Estimating the Value of Water Quality

Jay R. Corrigan, Kevin J. Egan, and John A. Downing*

June 2006

Abstract

This paper presents the results of an environmental valuation study designed to estimate the value that local residents and visitors are willing to pay to preserve the current level of water quality in Clear Lake, a spring-fed glacial lake in north-central Iowa. We estimate willingness to pay using both revealed preference and stated preference techniques. When using revealed preference techniques, we compare the number of times respondents plan to visit the lake given its current condition with the number of times they would plan to visit if the lake’s water quality were allowed to deteriorate. When using stated preference techniques, we present respondents with a hypothetical ballot initiative offering improved water quality and resulting higher taxes. Key words: Environmental valuation, revealed preference, stated preference. * The authors are assistant professor of economics at Kenyon College, Gambier, OH; assistant professor of economics at the University of Toledo, Toledo, OH; and professor of ecology, evolution, and organismal biology at Iowa State University, Ames, IA. The authors would like to thank Joseph Herriges and Catherine Kling for their helpful comments. Correspondence: Jay Corrigan, Kenyon College, Gambier, OH 43022. E-mail: corriganj@kenyon.edu. Tel: 740-427-5281. Fax: 740-427-5276.

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Estimating the Value of Water Quality

I. Introduction: Nonmarket Valuation

Public goods such as lakes are valuable assets to the citizenry, offering various

recreational services like fishing, swimming, boating, hunting, picnicking, or nature appreciation

in general. However, most lakes do not charge an entrance fee, or the fee is nominal and offers

no information as to the intrinsic value to the citizenry of the lake, its habitat, the biodiversity it

supports, and the recreational opportunities it provides.

Economists estimate the value of any good, including a lake, using the concept of

maximum willingness to pay, which is the maximum dollar amount an individual would pay for

a certain quantity or quality level of a good. In other words, the maximum willingness to pay

(WTP) represents the value of other goods and services the individual is willing to forgo for

more of this “commodity”. For a public good, such as a lake, essentially economists infer an

entrance price one would be “willing to pay”.

The usefulness of WTP is due to it being an appropriate measure to use in cost-benefit

analysis. For example, consider the cost-benefit analysis of undertaking a water quality

improvement project at a lake. The analyst quantifies the tradeoffs individuals are willing to

make to get improved water quality (measured by WTP) and compares these to the tradeoffs

required, which are the costs of cleaning up the lake, such as public resources to fund clean-up

efforts or private costs associated with altering land use.

For comparison, local economic impact studies, which estimate the value of the marketed

goods sold near the lake, are of interest to local communities who benefit economically from the

lake, but are not appropriate valuation measures for the intrinsic value of the lake used in cost-

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benefit analysis. One reason is that sales that occur in the local region due to the lake, such as

camping fees or restaurant sales, are likely just being transferred from somewhere else (if you

didn’t buy the sandwich here, you still need to eat and buy a sandwich somewhere else), and not

a net increase in society’s overall wellbeing. Moreover, local sales receipts may not be

correlated at all with the intrinsic value of the lake. For example, if there are no local

communities near the lake to capitalize on the lake’s presence, does that mean it has no value?

Of course it doesn’t, and the value of the lake may actually be enhanced for some visitors due to

its remoteness.

A. Revealed Preferences: Introduction to the Travel Cost Model

For most goods a market readily exists where equilibrium prices signal the marginal

value of the resource, for example farm land. However, for public goods such as lakes there is

no market transaction to measure value (except for possibly a nominal entrance fee, which as

discussed above does not represent the true value). Economists must gather nonmarket data to

value public goods. One approach is the travel cost model, also known as recreation demand

modeling, for which data is collected on the observed recreational trips to the lake. The key

insight is that visitors’ trips to the lake require time and costs, such as fuel, that vary with the

distance traveled. Economists monetize the required time and costs, labeling them “travel costs”

which serve as a proxy for the “price” of the recreational trip. The variation in distances traveled

leads to price variation and allows for the estimation of the demand for the lake trips.

Economists refer to the travel cost method as a revealed preference technique, because it allows

us to infer respondents’ willingness to pay for a proposed change (e.g., a water quality

improvement at a lake) by observing respondents’ actions (e.g., recreation trips to that lake).

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Therefore, individuals “reveal” their preferences for water quality through their trip taking

behavior. For example if data on trips to multiple lakes are collected, some individuals will

travel further (i.e. incur higher travel costs) to visit lakes with better water quality and thus reveal

a “money” versus “water quality” tradeoff that can be exploited to estimate the value to society

of water quality changes. In this paper only one lake is analyzed, therefore the individuals are

asked hypothetically how many trips they would take if the water quality at the visited lake were

changed. This is discussed further in section II.A.

Once the demand for lake visits is estimated it is possible to infer WTP values for the

lake as areas under the recreation demand curve and above the respective travel cost of the

individual.1 Consider figure 1 for demonstration. Compare visitor i who incurs travel cost iTC

to visit the lake and chooses iy annual trips, with visitor j who incurs a higher travel cost jTC

(due to living further away) and therefore chooses a lower jy annual lake trips. It is assumed the

estimated recreation demand curve maps the maximum WTP each individual would pay for

access to the lake, given their chosen number of trips. Since individual j lives further away and

incurs high travel cost to visit the lake, she would not pay much more if need be for her jy trips,

as shown by the area with endpoints “ jTC ac ” in figure 1. This area is individual j’s maximum

WTP for her jy trips, as it represents in dollars the value of the lake to her by representing the

tradeoff of other goods forgone which those dollars could have purchased. In contrast,

individual i only has to pay iTC for access to the lake and therefore is estimated to be willing to

pay the area with endpoints “ iTC bc ” in figure 1 for his iy trips. Basically, individual i

purchases access to the lake at a discount and in theory should be willing to pay an additional

1 Economists more commonly refer to this area as “consumer’s surplus,” but the WTP concept is maintained for consistency.

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amount equal to this area; an amount other less fortunate individuals must pay to visit the lake

since they live further away. A lakes value to society is the summation of each individual’s

maximum WTP, or if there are only two individuals, then the lakes value to society is the area

jTC ac + iTC bc .

Travel cost models have been used to estimate WTP values for over 45 years and

beginning in 1979 Federal agencies were required to use the travel cost method (and the

contingent valuation method discussed in the next section) to value recreation benefits for

projects involving high visitation levels (Loomis, 2005). For example, dam construction must

consider the possibly lost whitewater rafting opportunities, and also the potentially gained

recreational opportunities from the lake formed behind the dam. Travel cost models are also

employed to estimate damage assessment payments, for example from the 1989 Exxon Valdez oil

spill which drastically harmed the recreational fishing opportunities in Prince William Sound

(Carson and Hanemann, 1992). Usually, the travel cost method is used to estimate the

recreational value of a public good, such as a lake, to be used in a cost-benefit analysis to

determine what amount of public resources, such as tax payer dollars, is warranted to protect or

improve the lake. The travel cost model discussed in this paper falls in this category, as we

estimate the recreational value of avoiding deteriorated water quality at a lake in north-central

Iowa.

B. Stated Preference: Introduction to the Contingent Valuation Method

A second approach for gathering nonmarket data is the contingent valuation (CV)

method, which is a stated preference technique as individuals are asked directly about their

willingness to pay for proposed changes, and therefore “state” their preferences.

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Mitchell and Carson (1989) describe the CV method as using survey questions to

estimate the respondent’s willingness to pay for specified improvements to an environmental

amenity, such as a lake. The CV method was originally developed by Davis (1963) to estimate

the recreational value of Maine’s North Woods and the method can be used to value various

environmental goods. Respondents are typically presented with a survey instrument made up of

three parts: (1) a detailed description of the good being valued and the hypothetical

circumstances under which it will be made available to them, (2) questions eliciting respondents’

willingness to pay for the good, and (3) questions about the respondents’ socioeconomic

characteristics. The most common format for the value-elicitation question is a hypothetical

ballot initiative where the respondents vote “yes” if they are willing to pay a given dollar amount

for a proposed water quality improvement, and vote “no” otherwise. For example, “Would you

be willing to pay $X to preserve the water quality of Smith Lake?”

The importance of CV is underscored by Executive Orders 12044, 12291, and 12866

issued by Presidents Carter, Reagan, and Clinton, respectively. Each order requires federal

agencies to consider both the costs and benefits of potential regulatory actions. But the

importance of CV was brought to the forefront by the Exxon Valdez oil spill, which lead to the

Oil Pollution Act of 1990 and the subsequent NOAA Panel report on the reliability of CV as a

means of assessing legal damages (Arrow et al. 1993). The panel ultimately supported the use of

CV in assessing damages so long as the CV study followed the panel’s guidelines, among which

were the recommendations to use dichotomous choice questions in the framework of a referenda,

that respondents be reminded of their income constraints, and that respondents be informed of

the existence of substitute goods.

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CV enjoys widespread use within the environmental valuation literature, where it is

generally accepted that there are certain types of nonmarket goods whose value can only be

estimated using CV or other similar stated preference techniques. To give an example, think of

Americans’ willingness to pay to preserve the Artic National Wildlife Refuge. Only the CV

method can estimate the full WTP for this preservation, as the travel cost method would estimate

only the “use value” of those who actually visit the refuge.

Another of CV’s primary appeals is its flexibility. This allows for the valuation of goods

as varied as increased visibility (Rowe, d’Arge, and Brookshire 1980), mortality risk reduction

(Krupnick et al. 2002), and the existence value of endangered species (Ekstrand and Loomis

1998). By creating a hypothetical market where no real market exists, CV allows economists to

estimate values that would be difficult, if not impossible, to estimate using revealed preference

techniques, such as the travel cost model.

However, the flexibility afforded by CV’s hypothetical nature is also viewed as one of its

principal drawbacks. Some economists suggest that the hypothetical nature of the questions and

the lack of market discipline introduces what has come to be called “hypothetical bias”

(Cummings et al. 1997). Hypothetical bias refers to respondents’ tendency to be more generous

when answering hypothetical willingness-to-pay questions than when proposed payments are

real.

Whether hypothetical bias does in fact pose a major problem is an empirical question.

Carson et al. (1997) reexamine eighty-three studies where both CV and travel cost value

estimates are reported. They show that CV estimates are, on average, less than travel cost

estimates, which are generally considered to be less controversial. Likewise, Cummings and

Taylor (1999) find that explicitly instructing respondents to think of the payment as if they were

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real can eliminate hypothetical bias for a variety of environmental amenities. Moreover, as

Sommer and Sohngen (2002) state, “the contingent valuation method is similar to polling

practices and market research conducted by most large companies,” highlighting the fact that

although the information gathered is hypothetical, the general technique is broadly applied to

obtain important information under different not-observed scenarios.

C. Application: Clear Lake Survey

This paper estimates the value of maintaining the current level of water quality at Clear

Lake, a spring-fed glacial lake in north-central Iowa. A team of limnologists and environmental

economists designed a mail survey instrument detailing the current conditions of the lake in

terms of water clarity, color, odor, abundance of fish, and the frequency of algae blooms and

beach closings. Then the deteriorated conditions of the lake were given if nothing is done over

the next decade to prevent the decline.2 Clear Lake is a popular destination and is especially

lively in the summer months when anglers, recreational boaters, and beach users all frequent the

lake. The concern is that deteriorating water quality conditions would lessen the recreational

experiences.

Sections II discusses the use of the travel cost model to estimate the WTP to maintain the

current water quality at Clear Lake, while section III details the use of the contingent valuation

technique to estimate the WTP for the same scenario.

II. Revealed Preference: Using the Travel Cost Method

A. Contingent Behavior Data

2 The survey also described two plans that would, respectively, yield moderate and substantial improvements in water quality over the next decade.

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To value the maintenance of the current level of water quality within the travel cost

framework requires information on how the visitors would reduce recreational trips to Clear

Lake, given the described deteriorated water quality conditions. In the mail survey, the visitors

were asked, “…How many trips per year would you have made to Clear Lake if conditions were

as described in Plan A [the deteriorated water quality scenario]?” This trip data is referred to as

contingent behavior trips, since the trips are contingent upon the deteriorated water quality

scenario preceding the question. Notice the contingent behavior trips are “stated preference”

data similar to the contingent valuation data since we do not observe these trips.3 However,

since the contingent behavior question is similar to the observed behavior question (i.e., asking

for last season’s trips), the information required is familiar. The visitor may more easily

understand his “price” savings from taking fewer trips.

Returning to the concept of maximum willingness to pay, our interest is now to value a

change in the quality of a lake. The process is to estimate the WTP under current conditions and

then the WTP given deteriorated conditions. The difference between the two WTP estimates is

the value of avoiding the deteriorated conditions,

.avoidlowWQ currentWQ lowWQ

i i iWTP WTP WTP= − (1)

Each individual’s WTP to avoid the deteriorated conditions can be shown graphically as in

Figure 2. Given the lower water quality, individual i reports visiting the lake less, taking only

lowWQ

iy trips versus currentWQ

iy trips. Then the area abcd represents individual i’s value

( avoidlowWQ

iWTP in equation 1) to avoid the scenario of taking less trips to the lake with worse

water quality.

3 Since this paper only considers one lake, to value water quality changes using only revealed preference data would require longitudinal data over a time period of changing conditions. An alternative is to model a system of lakes with varying water quality levels (Egan, Herriges, Kling, and Downing, 2006).

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B. Empirical Specification

A bivariate count data model, specifically a bivariate Poisson-lognormal mixture model,

is utilized which correctly models the observed behavior and contingent behavior trips as

nonnegative integers and also accounts for the positive correlation between the two counts (i.e. if

individual i takes a high number of observed trips then he will most likely report a high number

of contingent behavior trips). The model also allows for overdispersion (the conditional variance

of the count exceeding the conditional mean) which is typically encountered with recreation data.

The overdispersion is assumed to be due to heterogeneous preferences not captured by the

included explanatory variables. To begin, the univariate Poisson distribution is reviewed, then a

simple bivariate extension of this model, before discussing the bivariate Poisson-lognormal

mixture model.

The univariate Poisson distribution is,

( ) ( ) ( )exp| , 0,1,2,

!

iy

i i

i i i

i

f y x yy

λ λ−= = … (2)

where iy denotes the number of trips taken by individual i. The Poisson distribution only has

one parameter, iλ , and to utilize the distribution as a regression analysis, iλ is specified as

( )( )|

exp

i i i

i

E y x

x

λ

β

=

′= (3)

where iλ is the expected number of trips for an individual with characteristics vector ix , and β

denotes the unknown parameters of the distribution to be estimated. The simplest extension of

the univariate Poisson count data model to the bivariate setting is to assume the trip data follow

independent Poisson distributions. Then the joint conditional distribution is

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( ) ( ) ( ) ( ) ( )exp exp, | , , 0,1,2, where ,

! !

io icy y

io io ic ic

io ic io ic ij

io ic

f y y x x y j o cy y

λ λ λ λ− −= = =… (4)

where ioy denotes the observed behavior trips and i cy denotes individual i’s contingent behavior

trips (contingent upon the proposed decreased water quality). The parameter ijλ denotes

individual i’s expected number of trips, either the observed behavior trips (j=o) or the contingent

behavior trips (j=c),

( )( )|

exp , .

ij ij ij

j ij

E y x

x j o c

λ

β

=

′= = (5)

However, it is more realistic to drop the independence assumption and model the correlation

between the observed and contingent behavior trips. As mentioned, an individual who reported a

large number of trips in the past (i.e., observed behavior trips) is also more likely to report a

large, albeit smaller, number of contingent behavior trips.

Also, a limitation of the univariate and bivariate Poisson models presented so far is the

equidispersion property,

( ) ( )| | ,ij ij ij ij ijE y x Var y x j o cλ = = = , (6)

requiring the equality of the conditional mean and variance, when in practice the conditional

variance exceeds the conditional mean (i.e., overdispersion). To allow for overdispersion and

account for correlation between the counts, a mixed bivariate Poisson model is employed which

allows, “for a common shared source of unobserved heterogeneity in the counts for a given

individual (Egan and Herriges, forthcoming).” The trips taken by individual i given scenario j

are associated with an unobserved factor, ( )expij ijv ε= . If ijv were known, then the

corresponding trips would follow the bivariate Poisson model given above,

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( )�( ) �( ) �( ) �( )exp exp

, | , , , , 0,1,2, ; ,! !

io icy y

io io ic ic

io ic io ic io ic ij

io ic

f y y x x y j o cy y

λ λ λ λε ε

− −= = =… (7)

where

( )

( )

| ,

exp .

ij ij ij ij

ij ij

j ij ij

E y x

x

ν λ

λ ν

β ε

=

=

′= +

ɶ

(8)

Assuming the ijv follow a bivariate lognormal distribution, or equivalently that ijε follows a

bivariate normal distribution,

( ) { }2 2, (0,0), ( , , )io ic o o c cNε ε σ ρσ σ σ∼ , (9)

results in the bivariate Poisson-lognormal model. Since the ijv is unobserved, the relevant joint

distribution for the trip counts becomes

( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

( )

2

22

, | , | , | , ,

exp exp

! !

1 1 exp 2

2 12 1

io ic

io ic io ic io io io ic ic ic o c

y y

io io ic ic

io ic

o o c c

o o c co c

f y y x x f y x f y x f

y y

ε ε ε ε

λ λ λ λ

ε ε ε ερ

σ σ σ σρπσ σ ρ

=

− −=

× − − + −−

∫ ∫ɶ ɶ ɶ ɶ

2

,

0,1,2,

o c

ij

d d

y

ε ε

= …

(10)

The conditional trip means and variances are

( )212

| expij ij ij j ijE y x λ σ δ = ≡ (11)

and

( )2 2| exp 1ij ij ij j ijVar y x δ σ δ = + − , (12)

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where ( )2 |j ij ijVar xσ ε= . Equations (11) and (12) show the model allows for overdispersion

since the conditional variance is greater than the conditional mean as long as 0jσ > .

Correlation among the trips emerges because

[ ] ( ), exp 1 ,io ic io oc icCov y y δ σ δ= − (13)

where oc o cσ ρσ σ= , is the covariance between the counts. Notice the correlation between the

trips can be positive, negative, or zero depending directly upon the sign of ocσ . The cost of the

added flexibility of the bivariate Poisson-lognormal distribution is that it does not have a closed

form solution, although simulation techniques are readily available to approximate the integrals.4

Lastly, the Clear Lake dataset was collected on-site to more cost effectively obtain a

sample of visitors (i.e., as opposed to sending a random population survey to Iowans, many of

whom would not have visited Clear Lake). However, intercepting the visitors on-site leads to

oversampling of the avid recreators (endogenous stratification) and the exclusion of non-visitors

(truncation). The modeling procedure employed below corrects for the truncation and

endogenous stratification by assuming a visitor who takes iy trips is iy times more likely to be

intercepted, and that of course a non-visitor has zero probability of being intercepted. The

probability density for recreation trips is appropriately reweighted based on this assumption. In

particular, the joint distribution is reweighted by, ( )

1

1 1 2| ,i

i i i

y

E y x x, which gives proportionately

more weight to the trip probabilities as the visitor takes more trips, relative to the average

number of trips. The on-site joint distribution is then

4 We employ maximum simulated likelihood, using 3,000 random draws in the simulation.

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( )( ) ( ) ( ) ( )

( )

1

1

2 2

22

exp exp, | ,

! !

1 1 exp 2 ,

2 12 1

io icy y

io io ic icios io ic io ic

i io ic

o o c co c

o o c co c

yf y y x x

y y

d d

λ λ λ λ

δ

ε ε ε ερ ε ε

σ σ σ σρπσ σ ρ

− −=

× − − + − −

∫ ∫ɶ ɶ ɶ ɶ

1 2

1,2, ; 0,1,2,i iy y= =… …

(14)

C. Empirical Application

To obtain visitors’ addresses, potential respondents were intercepted while recreating at

Clear Lake between May and September of 2000, and then subsequently mailed the survey in

November of 2000. For the contingent valuation analysis, local residents were also used, and

their addresses were drawn at random from the white pages listings for the cities of Clear Lake

and Ventura, Iowa, both of which are located on Clear Lake. Survey Sampling, Inc., a

Connecticut-based market research firm, created this sample. Following the procedure laid out

by Dillman (1978), a follow-up postcard and survey instrument were sent to those households

that did not respond to the initial mailing. The eventual response rate among surveys

successfully delivered to visitors was 67%. Similarly, the eventual response rate among surveys

successfully delivered to local residents was 69%. These response rates compare favorably with

other similar surveys. All respondents received $5 for completing the survey.

In the analysis below, fifty-nine responses were excluded because respondents failed to

answer one or more of the travel cost questions or answered them in a way suggesting that they

misunderstood the questions. An additional fifty-two responses were excluded because

respondents traveled more than five hours to reach Clear Lake or made more than fifty-two trips

to the lake during the year. We felt that such respondents were atypical and, therefore, their

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responses should not be included in our analysis. The final sample size for visitors was 498

individuals. In addition, thirty-nine respondents failed to answer one or more of the relevant

socioeconomic questions, but instead of excluding these surveys, we chose to substitute the

relevant sample mean in place of non-responses. While we view this as the most economical

approach, results excluding the responses of those residents who did not answer all of the

socioeconomic questions are qualitatively unchanged from those presented here. A summary of

the socioeconomic characteristics of visitors responding to the survey can be found in Table 1.

Turning to the estimation of the bivariate Poisson-lognormal model discussed in the

previous section, the expected number of trips is estimated as

( )0expij j Pj i Ij i iP I zλ β β β δ ′= + + + (15)

where iI is the visitor’s income, and iz is a vector of socio-demographic characteristics of the

household, including:

• Male =1 if the survey respondent is male, = 0 otherwise;

• Age = the age of the survey respondent;

• Age2;

• School = 1 if the survey respondent has attended or completed some level of post-high

school education; and

• Household = the total number of household members.

Lastly, iP denotes the roundtrip travel costs from visitor i’s home to Clear Lake. The travel

costs have two main components, the first being the out-of-pocket expenses calculated as

$0.25/mile for the roundtrip distance from the visitors’ home to Clear Lake. The other

component estimates the value of time spent traveling. Economists calculate the value of time

using the concept of “opportunity cost,” or the value of the time spent traveling is the next best

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alternative of that time that is given up. It could be either other leisure activities or possibly

working additional hours. It is important to include the value of time as a visitor will consider

the opportunity cost of time to reach Clear Lake, beyond the cost per mile expense. However, it

is difficult to ascertain the most appropriate opportunity cost of time, therefore three different

estimates will be calculated, using one-fourth, one-third, and one-half the wage rate multiplied

by the round trip travel time.5 In summary,

( )i i i0.25 distance wage travel timeiP v= × + × × (16)

where v equals 1 1 1, , or ,

4 3 2 and the wage is calculated as income divided by 50 (weeks) and

divided by 40 (hours).

Lastly, since the bivariate Poisson-lognormal model uses the mean exponential function,

WTP estimates are easily obtained. As defined earlier, WTP is the area under the market

demand curve from the visitor’s price of the trip up to the choke price, at which zero trips are

taken. Since at the choke price demand is zero and at the beginning price demand is the

observed number of trips, the visitor’s annual WTP is,

( )

.

choke

i

P

ij ijP

ij

Pj

WTP P dPλ

λ

β

=

−=

∫ (17)

The visitors reported on average considerably fewer trips (about three vs. twelve given

current conditions) if Clear Lake’s water quality deteriorated to the levels described in the

survey. Notice also the standard deviation of the contingent behavior trips is twice the sample

mean, whereas for the observed behavior trips they are roughly the same order of magnitude.

5 See Haab and McConnell (2002) for a more complete discussion on the role of time, and insights into using a fraction of the wage rate as the opportunity cost of time.

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The contingent behavior trips having higher variability indicates some visitors did not report

decreasing trips due to the deteriorated conditions as much as others. The travel costs varied

from $5.40 to about $377 per roundtrip with the mean travel cost being about $61.

D. Empirical Results

Table 3 reports the results from the bivariate Poisson-lognormal model assuming the

opportunity cost of time is valued at one-fourth, one-third, and one-half the wage rate. Valuing

the opportunity cost of time at one-third the wage rate is recommended by Cesario (1976) and

adopted by Egan and Herriges (forthcoming) among other recreation demand papers. The other

two specifications allow for sensitivity analysis of the WTP estimates.

All of the parameters across all three specifications are significant at the 1% level except

the socio-demographic parameters. In general, the visitor’s gender, amount of schooling, or

number of household members has no significant effect on the chosen number of recreational

trips. The visitor’s age is significant at the 5% level, and the quadratic relationship to trips

indicates visitors take more trips when young and old, possibly due to having more leisure time.

The price and income parameters are of the expected sign with higher travel costs decreasing

trips and trips increasing with income. In general, the contingent behavior trips are less

responsive to price and more responsive to income, indicating that the estimated recreation

demand curve for the contingent behavior trips is not a parallel shift inward, as would be the case

if only the constant, 0cβ , was smaller. Also, for both the observed and contingent trips, the

responsiveness to price decreases as the opportunity cost of time is more highly valued from one-

fourth, up to one-half the wage rate. Finally, the variance coefficients are very stable across the

three specifications and always significantly greater than one, indicating the presence of

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overdispersion. The estimated variance for the contingent behavior trips is 70% higher than the

variance for the observed behavior trips, as was expected since the sample data for the contingent

behavior trips exhibits more variability. The correlation coefficient ( )ρ is always significantly

estimated at about 0.75, indicating, as expected, high positive correlation between the observed

and contingent behavior trips. Lastly, the log-likelihood value indicates the lower the

opportunity cost of time is valued, the better the model fits the data, although the improvements

are marginal.

The fitted trips and WTP estimates are reported in Table 4. Beginning with the fitted

trips, notice controlling for on-site sampling reduces the observed behavior trips by a factor of

three and reduces the contingent behavior trips by about a factor of two, which is consistent with

the results reported in Egan and Herriges (forthcoming). As expected, the WTP estimates given

the deteriorated water quality conditions ( )cWTP are always lower than the WTP estimates given

the current conditions of the lake ( )oWTP . As defined earlier, the WTP to maintain the current

water quality conditions, and therefore avoid the deteriorated conditions, is simply the difference

between the two previous estimates, and is reported in the last row of Table 3. The various

opportunity cost of time specifications lead to significant differences in the WTP estimates. As

expected, increasing the opportunity cost of time, which corresponds to shifting out the

recreation demand curve, leads to higher WTP estimates. The average per person annual WTP

to maintain the current water quality conditions varies from $148 using one-third the wage rate,

up to $233 using one-half the wage rate.

III. Stated Preference: Using the Contingent Valuation Method

A. Contingent Valuation Survey Design

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In the mail survey received by the respondents, first was the description of the current

and deteriorated water quality conditions, followed by the contingent behavior trip question used

in the travel cost model just discussed, and finally the respondents answered a referendum-

format CV question designed to elicit their willingness to pay to avoid the deteriorated water

quality conditions. Specifically, respondents answered questions such as the following:

Would you vote “yes” on a referendum that would adopt the proposed program, but cost

you $100 (paid over five years at $20 per year)?

The cost of the proposed policy was varied across respondents, for reasons discussed in the next

section. Visitors faced policy prices ranging from $15 to $150. Local residents faced policy

prices ranging from $45 to $450. Hoehn and Randall (1987) show that the referendum

mechanism motivates respondents to answer honestly so long as each respondent believes that all

others face the same policy price, and that the referendum will pass if the majority votes in favor

of the proposed project. Carson, Groves, and Machina (2000) argue that responses to such stated

preference questions will contain relevant economic information so long as respondents perceive

there to be some positive probability that their responses will influence policy, and so long as

they care about the outcome of that policy. Prior to the actual mailing of the survey, the survey

instrument was presented to a focus group of local residents to test its clarity and realism. This

was followed by a mailed pretest. A copy of the survey instrument can be found in the appendix.

B. Empirical Application

Following Cameron (1988), respondent i’s willingness to pay iWTP can be estimated

from hypothetical referendum data by first assuming that the probability that respondent i votes

“yes” on a referendum to improve environmental quality is

19

( ) ( )Pr Pr ,i i iyes WTP T= > (18)

where Ti is the policy price respondent i faces. By varying iT across respondents, we were able

to estimate median WTP for the sample as a function of individual respondents’ socioeconomic

characteristics. In order to limit iWTP from below at zero and from above at respondent i’s

income, we assume iWTP is of the form

( )i i i iWTP f X mβ ε′= + , (19)

where ( ) [ ]0,1i if Xβ ε′ + ∈ is willingness to pay as a fraction of household income im , iε is an

independent and identically distributed error term, β is the vector of coefficients to be

estimated, and iX is a vector of household socioeconomic characteristics including

• Male = 1 if the survey respondent is male, = 0 otherwise;

• Age = the age of the survey respondent;

• Age2;

• School = 1 if the survey respondent has attended or completed some level of post-high

school education; and

• Household = the total number of household members

for visitors, and also including

• Homeowner = 1 if the survey respondent is a homeowner, = 0 otherwise;

• Year-round = 1 if the survey respondent is a year-round resident, = 0 otherwise

for local residents.

For tractability, we use the following functional form for ( )f ⋅ :

( )( )1

1 expi i

i i

f XX

β εβ ε

′ + =′+ − −

(20)

20

Assuming iε is normally distributed with mean zero and variance 2σ , then i iη ε σ= is a

standard normal random variable. This allows us to rewrite (18) as

( )( )

Pr Pr ,1 exp

ln

Pr .

ii i

i i

i ii

i

i

myes T

X

m TX

T

β ση

βη

σ

= > ′+ − −

−′− − = >

(21)

Recognizing that the standard normal distribution is symmetric allows us to rewrite (21) as

( )ln

Pr Pr ,

ln

,

i ii

i

i i

i ii

i

m TX

Tyes

m TX

T

βη

σ

β

σ

−′ + = <

−′ + = Φ

(22)

where ( )Φ ⋅ is the standard normal cumulative distribution function. We can now use any

standard statistical software package to run probit analysis on (22), where the dependent variable

is whether respondent i voted yes on the referendum, and the independent variables are

iXβσ′

and

ln i i

i

m T

T

σ

− . (23)

21

C. Empirical Results

A summary of the socioeconomic characteristics of local residents responding to the

survey can be found in Table 2. The characteristics are similar to the visitors’. Table 5 presents

the results of the probit analysis described in equation (22). For both local residents and visitors,

the coefficient associated with the income/price term is positive and significantly different from

zero at the 1% confidence level ( t = 3.45 and 5.75, respectively). Given the specification of our

model, this indicates that as household income rises or as the price associated with maintaining

the lake’s water quality falls, the probability of a “yes” vote increases. And while the data

suggest that among local residents men are willing to pay more to maintain water quality than

women, there seems to be no statistically significant effect among visitors to the lake ( t = 2.50

and -1.28, respectively). Conversely, educational attainment is a statistically significant

determinant for visitors but not for local residents ( t = 2.78 and 1.64, respectively). The

coefficients associated with age and family size are not significantly different from zero for

either sample. Likewise, the data do not imply that home ownership or year-round residency

significantly affect willingness to pay to maintain water quality.

Though there is no closed-form solution for the mean value of WTP given the

specification from equations (19) and (20), we follow Haab and McConnell (2002) and calculate

median WTP (i.e., the value at which there is a 50% probability of a yes response) as follows:

( )

Median ,1 exp

mWTP

Xβ=

′+ (24)

where m and X are the sample-average values for mi and Xi, respectively. Median WTP for

local residents is $461 with a 95% confidence interval of ($272, $1,490). Because WTPi is

nonlinear, we estimate this confidence interval using a bootstrapping technique developed by

Krinsky and Robb (1986). Specifically, we drew 10,000 realizations of the coefficient estimates

22

presented in Table 5 from a multivariate normal distribution with a variance-covariance matrix

and mean vector taken from the probit estimation whose results are presented in Table 3. For

each of these draws, we calculated median WTP. The reported confidence intervals were

generated by ranking these 10.000 WTP estimates and deleting the highest and lowest 250.

As discussed previously, an additional issue we consider when estimating WTP among

visitors is that those who visit the lake more frequently are more likely to be intercepted, and

thus are overrepresented in our sample. In order to address this problem, we have calculated

median WTP for visitors using a weighted average of the socioeconomic characteristics used to

calculate mi and Xi. The weights that each visitor’s characteristics receive is inversely

proportional to the number of trips he or she made to the lake over the course of the year. For

example, the weight for a visitor who reported making four trips to the lake during the course of

a year would be half that of a visitor who reported making just two trips. Using this technique,

our weighted median WTP estimate for visitors is $148 with a 95% confidence interval of ($108,

$236).

IV. Conclusions

This paper discusses the two most common approaches economists use for estimating the

valuation of public goods. Specifically, we estimate the willingness to pay to maintain current

water quality conditions at Clear Lake in north-central Iowa. The first approach, the travel cost

model, infers the respondent’s WTP by estimating the area under the recreation demand curve.

This demand curve is estimated using individual variations in number of trips taken, recognizing

that each respondent incurs different travel costs to visit the lake. The second approach, the

contingent valuation model, directly asks for respondents’ WTP. For a proposed policy, either

23

approach leads to valid benefit estimates to be used in a cost-benefit analysis, as opposed to local

economic-impact studies, which are only relevant to the local economy.

For comparison, we use the CV and the travel cost models to estimate WTP among

visitors to Clear Lake, and we also use the CV model to estimate WTP among a sample of local

residents who live in the cities of Clear Lake and Ventura, both bordering the lake. As expected,

the median resident is willing to pay more to maintain the water quality in Clear Lake, placing

more than 3 times as much value on the proposal than the median visitor. Local residents clearly

have more of a vested interest in the lake, as their housing values, and local businesses could be

affected by the lake deteriorating.

Finally, the travel cost model is viewed as less controversial since the basis is actual

behavior (trips taken) as opposed to answering a hypothetical CV question. However, research

has shown that a well designed and tested survey instrument will minimize hypothetical bias.

Moreover, the CV model can be used to analyze policy scenarios that are not possible with

revealed preference techniques. For example, the travel cost method cannot be used for the local

residents’ WTP, as there is very little travel cost variation among residents who all live on the

lake.

24

Trips (y)

currentWQ

iy

Estimated Recreation Demand (currentWQ)

Maximum Willingness to Pay ( avoidlowWQ

iWTP )

Figure 2

. b

TCi

lowWQ

iy

. a

d

Travel Costs (TC)

Trips (y) iy

Estimated Recreation Demand

Maximum Willingness to Pay (iWTP )

Figure 1

. b

TCj

jy

. Maximum Willingness to Pay (jWTP )

c

a

TCi

c

Estimated Recreation Demand (lowWQ)

25

Table 1. Visitors’ Summary Statistics ( 498=n )

Variable Definition Mean Std. dev. Minimum Maximum

OB trips 1( )iy Observed behavior trips 12 12 1 52

CB trips 2( )iy Contingent behavior trips 2.8 5.8 0 50

Travel cost ( )iP Travel costs per trip 61.22 57.50 5.40 376.82

Income Total household income 60,000 38,000 7,500 200,000

Male 1 if male 0.64 0.48 0 1

Age The respondent’s age 44 13 15 82

School 1 if attended college 0.75 0.43 0 1

Household Adults and children 3.1 1.4 1 9

26

Table 2: Local Residents’ Socioeconomic Characteristics ( 406=n )

Variable Definition Mean Std. dev. Minimum Maximum

Income Total household income 57,000 41,000 7,500 20,000

Male 1 if male 0.66 0.47 0 1

Age The respondent’s age 54 15 15 82

School 1 if attended college 0.35 0.47 0 1

Household Adults and children 2.6 1.3 0 10

Homeowner 1 if own home 0.92 0.27 0 1

Year-round resident

1 if year-round resident 0.94 0.23 0 1

27

Table 3. Travel Cost Model Regression Results: BVPLN Model

Parametera 1/4 wage 1/3 wage 1/2 wage

0oβ 1.38** (0.38)b 1.34** (0.40) 1.87** (0.36)

0cβ -1.62** (0.42) -1.63** (0.44) -0.94* (0.39)

Poβ -1.53** (0.09) -1.36** (0.09) -1.01** (0.07)

Pcβ -0.93** (0.18) -0.84** (0.16) -0.69** (0.13)

Ioβ 1.09** (0.14) 1.23** (0.16) 1.19** (0.14)

Icβ 1.44** (0.25) 1.55** (0.29) 1.42** (0.24)

Male 8.51 (8.68) 9.19 (8.80) -0.35 (8.72)

Age -3.33* (1.62) -3.43* (1.69) -4.42** (1.53)

2Age 0.037* (0.017) 0.038* (0.018) 0.044** (0.016)

School 15.05 (10.06) 14.04 (10.47) 3.13 (8.87)

Household -0.20 (3.04) -0.36 (3.76) -5.23* (2.98)

oσ 1.13** (0.04) 1.13** (0.04) 1.10** (0.04)

cσ 1.95** (0.08) 1.94** (0.08) 1.92** (0.08)

ρ 0.75** (0.03) 0.75** (0.03) 0.73** (0.03)

Log likelihood -2,589.31 -2,591.13 -2,596.17

*Significant at 5% level; **Significant at 1% level. a All of the parameters are scaled by 100, except the constants (which are unscaled), and the income coefficient (which is scaled by 100,000). b Standard errors in parentheses.

28

Table 4. Travel Cost Model: Fitted Trips and WTP estimates (Standard Errors in Parentheses)

1/4 wage 1/3 wage 1/2 wage

Mean annual WTP

oWTP $292.87 (17.07) $330.21 (19.74) $418.44 (26.11)

cWTP $145.29 (28.32) $162.06 (32.17) $185.13 (34.73)

Mean annual WTP to maintain current water quality conditions

avoidlowWQWTP $147.58 $168.15 $233.31

Fitted population trips

[ ]|io ioE y x 4.43 (8.27) 4.45 (8.36) 4.20 (7.58)

[ ]|ic icE y x 1.28 (9.90) 1.29 (10.0) 1.21 (8.58)

29

Table 5. Contingent Valuation: Regression Results

Variablea Residents Visitors

Constant -0.455 (0.924)b -2.59** (0.584)

Income/price 0.234** (0.0675) 0.368** (0.0641)

Male 33.2* (14.1) -16.0 (12.5)

Age -1.66 (2.79) 1.86 (2.26)

Age2 -0.00565 (0.0247) -0.0261 (0.0242)

School 25.1 (14.4) 38.8** (14.0)

Household -9.38 (6.03) -3.86 (4.58)

Homeowner -1.04 (24.3) —

Year-round -0.744 (29.0) —

Sample size 406 498

Log likelihood -261 -312

Median WTP $461 $148

*Significant at 5% level; **Significant at 1% level. a All of the parameters are scaled by 100, except the constants and the income/price coefficients (which are unscaled). b Standard errors in parentheses.

30

References

Arrow, K., R. Solow, E. Leamer, P. Portney, R. Randner, H. Schuman, “Natural Resource

Damage Assessments under the Oil Pollution Act of 1990,” Federal Register, 58 (1993),

355-79.

Cameron, T., “A New Paradigm for Valuing Non-Market Goods Using Referendum Data:

Maximum Likelihood Estimation by Censored Logistic Regression,” Journal of

Environmental Economics and Management, 15 (1988), 355-79.

Carson, R., T. Groves, M. Machina, “Incentive and Informational Properties of Preference

Questions,” working paper, University of California, San Diego, 2000.

Carson, R.T., and W.M. Hanemann (1992). “A Preliminary Economic Analysis of Recreational

Fishing Losses Related to the Exxon Valdez Oil Spill,” A Report to the Attorney General of

the State of Alaska.

Carson, R., M. Hanemann, R. Kopp, J. Krosnick, R. Mitchell, S. Presser, P. Ruud, and V. K.

Smith, “Temporal Reliability of Estimates from Contingent Valuation,” Land Economics 73

(1997), 151-63.

Cesario, F.J. (1976). "Value of Time in Recreation Benefit Studies." Land Economics 52: 32-41.

Cummings, R., S. Elliot, G. Harrison, J. Murphy, “Are Hypothetical Referenda Incentive

Compatible?” Journal of Political Economy, 105 (1997), 609-21.

Cummings, R., L. Taylor, “Unbiased Value Estimates for Environmental Goods: A Cheap Talk

Design for the Contingent Valuation Method,” American Economic Review, 89 (1999), 649-

65.

Davis, R., The Value of Outdoor Recreation: An Economic Study of the Maine Woods, Ph.D.

dissertation, Harvard University, 1963.

31

Dillman, D.A. (1978). The Total Design Method. New York, NY: John Wiley & Sons.

Egan, K.J., and J.A. Herriges (forthcoming). “Multivariate Count Data Regression Models with

Individual Panel Data from an On-site Sample,” Journal of Environmental Economics and

Management.

Egan, K.J., J.A. Herriges, C.L. Kling, and J.A. Downing (2006). “Valuing Water Quality as a

Function of Physical Measures,” working paper.

Ekstrand, E., J. Loomis, “Incorporating Respondent Uncertainty When Estimating Willingness to

Pay for Protecting Critical Habitat for Threatened and Endangered Fish,” Water Resources

Research, 34 (11), 3149-55.

Haab, T.C., and K.E. McConnell (2002). Valuing Environmental and Natural Resources: The

Econometrics of Non-Market Valuation. Edward Elgar Publishing.

Hoehn, J., A. Randall, “A Satisfactory Benefit-Cost Indicator From Contingent Valuation,”

Journal of Environmental Economics and Management, 14 (1987), 226-47.

Krupnick, A., A. Alberini, M. Cropper, N. Simon, B. O'Brien, R. Goeree, M. Heintzelman,

“Age, Health and the Willingness to Pay for Mortality Risk Reductions: A Contingent

Valuation Survey of Ontario Residents,” Journal of Risk and Uncertainty, 24 (2002), 161-86.

Krinsky, I., A.L. Robb. 1986. “On Approximating the Statistical Properties of Elasticities.”

Review of Economics and Statistics 68:715-19.

Loomis, J. (2005). “Economic Values without Prices: The Importance of Nonmarket Values and

Valuation for Informing Public Policy Debates,” Choices 20(3) p.179-182.

Mitchell, R., R. Carson, Using Surveys to Value Public Goods: The Contingent Valuation

Method, (Washington, D.C.: Resources for the Future, 1989).

32

Rowe, R., R. d’Arge, D. Brookshire, “An Experiment on the Economic Value of Visibility,”

Journal of Environmental Economics and Management, 7 (1980), 1-19.

Shaw, D. (1988). "On-site Samples' Regression: Problems of Non-Negative Integers, Truncation,

and Endogenous Stratification." Journal of Econometrics 37: 211-23.

Sommer, A. and B. Sohngen (2002). “Pricing the Environment: An Introduction,” The Ohio

State University Extension Fact Sheet, AE-9-02.