Defrancesco E., Gatto P., Rosato P., (2014) A 'component-based' approach to discounting for nature...

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Analysis

A component-basedapproach to discounting for natural resourcedamage assessment

Edi Defrancesco a,, Paola Gatto a,1, Paolo Rosato b,2

a Department TESAF - Territorio e Sistemi Agro-forestali, University of Padova, Agripolis, Viale dell'Universit, 16, 35020 Legnaro, PD, Italyb Department DICAr - Ingegneria e Architettura, University of Trieste, Piazzale Europa 1, 34127 Trieste, Italy

a b s t r a c ta r t i c l e i n f o

Article history:

Received 12 April 2013Received in revised form 23 December 2013

Accepted 30 December 2013

Available online 24 January 2014

Keywords:

Damage compensation

Remediation

Environmental liability

Social discount rate

Dual discounting

Declining discounting

The paper proposes a component-basedapproach to guide the choice of the social discount rate in natural

resources damage assessment, where time and discounting are key features. It is a multi-rate discounting

scheme, which draws on concepts from dual-rate and time-declining approaches. Each damage component is

discounted at a component-specic constant rate, related to its time-trajectory. Assuming a normatively dened

declining schedule of rates as a starting reference, components with longer timeproles generally represented

by welfare lossesare discounted at lower rates than short-term damage components mainly remedial costs.

The rationale behind this choice is thatthe longer the duration of the damage component, the higher the related

nonincident specic uncertainty on the resource values and the more relevant the equity issues. When estimat-

ingthe total damage,the resulting implicit averagediscount ratedepends on theduration of eachcomponentand

its relativerelevance in the total damage in eachmoment. From an operational point of view, anchoring the rates

to government prescriptions would support the robustness of the damage estimates in a court of law, whereas

the dual-based environmental discount rate is based on ad-hoc assumptions that are more difcult to justify.

2014 Elsevier B.V. All rights reserved.

1. Introduction

Natural Resource Damage Assessment (NRDA) is the process

through which injuries to naturalresources areidentied andmeasured

and actions dened in order to compensate the public for the loss of

ecosystem services. The approach has been enforced by normative

acts the Comprehensive Environmental Response, Compensation,

and Liability Act (CERCLA) for the USA (NOAA, 1999) and the Environ-

mental Liability Directive (ELD) for the European Union (2004/35/CE).

The basic principles underpinning both the US and EU legislation are

the denition of damage liability and the rights of injured parties

the authorities acting as trustees for natural resources on behalf of

societyto receive compensation. The preferred form of compensation

is full restoration, when possible, of the injured resources, dened by

the ELD asprimary remediation; when interim and/or permanent losses

occur, compensatory and/or complementary remediation measures

should also be undertaken, even off-site, to cover those losses. The

costs incurred in these actions, together with the damage response

and assessment costs, represent the measure of damage (Dumax

and Rozan, 2011; Jones and Pease, 1997; Thur, 2007; Zafonte and

Hampton, 2007).

Habitat Equivalency Analysis (HEA) (Dunford et al., 2004; NOAA,2006; Roach and Wade, 2006), now rened in Resource Equivalency

Analysis (REA) (Zafonte and Hampton, 2007) is the method used to

assess equivalency between discounted values of restoration gains

and interim losses until full remediation is reached, when possible

(NOAA, 2006). If the costs of the actions are a measure of the damage,

HEA/REA allow grading of the remediation project to the appropriate

spatial scale.

Although greeted as a paradigm shiftfrom approaches based solely

on a monetary evaluation of ecosystem services (Flores and Thacher,

2002) and allowing law courts' difculties in using evidence from Con-

tingent Valuation studies in NRDA to be overcome (Thompson, 2002),

there have recently been criticisms about the use of HEA/REA. Indeed,

HEA/REA are based on the implicit assumption that the public is willing

to accept a one-to-one trade-off between a unit of lost habitat services

and a unit of restoration project services (NOAA, 2006 p. 3), thus,

undercertain circumstances, dispensingwith the problem of measuring

monetary values for these trade-offs. However, in the real world, this

assumption may not hold, mostly for three reasons (Zafonte and

Hampton, 2007): i) differences in type and quality between restored/

replaced resources and those injured; ii) variation in time preferences

and iii) heterogeneity of preferences. To put it simply, HEA/REA do not

fully take into accounthuman welfare considerations(Martin-Ortega

et al., 2011).Conversely, it has been claimed that monetary evaluation

allows heterogeneity of preferences and their variations over time to

be considered (Flores and Thacher, 2002), including both efciency

and equity concerns in the assessment process. Operational purposes

Ecological Economics 99 (2014) 19

Corresponding author. Tel.: +39 049 8272721; fax: +39 049 8272750.

E-mail addresses: [email protected](E. Defrancesco),[email protected]

(P. Gatto),[email protected](P. Rosato).1 Tel.: +39 049 8272719; fax: + 39 049 8272750.2 Tel.: +39 040 5588092; fax: +39 040 558358.

0921-8009/$ see front matter 2014 Elsevier B.V. All rights reserved.

http://dx.doi.org/10.1016/j.ecolecon.2013.12.017

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also call for a measure of the damagein economicterms,on thegrounds

that this allows judgement of whether compensation is adequate or, on

thecontrary, thecosts of therestoration project are disproportionate to

thebenets obtained (Flores and Thacher, 2002). Thisis also inlinewith

some normative approaches, for example the Italian legislation permits

compensation via monetary equivalent when primary, compensatory

and/or complementary remediation is technically or economically

unfeasible (Article 2058 of Italian Civil Code). Based on the claim that

evaluation of the economic dimension of damage still has a key-role toplay in NRDA, various theoretical papers and case studies have been

published attempting to complement HEA/REA with economic analysis

(Brouwer and Martin-Ortega, 2012; Brown Gaddis et al., 2007; Dumax

and Rozan, 2011; Kosugi et al., 2009; Loureiro et al., 2009; Martin-

Ortega et al., 2011; Thur, 2007), or working specically on violations

of HEA/REA assumptions (Zafonte and Hampton, 2007). In line with

the ideas expressed by these papers, the monetary evaluation in NRDA

is also central in this work.

All approaches based only on HEA/REA, as well as those coupling

REA with economic approaches and, even more so, strict monetary

approaches to damage evaluation, emphasise that a key feature of

damage and its remediation process is its time-dimension. Time passes

between the injury and the start of the remediation process and time is

needed for the complete (or partial) re-establishment of the baseline

conditions and for completing complementary/compensatory projects.

In a given ecosystem, depending on the extent and gravity of the

damage, it may happen that more than one resource and more than

one service are impaired or lost because of the injury. In order to return

to the baseline condition, each resource and/or service may have a

specic recovery trajectory, stretching over a different time-scale. Each

NRDA is thus characterised by a specic time-prole, whose complexity

depends on thestarting conditions, theextent and gravityof thedamage,

the possibility of undertaking mitigation and/or remediation actions, and

the specic recovery trajectoryof each affected resource component and/

or service. Damage components' time-proles and how they can be

framed in the NRDA context is the rst issue discussed in this paper.

Intertwined with the issue of time-proles is the problem of

identifying present values of the damage components, which implies

choosing an appropriate discount rate. This choice is critical, given theseveral cost and welfare elements with different time-proles (short,

medium, longand sometimes perpetualterm) that have to be taken

into account (Boyd, 2000; Defrancesco et al., 2008; EU Commission,

2001; Howe, 1990; Oara, 2002). The setting of an appropriate social

discount rate has long been debated in the Cost Benet Analysis (CBA)

literature. Controversy has arisen over the theoretical foundation of the

standard exponential discounting approach and the use of single-rate

discounting mainly when valuing projects with a very long time

horizon which arguably substantially under-evaluates events in the

distantfuture. In thelast decadestherehasbeen a strongupsurgeof inter-

est in social discounting issues when the debate on sustainable growth

and prominent environmental problems, e.g. the climate change related

risks, has arisen in the policy arena, and relevant intergenerationalequity

issues have emerged. Given this increased interest, in more recent yearstheoretical and empirical justications have been provided for time-

declining discounting (for a review, see:Oxera, 2002; Pearce et al.,

2003; Groom et al., 2005; Hepburn, 2007, among others). In line

with the literature ndings starting with theRamsey (1928)argument

in favour of a zero utility discount rate developed countries have

generally reduced the recommended rates to adopt when valuing public

projects (Harrison, 2010). Alternatively, discrete time-declining discount

rates have been set (HM Treasury, 2003; Lowe, 2008), helping to achieve

a trade-off between intergenerational equity and efciency issues

(Hepburn, 2007).

Given the richness of contributions and operational indications

provided in the CBA context on the choice of the discount rate and

also its relevance in the damage assessment context (Kopp, 1994), our

paper draws on concepts from dual rate discounting and from time-

declining discounting approaches and proposes a hybridcomponent-

based approach to discounting in NRDA. With this approach each

damage component is discounted at a component-specic constant

rate, which is related to the component's time trajectory. Assuming as

a starting reference a normatively dened stepwise-declining schedule

of rates, components with longer time prolesgenerally represented

by individuals' welfare losses are discounted at lower rates than

short-term damage components mainly remediation costs. When

estimating the total damage, the resulting implicit average socialdiscount rate depends on the duration of each damage component

and its relative relevance on the total damage measure at each timet.

The approach is developed within the rationale of monetary damage

evaluation, but is also consistent with a HEA/REA perspective. The

component-based approach is exemplied through a case-study

referring to a coastal contamination that occurred in Northern Italy.

2. Damage Components and NRDA Time-Prole

The theoretical framework of reference for the monetary evaluation

in NRDA lies in individuals' utility theory (Jones and Pease, 1997;Flores

and Thacher, 2002; Defrancesco et al.,2008) and looks at environmental

damage as an event diminishing the welfare of the affected individuals.

Welfare losses can be assessed through observation of changes in the

expenditure function (Nicholson, 1995) and are at least equal to the

costs that society is willing to pay in order to stop the damage, mitigate

its effect, restore the resource or substitute the environmental goods

and services lost because of the injury (World Bank, 1998).

An additional source of complexity in NRDA lies in two attributes,

one accruing to the damage and the other to the affected resource,

namely the damagereversibilityand resourceremediability. The former

is considered here in relation to the capacity of the damaged resource

to recover, i.e. to return spontaneously to the baseline condition prior

to the injury.3 Instead, resource remediability means the possibility of

catalysing, accelerating the process and fully or partially resolving the

damage through human intervention.

With both a monetary evaluation approach and HEA/REA, combined

damage and resource attributes produce composite damage scenarios,

which also depend on the specic features of the remedial process.Table 1presents four scenarios referred to one resource providing one

service.

The defensive costs i.e. the costs met for measures taken in

response to an event with a view to preventing or minimising the

damages and the damage monitoring and assessment costs are

components that occur in any scenario. Other additional components

are scenario-specic:

i) if the resource is remediable, the damage components include the

cost for remedying the injured environmental resource and the

interim (temporary) welfare losses. The human intervention can

compensate for lack of capacity of spontaneous natural regeneration

or accelerate it;

ii) if the resource is not remediable, two cases can occur: a) the damageis reversible, i.e. the resource is capable of spontaneous recovery:

interim welfare losses occur; b) the damage is irreversible: there

are permanent welfare losses.

The occurrence of either interim or permanent welfare losses

implies the adoption of compensatory/complementaryremedial actions

in HEA/REA and, more generally, generates substitution costs.

Finally, not only can the damage components be of different types

linked to damage and resource characteristics, but they can also have

3 Thischaracteristic is,to a certainextent,whatthe ELDcalls capacity for natural regen-

eration, dened as the capacity to recover,within a short time and without intervention,

[] to the baseline condition [], solely by virtue of the dynamics of the species or habi-

tat, with no direct human intervention in the recovery process.

2 E. Defrancesco et al. / Ecological Economics 99 (2014) 19


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different time trajectories. In other words, they can emerge and termi-

nate at different times and also overlap for some periods. This adds a

further dimension to the discussion of the damage components i.e.

the damage time-prole as depicted in Fig. 1. The time axis represents

the baseline condition, i.e. thestatus quowithout the damage.

In order to deal with thecomplexity of components and time trajec-

tories from an operational point of view, three moments are relevant: 0,

the moment of damage occurrence;m , the moment of the claim for

compensation;n the threshold between thetemporary phaseand thepermanent phaseof damage. These are dened as:

i) temporary phase (time 0n), during which the capacity of the

damaged resource to provide public goods and services is lower

thanthe baseline and society meets thecosts to mitigate thedamage

and remediate or compensate for its effects (Fig. 2). This phase is

characterised by the variability of some damage components over

time, as a consequence of the time trajectories of the primary,

compensatory and/or complementary remediation. During this

phase, individuals may suffer interim welfare losses linked to use

values and possibly also to option values and permanent welfare

losses (Fig. 1). After momentnthe baseline conditions are regained

and the damage streams end or, alternatively, an innite stream of

constant welfare losses continues into the permanent phase. From

an operational point of view, as m is the moment of the claim forcompensation and, consequently, the reference time of the analysis

(Kopp, 1994), the temporary phase can be divided in two sub-

periods marked by the momentm.

ii) permanent phase(n), if any, during which only the permanent

welfare losses due to use and passive values remain and are

constant over time. This phase, even if possible, is relatively uncom-

mon in most damage cases (Thur, 2007). It occurs only when the

damage is irreversible and the resource not fully remediable; it is

characterised by annual permanent welfare losses that do not vary

over time. When the permanent losses do vary, the permanent

phase does not occur.

Under the monetary approach, the estimated environmental dam-

age present value DPVm isthesumof all the Kcomponents compounded

or discounted to the moment m of the claim for compensation. The

general formulation, which applies to any injury scenario, is:

DPVmXnt0

XKk1

Dtk 1r mt

D

r 1r

mn1

where: Dtk is the expected value of the damage component k at time tin

thetemporary phase (cost,interim or permanentwelfare loss); D isthe

expected value of the annual permanent welfare loss in the permanentphase;ris the social discount rate.

Under the HEA approach, the NOAA (2006) general formula

equating the sum of the present discounted value of the services lost

at the damaged site with the sum of the present discounted value of

the services provided at the replacement siteis:

JVjXnt0

1 r mt

bjxjt

bj

24

35 b

jxjtn1

bj

24

351

r 1r

mn

2

where:Jis the extentof the injury (in physical terms); Vj is the expected

value of the annual unit value of the services provided by the damaged

resource;Pis the number of compensatory/complementary units; Vpis

the expected value of the annual unit value of the services provided by

the compensatory/complementary project; bj is the baseline level of

services provided by the injured resource; xtj is the level of services

provided per unit by the injured resource at time t; bp is the initial

level of services provided by the resources at the compensatory/

complementary site; xtp is the level of services provided per unit by the

resources at the compensatory/complementary site at time t; lis the

time when the compensatory/complementary project reaches full

maturityi.e. maximum services provision is reached and the services

provision continues perpetually or the compensatory/complementary

project senesces.

Table 1

Damage components according to four scenarios linked to damage reversibility and resource remediability.

Resource

Remediable Not remediable

Damage Reversible Defensive costs Defensive costs

Monitoring and assessment costs Monitoring and assessment costs

Remediation costs

Interim welfare losses (compensatory remediation) Interim welfare losses (compensatory remediation)

Irreversible Defensive costs Defensive costs

Monitoring and assessment costs Monitoring and assessment costs

Remediation costs

Interim welfare losses (compensatory remediation) Permanent welfare losses (complementary remediation)

Fig. 1.Damage time-prole: interim and permanent welfare losses.

3E. Defrancesco et al. / Ecological Economics 99 (2014) 19


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However, judging from the literature, the debate on discounting

in NRDA seems to have received less attention than in the parallel

CBA context. This is despite the choice ofrbeing equally important,

as it may signicantly affect both the DPVm under the monetary

approach and the scale Pof compensatory and/or complementary

remedial actions under HEA/REA. This apparently scarce consider-

ation could be explained on the grounds that the underlying theoret-

ical basis on discounting is common to CBA and NRDA, or that the

legal context of the latter requires that social discount rates aredecided upon by public authorities' guidance documents. Whatever

the reasons, we feel that the choice of the social discount rate

deserves to be more specically addressed in the specic context of

NRDA.

Our paper proposes a component-based approach to social

discounting in NRDA that is a hybrid approach combining the ratio-

nale of dual-rate discounting with that of time-declining social

discounting, the latter being the one currently prevailing in the

CBA context.

Sharing the theoretical justications of the dual-rate discounting,

our approach draws the idea from it that different discount rates should

be used when considering either tangible (cost components) or

medium-long term intangible effects (i.e. welfare losses). In addition,

NRDA focuses on a specic illegal action causing an injury to the envi-

ronment: consequently, lowering the discount rate allows the incorpo-

ration of the uncertainty related to imperfect information on the

resource values outside the incident-specic losses. From a NRDA

operational point of view, this solution is a more feasible alternative

than modelling the impact on values of e.g. the increasing resource

scarcity or reduced availability of substitutes (Yang, 2003; Kgel, 2009,

among others in the CBA context). General uncertainty about the future

incomegrowthrate,life expectancy and discount rate as well as sustain-

ability and intergenerational equity issues, which support declining

discounting, arealso relevant in the NRDA context. Our hybrid approach

links all these off-sitenon environmental- and environmental-related

uncertainty issues, as well as the intra- and inter-generational equity

ones, to the specic time-span of each damage component via the

choice of component-specic rates: the longer the duration of the

damage component the higher the uncertainty. Conversely, most ofthe literature indicates that the damage-specic uncertainty about

predicted outcomes should preferably be taken into account by

properly incorporating it into the values of losses due to the injury

and gains from the restoration project (NOAA, 1999; Dunford et al.,

2004; Moilanen et al., 2009, among others). However, the literature

suggests that a lower discount rate can be chosen when a specic

damage component, including a cost, is persistently uncertain

and therefore difcult to evaluate because of its very long time-

span. Consequently, the component-based approach discounts

each damage component with a constant separate rate chosen from

a menu of declining rates. The choice criterion is the duration of

the damage component: the longer the damage effect, the lower

the associated rate. Using constant separate rates for the different

damage components qualies our approach as a multi-rate discountingscheme, in principle an extension of the dual-rate approach, as it shares

its theoretical foundations.

However, the specic legal context of NRDA requires that the chosen

rates are anchored to social discount rates recommended by public

authorities, especially when societal value judgments based on equity

issues are incorporated, as is the case of rates associated to welfare

losses. To our knowledge, no prescriptions on dual-rates are provided

by governments, apart from in the USA (NOAA, 1999; US Federal

Register, 1996a and b).The component-basedapproach lls this gap

by making reference to country-specic declining either continuous

or approximated by a discrete schedulerates, which are recommend-

ed in some CBA national frameworks. This link provides a robust

operational support to the choice of the discount rate associated to

each damage component.

Formally, each damage componentk is discounted with a selected

social raterkchosen according to its length among those prescribed by

the public authority: the chosen rate is that associated to the last year

in which the signicant effect occurs.

When occurring, the whole permanent welfare losses streamwhich

constantly continues after moment n and equals D is discounted at the

lowest social raterklo.

Under these assumptions, and according to the monetary approach

to NRDA, Eq.(1)becomes:

DPVmXnt0

XKk1

Dtk 1rk mt

D

rklo1rklo

mn: 4

Let us focus on the temporary phase, the rst part of Eq.(4), and

dene the total damage at timet:

Dt

XKk1

Dtk: 5

Multiplying and dividing the temporary phase part of Eq.(4)byDt,

DPVmbecomes:

DPVmX

n

t0

Dt

XK

k1

1 rk mtDtk

Dt

!D

rklo1rklo

mn: 6

So, within the temporary phase, at a given timetthe total damage

(Dt) is discounted with an implicit average discount factor dtthat is

the weighted average of the discount factors associated to the damage

components (Dtk); the weight associated to each Dtkequals its share in

the total observed damage (Dt):

dt 1r

t

mtXKk1

1 rk mtDtk

Dt7

while, at each timet, theimplicit average social discount ratertis the

solution to Eq.(7).

Consequently, the resulting implicit average rate rtvaries overtime according to the time-prole and to the relative weight on

the estimated total damage (Dt) of each component of the damage

under evaluation. Thus, when an environmental damage occurs

that has no relevant long-term interim or permanent welfare losses,rtis relatively high over the damage time path the cost compo-

nents of the damage prevailing whilertis reduced when long-

term interim welfare losses are relevant; rtis equal to rklo in the

permanent phase, where most ethical issues arise.

It is interesting to note that in some frequently-occurring environ-

mental damage cases a not increasing prole of each damage compo-

nent is generally observed4 and the most relevant costs are usually

concentrated at the initialstage of the temporary phase, while theinter-

im losses damage components show a longer time-prole than that of

the remedial costs. It follows that, in several typical environmentaldamage cases, a substantially time-declining prole of the implicit

average rate is obtained.

Our proposed approach can also be adopted under HEA/REA. On the

one hand, in frequent cases, the time-proleof theprimary remediation

costs determines a cost-specic time-varyingrt, whereris constant if

the remedial measures are undertaken within a limited length of time

(e.g. 30 years when HM Treasury social rates schedule is adopted). On

theother,the scale Pof the compensatory and/or complementary reme-

diation measures is determined adopting differentiated social ratesrkchosen according to the partial or total damage remediation trajectories

and the maturation functions of the compensatory and complementary

4 Increasing restoration and/orsubstitution costscan be observedwhen tisverycloseto

0, sort

might increase for a limited length of time.



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projects. So Eq. (3) is replaced by Eq. (8) in order to determine the scalePof the compensatory/complementary actions:

P JVjVp

Xnt0

1 rj

mt b

jx

jt

bj

24

35 b

jx

jtn1

bj

24

35 1

rj1rj

mn

Xl

t1

1rp mt xptb

p

bj" #

xp

tl1bp

bj

24

35

1

rp1rp

ml

:

8

When the injured resource provides the baseline services at the end

of the temporary phase, the second part of the numerator equals zero

andrjis chosen according to the length of recovery time, whilerj= rklowhen permanent welfare losses occur. Similarly, in the denominator,rpis selected according to the compensatory/complementary maturation

function. If the project senesces at time l, the second part of the denom-

inator equals zero, whilerj = rklowhen the service provision continues

perpetually. Consequently, a damage-specic time-varying discount

rate is implicitly determined by the NRDA.

However, when compared to the monetary approach, HEA/REA

requires an additional source of uncertainty to be considered linked to

the non-monetary natureof the remediation actions, since the effective-ness of both primary and compensatory/complementary measures is

not fully guaranteed.Moilanen et al. (2009)have thoroughly explored

this issue and proposed a framework to incorporate this source of

uncertainty when estimating a robustly fairP. As already pointed out

under the monetary case, solving this problem by adjusting the rate

(e.g. increasing it when the uncertainty regards the success of the

compensatory actions) is not a recommended option.

Stemming from the theoretical discussion of the component-based

approach, some operational rules to help in the choice of the discount

ratesrkcan be sketched out:

each damage component has to be identied, as well as the duration

of its signicant effects;

the damage-specic uncertainty about predicted outcomes should

preferably be taken into account by incorporating it into theestimations;

the off-site non-environmental and environmental related

uncertainty, as well as the intra- and inter-generational equity

issues, are resolved through the choice of component-specic

rates: the longer the duration of the damage component, the

higher the uncertainty and the equity issues arising and the

lower the associated rate;

given the specic legal context, using social rates recommended

by public authorities lends robustness to the selected rates.

Country specic discrete schedules of declining rates could

provide a credible operational reference to support the choice of

the discount rate to be associated to each damage component:

the chosen rate being that associated to the last year in which its

signicant effect occurs; the choice of the specic reference schedule, from those recom-

mended by the government (as in the case of the UK), can be

strictly related to the specic damage context: while the HM

Treasury (2003) rates can be generally considered, the lowest

schedule of declining rates (Lowe, 2008) is recommended only

when the extent and/or intensity of the injury to the environment

affects intergenerational welfare in a very relevant way.

4. An Exemplicative Case-Study

The discount rate decisions across a schedule of declining rates

under the component-based approach are exemplied through a

case-study located in Italy, on the Northern Adriatic Sea coast. It

refers to the building of an embankment 800 m long and 35 m wide

(2.8 ha) to protect part of the coastline from storm surges. According

to the project prescriptions, the embankment had to be built using

blocks of natural rock obtained from excavation works and/or inert

material coming from building demolition. In order to create a seaside

recreational area, the project required turng the embankment,

planting trees and building some kiosks. Violating the prescriptions,

the building company used wastes classied as special and hazardous

according to the Italian waste disposal law5 as material for the embank-

ment. This illegal action caused environmental damage.An investigation of the material in the embankment was commis-

sioned by the local council in order to identify the specic sources of

pollution (Bevilacqua, 2010; Dazzan et al., 2010) and to assess the risk

of dispersion of pollutants into water and air (Bevilacqua and D'Aprile,

2011). The resultsled to thezoning of the embankment into four differ-

ently polluted sub-areas. An in-depth CBA (Massiani, 2010; Massiani

and Barbieri, 2013) was performed in order to choose the best remedi-

ation activities with the aim of regaining, as fully as possible, the recre-

ational uses. Two actions were undertaken on the whole area (Table 2)

in order to reduce the risk generated by the polluted materials, namely:

(i) the construction of a permanent steel sheet pile on the sea front to

avoid the pollutantsbeing washed out by the waves;(ii) the implemen-

tation of a monitoring system of the contaminant leaching into the

groundwater and the sea. In addition, other specic defensive and

remedial actions were designed for each sub-area according to the

type and extent of contamination.Table 2also highlights the original

recreational uses of the different sub-areas (without the damage

representing the baseline) and the present with the damage ones,

after the remedial actions.

Four damage components having different time trajectories and

characteristics are identied (Table 3): i) several defensive and remedi-

al actions, which occur in the rst two years; ii) monitoring of pollut-

ants, which occurs till year 50; iii) permanent recreational welfare

losses affecting both present and future generations, starting at year 2,

when the remedial actions nish; and iv) interim welfare recreational

losses, which affect the present generation from year 2 to 35. The

occurrence of damages, and the moment in which they emerge, are of

course determined by comparing the with the damagescenario to

thewithout the damagebaseline.6

Under a monetary approach to NRDA, the values have been estimat-

ed andsubsequently discounted to thereference time for theanalysis m,

which in our case coincides with the damage occurrence (m= 0). The

following values have been considered:

(i) the defensive and remedial costs, assessed on the basis of the

project estimates;

(ii) the costs for monitoring of pollutants, estimated as 1500 per

year. This long-term monitoring is needed to control the risk of

pollutant losses until recovery stabilisation;

(iii) the permanent recreational welfare losses, due to the unavail-

ability of sub-area 3 for sporting activities, sun-bathing and

swimming. Only 25% of sub-area 3 is affected by these losses,

while the remaining 75% would anyway have been used for in-frastructure and services, even without the damage.Massiani

(2010)has estimated the permanent recreational losses for the

area using a Value Transfer approach (Spash and Vatn, 2006).

The willingness to pay for sporting activities/sun-bathing/

swimming inthe area is 4.90 perperson-day in thehigh season

(MaySeptember). With the more conservative estimate, around

16,000 person-days per year were lost in sub-area 3, giving per-

manent welfare losses of almost 78,000 /year;

5 Legislative Decree 152/2006prescribes that these types of wastes must only be dis-

posed of in appropriate landlls and cannot be used for building purposes.6 Evenwithoutthe damage,the recreational activitiescouldnot havetakenplace forthe

rst twoyears, since the originalproject would also have required two years to complete.



7/9

(iv) the interim recreational welfare losses in the other sub-areas,

due to the temporary loss of reputation of the site caused by

pollution. It is well-known that a polluted site, even after reme-

diation, is affected by a loss of appreciation by users (Easterling,

1997; Levi and Kocher, 2006; Miller and Sinclair, 2012) for a

length of time that depends on their risk aversion. The remedia-

tion of the site does not achieve the complete removal of

contaminants: consequently, we have assumed a rather slow

reputation recovery. Under a conservative assumption, wehave considered that risk aversion affects only one third of the

total users and that it exponentially diminishes over time: the

initial value of the interim welfare losses is 503,067 (102,667

lost person-days at 4.90 /person-day) becoming negligible

after the 35th year.

The next step of our component-based approach requires the

duration of each damage component to be analysed and to associate

an appropriate discount rate to each of them. The rates choice problem

has been solved according to the provided operational rules. With

reference to the rates menu of declining rates recommended by HM

Treasury (2003), we have chosen the rates reported in the last column

ofTable 3, namely 3.5% for duration until 30 years; 3% for duration

until 75 years and 1% for permanently persisting welfare losses.This environmental damage example shows a rather common time

prole, with the majority of the costs arising within a limited time

horizon and the welfare losses spanning a longer period of time. In

similar cases, the environmental and economic uncertainty over the

future state of the world affects the welfare-related values in a more

relevant way than the remedial costs. Therefore, lower discount rates

are justied for the former. In our case, discounting the permanent

recreational welfare losses at a lower rate than the interim ones to

account for the higher off-site uncertainty and the intergenerational

equity issues affecting them is even more justied since the same

expected annual unit value is used for both.

Fig. 3shows the time prole of the implicit average social discount

rate, which, in our example, is declining. TheDPVmestimated with the

component-based approach is compared with that obtained using

different approaches inTable 4. With our approach, theDPVmequals

12.3 million, while directly adopting the Green Book (HM Treasury,

2003) declining rate, it reduces to nearly 8 million. The latter is

signicantly lower as the discount rate is the same for all the damage

components in each moment and therefore the rate declines more

slowly over time when compared to the implicit average rate of our

approach. Finally, theDPVmobtained by discounting all the damage

components at the 3.5% constant rate (EU Commission, 2008) providesthe lowest damage estimate (6.7 million). These results are obviously

case-specic, depending on the time trajectories of the damage

components.

5. Conclusions

The component-based approach provides a rationale for social

discounting within the NRDA framework, where the issue of

discounting has not been adequately explored, despite the key role

played by the discount rate in the context of environmental damage

being undeniable. Indeed, it can dramatically inuence the DPVmwhen a monetary approach is adopted, but also the scale Pof com-

pensatory and/or complementary remedial actions under HEA/REAapproaches.

Theproposed approach is a combination of some theoretical founda-

tions of dual-rate discounting and time-declining social discounting.

The former provides the principle that different discount rates should

be used when considering either tangible (cost components) or

medium-long term intangible effects (i.e. welfare losses), the latter

that uncertainty and intergenerational equity issues play in favour of

time-declining social discount rates. Our approach agrees on the princi-

ple that very long-term welfare losses, e.g. the permanent components

of the damage, have to be discounted at a low rate in order to mitigate

the tyranny of the presenteffect and take into account the relevant

uncertainty affecting the values. Conversely, when the interim welfare

losses time-prole does not exceed the present generation's lifetime, a

Table 3

The damage components, their time trajectories and the associated discount rates.

Damage component Cost / value () Time-trajectory Discount rate (%)

Frequency Duration

Defensive and remedial actions:

Construction of steel sheet pile 800,000 Single sum 0 3.5%

Removal/disposal of special wastes (sub-area 1) 918,000 Single sum 0 3.5%

Removal/disposal of hazardous wastes (sub-area 2) 300,000 Single sum 0 3.5%

Covering with clean topsoil (sub-areas 1 and 2) 480,000 Single sum 1 3.5%

Capping (hard) (sub-area 3) 500,000 Single sum 1 3.5%

Capping (light) (sub-area 4) 420,000 Single sum 1 3.5%

Monitoring of pollutants 1500 Constant annuity 050 3.0%

Interim welfare losses 503,067 Annually declining 235 3.0%

Permanent welfare losses 77,794 Constant annuity 2 1.0%

Table 2

The defensive and remedial actions and the sub-areas uses with and without the damage.

Sub-area 1 Sub-area 2 Sub-area 3 Sub-area 4

Size (m2) 13,500 2500 5000 7000

Actions Construction of a steel sheet pile

Implementation of a monitoring system

Removal anddisposal of thespecial

and hazardous wastes and

replacement with clean topsoil

Capping (hard) Capping (light)

With-the-damage uses Sports, sun-bathing and swimming Sports, sun-bathing and

swimming + Services

Sports, sun-bathing and swimming

Without-the-damage uses (after remediation) Sports,sun-bathingandswimming Parking + Services Sports, sun-bathing and swimming



8/9

higher social rate is considered. The rationale behind this choice is that

the interim welfare lossesare mainly due to temporarily reduced values

of the damaged resource and individuals may generally adapt their

behaviour to the temporary change, so the tyranny of the futureeffectcould be mitigated.

Overall, our component-basedapproach discounts each damage

component with a constant separate rate chosen from a menu of

declining rates prescribed by the government: the choice of the rate is

anchored to the damage component duration. Thus, an implicit average

social discount ratertis derived that varies over time. The distinctive

characteristic of our approach is that the rtswitch from one rate to

another, which characterises the discrete time-declining approach

and its value at a given timet are tailored to each specic damage

prole. In other words, given the chosen time-declining r which

reects the social rate of time preferences rttime-varying prole

(which is declining in some frequently-occurring cases of environmen-

tal damage) is more intrinsically related to the specic time-prole of

each damage component. When the recommended rates incorporatesocietal value judgements based on equity issues (Baum, 2009) and

general uncertainty about the future,rtis adapted, in a sense, to the

relative relevance and duration of the welfare losses of the affected

individuals.

An additional advantage of the proposed approach is that anchoring

the choiceof the rates to government prescriptions may help to support

the robustness of NRDA estimates in a court of law, while EDR is based

on ad-hoc assumptions that are more difcult to justify.

Acknowledgements

The authors are grateful to the anonymous reviewers for their valu-

able comments and suggestions for improving earlier versions of the

paper. The usual disclaimer applies. They also thank Paolo Bevilacqua

and Bruno Della Vedovaof theDepartment of Engineering and Architec-

ture at the University of Trieste for the technical information provided

on the case study.

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0.0%

0.5%

1.0%

1.5%

2.0%

2.5%

3.0%

3.5%

4.0%

0 10 20 30 40 50

Implicit

averagediscountrate

Years

Fig. 3.Time prole of the implicit average social discount rate in the case-study.

Table 4

The environmental damage present value (DPVm) under various discounting

approaches.

Discounting approach DPVm()

Component-based 12,339,724

Green Book (HM Treasury, 2003) 7,981,238

EU Commission, 2008 6,747,865

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