Extra Material Poster

Natural Experiment: Drought and Forest Loss

Outstanding Drought Event

Drought intensity in the vegetation period from April to October for total soil between 1950 to 2025 in Germany. Taken from UFZ (see https://www.ufz.de/index.php?de=47252).

Forest Loss in Germany

Forest changes (percentage loss of forest cover per hexagon) for all forest types and the period January 2018 – April 2021 (left panel), 2018, 2019, 2020, and January–April 2021. Each hexagon has an area of approx. 87 km. Taken from Thonfeld et al. (2022), Figure 8, Page 562.

Survey Material

Attributes and Levels in the DCE

Attribute	Levels	Description
Type of forest	Broadleaved, Coniferous, Mixed	The basic type of the forest.
Number of tree species	1, 2, 3, 4*	The number of different tree species in the forest.*
Height of tallest trees in the forest	8m, 18m, 24m	Height of the tallest trees in the forest measured in meters.
Forest age variation	Single-aged, Two-aged, Multi-aged	Size and age-class variation in the forest.
Trees left for natural decay	None, Low, Medium	Indicator for the presence of deadwood in the forest.
Visitor facilities	None, Picnic facilities, Marked trails, Picnic facilities and marked trails	Available visitor facilities and infrastructure elements in the forest.
Distance to forest (in kilometers, one-way)	I: 0.5, 1, 2, 4, 6, 8, 10, 12; II…; III…; IV…; V: 3, 6, 12, 25, 50, 65, 90, 125	One-way travel distance to the forest. The attribute levels were conditional on the stated status quo travel distance.

Methodology

Methodology: DiD Mixed Logit Model

\[ \begin{aligned} U_{ijt} &= -\beta_{TD} \cdot \biggl( \left( \beta_{FS} + \textcolor{red}{\delta_{TP}^{(FS)} \cdot \text{Treat}_i \cdot \text{Post}_t} + \textcolor{BurntOrange}{\delta_T^{(FS)} \cdot \text{Treat}_i} + \textcolor{CadetBlue}{\delta_P^{(FS)} \cdot \text{Post}_t}\right) \cdot \text{ForestStructures}_{ijt} \\ &\quad \quad - \text{TravelDistance}_{ijt} \bigg) + \epsilon_{ijt} \end{aligned} \]

With:

• \(\text{TravelDistance}\) and \(\text{ForestStructures}\): attributes from the choice experiment
• \(\textcolor{BurntOrange}{\text{Treat}}\) and \(\textcolor{CadetBlue}{\text{Post}}\): dummy variables \(\in \{0,1\}\)
• \(\beta_{TD}\) and \(\beta_{FS}\): effect of travel distance and different forest structures on utility \(U_{ijt}\)
• Apply propensity score matching to account for sample imbalances

Methodology: DiD Ordinary Least Squares

\[ Y = \beta_0 + \textcolor{red}{\beta_{TP} \cdot \text{Treat}_i \cdot \text{Post}} + \textcolor{BurntOrange}{\beta_{T} \cdot \text{Treat}_i} + \textcolor{CadetBlue}{\beta_{P} \cdot \text{Post}} + \beta_{SocDem} \cdot \text{SocDem} + \epsilon \tag{1}\]

With:

• \(Y \in \{\text{Number of Forest Visits, Travel Distance to Forest, Time Spent in Forest}\}\)
• \(\textcolor{red}{\beta_{TP}}\): effect of the treatment on the dependent variable
• \(\epsilon\): error term
• Include fixed effects to account for sample imbalances

Treatment group assignment: last forest vs place of residence

ggplot() +   geom_spatraster(data = forest_loss_1km* 100) +
  scale_fill_gradient(
    low = "white",
    high = "orange",
    na.value = "transparent",
    name = "Forest Loss \nwithin 1x1km Cell (%)",
    trans = "sqrt"
  ) +
  geom_sf(data = germany_fed, fill = NA, color = "grey50") + 
  geom_sf(data = buffer_10km, fill = "blue", alpha = 0.15, color = NA) + 
  geom_sf(data = lines_sf, linewidth = 0.7, alpha = 0.5) + 
  geom_sf(data = dep_sf, aes(color = "Departure point", shape = "Departure point"), size = 2, alpha = 0.9) + 
  geom_sf(data = for_sf, aes(color = "Forest", shape = "Forest"), size = 2, alpha = 0.9) + 
  scale_color_manual( name = NULL, values = c( "Departure point" = "blue", "Forest" = "forestgreen" ) ) + 
  scale_shape_manual( name = NULL, values = c( "Departure point" = 16, # filled circle 
                                               "Forest" = 17 # filled triangle
                                               ))  +
                                               theme_minimal() +
  ggspatial::annotation_scale(
    location = "br",          # bottom-left ("br" for bottom-right)
    width_hint = 0.25         # relative width of scale bar
  )

Treatment group assignment: forest loss around place of residence

Sample balance prior to exposure

	Control			Treatment
Variables	n	mean	sd	n	mean	sd	Diff
Age (years)	347	45.59	13.74	347	44.86	13.60	-0.735
Gender (1=female)	347	0.48	0.50	347	0.47	0.50	-0.006
Settlement (1=urban)	347	0.68	0.47	347	0.45	0.50	-0.233***
Higher Education (1=University degree)	347	0.32	0.47	347	0.27	0.45	-0.049
Number forest visits (last visited forest)	347	19.82	51.43	347	24.37	58.15	4.553
Time spent in forest during last visit	347	2.46	1.80	347	2.25	1.58	-0.210
Income categories	340	–	–	342	–	–	\(\chi^2\)=4.46
Environmental attitudes	346	–	–	345	–	–	\(\chi^2\)=3.52
Federal state	347	–	–	347	–	–	\(\chi^2\)=214.10***

Between Sample Balance: Propensity Score Matching

love.plot(
  m.out,
  stats     = "mean.diffs",
  abs       = TRUE,
  var.order = "unadjusted",
  line      = TRUE,
  thresholds = c(m = .1)   # optional threshold line at |SMD| = 0.1
)

Results

Mixed logit models survey waves

ggplot(
  filter(ci_data_match, Group == "match_base"), 
  aes(
    x = factor(
      Coefficient,
      levels = c(
        "Tree height (m)",
        "Low amount of deadwood",
        "High amount of deadwood",
        "Two age classes",
        "Multiple age classes",
        "Monoculture coniferous",
        "Two species coniferous",
        "Two species broadleaf",
        "Two species mixed forest",
        "Three species mixed forest",
        "Four species mixed forest",
        "Picnic facilities",
        "Marked hiking trails",
        "Picnic facilities + hiking trails",
        "ASC (status quo)",
        "Distance (km)"
      )
    ),
    y = Mean,
    color = Model
  )
) +
  geom_rect(
    data = bg_data,
    inherit.aes = FALSE,
    aes(xmin = xmin, xmax = xmax, ymin = -Inf, ymax = Inf),
    fill = "grey95"
  ) +
  geom_point(size = 3, position = position_dodge(width = 0.6)) +
  geom_errorbar(
    aes(ymin = Lower_CI, ymax = Upper_CI),
    width = 0.2,
    position = position_dodge(width = 0.6)
  ) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  labs(
    x = "Coefficient",
    y = "WTT Estimate (km)",
    color = "Model"
  ) +
  theme_minimal() +
  theme(axis.text.x = element_text(angle = 45, hjust = 1)) +
  coord_trans(y = "pseudo_log")

Mixed logit interaction effects: Mixed Species (pooled model)

ggplot(all_df, aes(x = group, y = estimate, color = effect)) +
  geom_point(size = 3, position = pd) +
  geom_errorbar(aes(ymin = lower, ymax = upper), width = 0.2, position = pd) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  theme_minimal(base_size = 14) +
  labs(
    x = "DiD parameter",
    y = "Coefficient estimate",
    color = "Interaction effect"
  ) +
  coord_flip() 

Mixed logit distributions: four species mixed forest

plot_mxl_mirrored(models, "four_mix")

Alternatvie treatment classification

ggplot(did_all_mxl, aes(x = factor(clean_param, levels=param_order), y = estimate, color = model)) +
  geom_point(position = position_dodge(width = 0.6), size = 3) +
  geom_errorbar(aes(ymin = lower, ymax = upper),
                position = position_dodge(width = 0.6),
                width = 0.2) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  coord_flip() +
  theme_minimal(base_size = 14) +
  labs(
    x = "DiD parameter",
    y = "Coefficient estimate",
    color = "Model"
  )

Effects on recreational behavior

	Num forest visits	Travel distance (log)	Time spent (h)
Did	\(0.29\)	\(0.43^{**}\)	\(0.29^{*}\)
	\((5.07)\)	\((0.15)\)	\((0.16)\)
high forest loss	\(5.12\)	\(-0.31^{**}\)	\(-0.22^{*}\)
	\((5.08)\)	\((0.13)\)	\((0.12)\)
year2025 (post)	\(-4.87\)	\(-0.28\)	\(-0.79^{***}\)
	\((2.84)\)	\((0.16)\)	\((0.07)\)
age	\(0.17^{*}\)	\(-0.01^{***}\)	\(-0.01^{***}\)
	\((0.10)\)	\((0.00)\)	\((0.00)\)
female	\(1.73\)	\(0.05\)	\(-0.08\)
	\((2.18)\)	\((0.05)\)	\((0.07)\)
university degree	\(-2.39\)	\(0.37^{***}\)	\(0.32^{***}\)
	\((2.43)\)	\((0.11)\)	\((0.07)\)
hh income: €2,000–2,499	\(-3.24\)	\(0.01\)	\(0.01\)
	\((2.95)\)	\((0.14)\)	\((0.11)\)
hh income: €2,500–4,599	\(-2.73\)	\(0.33^{**}\)	\(0.33^{***}\)
	\((2.80)\)	\((0.13)\)	\((0.10)\)
hh income: \(\ge\) €4,600	\(-2.23\)	\(0.35^{***}\)	\(0.60^{***}\)
	\((3.89)\)	\((0.12)\)	\((0.12)\)
hh income: DK/Refuse	\(1.45\)	\(0.13\)	\(-0.06\)
	\((6.80)\)	\((0.14)\)	\((0.14)\)
Num. obs.	\(2178\)	\(2176\)	\(2178\)
Num. groups: bundesland_depart	\(16\)	\(16\)	\(16\)
Num. groups: urban	\(2\)	\(2\)	\(2\)
Adj. R\(^2\) (full model)	\(0.03\)	\(0.10\)	\(0.12\)
Adj. R\(^2\) (proj model)	\(0.00\)	\(0.04\)	\(0.08\)

\(^{***}p<0.01\); \(^{**}p<0.05\); \(^{*}p<0.1\).

Correlation forest loss and perceived drought

Effect of perceived drought on behavior

	Num forest visits	Travel distance (log)	Time spent (h)
drought index	\(0.61\)	\(-0.04\)	\(-0.06^{***}\)
	\((0.54)\)	\((0.03)\)	\((0.02)\)
age	\(0.18^{**}\)	\(-0.02^{***}\)	\(-0.02^{***}\)
	\((0.07)\)	\((0.00)\)	\((0.00)\)
female	\(2.59\)	\(0.02\)	\(-0.02\)
	\((1.99)\)	\((0.11)\)	\((0.06)\)
university degree	\(-1.09\)	\(0.27^{*}\)	\(0.24^{***}\)
	\((3.82)\)	\((0.14)\)	\((0.08)\)
hh income: €2,000–2,499	\(-1.97\)	\(0.14\)	\(0.12\)
	\((3.72)\)	\((0.13)\)	\((0.14)\)
hh income: €2,500–4,599	\(-3.82\)	\(0.37^{***}\)	\(0.32^{***}\)
	\((5.07)\)	\((0.11)\)	\((0.08)\)
hh income: \(\ge\) €4,600	\(-2.75\)	\(0.58^{***}\)	\(0.51^{***}\)
	\((4.88)\)	\((0.15)\)	\((0.13)\)
hh income: DK/Refused	\(-3.85\)	\(0.43^{**}\)	\(0.09\)
	\((6.49)\)	\((0.18)\)	\((0.13)\)
life satisfaction	\(-0.81^{*}\)	\(0.04^{*}\)	\(0.07^{***}\)
	\((0.42)\)	\((0.02)\)	\((0.01)\)
Num. obs.	\(2263\)	\(2263\)	\(2263\)
Num. groups: bundesland	\(16\)	\(16\)	\(16\)
Num. groups: urban	\(2\)	\(2\)	\(2\)
Adj. R\(^2\) (full model)	\(0.04\)	\(0.11\)	\(0.19\)
Adj. R\(^2\) (proj model)	\(0.00\)	\(0.06\)	\(0.10\)

\(^{***}p<0.01\); \(^{**}p<0.05\); \(^{*}p<0.1\).

Further material

Socio-demografics matched sample

Variable	2017_C	2017_T	2025_C	2025_T
Age (mean)	45.37	44.64	47.67	46.76
Household size (mean)	2.17	2.37	2.18	2.20
Education: Lower secondary	4.27	2.10	5.06	2.50
Education: Upper secondary	18.60	21.56	17.86	18.44
Education: Vocational training	44.51	48.80	46.13	51.88
Education: Bachelor	10.67	9.88	9.82	10.00
Education: Master / PhD	21.95	17.66	21.13	17.19
Settlement: Rural \(<\)500	5.49	14.67	4.46	8.75
Settlement: Small town 500–20k	26.83	41.32	30.65	42.19
Settlement: Town 20–100k	20.12	20.36	16.67	21.88
Settlement: City \(>\)100k	47.56	23.65	48.21	27.19
Gender: Female	47.56	47.01	48.81	47.50
Gender: Male	52.44	52.99	51.19	52.50
HH income: \(<\) €2,000	35.37	31.44	31.85	35.00
HH income: €2,000–2,499	15.24	18.56	15.18	16.56
HH income: €2,500–4,599	20.43	21.56	26.19	21.88
HH income: \(\ge\) €4,600	19.82	16.47	17.86	19.06
HH income: DK/Refused	9.15	11.98	8.93	7.50
Observations	328	334	336	320