\[ \newcommand{\cA}[1]{{\color{steelblue}{#1}}} \newcommand{\cB}[1]{{\color{seagreen}{#1}}} \newcommand{\cC}[1]{{\color{chocolate}{#1}}} \newcommand{\cD}[1]{{\color{darkorchid}{#1}}} \newcommand{\off}[1]{{\color{silver}{#1}}} \newcommand{\on}[1]{{\color{black}{#1}}} \newcommand{\cUse}[1]{{\color{seagreen}{#1}}} \newcommand{\cNon}[1]{{\color{firebrick}{#1}}} \]

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

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

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 randomized

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

Choice Card

Choice Card - Maps

Choice Card - Attributes

Methods

Coding and Interpretation of Attributes

  • Size and Use/Non-Use are separate attributes in the choice card.

  • In modelling we reparameterize them into five types of natural capital (\(NC\)):

Area \(\times\) Use / Non-Use

\[ \begin{aligned} \cNon{\text{PA}_{\text{no}}} &= \text{PA} \times \cNon{\text{No}} &\qquad \cNon{\text{HNV}_{\text{hidden}}} &= \text{HNV} \times \cNon{\text{Hidden}}\\ \cUse{\text{PA}_{\text{half}}} &= \text{PA} \times \cUse{\text{Half}} &\qquad \cUse{\text{HNV}_{\text{visible}}} &= \text{HNV} \times \cUse{\text{Visible}}\\ \cUse{\text{PA}_{\text{full}}} &= \text{PA} \times \cUse{\text{Full}} \end{aligned} \]

  • \(\text{PA}\), \(\text{HNV}\): size of the proposed change, in hectares
  • \(\text{No}\), \(\text{Half}\), \(\text{Full}\), \(\text{Hidden}\), \(\text{Visible}\): 1/0 indicators for the quality level, mutually exclusive within each type

Choice and Cost

Respondents trade off a status quo against costly alternatives:

\[\cA{U_i} \on{=} \cA{-\beta_c} \cA{\Bigl[} \cA{\alpha'\,\text{ASC}} \off{+ \sum_{NC}} \off{\Bigl(} \off{1} \off{+ \delta_{NC}\,\log D} \off{+ \gamma\,\log I} \off{\Bigr)} \off{\Bigl(} \off{\beta_{\text{NC}}\,\text{NC} + \beta_{\text{NC}_{\text{sq}}}\,\text{NC}^2} \off{\Bigr)} \cA{-\,C} \cA{\Bigr]} \cA{+\,\epsilon_i}\]

  • \(U_i\): utility of choice option \(i\); \(\epsilon_i\): random error
  • \(\text{ASC}\): vector of status-quo variables — the status-quo indicator (\(=1\) for the status-quo option) and its interactions with income, distance and scope
  • \(\alpha = (\alpha_0, \alpha_{\text{Inc}}, \alpha_{\text{Dist}}, \alpha_{\text{Scope}})'\): matching parameter vector
  • \(C\): annual payment; \(\beta_c\): price coefficient
  • \(\text{NC}\): change in natural capital, one of five types \(NC \in \{\text{PA}_{\text{no}}, \text{PA}_{\text{half}}, \text{PA}_{\text{full}}, \text{HNV}_{\text{hidden}}, \text{HNV}_{\text{visible}}\}\)
  • \(\beta_{\text{NC}}, \beta_{\text{NC}_{\text{sq}}}\): parameters of the quadratic value function
  • \(D\): distance from home to the change; \(\delta_{NC}\): distance-decay parameter
  • \(I\): local income; \(\gamma\): common income-scaling parameter

Natural Capital

Each of five types of natural capital enters with a quadratic value function:

\[\on{U_i} \on{=} \on{-\beta_c} \on{\Bigl[} \on{\alpha'\,\text{ASC}} \cB{+ \sum_{NC}} \off{\Bigl(} \off{1} \off{+ \delta_{NC}\,\log D} \off{+ \gamma\,\log I} \off{\Bigr)} \cB{\Bigl(} \cB{\beta_{\text{NC}}\,\text{NC} + \beta_{\text{NC}_{\text{sq}}}\,\text{NC}^2} \cB{\Bigr)} \on{-\,C} \on{\Bigr]} \on{+\,\epsilon_i}\]

  • \(U_i\): utility of choice option \(i\); \(\epsilon_i\): random error
  • \(\text{ASC}\): vector of status-quo variables — the status-quo indicator (\(=1\) for the status-quo option) and its interactions with income, distance and scope
  • \(\alpha = (\alpha_0, \alpha_{\text{Inc}}, \alpha_{\text{Dist}}, \alpha_{\text{Scope}})'\): matching parameter vector
  • \(C\): annual payment; \(\beta_c\): price coefficient
  • \(\text{NC}\): change in natural capital, one of five types \(NC \in \{\text{PA}_{\text{no}}, \text{PA}_{\text{half}}, \text{PA}_{\text{full}}, \text{HNV}_{\text{hidden}}, \text{HNV}_{\text{visible}}\}\)
  • \(\beta_{\text{NC}}, \beta_{\text{NC}_{\text{sq}}}\): parameters of the quadratic value function
  • \(D\): distance from home to the change; \(\delta_{NC}\): distance-decay parameter
  • \(I\): local income; \(\gamma\): common income-scaling parameter

Distance

The value declines with distance \(D\) to the change:

\[\on{U_i} \on{=} \on{-\beta_c} \on{\Bigl[} \on{\alpha'\,\text{ASC}} \on{+ \sum_{NC}} \cC{\Bigl(} \cC{1} \cC{+ \delta_{NC}\,\log D} \off{+ \gamma\,\log I} \cC{\Bigr)} \on{\Bigl(} \on{\beta_{\text{NC}}\,\text{NC} + \beta_{\text{NC}_{\text{sq}}}\,\text{NC}^2} \on{\Bigr)} \on{-\,C} \on{\Bigr]} \on{+\,\epsilon_i}\]

  • \(U_i\): utility of choice option \(i\); \(\epsilon_i\): random error
  • \(\text{ASC}\): vector of status-quo variables — the status-quo indicator (\(=1\) for the status-quo option) and its interactions with income, distance and scope
  • \(\alpha = (\alpha_0, \alpha_{\text{Inc}}, \alpha_{\text{Dist}}, \alpha_{\text{Scope}})'\): matching parameter vector
  • \(C\): annual payment; \(\beta_c\): price coefficient
  • \(\text{NC}\): change in natural capital, one of five types \(NC \in \{\text{PA}_{\text{no}}, \text{PA}_{\text{half}}, \text{PA}_{\text{full}}, \text{HNV}_{\text{hidden}}, \text{HNV}_{\text{visible}}\}\)
  • \(\beta_{\text{NC}}, \beta_{\text{NC}_{\text{sq}}}\): parameters of the quadratic value function
  • \(D\): distance from home to the change; \(\delta_{NC}\): distance-decay parameter
  • \(I\): local income; \(\gamma\): common income-scaling parameter

Income

Utility scales with household income \(I\):

\[\on{U_i} \on{=} \on{-\beta_c} \on{\Bigl[} \on{\alpha'\,\text{ASC}} \on{+ \sum_{NC}} \on{\Bigl(} \on{1} \on{+ \delta_{NC}\,\log D} \cD{+ \gamma\,\log I} \on{\Bigr)} \on{\Bigl(} \on{\beta_{\text{NC}}\,\text{NC} + \beta_{\text{NC}_{\text{sq}}}\,\text{NC}^2} \on{\Bigr)} \on{-\,C} \on{\Bigr]} \on{+\,\epsilon_i}\]

  • \(U_i\): utility of choice option \(i\); \(\epsilon_i\): random error
  • \(\text{ASC}\): vector of status-quo variables — the status-quo indicator (\(=1\) for the status-quo option) and its interactions with income, distance and scope
  • \(\alpha = (\alpha_0, \alpha_{\text{Inc}}, \alpha_{\text{Dist}}, \alpha_{\text{Scope}})'\): matching parameter vector
  • \(C\): annual payment; \(\beta_c\): price coefficient
  • \(\text{NC}\): change in natural capital, one of five types \(NC \in \{\text{PA}_{\text{no}}, \text{PA}_{\text{half}}, \text{PA}_{\text{full}}, \text{HNV}_{\text{hidden}}, \text{HNV}_{\text{visible}}\}\)
  • \(\beta_{\text{NC}}, \beta_{\text{NC}_{\text{sq}}}\): parameters of the quadratic value function
  • \(D\): distance from home to the change; \(\delta_{NC}\): distance-decay parameter
  • \(I\): local income; \(\gamma\): common income-scaling parameter

Endowment Natural Capital

Results

Mixed Logit Model

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.

Marginal WTP for Natural Capital


We find that marginal WTP …

  • decreases with the endowment — diminishing marginal utility of natural capital
  • is higher for use values — accessible protected areas and visible farmland are valued more
  • decreases with distance to the proposed change
  • increases with household income at a decreasing rate

Aggregation

Aggregation Steps

“How much is a household willing to pay for an area change?”

Step 1 — Estimate marginal WTP from the status quo endowment in the surrounding and cell characteristics

Step 2 — Scale to the cell population by multiplying marginal WTP by the number of households in the cell

“What is the aggregated willingness to pay for a change at a specific location, across all households living nearby?”

Step 3 — Identify all contributing cells and their distance to the site; sum their WTP, weighted by distance decay

Step 4 — Derive alternative measures that account for inequality in income and number of beneficiaries

WTP per Household for Change within a Cell’s Surrounding




  • Willingness to pay per household for an increase of protected area within a 30 km radius of a cell

  • Depending on: status quo endowment and household income within the cell

Min
-26.99
Median
9.57
Mean
9.22
Max
13.76

Total Cell WTP for Change within a Cell’s Surrounding




  • Willingness to pay of the cell population for an increase of protected area within a 30 km radius
  • Depending on: status quo endowment, household income within the cell, and the cell’s population
Min
-16,020.89
Median
618.16
Mean
2,463.62
Max
163,742.94

What is the Aggregated WTP for a Change at a Specific Location?

Aggregated WTP at a Specific Location




  • Aggregated WTP for an increase in Protected Area within a cell of all HH living within 30 km surrounding
  • Contributions decline with distance between the contributing and the focal cell
Min
-10.76
Median
200.93
Mean
304.46
Max
2,767.90

Aggregated WTP per Contributing Household




  • Aggregated WTP divided by the number of contributing households — i.e. all HH living within 30 km of the cell
Min
-1.72
Median
1.00
Mean
0.99
Max
1.70

Aggregated WTP per Contributing Household as Income Share




  • Aggregated WTP divided by the number of contributing households and the respective households’ income
Min
-0.072
Median
0.033
Mean
0.033
Max
0.063

Comparing Aggregation Measures

✅ largest accumulated benefits

✅ maximizes welfare

❌ ignores inequalities

❌ mainly driven by population density

✅ largest individual benefits

✅ accounting for endowment inequality

❌ gives higher weight to richer individuals

❌ number of beneficiaries may be low

✅ accounts for income and endowment inequality

✅ public good is supplied where relative WTP is highest

❌ accumulated benefits are rather low

❌ number of beneficiaries may be low

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, magnitude depends on the functional form chosen

🏕️ 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

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

Survey Structure

The Referendum

Split samples

Figure 1: Split-samples used in survey

Payment Vehicle

  • Program financed by a mandatory annual payment per household

  • Half is paid by European Union

  • Payment duration varied with split samples

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).

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, \(\alpha = (\alpha_0, \alpha_{\text{Inc}}, \alpha_{\text{Dist}}, \alpha_{\text{Scope}})\)
  • \(\text{NC}\): 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)
  • \(\beta_{\text{NC}}, \beta_{\text{NC}_{\text{sq}}}\): parameters of the quadratic value function
  • \(C\): 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)

Compare WTP Estimates

Randomisations

🎲 Randomized

  • 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

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

Marginal WTP varies with endowment

And with distance

  • Use split sample variation in maximum distance of new areas

  • \(\on{\text{WTP}_{PA_i}} \on{=} \cC{\Bigl(} \cC{1} \cC{+ \delta_{PA_i} \cdot \log(\text{D})} \off{+ \gamma \cdot \log(\text{I})} \cC{\Bigr)} \cB{\Bigl(} \cB{\beta_{\text{PA}_i} + 2 \cdot \beta_{\text{PA}_{i,sq}} \cdot \text{PA}_i} \cB{\Bigr)}\)

And household income

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

  • \(\on{\text{WTP}_{PA}} \on{=} \cC{\Bigl(} \cC{1} \cC{+ \delta_{PA} \cdot \log(\text{D})} \cD{+ \gamma \cdot \log(\text{I})} \cC{\Bigr)} \cB{\Bigl(} \cB{\beta_{\text{PA}} + 2 \cdot \beta_{\text{PA}_{sq}} \cdot \text{PA}} \cB{\Bigr)}\)

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

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?

Policy Implications

  • Implementation of biodiversity policies should incorporate spatial heterogeneities

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