A Novel Approach to Determining Spatially Explicit Values of Natural Capital
Research Question & Hypotheses
Research Question:
How do people value changes in the stock of natural capital, in the form of protected areas and high nature value farmland, across regions?
Hypothesis 1: People place significant value on natural capital in the form of protected areas and high nature value farmlands.
Hypothesis 2: The marginal value of natural capital decreases as endowment in- creases, suggesting diminishing returns.
Hypothesis 3: Use-related values of natural capital are higher than non-use-related values.
Survey Structure
Sample: Endowment Natural Capital
Methodology
General utility specification:
\[U_i = f(\text{NC},\Phi) + \beta_c \cdot C +\beta_Y \cdot Y + \epsilon_i\]
with: \(NC = \{\text{PA}_{a}, \text{HNV}_{v}\}\) and \(a=\{1, 2, 3\}\) and \(v=\{1, 2\}\)
Different functional forms:
| 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 | \(\beta_{\text{NC}} \cdot \text{NC} + \beta_{\text{NC}_{\text{log}}} \cdot \log(\text{NC})\) | \(\{\beta_{\text{NC}}, \beta_{\text{NC}_{\text{log}}}\}\) |
Example: Quadratic model with interaction effects:
\[U = \beta_{NC} \cdot \text{NC} + \beta_{NC_{sq}} \cdot \text{NC}^2 + \beta_{NCX} \cdot \text{NC} \cdot X + \beta_{NCX_{sq}} \cdot \text{NC}^2 \cdot X + \beta_{C} \cdot C + \beta_{Y} \cdot Y + \epsilon\]
with: \(X\) capturing socio-demographic and spatial factors
Mixed Logit Model Estimation Results
| Mean | SD | |
|---|---|---|
| Protected Areas NA | 9.32 (0.65)*** | -3.44 (0.14)*** |
| Protected Areas NA Squared | -0.06 (0.01)*** | 0.16 (0.01)*** |
| Protected Areas HA | 15.64 (1.08)*** | -2.72 (0.34)*** |
| Protected Areas HA Squared | 0.02 (0.02) | 0.02 (0.01)** |
| Protected Areas FA | 20.84 (1.18)*** | 6.31 (0.19)*** |
| Protected Areas FA Squared | -0.11 (0.03)*** | -0.05 (0.01)*** |
| HNV NV | 12.11 (0.55)*** | -5.96 (0.14)*** |
| HNV NV Squared | -0.11 (0.01)*** | 0.01 (0.01) |
| HNV V | 15.53 (0.66)*** | -5.53 (0.21)*** |
| HNV V Squared | -0.11 (0.01)*** | -0.02 (0.00)*** |
| ASC SQ | -52.26 (0.45)*** | -133.03 (0.62)*** |
| Annual Payment | -3.25 (0.03)*** | -1.92 (0.04)*** |
| Radius | -1.03 (0.04)*** | -1.40 (0.01)*** |
| Scope high | 0.44 (0.64) | -9.79 (0.27)*** |
| No Observations | 142250 | |
| No Respondents | 14225 | |
| Log Likelihood (Null) | -98600.19 | |
| Log Likelihood (Converged) | -64239.65 | |
| ***p < 0.005; **p < 0.025; *p < 0.05 (one-sided). Robust standard errors in parentheses. | ||
Relationship between WTP and Endowment
Aggregation of willigness to pay values
Results are useful if aggregated to spatial scales
Each raster cell has a unique value
Value depends on status quo endowment and the number and characteristics of beneficiaries close to the cell
Warning: Removed 1 row containing missing values or values outside the scale range
(`geom_point()`).
Steps to Aggregate WTP values
Calculate the status quo endowment
Compute estimated marginal WTP per person
Multiply it with the population in the cell
Compute for each cell all other cells where people would benefit from the change
Aggregate WTP by summing up associated cells
Example: Protected Areas (No Access)
First Insights
Willingness to pay for natural capital is positive but decreases with increasing endowment
Use values higher than non-use values
Values differ substantially across space
Next Steps
Test different utility specifications and compare
Integrate income and distance decay in the WTP function and aggregation
Identify measure for substitutes and include it in WTP function
ValuGaps Team
Joint work within the ValuGaps Team since 2020
Several institutions and collaborators involved
Visit https://valugaps.de/en/ for more information
Appendix
Attributes and levels in the DCE
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Benutzen Sie stattdessen 'xfun::attr2()'
Siehe help("Deprecated")| Attribute | Levels | Description |
|---|---|---|
| Size of protected areas | Vector A*: Status quo, +100, +200, +300, +500, +800; hectares | The total area designated as protected area. Levels indicate the expansion in hectares from the current status. |
| High nature value farmland | Vector B*: Status quo, +200, +400, +600, +1000, +1600; hectares | 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, 80, 60, 120, 150, 200, 250; euros | The amount each household contributes annually to a fund dedicated to nature conservation efforts. |
Results Conditional Logit
Model Fit of Conditional Logit Models
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Benutzen Sie stattdessen 'xfun::attr2()'
Siehe help("Deprecated")| Model | AIC | BIC | LLout |
|---|---|---|---|
| Quadratic Utility Function | 163578.88 | 163696.03 | -81777.44 |
| Log Utility Function | 77308.98 | 77371.99 | -38647.49 |
| Linear Utility Function | 77268.21 | 77331.22 | -38627.11 |
| Box Cox Utility Function | 77231.68 | 77339.7 | -38603.84 |
| Log-Linear Utility Function | 77254.71 | 77362.73 | -38615.35 |
Plot and Map WTP
Different Functional Forms: HNV Example
Compare WTP Estimates
