alison Fairbrass, and Rachel Neugarten. 2021. “Integrating Natural Capital into National Accounts: Three Decades of Promise and Challenge.” Review of Environmental Economics and Policy 15 (1): 134–53.
Chiesura, Anna, and Rudolf De Groot. 2003. “Critical Natural Capital: A Socio-Cultural Perspective.” Ecological Economics 44 (2-3): 219–31.
Costanza, Robert. 2020. “Valuing Natural Capital and Ecosystem Services Toward the Goals of Efficiency, Fairness, and Sustainability.” Ecosystem Services 43: 101096.
Dasgupta, Sir Partha. 2021. The Economics of Biodiversity the Dasgupta Review Abridged Version.
Glenk, Klaus, Robert J Johnston, Jürgen Meyerhoff, and Julian Sagebiel. 2020. “Spatial Dimensions of Stated Preference Valuation in Environmental and Resource Economics: Methods, Trends and Challenges.” Environmental and Resource Economics 75: 215–42.
Guerry, Anne D, Stephen Polasky, Jane Lubchenco, et al. 2015. “Natural Capital and Ecosystem Services Informing Decisions: From Promise to Practice.” Proceedings of the National Academy of Sciences 112 (24): 7348–55.

Appendix

Compare WTP Estimates

Randomisations

🎲 Randomised

  • Opt-out position: left or right
  • Order of the attributes

🚧 Restrictions

  • Price: only at top or bottom
  • High nature value farmland kept with its visibility
  • Protected areas kept with their accessibility