Application: Global biodiversity conservation

5.5.1 Data

This section introduces our case study on WTP for global ecosystem services and biodiversity.

An overview of the inputs to our empirical application is given in Table 5.2.

For the initial global income distribution we draw on Pinkovskiy and Sala-i-Martin (2009), who estimate the global per-capita income distribution for 2006 nding a mean of µY0 = 9,550 [2006-PPP-USD] and a standard deviation of σY0 = 15,400 [2006-PPP-USD] (Pinkovskiy, personal communication). This corresponds to a coecient of variation of CVY0 = 1.61. For the forecasted growth rate of income,gY, we draw on an expert survey by Drupp et al. (2018). Almost two hundred experts on long-term societal decision-making were asked to provide their best guess of the global average, long-term (>100years) annual growth rate of real per-capita consumption. They nd a mean consumption growth rate of g^mean_Y = 1.7 percent. The lower bound (abbreviated as `lb') is -2 percent and the upper bound (`ub') is g^ub_E = 5 percent. As only three experts stated negative growth rates and, in order to stay consistent with our model assumptions, we takeg_Y^lb= 0.1percent as lower bound value in our application.

We normalize the initial level of the global environmental good toE0= 1. For the growth rate of the environmental good,g_E, we focus on non-use ecosystem services, as this provides the best t for our simple mapping from natural capital to ecosystem service provision-ing. We take the global mean annual growth rate of cultural ecosystem services estimated by Baumgärtner et al. (2015), based on the best available time-series data for dierent ecosystem services and countries. These include as ecosystem service measures landscape connectedness, forest area, living planet index, red-list-index and national biodiversity indi-cators. Baumgärtner et al. (2015) estimate the global average growth rate asg_E^mean=−0.52 with a lower bound of g^lb_E =−1.28 percent and an upper bound ofg^ub_E =−0.08 percent.

Table 5.2: Variable and parameter values used in the application

Parameter Value(s) Description Source

CVY0 1.61 Coecient of variation of global per-capita income

Pinkovskiy and Sala-i-Martin (2009)

µ_Y0 9,550 Mean global per-capita income in 2006-PPP-USD

Pinkovskiy and Sala-i-Martin (2009)

gY 0.017 Annual real per-capita Drupp et al. (2018) [0.001; 0.050] (consumption) growth rate

E₀ 1 Normalized to one

gE −0.0052 Growth rate of global non-use Baumgärtner [−0.0128;−0.0008] environmental goods et al. (2015) α 0.85 [0.7; 1] Utility share parameter for

con-sumption goods

Kopp et al. (2012)

θ 2.31 [0.86; 7.14] Elasticity of substitution Drupp (2018) ρ 0.989 [0.926; 1] Pure time discounting factor Drupp et al. (2018) δ 0.977 [0.94; 1] Risk-free market interest factor Drupp et al. (2018) Note: Numbers in brackets correspond to lower and upper bound values. We approximate the up-per bound discount and interest factors with 0.999 instead of 1.

We take preference parameters from the literature, in particular from meta-studies and international expert surveys. For the utility share parameter of consumptions goods relative to environmental goods, α, we draw on the parameter range considered by Kopp et al.

(2012), ranging from 0 to 0.3, with a mean of 0.15, for the environmental good. Thus, the parameter value for the consumption good ranges from 0.7 to 1, with a mean of 0.85.⁷¹ For the elasticity of substitution between the environmental and the market-traded consumption good, we use data from a meta-study by Drupp (2018), who gathers indirect evidence from 18 environmental valuation studies. This yields a mean elasticity of substitution ofθ^mean= 2.31, implying that environmental goods are considered as substitutes to market-traded goods on average, with a lower and upper bound ofθ^lb= 0.86and θ^ub = 7.14 respectively.⁷² For the pure time discount factor, the elasticity of marginal utility of consumption and the market interest factor, we again draw on survey data from Drupp et al. (2018), who elicited expert recommendations and long-run forecasts. They obtain a mean rate of pure time preference of 1.1 percent, with a lower and upper bound of 0 and 8 percent. This translates into an initial mean pure time discount factor of ρ^mean = 0.989, with a lower and upper bound of

71This encompasses parameter values chosen by Sterner and Persson (2008), who assume1−α= 0.1, and Gollier (2010), who assumes1−α= 0.29.

72Note that values implying stronger complementarity have been used in the applied theory and modelling literature. For example, Sterner and Persson (2008) used a central value of 0.5.

Theory Intergenerational Distribution and Natural Capital 0.926 and 1.⁷³ The mean forecasted real risk-free market interest rate is 2.38 percent, with a lower and upper bound of 0 and 6 percent. This translates into an initial mean market interest factorδ^mean= 0.977, with a lower and upper bound ofδ^lb= 0.943and δ^ub= 1.⁷⁴

We quantify our results for a time horizon of hundred years,T = 100, and a hypothetical one percent increase in the level of the environmental good. The corresponding changedE= 0.01 that we seek to value is a pure scaling factors in the mean WTP-function (Eq. 5.14).

Before quantifying our main results, we need to make sure, that the conditions on the growth paths hold (Eqs. 5.7a and 5.7b). The set of growth rates that meet the existence con-dition for the closed-form intertemporal utility function for a given elasticity of substitution, θ, and discount factor, ρ, is given as⁷⁵

ρ(1 +g)^θ−1θ <1 ⇐⇒







g < ρ^θ−1−θ −1 =:g^max for θ >1 g > ρ^θ−1−θ −1 =:g^min for θ <1

. (5.43)

Thus, the growth path condition for substitutes implies a supremum dened by g^max, which is always positive and thus bites only for the income growth rate g_Y, but not for the growth rate of the environmental good which is by denition always negative, gE < 0. In contrast, the growth rate condition for complements implies a inmum for the growth rates g^min, below which the closed-form intertemporal utility function does not exist. As g^min is always negative, this condition is generally fullled for the income growth rate,g_Y >0, but applies for the growth rate of the environmental good,gE <0.

Figure 5.1 displays this frontier for the growth rates of income and the environmen-tal good for a range of empirical elasticities of substitution, θ, and pure time discount factors, ρ, depicted in Table 2. The supremum for the income growth rate in the mean case of substitutes, with θ^mean = 2.31, depends on ρ = 0.989 [0.926; 0.999] and is given by g^max_θ=2.31 = 0.0197 [0.1452,0.0018]. For the upper bound substitutability, with θ^ub = 7.14, it is given by g^max_θ=7.14 = 0.0129 [0.0935; 0.0012]. For the lower bound complementarity case, with θ^lb = 0.86, the inmum for the growth rate of the environmental good is g^min_θ=0.86 = −0.0657 [−0.3764;−0.0061]. We observe that the closer the discount factor ρ is to one, i.e. the closer the pure time prefernece rate is to zero, the smaller is the set ofg_E in case of complements and ofg_Y in case of substitutes that fulls the growth path condition.

73We use a value of 0.999 instead of 1 to ensure that our intertemporal welfare function is bounded.

74We use a value of 0.999 instead of 1 to ensure that the present value WTP as a constant payment fraction is bounded.

75As the condition is identical forgE andgY we suppress the subscript on the growth rate in the following formula and only writeg.

g^min =-0.38 g^min =-0.066 g^min =-0.0061

lb =0.86

0 0.5 1

-0.4 -0.2 0

g^max =0.15

g^max =0.02 g^max =0.0018

g^max =0.094

g^max =0.013 g^max =0.0012

mean =2.3 ^ub =7.1

1 5 9

0 0.1 0.2

= 0.926 = 0.989 = 0.999

Figure 5.1: Minimal value forgEin case of complements,θ <1, (left side) and maximal value forgY in case of substitutes,θ >1, (right side) to ensure the existence of a closed-form intertemporal utility function (Eq. 5.3) for dierent values of the discount factor,ρ, and the elasticity of substitution,θ. The shaded area depicts the set of growth ratesgE(left side) orgY (right side) that meets the growth path condition (Eq. 5.7b or 5.7a) for the transfer factor for the mean pure time discount factor,ρ= 0.989.

Moreover, the higher the degree of substitutability,θ→ ∞, the smaller is the set ofgY that still meets the condition, and the stronger the complementarity,θ→0, the larger is the set of gE that meets the condition.

When we compare these inma and suprema of the growth rates, g_E and g_Y, for which a closed-form intertemporal utility function exists, with empirical data on growth rates, we see that these conditions appear generally uncritical for the loss rate of ecosystem services g_E. This is not the case for the income growth rateg_Y. For the mean estimate on the pure time discount factor, ρ^mean = 0.989, and complements with the strongest complementarity, θ^lb = 0.86, estimated from valuation studies reviewed in Drupp (2018), the growth rate inmum g^min_θ=0.86 = −0.0657 is well below the lower bound rate of global loss of ecosystem servicesg_E^lb=−0.0128estimated by Baumgärtner et al. (2015). Also for the mean pure time discount factor and the best guess estimate for the degree of substitutability,θ^mean = 2.31, the income growth rate supremum is withg_θ=2.31^max = 0.0197higher than the mean of the long term growth rate expected by international experts of g^mean_Y = 0.017. Thus, for the main

Theory Intergenerational Distribution and Natural Capital specication of our model the growth path condition is fullled. However, the upper bound of the expected annual global income growth rate of g_Y^ub = 0.05 does not meet the growth path condition for the mean substitutability parameter g^max_θ=2.31. Moreover, for the upper bound of the substitutability parameter, θ = 7.14, the mean growth rate, g^mean_Y , is already higher than the supremum g^max_θ=7.14 and thus the growth path condition is not fullled.

5.5.2 Quantication of main results

We estimate how intra- and intertemporal distribution aects mean WTP for global ecosys-tem services derived from biodiversity. Moreover, we compute transfer factors that allow controlling for the intertemporal aspects of natural capital valuation. We focus on the case of mean WTP measured as a constant payment fraction for a marginal change in the envi-ronmental good,W T P_CPF,dE, throughout this subsection, as the bulk of empirical valuation studies falls within this category.

Figure 5.2 depicts how mean income (left side) and income inequality (right side) aect global mean WTP measured as a constant payment fraction for an initial increase in global ecosystem services. First of all, it is apparent that the degree of substitutability,θ, is crucial in determining mean WTP, WTP_CPF,dE. For initial global mean income and the mean substitutability estimate θ^mean = 2.31, we obtain a mean WTP of 0.63 [2006-PPP-USD].

However, if ecosystem services were a complement to manufactured consumption goods, θ^lb = 0.86, mean WTP would be magnitudes higher and amount to 8.40×10³ [2006-PPP-USD]. These estimates highlight that the societal value of global ecosystem services strongly depends on their substitutability: The harder it is to substitute ecosystem services with human-made goods, the higher is their societal value.

Mean WTP for global biodiversity conservation is increasing with mean income (see Proposition 5.1). For substitutes mean WTP is a strictly increasing concave function of mean income (Figure 5.2 top left subplot), while it is a convex function for complements (bottom left subplot). For a hypothetical doubling of global per-capita income, mean WTP would be34.99%higher for the mean substitutability estimate. In this case WTP-estimates would need to be adjusted with a factor of T_µ(2µ^GLO_Y

0 , µ^GLO_Y

0 ;θ^mean) = 1.35. For the lower bound range of complements, θ^lb = 0.86, it would be even 123.89% higher as initially, corresponding to an adjustment factor ofT_µ(2µ^GLO_Y

0 , µ^GLO_Y

0 ;θ^lb) = 2.24.

The subplots on the right of Figure 5.2 illustrate how mean WTP for global biodiversity conservation changes for a change in relative intratemporal income inequality as measured

10,000 20,000

Figure 5.2: Eect of mean income,µY₀, (left side) or relative intratemporal income inequality, CVY₀, (right side) on the present value mean WTP for a one percent increase in global non-use environmental goods measured as a constant payment fraction,W T P_CPF,dE, for dierent degrees of substitutability between the consumption and the environmental good,θ.

by the coecient of variation of per-capita income, CVY0. While mean WTP decreases with income inequality for the mean case of substitutes (top right subplot), it increases for complements (bottom right subplot) (see Proposition 5.2). A hypothetical reduction of the current level of global income inequality, CV^GLO_Y0 = 1.61, to zero would increase mean WTP by17.00%corresponding to a transfer factor ofT_CV(0,CV^GLOY0 ;θ^mean) = 1.17given the mean empirical estimate for the elasticity of substitution,θ^mean= 2.31. To the contrary, the lower bound elasticities of substitution,θ^lb= 0.86, produces a decrease by11.40% corresponding to a transfer factor of T_CV(0,CV^GLO_Y0 ;θ^lb) = 0.89.

The left side of Figure 5.3 illustrates how mean WTP for global biodiversity conservation changes with the income growth rate. Mean WTP increases with income growth for comple-ments and Cobb-Douglas substitutability (Proposition 5.3). Yet, for the case of substitutes, mean WTP can also decreases with income growth.⁷⁶ We nd that for a hypothetical re-duction of the currently expected global income growth rate by half, mean WTP would increase by 192.83% for a substitutability of θ^mean = 2.31 and decrease by 36.54% for a substitutability of θ^lb= 0.86.

76In our central calibration and for an innite time horizon, mean WTP starts to decrease with income growth atg^mean_Y already for a medium-degree of substitutabilityθ^∗= 1.93(see Figure 5.8 and Eq. 5.96).

Theory Intergenerational Distribution and Natural Capital

Figure 5.3: Eect of global per-capita income growth rate,gY, (left side) or growth rate of non-use environmental goods,gE, (right side) on the present value mean WTP for a one percent increase in global non-use environmental goods measured as a constant payment fraction,W T P_CPF,dE, for dierent degrees of substitutability between the consumption and the environmental good,θ. Grey coloured lines indicate parameter combinations that do not meet the growth path condition for the closed-form

intertemporal utility function (Eq. 5.7a).

Concerning the eect of the growth rate of environmental goods, the right side of Fig-ure 5.3 shows that mean WTP increases with the growth rate of the environmental good for substitutes, but decreases for complements (Proposition 5.4). For the non-use environ-mental goods from global biodiversity, a hypothetically slowing down of the loss rate by half will increase mean WTP by 11.72% for substitutes, θ^mean = 2.31, and decrease mean WTP by 3.97% for complements, θ^lb = 0.86. In this empirical illustration, the eect of income growth on societal WTP is relatively stronger as compared to the growth rate of environmental goods.

Next, we study whether the new structural benet transfer factors for dierences in growth rates and market interest rates (Proposition 5.5) lead to notable WTP adjustments.

Specically, we perform hypothetical transfers of mean WTP elicited at the mean of empirical estimates to a site characterised with the lower or upper bound parameters within the empirically plausible parameter a value ranges (cf. Table 5.2).

-12 -10 -8 -6 -4 -2 10^-3 0.7

0.8 0.9 1 1.1 1.2 1.3 1.4

g_E^mean =-0.0052

g_E^lb =-0.0128 g_E^ub =-0.0008

T_g

E

(g_E^lb, g_E^mean; ^mean) =0.7649 T_g

E

(g_E^ub, g_E^mean; ^mean) =1.216

lb = 0.86 mean = 2.31 ub = 7.14

Figure 5.4: Transfer factor to adjust mean WTP for a one percent increase in the level of the environmental good from a study site with a growth rate ofg^study_E =−0.0052to the growth rate at a policy site. Colours depict dierent degrees of substitutability between the manufactured consumption and the

environmental good,θ.

First, we turn to the transfer factor for dierences in the growth rate of the environmen-tal good T_g^(dE)_E (Eq. 5.38). Figure 5.4 displays the required adjustment when transferring mean WTP from a study site with the global average growth rate of non-use ecosystem services, g_E^mean = −0.0052, to a policy site with a growth rate within the range of global growth rates for dierent non-use ecosystem services estimated by Baumgärtner et al. (2015).

Applying environmental values elicited at a study site with g_E^study :=g_E^mean at a policy site with a higher growth rate of the environmental good, that is where the loss of biodiversity is at a lower rate, equal to g_E^ub = −0.0008, would require an upward adjustment of soci-etal WTP by 21.58%, corresponding to a transfer factor of T_g^(dE)_E (g_E^ub, g^mean_E ;θ^mean) = 1.22. To the contrary, societal WTP-estimates for a transfer to a policy context with a higher rate of biodiversity loss of g^lb_E = −0.0128 would need to be lowered by 23.51%, i.e. be adjusted by the factor T_g^(dE)_E (g^lb_E, g^mean_E ;θ^mean) = 0.77. Again, the transfer factor cru-cially depends on the substitutability between the two goods. A higher degree of sub-stitutability would reinforce these required adjustments, T_g^(dE)_E (g_E^ub, g^mean_E ;θ^ub) = 1.32 and T_g^(dE)_E (g_E^lb, g_E^mean;θ^ub) = 0.70, but complementarity would reverse the direction of the re-quired adjustments,T_g^(dE)_E (g^ub_E , g_E^mean;θ^lb) = 0.94and T_g^(dE)_E (g^lb_E, g^mean_E ;θ^lb) = 1.14.

Second, adjusting environmental values for dierences in income growth rates, T_gY,δτ (Eq. 5.42), can be substantial (Figure 5.5). To isolate the eect of the income growth rate,

Theory Intergenerational Distribution and Natural Capital we assume for now that the market interest factor is identical at the policy and the study site and constant over time, δ^policy=δ^study. Thus, the market interest factors cancel out of the transfer factor T_gY,δτ (Eq. 5.42). Note that depending on the degree of substitutability, θ, we end up in parameter constellations in which the growth path condition on g_Y is not fullled and the closed-form transfer factorT_gY,δτ cannot be applied any more. In Figure 5.5 the estimates of the transfer factor for income growth rates are coloured grey at growth rate where the growth path condition does not hold (Eq. 5.7a). Applying WTP-estimates elicited for an income growth rate at the expected global mean, g^study_Y := g_Y^mean = 0.017, in a policy context where the income growth rate is g^lb_Y = 0.001 would imply a transfer factor of T_gY,δτ(g_Y^lb, g_Y^mean;θ^mean) = 3.75. That is, the societal WTP-estimate would have to be adjusted upwards by 274.65%. The direction of adjustment is reversed for comple-ments requiring a downward adjustment with T_gY,δτ(g^lb_Y, g^mean_Y ;θ^lb) = 0.44. For the upper bound substitutability estimate,θ^ub= 7.14, the growth path condition is not meet atg_Y^mean. Hence, we cannot apply the transfer factor. The required adjustmentsT_gY,δτ are even more pronounced, when applying WTP-estimates in contexts with higher income growth equal to the maximal expected rate, g^ub_Y = 0.05. However, for the parameter constellation in this empirical application the growth path condition is also not met for the mean sub-stitutability estimate, θ^mean, at g^ub_Y = 0.05.⁷⁷ For the case of complements, θ^lb = 0.86, applying WTP-estimates from a site characterised by the mean expected income growth rate in a context characterised by the maximal expected rate implies a transfer factor of T_gY,δτ(g^ub_Y , g_Y^mean;θ^lb) = 8.76 and thus an upward adjustment of societal WTP of 776.30%.

Third, Figure 5.6 depicts again the transfer factorT_gY,δτ, but this time for dierences in the market interest factor between a study and a policy site. For illustration, the market interest rate is kept constant over time at both sites, thusδτ =δ∀τ, and the income growth rate at policy and study site are identical and equal to the global average, g_Y^study=g_Y^policy= g^mean_Y . For identical growth rates at both sites the rst factor in T_gY,δ reduces to one and hence the entire transfer factor does not depend on the elasticity of substitution,θ, any more.

It shows that dierences in market interest rates within the range expected by international experts lead to substantial WTP adjustments: For a hypothetical transfer of mean WTP elicited at δ^mean = 0.977 to a policy site with δ^ub = 0.999the required adjustment would be T_gY,δ(g^mean_Y , δ^ub, g^mean_Y , δ^mean) = 3.35 and thus increase mean WTP by 235.39%. To the contrary a hypothetical transfer to the lower bound forecasted market interest factor,

77The maximum value for applying Tg_Y,δ_τ is forθ^mean = 2.31 at g^max_θ=2.31 = 0.0197, where the transfer factor approaches zero, while it is generally uncritical for complements.

0 0.005 0.01 0.015 0.02

Figure 5.5: Transfer factor to adjust societal WTP for a one percent increase in the level of the environmental good from a study site with an income growth rate ofg^study_Y :=g_Y^mean= 0.017to an income growth rate at a policy site, such as the lower bound growth rateg^lb_Y = 0.001. Coloured lines depict dierent degrees of substitutability between the manufactured consumption and the environmental good,θ. Grey coloured lines indicate parameter combinations that do not meet the growth path condition for the closed-form intertemporal utility function (Eq. 5.7a).

δ^lb = 0.94, i.e. a situation with a high market interest rate, would imply a transfer factor of T_gY,δ(g_Y^mean, δ^lb, g_Y^mean, δ^mean) = 0.29. Moreover, we see that the required adjustment of mean WTP in absolute terms, i.e. |T_gY,δ−1|, is larger for higher levels of the common income growth rate at study and policy site.

Theory Intergenerational Distribution and Natural Capital

Figure 5.6: Transfer factor to adjust mean WTP for a one percent increase in the level of the environmental good from a study site with a market interest rate ofδ^study= 0.977to the market interest rate at the policy site when the income growth rate at both the study and policy site is identical. Colours

Figure 5.6: Transfer factor to adjust mean WTP for a one percent increase in the level of the environmental good from a study site with a market interest rate ofδ^study= 0.977to the market interest rate at the policy site when the income growth rate at both the study and policy site is identical. Colours

Im Dokument Inequality and the Value of Nature (Seite 175-200)