Choices and the value of natural capital

Abstract

Sustainability requires maintaining opportunities for future generations, so they can meet their needs. Opportunities are passed to future generations through a set of capital assets. Nature provides an important class of these assets, but markets seldom reveal the marginal value of natural capital. Rather, the marginal social worth or asset price must be imputed based on intertemporal exchange. In the context of assessing whether intertemporal allocation rules lead to sustainable development, appropriate asset prices must be based on the actual allocations and trade-offs society makes. Therefore, measuring economic programmes that enable the measurement of asset prices is an important empirical task. We review the theory of measuring natural capital asset prices and discuss the key elements of measuring economic programmes that enable the measurement of natural capital asset prices. We place the measurement of economic programmes and natural capital asset prices in the context of wealth-based sustainability metrics.

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Choices and the value of natural capital
Eli P.Fenichel* and YukikoHashida**
Abstract: Sustainability requires maintaining opportunities for future generations, so they can meet
their needs. Opportunities are passed to future generations through a set of capital assets. Nature
provides an important class of these assets, but markets seldom reveal the marginal value of nat-
ural capital. Rather, the marginal social worth or asset price must be imputed based on intertempo-
ral exchange. In the context of assessing whether intertemporal allocation rules lead to sustainable
development, appropriate asset prices must be based on the actual allocations and trade-offs society
makes. Therefore, measuring economic programmes that enable the measurement of asset prices is an
important empirical task. We review the theory of measuring natural capital asset prices and discuss
the key elements of measuring economic programmes that enable the measurement of natural capital
asset prices. We place the measurement of economic programmes and natural capital asset prices in the
context of wealth-based sustainability metrics.
Keywords: sustainability, wealth, natural capital, ecosystem services, green accounting
JEL classication: E01, Q01, Q56
I. Introduction
‘Sustainable’ cannot be a mere synonym for good; the sustainability concept must be
achievable and measurable. Asking whether society is sustainable without some clear
metric is not particularly useful (Solow, 1993). The World Commission on Environment
and Development (1987) added some precision by dening sustainable development as
meeting the needs of present generations without compromising the ability of future
generations to meet their needs. Said differently, sustainable development requires that
society maintains an opportunity set. Therefore, whether society is on a sustainable
path is a question of intertemporal allocation of resources: how much is consumed
and how much is saved, invested, or conserved? The majority of economic research on
intertemporal allocation has focused on optimal and efcient allocation. Sustainability,
however, only requires preserving an opportunity set, which does not ensure nor require
optimal or efcient allocation. Indeed, Dasgupta and Heal (1974) established that
* Yale School of Forestry and Environmental Studies; e-mail: eli.fenichel@yale.edu
** Yale School of Forestry and Environmental Studies; e-mail: yukiko.hashida@yale.edu
This research was supported by the Knobloch Family Foundations and beneted from discussions with
Joshua Abbott, Dieter Helm, Alexander Teytelboym, and the notes of an anonymous reviewer.
Oxford Review of Economic Policy, Volume 35, Number 1, 2019, pp. 120–137
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optimal intertemporal allocation of essential resource stocks might not lead to sus-
tainable consumption.1 Therefore, it is helpful to be able to discuss sustainability in a
world where intertemporal allocation is not optimal nor even efcient (Dasgupta, 2007;
Dasgupta and Maler, 2000). To address this challenge, Dasgupta and Maler (2000)
introduced the concept of a forecastable economic programme where economies or
governments may not allocate resources optimally or efciently.2 They call the map-
ping from a set of current capital assets levels to a future set of ows and stocks a
resource allocation mechanism.3 The policy question is whether the observed or likely
economic programme maintains opportunities for future generations, which is ultim-
ately an empirical question.
A quantitative measure to evaluate whether an economic programme sustains an
opportunity set is the change in the value of a portfolio of capital stocks conditional on
following a specic economic programme (Maler, 1991; Hamilton and Clemens, 1999;
Dasgupta and Maler, 2000; Dasgupta, 2007; Barbier, 2011; Helm, 2015). This port-
folio, comprising 123,,,
…
S stocks, indexed by
i
, including traditional reproducible
(built or manmade), natural, and human capital.4 The measure of the state of the broad
portfolio of capital stocks or assets is Inclusive or Comprehensive Wealth or Genuine
Savings (Arrow etal., 2004; World Bank, 2011; Hamilton and Hartwick, 2014; UNU-
IHDP and UNEP, 2014; Hanley et al., 2015). Dasgupta (2007) argues that if society
follows a sustainable economic programme then (inclusive, comprehensive, or genuine)
wealth, =
∑
i
ii
ps , measured using ‘appropriate’ and constant accounting prices, pi,
applied to quantities of stocks, si, is non-declining, i.e.
∆∆

=≥
∑
ps
ii 0 and approx-
imates changes in welfare.5 This measurement concept is increasingly embraced out-
side of economics (Matson et al., 2016). Though Irving Fisher (1906) and Theodore
Roosevelt (1910) expressed this idea over 100years ago. In 1910, Roosevelt comes close
to articulating the current denition of wealth-based sustainability, at least with respect
to natural resources:
The nation behaves well if it treats the natural resources as assets which it
must turn over to the next generation increased, and not impaired, in value;
and behaves badly if it leaves the land poorer to those who come after it. That
is all Imean by the phrase, Conservation of natural resources. Use them; but
use them so that as far as possible our children will be richer, and not poorer,
because we have lived.
1 Dasgupta and Heal (1974) focus on technological innovation. For recent treatments of this issue see
Groth (2007).
2 An efcient economic programme requires that intertemporal and Pareto improvement opportunities
are exhausted, so there is a unique efcient economic programme, conditional on initial conditions. It is
unlikely that there is a unique sustainable economic programme.
3 The distinction between economic programme and resource allocation mechanism is lost in the subse-
quent literature, and we use the terms interchangeably.
4 Fleurbaey and Blanchet (2013) provide a review of the development of sustainability metrics. Helm
(2015) provides a rich description of limits on substitution and aggregation rules discussed in the context of
sustainability.
5 Importantly, total wealth has no welfare theoretic interpretation.
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Whether inclusive wealth is rising or falling is an empirical question. Physical scientists
are increasingly adept at measuring changes in stocks of natural resources. Economists
struggle to determine the appropriate prices,
p,
to use in change of wealth assessments
when the prices are not observable in markets. Smulders (2012) writes ‘The Achilles’
heel of the [wealth based] method [for measuring sustainability] is the determination
of the shadow prices’, where shadow prices refer to the appropriate natural capital
asset prices. Even if the price of stock i were known at time
t
and
t+∆
, the
p
in
∆
must be constant and formed as a convex combination of the two measures of price
(Fenichel etal., 2016b; Fenichel etal., 2018). The challenge is determining ‘appropriate’
price functions to measure changes in wealth, particularly for assets that are subject to
thin, distorted, or missing markets—as is the case with many important forms of nat-
ural capital.6
Observed prices reveal the exchange ratios that society is accepting, even in ‘distorted’
economies. These prices reect political and non-market trade-offs, power dynamics,
institutional arrangements, and expected technological developments, in addition to
preference orderings. Prices capture the extent to which society behaves as if goods or
assets have substitutes or complements. Therefore, measured prices and shadow prices
are the best estimates of revealed opportunity costs and are the appropriate prices to
use in
∆
. They inform the question of whether an observed economic programme can
be considered sustainable. Appropriate prices for sustainability accounting are revealed
shadow prices based on prevailing institutions and behaviours or in the case of pro-
spective analyses, feasible and realistic alternative institutions (Fenichel etal., 2018).7
There are three reasons why prices for sustainability assessment must be based on the
observed economic programme rather than a hypothetical optimal programme. First,
the optimal economic programme is one of many possible economic programmes, but
the observed programme is likely to be full of market failures. Second, analysis of opti-
mal allocation is important to make policy recommendations, but such counterfactual
economic programmes do not reect the actual trade-offs that society is currently mak-
ing. There is an analogue in the non-market demand literature—replacement costs are
only valid measures of the value for the lost capital stocks if people are actually willing
to make investments to replace the damaged or lost stocks (Freeman, 2003). If society
will never shift to an ‘optimal’ programme, then the marginal user cost associated with
the optimal programme is hardly the correct measure of opportunity cost for use in
sustainability assessment. Third, the economic programme describes how people are
using resources today versus saving for tomorrow, and therefore is central to under-
standing sustainability. In cases where the consensus is that current consumption is
excessive and asset management is poor, then the shadow price of a stock will be lower
than expected, all else equal. Improved management of an asset is expected to raise
the asset’s value, all else equal. Such changes would be important for the users of sus-
tainability assessments. Assuming that shadow prices were associated with an optimal
programme would obscure thesegains.
6 We focus on natural capital, but many other forms of capital may also suffer from distorted or missing
markets, and our exposition may be relevant to those capital stocks as well.
7 Realized shadow prices are also called accounting prices (Dasgupta and Maler, 2000) and exchange
prices (Obst and Vardon, 2014).
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Society’s choice of economic programme is the only vehicle available to it to inuence
whether or not the future is sustainable, because the economic programme determines
how resources are allocated. Generating a forecastable economic programme requires
measurement, and a forecastable economic programme is imperative for measuring the
appropriate prices to use in the inclusive wealth index, especially for natural capital.
In this article we contribute to the literature on sustainability assessment and natural
capital valuation by focusing on the necessary steps to describe and measure prevail-
ing economic programmes, which complements prior work on deriving approximat-
ing approaches for natural capital asset prices conditional on measured economic
programmes.
II. Asset shadow prices and the measurement of
sustainability
It is helpful to review the connection between welfare, wealth, and capital asset prices in
order to understand the importance of the economic programme or resource allocation
mechanism, which is the feedback rule, xs
()
, that maps society’s current set of assets,
s
, into the uses of those assets
x
. Maler etal. (2008), Hamilton and Ruta (2009), and
Lange (2004) argue biophysical dynamics inuence the asset value of natural capital.
Fenichel and Abbott (2014b) extend these ideas and incorporate the importance of a
dynamic economic programme to develop a theory of measuring shadow prices that
generalizes Jorgenson’s (1963) approach to valuing invested capital assets.8 Fenichel
etal. (2016a), Yun etal. (2017b), Fenichel etal. (2018), and Abbott etal. (2018) extend
Fenichel and Abbott’s approach to address general equilibrium effects among real
assets and correlated stochastic stock dynamics. The principal insight from Fenichel
and Abbott (2014a), building off Dasgupta and Maler (2000), is that the Hamilton–
Jacobi–Bellman relationship does not depend on optimization, so long as the analyst
possesses an empirical forecastable economic programme. This opens a path to measur-
ing theoretically consistent revealed natural capital asset values or shadow prices condi-
tional on actual decisions rather than hypothetically optimal decisions. If capital stock
dynamics are deterministic and autonomous in time, then intertemporal welfare,
V
, as
a function of holding a set of stocks,
s
, at a point in time
t
(see Appendix for formal
description), is the present value of real net income or dividends from those stocks con-
ditional on how they are used (Fisher, 1906).9
Wealth-based sustainability theory focuses on changes in wealth and intertemporal
welfare. The change in intertemporal welfare over time is ∂
()
()
∂=Vt t
sp
s/¢, where
p
¢
is the transpose of the vector of constant prices. Part of the challenge emerges in
a theory of measurement because measurement is always over time periods where the
8 Maler etal. (2008) and Hamilton and Ruta (2009) note the importance of institutional arrangements.
9 We use Fisher’s rather than Hicks’s (1939) concept of income because Fisher’s income concept allows a
decomposition of welfare changes and the connection between income and capital, whereas Hicks’s income
concept combines current period income ows with future potential ows so that capital disappears as a con-
cept. Weitzman (2016) provides further discussion about the relationship between Hicksian and Fisherian
income.
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change in time is non-trivial. Once the time interval is not trivially small, then there can
be meaningful changes in the stock of capital and the price. In the capital accounts of
price-taking rms, the rm’s own level of capital would not inuence the price for the
asset, and constant prices are a reasonable assumption. However, changes in the value
of society’s aggregate stock of a capital asset can affect the price. Aweighted aver-
age of prices at time
t
and
tt+∆
exists to make the accounting notion of a change
in wealth and the economic concept of a change in intertemporal welfare identical
(Figure1). This interpretation is similar to Harberger’s (1971) argument that change in
net national product is a rst-order approximation of a welfare change.
Markets implicitly (or explicitly) forecast changes in assetallocation and scarcity.
If the dynamics of
s
can be forecast using ex ante knowledge of the economic pro-
gramme xs
()
for non-market assets, then the asset price is marginal net real income
or marginal net dividends plus own and cross-price capital gains terms, and a cross-
stock capital gains term all divided by the discount rate plus the marginal physical net
appreciation rate of the asset (see Appendix for a formal description). The cross-price
and cross-stock capital gains terms reect general equilibrium interactions between real
assets, and in the case of natural capital these can occur through ecological interactions
or interactions created by the economic programme (Fenichel etal., 2018).
Figure1: The connection between change in welfare, change in wealth, and shadow prices
Notes: Consider the change from stock s1 to stock s2. Panel Ashows the change in welfare, vertically hashed
area. The difference between the grey region and checked region in Panel B shows ps ps
11
22
−
, which is not
the change in wealth. Panel C shows the correct change in wealth using the arithmetic mean of p1 and p2
at the constant asset price as the vertically hashed region plus the checked region. If the checked region
equalled the horizontally hashed region, then change in wealth would equal change in welfare. Panel D illus-
trates that aweighted mean of p1 and p2 can be chosen to make the checked region equivalent to the hori-
zontally hashed region, aligning changes in wealth and changes in welfare.
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The intertemporal welfare function
V()
s and its nth order derivatives are not revealed
through data. Fenichel etal. (2018) and Yun etal. (2017a) describe how asset prices and
changes in intertemporal welfare can be approximated to arbitrary precision, assuming
the stock dynamics, conditional on the economic programme, are bounded. Yun et al.
(2017a) provide an R package, capital asset pricing for nature, capn (https://cran.r-project.
org/web/packages/capn/index.html), for conducting the functional approximation.
Once measured, the price and intertemporal welfare functions, pi
()
s and
V
s
()
,
provide two paths towards resolving the challenge of selecting the appropriate set of
prices to use to measure
∆
. First, it is possible to exploit the fundamental theorem
of calculus and integrate under the recovered pi functions (Fenichel et al., 2016b).
However, for a bounded system it is often possible to recover
Vt
s
()
()
, which is help-
ful when
s
is more than one stock. If the intent is to measure changes in wealth as a
proxy for changes in intertemporal welfare, then changes in wealth can reasonably be
redened as
∆∆
=+
()
()
−
()
()
Vt
Vtss
, and there is a convex combination of
pt
s
()
()
and pts+
()
()
∆ that can make this true (Figure1). These measures reect the trade-
offs society is currently making, when based on the forecastable economic programme,
but say nothing about what society should do. Rather, they provide a mirror that helps
society to confront trade-offs that are often obscured by complex institutional arrange-
ments. That is because realized natural capital asset prices do not directly drive the eco-
nomic programme, but are reected by the prevailing economic programme.
III. Measuring the economic programme
The economic programme, xs
()
, sits at the core of wealth-based sustainability theory
(Dasgupta, 2007; Hamilton and Hartwick, 2014). The economic programme encapsu-
lates the decisions and policy choices that people make with respect to using resources
today or saving them for the future—realized intertemporal exchange.
(i) Conceptualissues
The economic programme may be thought of as a model of behavioural ‘inputs’ into
the production of service ows. In some cases the economic programme may be con-
sidered similar to input factor demands. However, it is not clear that these ‘demands’
satisfy the duality properties of a demand function. The economic programme may
include decisions that do not lead directly to stock changes. Three cases, sheries,
groundwater use, and emissions of stock pollutants, illustrate this point. Units must be
dened for the stocks. The sheries case provides an example where the economic pro-
gramme could be a single composite input called ‘effort’ (Squires, 1987). In this case,
the economic programme is closely related to input demand that results in gross natural
capital depreciation. Asingle stock of groundwater provides a more complicated case
(Fenichel etal., 2016a). In the groundwater case the economic programme may include
a crop choice, eld size choice, and water withdrawal choice. Only water withdrawal is a
direct demand for the resource, but is not separable from the other choices. This means
that a transformation of the economic programme enters the stock dynamic equation
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and the economic programme is broader than factor input demand. The third case of
emission of a stock pollutant is more complicated still. In this case, an incidental bad is
produced to create a liability, along with the intended good. This model of the system
suggests that the economic programme related to the stock pollutant is not an input
demand. However, an alternative model of the system expands the set of ‘services’ to
include waste storage. In this expanded model, there would be an input demand for the
services of the pollutedasset.
Determining what is part of the economic programme and what is part of the set
of stocks is an important choice in analysing the sustainability of a given economic
programme. Implicit in the theory of natural capital asset pricing is the existence of
a behavioural equilibrium (Fenichel et al., 2018). A behavioural equilibrium implies
that people adjust choices within the economic programme quickly compared to the
dynamics of the stocks, and stock dynamics evolve slowly relative to the human deci-
sions captured by the economic programme. Substituting an equilibrating economic
programme provides the expected and average long-run dynamics. The assertion of a
behavioural equilibrium may require explicitly modelling stocks of capital aside from
natural capital. Two prominent types of capital stocks that might merit consideration
alongside natural capital are ‘social or institutional capital’ and reproducible, built, or
man-made capital (which may change as a function of human capital investment).10
There is substantial evidence that institutional change can lag environmental change
(Greif and Laitin, 2004). In such cases, it may be important to explicitly model insti-
tutional dynamics as a function of ‘institutional stocks’ or institutional state varia-
bles, sometimes called ‘social capital’. Yet, dening institution stocks may be fraught
with ill-dened units and measurement problems (Dasgupta, 2007). One could think
of political paradigms or administrative rule sets as determining institutional stocks,
but general models of institutional change remain aspirational and an area of import-
ant research. In reviewing the literature on social capital, Dasgupta (2007) argues that
institutions are the rules for allocating capital—they are the fabric of the economic pro-
gramme. Nevertheless, theory suggests that, like the economic programme, institutional
arrangements have a strong impact on asset values and prices. Libecap (1994) provides
examples where strengthening property rights enhanced productivity in the context
of ranching, farming, mining, and shing, and Besley (1995) establishes foundations
for linking property rights and investment incentives in agriculture. Melesse and Bulte
(2015) argue that land titling programmes have been instrumental to development. Yet,
a direct link between asset prices and strength of property rights is difcult to establish
because when property rights are weak there are seldom markets to observe asset prices.
Grainger and Costello (2014) use tradable permits in sheries, with varying levels of
security to conclude, ‘stronger property rights lead to greater quota asset values’. While
human relationships are an important part of institutional arrangements, Dasgupta
(2007) points out that some features of human networks can be thought of as human
capital.
Capital stock frictions and dynamics associated with reproducible capital may
require explicit modelling and are likely more tractable than modelling stocks of insti-
tutional or social capital. Clark et al. (1979) and Fenichel et al. (in press) provide
10 It may also be important to consider changes in human capital.
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theoretical models where the optimal economic programme with respect to natural
capital is a jointly determined economic decision along with investment in capital
stocks of machines and nancial capital, which are traded in imperfect capital markets.
When these additional stocks materially impact the economic programme, then the
ecological-economic system model must be rich enough to include these non-natural
capital stocks. We expect similar effects arise in non-optimizing systems. Fenichel etal.
(2016a) suggest that a connection between the economic programme of groundwater
use and investment in irrigation technology could impact the implied shadow price of
groundwater. Connections between natural and other forms of capital are critical for
sustainability assessment because substitution and complementarity relationships sit at
the core of wealth-based sustainability metrics (Quaas etal., 2013; Fenichel and Zhao,
2015; Drupp, 2018). To date, however, theoretical and empirical modelling in natural
resource economics has focused mostly on natural resource dynamics, holding allo-
cation of other capital stocks xed, with the exception of the macroeconomic growth
literature that incorporates non-renewable resources (reviewed by Groth (2007)).
Allowing other capital stocks to evolve dynamically, as inuenced by the economic
programme, may be important for improved forecasts of natural capital asset dynamics
and prices. This is particularly important because technological innovation is import-
ant in a world with a growing human population and nite stocks of important non-
renewable resources (Groth, 2007). When reproducible capital is traded in markets, it
may provide identifying conditions for the asset value of natural capital, because the
reproducible asset prices will constrain cross-derivatives of the intertemporal welfare
function,
V()
s.
Additional questions include the scope of feedbacks and shocks and the spatial
extent of the ecological-economic system. Yun etal. (2017b) allow for general equilib-
rium effects between modelled capital stocks. This observation, coupled with the inn-
ite horizon nature of the asset pricing approach, makes it somewhat strange to assume
away other long-run changes in the economy, e.g. other input prices.
A challenge is that price dynamics for other inputs or dynamics of other capital
stocks may be non-autonomous with respect to time from the standpoint of the nat-
ural resource system. For example, from the standpoint of most local natural resource
management decisions, climate change is exogenous. To the extent that climate change
degrades or enhances local natural capital and to the extent that economic programmes
anticipate these changes, the effects likely manifest as pure time effects. Another import-
ant source of non-autonomous dynamics is exogenous technological change or tech-
nology spill-overs. Allowing time to enter directly and creating a total factor production
measure is theoretically sound (Arrow et al., 2003), but a practical challenge remains
for recovering asset prices in such a system because time cannot be placed on a bounded
interval. Resolving this challenge is an open question.
In some cases the localized nature of the services provided by natural capital stocks
may ameliorate general equilibrium concerns, but determining the spatial extent at
which to measure the economic programme is challenging. Interactions between seem-
ingly distinct natural capital stocks connected by human behaviours may be an espe-
cially large challenge for natural capital stocks that support recreational services at
distinct recreational sites (Post et al., 2008). The broader landscape may impact the
value and the way people interact with natural resource stocks, as juxtaposition may
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drive complementarity and substitute relationships (Kopits et al., 2007; Abbott and
Klaiber, 2010).
Spatial aggregation raises questions as to the units of the stock and whether
locally sustainable economic programmes can aggregate to nationally sustainable
economic programmes. Implicitly, if all units of a natural capital stock are com-
bined into a single stock for measurement and valuations, then heterogeneities in
the stocks or local economic programmes are eliminated. Potentially heterogeneous
stocks or stocks subject to localized heterogeneous economic programmes appear
as if they are perfect substitutes, when they may not be. One reason for this is that
many forms of natural capital are difcult or impossible to arbitrage in space. So, it
is not possible to appeal to a law of one price for natural capital. Local variation in
stocks matters for asset prices, and local variation in the economic programme can
shift the pricecurve.
The economic programme itself may vary spatially and at sub-national scales for
idiosyncratic reasons that are not directly linked to the natural capital stock in ques-
tion. If the focus is on an iconic ecosystem or region, e.g. the Goulburn–Broken
Catchment in Australia, it is reasonable to focus on the economic programme within
that region (Pearson etal., 2013). Addicott (2017) shows that, even within the seem-
ingly homogeneous system of Kansas irrigated row crop agriculture, the economic pro-
gramme guiding resource use, e.g. groundwater withdrawal, may respond to resource
changes differently because of local institutional variation. He argues that aggregation
can induce a sort of omitted variables bias when local institutions drive the economic
programme. In federated systems that devolve control of resources, the economic pro-
gramme needs to be measured locally.
(ii) Empirical and dataissues
Measuring natural capital asset prices requires empirical measurement of the economic
programme. Measurement requires data and a model for organizing and interpreting
those data. Expanding data availability and modelling techniques are facilitating meas-
uring economic programmes as an input into natural capital asset prices. However,
challenges and necessary modelling decisions persist. With the pace of development,
data availability, and techniques, it may not be long before it will be possible to populate
local wealth accounts with many natural capital asset prices, enabling society to track
the change in a fair number of critical natural capital assets. However, this will not
be the case for all natural capital assets, leading to partial accounts. The assets that will
be the hardest to include in accounts are those that are hardest to dene in quantitative
terms. The lack of data is ceasing to be a reasonable excuse for not coordinating on the
measurement of, and accounting for, changes in natural capital asset values.
Data availability and computational approaches for handling data are developing
rapidly in environmental and ecological science (Willig and Walker, 2016) and econom-
ics (Einav and Levin, 2014). Unfortunately, the ecological and economic data are sel-
dom collected in tandem, leading to spatial and temporal scale mismatches. Afurther
challenge with measuring economic programmes is that for many important stocks of
natural capital, market transactions data are often weak complementary goods, which
presents well-known challenges for estimating demand (Phaneuf and Requate, 2017),
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including valuation and behaviour. Nevertheless, time-use data, scanner data, and
social media data are all providing new digital records of human decisions.
Increasing data availability only facilitates measuring the economic programme; the
challenge is to estimate an economic programme across the domain of stocks for which
asset prices are desired. The challenge is greater than recovering rst-order marginal
effects at the current level of stock, as is common in programme evaluation. The goal is
to predict behaviour under foreseeable and likely institutional arrangements. The task
of rst-order importance is dening the appropriate future scenarios, which are likely
best treated as hypotheticals, and identication of material parameters is a secondary
concern (Heckman, 2010). In many cases, the economic programme of today, as a state
varying feedback rule, may be the best predictor of the economic programme of tomor-
row. When the goal is to measure the economic programme under prevailing institu-
tions, then the material parameters to identify are the parameters that explain human
responses to changes in stock, which may or may not be an out-of-sample counterfactual.
In cases where relevant stock levels have been visited or nearly visited within the range
of the historic data, machine learning may be a viable alternative to traditional econo-
metric approaches (Friedman et al., 2001; Varian, 2014). The identication challenge
increases in importance when states far from observed conditions are expected or there is
an effort to forecast alternative economic programmes ex ante and assess natural capital
asset values under novel institutional arrangements. However, in these cases, structural
identifying assumptions sufciently capable of producing observable moments in the
data are likely preferred to relying on strong local identifying assumptions that provide
average (linear) treatment effects and are motivated solely through an appeal to replicat-
ing randomization, rather than predicting behaviour (Manski, 2007; Heckman, 2010).
This is particularly true because ecological-economics systems are notoriously nonlinear
(Barbier etal., 2008; Smith, 2008; Koch etal., 2009). An alternative to relying on struc-
tural assumptions might be greater reliance on stated choice surveys structured under
novel scenarios. Stated choice surveys can elicit likely behaviour under novel states of the
world, including novel institutional arrangements. Stated choice data collection methods
come with their own well-known challenges (Johnston etal., 2017).
IV. Connecting the economic programme to social
realincome
The actions encapsulated in the economic programme generate real income, so the eco-
nomic programme is the result of prevailing incentives, constraints, and expectations.
Aggregate net real income is a money denominated social welfare index that includes
monetized net benets acquired outside of market transactions (Fenichel etal., 2018).11
Fisher (1906) described real income as ‘enjoyable commodities and services’, includ-
ing ‘the supplementary elements which we found lacking under the head of money-
income.... for it [real income] recognizes that money is only an intermediary, and seeks
to discover the real elements for which that money-income stands’. Krutilla (1967)
11 See Weitzman (2016) for a discussion of economic income concepts.
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writes, ‘When the existence of a grand scenic wonder or a unique and fragile ecosystem
is involved, its preservation and continued availability are a signicant part of the real
income of many individuals.’ Theory provides no guidance about the shares of market
and non-market contributions to real income.
The challenge with measuring the real income component associated with service
ows from natural capital (what Fenichel et al. (2018) call ecosystem income) is that
the ecological contributions are unlikely to be additively separable (Boyd and Banzhaf,
2007). However, there is a marginal income or marginal dividend associated with changes
in quantity of the natural capital asset. The focus on the marginal impact on net real
income from a change in asset quantities overcomes the additive separability assump-
tions, but requires the production process embedded in the economic programme.
Capital stocks inuence the economic programme, which in turn affects real income
through three pathways: market production, household production, and direct services
(Fenichel et al., 2018). To date, research connecting the economic programmes and
natural capital dynamics to produce realized natural capital asset prices has focused
primarily on market production, where the real income contributions are ultimately
measured through market exchange (e.g. Fenichel and Abbott, 2014b; Fenichel etal.,
2016a; Bond, 2017; Yun etal., 2017b). However, this does not mean that all the services
provided by natural capital must enter directly into the market. Bond (2017) and Yun
etal. (2017b) capture intermediate, within-ecosystem, production contribution within
the natural capital asset prices, but the asset values are based on nal services.
Decisions captured in the economic programme also direct services ows from nat-
ural capital into real income through household production, production consumed dir-
ectly within the household, but that requires active inputs or actions (Bockstael and
McConnell, 2007). Household production income appears to be what concerned Fisher
(1906). Recreational and amenity services that are often weak complements to market
consumption are chief examples of household production in industrialized countries.
In developing countries, the set of household production service ows may be greater,
particularly in the case of subsistence agriculture, shing, or fuel wood collection.
Direct services seemingly leave no trace via the economic programme. The traditional
approach to valuation of direct services is through stated preference techniques. This
is because there is not a direct behaviour that can be observed or stated that yields the
real income, e.g. enhanced wellbeing from the knowledge of the existence of more of
an iconic species. This is the real income contribution that concerned Krutilla (1967).
The purpose of many attempts to measure direct services is benet–cost analysis with
respect to how society should conserve species or places (e.g. Loomis and White, 1996).
Our goal is different; it is to determine how society is currently valuing these stocks,
and how the valuation changes through time, given society’s observed behaviours. We
start by recognizing that changes in the ability of natural capital to provide such ser-
vices likely occur because of opposing demands, e.g. development pressure within the
habitat of an iconic species. The opposing demands are also subject to an economic
programme. When natural capital provides direct services, there are often restrictions
within these economic programmes for the market services associated with reducing
natural capital that may be tied to the stock of natural capital of interest. For example,
land-use regulations or social pressure may exist because of an iconic species. That
iconic species may provide existence value to people, but the land-use restrictions imply
that society is willing to forgo a development path sans restrictions in order to conserve
Eli P. Fenichel and Yukiko Hashida
130
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the species. This provides the realized exchange made to protect the iconic species. In
these cases, it is important to measure the economic programme associated with the
countervailing use of the capital stock. Then, the marginal value of the stock can be
measured by measuring what the user cost of conservation is to the users who would
draw down the stock. This can provide a lower bound on the implied marginal value,
asset price, of the protected species. There are two reasons the measure might be a
lower bound. First, the behavioural equilibrium captured in the feedback rule of the
economic programme may have been formed with substantial free-riding from the ben-
eciaries given the non-excludability of existence value. Second, in a pure conservation
case, the equilibrium may be a corner solution. For example, when a particular forest
will never be harvested, all that is known is the minimum asset price of standing forest
that prevents harvest.
Decisions about which feature of real income to include are interconnected with nor-
mative decisions about the boundaries of who counts and what feature of the eco-
nomic programme to include when aggregating individual real income into social real
income. This is relatively easy for ex post evaluation of marketed services. The challenge
increases when household production and direct services are included. In the valuation
of environmental services, the extent of the market is often more important than per
capita marginal values (Smith, 1993). Importantly, those who value services provided
by natural capital may not make decisions about the allocation of natural capital or
direct the economic programme. In these cases, or in cases where there are sufcient
heterogeneity and a lack of market-based allocation, the average behaviour captured
by the economic programme will not produce the average contribution to aggregate real
income (Fenichel and Abbott, 2014a).
V. Examples
We review published efforts to price natural capital assets conditional on observed
economic programmes to focus on the measurement of the economic programme.
We exclude efforts to measure natural capital asset price that assume the economic
programme comes from a competitive optimizing market (e.g. Halvorsen and Smith,
1984), or that the system is in equilibrium so that the net present value of a constant
ow of resource rents provides the value of the asset (e.g. Lange, 2004). Examples of
measuring economic programmes in order to measure asset price for natural capital
tend to be data intensive. Requirements to measure economic programmes and natural
capital asset prices are that quantities of stocks have well dened units, actions within
the economic programme have well dened units, and there are available data. These
requirements have led to applications that are seemingly narrow. However, we expect
researchers to apply the approach to increasingly complex systems in the future.
Fenichel et al. (2016a) use a 10-year panel of the universe of Kansas groundwater
withdrawal and crop choice data to estimate a linear selection model (Pfeiffer and Lin,
2014) for water withdrawal as a function of crop choice, stock of groundwater, and
other observables. Crop choice is also a function of stock of groundwater. Fenichel
etal. (2016a) estimate a multinomial logit model for crop choices as a function of water
stock and other observables. They model unirrigated elds as a ‘crop’ choice thereby
Choices and the value of natural capital 131
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including information about extensive margin planting decisions. The authors imply
that xs
()
is the water withdrawal function, but the economic programme also impli-
citly contains the crop choice response to the waterstock.
Yun etal. (2017b) develop the economic programme needed to measure natural capi-
tal asset prices for sh stocks in the Baltic Sea based on Hutniczak’s (2015) model of
harvester behaviour. The authors develop an effort index as a function of three sh
stocks. The empirical approach uses a production framework, a multi-product distance
function that takes advantage of detailed landing and effort data for all 411 vessels
in the Polish shing eet. The modelling approach yielded vessel specic parameters,
which Yun et al. (2017b) simulate at the individual vessel level to measure harvester
response to changing sh stock and management regimes.
Fenichel and Abbott (2014b) use a seemingly simple economic programme that
denes aggregate effort for the US commercial Gulf of Mexico reef shing eet. They
summarize Zhang’s (2011) empirical estimates into xs ys
()
=
γ
, where
y
and
γ
are
scale and elasticity parameters averaged from Zhang (2011). However, Zhang’s (2011)
underlying count data model was estimated using 126,131 shing trip records and
included gear specic effort. Furthermore, the shing production model in Fenichel
and Abbott (2014b) is an aggregation of the generalized Schaefer function developed
by Zhang and Smith (2011) that makes use of the same dataset as Zhang and accounts
for gear and spatial variation along with other observables. The generalized Schaefer
harvest function implies that the impact of the economic programme on the capital
stock is non-linear, with harvest dened as qs txs
() ()
()
α
, where
q
is a catchability par-
ameter and
α
is an elasticity parameter. Bond (2017) uses a similar economic pro-
gramme, but he conditions the production of sh on an exogenously declining stock
of wetlands. He considers the asset value of wetlands that provide sh nursery habitat
and storm protection. Bond uses an ad hoc economic programme that yields constant
wetland loss for illustrative purposes.
To illustrate the sensitivity of natural capital asset prices to changes in the economic
programme, consider the economic programme used by Fenichel and Abbott (2014b)
to recover the shadow price function for the Gulf of Mexico reef sh stock between
the mid-1990s and 2005. To illustrate how the natural capital asset prices are depend-
ent on the economic programme, consider a change to the elasticity parameter
γ
in
the economic programme.12 Figure2(a) shows a 2 per cent decrease in the behavioural
elasticity relative to the base case. Such a response could occur because of increased
outside opportunities or barriers to entry, slowing the rate shers enter the shery when
stocks rise (or xed cost slowing the rate of exit as the stock falls). Figure2(b) shows
how making shers less responsive to an increase in the stock increases the asset price
at low stocks, but lowers the asset prices at high stocks.
VI. Discussion and conclusion
The theory of sustainability must be a theory of measurement. Measuring the value of
natural capital assets requires empirically measuring changes in stocks and valuation,
12 Parameters and functions for this example are included in the ‘GOM’ example of the capn package
forR.
Eli P. Fenichel and Yukiko Hashida
132
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but it is the measurement of economic programmes that often provides the bottleneck
to reliable natural capital asset prices. Resolving the challenges of measuring economic
programmes requires balancing theory and data and developing sufcient structure to
enable forecasts of economic decisions as the state of the world changes.
Sustainability assessment using the wealth framework will be most useful when mul-
tiple stocks are considered and the economic programme is vector valued. Multiple
stocks create the possibility of substitute and complementarity relationships among
assets (Yun etal., 2017b). Whether or not assets can be substitutes is at the core of the
sustainability question. Helm (2015) and Barbier (2011) review the weak versus strong
sustainability debate. Helm (2015) specically argues for careful consideration of aggre-
gation rules. We argue that state varying shadow prices reect the current implicit aggre-
gation rules because they reect substitute and complementary relationships. As stocks
increase in scarcity the degree of substitutability may weaken. It is even possible that
stocks become complements. In order to measure complementarity or substitute rela-
tionships, natural capital must be valued within the context of a broader system. The
degree of substitutability or complementarity is inuenced by the scope of decisions
people make—the economic programme. Failing to consider vector-valued economic
programmes, when multiple decision margins are possible, seems likely to make a single
resource appear scarcer than it is, overvaluing the asset and, all else equal, making it
appear as if society is less likely to preserve the opportunity set for future generations.
This could lead to fewer members of the current generation having their needs met.
However, the reverse may be true if multiple assets are aggregated into a singleasset.
Beyond the aggregation–disaggregation challenge, is the challenge of coordinating
data collections at appropriate scales. Measuring economic programmes and valuing
natural capital is an inherently interdisciplinary endeavour. Economists and natural
scientists need to continue to expand collaborative efforts to collect data so that envir-
onmental dynamics and the economic programme articulate.
Figure2: Illustration of how changes in the economic programme can affect the shadow price of nat-
ural capital
0
200000
400000
600000
(a)(b)
0 100000000 200000000 300000000
stock
effort
0
5
10
15
0 100000000 200000000 300000000
stock
shadow price
Notes: Panel (a)shows the change in the economic programme. Panel (b) shows the resulting change in stock.
Solid curve is the parameterization from Fenichel and Abbott (2014b). Dashed curve is a 2 per cent decrease
in the elasticity parameter.
Choices and the value of natural capital 133
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GDP and national accounts have had an outsized impact on policy because they
produce a measurement. Kuznets (1934) argues that, ‘there is considerable value, how-
ever, in checking the unarmed observation of even a careful student by the light of a
quantitative picture’. Kuznets also acknowledged the simplications necessary and data
challenges inherent in measurement.13 It is not sufcient for sustainable development
or sustainability more broadly to be an abstract unachievable goal. Sustainability must
be measurable, and early attempts to measure sustainability suggest it is also achievable
(Arrow etal., 2004; UNU-IHDP and UNEP, 2014; Lange etal., 2018). Measurement
of economic programmes that inform natural capital asset prices is an essential element
in providing actionable sustainability measurements.
Appendix
The present value of real net income can be formally writtenas
Vt
WedW V
t
t
s
ssxs sxss s
()
()
=
()
()
=
()
()
+∇
()
()
∞−−
()
−
∫
,,
,
δτ
τδ
1¢ (1)
where
W
is a real net income index,
s
is
S
-length vector of capital stocks,
x
is
X
-
length vector of feedback rules that comprise the economic programme,
δ
is a discount
rate,

s¢
is the transpose of the vector of differential equations dening stock dynamics
conditional on the economic programme, and
∇
s is the gradient operator with respect
to the vector of stocks. The nal equality connects the Fisherian (Fisher, 1906) and
Hicksian (Hicks, 1939) income concepts.
Taking the derivative of Eq (1) with respect to the stock provides the asset price,
which is formally written
pV
Wp
ssp
s
sp
i
s
s
i
i
i
ji
j
i
j
ji
j
i
i
s
sx s
()
==
()
()
+∂
∂+∂
∂




+
≠≠
∑∑
,
∂∂
∂
−
()
()


s
s
s
j
i
s
i
i
δ
(sxs (2)
where
ji≠.
Abbott et al. (2018) show that stochastic process adds endogenous risk
and prudence capital gains terms to the numerator. If the asset is depreciating,

ss
<
0
as Jorgenson (1963) assumes, then depreciation effectively increases the rate of discount.
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