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1

 According to Freeman (1993), this additive property holds under traditional conditions related to resource levels and prices for

substitute goods in the household production model.

A12-1

	



	





Comprehensive, appropriate estimates of total resource

value include both use and non-use values, such that the

resulting total value estimates may be compared to total

social cost. “Non-use values, like use values, have their

basis in the theory of individual preferences and the

measurement of welfare changes. According to theory, use

values and non-use values are additive” (Freeman, 1993).1

Therefore, use values alone may seriously understate total

social values. Recent economic literature provides

substantial support for the hypothesis that non-use values

are greater than zero. Moreover, when small per capita

non-use values are held by a substantial fraction of the

population, they can be very large in the aggregate. As

stated by Freeman (1993), “... there is a real possibility that

ignoring non-use values could result in serious

misallocation of resources.”

Given that aquatic species without any direct uses account

for the majority of cooling water intake structure losses, a

comprehensive estimate of benefits of reduced

impingement and entrainment (I&E) losses requires an

estimate of non-use benefits. Stated preference methods,

or benefit transfers based on stated preference studies, are

the generally accepted techniques for estimating non-use

values. Stated preference methods rely on surveys that

assess individuals’ stated willingness-to-pay (WTP) for

specific ecological improvements, such as increased

protection of fishery resources. Benefit transfer involves

adapting research conducted for another purpose in the

available literature to address the policy questions in hand (Bergstrom and De Civita, 1999). Because benefit-cost analysis of

environmental regulations rarely affords sufficient time to develop original stated preference surveys specific to policy effects,

benefit transfer is often the only remaining option for providing information to inform policy decisions. 

Benefit transfer methods fall in three fundamental classes: 1) transfer of an unadjusted fixed value estimate generated from a

single study site, 2) the use of expert judgment to aggregate or otherwise alter benefits to be transferred from a site or set of

sites, and 3) estimation of a value estimator model derived from study site data, often from multiple sites (Bergstrom and De

Civita, 1999). Recent studies have shown little support for the accuracy or validity of method 1, leading to increased attention

to, and use of, adjusted values estimated by one of the remaining two approaches (Bergstrom and De Civita, 1999).

The following describes how EPA considered to apply method 3, often cited as a more appropriate means of benefit transfer,

for the calculation of non-use values. Meta-analysis techniques have been increasingly explored by economists as a potential

basis of policy analysis conducted by various government agencies charged with the stewardship of natural resources. 

	

A12-1 Literature Review Procedure and Organization . . A12-2

A12-2 Description of Studies . . . . . . . . . . . . . . . . . . . . . A12-3

A12-3 Semi-Log Meta-Analysis Regression Model . . . . A12-6

A12-3.1 Meta-Data for Semi-Log Model . . . . . A12-6

A12-3.2 Semi-Log Model and Results . . . . . . A12-11

A12-3.3 Interpretation of Semi-Log Regression

Analysis Results . . . . . . . . . . . . . . . . A12-14

A12-4 Log-Log Meta-Analysis Regression Model . . . A12-17

A12-4.1 Meta-Data for Log-Log Model 

(Alternative Specification) . . . . . . . . A12-17

A12-4.2 Log-Log Model and Results . . . . . . . A12-19

A12-4.3 Interpretation of Log-Log Regression

Analysis Results . . . . . . . . . . . . . . . . A12-21

A12-5 Application of the Meta-Analysis Results to the

Analysis of Non-Use Benefits of the Section 

316(b) Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . A12-22

A12-5.1 Estimating Non-Use Values Per 

Household . . . . . . . . . . . . . . . . . . . . . A12-23

A12-5.2 Estimating the Affected Populations . A12-23

A12-5.3 Estimating the Total Non-Use Value 

to the Affected Populations . . . . . . . . A12-24

A12-6 Limitations and Uncertainties . . . . . . . . . . . . . . A12-24

A12-6.1 Sensitivity Analysis of Semi-Log

 Model Based on Krinsky and Robb

 (1986) Approach . . . . . . . . . . . . . . . A12-24

A12-6.2 Sensitivity Analysis of Variable 

Assignments for Independent

Regressors . . . . . . . . . . . . . . . . . . . . . A12-24

A12-6.3 Affected Population . . . . . . . . . . . . . . A12-24
	

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2

 Meta-analysis is “the statistical analysis of a large collection of results for individual studies for the purposes of integrating the

findings” (Glass, 1976). 

A12-2

Despite the increasing application of such methods, there are few generally accepted guidelines for meta-analyses applied to

environmental policy. EPA believes that this is a promising methodology for policy valuation. However, EPA did not

include the results of this approach in the benefit analysis of the final section 316(b) regulation because of limitations and

uncertainties associated with estimation of non-use benefits on a national scale. 

The first step in implementing an “adjusted value” benefit transfer approach for estimating non-use values of environmental

regulations is a systematic analysis of the available economic studies that estimate non-use values. EPA explored available

evidence concerning total benefits (including use and non-use values) applicable to the section 316(b) regulation. EPA

identified 33 surface water valuation studies that used either stated preference or a combination of stated and revealed

preference techniques to elicit total (including use and non-use) benefit values of aquatic habitat improvements. These studies

vary in several respects, including the specific environmental change valued, the types of values estimated, the geographic

region affected by environmental changes, and survey administration methods. 

To examine the relative influence of study, economic and resource characteristics on WTP for aquatic habitat improvements

(specifically, water quality improvements that would benefit various species groups), the Agency conducted two

regression-based meta-analyses of over 78 WTP estimates for improvements to water resources, provided by the 33 original

studies.2

 The estimated econometric models can be used to calculate a range of non-use values of aquatic resources that are

potentially affected by I&E.

The following discussion summarizes results of EPA’s analysis of surface water valuation studies and outlines the

methodology for applying meta-regression results to estimating the benefits from reduced I&E attributable to the section

316(b) regulation.

	

	 !"	
#	
$	


EPA performed an in-depth search of the economic literature to identify valuation studies that estimate total WTP for quality

changes that affect aquatic life habitats and/or recreational fishing and other recreational uses. EPA used a variety of sources

and search methods to identify relevant literature:

 Review of EPA’s research and bibliographies dealing with non-market benefits associated with water quality

changes;

 Selection of surface water valuation studies from a meta-analysis conducted by Brown (1993), which includes

valuation studies addressing a wide range of resources, all of which present separate estimates of non-use value;

 Systematic review of recent issues of resource economics journals (e.g., Land Economics, Marine Resource

Economics, Journal of Environmental Economics and Management);

 Searches of online reference and abstract databases (e.g., Environmental Valuation Resource Inventory (EVRI),

Benefits Use Valuation Database (BUVD), AgEcon Search);

 Visits to homepages of authors known to have published contingent valuation studies and or water quality research;

 Searches of Web sites of agricultural and resource economics departments at several colleges and universities; and

 Searches of Web sites of organizations and agencies known to publish environmental and resource economics

valuation research [e.g., Resources for the Future (RFF), National Center for Environmental Economics (NCEE),

Natural Resource Conservation Service (NRCS), National Bureau of Economic Research (NBER)].

From this review, EPA identified approximately 300 surface water valuation studies that are potentially relevant for this

analysis, and compiled a bibliographic database to organize the literature review process. Thirty-four of these studies met the

criteria identified for inclusion in the meta-analysis, which are as follows:

 Specific amenity valued: Selected studies were limited to those in which the environmental quality change being

valued affects aquatic life and/or habitat in a waterbody that provides recreational fishing uses or other recreational

activities, such as boating, swimming, or wildlife viewing; 

 U.S. studies: Selected studies were limited to those that surveyed U.S. populations to value domestic resources; and

 Research methods: Selected studies were limited to those that applied research methods supported by journal

literature.
	

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3

 All of the selected studies used contingent valuation surveys (either discrete choice or open-ended), except for one study, which is

based on a conjoint analysis survey. One study presented combined revealed and stated preference techniques in addition to contingent

valuation results.

4

 The number of studies employing each elicitation technique does not sum to the total number of studies because some studies used

different elicitation methods, from which multiple observations were derived.

A12-3

Based on these criteria, the Agency obtained the full text articles of the 33 studies that seemed most relevant for benefit

transfer and compiled extensive information from the selected studies. The complete data set used in the meta-analysis is

provided in the public record for the final rule (see DCN #6-2900), and includes the following information:

 full study citation;

 study location;

 sample data and description (e.g., size, response rate, income);

 resource characteristics (e.g., affected waterbody type, recreational uses, baseline quality);

 environmental quality change description, including geographic scale, affected species, and affected recreational

uses (i.e., 50 percent increase in catch rates or water quality change from fishable to boatable);

 quantitative measure of environmental quality change (measured on quantitative scale based on the RFF water

quality ladder);

 study WTP values updated to 2002 dollars; and

 WTP estimation characteristics (i.e., parametric vs. nonparametric, inclusion of protest bids and outlier bids, WTP

description). 

	
%"
&%%

As noted above, EPA selected 33 surface water valuation studies that allow estimation of total values from aquatic habitat

improvements. These studies were conducted between 1973 and 2001, and applied standard, generally accepted valuation

methods (mostly stated preference techniques) to assess WTP.3

 Studies were excluded if they did not conform to general

tenets of economic theory, or if they applied methods not generally accepted in the literature. 

All selected studies focus on environmental quality changes that affect surface water resources in the contiguous U.S. Beyond

this general similarity, the studies vary in several respects. Differences include the specific environmental change valued, the

scale of environmental improvement, the geographic region affected by environmental changes, the types of values estimated,

survey administration methods, demographics of the survey sample, and statistical methods employed. The 33 studies include

17 journal articles, seven reports, four Ph.D. dissertations, three academic or staff papers, one book, and one Master’s thesis. 

Two studies (Whitehead et al., 1995; and Whitehead and Groothuis, 1992) had the same primary author and a total of nine

individuals appear as an author on more than one study.

The 33 studies selected for the meta-analysis provided 78 observations in the final data set because multiple estimates of

WTP were available from 23 studies. Some of the characteristics that allowed multiple observations to be derived from a

single study include the extent of the amenity change, the respondent population type, elicitation method(s), waterbody type,

number of waterbodies affected, recreational activities affected by the quality change, and species affected by the quality

change. Table A12-1 lists key study and resource characteristics and indicates the number of observations derived from each

study.

Surveys in 20 studies were administered by mail; seven studies collected information through personal interviews in the home,

on-site, or in a centralized location; and six surveys were conducted by telephone. Survey response rates range from 25 to 90

percent, and study sample sizes range from 109 to 2,907 responses.

The two most common methods for eliciting WTP values were the dichotomous choice method, used in 12 studies, and the

open-ended response used in 8 studies. Seven studies used the payment card approach, and 3 used the iterative bidding

method. Two studies used multiple elicitation methods to generate a single WTP estimate.4
	

  !"

A12-4

	






Author and Year Number of Observations State Waterbody Type Affected Species Affected 

Aiken (1985) 1 CO all freshwater game fish fishingAnderson and Edwards (1986) 1 RI salt pond/marshes unspecified fishing and swimAzevedo et al. (2001) 5 IA lake game fish fishing and swimBockstael et al. (1989) 2 MD estuary unspecified swimmingCameron and Huppert (1989) 1 CA river/stream game fish game fishingCarson et al. (1994) 2 CA estuary game fish; multiple categories fishingClonts and Malone (1990) 3 AL river/stream unspecified multiple usesCroke et al. (1986-1987) 9 IL river/stream all recreational fish; none boating and fishiCronin (1982) 4 DC river/stream all recreational fish fishing and swimDe Zoysa (1995) 2 OH lake; river and lake multiple categories multiple usesDesvousges et al. (1983) 2 PA river/stream unspecified boatingHayes et al. (1992) 2 RI estuary shellfish; none fishing; swimminHerriges et al. (1996) 2 IA lake all recreational fish boating and fishiHuang et al. (1997) 2 NC estuary multiple categories fishingKaoru (1993) 1 MA salt pond/marshes shellfish fishingLant and Roberts (1990) 3 IA/IL river/stream game fish; all recreational fish boating, fishing, 

and fishing

Loomis (1996) 1 WA river/stream game fish fishingLyke (1993) 2 WI lake game fish fishingMagat et al. (2000) 2 CO/NC all freshwater all aquatic species fishing; fishing aMatthews et al. (1999) 2 MN river/stream all aquatic species boating and fishiMitchell and Carson (1981) 1 National all freshwater all aquatic species fishingOlsen et al. (1991) 3 Pacific NW (ID, MT, OR, WA) river/stream game fish fishingRoberts and Leitch (1997) 1 MN/SD lake multiple categories multiple usesRowe et al. (1985) 1 CO river/stream game fish boating, fishing, Sanders et al. (1990) 4 CO river/stream unspecified swimmingSchulze et al. (1995) 2 MT river and lake multiple categories boating, fishing, Stumborg et al. (2001) 2 WI lake multiple categories multiple usesSutherland and Walsh (1985) 1 MT river and lake unspecified swimming
	

  

	






Author and Year Number of Observations State Waterbody Type Affected Species 

Welle (1986) 6 MN all freshwater multiple categories; game fish game f

fishing

Wey (1990) 2 RI salt pond/marshes shellfish otherWhitehead and Groothuis (1992) 3 NC river/stream all recreational fish multipWhitehead et al. (1995) 2 NC estuary multiple categories boatingWhittington et al. (1994) 1 TX estuary all aquatic species multipa Where multiple observations are available from a given study, waterbody type, affected species, and/or affected recreational uses may take on diffe

observations from that study. In such cases where characteristics vary within a single study, these different characteristics are listed. For example, “boating and fishing,” represents a study where one or more observations from a given study dealt with quality changes that affected boating, fishing, 

other observation from the same study dealt with boating and fishing. 

b “Multiple uses” signifies that the water quality change would affect a wide variety of uses. For most of the studies with this designation, the uses w

Source: U.S. EPA analysis for this report.
	

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A12-6

The Agency’s review of the relevant economic literature showed that available surface water valuation studies focus primarily

on water quality changes. Only 5 of the 33 studies specified environmental quality change in terms of increased fish

abundance or harvest. In addition, 2 studies valued changes in the number of acres of shellfish beds. However, most of the

reviewed studies (22) focusing on water quality improvements indicated these improvements would affect recreational fishing

among other uses, and 24 studies specifically indicated that water quality improvements would affect fish abundance or

diversity. 

From these 33 studies, the Agency compiled a data set for the meta-analysis of WTP values. EPA specified two regression

models based on these data to estimate a range of household non-use benefits. These two models include a model based on a

semi-log functional form and a model based on a log-log specification. Section A12-3 focuses on the semi-log model; the

alternative log-log specification is presented in section A12-4. Based on the peer-review results (see DCN 6-2500), the

semi-log specification can be used in the main analysis of policy alternatives; the log-log specification can be used in a

sensitivity analysis.

	

	


	

EPA estimated a semi-log model based on 78 WTP estimates for improvements in water resources, derived from 33 original

studies. These meta-data, the model specification, model results, and interpretation of results, are described in sections A12-

3.1 through A12-3.3. 

In a frequently cited work, Glass (1976) characterizes meta-analysis as “the statistical analysis of a large collection of results

for individual studies for the purposes of integrating the findings. It provides a rigorous alternative to the casual, narrative

discussion of research studies which is commonly used to make some sense of the rapidly expanding research literature” (p. 3;

cited in Poe et al. (2001), p. 138). Meta-analysis is being increasingly explored as a potential means to estimate resource

values in cases where original targeted research is impractical, or as a means to reveal systematic components of WTP (e.g.,

Poe et al., 2001; Bateman and Jones, 2003; Santos, 1998; Rosenberger and Loomis, 2000a; Smith and Osborne, 1996;

Woodward and Wui, 2001). While the literature urges caution in the use and interpretation of benefit transfers for direct

policy application (e.g., Poe et al., 2001; Desvousges et al., 1998), such methods are “widely used in the United States by

government agencies to facilitate benefit-cost analysis of public policies and projects affecting natural resources” (Bergstrom

and De Civita, 1999). Transfers based on meta-analysis are likewise common in both the United States and Canada 

(Bergstrom and De Civita, 1999). 

Depending on the suitability of available data, a meta-analysis can provide a superior alternative to the calculation and use of

a simple arithmetic mean WTP over the available observations, as it allows estimation of the systematic influence of study,

economic, and natural resource attributes on WTP. The primary advantage of a regression-based (statistical) approach is that

it accounts for differences among study characteristics that may contribute to changes in WTP, to the extent permitted by

available data. An additional advantage is that meta-analysis can reveal systematic factors influencing WTP, allowing

assessments of whether, for example, WTP estimates are (on average) sensitive to scope (Smith and Osborne, 1996).

		

Meta-analysis is largely an empirical, data-driven process, but one in which variable and model selection is guided by theory. 

Given a reliance on information available from the underlying studies that comprise the meta-data, meta-analysis models most

often represent a middle ground between model specifications that would be most theoretically appropriate and those

specifications that are possible given available data. Poe et al. (2001), Bateman and Jones (2003), Rosenberger and Loomis

(2000a), Smith and Osborne (1996), Dalhuisen et al. (2003), and others provide insight into the mechanics of specifying and

estimating meta-equations in resource economics applications.

Past meta-analyses have incorporated a range of different statistical methods, with none universally accepted as superior (e.g.,

Poole and Greenland, 1999; Bateman and Jones, 2003; Poe et al., 2001; Santos, 1998). Nonetheless, the model is estimated

following standard methods illustrated in the most recent literature. For example, there is significant consensus that models

must somehow address (or at a minimum, test for) potential correlation among observations provided by like authors or

studies and the related potential for heteroskedasticity (Bateman and Jones, 2003; Rosenberger and Loomis, 2000b). EPA

followed recent work of Bateman and Jones (2003) in applying a multilevel model specification to the meta-data, to address

potential correlation among observations gathered from single studies. Also following prior work (e.g., Poe et al., 2001;

Smith and Osborne, 1996) EPA applied the Huber-White robust variance estimation. As described by Smith and Osborne
	

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5

 EPA notes that only 10 of the 33 studies provided WTP values for non-users.

A12-7

(1996, p. 293), “this approach treats each study as the equivalent of a sample cluster with the potential for

heteroskedasticity...across clusters.” Weighted models are avoided following the arguments of Bateman and Jones (2003). 

For comparison, models were also estimated using ordinary least squares (OLS) with robust variance estimation, weighted

least squares (WLS) with robust variance estimation, and multilevel models with standard (non-robust) variance estimation. 

None of these models outperformed the illustrated model in terms of overall model significance and fit, and statistical

significance of individual coefficients (see section A12-3.2 for further details concerning the specification of the semi-log

model).

To guide development of the semi-log model and variable specifications, EPA relied upon a set of general principles. These

principles are designed to help prevent excessive data manipulations and other factors that may lead to misleading model

results. The general principles include, all else being equal:

 Fewer and simpler data transformations are preferred to more extensive ones;

 In the absence of overriding theoretical considerations, continuous variables are generally preferred to discrete

variables derived from underlying continuous distributions;

 Models should attempt to capture elements of scope and scale of resource changes;

 Models should distinguish WTP associated with different types of resources and resource uses, particularly where

relevant to the policy question at hand; and

 Where possible, exogenous constraints should be avoided in favor of “letting the data speak for themselves.”

The dependent variable in the meta-analysis is the natural logarithm of estimated household WTP for water quality

improvements in aquatic habitat, as reported in each original study. For this analysis, original study values were adjusted to

2002$ based on the relative change in Consumer Price Index (CPI) from the study year to 2002. Total WTP over the sample

ranged from $7.26 to $376.61, with a mean value of $110.70. As expected, WTP for non-users had a lower mean value of

$86.60, with a range from $27.74 to $242.34.5

All right-hand-side variables are linear, resulting in a standard semi-log functional form. This functional form has advantages

because of 1) its fit to the data, 2) the intuitive results provided by the functional form, and 3) the common use of this

functional form in the meta-analysis literature (e.g., Smith and Osborne, 1996; Santos, 1998). While linear forms are also

common in this literature (Bateman and Jones, 2003; Poe et al., 2001; Rosenberger and Loomis, 2000a,b), specifications

requiring more intensive data transformations (e.g., Box-Cox, log-log) are less common.

As noted in the preceding section, the meta-data include independent variables characterizing specifics of the resource(s)

valued such as the baseline resource conditions; the extent of resource improvements and whether they occur in estuarine or

freshwater; the geographic region and scale of resource improvements (e.g., the number of waterbodies); elicitation and

survey methods; characteristics of surveyed populations (e.g., users, non-users); and other specifics of each study. For ease of

exposition, these variables are categorized into those characterizing 1) study and methodology, 2) surveyed populations, 3)

geographic region and scale, and 4) resource improvements. Attributes included within each category are summarized below.

Study and methodology variables characterize such features as:

 The year in which a study was conducted;

 The payment vehicle and elicitation format (e.g., discrete choice versus open-ended, voluntary versus non-voluntary,

interview versus mail versus phone);

 WTP estimation methods and conventions (e.g., approaches to protest and outlier bids, use of parametric versus

nonparametric statistical methods, estimation of mean or median WTP, the use of annual or lump-sum payments);

 Reported survey response rates; and

 Whether the original survey represented water quality changes using the Resources for the Future water quality

ladder.

Surveyed populations variables characterize such features as:

 The average income of respondents; and

 Whether the survey specifically targeted non-users.
	

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6

 For example, a study by Huang et al. (1997) described current water quality as degraded from 1981 levels in terms of reduced fish

catches (60 percent) and reduced number of open shellfish beds (25 percent). However, because the water resource was still supporting

recreational fishery, the baseline water quality was set to “fishable” on the water quality ladder.

7

 For example, a study by Lyke (1993) describes the baseline conditions as follows: (1) “there are no naturally reproducing lake trout

in Lake Michigan; all lake trout found there are from hatcheries.” 2) “Lake Superior stocks of self-reproducing lake trout were much

reduced, but not wiped out, and both natural and hatchery-raised lake trout are found there.” These baseline conditions correspond to the

“game-fishable” level on the water quality ladder. The study estimates WTP for restoring natural populations of lake trout to the Wisconsin

Great Lakes. Therefore, the expected change that will occur within the “game-fishable” category is likely to be small.

A12-8

Geographic region and scale variables characterize such features as:

 The number of waterbodies affected by the policy; and

 The geographic area of the country in which the study was conducted.

Resource improvement variables characterize such features as:

 The extent of water quality change affecting different species groups;

 Baseline water quality;

 Those studies for which changes in uses other than fishing are specifically noted in the survey;

 Those studies identifying large increases in fish populations (i.e., greater than 50 percent); and

 Those studies in which the resource improvements are described (within the associated survey) as affecting uses that

are not directly affected by improvements in fishery resources (e.g., outing and swimming).

Although the interpretation and calculation of most independent variables requires little explanation, a few variables require

additional detail. These include the variables characterizing surface water quality and its measurement. Many (23)

observations in the meta-data characterize quality changes using variants of the RFF water quality ladder (e.g., Mitchell and

Carson, 1989). This scale is linked to specific pollutant levels which, in turn, are linked to presence of aquatic species and

recreational uses. However, some observations provide water quality measures using other, primarily descriptive, means that

differ from the RFF water quality ladder. 

To allow consistent comparisons of water quality change using a single scale, EPA mapped all water quality measures to the

original water quality scale (or ladder) developed and tested by RFF. Water quality ladder values were therefore developed

for those studies that did not originally use the RFF ladder. This scale was chosen for two reasons. First, a large number of

the original studies in the meta-data included RFF ladder measures as “native” components of the original surveys. Hence,

for these studies, no additional transformations were required. Second, it was decided that the use of an existing, well-tested

and accepted water quality index was in general superior to the development of a unique scale for this study.

While not all studies in the meta-data included the RFF ladder as a native survey component, in most cases the descriptions of

water quality (present in the studies that did not apply the water quality ladder) rendered mapping of water quality measures to

the RFF ladder straightforward. In cases where baseline and improved (or declined) water quality was not defined by

suitability for recreational activities (e.g., boating, fishing, swimming) or corresponding qualitative measures (e.g., poor, fair,

good), EPA used descriptive information available from studies (e.g., amount/indication of the presence of specific pollutants,

historical decline of the quality of the resource) to approximate the baseline level of water quality and the magnitude of the

change.6

 For studies that valued discrete changes in the size of species populations, EPA characterized the baseline quality

based on the current presence and prevalence of the species at hand, and assumed population increases to correspond to

modest increases in water quality in order to be conservative.7

 To account for the uncertainty involved in mapping those

studies that are not based on the RFF water quality ladder, EPA introduced the binary variable wq_ladder, which indicates

those studies in which water quality ladder measurements were an original component of the survey instrument.

Variables incorporated in the final model are listed and described in Table A12-2.
	

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A12-9

 !"#"$%&"$"'""#	

Variable Description Units and

Measurement

Mean

(Std. Dev.)

ln_WTP Natural log of WTP for specified resource improvements. Natural log of dollars

(Range: 1.98 to 5.93)

4.45

(0.78)

year_indx Year in which the study was conducted, converted to an index by

subtracting 1,970.

Year index (Range: 3 to

31)

18.51

(6.54)

discrete_ch Binary (dummy) variable indicating that WTP was estimated using a

discrete choice survey instrument.

Binary 

(Range: 0 or 1)

0.32

(0.47)

voluntary

Binary (dummy) variable indicating that WTP was estimated using a

payment vehicle described as voluntary as opposed to, for example,

property taxes.

Binary 

(Range: 0 or 1)

0.08

(0.27)

interview Binary (dummy) variable indicating that the survey conducted through

in-person interviews (default value for this dummy is a phone survey).

Binary 

(Range: 0 or 1)

0.19

(0.40)

mail Binary (dummy) variable indicating that the survey was conducted

through mail (default value for this dummy is a phone survey).

Binary 

(Range: 0 or 1)

0.54

(0.50)

lump_sum

Binary (dummy) variable indicating that payments were to occur on

something other than an annual basis over a long period of time, such as

property taxes. For example, some studies specified that payments

would occur over a five-year period.

Binary 

(Range: 0 or 1)

0.18

(0.39)

nonparam Binary (dummy) variable indicating that WTP was estimated using

nonparametric methods.

Binary 

(Range: 0 or 1)

0.47

(0.50)

wq_change

Change in mean water quality, specified on the RFF water quality ladder

(Mitchell and Carson, 1989). Defined as the difference between

baseline and post-compliance quality. Where the original study (survey)

did not use the RFF water quality ladder, EPA mapped water quality

descriptions to analogous levels on the RFF ladder to derive water

quality change (see text). Note that this variable was only included in

the final model as part of an interaction term (WQ_fish, WQ_shell,

WQ_many, WQ_non).

Water quality ladder

units (Range: 0.5 to

5.75)

2.45

(1.06)

wq_ladder Binary (dummy) variable indicating that the original survey reported

resource changes using a standard RFF water quality ladder.

Binary 

(Range: 0 or 1)

0.29

(0.46)

protest_bids Binary (dummy) variable indicating that protest bids were excluded

when estimating WTP.

Binary 

(Range: 0 or 1)

0.47

(0.50)

outlier_bids Binary (dummy) variable indicating that outlier bids were excluded

when estimating WTP.

Binary 

(Range: 0 or 1)

0.23

(0.42)

median_WTP Binary (dummy) variable indicating that the study reported median, not

mean, WTP.

Binary 

(Range: 0 or 1)

0.06

(0.25)

hi_response Binary (dummy) variable indicating that the survey response rate

exceeds 74 percent (i.e., 75 percent or above).

Binary 

(Range: 0 or 1)

0.32

(0.47)

income

Mean income of survey respondents, either as reported by the original

survey or calculated by EPA based on U.S. Census Bureau averages for

the original surveyed region.

Dollars (Range: 30,396

to 137,693)

47,189.37

(13,010.15)

nonusers

Binary (dummy) variable indicating that the survey is implemented over

a population of non-users (default category for this dummy is a survey

of any population that includes users).

Binary 

(Range: 0 or 1)

0.19

(0.40)

single_rivera Binary (dummy) variable indicating that resource change explicitly takes

place over a single river (default is a change in an estuary).

Binary 

(Range: 0 or 1)

0.21

(0.41)

single_lake b Binary (dummy) variable indicating that resource change explicitly takes

place over a single lake (default is a change in an estuary).

Binary 

(Range: 0 or 1)

0.13

(0.34)

multiple_river Binary (dummy) variable indicating that resource change explicitly takes

place over multiple rivers (default is a change in an estuary).

Binary 

(Range: 0 or 1)

0.09

(0.29)
	

  !"	#$%& %'

 !"#"$%&"$"'""#	

Variable Description Units and

Measurement

Mean

(Std. Dev.)

A12-10

salt_pond Binary (dummy) variable indicating that resource change explicitly takes

place over multiple salt ponds (default is a change in an estuary).

Binary 

(Range: 0 or 1)

0.05

(0.22)

num_riv_pond

Number of rivers or salt ponds affected by policy; if unspecified

num_riv_pond = 0. (In the present data, only studies addressing rivers

and lakes specified >1 number of waterbodies. All others specified

either 1 waterbody, or the number was unspecified.)

Number of specified

rivers or ponds (Range:

0 to 15)

1.41

(3.63)

regional_fresh

Binary (dummy) variable indicating that resource change explicitly takes

place in a fresh waterbody (default is a change in a salt waterbody or an

estuary).

Binary 

(Range: 0 or 1)

0.37

(0.49)

southeast Binary (dummy) variable indicating that survey was conducted in the

USDA southeast region (default is northeast region).

Binary 

(Range: 0 or 1)

0.13

(0.34)

pacif_mount Binary (dummy) variable indicating that survey was conducted in the

USDA pacific/mountain region.

Binary 

(Range: 0 or 1)

0.21

(0.41)

plains Binary (dummy) variable indicating that survey was conducted in the

USDA northern or southern plains region.

Binary 

(Range: 0 or 1)

0.03

(0.16)

mult_reg Binary (dummy) variable indicating that survey included respondents

from more than one of the section 316(b) regions.

Binary 

(Range: 0 or 1)

0.04

(0.19)

WQ_fish

Interaction variable: wq_change multiplied by a binary (dummy)

variable identifying studies in which water quality improvements are

stated to benefit only fin fish species.c

 Default is zero (i.e., water quality

change did not affect fish).

Water quality ladder

units (Range: 0.5 to

5.75)

1.13

(1.54)

WQ_shell

Interaction variable: wq_change multiplied by a binary (dummy)

variable identifying studies in which water quality improvements are

stated to benefit only shellfish.c

 Default is zero (i.e., water quality

change did not affect shellfish).

Water quality ladder

units (Range: 0.5 to

4.0)

0.13

(0.65)

WQ_many

Interaction variable: wq_change multiplied by a binary (dummy)

variable identifying studies in which water quality improvements are

stated to benefit multiple species types (including fish, shellfish, and

birds).c

 Default is zero (i.e., water quality change did not affect multiple

species).

Water quality ladder

units (Range: 0.5 to

4.0)

0.65

(1.21)

WQ_non

Interaction variable: wq_change multiplied by a binary (dummy)

variable identifying studies in which species benefitting from water

quality improvements remain unspecified.c

 Default is zero (i.e., water

quality change affected specified species).

Water quality ladder

units (Range: 0.5 to

2.5)

0.53

(0.94)

nonfish_uses Binary (dummy) variable identifying studies in which changes in uses

other than fishing are specifically noted in the survey.

Binary 

(Range: 0 or 1)

0.76

(0.43)

fishplus Binary (dummy) variable identifying studies in which a fish population

or harvest change of 50 percent or greater is reported in the survey.

Binary 

(Range: 0 or 1)

0.13

(0.34)

baseline Baseline water quality, specified on the RFF water quality ladder. Water quality ladder

units (Range: 0 to 7)

4.66

(2.49)

a. Examples of rivers and streams considered in the studies include the Columbia, Potomac, Elwha, Eagle, and Tar-Pamlico rivers.

b

 Includes one study that focused on a segment of the Lake Erie shoreline.

c

 The variable wq_change is defined earlier in this table as the difference between baseline and post-compliance quality, specified on

the RFF water quality ladder (Mitchell and Carson, 1989).

Source: U.S. EPA analysis for this report.
	

  !"	#$%& %'

8

 EPA estimated the Box-Cox exponent (Lambda ) for the independent variables only. In addition, the Box-Cox transformation was

only tested for continuous variables (i.e., dummy variables were not transformed, following standard practice). The Box-Cox test strongly

rejects the log-log specification (Lambda= 0); it also strongly rejects the multiplicative inverse specification of independent variables

(Lambda= -1). However, it fails to reject the semi-log specification, or linear specification of independent variables (Lambda=1). 

A12-11

	#"("



As noted above, EPA estimated the meta-analysis regression using a multilevel, random-effects specification. This model

follows the general approach of Bateman and Jones (2003). Multilevel (or hierarchical) models may be estimated as either

random-effects or random-coefficients models, and are described in detail elsewhere (Goldstein, 1995; Singer, 1998). The

fundamental distinction between these and classical linear models is the two-part modeling of the equation error to account

for hierarchical data. Here, the meta-data are comprised of multiple observations per study, and there is a corresponding

possibility of correlated errors among observations that share a common study or author.

The common approach to modeling such potential correlation is to divide the residual variance of estimates into two parts, a

random error that is independently and identically distributed across all studies and for each observation, and a random effect

that represents systematic variation related to each study. The model is estimated as a two-level hierarchy, with level one

corresponding to non-use value estimates (individual observations), and level two corresponding to individual studies. The

random-effect may be interpreted as a deviation from the mean equation intercept associated with individual studies (Bateman

and Jones, 2003). The model is estimated using a maximum likelihood estimator (MLE), assuming that random effects are

distributed multivariate normal. Following Bateman and Jones (2003), observations are unweighted. Covariances are

obtained using the Huber-White covariance estimator (Smith and Osborne, 1996). Random-effects models such as the

multilevel model applied here are becoming increasingly standard in resource economics applications, and are estimable using

a variety of readily available software packages.

 A note on functional form

The dependent variable in the semi-log model is the natural log of WTP for surface water quality improvement, as shown by

Table A12-2. The combination of this dependent variable with linear independent variables results in a common semi-log

functional form. This functional form was chosen based on a combination of theoretical and empirical factors. Of particular

importance was the performance of the semi-log model with regard to 1) data fit, 2) intuitive nature of results, and 3) history

in the meta-analysis literature (e.g., Smith and Osborne, 1996; Santos, 1998). 

The semi-log model was chosen over the linear model based on the ability of the semi-log form to capture curvature in the

valuation function and its improved fit to the data. It also allows independent variables to influence WTP (after

transformation from its natural log) in a multiplicative rather than additive manner.

The choice between log-log and semi-log functional forms is somewhat less straightforward. An appropriately specified loglog model has the theoretical advantage of requiring WTP to be zero when quality change is also equal to zero. The semi-log

model does not impose this exogenous restriction. However, in the present context, it is questionable whether this restriction

is justified by the meta-data. Average WTP in the data is approximately $111, with WTP values in the lowest 95th percentile

of approximately $21. There are no zero WTP values in the data, and no studies for which water quality change approaches

zero. Hence, the extreme low-end of any model specification forecasts beyond the range of available data. The ability of a

model specification to restrict the WTP equation at a point beyond the reach of the available data may be of questionable

empirical value — particularly given that threshold effects or nonconvexities may influence WTP at extremely low levels of

quality change. 

Given the questions about a priori restrictions on the functional form, final decisions regarding functional forms were made

based on a combination of general principles and empirical performance. Based on these criteria, the semi-log model seems

to outperform the log-log model. First, EPA used the Box-Cox method to see wether the data suggest linear independent

variables or log dependent variables.8

 The Box-Cox test rejected the log specification. Moreover, the overall significance

level of many variables is better in the semi-log model, including key variables characterizing such features as baseline water

quality, water quality change, and the number of waterbodies affected by a policy.

From an empirical standpoint, another benefit of the semi-log specification is that it provides intuitive forecasts of WTP for

marginal (small) quality changes at the low end of the data. For example, using the final semi-log specification, the difference

in WTP between a 1 percent and 3 percent improvement in water quality (a barely perceptible difference for most
	

  !"	#$%& %'

A12-12

respondents) is fairly small: far less than $1 in most model specifications. In contrast, log-log models tend to forecast fairly

large relative changes in WTP for very small changes in water quality improvements.

 A note on model specification

Following standard econometric practice, the final model is specified based on guidance from theory and prior literature. For

example, Arrow et al. (1993) make a fundamental distinction between discrete choice and open-ended payment mechanisms

(where open ended include iterative bidding, payment cards, etc.). Hence, this is the distinction made in the final model (i.e.,

including the variable discrete_ch). Similarly, other “survey methodology” variables in the model were chosen based on

theoretical considerations and prior findings in the literature (e.g., voluntary vs. mandatory payment vehicles, parametric vs.

non-parametric, treatment of protest and outlier bids, use of mean versus median WTP). 

Few variables were excluded solely because of lack of statistical significance. Individual variables were only excluded if they

could not be shown to be statistically significant in any version of the model (restricted or unrestricted), and there was no

overriding rationale for retaining the variable in the model. For example, variables distinguishing different types of discrete

choice instruments (e.g., conjoint vs. dichotomous choice) added no significant explanatory power to the model (p=0.44). 

Another example of excluded variables involves a set of variables identifying waterbody uses. While the model includes a

key variable (nonfish_uses) distinguishing studies in which non-fishing uses were emphasized, the model excludes variables

characterizing specific uses of included waterbodies. These variables are suppressed for a variety of reasons. First,

substantial variability of types and magnitudes of uses present in the 78 different observations prevented a simple

characterization of specific uses in a reasonable number of variables. Attempts to approximate such effects using information

available in the original published studies produced unsatisfactory results — the associated variables were insignificant as a

group in all model variants (tested as a group in the final model, 2

=9.04 with df=8, such that p=0.31). Moreover, the

primary purpose of the model is to assess non-use values for habitat improvements (affecting fish) in “average” waterbodies

supporting a variety of uses. 

It is important to note that although empirical considerations certainly play a role in model development, certain variables

were retained in the model for theoretical reasons, even if significance levels were low. Such specification of meta-analysis

models using a combination of theoretical guidance and empirical considerations is standard in modeling efforts. 

"("

Table A12-3 presents results of the semi-log model. 
	

  !"	#$%& %'

A12-13

 "	(&	"("'	 

)*+($,
%&#"

Variable Parameter Estimate Standard Error t Value Prob > |t|

intercept 6.0158 0.6163 9.7600 <.0001

year_indx -0.1072 0.0187 -5.7400 <.0001

discrete_ch 0.3956 0.3728 1.0600 0.2961

voluntary -1.6330 0.2441 -6.6900 <.0001

interview 1.3252 0.2330 5.6900 <.0001

mail 0.5666 0.1774 3.1900 0.0030

lump_sum 0.5954 0.2526 2.3600 0.0243

nonparam -0.4472 0.2228 -2.0100 0.0527

wq_ladder -0.3799 0.2069 -1.8400 0.0751

protest_bids 0.9537 0.1580 6.0400 <.0001

outlier_bids -0.8764 0.1212 -7.2300 <.0001

median_WTP 0.2206 0.1625 1.3600 0.1836

hi_response -0.8094 0.1223 -6.6200 <.0001

income 0.0000 0.0000 0.1100 0.9128

nonusers -0.5017 0.1189 -4.2200 0.0002

single_river -0.3378 0.2189 -1.5400 0.1321

single_lake 0.3193 0.2723 1.1700 0.2492

multiple_river -1.6050 0.3020 -5.3200 <.0001

salt_pond 0.7574 0.3650 2.0800 0.0456

num_rivers_ponds 0.0791 0.0094 8.4100 <.0001

regional_fresh -0.0073 0.1664 -0.0400 0.9655

southeast 1.1482 0.2175 5.2800 <.0001

pacif_mount -0.3125 0.1329 -2.3500 0.0246

plains -0.8153 0.3173 -2.5700 0.0147

mult_reg 0.5951 0.2548 2.3400 0.0256

WQ_fish 0.2055 0.0861 2.3900 0.0227

WQ_shell 0.2561 0.0999 2.5600 0.0149

WQ_many 0.2332 0.1107 2.1100 0.0426

WQ_non 0.4695 0.2117 2.2200 0.0334

nonfish_uses -0.1412 0.1841 -0.7700 0.4484

fishplus 0.8052 0.1951 4.1300 0.0002

baseline -0.1265 0.0425 -2.9800 0.0053

Error Term (2

) 0.1151

-2 Log Likelihood 65.6

Covariance Factors:

Study Level (u) 6.19 x 10-18

Residual (e) 0.1357

Source: U.S. EPA analysis for this report.
	

  !"	#$%& %'

9

 The Northeast region, as defined in Feather et al. (1999), encompasses all of the states in the National Marine Fisheries Service

(NMFS) Marine Recreational Fisheries Statistics Survey (MRFSS) North Atlantic region. The Northeast region also corresponds most

closely to the MRFSS Mid-Atlantic region, as well as those states bordering the Great Lakes, which comprise the Great Lakes region used

in this analysis.

10 Technically, this variable is the sum of two interaction variables: 1) an interaction between multiple_river and the number of

waterbodies noted in the survey (0 if unspecified), and 2) an interaction between salt_pond and the number of waterbodies noted in the

survey (0 if unspecified).

A12-14


#%#""##-"""("

Regression results reveal strong systematic elements influencing WTP. The analysis finds both statistically significant and

intuitive patterns that influence WTP for water quality improvements in aquatic habitats. In general, the statistical fit of the

equation is quite good; there is a strong systematic element of WTP variation that allows forecasting of WTP based on site

and study characteristics. The model as a whole is statistically significant at p<0.0001. The adjusted R-square is 0.77. Of the

31 independent variables in the restricted model (not including the intercept), 24 are statistically significant at the 10 percent

level, with most statistically significant at the 1 percent level. Signs of significant parameter estimates generally correspond

with intuition, where prior expectations exist. As shown in Table A12-3, the random effect is statistically insignificant (i.e.,

study level covariance factors are essentially zero). Considering these factors, the statistical fit of the semi-log model

compares quite favorably to prior meta-analyses present in the literature.

"($%&#$"

Seven variables characterize resource improvements; all are of the expected sign. The variables WQ_fish, WQ_shell,

WQ_many, and WQ_non indicate the effects of water quality improvements associated with gains in fish, shellfish, multiple

species, and unspecified habitat, respectively (see Tables A12-2 and A12-3). (One of the key advantages of the model is that

it distinguishes among marginal water quality gains that influence these different types of aquatic species.) All signs are as

expected. All four associated coefficients are positive and statistically significant (p<0.05 or better), indicating that higher

WTP is associated with larger gains in water quality. This is an important result, and indicates that WTP is sensitive to the

scope of water quality improvements. Moreover, the model reveals that water quality changes affecting different types of

habitat (e.g., fish only, shellfish only, unspecified, or multiple species) may have substantially divergent WTP values. Given

the focus of the section 316(b) rule on fish only, the ability of the model to distinguish habitat quality improvements targeted

solely at fish is an important element of the model.

Another important and theoretically intuitive finding is that WTP for water quality improvements declines as baseline water

quality increases. The variable baseline represents the baseline water quality from which water quality change would occur. 

The associated parameter estimate is significant (p<0.01) and has the expected negative sign, revealing diminishing returns to

scale for water quality improvements. This finding suggests that the model is not only sensitive to scope at a broad level (i.e.,

larger water quality improvements generate larger WTP), but also is able to distinguish more subtle, if no less important,

scope effects (WTP for marginal water quality improvements declines as baseline water quality improves).

Finally, the variable fishplus identifies those studies for which the associated survey identified particularly large gains in fish

populations or harvest rates (>50 percent). The positive and statistically significant result (p<0.01) indicates that large gains

in fish populations or harvests are associated with statistically significant increases in total WTP.


%'$##"$$"

Ten binary variables characterize geographic region and scale; seven are statistically significant at p<0.10. The default

category from which these variables allow systematic variations in WTP is an estuarine waterbody in the northeast U.S.9

Compared to this baseline, WTP associated with rivers is lower (single_river and multiple_river both have negative and

significant values). Single_lake and regional_fresh both have positive values, but neither is significant. WTP for water

quality gains in salt ponds (salt_pond) is higher than for estuaries (p<0.05). This is not surprising since water quality gains in

salt ponds correspond to an increase in the number of acres of shellfish beds.

Of particular importance for the general validity of empirical findings, the model results further suggest that WTP is sensitive

to the number of waterbodies under consideration. Of the waterbody categories distinguished above, both rivers and salt

ponds allowed variation in numbers of affected waterbodies explicitly described by the survey. This variation is captured by

the variable num_riv_pond (see Table A12-2).10 The associated parameter estimate is statistically significant (p<0.01) and

indicates that WTP increases with the number of waterbodies considered. This result, combined with the statistical
	

  !"	#$%& %'

A12-15

significance of the water quality change variables noted above, suggests that WTP values (in this case for water quality

improvements) are strongly sensitive to scope, both in terms of the number of waterbodies considered and the magnitude of

water quality change. 

Finally, the regional indicator variables southeast, pacif_mount, plains, and mult_reg are statistically significant at p<0.05,

suggesting that there are significant differences among WTP estimates from surveys in different geographical regions of the

U.S. This suggests that socio-economic and cultural factors that vary by region (but that could not be included in this model),

such as education level or occupation, may affect WTP. In some cases, however, the large magnitude of these regional effects

suggests that spurious or otherwise unexplained effects (e.g., the effect of specific researchers who appear more than once in

the data) may drive their overall magnitude. For example, the size of the positive parameter estimate associated with WTP in

the southeast U.S. leads in many cases to relatively large increases in WTP for southeast policies — a finding that defies

simple intuitive explanation. Hence, EPA believes that particular, spurious, or unexplained aspects of studies from this region

may have caused the associated parameter estimate to have a larger-than-expected influence on WTP. 

$(&-%%(#"$"

Only two variables, nonusers and income, are used to characterize surveyed populations. In particular, the nonusers variable

is of substantial policy relevance. The negative and strongly significant (p<.0001) parameter estimate indicates that surveys

of non-users only, who by definition only have non-use values for the resource improvements in question (cf. Freeman, 2003,

p. 142), generate lower WTP values than surveys that include users, who may have both use and non-use values. Based on

this statistically significant result, EPA is able to use the model to estimate non-use values, interpreted as the mean WTP

values estimated by surveys of non-users only (see section A12-5). Such methods, however, may underestimate non-use

values of the general population, if the non-use values of users exceed those of non-users (Whitehead and Blomquist, 1991b).

The income parameter estimate is positive, as expected, but is not statistically significant. 

(-#'-$"

A variety of study and methodology effects can be shown to influence WTP for water quality improvements. While not

surprising, this does indicate that the methodological approach influences WTP, as argued by Arrow et al. (1993). Of 12

variables characterizing study and methodological effects, 10 are statistically significant at p<0.10. Among these is the year

in which a study was conducted (year_indx, a continuous variable), with later studies associated with lower WTP. This is the

expected result, as the focus of survey design over time has often been on the reduction of survey biases that would otherwise

result in an overstatement of WTP (Arrow et al., 1993). 

Model results reveal that voluntary (voluntary=1) payment vehicles (i.e., surveys that describe hypothetical payments as

voluntary) are associated with reduced WTP estimates. This result counters common intuition and empirical findings that

voluntary payment vehicles are associated with overstatements of true WTP (Carson et al., 2000). The reason for this

counter-intuitive finding is unknown, but may be a feature of the small number of studies that applied voluntary mechanisms. 

Reduced WTP estimates are also associated with studies applying nonparametric methods to WTP estimation (nonparam). 

Survey elicitation method does not have a strong effect in this model; studies using discrete choice formats have higher WTP

values, but this difference is not statistically significant. 

Smaller WTP estimates are associated with studies that eliminate or trim outlier bids when estimating WTP (outlier_bids=1;

p<0.01). However, increased WTP estimates are associated with studies that seek to eliminate protest bids (protest_bids=1;

p<0.01). While one might assume that elimination of protest bids would reduce WTP, this is based on a perhaps mistaken

presumption that only high protest bids are excluded. In many cases WTP estimates may also exclude protest “zeros,” or zero

bids. As a result, there is no a priori necessary expected sign for this effect. Studies that report median WTP (median_WTP)

have higher WTP values, but this effect is not statistically significant. Nonetheless, this variable is retained for theoretical

reasons.

Studies with high response rates (hi_response=1; p<0.01) are associated with lower WTP estimates — an expected result. In

addition, lower WTP is associated with the use of the RFF water quality ladder in the original survey (wq_ladder=1; p<0.10). 

As is the case with a variety of study design variables, there is no necessary expectation with respect to the direction of this

effect. Nonetheless, this finding might suggest the capacity of such scales to clarify the specific magnitude and implications

of water quality change, and hence (perhaps) reduce methodological misspecification or symbolic biases that might act to

systematically inflate estimated WTP.
	

  !"	#$%& %'

A12-16

Survey format variables also have an effect on WTP, as might be expected. Interview and mail both have positive and

statistically significant coefficients (p<0.01), compared to the default of telephone surveys. It may be possible that the

interview survey format results in larger WTP values either because the respondents are better able to understand the

valuation scenario, or because respondents may feel pressure from interviewers to bias their WTP estimates upward. There is

no a priori explanation for the difference between mail surveys and phone surveys. Finally, as expected, studies that ask

respondents to report an annual payment (as opposed to a lump_sum payment) have lower WTP estimates (p<0.05).

	#"

The validity and reliability of benefit transfer — including that based on meta-analysis — depends on a variety of factors. 

While benefit transfer can provide valid measures of use and non-use benefits, tests of its performance have provided mixed

results (e.g., Desvousges et al., 1998; Vandenberg et al., 2001; Smith et al., 2002). Nonetheless, benefit transfers are

increasingly applied as a core component of benefit cost analyses conducted by EPA and other government agencies

(Bergstrom and De Civita, 1999; Griffiths, undated). Moreover, Smith et al. (2002, p. 134) argue that “nearly all benefit cost

analyses rely on benefit transfers, whether they acknowledge it or not.” Given the increasing [or as Smith et al. (2002) might

argue, universal] use of benefit transfers, an increasing focus is on the empirical properties of applied transfer methods and

models.

Although the statistical performance of the model is quite good, EPA notes several limitations of the model. These limitations

stem largely from information available from the original studies, as well as degrees of freedom and statistical significance. 

An important factor in any benefit transfer is the ability of the study site or estimated valuation equation to approximate the

resource and context under which benefit estimates are desired. As is common, the meta-analysis model presented here

provides a close but not perfect match to the context in which values are desired. Specifically, the model estimates WTP for

marginal improvements to aquatic habitat that directly benefit fish populations. The specification of the model distinguishes

improvements that benefit only fish populations from those that benefit other aquatic or non-aquatic species (as stated in the

original surveys whose WTP estimates are incorporated in the meta-analysis). The model also distinguishes effects related to

surveys emphasizing non-fishing uses of affected waterbodies. However, the original studies in the meta-analysis do not (in

general) value individual fish. Hence, additional assumptions are required to estimate non-use values; these are discussed in

section A12-5.

Additional limitations relate to the paucity of demographic variables available for inclusion in the model. The only

demographic variable incorporated in the analysis (income) was not statistically significant. Moreover, other demographic

variables are unavailable. EPA recognizes that the model is statistically significant and allows estimation of WTP from study

and site characteristics. However, strictly speaking, model findings are relative to the specific case studies considered, and

must be viewed within the context of 78-observation data set, with all the appropriate caveats. Although this represents a

fairly standard-to-large sample-size for a meta-analysis in this context, it is relatively small relative to other statistical

applications in resource and environmental economics. Model results are also subject to choices regarding functional form

and statistical approach, although many of the primary model effects are robust to reasonable changes in functional form

and/or statistical methods. The rationale for the specific functional form chosen here (the semi-log form) is detailed above.

Finally, the relatively large (positive) magnitude of the parameter estimate for the southeastern U.S. regional dummy variable 

(southeast) leads EPA to question the appropriate interpretation of this effect. While it is theoretically possible that WTP for

water quality changes is substantially higher in the southeast, the magnitude of the effect suggested by the model seems

unlikely from an intuitive perspective. As suggested above, it is possible that spurious, unexplained factors influence the

magnitude of this parameter in the present model. However, assessments of preliminary model runs suggest that this effect is

relatively robust given the present data and selection of variables available. Nonetheless, EPA recommends that the

magnitude of the predicted shift in WTP associated with the southeast region should be viewed with caution.

Based on the results presented in Table A12-3, EPA estimated WTP for water resource changes as a function of resource,

regional, and study design attributes (see section A12-5). This, in general, provides a superior alternative to the calculation

and use of a simple arithmetic mean over the 78 observations, as it allows WTP to be adjusted to account for the

characteristics of the transfer site. The ability of the model to appropriately adjust WTP is suggested by the many systematic

(statistically significant) patterns revealed by the meta-analysis regression model. Nonetheless, the use (and interpretation) of

such WTP estimates for benefit transfer is subject to the constraints and concerns expressed elsewhere in the literature (e.g.,

Vandenberg et al., 2001; Desvousges et al., 1998; Poe et al., 2001).
	

  !"	#$%& %'

A12-17

.

	


	

The following sections present the results for the alternative log-log meta-analysis regression model. Section A12-4.1

presents the data and variable specifications used to estimate the log-log model; section A12-4.2 presents the results of the

log-log model; and section A12-4.3 discusses and interprets the findings of the log-log model.

.		/#&%$$#0

The dependent variable in the log-log meta-analysis is the natural log of estimated WTP (2002$) for water quality

improvements as reported in each original study. Right-hand-side continuous and categorical variables relate to study and

methodology, population, spatial, and water quality characteristics.

Study and methodology variables characterize such features as:

 The year in which the study was conducted. For this model, a binary variable that identifies those studies conducted

in 1990 or before was employed. A continuous variable for the study year would be problematic for the log-log

form. EPA selected 1990 for the break in light of the increased attention to stated preference methods following the

Exxon Valdez disaster.

 Whether a discrete choice model was used.

 The survey mode of administration (telephone surveys are the default category).

 Whether the payment vehicle was voluntary.

 Whether WTP was expressed in terms of something other than an annual payment, such as a lump sum or a series of

installments.

 Whether the WTP was estimated using a parametric model.

 Whether protest or outlier bids were discarded before WTP was estimated.

Surveyed population variables characterize such features as:

 Mean income of respondents.

 Whether the sample or sub-sample consisted of users, non-users, or a general population that included both. These

appear in the model as interactions with the water quality change variable.

 Whether the sample included non-local respondents, such as might occur using an intercept survey.

Spatial variables characterize such features as:

 The waterbody type and scale. The default category reflects large saltwater bodies.

 Region of the country. The Northeast is the default region.

 Whether the aquatic resource is known primary as a Superfund site on the National Priority List. This variable is

intended to single out and control for one particular study (Schulze et al., 1995).

Water quality variables characterize such features as:

 Whether the change scenario focused on wildlife, on fish specifically, or on a broader set of attributes (that may

have included recreational opportunities or aesthetic qualities). Those that are more general compose the default

category.

 The desired level of water quality. This performs a function analogous to incorporating the baseline water quality

level into the model but avoid issues associated with taking the natural log of 0.

 The extent of water quality change.

Eighty-two observations from 33 studies were used to estimate the model. Variables incorporated in the final model are listed

and described in Table A12-4.
	

  !"	#$%& %'

A12-18

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Variable Description Units and

Measurement

Mean

(Std. Dev.)

ln_wtp Natural log of WTP for specified resource improvements. Natural log of dollars 4.55 (0.80)

year1990 Binary (dummy) variable indicating that the year of the study was 1990

or earlier.

Binary 0.66

discrete_ch Binary (dummy) variable indicating that WTP was estimated using a

discrete choice survey instrument.

Binary 0.33

interview Binary (dummy) variable indicating that the survey used an interview

mode of administration. Binary 0.24

mail Binary (dummy) variable indicating that the survey used an mail-in mode

of administration. Binary 0.54

voluntary Binary (dummy) variable indicating that WTP was estimated using a

payment vehicle described as voluntary.

Binary 0.16

lump_sum Binary (dummy) variable indicating that payment was to occur on

something other than an annual basis. Binary 0.20

nonparam Binary (dummy) variable indicating that WTP was estimated using

nonparametric methods.

Binary 0.46

protest_bids Binary (dummy) variable indicating that protest bids were excluded when

estimating WTP.

Binary 0.44

outlier_bids Binary (dummy) variable indicating that outlier bids were excluded when

estimating WTP.

Binary 0.24

ln_income Natural log of the mean income of survey respondents. Natural log of

thousands of dollars 3.82 (0.20)

nonusers Binary (dummy) variable indicating that the WTP estimate is based upon

a sample of non-users. Binary 0.17

users Binary (dummy) variable indicating that the WTP estimate is based upon

a sample of users. Binary 0.26

genpop Binary (dummy) variable indicating that the WTP estimate is based upon

a sample of a general population consisting of both users and non-users. Binary 0.57

nonlocal Binary (dummy) variable indicating that the WTP estimate is based upon

a sample not limited to locals. Binary 0.46

small_rivers Binary (dummy) variable indicating that the water quality change affects

river resources of a small region, e.g., the Potomac River in DC. Binary 0.18

large_rivers Binary (dummy) variable indicating that the water quality change affects

river resources of a large region, e.g., the Columbia River Basin. Binary 0.21

small_lakes Binary (dummy) variable indicating that the water quality change affects

lake resources of a small region, e.g., Clear Lake, IO. Binary 0.12

large_lakes Binary (dummy) variable indicating that the water quality change affects

lake resources of a large region, e.g., Lake Michigan. Binary 0.05

small_fresh

Binary (dummy) variable indicating that the water quality change affects

fresh water resources — either unspecified or a combination of types —

of a small region.

Binary 0.09

large_fresh

Binary (dummy) variable indicating that the water quality change affects

fresh water resources — either unspecified or a combination of types —

of a large region, e.g., lake and streams of northeastern MN.

Binary 0.11

natl_fresh Binary (dummy) variable indicating that the water quality change affects

fresh water resources nationwide. Binary 0.06

small_salt Binary (dummy) variable indicating that the water quality change affects

saltwater resources in a limited area. Binary 0.07
	

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Variable Description Units and

Measurement

Mean

(Std. Dev.)

A12-19

great_lakes Binary (dummy) variable indicating that survey was conducted in the

Great Lakes region. Binary 0.37

pacif_mount Binary (dummy) variable indicating that survey was conducted in the

Pacific/mountain region. Binary 0.18

plains Binary (dummy) variable indicating that survey was conducted in the

Plains region. Binary 0.09

southeast Binary (dummy) variable indicating that survey was conducted in the

Southeast region. Binary 013

multi_reg Binary (dummy) variable indicating that survey was conducted in

multiple regions. Binary 0.09

npl Binary (dummy) variable indicating that the aquatic resource is known

primarily as a Superfund site. Binary 0.02

wildlife Binary (dummy) variable indicating that the changes valued relate

expressly to wildlife populations. Binary 0.05

fish_only Binary (dummy) variable indicating that the changes valued relate

expressly to fish populations. Binary 0.15

ln_hiwq Natural log of desired water quality level expressed on a 0-100 scale.

Natural log of

desired water quality

level

4.30 (0.35)

ln_chwq Natural log of water quality change expressed on a 0-100 scale. Natural log of water

quality change 3.77 (0.38)

Source: U.S. EPA analysis, for this report.

.	#"("



In light of the absence of a standard approach to developing parametric models to synthesize valuation summary results, there is

good reason to explore and report on an alternative to the semi-log model that makes different, though plausible, assumptions

for a few critical aspects of the meta-analysis. Although the two models share many features (e.g., their consideration of random

effects), the alternative model developed by EPA departs from the former in three significant ways:

 Functional form

The first significant difference between the two models is that the alternative model takes a log-log form, i.e., the natural log

of both the dependent variable and all covariates are taken. This functional form makes sense on three counts. First, study

features and resource characteristics likely affect WTP in a multiplicative, rather than additive, fashion. With the log-log

form, this is how explanatory variables affect the underlying (un-logged) dependent variable. Second, this functional form

has the desirable feature of associating a WTP of $0 with any scenario in which no water quality change has occurred. Third,

by forcing the curve through the origin, the model increases sensitivity of the WTP estimates to the magnitude of the water

quality change, i.e., scope.

 Water quality change index

The second difference between the two models is that the alternative model uses a different approach to mapping the

somewhat disparate scenarios valued by respondents in the original studies onto a water quality metric. For the alternative

model, EPA first established what the upper and lower bounds of water quality were for each study, i.e., how the researcher

explicitly or implicitly defined the level at which the waterbody was “dead” or totally impaired and that at which it was

considered pristine. These points of reference were used to define the endpoints on a scale of 0 to 100. With the endpoints

established, the Agency mapped the baseline water quality levels and the magnitude of the water quality change onto this new

ratio scale.
	

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A12-20

The way that EPA mapped water quality changes onto the meta model’s index depended on how they were characterized in

the original studies: 

 For water quality changes specified by a study as movements along a generic ordinal scale (e.g., poor, fair, good,

excellent), the original levels were positioned at uniform intervals across the new index (e.g., 0, 33, 67, 100) and

changes calculated as the difference between the two relevant values. 

 For water quality changes that refer to levels at which particular recreation types are possible (e.g., non-boatable,

boatable, fishable, swimmable), the original levels were placed on the index at the same relative position in which

they would be found on the “RFF water quality ladder” (e.g., 0, 2.5, 5, 7), which some studies handed to respondents

during interviews. 

 For water quality changes expressed in terms of species’ populations (e.g., 25 percent increase in trout populations),

the baseline value on the index was selected according to whatever narrative or quantitative information was

provided in the original survey or study, and considering that 0 would equate to extirpation of the species and 100 to

historic, peak population levels. The change upon which a valuation scenario was based was then applied to this

baseline index value. For example, a 25 percent increase in a trout population described as currently being in fair

condition would be translated into a 25 percent shift in the index from 33 to 42. 

 Focusing on non-use value for changes in fish populations 

The third difference between the two models is that the alternative model includes the sample type dummies as interactions

with ln_chwq, allowing the relationship between WTP and water quality change to vary according to the degree to which use

values are reflected in WTP responses. While consideration was given to further interacting ln_chwq with the species focus

dummies, the lack of observations in some of the cross-categories effectively precluded it.

The log-log meta model facilitates policy simulations. For example, estimating the WTP for the non-use value of the section

316(b) rule effects would require a focus both on a water quality change that affects solely fish and on non-use values. Use of

the model for this purpose is straightforward, essentially involving assigning a value of 1 to both fish_only and nonusers, the

latter of which is interacted with the appropriate water quality change measured on the index as well as its ln_chwq parameter.

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Table A12-5 presents results of the log-log model. 

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Variable Parameter

Estimate Robust Std. Error t Statistic Prob>|t

intercept 6.64 1.57 4.23 0.00

year1990 0.89 0.21 4.19 0.00

discrete_ch 0.69 0.25 2.72 0.01

interview 0.50 0.16 3.07 0.00

mail 0.11 0.26 0.41 0.68

voluntary 0.55 0.21 2.71 0.01

lump_sum 0.82 0.27 3.00 0.00

nonparam -0.38 0.18 -2.10 0.04

protest_bids 1.00 0.15 6.88 0.00

outlier_bids -0.23 0.10 -2.27 0.03

ln_inc -1.32 0.31 -4.29 0.00

nonlocal -0.63 0.29 -2.20 0.03

small_river -1.78 0.61 -2.94 0.01

large_river -0.37 0.33 -1.13 0.27

small_lake 0.13 0.25 0.53 0.60
	

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Variable Parameter

Estimate Robust Std. Error t Statistic Prob>|t

A12-21

large_lake 1.56 0.46 3.40 0.00

small_fresh 0.27 0.16 1.68 0.10

large_fresh 0.78 0.31 2.50 0.02

natl_fresh 0.99 0.42 2.34 0.02

small_salt 2.79 0.33 8.39 0.00

great_lakes -0.50 0.56 -0.90 0.38

pacif_mount -1.28 0.28 -4.52 0.00

plains -0.38 0.23 -1.70 0.10

southeast -3.01 0.68 -4.44 0.00

multi_reg -0.50 0.22 -2.28 0.03

npl -1.09 0.22 -4.93 0.00

wildlife -0.32 0.25 -1.26 0.22

fish_only -0.48 0.23 -2.04 0.05

ln_hiwq -0.07 0.33 -0.22 0.83

ln_chwq*nonusers 0.66 0.31 2.12 0.04

ln_chwq*users 0.82 0.31 2.63 0.01

ln_chwq*genpop 0.70 0.28 2.48 0.02

-2 Restricted Log Likelihood 118.0

Covariance Factors

Study Level (u) 0.12

Residual (e) 0.21

2 for significance of randomeffects 0.00

Source: U.S. EPA analysis, for this report.

.
#%#""##-"""("

The log-log model finds both statistically significant and economically reasonable patterns influencing WTP for water quality

improvements. The statistical fit of the equation is good; there is a strong systematic element of WTP variation which allows

forecasting of WTP based on site and study characteristics. The model as a whole is statistically significant at better than

p<0.0001. 

While author-level random-effects are not statistically significant (2 of 0), 25 of the 31 fixed-effects (disregarding the

intercept) in the model are significant at p<0.1. Nearly all of the signs of the significant parameter estimates correspond with

prior expectations.

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EPA included two dummy variables in the log-log model, wildlife and fish_only, that measured the species that were affected

by the water quality change. The negative signs on these parameter estimates support the expectation that respondents

provide a lower WTP for water quality improvements described solely in terms of changes in species populations. Further, a

description that is limited to effects on fish relates to a lower WTP than one depicting effects on other wildlife as well, e.g.,

fish-eating birds.
	

  !"	#$%& %'

A12-22

The model included several water quality variables. The positive and statistically significant (p<0.05) estimates for the three

ln_chwq interaction terms support the hypothesis that higher WTP values are associated with larger water quality changes. 

Moreover, the relative sizes of the estimates provide support to prior expectations in that the non-user value is smallest and

the user value largest. The statistically insignificant estimate for ln_hiwq suggests that the level of water quality has little

effect on the WTP for the change in water quality, i.e., there may not be a big difference in the respondent’s mind between an

improvement that raises water quality from a poor to a mediocre state and one that raises it to a mediocre to an excellent state

as long as the changes are thought to be of the same magnitude. 


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Most of waterbody scale and type dummies have parameter estimates that are statistically significant at p<0.1. For the most

part, the estimates for the “large” dummies are larger than the “small” ones, which would be expected. Surprisingly, the

estimates for small_lake and large_lake are both significant and relate to each other in the opposite manner. This may be due

to that these two categories may differ in kind more than degree, as Great Lakes studies exert a strong influence in the latter. 

The negative and statistically significant (p<0.01) estimate for npl indicates that waterbodies that are recognized Superfund

sites may be considered by respondents to be qualitatively different, and of lesser value, than other waterbodies.

Although there are no prior expectations for the regional dummies, all estimates are significant at p<0.1. The results suggest

that the default region, the North Atlantic, has higher WTP values than elsewhere, whereas the Inland region has the lowest.

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The negative and statistically significant (p<0.01) estimate for ln_inc indicates that lower incomes are associated with

relatively higher WTP estimates. This does not correspond well with the commonly held notion of environmental quality as

luxury good. However, since ln_inc is the only variable in the model that relates to respondent socioeconomic characteristics,

it is possible that it is picking up the influence of omitted factors, such as demographics (e.g., retirees may appreciate aquatic

resources more) or locale (e.g., rural respondents may as well).

The negative and statistically significant (p<0.05) estimate for nonlocal supports the hypothesis that respondents who live

further from a resource do not value it as highly.

(-#'-$"

There are no strong theoretical expectations about the sign or magnitude of several of the study and methodology variables. 

The results from the log-log model show positive and statistically significant (p<0.01) parameter estimates for discrete_ch,

interview, voluntary, and lump_sum. These results indicate that the discrete choice study type, the interview solicitation

method, the voluntary payment mechanism, and the lump sum payment type are all associated with higher WTP values. 

The signs of the remaining variables generally correspond with prior expectations. The statistically significant estimates for

nonparam (negative, p<0.05), protest_bids (positive, p<0.01), and outlier_bids (negative, p<0.05) indicate that studies that

use a parametric model, exclude protest bids, or include outlier bids have relatively higher WTP values. The positive and

statistically significant (p<0.01) estimate for year1990 supports the hypothesis that earlier surveying and modeling

approaches may have biased WTP estimates upward.

1**
2
3,	
4,
3

453
3,2
6/50 4

The results of the meta-analysis in conjunction with information specific to the affected aquatic resources and the populations

that will benefit from reduced I&E impacts can be used to estimate the non-use value of the section 316(b) regulation. This

analysis involves the following steps: 

 Estimating annual non-use value of the affected fishery resources per household for completely eliminating baseline

I&E losses, and for reducing I&E losses from the baseline to post-compliance levels;

 Estimating the population of households holding non-use value for the affected resources; and

 Estimating the total non-use value to the affected populations for completely eliminating baseline I&E losses, and

for reducing I&E losses from the baseline to post-compliance levels.
	

  !"	#$%& %'

11 This 10 mile criterion is a conservative assumption that excludes households in counties that abut large, affected waterbodies, but

that are distant from section 316(b) facilities.

12 The relevant population in this analysis is the number of households because WTP for environmental improvements are estimated

on per-household basis.

A12-23

1"##4"!("%,("'

Region-specific non-use WTP values for aquatic habitat improvements can be estimated for two population classes: (1) all

households in the vicinity of the waterbodies affected by I&E, and (2) recreational anglers who may visit the affected

waterbody. Separate household values can be estimated using the semi-log and log-log regression equations specified in

sections A12-3.2 and A12-4.2, respectively. To estimate the non-use values of baseline I&E losses and reduced I&E impacts,

values should be assigned to independent variables to reflect resource characteristics, area demographics, and other factors. 

These values are then multiplied by the estimated regression coefficients to predict the average non-use WTP for aquatic

habitat improvements for a household with specific characteristics (e.g., non-user household in the North Atlantic region). 

Two variables are of particular importance to the valuation of benefits of the final section 316(b) rule: baseline and WQ_fish.

For example, it can be assumed that all waterbodies affected by cooling water intakes meet water quality standards

(baseline=7.0 or swimmable conditions). In reality, some waterbodies may not meet water quality standards. EPA notes that

this assumption leads to more conservative estimates of non-use values for aquatic habitat improvements, because higher

baseline quality leads to lower WTP for environmental improvements. If feasible, site specific values should be used for the

baseline variable.

The WQ_fish variable, the effect of aquatic habitat quality change on fish, is a key policy variable. The value assignments of

the WQ_fish variable should be based on the expected change in recreational fishing quality at the affected sites, which is

measured by the expected change in recreational catch rate. For example, the estimated changes in recreational catch rates

from eliminating baseline I&E losses range from 2.5 percent to 25.9 percent, with a mean value of 12.9 percent. The

estimated changes in recreational catch rates under the final option range from 1.2 percent to 12.6 percent, with a mean value

of 6.3 percent.

Using the equation specified in the preceding section and the values of independent variables described above, one can derive

region-specific WTP values for all households in the vicinity of the waterbodies affected by I&E losses. 

1"#'$*%(#"

Two non-use benefit population categories should be considered in this analysis: 1) households in the counties abutting the

affected waterbodies, and 2) recreational anglers residing outside of the abutting counties but who visit recreational fishing

sites in each study region. Households in the counties abutting the affected waterbodies can be further restricted to include

only households in counties where some part of the county is within 10 miles of a power plant subject to the Phase II section

316(b) rule.11 The sum of the two affected household categories for a given study region, assuming one user household per

recreational angler, represents the total population of households affected by I&E impacts at section 316(b) facilities.12 The

following data sources can be used to obtain information on the number of anglers visiting recreational fishing sites in a given

region:

 Coastal region — National Marine Fisheries Statistics Survey (NMFS, 1997-2001); and

 Great Lakes region — 2001 National Survey of Fishing, Hunting, and Wildlife-Associated Recreation (U.S. Fish

and Wildlife Service, 2001).

U.S. Census Bureau data can be used to estimate the number of households residing in the counties abutting the affected

waterbodies (U.S. Census Bureau, 2002).

EPA notes that resource users typically hold higher non-use values than the non-use values held by non-users for the same

resource, and therefore the application of total non-user value, which is used in this analysis to approximate total non-use

value, may underestimate the total non-use value of aquatic habitat improvements. In addition, the two population categories

considered in the non-use benefits analysis do not represent all the households that may hold values for these natural resources

(e.g., households in coastal states outside of the counties abutting the affected waterbodies). Furthermore, most of the studies

on which the meta-analysis was based analyzed sample populations from larger geographic areas than the area considered
	

  !"	#$%& %'

A12-24

here. For these reasons, the resulting non-use estimates are likely to represent a lower-bound estimate of the value of reduced

baseline I&E losses.

1"#'#4"!('$*%(#"

Total regional non-use value can be calculated by multiplying the region-specific non-use value per household from each

regression model by the corresponding estimate of the total number of affected households in each 

region. 

6
	

42



A number of issues are common to all benefit transfers. Benefit transfer involves adapting research conducted for another

purpose in the available literature to address the policy questions at hand. Because benefits analysis of environmental

regulations rarely affords enough time to develop original stated preference surveys that are specific to the policy effects,

benefit transfer is often the only option to inform a policy decision. Specific issues associated with the estimated regression

model and the underlying studies are discussed in discussed in section A12-3.3e. Additional limitations and uncertainties

associated with implementation of the meta-analysis approach are addressed below.

6#"&-#-""	5"#7#"8-#/9:60

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The semi-log model presented above can be used to predict WTP for each of the studies in the database; however, estimates

derived from regression models are subject to some degree of error and uncertainty. To better characterize the uncertainty or

error bounds around predicted WTP, EPA recommends using the procedure described by Krinsky and Robb in their 1986

Review of Economics and Statistics paper “On Approximating the Statistical Property of Elasticities.” The procedure

involves sampling the variance-covariance matrix of the estimated coefficients, which is standard output from the statistical

package used to estimate the meta model. WTP values are then calculated for each drawing from the variance covariance

matrix and an empirical distribution of WTP values is constructed. By varying the number of drawings, it is possible to

generate an empirical distribution with a desired degree of accuracy (Krinsky and Robb, 1986). The lower or upper bound of

WTP values is then identified based on the 10th and 90th percentile of WTP values from the empirical distribution. These

bounds may help decision-makers understand the uncertainty associated with the benefit results. 

6#"&-#-""!""##"
#%##"""

In addition to developing the WTP values and bounds based on best estimates of values for independent variables, EPA

recommends performing a sensitivity analysis to show how these values could change based on more site-specific or

geographic-specific conditions and alternative assumptions regarding desirable study characteristics. 

6$*%(#

As noted above, the two population categories considered in the non-use benefits analysis do not represent all the households

that may hold values for these natural resources (e.g., households in coastal states outside of the counties abutting the affected

waterbodies). The resulting non-use estimates therefore are likely to represent a lower-bound valuation of reduction in

baseline I&E losses. However, EPA notes that some resource valuation studies have found that respondents in the typical

contingent market situation may overstate their WTP compared to their likely behavior in a real world situation. EPA

recommends conducting a sensitivity analysis to assess the effect of hypothetical bias on the estimated non-use values. For

example, one can assume that only 50 percent of the households residing in the vicinity of the affected waterbodies would

actually pay for aquatic habitat improvements resulting from reduced I&E.