Exploring welfare implications of resource equivalency analysis in natural resource damage assessments

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a v a i l a b l e a t w w w. s c i e n c e d i r e c t . c o m

w w w. e l s e v i e r. c o m / l o c a t e / e c o l e c o n

ANALYSIS

Exploring welfare implications of resource equivalency analysis in natural resource damage assessments Matthew Zafonte⁎, Steve Hampton 1 California Department of Fish and Game, Office of Spill Prevention and Response, 1700 K Street, Suite 250, Sacramento, CA 95814, United States

AR TIC LE I N FO

ABS TR ACT

Article history:

Resource equivalency analysis (REA) has become the dominant method for calculating

Received 7 September 2005

natural resource damages for biological injuries from pollution incidents. This methodology

Received in revised form

compares resources lost as a result of an incident to benefits that can be gained from a

4 January 2006

habitat or wildlife restoration project. Compensation is evaluated in terms of resource

Accepted 2 February 2006

services instead of market currency. Recently, this approach has been questioned regarding

Available online 20 March 2006

its ability to provide adequate compensation based on economic welfare principles. The following paper examines these critiques and develops a model to quantify the welfare

Keywords: NRDA

implications of using REA when some of its implicit assumptions are violated. We focus on the situation where compensatory restoration projects provide services that

Natural resource damage

are comparable to those lost as a result of an incident. We examine simulation scenarios

assessment

where the public has heterogeneous preferences for resources and where resource values

Natural resources

change over time. Using the Hicks–Kaldor criterion, we find that the traditional REA provides

Damages

an acceptable approximation of aggregate compensation for a reasonably wide range of

Restoration

economic and biological parameter combinations.

Habitat equivalency analysis

© 2006 Elsevier B.V. All rights reserved.

Resource equivalency analysis

1.

Introduction

In 1997, the National Oceanic and Atmospheric Administration (NOAA) issued a guidance document for conducting natural resource damage assessments (NRDA) under the Oil Pollution Act of 1990 (NOAA, 1997). These assessments determine the compensation that parties responsible for oil spills owe to the public. NOAA recommended that the calculation of compensation for biological injuries be based

upon restoration projects, where the sizes of those projects are “scaled” using habitat equivalency analysis (HEA) and the cost of the projects becomes the measure of damages. At the same time, natural resource agencies were suffering negative experiences using more traditional valuation methods, especially contingent valuation (Thompson, 2002). Since that time, HEA has evolved into the more generic resource equivalency analysis (REA) and has become the primary method for calculating damages from pollution events nationwide.2

⁎ Corresponding author. E-mail address: [email protected] (M. Zafonte). 1 The ideas presented in this paper are the personal thoughts of the authors and do not reflect the official position of the California Department of Fish and Game. The authors would like to thank David Chapman, Mark Curry, Chris Leggett, Neil Pelkey, Douglas Shaw, Julie Yamamoto, and two anonymous reviewers for their helpful reviews and comments. 2 While HEA only refers to habitat-based analyses, REA includes analyses that focus on any natural resource (e.g. birds, sea turtles, etc.). 0921-8009/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.ecolecon.2006.02.009

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Flores and Thacher (2002) have accurately described this as a “paradigm shift”. Indeed, nearly every pollution damages case in the past five years has employed REA as the primary method to quantify damages to wildlife and habitat. Furthermore, the method has recently been affirmed by two courts as an appropriate measure to determine the scale of compensatory restoration projects (United States v. Fisher, 1977; United States v. Great Lakes Dredge and Dock Co., 1999). While REA has been widely applied and evaluated within numerous natural resource damage assessments, the methodology has not been explored in the academic literature to the same extent as other valuation approaches (e.g., contingent valuation). Most papers describing REA have focused on either the policy and legal contexts within which it is applied (Mazzotta et al., 1994; Jones and Pease, 1997) or specific applications (Unsworth and Bishop, 1994; Penn and Tomasi, 2002; Strange et al., 2002; Sperduto et al., 2003; French McCay et al., 2003a,b; French McCay and Rowe, 2003; Donlan et al., 2003). The two most prominent critiques evaluate the methodology from different perspectives. Flores and Thacher (2002) use welfare economic principles to ground their evaluation of restoration-based damages calculations. Prominent among their concerns is the effect of value changes over time and heterogeneity of preferences. The main limitation of their analysis is that they do not inform the practitioner of how much and when these factors substantively influence results. Dunford et al. (2004) provide a broader review of the REA methodology and include many practical considerations associated with its application in NRDA. Their critique is especially intriguing because it includes sensitivity analyses of REA results to several price change scenarios. However, since they do not motivate their value changes with an economic model, the reader is left to speculate on the assumptions made about individual preferences and the supply of natural resources. This paper builds on the work of Flores and Thacher (2002) and Dunford et al. (2004). It explores the degrees to which violations of REA assumptions can result in either undercompensation or over-compensation of the public. We achieve this end by developing a “monetized” variation of the traditional REA model that incorporates monetary resource values explicitly. We treat the biological state of the world as given, and focus on the two main economic issues of Flores and Thacher (2002): price changes and heterogeneity of preferences. We conduct two sets of simulations using this model to examine how the traditional REA approach fares under a range of conditions relevant to typical applications. Finally, we discuss the implications of our results to economists performing NRDA. We conclude that REA provides a close approximation of compensating wealth under many but not all conditions where it is reasonable to assume substitutability between injured and restored resource services.

lent” of the injured resources (15 CFR 990.30). REA is a tool that is intended to evaluate the amount of restoration needed to compensate from incident-related losses. It involves two steps. The first is to quantify the natural resource injury in terms of the loss of ecological services. This utilizes information on the degree of injury (e.g., the impact per unit area), the duration of injury (e.g., time for the resource to recover), and spatial extent of the injury (e.g., the number of acres, miles of stream, or number of birds affected). The second step is to identify an appropriate restoration project (usually offsite) and evaluate it in terms of the degree and duration of ecological benefits that it is likely to provide. The project is then “scaled” in size so that the total value of ecological service benefits from a compensatory restoration project offsets the value of ecological service losses that resulted from the injury (Jones and Pease, 1997).3 In its simplest single-period formulation, the above resource equivalency problem solves the following equation for the scale, or spatial extent, of the required compensatory restoration project (denoted AR): vI AI Ið1 þ rÞ−tI ¼ vR AR Rð1 þ rÞ−tR

The parameters AI, tI, I, tR, R, and AR summarize the “biology” of resource injury and restoration. AI is the spatial extent of the injury, tI is the time of the injury, I is the severity of injury over space (over AI at tI), tR is the time the compensatory restoration project provide benefits, and R is the magnitude of the restoration benefits/improvements (over AR at tR). Although topics of considerable debate during litigation and settlement (Dunford et al., 2004), these biological parameters (and their units of measurement) are predetermined by the incident and the restoration concept(s) being examined. The “economics” of the equivalency come from the parameters vI, vR, and r. These are the values (in market currency) attributed to each injured and restored resource unit, along with the discount rate. When the above equivalency is satisfied, the project cost of conducting restoration of size AR is estimated, and this becomes the measure of damages. In practice, Trustee agencies are directed to restore resources that are “of the same type and quality, and of comparable value” as the injured resource (NOAA, 1995). This reasoning is used to assume that vI = vR, which allows per-unit resource value to drop out the equation (Jones and Pease, 1997). This leaves the discount rate (r) as the only nonbiological parameter in the REA solution. Multiple time periods are then added to produce a more thorough examination of the “biology” of the problem, resulting in some variant of the following (depending on whether calculations are made in discrete or continuous time): AI

TI TR X X ð1 þ rÞ−t It ¼ AR ð1 þ rÞ−t Rt t¼1

2. The new paradigm for natural resource damage assessment Resource equivalency analysis: an overview

Trustee agencies are required to spend damage recoveries “restoring, rehabilitating, replacing or acquiring the equiva-

t¼1

ðorÞ Z TI Z e−rt IðtÞdt ¼ AR AI 0

2.1.

ð1Þ

ð2Þ TR

e−rt RðtÞdt

0

3 This compensatory restoration differs from “primary restoration”. The latter targets the injured area in an attempt to improve the recovery and thus shorten the duration of the injury, while compensatory restoration may occur off-site.

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RESOURCE SERVICES PER UNIT AREA

INJURY RESTORATION

TIME

Fig. 1 – Conceptual representation of the REA problem.

where TI and TR are the terminal times of the injury and restoration calculations, respectively. Fig. 1 provides a common conceptual representation of the typical, multi-period REA problem. It depicts how the degree of injury (as measured in percentage of resource services) and the duration of injury are compared to the benefits generated by the restoration project, where both are free to change over time. Since restoration projects are performed to compensate for incidents after the fact, restoration benefits typically begin after the initial injury (but not necessarily after full recovery of the injured resource). While an injury may result in a nearly total loss of resource services from a given habitat, as depicted in Fig. 1, restoration projects are typically assumed to provide less than a 100% gain in resource service value. This is usually assumed because the restoration site already has a partially functioning ecosystem prior to the restoration actions, or because the restoration is not expected to provide the full level of services of a pristine habitat (see Strange et al., 2002). Using the solution to AR in Eq. (1) or (2), trustee agencies no longer ask the question, “How much does the public value this resource?” but rather “How much does it cost to provide a compensating amount of the resource (so that it can be provided)?” From a welfare economics perspective, the first question focuses on the amount of monetary compensation that will leave the public indifferent to the injury, while the new question examines the amount of restoration that will be sufficient in value to leave the public indifferent (see Jones and Pease, 1997). In essence, the public is being paid in resource units instead of dollars, and the party responsible for the pollution is given the financial responsibility for providing those units. This approach has been justified from the perspective that they are both cost-effective and grounded in the legal requirements of compensation (Jones and Pease, 1997). Of course, a critical assumption from a welfare perspective is the “cancellation of v”. We will examine this in more detail in the next section.

2.2.

Compensation without money?

The elimination of monetary value from the model has been subject to economic criticism. Both Flores and Thacher (2002) and Dunford et al. (2004) note that the manner in which traditional REA analyses handle value makes significant a priori assumptions that complicate the linkage between REA and economic principles of compensation. We will describe three situations where v may not cancel.

First, there may be inherent differences between the resources that were injured and the resource being restored. Clearly, when dealing with different resource types, there is no guarantee that the value of the injured resources (vI) equals the value of the restored resources (vR). Despite the desire to restore resources “of the same type and quality”, similar sites (e.g., two separate designated wetlands) can exhibit variation in the types of resource services they provide (King, 1997). Eqs. (1) and (2) clearly allow the analyst to specify differences between the resource service losses (due to an incident) and the magnitude of resource service gains (per unit of restoration). When quality (or magnitude) differences are the most tangible distinction between injured and restored resources, the incorporation of these differences into restoration and injury trajectories (R(t) and I(t)) may be sufficient to allow the cancellation of v. The problem arises here with regard to the degree to which the injured and restored resources share a common metric. Flores and Thacher (2002) call this a problem of “substitutability,” which both they and Dunford et al. (2004) note cannot be addressed without an investigation of preferences for the different resources in question. In situations where this is the only issue of concern, the theoretical consequences of differing values appear to be straightforward: the estimated scale of compensation estimated by Eqs. (1) and (2) are off by the proportional per-unit values of the injured and restored resources, vI / vR. A second main complication of REA is that the per-unit value of injured and restored resources may change over time (Flores and Thacher, 2002; Dunford et al., 2004). The constant value of v over time allows the mathematical separation of the biological dynamics of injury/restoration from the per-unit valuation of those services. The time horizon over which these values must remain constant in REA analyses can be quite long. For example, it is not atypical for a habitat proximate to a hazardous waste site to take decades to recover, or for a restoration project to have the potential of providing decades of biological service benefits. One mechanism by which we might expect the marginal resource value to shift is that the baseline supply of natural resource services is changing over time. As a qualitative example, one can consider the changes in wetlands acreage in the United States. On a national scale, most wetland habitat types have declined considerably from historic levels. Consistent with the Law of Demand, we would expect decreasing acreage would increase the marginal value of having an

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additional unit, ceteris paribus. However, increases in restoration activity and improvements in restoration technology can significantly increase wetland supply in some local areas. One such example is the 16,000-acre increase in wetlands in Yolo County, California resulting from the creation of the Yolo Bypass Wildlife Area and City of Davis Wetlands. These projects more than doubled the amount of permanent wetlands in the county. The existence of such trends clearly suggests v is subject to change.4 A third complication is that the REA scaling equation is stated as if everyone in society shares the same value for the natural resource of interest. Flores and Thacher (2002) argue that even in the case of perfect substitutability individuals are likely to vary in the value they place on the resources, which can lead to heterogeneity in the level of restoration needed to provide compensation for each person. In these cases, it is not clear that the REA solution for restoration scale (AR) will satisfy the criterion that the sum of individuals' willingness to accept the injury across society is zero. They further note that making such determinations, along with assessment of the distributional welfare impacts of a given compensatory scheme, is not possible without the use of money (versus resources) as the numeraire. The heterogeneity problem occurs when different groups require alternate scales of restoration (AR) to achieve full compensation. Interestingly enough, heterogeneity in a constant value v does not provide such a conceptual challenge. If the only difference across society is the constant per-unit value that individuals place on affected natural resource services, the constant values for injured and restored resource services (e.g., vI) would still cancel out of the scaling equation. In other words, it is not sufficient to argue that heterogeneity is a problem for REA simply because people place different values on natural resource services. When there is substitutability between injured and restored resources, there must be some other factor that affects the valuation of resource units over time. An example of when this problem might arise would be when groups in society evaluate the injury/restoration from different geographic reference points. As Flores and Thacher (2002) note, distance to the resource is likely to play a role in how individuals value natural resource losses and compensatory restoration benefits (e.g., Sutherland and Walsh, 1985; Bateman and Langford, 1997; Loomis, 2000). Individuals who are local to the injury may perceive the injury as affecting a local resource of limited size, while those who are far away view the injury as an impact on a larger resource supply. This may result in the incident having a “market-level” affect on marginal value for individuals who are proximate to injury and restoration, while having no “market-level” affect on marginal value for those who are distant from the injury and 4 In theory, per-unit values can also vary over time with changes in both preferences for natural resource services and with changes in relative market prices. The importance of the latter affects the quantity of market goods the individual can buy with payments to compensate the individual for utility lost as a result of the incident. Forecasting the magnitude of such changes over the time horizons for long-term injuries and/or restoration projects involves uncertainty. This problem affects multiple valuation methodologies and is not unique to REA.

137

restoration. In the later case, the assumption of constant value v over time is more likely to hold. In the case where the injury and compensatory restoration induce a change in the marginal value of the resource, the valuation of gains and losses will be changing over time as the injury recovers and the restoration project generates benefits. Clearly, it is possible for any or all of the above complications to be present in any specific case. For example, problems with substitutability can be combined with significant disagreement across society on the relative values of injured and restored resources. From an economic welfare perspective, imperfect substitutability between injured and restored resources will always be an issue in REA applications. The method was not originally intended for such applications; when it is used, relative (not absolute) values must somehow be incorporated.5 The other issues, changing values over time and heterogeneity of preferences, are potentially problems even when there is perfect substitutability. Moreover, the implications, especially the size of the impact, are less clear. We will examine these in the next section.

3. Model for incorporating monetary values into resource equivalency analysis 3.1.

Modeling approach and welfare condition

To examine the impact of neglecting monetary value in the REA framework, it is necessary to provide a mechanism by which to incorporate consumer preferences. We examine the case where the restored resource is of the “same type and quality” as the injured resource (i.e., perfect substitutability). This manifests itself as injured and restored resource services both being treated as supply shifts on the same quantity axis (q). We start by using compensating wealth (CW) as the conceptual basis for evaluating adequate compensation. Resource flows resulting from the combined effects of injury and restoration are viewed as shifts in the quantity of resource services supplied over time. In this context, CW is the payment that the individual would make at the time of the incident to equate lifetime utilities with and without injury/ restoration. Formally, we write this as:  vk⁎ W⁎−CWk ; p1 ; N ; pt ; N ; pT ; qB;1 þ Dq1 ; N ; qB;t þ Dqt ; N ;    qB;T þ DqT ¼ vk⁎ W⁎; p1 ; N ; pt ; N ; pT ; qB;1 ; N ; qB;t ; N ; qB;T ð3Þ where vk⁎(·) is the lifetime indirect utility function for individual k, W⁎ is the value of lifetime wealth at the time of the incident, pt is prices for market goods at time t, qB,t describes the trajectory that resource services would follow without injury/restoration (i.e., “baseline”), and ΔqB,t is the net effect of injury/restoration on resource services. If CW is greater than zero, the individual is willing to pay for the resource service change resulting from the combined effects of injury and restoration. When CW is less than zero the individual must be compensated to remain indifferent. Following previous papers on REA (Jones and Pease, 1997;

5 Dunford et al. (2004) provide an economic discussion of estimating relative values.

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Flores and Thacher, 2002), we focus on the Hicks–Kaldor criterion that CWk sums to zero across all of society (i.e., so that gainers could compensate the losers in theory for the changes in resources services resulting from the combined effects of injury and compensatory restoration). In the language of REA, we achieve this compensation by scaling the size of the restoration project so that the trajectory {Δqt} is sufficient to satisfy the CW welfare criterion. Similar to Jones and Pease (1997), we approximate CW using a single-period compensating surplus (CS) welfare measure. For a change in a single-period resource service level, CS is the change in income that would make the individual indifferent to a given change in resource services. Formally, the CS for individual k at time t for a resource change qB,t to qB,t + Δqt is the solution to the equation:   vk;t Mt −CSk;t ; pt ; qB;t þ Dqt ¼ vk;t ðMt ; pt ; qB;t Þ

ð4Þ

where vk,t(·) is the indirect utility function for individual k at time t, pt is prices, and Mt is money income.6 Similar to CW above, if CSk,t is greater than zero, the individual is willing to pay for the resource service shift that has occurred at time t. When CSk,t is less than zero the individual must be compensated to remain indifferent to the service change. We assume that the individual can borrow and lend in a perfect capital market. Following Freeman (2003), this allows the approximation of CW using the discounted sum of single period CS estimates. In continuous time, this is: Z CWk c

T 0

e−rt CSk ðtÞdt

ð5Þ

where CSk(t) is the compensating surplus for individual k at time t (measured in real dollars) and r is the real interest rate. Blackorby et al. (1984) note that the practice of aggregating single period welfare measures induces a bias in the estimation of lifetime welfare changes. When using CS (versus equivalent surplus), the bias favors the underestimation of resource gains and the overestimation of resource losses (Freeman, 2003). However, the bias is small when compensating payments have small impacts on individuals' single period marginal utilities of consumption (Keen, 1990; Freeman, 2003). This is likely to be the case for many natural resource injuries.7 To link the combined effects of injury and restoration [Δq(t)] to CW, we focus on an expenditure-based formulation of CS (see Freeman, 2003): Z CSk ðtÞ ¼ −

qB ðtÞþDqðtÞ qB ðtÞ

Z Aek ðp;q;u0 Þ=Aqdq ¼

qB ðtÞþDqðtÞ

qB ðtÞ

bk ðp;q;u0 Þdq ð6Þ

6 This is for the case where the enjoyment of the quantity constrained resource does not require a per-unit payment which affects the budget constraint (as is commonly the case with existence and bequest value), see Freeman (2003). This assumption is made without loss of generality. 7 For example, Loomis and White (1996) found that household compensatory annual payments ranged from $6 to $95 to compensate for 50–100% losses in regional populations of threatened and endangered species. These dollar amounts for such large injures are still relatively small compared to discretionary household incomes.

where bk(·) is the compensated inverse demand (or marginal willingness-to-pay) function for q and ek(·) is the minimum expenditure to achieve pre-incident utility levels u0 given the resource service quantity (q) and prices (p). Combining Eqs. (5) and (6) with our welfare condition yields: ( X Z k

0

T

e−rt

Z

qB ðtÞþDqðtÞ

qB ðtÞ

) bk ðp;q;u0 Þdqdt c0

ð7Þ

This is where the net change in resource service over time Δq(t) is such that compensating wealth across society is approximately zero. In the remainder of this section, we specify two models for quantifying welfare implications of REA that build off Eq. (7). We first explore a simple case where everyone in society shares the same preferences for the natural resource services lost as a result of an incident. We then extend this framework to allow for the examination of compensation in a society where preferences are heterogeneous.

3.2. Application of welfare criterion in a homogeneous society In a society that is homogeneous with respect to demand for the changes in natural resource services, every individual receives the same welfare from the combined effect of resource injury and compensatory restoration. Consider the hypothetical compensated inverse demand for resource services of an individual in a homogenous society, as depicted in Fig. 2. It is continuous in the neighborhood of current baseline resource services (qB) existing in a homogeneous society. When there is a natural resource injury (e.g., an oil spill), there is a loss of resource services that can be depicted as a supply shift from qB to qI. This results in an instantaneous welfare loss to the individual (area MBIqIqBMBB) and, consistent with the Law of Demand, causes the value of the marginal resource unit to increase (MBI > MBB). This illustrates a “market level” effect of the injury on the value of the resource. Conversely, restoration that increases resource services shifts the supply curve to the right (e.g., from qB to qR). There is a welfare gain (area MBBqBqRMBR) that coincides with a decline in value of the marginal resource unit (MBR < MBB). In REA, the injury losses and restoration gains are dynamic. Biological services can return over time as ecological systems recover from injury. Similarly, restoration actions can also provide changing benefits over time (e.g., new vegetation takes time to become established and provide habitat services). We use injury and restoration quantities from Eqs. (1) and (2) to describe supply of natural resource services in this dynamic context. With respect to baseline resource levels (qB), we write the level of resource services for a given time t as:8 qðtÞ ¼ qB ðtÞ þ DqðtÞ ¼ qB ðtÞ þ AR RðtÞ−AI IðtÞ

ð8Þ

where R(t) is the gained biological services per unit area of restoration, I(t) is the lost biological service (or “debit”) per unit

8

This specification assumes constant returns to scale per area of restoration to be consistent with other REA analyses. This assumption is not necessary for numerical solution.

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$

MBI MBB

pB

MBR

Injury

Marginal Willingness to Pay b(p,q,u0)

Restoration qI

qB

qR

Natural Resource Services/Year (q(t))

Fig. 2 – Change in individual welfare from injury and restoration of natural resource services.

area, and qB(t) is the baseline supply of services. As noted above, the values of AI and I(t) are typically dictated by the nature of the incident, and R(t) depends on the restoration concept being examined.9 The solution to the restoration scaling problem is to determine AR. The addition of the time dependent term qB(t) allows for the possibility of future resource service scarcity (e.g., due to pollution events, human disturbance) or future resource abundance (e.g., due to restoration actions, regeneration) that occurs outside the frame of reference of the specific case. Combining Eq. (8) with Eq. (7) yields the following approximation for a homogeneous society: Z

T

0

e−rt

Z

qB ðtÞþAR RðtÞ−AI IðtÞ qB ðtÞ

bðp;q;u0 Þdqdtc0

ð9Þ

Solving for the restoration project size (AR) using this formulation of the REA problem explicitly considers the biological attributes of the injury and restoration (i.e., I(t), R(t), AI) along with public preferences. Of course, estimating attributes of b(p,q,u0) is both a theoretically important and an empirically difficult issue that has been a topic of considerable research in environmental valuation.

local supply (Δq(t) is large relative to qB(t)) versus those who view the service changes as being a part of a more global market (Δq(t) is small relative to qB(t)) (e.g., Sutherland and Walsh, 1985). Third, individuals may not share the same time preference for natural resource services (e.g., Weitzman, 2001). Using the Hicks–Kaldor criterion and generalizing the model in Eq. (9) to a society with S factions, we write: S X s¼1

"Z /s

0

T

e−rs t

Z

qB;s ðtÞþAR RðtÞ−AI IðtÞ

qB;s ðtÞ

# bs ðp;q;u0 Þdqdt c0

ð10Þ

where ϕs is the proportion of the population that falls in faction s. Clearly, when one group only comprises a small proportion of society (ϕs is small), that group will have little impact on the estimated restoration scale (AR), ceteris paribus. Of course, the effect of faction size will be mitigated by the extent to which that particular faction values the marginal units of the resource services in question. The subscript s on qB,s(t) allows the impact of the injury and restoration to affect different resource service markets (e.g., a local market for people in the vicinity of the spill versus a more global market for individuals who are not local to the spill). We will explore a simple case in the next section.

3.3. Application of the welfare criterion in a heterogeneous society In a heterogeneous society, different subsets of the population place different values on the affected resource services. This provides challenges for any economic welfare analysis. In the context of the simplified model presented here, we can envision differences manifesting themselves through three main mechanisms. First, some consumers may be willing to pay more than others for marginal units of the injured natural resource. Second, individuals may view the injury and restoration from different spatial frames of reference. Those who are proximate to the injury and/or restoration projects may view the change in local resource services as affecting the

9

The effect of “primary restoration” occurring at the site of the injury to speed resource recovery can be incorporated through the injury trajectory I(t).

4.

Simulation analysis

4.1.

Specifying the biological and economic scenarios

The importance of including relative resource values in REA calculations is expected to vary across applications. It is instructive to explore the sensitivity of restoration scaling results to various economic scenarios. We focus on cases where there are: (1) long-term shifts in the baseline supply of the resource, resulting in a value change over time; and (2) “market level” effects due to the injury, but only at the local level in a heterogeneous population. When assessing these scenarios, we compare the estimated compensatory restoration scale AR using traditional REA assumptions (i.e., vI and vR cancel in Eq. (1)) with the restoration scales that solve either Eq. (9) or Eq. (10), the monetized REA.

140 4.1.1.

EC O LO GIC A L E CO N O M ICS 6 1 ( 2 00 7 ) 1 3 4 –1 45

The injury and restoration trajectories

Because the REA scaling results are dependent on the dynamic of resource recovery [I(t)] and the benefits generated from restoration [R(t)], it is necessary to define the biological contexts of each of the economic simulations. For each economic scenario, we examine two stylized types of injuries [I(t)]. The first type of injury depicts a temporary loss of resource services (similar to Fig. 1). It is analogous to a habitat injury from a typical oil spill, where the initial release of oil kills vegetation and otherwise disrupts biological function. The second is a case where there is a “permanent” injury. This is consistent with some hazardous materials releases (e.g., heavy metals, acids) that accumulate in an area over a long period and result in a long-term alteration of resource services. For ease of comparison, we use the same benefit trajectory [R(t)] for offsite restoration actions taken to compensate for both types of resource services losses. This trajectory is consistent with a habitat enhancement project that improves the biological service value of a low quality habitat. These benefits start accruing several years after the initial injury, allowing time for settlement of the case and restoration planning. Fig. 3 depicts the injury and restoration trajectories graphically and includes the relevant injury parameters. Both injury trajectories describe an initial 80% resource service loss. This would reflect, for example, an incident that initially reduced the service quality of the habitat from 100% resource

services to 20% resource services. This injury persists in the “permanent injury” scenario and fully recovers in 6years in the “temporary injury” scenario. Restoration benefits begin accruing 3years after the initial injury and eventually provide an absolute 50% increase in resource services (measured in the same units as the injury). Since the initial injury is 80% and the maximum restoration is 50%, the value of the initial resource loss [vI(0)] using the framework in Eqs. (1) and (2) is 1.6 times the value of the eventual restoration gain [vR(t) ∀ t ∈ (9,100)], when both are considered over the same unit area. Assuming a discount rate (r) of 3% and project benefits accruing through year 100, a traditional REA model (in continuous time) would predict that the ratio of compensatory restoration to the injured area would be 0.173units of restoration (AR) for every 1unit of injury (AI), in the case of the temporary injury. The ratio would be 1.93units of restoration for one unit of injury in the permanent injury scenarios.

4.1.2.

Economic formulation

For the purpose of simulation, it is necessary to specify a functional form for compensated inverse demand b(p,q,u0). We use the following constant elasticity formulation:  bðqðtÞ; b; MB0 ; q0 Þ ¼ MB0

 qðtÞ b q0

where q(t) is the quantity of resource services at time t, β is the elasticity of inverse demand, q0 is the quantity of resource

(a) Injury Trajectories (Loss) 100% I(t)=0.8

% ServicesLost per Area

Permanent Injury 80%

60%

Temporary Injury I(t)=(0.8)(1-t/6)

40%

20% SERVICE LOSS 0% t1=0

t2=3

I(t)=0 t3=6

t5=100 Time (years)

t4=9

(b) Restoration Trajectories (Gain)

% Services Gained per Area

100%

80%

60%

R(t)=0.5

40% R(t)=(0.5)(t-3)/6 20% SERVICE GAIN

R(t)=0 0% t1=0

t2=3

t3=6

ð11Þ

t4=9

t5=100 Time (years)

Fig. 3 – Piecewise linear injury and restoration trajectories underlying monetized REA simulations.

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services at the time of the initial injury, and MB0 is the marginal real value of the q0th unit. The constant elasticity specification highlights the difference between restoration gains and losses (compared to the linear specification, for example). This is especially true for large reductions in resource services (q), as marginal value [b(•)] approaches +∞ when the demand curve slopes downward (β < 0) and quantity goes to zero. The result is a more stringent test for the conditions under which the standard “non-monetized” REA approach may poorly approximate compensation, at least compared to the typical linear alternative.10 The full mathematical formulations of the monetized REA problem for homogeneous and heterogeneous societies described by (11) are presented in the Appendix.

4.2. time

Scenario 1: a decline in baseline resource services over

When the resource injured in an event is also suffering a longterm decline (e.g., due to development or increasing human disturbance), there will be a leftward shift of the baseline resource supply curve (in Fig. 2) over time. This increases the value of resource services late in the time horizon, thereby increasing the value of resource changes that occur late in the time horizon of the analysis. In cases where there are temporary injuries and long-term restoration benefits, our basic intuition suggests that such a trend would increase the relative value of the compensatory restoration project, thereby reducing the amount of restoration (AR) needed to compensate for the injury. In the case where both injury and restoration projects have long-term effects on resource service levels, it is intuitive to expect that the impact of increased service value over time would be mitigated, as both the injury and restoration are affected in a similar (although not equal) fashion. While the intuition is straightforward, the magnitude of the impact of including monetary value is not. Clearly, the extent to which the current per-unit value of the resource service changes is a function of both the rate at which the resource is declining and the elasticity of the inverse demand curve. However, elasticities of inverse demand for non-use values of non-market resources are difficult to evaluate. In fact, we know of very little research upon which to draw. Our goal here is to use a wide range of possible elasticities. We start with Loomis and White's (1996) meta-analysis of contingent valuation results on threatened and endangered species. They found a 0.769– 0.803% increases in willingness-to-pay for rare and endangered species (and their habitats) for a 1% decrease in population size. One might argue that the marginal resource values of these species are more sensitive to resource changes than more common resources affected in most incidents (Rollins and Lyke, 1998). Alternatively, the criticism that contingent valuation studies are relatively insensitive to scale (Kahneman and Knetsch, 1992; although see Carson et al., 2001) would suggest that the meta10 Although we do not develop the linear model here, we footnote results from a linear specification of b(·) throughout the remainder of the paper, for purposes of comparison.

Table 1 – Percentage of compensation (in AR) calculated by a traditional REA relative to a to monetized REA for longterm resource decline scenarios Decline over 100years 25% 50% 75%

Temporary injury (%)

Permanent injury (%)

β= − 0.25

β= − 0.80

β= −2.5

β= −0.25

β= −0.80

β= −2.5

102.1 104.7 108.2

107.1 116.6 131.2

125.1 171.1 299.0

100.3 100.8 101.3

101.1 102.4 104.2

103.5 107.5 112.8

analysis estimate may be low. To be conservative with regard to the range of elasticities, we examine values of β = − 2.5, − 0.80, and − 0.25. This includes the approximate Loomis and White (1996) estimate along with over threetimes and under one-third its value. At the extremes, this means that a 50% reduction in resource services results in anywhere from a 19% increase in value to a 466% increase in value (using the constant elasticity functional form in (11)). Table 1 presents a comparison of the traditional and monetized REA results for simulations where the resource services decline linearly in amount by 75%, 50%, and 25% over the 100-year time horizon.11 This range is not inconsistent with long-terms trends for heavily impacted natural resources. For example, Dahl (1990) reports a 53% long-term decline in wetlands in the contiguous United States, and 91% for California. Each cell of the table is a ratio of the estimated compensatory restoration scales (AR) for traditional to monetized REAs. A 100% result denotes that the traditional REA provides the public with 100% of the compensation predicted as necessary when explicitly including the value of the resource as calculated by the monetized REA. In interpreting these results, it is important to keep in mind that a 75% reduction in resource service supply across a society where β = −2.5 results in a 32-fold increase in the marginal value of the relevant resource services.12 In the majority of the cases presented in Table 1, the results of the monetized REA differ little from those of a traditional REA. In only four instances do they diverge by more than 17%.13 In the NRDA context, where there is often uncertainty with regard to degree of injury and the level of restoration benefits, differences of this magnitude are common (Dunford et al., 2004). In large sample contingent valuation studies, standard errors are often above 5% for a given model specification (e.g., Carson et al., 1992, 1998), and can be significantly higher. In the context where the costs to refine

11 We assume that the area of injury is 1 unit (e.g., acre) and the baseline supply of the resource is initially qB(0) = 50,000. 12 The simulations in Dunford et al. (2004) do not explicitly incorporate resource supply shifts nor do they incorporate elasticity of demand. They examine a 2% annual change in value, which they note is “small”. This equates to a 610% increase or 86% decrease in value over a 100-year time horizon. When combined with the fact that they only examine the temporary injury case, this drives their results. 13 With a linear specification of the demand curve (versus constant elasticity), only four instances diverge by more than 12%, with results ranging from 100.3% to 156.7%.

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compensatory restoration estimates are born by the responsible party, differences of less than 10% are unlikely to pass the cost/expected-benefit litmus test for additional funding. Simply put, the extra effort required to conduct additional research, which would still yield results with a standard error, may not be worth it in many cases. In four of the cases in Table 1, the traditional REA overcompensates the public by more than 25%. This does not occur in the case of a permanent injury, when both the injury and restoration occur over long time horizons. Here, the long-term resource value increase affects both the injury and restoration, largely canceling itself out. In the case of a short-term injury combined with a restoration package that provides benefits over a long time horizon (a common scenario in many oil spill cases), use of a traditional REA can be problematic in extreme cases. Specifically, this occurs when the demand for natural resources is relatively inelastic and/or the estimated decline in the resource over the next 100years is projected to be severe and does not affect the success of the restoration.14 Note that it is the extreme case, where demand is very inelastic and the resource declines 75% over 100years, when the traditional REA grossly overestimates compensation. The difficulties in forecasting such a precipitous resource decline a priori would apply to any economic valuation methodology. An additional complication of this scenario is that the rate of value increase may exceed the discount rate, implying the possibility of a degenerate solution whereby the public may be compensated with a project of infinitely small size.

4.3. Scenario 2: “market-level” effects on resource value at the local level When there is a significant local injury, it is not uncommon for local groups to be vocal about compensatory restoration actions, while state and national public interest groups may have limited knowledge of the incident. To the local consumer, the impact of the injury can be so severe that there is a significant decrease in the local supply of the resource (i.e., Δq is large relative to qB). This results in an immediate change in marginal value, which increases along the demand curve as resource service supply shifts left. Compensatory restoration that is undertaken locally (as well as resource recovery, if applicable) increases local resource supply. To compensate for the injury, the resource supply curve must move above the baseline level where the value of the marginal unit is lower than it would be without the incident. To the larger public, no large scale impact or “market level” effect has occurred (i.e., Δq is small relative to qB) and the resulting changes in marginal value associated with the injury and the restoration are negligible.

14 If the same factors that cause the severe decline in baseline resource services also affect the success of the compensatory restoration project, the project may cease to produce benefits in the long-term and the increased per-unit value of it may never be realized. This may be the case with restoration projects that address endangered and/or declining species.

Table 2 – Percentage of compensation (in AR) of traditional REA to a monetized REA limited to the local resource market Initial injury as a % of local supply 10% 25% 50%

Temporary injury (%)

Permanent injury (%)

β= −0.25

β= −0.80

β= −2.5

β= −0.25

β= − 0.80

β= −2.5

99.0 97.5 94.6

96.9 91.9 82.9

90.3 75.6 50.4

99.8 99.4 98.7

99.3 98.1 95.4

97.6 92.9 78.1

In this case, the effect of including monetary value is unambiguous. The resource has increased in marginal value in the short term, at least as far as the locals are concerned, and decreased over the long run. To them, the injury is thus more severe and the restoration less beneficial per unit than would be assumed by a traditional REA without prices. Therefore, they would require more restoration (i.e., larger AR) than predicted by a traditional REA. On the other hand, the traditional REA method will approximate full compensation for non-locals who do not face a change in price. For them, marginal values of injury and restoration have not changed, and the REA problem laid out in Eq. (2) applies directly. Given the monetized REA framework, the qualitative conditions under which a traditional REA fails to approximate welfare compensation appear straightforward. The interaction between the magnitude of the initial injury [AII (t)] relative to initial local resource supply [qB,1(0)] and the elasticity of inverse demand (β1), will determine the extent to which a traditional REA under-compensates locals. Further, the relative size of the local population (ϕl) combined with the value they ascribe to the resource when compared to non-locals will determine the extent to which local under-compensation will affect aggregate social welfare measures. For the purpose of simulation, we focus on the case where we would expect that the incorporation of monetary value might have the greatest impact on aggregate social compensation. This is when the local population is sizeable and local actors place much greater value on the resource than non-locals. Table 2 presents results from the perspective of the local population when the initial service loss from the incident results in a 10–50% decrease in the affected resource services available to the local population. As already noted, a 50% injury with an elasticity of inverse demand of β = −2.5 implies that the marginal value of the resource increases by 466% immediately following the incident. This is probably extreme. Table 2 illustrates that the traditional REA estimates differ a little from the monetized REA in most cases. These results are qualitatively similar to those in Table 1, except the traditional REA now under-compensates the public. As in the first scenario above, having long and largely overlapping time horizons for both injury and restoration appear to largely mitigate the effects of including monetary value. It is the extreme case, when elasticity of demand for local resources is high and the pollution incident injures a large percentage of the local supply of the resource, the traditional REA most

EC O L O G IC A L E C O N O M IC S 6 1 ( 2 0 07 ) 13 4 –1 45

Table 3 – Percentage of compensation (in AR) of traditional REA to a monetized REA when examining a heterogeneous society composed of local and non-local markets Initial injury as a % of local supply 10% 25% 50%

Temporary injury (%)

Permanent injury (%)

β= −0.25

β= −0.80

β= −2.5

β= − 0.25

β= −0.80

β= − 2.5

99.5 98.6 97.1

98.3 95.6 90.4

94.6 85.9 68.1

99.9 99.7 99.3

99.6 99.0 97.6

98.7 96.3 89.3

under-compensates the local public, providing only 50.4% of full compensation in the case of the temporary injury.15 The latter characteristic, whereby a large percentage of a local resource is impacted, can occur in large oil spills (e.g., Exxon Valdez). If the elasticity of inverse resource demand is high for these spills, under-compensation of local populations is likely to be an issue. Table 3 explores the same scenarios as in Table 2, but this time from the perspective of aggregate social welfare. To highlight the potential differences between traditional and monetized REA, we choose a more extreme case where the local population (ϕl) is 10% of the total population (e.g., the approximate proportion of Californians living in coastal towns in Los Angeles and Orange Counties) and places a marginal value on resource loss that is 10times greater than that of the non-local population.16 As we expect, the results here are similar to those in Table 2, only less severe because the locals make up only a portion of the total population. Nevertheless, the same basic conclusion holds: a traditional REA is consistent with the monetized REA except in cases where the demand for resources is inelastic and the impact to local resources is severe. In fact, all but three cases provide within 10% of full compensation.17

5.

Discussion and conclusions

The simulation results demonstrate several important points. In general, the direction of the bias in a traditional REA will be known for relatively general situations like those found in this paper. The magnitude of this bias can

15 With a linear specification of the demand curve (versus constant elasticity), this effect is dampened. The equivalent results for the scenarios in Table 2 range from 63.4% to 99.8%. 16 For the purpose of simulation, the marginal value at the initial service quantity for locals (MB0,1) is 10, and the same quantity for non-locals (MB0,2) is 1. Although we use the same elasticity of inverse demand for locals and non-locals (i.e., β1 = β2 = β ), we assume that the injury results in only a 0.002% reduction in resource services from the perspective of the nonlocal population. In essence, the incident has no affect on their marginal valuation of the injured resource services. 17 With a linear specification of the demand curve (versus constant elasticity), all but two scenarios in Table 3 are within 10% of full compensation, with results ranging from 78.4% to 99.9%.

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be explored. Specifically, when the injury and restoration trajectories occupy similar time horizons, they will dampen the effect of value changes over time, partially canceling each other. The traditional and monetized REA results diverge strongly from each other only when the pricechanging mechanism is strong and/or when the demand for natural resources is inelastic. The divergence is most pronounced when both occur. In most other cases, however, the difference between the two is minimal. It is also important to note that the Scenarios 1 and 2 explored above are not mutually exclusive. Should they occur simultaneously, we would expect the biases to work in opposite directions, so that they partially offset one another. Thus, while the concerns of Flores and Thacher (2002) certainly have merit, they may only be of practical importance in a limited number of cases. In evaluating both the traditional REA and the monetized REA calculations, it is important to remember that REA is intended for the calculation of “compensation”. The welfare goal is to make society indifferent to the occurrence of the incident. As Flores and Thacher (2002) note, when there is disagreement in society regarding the adequacy of a given restoration scale (AR), compensation through restoration cannot guarantee that all individuals will be indifferent to the joint resource changes resulting from injury and restoration. This is because a restoration project of scale AR is a public good. Even with the inclusion of value, the monetized REA only approximates the Hicks– Kaldor criterion and does not address the issue of postpolicy redistribution. Thus, it cannot guarantee that everyone in society is indifferent to the joint resource impacts of injury and restoration Likewise, methods that estimate the aggregate public value in market currency (e.g., contingent valuation) would face the same limitation. Even if separate values are successfully estimated for every person in society, under regulation, compensation ultimately must be provided in the form of restoration projects. Moreover, such valuation methods cannot guarantee that sufficient funds are recovered to implement the necessary restoration project(s). Alternatively, they may over-compensate the public and thereby place an unnecessary financial burden on the responsible party. Given that compensation must ultimately be “paid” in restoration projects, use of restoration-based methods for calculating compensation is attractive. For most situations examined in this paper, the assumptions used to eliminate monetary value from REA scaling calculations were not found to create a significant bias in aggregate welfare compensation. Unlike previous analyses of the potential bias, our assumptions were derived from a conventional description of preferences consistent with economic theory. Although there is often considerable uncertainty associated with the key input parameters used in our analysis (e.g., the elasticity and functional form of demand for resource services, long-term forecasts of baseline resource service quantities), our results were robust for a relatively wide range of parameter choices. We believe that this suggests the welfare biases intrinsic to a traditional REA methodology are probably minor for many NRDA cases.

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Appendix A Under the constant elasticity formulation in (11), the solution to the monetized REA problem for the homogeneous society is:

f

z X

(Z

# ) −rt h q−b bþ1 bþ1 0 e ðqB ðtÞ−AI Ij ðtÞ þ AR Rj ðtÞÞ −ðqB;j ðtÞÞ dt ;8b p −1 fta½tlj ;tuj g b þ 1

j¼1

0c

z X

(Z fta½tlj ;tuj g

j¼1

ð12Þ

) q0 e−rt ½lnðqB ðtÞ−AI Ij ðtÞ þ AR Rj ðtÞÞ−lnðqB;j ðtÞÞdt ;b ¼ −1

The right-hand side of Eq. (12) must be integrated separately over time (t) for each differentiable segment j of I(t), R(t), and qB(t), where the upper-bound of the interval is tuj and lower bound is tlj. The marginal real benefit at baseline service levels (MB0) drops out of the solution, while other economic variables, like elasticity of inverse demand (β ) and discount rate (r) do not. The solution to the analogous heterogeneous society problem becomes:

f

S X

/s

s¼1

z X

(Z

j¼1

0¼

S X

/s

s¼1

z X j¼1

) −b i MB0;s q0 s e−rs t h bs þ1 bs þ1 dt ;8Bj ðtÞ p −1 ðqB;j;s ðtÞ−AI Ij ðtÞ þ AR Rj ðtÞÞ −ðqB;j;s ðtÞÞ fta½tlj ;tuj g bj;s ðtÞ þ 1

(Z fta½tlj ;tuj g

)

ð13Þ

MB0;s q0 e−rs t ½lnðqB;j;s ðtÞ−AI Ij ðtÞ þ AR Rj ðtÞÞ−lnðqB;j;s ðtÞÞdt ;Bj ðtÞ ¼ −1

This result is of similar structure to (12), except that the absolute marginal value of each segment in society (MB0,s) now explicitly enters into the solution, along with the proportion of the population that falls within that segment (ϕs). Eqs. (12) and (13) can be solved for AR using a bisection root-finding algorithm (see Press et al., 1992), where values of the integrals are solved numerically at each iteration.

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