# Limited substitutability, relative price changes
and the uplifting of public natural capital values

Moritz A. Drupp${}^{\text{a,b}}$, Zachary M. Turk${}^{\text{c,d}}$,
Ben Groom${}^{\text{e}}$, Jonas Heckenhahn${}^{\text{f}}$111We thank Jasper
Meya, Sjak Smulers, Daan van Soest and Martin Quaas as well as seminar
audiences at the World Bank, idiv Leipzig and EAERE 2023 for helpful
discussions, and are grateful to Johanna Darmstadt, Mark Lustig and Jasper
Röder for excellent research assistance. We gratefully acknowledge funding by
the World Bank. M.D. additionally acknowledges support from the German Federal
Ministry of Education and Research (BMBF) under grant number 01UT2103B.
${}^{\text{a}}$ Department of Economics, University of Hamburg, Germany
${}^{\text{b}}$ CESifo Munich, Germany
${}^{\text{c}}$ Department of Geography and Environment,
London School of Economics and Political Science, UK
${}^{\text{d}}$ Landscape Policy and Governance Team,
Manaaki Whenua - Landcare Research, New Zealand
${}^{\text{e}}$ Department of Economics, University of Exeter, United Kingdom
${}^{\text{f}}$ Faculty of Management and Economics, Ruhr-University Bochum,
Germany

###### Abstract

As the global economy continues to grow, ecosystem services tend to stagnate
or degrow. Economic theory has shown how such shifts in relative scarcities
can be reflected in the appraisal of public projects and environmental-
economic accounting, but empirical evidence has been lacking to put the theory
into practice. To estimate the relative price change in ecosystem services
that can be used to make such adjustments, we perform a global meta-analysis
of environmental valuation studies to derive income elasticities of
willingness to pay (WTP) for ecosystem services as a proxy for the degree of
limited substitutability. Based on 749 income-WTP pairs, we estimate an income
elasticity of WTP of around 0.78 (CI: 0.6 to 1.0). Combining these results
with a global data set on shifts in the relative scarcity of ecosystem
services, we estimate relative price change of ecosystem services of around
2.2 percent per year. In an application to natural capital valuation of non-
timber forest ecosystem services by the World Bank, we show that their natural
capital value should be uplifted by more than 50 percent (CI: 32 to 78
percent), materially elevating the role of public natural capital. We discuss
implications for relative price adjustments in policy appraisal and for
improving estimates of comprehensive national accounts.

Keywords: Willingness to Pay; Ecosystem Services; Limited Substitutability;
Growth; Relative Prices; Contingent Valuation; Forests

JEL codes: D61, H43, Q51, Q54, Q58

##  1 Introduction

Measuring economic progress towards sustainability requires addressing the
limited substitutability among the various constituents of comprehensive
wealth (Smulders and van Soest, 2023). Potential limits to substitutability
imply that society must strike a balance between the two opposing paradigms of
Weak and Strong Sustainability (e.g., Neumayer, 2003; Hanley et al., 2015;
Dasgupta, 2021). Many contemporary measures of economic progress and wealth
have explicitly or implicitly followed a Weak Sustainability approach. In
doing so, they consider natural capital and ecosystem services as largely
substitutable—sometimes even perfectly substitutable—with human-made capital
stocks. In light of the continued growth of human-made capital and the
stagnation or degradation of many natural capital stocks, the Weak
Sustainability approach is increasingly being called into question. From a
theory perspective, we should consider some degree of imperfect
substitutability when estimating shadow prices. This is relevant both for
natural capital that serves as an intermediate input to various production
processes as well as public natural capital as a direct source of utility
(see, e.g. Smulders and van Soest, 2023; Zhu et al., 2019). A common
constraint to implementation, however, has been a lack of sufficient empirical
evidence on the limits of substitutability of ecosystem services and natural
capital that can inform the computation of shadow prices (e.g., Cohen et al.,
2019; Drupp, 2018; Rouhi Rad et al., 2021).

This paper makes a step towards closing this important empirical evidence gap
to enable respecting a limited degree of substitutability and the change in
the relative scarcity of ecosystem services in policy appraisal and
environmental-economic accounting, by focussing on the limited sustainability
of ecosystem services in utility. To this end, we present the largest global
database to estimate the degree of limited substitutability of ecosystem
services vis-a-vis human-made goods, via the income elasticities of WTP for
ecosystem services, in order to compute relative price changes of ecosystem
services. We use these estimates of relative price changes to derive
adjustments to natural capital accounting, taking the assessment of forest
ecosystem service values in the Changing Wealth of Nations (CWON) as a case
study.

There are two general approaches to dealing with limited substitutability of
ecosystem services in a dynamic context, for example in project appraisals
with future costs and benefits or the assessment of comprehensive wealth. We
can either apply differentiated discount rates – often a lower discount rate
for non-market ecosystem services, or account for increasing relative scarcity
by adjusting our valuation of ecosystem services over time (e.g. Baumgärtner
et al., 2015; Drupp, 2018; Gollier, 2010; Hoel and Sterner, 2007; Traeger,
2011; Weikard and Zhu, 2005). Sterner and Persson (2008) have put a spotlight
on the detrimental effects of climate change on non-market ecosystem services,
such as the loss of biodiversity or environmental amenities. Sterner and
Persson (2008) and subsequent work (Drupp and Hänsel, 2021; Bastien-Olvera and
Moore, 2021) has studied how the increasing scarcity and limited
substitutability of non-market ecosystem services vis-à-vis manufactured goods
affects optimal climate policy via good-specific discount rates or relative
price changes. Drupp and Hänsel (2021), for instance, estimate that relative
prices of non-market goods increase by around 2 to 4 percent per year.
Incorporating this scale of adjustment leads to social cost of carbon
estimates that are more than 50 percent higher compared to the case where
goods are assumed perfectly substitutable. Accounting for relative price
changes of non-market goods is thus crucial to the appraisal of climate change
policy. It is likewise relevant for project appraisal and environmental-
economic accounting such as in the System of Environmental Economic
Accounting-Experimental Ecosystem Accounting (SEEA-EEA) and in CWON.

Previous empirical studies have estimated relative price changes of non-market
goods by calculating the elasticity of substitution indirectly via the income
elasticity of willigness to pay (WTP) from non-market valuation studies
(Baumgärtner et al., 2015; Drupp, 2018; Heckenhahn and Drupp, 2022). The
second key component are good-specific growth rates, estimated on historical
time series (Baumgärtner et al., 2015; Heckenhahn and Drupp, 2022) or as
endogenous outcomes in global integrated climate-economy assessment models
(e.g. Drupp and Hänsel, 2021). Relative price changes are then approximated by
the income elasticity of WTP multiplied by the difference in good-specific
growth rares. Baumgärtner et al. (2015) were the first to estimate relative
price changes. They applied national growth rates to arrive at country-level
results. However, they assumed that the elasticity of substitution is constant
across all countries and ecosystem service types. Specifically, they derive
the elasticity of substitution based on a single meta-analysis by Jacobsen and
Hanley (2009), who estimate an income elasticity of WTP for global
biodiversity conservation based on 46 contingent valuation (CV) studies.
Heckenhahn and Drupp (2022) provide the first comprehensive country-specific
evidence, estimating growth rates of 15 ecosystem services and the degree of
limited substitutability based on a meta-analysis of 36 German WTP studies.
They find that ecosystem services are complements to manufactured goods and
that their relative price has, on aggregate, increased by around 4 percent per
year.

Most government appraisal and environmental-economic accounting has yet to
explicitly address the limited substitutability of non-market goods (Groom et
al., 2022). Due to a lack of country-specific estimates of substitutability,
global-level estimates of relative price changes have recently been integrated
into governmental policy guidance (Groom and Hepburn, 2017). For instance, The
Netherlands consider relative price changes of 1 percent per annum as part of
their discounting guidance, and the UK Department for Environment, Food and
Rural Affairs (DEFRA) consider relative price adjustments by ‘uplifting’ the
damage costs of air pollution by 2 percent per year. Additionally, guidelines
by the Asian Development Bank and Canada suggest the use of lower discount
rates for environmental goods (Groom et al., 2022). The most recent CWON
report by the World Bank captures a few select non-market goods and capital
stocks. Most prominently, forest ecosystem service values are featured based
on a meta-regression and benefit transfer analysis by Siikamäki et al. (2015).
Even though Siikamäki et al. (2015) find positive and large GDP elasticities
of WTP, CWON does not apply relative price adjustments in response to the
increasing relative scarcity of forest ecosystem service values. This occurs
by assuming that per-hectare monetary values are constant over time, solely
adjusting for inflation. Given that a constant social discount rate of 4
percent is also applied to forest ecosystem service values, such an approach
implicitly assumes that non-market environmental values do not increase with
incomes and thus follow a perfect substitutability assumption.

Against this background, we provide the first systematic global empirical
evidence basis to inform relative price adjustments of ecosystem services for
application to CWON and beyond. Our main focus is on improving the estimation
of limited substitutability of ecosystem services vis-a-vis human-made goods.
To this end, we perform a meta-analysis of environmental values derived by the
contingent valuation (CV) approach to estimating the income elasticity of
WTP—a key parameter also for benefit transfer across space (Baumgärtner et
al., 2017; Smith, 2023). This builds on a large-scale keyword-based search
strategy and an in-depth analysis of a large random sample of the known
population of peer-reviewed CV studies. The subsequent inputs to our analysis
are aggregate income and WTP estimates as well as recurring covariates from
each study.

We find relative price changes of ecosystem services of around 2.2 percent per
year on aggregate. Relative price changes are slightly smaller (1.6 percent)
for forest ecosystem services, due to a lower rate of de-growth of forest area
offset by a larger income elasticity of WTP. These estimates can be employed
to adjust WTP estimates for project appraisal or environmental-economic
accounting. In an application on natural capital valuation, taking the
Changing Wealth of Nations (CWON) 2021 report by the World Bank (2021) as a
case study, we show that adjusting natural capital estimates for non-timber
ecosystem services for relative price changes results in uplifting the present
value over a 100 year time period by 52 percent (CI: 32 to 78 percent),
materially elevating the role of public natural capital. This echoes work on
the importance of limited substitutability in climate policy appraisal
(Bastien-Olvera and Moore, 2021; Drupp and Hänsel, 2021; Sterner and Persson,
2008). We close by discussing the results of our empirical analysis in context
and summarizing insights for environmental-economic appraisal and accounting.

##  2 Theoretical background

Well-being depends on the good and services that are derived in each period
from human-made and natural capital stocks. To provide the theoretical
background for our empirical analysis, we consider a simple model in which
intertemporal well-being is derived from both human-made goods, $C_{t}$ and
non-market environmental goods or ecosystem services, $E_{t}$. In the general
case of imperfect substitutability, ecosystem services feature explicitly in
the instantaneous utility function representing preferences over market-traded
human-made consumption goods and non-market goods, $U({C_{t},E_{t}})$. A
standard form of time-discounted Utilitarian social welfare function is given
by:

$W=\int_{t=0}^{\infty}U({C_{t},E_{t}})e^{-\delta t}dt\,.$ (1)

The theory of dual discounting or relative price changes has shown that there
are two approaches to addressing the intertemporal appraisal of non-market
goods (e.g., Baumgärtner et al., 2015; Gollier, 2010; Traeger, 2011; Weikard
and Zhu, 2005):

  1. 1.

Explicitly consider how the relative price of non-market goods vis-a-vis
market-traded consumption goods changes over time. Then, compute comprehensive
consumption equivalents at each point in time and use a single consumption
discount rate to on future comprehensive consumption equivalents.

  2. 2.

Use differentiated, good-specific consumption discount rates. In the most
general application, one discount rate is used for manufactured consumption,
$r_{C}$, and another for non-market goods, $r_{E}$.

In the first approach, we compute the value of non-market goods in terms of
the market good numeraire. This is given by the marginal rate of substitution
(MRS), $U_{E_{t}}/U_{C_{t}}$, which is the implicit price of non-market goods.
The MRS tells us by how much the consumption of market goods would need to
increase in reply to a marginal decrease in non-market goods to hold utility
constant. The $RPC_{t}$ measures the relative change in the valuation of non-
market goods – the change in the MRS between non-market and market goods – and
thus the change in their relative scarcity over time (Hoel and Sterner, 2007):

$RPC_{t}=\nicefrac{{\dfrac{d}{dt}\left(\dfrac{U_{E_{t}}}{U_{C_{t}}}\right)}}{{\left(\dfrac{U_{E_{t}}}{U_{C_{t}}}\right)}}\,.$
(2)

Future expected non-market values can then be adjusted using the $RPC_{t}$ and
a single SDR can be used to discount future flows of private and non-market
consumption.

In the second approach, we compute good-specific (dual) discount rates as:

$r_{C_{t}}=\delta+\eta_{CC_{t}}g_{C_{t}}+\eta_{CE_{t}}g_{E_{t}}$ (3)
$r_{E_{t}}=\delta+\eta_{EE_{t}}g_{E_{t}}+\eta_{EC_{t}}g_{C_{t}}$ (4)

where $g_{E}$ and $g_{C}$ are the growth rates, $\eta_{CC_{t}}$
($\eta_{EE_{t}}$) the elasticity of marginal utility of private-good (non-
market good) consumption with respect to private-good (non-market good)
consumption, and $\eta_{CE_{t}}$ ($\eta_{EC_{t}}$) denotes the cross-
elasticity of marginal utility of private-good (non-market good) consumption
with respect to non-market good (private-good) consumption (see, e.g.,
Baumgärtner et al., 2015). Expanding their applicability, these dual rates can
also be used in cases where non-market goods are not evaluated in monetary
units such as satellite accounts in national accounting and biophysical impact
assessments. It is important to stress that this approach also implies that we
have to adjust the ‘standard’ discount rate for private consumption with an
addition to the Simple Ramsey Rule by a substitutability effect
($\eta_{CE_{t}}g_{E_{t}}$).

To make this more concrete, let us consider the constant-elasticity-of-
substitution (CES) utility function, capturing various degrees of
substitutability or complementarity:

$U(C_{t},E_{t})=\left(\alpha
C_{t}^{\frac{\sigma-1}{\sigma}}+(1-\alpha)\,E_{t}^{\frac{\sigma-1}{\sigma}}\right)^{\frac{\sigma}{\sigma-1}}\
,$ (5)

$0<\sigma<+\infty$, is the constant elasticity of substitution between the two
goods, and $0<\alpha<1$ is the utility share parameter for private
consumption. The utility function given by equation 5 is strictly concave,
represent homothetic preferences, and both the private good, $C_{t}$, and non-
market good, $E_{t}$, are normal. It turns out that with CES preferences and
imperfect complements, i.e. $\sigma>0$, we get the following straightforward
equivalence between both approaches (Weikard and Zhu, 2005):

$RPC_{t}\,\,=\,\,\frac{1}{\sigma}\left[g_{C_{t}}-g_{E_{t}}\right]\,\,=\,\,r_{C_{t}}-r_{E_{t}}.$
(6)

Accordingly, the choice of whether one adjusts the numerator via a relative
price effect adjustment or the denominator via the use of dual discount rates
is not of theoretical importance in intertemporal valuation exercises.

In the setting of CES preferences, Ebert (2003) has shown that the constant
elasticity of substitution between a human-made consumption goods and a non-
market good is directly and inversely related to the income elasticity of WTP,
$\xi$, of the non-market good (cf. Baumgärtner et al., 2017). We can
accordingly write Equation 6 as:

$RPC_{t}\,\,=\,\,\xi\,\left[g_{C_{t}}-g_{E_{t}}\right].$ (7)

Our empirical approach is subsequently designed to estimate the income
elasticity of WTP for a variety of applications. We estimate $\xi$ at global
and regional scales, for a few nations where sufficient data is available, and
by specific types of non-market good.

##  3 Empirical strategy

We build on previous work by Jacobsen and Hanley (2009), Heckenhahn and Drupp
(2022), Subroy et al. (2019), Richardson and Loomis (2009), and Barrio and
Loureiro (2010) to estimate income elasticities of WTP for ecosystem services
based non-market valuation studies in the academic literature. Our meta-
analysis collects mean WTP and income estimates at the valuation exercise
scale. The resulting dataset is then used to estimate income elasticities of
WTP and subsequently the elasticity of substitution between ecosystem services
and human-made goods (cf. Heckenhahn and Drupp, 2022). In this section we
first discuss the meta-analysis, then the empirical strategy we implement to
arrive at estimates of $\xi$.

###  3.1 Meta-analysis of mean WTP-income value pairs

The data basis for this study is a meta-analysis of existing WTP studies. In
the first phase, we identify potentially relevant non-market valuation studies
through a keyword-based search string provided in Appendix A.1 based on the
authors’ experience and beta testing. To ensure better comparability of
ecosystem service valuation estimates, we focus our search on contingent
valuation (CV) studies that were published in peer-reviewed, English-language
literature since the year 2000. The keyword-based search results in a
preliminary data set where each row is a peer-reviewed journal article in
which we expect to find relevant contingent valuation-based mean WTP estimates
and respondent income data.

The search string employed is intended to cast a wide net. That is, we expect
to drop several studies due to irrelevance and informational shortcomings. The
data is then evaluated using the exclusion criteria reported in Appendix A.2.
After application of the first exclusion criteria—including whether each
article has been cited at least once in SCOPUS—2,174 articles remain. The next
exclusion criteria step is an abstract screening to check whether the articles
potentially report new, contingent valuation-based WTP estimates at all.
Strictly theoretical papers as well as reviews, secondary source estimates,
and benefits transfer approach (BTA)-focused papers are excluded to avoid
double-counting estimates. Naturally, whether we can access the articles is
important and rarely proved to be an issue. At this stage, 1,165 studies
remain on which to conduct a detailed screening and subsequently data
harvesting.

From the data set of 1,165 candidate WTP studies, we selected a random sample
of 100 studies as the basis to fine tune key steps in the screening and coding
processes and improve consistency between our two independent coders. Each
paper is carefully scrutinized for appropriate WTP and income data. A
recurring issue is that several papers do not report whether income data is
net of taxes or report gross income. We have subsequently contacted each
paper’s corresponding author in search of clarification. The review of each
paper and harvesting of relevant data was found to be a particularly time-
intensive process. However, we found it easier to first screen for the
inclusion of both mean WTP and mean income estimates—or the information
necessary to derive such estimates—before harvesting relevant data. We also
found that there is an important distinction between contingent valuation
estimates presented on a timescale basis versus per-use estimates. Namely,
without data on frequency of use at the respondent scale, per-use estimates
are not comparable to estimates based on timescales, which is why we chose to
set them aside. We then further constrain our data set to peer-reviewed,
contingent valuation studies that survey respondents on values based on
timescales such as annually, monthly, etc and convert estimates to an annual
scale.

Our main analysis subsequently builds on a random sample of studies surviving
our exclusion criteria and containing at least the minimum necessary
information—at least one mean WTP estimate and mean respondent income
estimate. An unfortunate but necessary result of our focus on comparability is
a substantially reduced number of studies contributing to the end result. Of
1,000 randomly selected studies of the 1,165 passing the first two rounds of
screening, 351 studies containing 749 distinct WTP-income pairs are of use.
Table 1 provides summary statistics of our sample.

Table 1: Prepared data set description Variable | Context | Value
---|---|---
Countries represented | Count | 68
Continent | Observations |
North America |  | 86
South America |  | 34
Africa |  | 33
Europe |  | 244
Asia |  | 345
Australia |  | 7
Study year | Mean (s.d.) | 2010 (6.8)
Income | Mean annual, 2020 USD (s.d.) | 3,176 (3,421)
WTP | Mean annual, 2020 USD (s.d.) | 162 (538)
Survey sample size | Mean (s.d.) | 616 (834)
Respondent age | Mean (s.d.) | 43 (6.4)
Respondent household size | Mean (s.d.) | 4.2 (1.5)
Forest-relevant estimates | Share of observations | 0.31

###  3.2 Estimation strategy

Our main result is based on a log-log specification of WTP and income values
while accounting for the structure of our data, and clustering standard errors
at the study level. The basic univariate version of estimation equation is
thus given by

$\displaystyle ln(WTP_{ij})=\alpha+\xi ln({INC}_{ij})+\epsilon_{i}$ (8)

We suspect a number of covariates might bias the estimated coefficient on
income if omitted. These variables would have a direct effect on WTP and as
such should be included in the model. For example, populations of different
ages may have different preferences impacting their WTP as their
lifestyles—and interaction with nature—may differ systematically. We might
also expect that people value different types of ecosystem services
differently and that different nations—with individual and unique
histories—may systematically differ in their resulting levels of WTP.
Importantly, the income (and WTP) is not always consistently on a household
level, but sometimes elicited at an individual level. We therefore rely as a
default on the multivariate estimate that contains controls for these
differences across estimates. The model specification then becomes:

$\displaystyle ln(WTP_{ij})=\alpha+\xi
ln({INC}_{ij})+\sum_{k=1}^{n}\beta_{k}x_{ij}+\epsilon_{i}$ (9)

where ${\sum_{k=1}^{n}\beta_{k}x_{ij}}$ is our list of ${n}$ covariates. These
include potentially relevant factors about the survey environment and
respondents (survey year, mean respondent, household size, nation or
continent), respondent incomes (income and WTP per-person or household, gross
or net income), WTP terms (annual, monthly, repeated), and survey methods
(elicitation format, data collection method). We also test for different time
periods (for example pre- and post-2010) and for differences between
regulating and cultural services as well as differences when estimates are
relevant to forests through the use of indicator variables. Interactions, for
example between income and country indicators can also be tests. We also
prepared a set of indicator variables for ecosystem service types based on the
ecosystem services listed in the Millenium Ecosystem Assessment MEA (2005)
framework. These indicators are at the WTP estimate-level as some papers
report estimates specific to certain ecosystem service types.

We are interested in arriving at defensible estimates of $\xi$, including
whether it differs by region and ecosystem service type. Inclusion of
covariates supports that effort. As is common practice, we conduct a
sensitivity analysis on our coefficient of interest by estimating a large set
of models with different variations of covariates included in our main model
in Equation 9. So, we estimate an $2^{13}=8,192$ versions of our main log-log
specification.

As noted, we also estimate the income elasticity of the WTP based on important
sub-samples. These include regional, by broad categories of regulating and
cultural services, and pre- and post-2010. As study sample size also varies
substantially—note a mean sample size of 616 with a standard deviation of
834—the result of alternative observation weights are compared. However, our
preferred weighting approach is to apply the square-root of the samples size
used at the WTP estimate scale. This implies that we put some weight on sample
size but avoid the risk that a few studies with particularly large sample
sizes drive our result entirely. In an additional analysis, we investigate
numerous specifications that have been used in the literature so far to
estimate income elasticity of WTP: From simple OLS, to random effects (e.g.
Jacobsen and Hanley, 2009; Heckenhahn and Drupp, 2022) fixed effects, to
clustered random regression as used here with sample size, inverse of square
root of sample size (cf. Subroy et al., 2019) to our preferred main
specification that uses the square root of sample size to weigh estimates.

###  3.3 Growth rates

We next assemble growth rates of ecosystem services to obtain a proxy for a
global measure of the shift in the relative scarcity of ecosystem services
vis-a-vis human-made goods. These estimates extend and update prior work by
(Baumgärtner et al., 2015), who found that ecosystem services have overall
declined by half a percent in the last decades. We focus on non-market (and
non-rivalrous) ecosystem services, i.e. we do not consider provisioning
services but capture regulating and cultural services. In a first step, we
update the data sources employed by (Baumgärtner et al., 2015), notably:
Forest cover, Living Planet Index (LPI), and IUCN’s Red List Index (RLI). We
complement this with two additional measures for regulating services that
capture highly salient aspects of environmental quality: air quality
regulation and climate regulation. We proxy the former by the negative of
changes in PM2.5 emissions, i.e. counting reductions in emission as an
improvement in air quality. We proxy for the latter with the change in the 2C
global mean temperature budget – the upper target of the UN Paris Agreement.
Table 2 shows the individual components, units of measurement, and data
sources.

Table 2: Components and data sources for estimates of growth rates Component | Unit of measurement | Data source
---|---|---
Forest area | Hectare | WorldBank (2023)
Living Planet Index (LPI) | Dimensionless | Zoological Society of London,
|  | and WWF 2022
Red List Index (RLI) | Various | IUCN RedList (2023),
|  | based on Butchart et al. (2010)
Air quality | Micrograms per m3 | WorldBank (2023)
(mean annual PM2.5) |  |
Climate regulation | Degrees Celsius | NOAA (2023)
GDP per capita | US dollars | WorldBank (2023)

Within regulating (forest, LPI, RLI, PM2.5, temperature) and cultural services
(forest, LPI, RLI) as well as aggregate ecosystem services we take the
arithmetic mean of relevant individual components. To calculate growth rates,
we use the time span with the longest comparable data across all indicators
(1993 to 2016) and estimate exponential growth rates, including standard
errors. We use the largest standard error of the individual growth rate
components – climate for regulating and aggregate services, and the living
planet index for cultural services – when aggregating standard errors. Akin to
estimating growth rates of ecosystem services, we also estimate the growth
rate of global GDP per capita. In contrast to (Baumgärtner et al., 2015), we
do not subtract provisioning services, and measure economic growth including
its standard error.222All time series show a clear trend over the time period,
except for air quality, which deteriorates from 1990 to 2010 and improves
again thereafter. We thus also redo the analysis of growth rates for the time
frame from 2010 to 2016.

##  4 Results

We present here estimates of income elasticities of WTP, $\xi$, for ecosystem
services globally as well as select regions. We also estimate $\xi$ based on
subcategories of ecosystem services as well as different time frames. We
subsequently couple the estimates of income elasticities with estimates of
good-specific growth rates to compute relative price changes of ecosystem
services.

###  4.1 Income elasticity of WTP for ecosystem services

We first estimate the income elasticity of WTP for aggregate ecosystem
services on our full sample via univariate regression (Equation 8) and by
adding key controls (different permutations of Equation 9). Our univariate
result is an estimate of the income elasticity of WTP for ecosystem services
of 0.57 (95-CI: 0.31 to 0.82) , see Table 3. Adding controls changes the
estimate of the income elasticity of WTP to 0.78 (95-CI: 0.56 to 0.99). This
change is almost entirely attributable to the inclusion of an indicator of
whether the income measure is at the household or individual level. Respondent
measures of income potentially overlook the dynamics around household size or
multiple streams of income resulting in seemingly more elastic estimates of
the income elasticity of willingness to pay for ecosystem services. As such,
we select our coefficient from multivariate estimation as our main result. We
develop a specification graph to investigate the sensitivity of our estimate
to various combinations of control variables. The result of 8,192 alternative
specifications represented in Figure 5 of Appendix A.4 and shows that our main
univariate estimate falls at the lower end of these alternative
specifications.

Our main estimate maps into a mean value for the elasticity of
substitutability between ecosystem services and human-made goods of 1.28
(95-CI: 1.00 to 1.79).

Table 3: Income elasticity of WTP for aggregate ecosystem services Sample | ln(INCOME) | S.E. | N | Adj. R2
---|---|---|---|---
Univariate | 0.57*** | 0.13 | 749 |  0.88
With controls | 0.78*** | 0.11 | 749 |  0.89

Estimates on subsets of aggregate ecosystem services allow us to investigate
the extent of heterogeneity. We consider different sub-types of ecosystem
services, and potential differences across continents and time frames. Table 4
reports income elasticities of WTP across different sub-types of ecosystem
services: regulating and cultural services as well as key sub-categories.
Overall, we find little variation in income elasticities, noting that
oftentimes projects valued in CV studies encompass contributions to multiple
services. Only the estimate of the income elasticity for recreation and
ecotourism is slightly lower—the category closest to being rivalrous. We also
split the sample into forest and non-forest ecosystem services as this serves
as a key input to our application on natural capital accounting in the CWON
framework in Section 5. We find that the income elasticity of forest ecosystem
services is slightly higher than the aggregate estimate. We present the
univariate and choice set of controls estimates alongside key subgroups to be
discussed in Figure 1.

Table 4: Heterogeneity of income elasticities of WTP across ecosystem service sub-types | ln(INCOME) | S.E. | N | Adj. R2
---|---|---|---|---
Climate regulation | 0.78** | 0.33 | 160 | 0.93
Air quality regulation | 0.78*** | 0.14 | 248 | 0.92
Water regulation | 0.84*** | 0.14 | 278 | 0.89
Erosion regulation | 0.84*** | 0.12 | 193 | 0.86
Regulating Services | 0.78*** | 0.15 | 503 | 0.93
Spiritual and religious values | 0.84*** | 0.12 | 119 | 0.63
Aesthetic values | 0.72*** | 0.11 | 386 | 0.89
Recreation and ecotourism | 0.65** | 0.26 | 307 | 0.84
Biodiversity preservation | 0.81*** | 0.11 | 316 | 0.89
Cultural Services | 0.73*** | 0.14 | 464 | 0.86
Forest ecosystem services | 0.81*** | 0.12 | 233 | 0.86
Non-forest ecosystem services | 0.77*** | 0.16 | 516 | 0.89
Figure 1: Point estimates of the elasticity of WTP from select models.

We next divide our sample by the continent in which the hypothetical
environmental project to be undertaken was located, and report the results in
Table 5. We note that the estimates are mostly concentrated in Asia, followed
by Europe, and relatively few estimates from the rest of the world. In terms
of income elasticities, we find lower estimates for North America—as well as
less consistency—versus the rest of the world.

Table 5: Heterogeneity of income elasticities of WTP across continents  | ln(INCOME) | S.E. | N | Adj. R2
---|---|---|---|---
North America | 0.57* | 0.30 | 86 | 0.95
South America | 0.23 | 0.30 | 34 | 0.96
Africa | 0.73*** | 0.20 | 33 | 0.97
Europe | 0.74*** | 0.25 | 244 | 0.80
Asia | 0.73*** | 0.13 | 345 | 0.92

We note that the broadest comparable meta-analysis on the income elasticity of
WTP (for biodiversity conservation only) was conducted by Jacobsen and Hanley
(2009). Their main result was an income elasticity of WTP estimate of 0.38,
but published more than a decade ago. It is therefore interesting to
investigate how our estimate of the income elasticity of WTP relates in a
comparable time frame, as well as in comparison to the most recent decade. In
Table 5 we break down the sample by sampling year. We conduct this analysis
based on our univariate estimation strategy such that year and other
covariates potentially correlated with the two periods are not included.
First, we consider estimates from publications based on samples collected up
to and including in year 2010, and find a smaller income elasticity of 0.49.
In contrast, the income elasticity based on articles data collected from 2011
onwards is considerably higher, at 0.69. If publication year is instead used,
the spread in income elasticities is even larger at 0.17 versus 0.79 for pre-
and post-2010 groups, respectively. This is a noteworthy increase in the
income elasticity of WTP in recent years. See Table 6.

Table 6: Heterogeneity of income elasticities of WTP across decades (publication year) | ln(INCOME) | S.E. | N | Adj. R2
---|---|---|---|---
pre-2010 | 0.49** | 0.20 | 377 | 0.82
2011-2021 | 0.69*** | 0.12 | 372 | 0.91

###  4.2 Growth rates

Table 7 reports estimates on the growth rates of ecosystem service categories
and their standard errors. We present these alongside the growth rate of GDP
per capita. Each growth metric is estimated based on data for the years 1993
to 2016. We find substantial heterogeneity in growth rates. The living planet
index and climate regulation metrics show the largest rates of de-growth,
while the change in forest area and air quality metrics show the lowest rates
of change.333Results are qualitatively similar when constraining the analysis
to the most recent trend data, except for air quality regulation which shows a
positive development in the current trend data (2010 to 2016), improving by
1.78% per year. In contrast, the decline rate for climate regulation is more
strongly negative. Overall, we find a somewhat smaller rate of de-growth of
-0.73 percent for the time period 2010 to 2016. Our estimate of aggregate
ecosystem service change is -1.01 percent (CI: -1.34 to -0.68), while GDP per
capita has increased by 1.82 percent (CI: 1.78 to 1.86) over the same period.
This amounts to a sizable shift in the relative scarcity of ecosystem services
vis-a-vis human-made goods. Ecosystem services have become relatively scarcer
by 2.83 percent per year (best to worst case scenarios of 2.46 to 3.20
percent).

Table 7: Good-Specific Growth Rates Indicator | Growth rate (S.E.)
---|---
Forest area | -0.11% (0.00%)
Living planet index | -2.84% (0.06%)
Red list index | -0.42% (0.01%)
Air quality (PM2.5) | -0.16% (0.17%)
Climate regulation | -1.50% (0.14%)
Aggregate Ecosystem Services | -1.01% (0.17%)
GDP per capita | 1.82% (0.02%)

###  4.3 Relative price changes of ecosystem services

We can now combine the two critical pieces of information – income elasticity
and growth rate estimates – to compute relative price changes (RPC) of
ecosystem services. Table 8 reports our estimates of relative price changes
both in the aggregate and for different ecosystem service categories. Our
central estimate for the relative price change of aggregate ecosystem services
is 2.21 percent (CI: 1.83 to 2.60) That is, the value of ecosystem services is
increasing by around 2.2 percent per year relative to human-made goods. This
is 2.4 times (and potentially over 4.6 times) the estimate of 0.91 $\pm$ 0.35
percent in Baumgärtner et al. (2015). The RPC estimate for regulating services
is only slightly higher than that for cultural ecosystem services, which is
qualitative similar to what Heckenhahn and Drupp (2022) find for a German case
study. While the income elasticity for forest ecosystem services is higher
than for ecosystem services on aggregate, the rate of decline of forest area
is considerably smaller; in combination, the relative price change of forest
ecosystem services (1.57 percent) is smaller than that of aggregate ecosystem
services (2.21 percent).

Table 8: Relative Price Changes (RPC) of Ecosystem Services Sample |  $\xi=1/\sigma$ (S.E.) |  $g_{C}-g_{E}$ (S.E.) |  $RPC$ (C.I.)
---|---|---|---
Regulating Services | 0.78 (0.15) | 2.83% (0.17%) | 2.21%
|  |  | (1.64% to 3.00%)
Cultural Services | 0.73 (0.14) | 2.95% (0.09%) | 2.15%
|  |  | (1.89% to 2.42%)
Aggregate E.S. | 0.78 (0.11) | 2.83% (0.17%) | 2.21%
|  |  | (1.83% to 2.60%)
Forest E.S. | 0.81 (0.12) | 1.94% (0.07%) | 1.57%
|  |  | (1.40% to 1.74%)

##  5 Application to Environmental-Economic Accounting

Relative price adjustments of ecosystem services are relevant for both
environmental-economic appraisal and accounting. Here, we explore implications
for environmental-economic accounting, considering the Changing Wealth of
Nations (CWON) 2021 report by the World Bank (2021) as a prominent case study.

CWON, like most measures of comprehensive wealth, only features natural
capital to a limited degree, with the bulk of natural capital components
relating to fossil energy resources and other provisioning services that are
traded on markets. CWON, however, also considers non-timber forest benefits as
part of its natural capital accounting. Non-timber forest benefits are
currently estimated to be around 12 percent of the total value of natural
capital World Bank (2021). Non-timber ecosystem service values in the year
2018, in WTP per hectare, are based on a meta-regression analysis based on 270
estimates from non-market valuation studies of non-timber forest benefits by
(Siikamäki et al., 2021). Per-hectare values are assumed to be constant over
time and only adjusted for inflation by using country-specific GDP deflators
(World Bank, 2021). The capitalized value of non-timber ecosystem services is
calculated as the present value of annual services, discounted over a 100 year
time horizon at a constant discount rate of 4 percent. This implies that no
adjustment for relative price changes is factored in despite forest de-growth,
particularly in comparison to GDP per capita. Implicitly, this carries the
assumption that WTP does not increase with income and—in the setting of our
model—that ecosystem services are considered perfect substitutes to human-made
goods.444Siikamäki et al. (2021) report positive and significant GDP
elasticities of WTP for recreation and habitat/species conservation, for
instance, but these are not considered in the CWON natural capital valuation.

We perform relative price change adjustments to the yearly WTP estimates for
non-timber forest ecosystem services based on our estimates and compare the
adjusted natural capital value to the current CWON approach. We show the
results in Figure 2, which depicts the estimated increase in CWON’s non-timber
forest natural capital value (in %), relative the CWON’s current estimate, as
a function of the degree of complementarity between forest ecosystem services
and human-made goods, measured by the income elasticity of WTP for forest
ecosystem services. For instance, Cobb-Douglas substitutability, as the knife-
edge case between substitutability and complementarity ($\sigma=\xi=1$), would
imply uplifting the public natural capital value of non-timber forest
ecosystem services by 72 percent. In comparison, a prominent assumption in the
integrated assessment modelling literature by Sterner and Persson (2008) of an
elasticity of substitution of 0.5, and thus a degree of complementarity of 2,
would translate into uplifting the public natural capital value by 270
percent.

Figure 2: Increase in public natural capital value along the degree of
complementarity.

For our central estimate of relative price changes of forest ecosystem
services, we find that the value of non-timber forest natural capital should
be uplifted by 52 percent, with a 95 percentile confidence interval around the
central estimate of the income elasticity resulting in a range of uplift-
factors of 32 to 78 percent (see Figure 2). For comparison, using the relative
price change of aggregate ecosystem services, which builds on a slightly lower
income elasticity but a much larger difference in growth rates, yields a
central uplift-factor for public natural capital of 88 percent.

Considering the limited degree of substitutability and the shifts in relative
scarcity by performing relative price adjustment of the annual WTP values in
computing the natural capital value of non-timber forest services makes a
material difference to natural capital accounting in CWON. The 52 percent
increase in non-timber forest value would lead to an increase of the overall
natural capital value in CWON of around 6 percent (CI: 3.8 to 8.8 percent). In
such a revised natural capital value, the adjusted non-timber forest value
would have an elevated contribution of around 17 percent (CI: 15 to 19
percent) instead of the current 12 percent.

##  6 Discussion

We discuss our empirical approaches and assumptions in turn, focusing on the
estimation of the income elasticity of WTP, as a proxy for the degree of
limited substitutability, and the aggregation of ecosystem services and the
computation of growth rates.

We identify the degree of complementarity via the income elasticity of WTP for
ecosystem services based on a meta-analysis of the peer-reviewed literature.
For this, we consider 749 unique (mean) income-WTP pairs across studies and
geographical contexts as well as across a 20 year time frame. A number of
remarks are in order.

First, our analysis is subject to concerns on the underlying data quality of
contingent valuation studies, including hypothetical bias etc., which has been
discussed at length in the literature (e.g., Kling et al., 2012). Schläpfer
(2008), for instance, argues that (too) small income effects in contingent
valuation studies may be an artefact of anchoring biases, but we are not aware
of a clear empirical test of this hypothesis. If this were the case, we might
capture too small income elasticities and thus undererstimate the degree of
complementarity. This implies that our estimates of the appropriate upward-
adjustment of natural capital values may represent a conservative estimate.

Second, besides contingent valuation specific concerns, our approach to
identifying the (aggregate) income elasticity of WTP—while building on the
state of the art in the literature—is very coarse, and rests on a very
heterogeneous, imbalanced panel. Broadly speaking, our new sample contains
studies that reflect both methodological refinements that have been introduced
over time that have arguably deflated WTP estimates Barrio and Loureiro
(2010), and an increasing share of studies from Asia and lower-income
countries over time. Ideally, we’d like to identify the income elasticity of
WTP based on a sample that is not subject to methodological revisions or major
changes in its geographical composition. While a few test-retest
investigations exist that draw repeatedly from the same sample (see Skourtos
et al., 2010, for an overview), these typically concern shorter time frames
and have not been designed to investigate income effects. Evidence to date
suggests that mean WTP estimates are relatively constant over time frames of
up to 5 years, but that this is not the case for longer time frames (Skourtos
et al., 2010).

Third, our approach of relying on a direct relationship between the income
elasticity of WTP and the elasticity of substitution holds under a very common
but still very specific assumption on preferences, specifically that
preferences are represented by a constant-elasticity-of-substitution (CES)
utility function (e.g., Ebert, 2003; Baumgärtner et al., 2017). We are not
aware of systematic studies trying to test the relative goodness-of-fit of CES
versus other utility specifications, but note that extensions exist in the
applied theoretical literature. One interesting case is an extension of
preferences that consider critical thresholds in the form of subsistence needs
(Baumgärtner et al., 2017; Drupp, 2018; Heal, 2009). If there exists some
critical level of ecosystem services, $\overline{E}>0$, then the degree of
substitutability becomes endogenous to the level of the ecosystem service over
and above the critical level, and the equation for the relative price change
of ecosystem services is adjusted to (cf. Drupp, 2018):555WTP estimates are
typically assumed to be a function of the ecosystem service level themselves
(Baumgärtner et al., 2017). Empirical evidence, however, is mixed—Barrio and
Loureiro (2010) and others find, for instance, that WTPs decrease with forest
cover, while Taye et al. (2021) find that WTPs increase with forest cover—as
it’s often challenging to isolate the pure effect of the level of the
ecosystem service.

$\quad\quad\quad
RPC_{t}\,\,=\,\,\xi\,\left[g_{C_{t}}-g_{E_{t}}\,\,\frac{E_{t}}{E_{t}-\overline{E}}\right].$
(10)

Such an extension implies slightly higher relative price changes that increase
substantially as one gets close to the critical basic need threshold (Drupp,
2018). It would lead to an upward revision of the natural capital values
adjustment discussed in Section 5.

Finally, we assume that preferences elicited primarily on small scale projects
aimed at improving ecosystem service conditions scale up to the global level.
However, services may be perceived as complements (substitutes) at the local
level, but as substitutes (complements) at a global scale. This issue may be
more pronounced when the focus is relatively more on local public goods as
compared to global public goods. We cannot directly test for this, but a
comparison of the income elasticity of WTP for recreational services versus
other services may serve as a proxy for this idea. Indeed, we find that the
income elasticity for recreational services is smaller than the estimate for
the other ecosystem services, but also that there is more variation around the
income elasticity of WTP for recreational services.

We have updated and extended the “Herculean task” (Baumgärtner et al., 2015,
p. 278) of assembling a proxy for the aggregate growth rates of ecosystem
services. There exists no accepted standard for how to aggregate various
measures of environmental quality, and also the data sources we draw on have
to be considered imperfect proxies themselves. We have followed Baumgärtner et
al. (2015) in using the unweighted arithmetic mean of the growth rates for the
different types of ecosystem services. This assumes that the elasticity of
substitution between different ecosystem services is equal to one (Cobb-
Douglas), which implies that WTPs would be the same for all types of ecosystem
services if their quantities were similar, an assumption we cannot properly
test. We note that there are other conceivable means of aggregation, using
different weightings to different degrees of substitutability. We leave a
systematic exploration of this issue to future work; the same holds for
exploring the role of uncertainty around projecting past growth estimates into
the future (Gollier, 2010) as well as the potential convergence of ecosystem
service and human-made goods growth rates, as the scarcity and limited
substituability of ecosystem services as intermediate inputs to production may
manifest itself as a drag on growth (Zhu et al., 2019).

##  7 Conclusion

We present the largest global database to estimate the degree of
complementarity of ecosystem services vis-a-vis human-made goods, via the
income elasticities of WTP for ecosystem services, in order to compute
relative price changes of ecosystem services. We find relative price changes
of ecosystem services of around 2.2 percent per year on aggregate. Relative
price changes are smaller (1.57 percent) for forest ecosystem services as
these show a slower rate of de-growth as compared to other ecosystem service
components. These estimates can be employed to adjust WTP estimates for
project appraisal or environmental-economic accounting. In an application on
natural capital valuation, taking the Changing Wealth of Nations (CWON) 2021
report by the World Bank (2021) as a case study, we show that adjusting
natural capital estimates for non-timber ecosystem services for relative price
changes results in uplifting the present value over a 100 year time period by
around 50 percent (CI: 32 to 78 percent), materially elevating the role of
public natural capital. This echoes work on the importance of limited
substitutability in climate policy appraisal (Bastien-Olvera and Moore, 2021;
Drupp and Hänsel, 2021; Sterner and Persson, 2008).

The adjustment techniques we present are generally applicable for
environmental-economic appraisal and accounting, while the specific numerical
inputs, such as on growth rates, need to be adjusted on a case-by-case basis.
Our results suggest that the case for making relative price adjustments is
reasonably robust and that more countries and institutions than present (Groom
et al., 2022) may consider making such adjustments to correct the current mis-
valuation of non-market goods in appraisal and of public natural capital
values in (comprehensive) wealth accounting.

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##  Appendix A Selection of relevant valuation studies

###  A.1 Search string

Our focus is on values for regulating ecosystem services and cultural
ecosystem services (not provisioning services) that have been elicited using
the contingent valuation method. The search string has three components (1)
focus on ecosystem services, (2) focus on WTP estimates, (3) focus on the
contingent valuation method.

( TITLE-ABS-KEY ( environment* OR natur* OR ecosystem OR biodiversity OR
biologic* OR ecologic* OR habitat* OR forest* OR species OR protected OR
conserv* OR endangered OR ”national park*” OR landscape* OR terrestrial OR
pollination OR tree* OR tropic* OR vegetation OR peatland* OR grassland* OR
dryland* OR pastoral OR soil OR animal* OR bird* OR wild* OR air OR water OR
aquatic OR marine OR coast* OR water* OR fish* OR wetland* OR mangrove* OR
reef* OR marsh* OR floodplain* OR river* OR climate OR storm* OR erosion OR
pest* OR hazard* OR recreat* OR touris* OR “urban green” OR sacred OR spirit*
OR sanctuary OR “natural heritage” OR aesthetic*)

AND TITLE-ABS-KEY ( wtp OR willingness-to-pay OR ”willingness to pay*” OR
”willing to pay*” OR ”shadow price*” OR ”shadow value*” OR ”implicit price*”
OR ”implicit value*”)

AND TITLE-ABS-KEY ( ”contingent valuation*” OR cvm OR ”contingent choice*”) )

AND ( LIMIT-TO ( SRCTYPE , ”j” ) ) AND ( LIMIT-TO ( DOCTYPE , ”ar” ) ) AND (
LIMIT-TO ( PUBYEAR , 2021 ) OR LIMIT-TO ( PUBYEAR , 2020 ) OR LIMIT-TO (
PUBYEAR , 2019 ) OR LIMIT-TO ( PUBYEAR , 2018 ) OR LIMIT-TO ( PUBYEAR , 2017 )
OR LIMIT-TO ( PUBYEAR , 2016 ) OR LIMIT-TO ( PUBYEAR , 2015 ) OR LIMIT-TO (
PUBYEAR , 2014 ) OR LIMIT-TO ( PUBYEAR , 2013 ) OR LIMIT-TO ( PUBYEAR , 2012 )
OR LIMIT-TO ( PUBYEAR , 2011 ) OR LIMIT-TO ( PUBYEAR , 2010 ) OR LIMIT-TO (
PUBYEAR , 2009 ) OR LIMIT-TO ( PUBYEAR , 2008 ) OR LIMIT-TO ( PUBYEAR , 2007 )
OR LIMIT-TO ( PUBYEAR , 2006 ) OR LIMIT-TO ( PUBYEAR , 2005 ) OR LIMIT-TO (
PUBYEAR , 2004 ) OR LIMIT-TO ( PUBYEAR , 2003 ) OR LIMIT-TO ( PUBYEAR , 2002 )
OR LIMIT-TO ( PUBYEAR , 2001 ) OR LIMIT-TO ( PUBYEAR , 2000 ) ) AND ( LIMIT-TO
( LANGUAGE , ”English” ) )

###  A.2 Exclusion criteria

  1. 1.

Citations: We excluded all studies that had not been cited (in SCOPUS).

  2. 2.

Abstract screening: We excluded non-topical publications based on abstract-
screening that do not report new primary WTP estimates. Specifically, we
excluded: Theory, reviews, comments, non-primary valuation (such as benefit
transfer), as well as WTPs for non-environmental goods, WTPs for provisioning
services, WTPs derived from valuation approaches other than CV

  3. 3.

PDFs obtainable: We excluded studies where we could not access the PDFs.

  4. 4.

Paper screening: We excluded non-topical publications based on abstract-
screening that do not report new primary WTP estimates. Specifically, we
excluded: Theory, reviews, comments, non-primary valuation (such as benefit
transfer), as well as WTPs for non-environmental goods, WTPs for provisioning
services, WTPs derived from valuation approaches other than CV PLUS XYZ

  5. 5.

WTP data screening: We excluded papers that reported a median WTP instead of
mean WTP.

###  A.3 Inflation and currency conversion

All monetary values were converted to 2020 US Dollar by first inflating the
respective national consumer price index and then applying purchasing-power-
parity (PPP) conversion. The relevant year for the inflation of the values was
the year of study data collection. When the authors did not provide the study
year, we estimate the average lag between study and publication years based on
the studies where both pieces of information is available. The difference is
approximately 4.0 years on average. We use this to estimate the study year
when missing.

###  A.4 Alternative specification results

This section presents a specification graph that suggests the robustness of
our results to the inclusion or exclusion of covariates. We also present
results based on alternative statistical models to suggest the robust of our
results to model selection.

Figure 3: Income elasticity of WTP estimates based on alternative model
specifications.

Figure 4: Income elasticity of WTP estimates based on alternative statistical
models.

Figure 5: Income elasticity of WTP estimates by weight selection.


deployment. We identify and analyze the seven patch granularity levels along
with two general patching strategies (state transformation and co-exists &
decay) and three responsible entities (vendor, consumer and third parties). We
further define a high-level workflow (Figure 5) of applying and activating
patches supporting the four identified key implementation capabilities that
are (i) memory management,(ii) resource transformation, (iii) safe execution
state determination and (iv) execution path dispatching. Finally, the review
highlights the challenges and suggests potential future prospects. We envision
the area mainly needs a systematic approach to develop practical and
convenient patching solutions applicable in a wide variety of infrastructures,
programming languages and execution environments. The area further requires
defining quantifiable metrics to identify the impact of a patch by semantics
and dependency tracking solutions. We observe many open opportunities and
concerns that need to be considered by vendors, end-users and third parties.

Future research lines include obtaining patching-related real-world data
through a practical field study. Analyzing this data would enable
understanding the statistics of existing patching challenges in various
critical domains. Notable research questions should focus on the patching
procedures commonly applied in practice, patch granularity distribution, the
complexity of the patches applied, patch-induced system downtime and service
continuity, as well as potential incompatibility issues. To conclude, an in-
depth understanding of the issues and concerns of practitioner and business
requirements is crucial to bridge the gap between runtime patching research
and practical implementation/deployment in production.

## Acknowledgment

The work has been partially supported by the Cyber Security Research Centre
Limited whose activities are partially funded by the Australian Government’s
Cooperative Research Centres Programme.

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