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MARINERESOURCE

ECONOMICS

Published by the MRE Foundation, Inc. in association with theNorth American Association of Fisheries Economists (NAAFE)

and the International Institute of Fisheries Economics & Trade (IIFET)

Valuing Beach Closures on the Padre Island National Seashore

GEORGE R. PARSONSAMI K. KANGUniversity of DelawareCHRISTOPHER G. LEGGETT Industrial Economics, IncorporatedKEVIN J. BOYLEVirginia Tech

213

Marine Resource Economics, Volume 24, pp. 213-235 0738-1360/00 $3.00 + .00Printed in the U.S.A. All rights reserved. Copyright © 2009 MRE Foundation, Inc.

George R. Parsons is a professor in the College of Earth, Ocean, and Environment and the Department of Eco-nomics at the University of Delaware, Newark, DE 19716 USA (email: [email protected]). Christopher G. Leggett is a special consultant at Industrial Economics, Inc., 2067 Massachusetts Ave., Cambridge, MA 02140 USA (email: [email protected]). Ami K. Kang is a doctoral student in College of Earth, Ocean, and Environment at the University of Delaware, Newark, DE 19716 USA (email: [email protected]). Kevin J. Boyle is a professor in the Department of Agricultural and Applied Economics, 208A Hutchenson Hall, Vir-ginia Tech, Blacksburg, VA 24061 USA (email: [email protected]). This research was funded by the National Park Service and the National Oceanic and Atmospheric Adminis-tration’s Coastal Response Research Center at the University of New Hampshire. We thank Bruce Peacock for his oversight and suggestion to study Padre Island; Marla Lindsay for managing the survey effort; Ben Sigman for his work on site definition and data assembly; Roger von Haefen for helpful comments at the 2007 Southern Economics Association Meetings; Nancy Bockstael and John Duffield for help in the early stages of designing our survey; Eric English and Steve Thur for comments on earlier presentations; and Stela Stefanova for coding. 1 Other national seashores include Assateague Island (VA), Canaveral (FL), Cape Hatteras (NC), and Fire Is-land (NY). For a complete listing of all parks in the National Park Service system go to <http://www.nps.gov/archive/parks.html>. The Padre Island web site is <http://www.nps.gov/pais/>.

Valuing Beach Closures on the Padre Island National Seashore

GEORGE R. PARSONSAMI K. KANGUniversity of DelawareCHRISTOPHER G. LEGGETT Industrial Economics, IncorporatedKEVIN J. BOYLEVirginia Tech

Abstract We estimate the economic loss due to hypothetical beach clo-sures on the Padre Island National Seashore on the Gulf Coast of Texas. We consider the closure of the entire park, groups of beaches in the park, and for comparison, beaches elsewhere on the coast. We estimate a linked site choice/trip frequency model of day trips. The site choice model is estimated using multinomial and mixed logit. The trip frequency model is estimated us-ing a negative binomial regression. Using the mixed logit model, the mean per-trip loss for the closure of all Padre beaches is about $20; the loss-to-trip ratio is about $180, and the aggregate loss for a season (May-September) is about $73 million (2008$). Key words Random utility model, beach use, mixed-logit.

JEL Classification Code Q26.

Introduction

Padre Island National Seashore is one of several seashores managed by the National Park Service (NPS).1 The NPS advertises Padre Island National Seashore as the longest re-maining stretch of undeveloped barrier island in the world. It is located on the Gulf Coast

Parsons, Leggett, Kang, and Boyle214

of Texas southeast of Corpus Christi, running approximately 70 miles from north to south (figures 1 and 2). It is accessible by road at its northern entrance and by water at several southern locations. The most popular beaches are located on the five northernmost miles of the island. These are accessible by paved road or packed sand and have ample parking and facilities for beach visitors, anglers, and others. From the five-mile marker south the beaches become more natural and remote with access by four-wheel drive vehicles only. Visitors use the park for typical beach activities like sunbathing, swimming, walking, surf fishing, windsurfing, wildlife viewing, and so on. Camping is also popular. Our purpose is to estimate the economic loss that might result due to beach closures on Padre Island. The results should be useful in damage assessment and benefit-cost analysis applied to the Texas Gulf Coast and, through transfer, to other coastal areas. We chose Padre Island as part of a larger project targeting valuation estimates for natural resource damages due to closures of national parks.2 The Natural Resources Defense Council recently reported over 250 beach closures or advisories in Texas in 2008 alone, mostly from unknown sources of contamination or storm-water overflow (see Dorfman and Rosselot [2009]). In addition, given the volume of oil tanker traffic in the Gulf, there is also the possibility of closure due to oil spill. Our valuation estimates are based on a travel-cost random-utility maximization (RUM) model. We estimated the model using data on beach trips to the Gulf Coast made by 884 randomly drawn Texas residents in 2001. Our focus is on day trips and our choice model includes 65 beaches of which six are part of the Padre Island National Seashore. We estimated the model in two stages: site choice and trip frequency. (See Bockstael and McConnell (2007, p.131-7) for a description of the two-stage approach.) The site choice model is estimated as a multinomial and mixed logit. The trip frequency model is esti-mated as negative binomial regression with the log-sum or expected utility of a trip from the site choice model as an argument. We use the model to simulate the closure of: (i) all Padre Island beaches, (ii) the three northernmost beaches on Padre Island, (iii) the three southernmost beaches on Padre Island, (iv) the most popular beaches in each of six coast-al regions in the state, and (v) the closure of all beaches in each of the six coastal regions. Scenarios (iv) and (v) consider non-Padre Island beaches for comparison. Our application builds on previously applied RUM models used to value beach use. Table 1 documents several major data sets constructed for RUM applications of beach use and shows selected papers published using the data. All previous studies use logit models to estimate site-choice, but the forms used vary widely, including standard multinomial logit (e.g., Hicks and Strand [2000], nested logit (e.g., Whitehead et al. [2009]), and mixed logit (e.g., von Haefen, Phaneuf, and Parsons [2004]). Some of the applications model trip frequency, but most do not. None of the previous applications have valued Texas beaches, and none have focused on valuing beaches at a national seashore. All, however, have esti-mated models capable of measuring losses from a beach closure, similar to the objective of the current paper. Table 9, to be discussed later, presents a comparison of per-trip values for beach closures for those studies that presented such estimates. The balance of the paper is outlined as follows: presentation of the two-stage model, description of data, presentation of results, and conclusions.

Model

We estimate separate site choice and trip frequency models. This approach was popular-ized by Bockstael, Hanemann, and Kling (1987) and used by Hausman, Leonard, and McFadden (1995). Herriges, Kling, and Phaneuf (1999) and Bockstael and McConnell

2 See Leggett et al. (2003) for another paper related to this project and applied to the Fort Sumter National Monument in South Carolina.

Valuing Beach Closures 215

(2007, 131-7) refer to this approach as a ‘linked’ model. We estimate our models sequen-tially. This enables us to consider a fairly sophisticated random parameter logit model at the site choice stage. Simultaneous estimation (Full Information Maximum Likelihood) was only possible with fixed parameters at the site level. Using random parameters led to convergence difficulties. Given the importance of capturing realistic substitution patterns across sites, which random parameters logit (also known as mixed logit) is good for, we decided to stay with sequential estimation. This lowers the statistical efficiency of our es-timates somewhat, but introduces no bias.3

Figure 1. Padre Island National Seashore

3 An alternative is the repeated discrete choice model where the frequency stage is estimated as a binary choice (see Morey, Rowe, and Watson [1993]). As discussed by Bockstael and McConnell (2007) and shown by Par-sons, Jakus, and Tomasi (1999) and Hellerstein (1999), the binary repeated discrete choice and Poisson (or negative binomial) at the frequency stage are nearly equivalent mathematically. The literature has somewhat favored the repeated binary trip frequency model because it is set in a time frame that is consistent with the site choice and allows for integration of the two stages in a consistent utility theoretic model. While appealing in practice, there is little difference in the welfare estimates obtained from the two approaches. Another alternative is the Kuhn-Tucker approach, which we have not attempted to estimate with these data (see Phaneuf, Kling, and Herriges [1998] or von Haefen, Phaneuf, and Parsons [2004]).


Site Choice

Consider the site choice portion of our model first. We assume a person has decided to make a beach trip and is considering which beach to visit. Each beach gives a site utility of unit, where n=1…, N is a person in our sample, i=1,…, Sn is a beach on the Gulf Coast within 300 miles of person n’s residence, and t=1,…,Tn is a trip taken by person n during the season. A person is assumed to choose the beach with the largest site utility giving trip utility of 1max( ,....., )

nnt n t nS tv u u on trip t. Site utility in our model takes the form:

Figure 2. The Texas Gulf Coast and Beaches Included in the Choice Set by Region


Tabl

e 1

Trav

el C

ost R

ando

m U

tility

Mod

els A

pplie

d to

Bea

ch R

ecre

atio

n

Dat

a Se

t

Publ

ishe

d St

udie

s

Res

ourc

e C

hang

es V

alue

d

1974

Bos

ton

Are

a–30

Bea

ches

B

inkl

ey a

nd H

anem

ann

(197

8); H

anem

ann

(197

8)

Cha

nges

in w

ater

qua

lity

mea

sure

d by

oil,

I

n-pe

rson

/At-h

ome

surv

ey

Feen

berg

and

Mill

s (19

80);

Boc

ksta

el, H

anem

ann,

tu

rbid

ity, C

OD

, and

feca

l col

iform

. B

osto

n ar

ea re

side

nts.

and

Stra

nd (1

984)

; Boc

ksta

el, H

anem

ann,

and

Klin

g (1

987)

1984

Che

sape

ake

Bay

–12

Bea

ches

B

ocks

tael

, McC

onne

ll, a

nd S

trand

(198

8);

Cha

nges

in w

ater

qua

lity

mea

sure

d by

nitr

ogen

, O

n-si

te a

nd p

hone

surv

ey o

f

Haa

b an

d H

icks

(199

7); H

icks

and

Stra

nd (2

000)

ph

osph

orou

s, an

d fe

cal c

olifo

rm.

are

a re

side

nts.

1987

New

Bed

ford

Har

bor–

5 B

each

es

McC

onne

ll (1

986)

; Haa

b an

d H

icks

(199

7)

n/a

1994

Flo

rida–

297

Bea

ches

En

viro

nmen

tal E

cono

mic

s Res

earc

h G

roup

(199

8)

Clo

sure

of b

each

es d

ue to

Tam

pa B

ay o

il sp

ill.

Pho

ne su

rvey

of C

trl. F

lorid

a re

side

nts.

1997

Mid

-Atla

ntic

–62

Bea

ches

Pa

rson

s, M

asse

y, a

nd T

omas

i (19

99);

Mas

sey

(200

2)

Clo

sure

of b

each

es a

nd c

hang

e in

bea

ch w

idth

s. M

ail s

urve

y of

Del

awar

e re

side

nts.

Pars

ons (

2003

); Pa

rson

s and

Mas

sey

(200

3);

H

aab

and

McC

onne

ll (2

002)

; von

Hae

fen,

Pha

neuf

, and

Pars

ons (

2004

); vo

n H

aefe

n, M

asse

y, a

nd A

dam

owic

z (2

005)

19

98 L

ake

Erie

–15

Bea

ches

(Ohi

o)

Mur

ray

(199

9); M

urra

y, S

ohng

en, a

nd P

ende

lton

(200

1);

Cha

nge

in sw

imm

ing

advi

sorie

s, w

here

adv

isor

ies

On-

site

surv

ey.

Yeh,

Haa

b, a

nd S

ohng

en (2

006)

ar

e m

easu

red

as n

umbe

r of a

dvis

orie

s in

past

two

ye

ars.

1999

-200

0 So

. Cal

iforn

ia–5

3 B

each

es

Han

eman

n et

al.

(200

4); H

anem

ann,

Pen

delto

n, a

nd

Clo

sure

of b

each

es a

nd c

hang

es in

wat

er q

ualit

y,

Ph

one

surv

ey o

f Sou

ther

n C

alifo

rnia

M

ohn

(200

5); H

ilger

and

Han

eman

n (2

006)

as

mea

sure

d by

a c

ompo

site

inde

x of

seve

ral

re

side

nts.

po

lluta

nts.

20

00-0

1 Sa

n D

iego

–31

Bea

ches

Le

w (2

002)

; Lew

and

Lar

son

(200

5a,b

);

Clo

sure

of b

each

es.

Pho

ne/M

ail/P

hone

surv

ey o

f Le

w a

nd L

arso

n (2

008)

San

Die

go C

ount

y re

side

nts.

2004

Nor

th C

arol

ina–

17 B

each

es

Whi

tehe

ad e

t al.

(200

9)

Cha

nge

in b

each

wid

ths

Ph

one

surv

ey o

f N

. Car

olin

a re

side

nts.


unit = βtctcni + βxxi + εnit, (1)

where tcni is the trip cost of reaching site i for person n. It includes out-of-pocket travel as well as time cost. The vector xi is a set of site characteristics and εnit is a random error term. Trip costs vary across sites and people by virtue of travel and time costs from residences to beaches. Site characteristics vary across sites and are constant across trips and people. Following conventional random utility theory, the observed trip data are treated as the outcome of a stochastic process, where individual n’s probability of choosing alterna-tive k on a given trip is:

(2)

where u′ni = βtctcni + βxxi represents the deterministic portion of site utility and εnit repre-sents the stochastic portion. The likelihood of observing the pattern of choices made by our sample then is:

nt nt1 1 1

( ) ( )n nS TN

n k t

pr k w k

(3) wnt (k) = 1 if person n chooses alternative k on trip t wnt (k) = 0 if not.

The standard multinomial logit specification for the probability of visiting a site has the well-known closed form:

1

exp( )( ) .

exp( )n

tc nk x knt nkt S

tc ni x ii

β tc β xpr k L

β tc β x

(4)

Equation (4) follows from the assumption that the error terms in equation (2) are indepen-dent and identically distributed type 1 extreme value random. In our mixed logit model, the assumption of independence of irrelevant alternatives is relaxed, allowing a more re-alistic pattern of substitution across sites. The mixed logit probability is an integral over a standard logit:

prnt(k) = ∫Lnkt(βtc,βx)ƒ(βx | μx,φx)dβx, (5)

where Lnkt is the multinomial logit probability shown in equation (4), f (βx | μx, φx) is a mixing distribution (normal in our case), with mean μx and standard deviation φx. Now, we seek estimates of the parameters βtc, μx, φx. Since integration of equation (5) is not possible, the parameters are estimated using simulated maximum likelihood. As noted, the mixed logit model relaxes the assumption of independence of irrelevant alternatives in the standard logit and allows for a more general pattern of substitution across sites (Train 2003, Ch. 6). Sites with the same attributes, such as the presence of lifeguards or same region, will exhibit correlation via the mixing distribution. The greater the standard deviation φx for a given attribute, the greater the degree of correlation and hence substitution (at least stochastically) among sites sharing the same attributes.

( ) ( ,) for allnt nk nkt ni nitpr k pr u' ε u' ε i k


Estimation proceeds as follows. Specify a distribution for f (βx | μx, φx) using hypo-thetical starting values for μx, φx. Draw R values of βx from this distribution giving r

xβwhere r = 1,…,R. Form a simulated probability:

1

1( ) ( ).R

rnt nk x

rpr k L β

R

(6)

This is an average logit probability, averaged over the R draws on rxβ from the mixing

distribution. In our application, we use a separate set of draws for each individual and assume independent normal distributions for each parameter. This allows for correla-tion across trips for each person—one draw is made for each person for all of his/her trips. The probability in equation (6) is then entered into the likelihood function for each success or visit made by a person in our sample. This gives a simulated likelihood. The maximum simulated likelihood estimator then is the value of the vector βtc, μx, φx that maximizes Λ. The procedure and numerical methods used to solve for the maximum are discussed in detail in Train (2003, Chapter 6).

Trip Frequency

To account for changes in the number of trips taken over a season due to site closures, we use a linked trip frequency model:

Tn = ƒ(E(vn)/ –βtc,zn), (7) where Tn is the number of trips taken to all sites in the season by person n, zn is a vector of individual characteristics believed to influence the number of trips taken in a season, and E(vn) / –βtc is the expected maximum value of a trip measured in the site choice model (‘linking’ site choice and trip frequency). In the standard multinomial logit model:

1

( ) ln exp( ).nS

n tc ni x ii

E v β tc β x

(8)

In the mixed logit model E(vn) takes the same form, but is constructed by simulation to account for the variability of the parameter estimates for βx. The expected trip utility is the mean of the log-sum, averaged over the draws on r

xβ :

1 1

1( ) ln exp( ) .nSR

rn tc ni x i

r iE v β tc β x

R

(9)

Since –βtc is the marginal utility of income from the site choice model, E(vn) / –βtc is the expected value of a trip. We expect a positive relationship between Tn and E(vn) / –βtc—the greater the expected value of a trip, the more trips a person takes.4 While short of being fully utility theoretic, one way to motivate the trip frequency equation is to view it as mapping out an individual’s increasing opportunity cost of taking trips as the number of trips taken increases. Consider figure 3, an inverted and linear ver-sion of equation (7). An individual’s marginal value of a trip exceeds the opportunity cost

4 See Bockstael and McConnell (2007, 131-8) for a full discussion and analysis of the linked model.


of a trip over the range of 0 to T*; hence the person takes the first, second, third, and up to the T*th trip. At T* the expected utility of a trip (E(v*)/ –βtc) is equal to the opportunity cost of another trip. The higher a person’s expected value of a trip, the greater his chosen number of trips. Observing different individuals then facing different E(vn)/ –βtc due to differences in location, we are able estimate a trip frequency equation.5 We use a negative binomial regression in our application to account for the integer nature of trip data and over dispersion that was evident in our simpler Poisson regression:6

( )Pr( ) (1 )( ) ( 1)

where / ( ) and exp( ( ( ) / ) ).

nT θnn n n

n

n n n n n tc n

θ TT r rθ T

r λ θ λ λ α E v β δz

(10)

The fitted form for equation (10) is used to predict the change in trips by each person in the sample due to a beach closure and, in turn, is used to estimate the seasonal change in trip utility as described in the next section.

5 For an alternative interpretation see Hausman, Leonard, and McFadden (1995).6 We used NegBin 2 discussed by Greene (2008, p. 913).

Figure 3. Trip Frequency


Three Measures of Value: Per-trip, Seasonal, and Loss-to-trips Ratio

Let C ∈{C1,C2} be the set of all beaches in Texas, where C2 is the set of Padre Island sites and C1 is the set of all other sites. The closure of the C2 Padre sites causes the ex-pected utility of a trip for each person in our sample to decline from

The expected per-trip loss for person n due the closure of Padre Island then is:

0( ) ( ) / ,cn n n tcw E v E v β

(11)

where –βtc monetizes the loss in utility (Hanemann 1999). Per-trip loss in equation (11) is an expected loss that applies to all trips made by respondents living within 300 miles of Padre Island whether they visited a Padre Island beach or not. Closure of Padre removes available sites from each person’s choice set resulting in an expected welfare loss. The closure may also induce a change in the number of trips a person takes during a season. Indeed, with the lower expected value of a trip, the trip frequency equation will predict a decline in trips from To to Tc as shown in figure 4. The seasonal welfare loss is the area A + B. Area A ({E(vo) – E(vc)/ –βtc}·Tc) is the loss associated with continuing to take trips but now having to choose from fewer beaches. Area B is the loss associated with the adjustment in the number of trips taken. The seasonal loss for the closure of Padre Island for person n then is the sum of Area A and B in figure 4 for person n or the integral under the trip frequency function from ( ) / to ( ) / ,o c

n tc n tcE v β E v β which in the negative binomial form is:

0( )

( )

( ( ) / ) / ,c

n

E Vn

E Vo c

n n tc EVW f E v β = T T δ (12)

where δEV is the coefficient estimate on the expected utility in the trip frequency model. Again, we stress that this interpretation is not fully utility theoretic since the models at the two stages are not formed from a single consistent utility model. The last measure of loss we consider is a loss-to-trips ratio sometimes used in benefit transfer applications. The loss-to-trip ratio applies only to the trips taken to the closed site or sites. The ratio for a Padre Island closure is:

1 1

/ ,N N

on n

n nltr W T

(13)

where onT is the predicted number of trips taken by person n to a Padre Island beach.

Equation (13) then is the total sample loss divided by the total number of trips to Padre predicted for the sample. If an actual closure were known to displace X trips from Padre, X · ltr is a reasonable measure of total loss.

21 1{ , } { }

1 1

1 1( ) ln exp( ) to ( ) ln exp( ) .R R

o r c rn tc ni x i n tc ni x ii C C i C

r rE v β tc β x E v β tc β x

R R


Data

The choice data used to estimate our model were collected in 2001 in two parts—survey data of trips and site characteristic data for the 65 beaches. The survey data were gathered in a phone-mail-phone survey from May through September—the peak season for beach visits. Texas residents living within 200 miles of the Gulf of Mexico (closest point on the coast) were sampled by random digit dialing and recruited to participate in a follow-up survey of beach use. The sample was stratified, as shown in table 2, to avoid a sample dominated by residents of Houston and to oversample residents living near the Gulf Coast and Padre Island. The initial telephone survey was conducted in May and administered to the adult member of the household (>17 years old) with the most recent birthday. English and Spanish versions of the survey were offered. We had a 23% response rate—complete in-terviews divided by total households contacted. Users and nonusers of Texas Gulf Coast beaches were identified in this initial survey. We define a user as anyone who had visited the coast in the past five years and reported that they were likely to make a visit during our survey period. Seventy-seven percent of the people contacted in our initial phone survey were users—1,154 people. Of these, 1,012 agreed to participate in five monthly surveys on Texas Gulf Coast beach use. Basic demographic information was gathered on each respondent in the initial phone survey. Those who agreed to participate in the follow-up survey received a mail packet that included a map of the coast, a list of beaches, a calendar to help record trips from May through September, and a decorative magnet of the state of Texas for posting the calendar. The materials included in the mailing were intended to help respondents identify beaches and remember/record the actual dates of their trips. As an incentive, individuals who agreed to participate in the follow-up survey were given a phone card with 100 minutes of free calls. They were also told that they would receive a second card upon completion

Figure 4. Trip Frequency with a Change in the Expected Value of a Trip Due to Closure


of entire follow-up survey. At the time phone cards were a popular way to make long dis-tance calls from any location at reasonable rates. Individuals were then contacted monthly by phone to report their beach trips for the previous month. Of the 1,012 respondents who agreed to participate in the follow-up surveys, 884 (87%) completed the June survey, 803 (79%) completed the survey through July, 741 (73%) through August, 670 (66%) through September, and 601 (59%) through October. Keeping respondents participating in the survey effort for five months was chal-lenging; this repeated survey approach was used to reduce errors in trip recall, and for another modeling effort focusing on the dynamics of trips over a season we needed time- specific trip data. We estimated our site choice model using observed trip data from all 884 respondents for the months they reported data. The characteristics of our sample respondents are shown in table 3. These are weight-ed means to account for sample stratification and are the variables used in the vector zn in equation (7) in estimation. The second part of our data set covers the characteristics of the 65 beach sites—the xi vector in equation (1). We collected data on all of the public beaches on the Texas Gulf Coast including information on facilities, amenities, services, and physical characteristics. The beaches included bay side and gulf beaches and were defined using the 2002 Texas Beach & Bay Access Guide and on-site visits to confirm the beach characteristics. This effort included interviews with beach managers at the city, county, and state levels; inde-pendent travel guides; visits to each of the beaches; and reviews of on-line maps of the area. The Padre Island National Seashore was divided into six separate beaches following the National Park Service definitions. As shown in table 4, 48 beaches (74%) are on the Gulf Coast, 4 (6%) are in state parks, 22 (34%) are remote, and 26 (40%) are vehicle free. We defined remote as requiring a visitor to leave major roads to access the beach. These beaches tend to be more natural but are more difficult access. Most beaches in Texas accumulate debris from the waters of the Gulf of Mexico. Some is natural (seaweed, etc.) and some is from human sources. For this reason, many of beaches are actively cleaned manually and/or by machine. We include separate variables for machine and manual cleaning. We also include separate dummy variables to identify beaches with restrooms, lifeguards, and concessions. To distinguish beaches by water quality, we included two variables: closure/advisory history and red tide. We had originally hoped to use an objective measure of water quali-ty, but such data are not gathered uniformly across the beaches. Some are monitored more heavily, some get intermittent readings, some none at all, and some are checked only when problems are expected. We opted for a subjective measure based on interviews with beach managers for the different areas. Among the questions we asked the managers was whether or not there had been any beach advisories, closures, or red tide events at any of the beaches in their area. This information was used to construct the closure/advisory his-tory and red tide dummy used in the model. We have 11 beaches (17%) with a closure/advisory history during the year and 12 beaches (18%) with red tide episodes. Respondents reported a total of 2,692 trips over the five-month period—28% of all trips were less than 30 miles one way, 44% were less than 50 miles, and 81% were less than 100 miles. Only 7% of all trips were taken to the beach closest to a person’s home, and only about 44% were taken to one of the five closest beaches. This implies a large number of trips taken to enjoy specific character-istics of a beach. For example, an individual may travel past a nearby beach because it does not have lifeguards or because it allows vehicles on the beach. Travel cost was calculated at $0.365 per mile plus any fee paid to use a beach.7 Time cost is valued at one-third of household income divided by 2,000 as a proxy for foregone household wages. Distances and times to beaches were calculated using PC Miler. Aver-age trip cost of reaching the chosen site was $56. The average cost to all sites was $182. 7 $0.36 per mile was the 2001 U.S. General Services Administration privately owned vehicle mileage reimburse-ment rate.


Each person’s choice set included all beaches within 300 miles of their residence.8 The average choice set size is 53 beaches. The minimum is 14, and the maximum is 65.

8 We chose 300 miles for a number of reasons. First, the travel time is feasible. Second, the maximum distance people trav-eled for a day trip in our data extended about this far for a few people. Third, as Parsons and Hauber (1998) show, the effect of expanding distance traveled from 150 to 200 to 300, typically has little effect on the model or welfare results, because the ex-panded distance brings in low probability sites for visiting. We reconcile the distance for sampling at 200 miles and the distance for the choice set at 300, based on a preliminary survey. We conducted a simple random phone survey asking people if they had made a day trip to the beach in recent years. The trips seemed to die out for people after 150 to 200 miles to the nearest beach. At the same time, since many people did not go to the nearest beach, distances traveled to the actual site visited could be, and in some cases was, further than 200 miles. So, even if their nearest beach was 200 miles, their choice set is probably wider than that. Again, our experience has been that adjusting these far-off distances does not affect the results in a significant way.9 All numbers reported in this paragraph are corrected for stratification.

Table 2Areas of Stratification

Strata Percent of All Respondents

Stratum 1: Padre Island Area Coastal Counties 40(9 counties closest to the Padre Island National Seashore) Stratum 2: Other Coastal Counties 25(10 counties adjacent to the coast and not included in Stratum 1)

Stratum 3: Harris County (Houston) 10 Stratum 4: Inland Counties 25(8 counties located within 200 miles of the coast and not included in Stratum 1, 2, or 3)

It is also useful to note that 42% of the respondents took only one trip during the five-month sampling period, 66% took two or fewer, and 76% took three or fewer.9 Also, most people visited only a few sites over the season. Seventy percent visited only one, 85% visited two or fewer, and 95% visited five or fewer. Galveston and Corpus Christi were the most heavily visited regions—56% of all were to the Galveston area and 25% were to Corpus Christi. About 10% of all trips are to Padre, with the northernmost three beaches (North, Malaquite, and South Beaches) accounting for 95% of these trips.

Table 3Individual Characteristics

Variable Mean or % of Sample (Adjusted for Stratification)Age 41 yearsYes/No Dichotomous Variables:Work Fulltime 62%Children Under 17 49%High School 32%College 24%Graduate School 10%Retire 9%Spanish 9%Female 60%Own Boat 24%Own Pool 24%Own Fishing Equip 49%Own Coastal Property 7%


Results

Coefficient Estimates

Our estimation results are shown in tables 5 and 6. First, let’s consider the MNL and MXL site choice models in table 5. The coefficient on Trip Cost, our marginal utility of income, is negative and significant in both models. All else constant, people prefer a beach closer to home. The Log(Length) variable scales beaches to account for size and is positive and significant in both models as well. Neither of these variables was estimated with a random coefficient in the MXL model. The coefficients in the MXL are somewhat larger than the MNL model. This scaling in estimation is common. The following variables (ignoring the regional dummies for now) have positive and statistically significant mean coefficient estimates in both the MNL and MXL models: Machine Cleaning, Manual Cleaning, Vehicle Free, and Rest Room. It is worth noting that beaches without vehicle access on the sand are required by law to have off-sand parking facilities to accommodate visitors, so the Vehicle Free variable may be picking up the effect of better parking facilities at these beaches over the beaches with vehicle access. Or, the variable may be simply capturing an average preference over the sample for beaches without cars for safety and aesthetic reasons.10 While it is not entirely surpris-ing that the coefficient on this variable is positive, it is somewhat surprising the estimated standard deviation in the MXL model is not larger. That would have signaled that these beaches have strong unobserved similarity, but that was not our finding.

Table 4Beach Characteristics

Beach Characteristics Number of Mean or % Beaches of Beaches

Length (miles) 5.35

Dichotomous Yes/No Variables: Gulf Access Beach is located on the Gulf 48 74%State Park Beach is part of a state park 4 6%Remote Beach has a remote location 22 34%Vehicle Free Vehicles not allowed on beach 26 40%Manual Cleaning Beach is routinely manually cleaned 33 51%Machine Cleaning Beach is routinely machined cleaned 36 55%Rest Room Restrooms located at beach 37 57%Lifeguard Lifeguards at beach 17 26%Concession Concession located at beach 15 23%Red Tide History Beach has a recent history of red tide 12 18%Closure/Advisory History Beach has a recent history of closures 11 17% and/or advisories

10 We originally thought the population would be divided on this attribute, so we included two interactive vari-ables (ownership of a four-wheel drive vehicle and ownership of surf-cast fishing equipment) to pick-up this anticipated effect. We thought these two groups would have a preference for beaches that allowed vehicles. The signs on the coefficients were as expected, but neither was large enough to suggest that people owning such equipment prefer beaches that allow vehicles and neither was significant.


Gulf Access, State Park, Lifeguard and Remote are positive in both models but with-out statistical significance on their mean coefficients in some cases. A positive sign on Gulf Access, State Park, and Lifeguard was expected, but we had no prior expectation on Remote. A positive sign indicates that, all else constant, people prefer a more natural beach. A negative sign might indicate the reverse or perhaps that there are costs beyond those controlled for in our trip cost variable, such as the need for a four-wheel vehicle and traveling over unpaved roads. The former effect appears to dominate in our choice data.

Table 5Site Choice Models

Variable Multinomial Logit Mixed Logit (t-stats in parentheses) (t-stats in parentheses) Log-Likelihood: –8,014.3 Log-Likelihood: –7,675.3

Mean Standard Deviation

Trip Cost –.0216* (34.6) –.0542* (23.0) –

Log(Length) .10* (5.4) .272* (10.6) –

Gulf Access .675* (7.5) .182 (1.3) .106 (0.4)

State Park .324 (1.8) .039 (0.08) 2.10* (2.9)

Remote .317* (5.4) .152 (1.79) .123 (.29)

Vehicle Free .709* (10.2) 1.22* (13.9) .042 (.31)

Manual Cleaning .272* (3.5) .34* (3.4) .291 (.255)

Machine Cleaning .829* (10.6) 2.08* (11.6) .838* (2.7)

Rest Room .650* (11.3) .706* (9.4) .028 (.12)

Lifeguard .008 (0.1) .655* (3.8) 4.17* (6.8)

Concessions –.501* (8.7) –1.04* (12.1) .038 (.12)

Red Tide History –1.29* (5.4) –1.40* (2.0) 1.01 (1.3)

Closure/Advisory History –.121 (0.9) –6.07* (4.4) 7.82* (6.5)

Padre .474* (3.9) –8.63* (4.4) 16.6* (8.0)

Sabine Pass – – 2.7* (3.1)

Galveston 1.08* (5.2) 3.43* ( 3.9) 5.42* (13.6)

Freeport 1.50* (4.3) 3.01* (3.0) 1.40 (0.8)

Port Lavaca –.400 (1.4) .364 (.36) .507 (0.7)

Corpus Christi 1.02* (4.0) 2.63* (2.9) 2.25* (5.9)

South Padre Island .114 (0.3) 4.68* (4.5) 1.49* (2.2)

# of people: 561; # of sites in choice set (max, min, mean): 53,14,65.* Statistical significance with 99% confidence.


The variables with negative and statistically significant mean coefficient estimates in both models include: Redtide History and Concession. The sign on the Redtide History coefficient is as expected, reflecting both fewer days a site is available during the season and perhaps the perception that a beach is prone to pollution problems. Concession is a surprise. This may be due to measurement error, or the coefficient may be capturing some congestion effects. The mean coefficient on Closure/Advisory History is negative in both models, but only significant in the MXL model. Among the site characteristic variables, State Park, Lifeguard, and Closure/Advisory History have large and significant estimated standard deviations in the MXL model (third column of coefficients in table 5). When the estimated standard deviation is large relative to its mean, this indicates correlation among the site utilities sharing the attribute and im-plies a high degree of substitution (in a stochastic sense) among these sites. The regional constants, Galveston through South Padre Island, are all positive and significant, with the exception of Port Lavaca. The excluded region is Sabine Pass, the northernmost region with the fewest visits among the six regions. The coefficients on the standard deviations for Corpus Christi and Galveston are the largest relative to their means, suggesting greater shared similarities within each of these regions and hence greater substitution among sites. The standard deviation estimate on the Padre constant is

Table 6Trip Frequency Models

Variable Negative Binomial Negative Binomial w/MNL Log-Sum w/MXL Log-Sum (t-stats in parentheses) (t-stats in parentheses)

Constant –4.21* (6.9) –4.01* (6.7)Log Sum/ –βtc .015* (16.1) .02* (16.4)Log (Age) .22 (1.4) .026 (1.7)Work Full Time .02 (0.2) .04 (0.4)Child Under 17 .07 (0.8) .07 (0.7)High School –.13 (1.2) –.15 (1.3)College .33* (2.8) .29* (2.5)Grad School .20 (1.1) .23 (1.3)Retire –.13 (0.7) –.10 (0.6)Spanish .17 (0.9) .11 (0.7)Female –.11 (0.2) –.12 (1.3)Own Boat .16 (1.5) .21* (2.0)Own Pool –.04 (0.3) .00 (0.0)Own Fish Equip. .19* (2.0) .15 (1.6)Own Coastal Property .10 (0.6) .12 (0.8)Number of Waves Completed .29* (7.6) .29* (7.8) Dispersion 1.20 1.15Log Likelihood 2,111.5 2,121.7No. People Taking at Least One Trip 561 561No. People Taking No Trips 323 323

* Statistical significance with 99% confidence.


also quite large, suggesting highly correlated unobserved site attributes and strong substi-tution among sites for Padre Island beaches. The trip frequency portion of the model is shown in table 6. The coefficient on the expected value of a trip, the log sum divided by the trip cost coefficient, has the expected sign and is the best predictor in the model. College and Owning Fish Equipment are the only variables estimated with statistical significance for predicting trip frequency. The number of months a person has been in survey works as expected—positive and sig-nificant. The longer a person is in the sample, the larger the predicted number of trips. In prediction, we set number of months to five for each respondent.

Welfare Estimates for Beach Closures

Our welfare results are shown in tables 7 and 8 for the multinomial (MNL) and mixed (MXL) models and are reported in 2008$. First, notice the impact of using MXL versus MNL. The loss for the closure of all of the Padre Island National Seashore is estimated at $3.44 per trip in the MNL model and $20.09 in the MXL model—different by a factor of more than 5. This is due to the large standard deviation estimated on the Padre coefficient in the MXL model. This estimate signals strong shared unobservables among the sites on Padre and hence high stochastic substitution among sites. When the substitution is ac-counted for (by estimating MXL with a random parameter on Padre), the loss is high for complete closure because individuals have to substitute to sites outside the Padre group, which is undesirable. On the other hand, the loss for closing only the three northern beaches is magnified by less than a factor of two in the MXL versus MNL and is actually lower for the loss of the southern three beaches. Indeed, in the MNL model the estimate for losing the three northern Padre beaches is 80% of loss of losing all Padre beaches. In the MXL model, it is only 22% of the loss of all the beaches. So, there is a considerable substitution effect being picked up by using MXL with variation on the Padre coefficient. The same results apply to the single beach and regional loss scenarios outside of Padre because we are allowing for variation in our regional constant in MXL estimation. The single beach losses (middle of tables 7 and 8) are all lower in the MXL versus MNL, capturing the effect of substitution within the region. Since only one beach in a region is closed, people can substitute another beach within the region with little loss. Notice that the difference between the MNL an MXL results are largest for the sites in regions with high estimated standard deviations on their regional constants. The MXL values range from as low as 30% of the MNL values to as high as 93%. At the same time, the regional beach losses (bottom of the tables 7 and 8) tend to be higher in the MXL. Again, this is because with all sites closed, individuals are forced to visit sites outside the group. Fur-ther, notice that the larger the estimated standard deviation (better substitution), the larger the loss tends to be in the MXL versus MNL.11 Focusing on the MXL results and comparing losses across different scenarios, we see that closure of all Padre gives a loss of $20.09 per trip for all six beaches, $4.53 for the three northern beaches, and $0.23 for the three southern beaches. Among the most popu-lar beaches in each region, East Beach in Galveston has the largest loss at $2.21 per trip. East Beach is the most frequently visited beach in Texas and, as noted above, is located near major population centers. The least-valued beach among each region’s most popular beach is Sea Rim State Park in the northernmost region of the Gulf Coast with per-trip values of $0.13. The loss due to the closure of all sites in a region is highest for Galveston at $55.63 per trip and lowest for Sabine Pass at $1.98. 11 The standard deviation coefficient estimate here is working much like an inclusive value coefficient in a nested logit model where the smaller the inclusive value coefficient is, the greater the loss for losing the full nest and the smaller the loss for losing individual sites within the nest. See Hauber and Parsons (2000) and Herriges and Kling (1997) for more discussion.


As noted earlier, mean per-trip values for each site or group of sites in a RUM model apply to trips taken to all sites in the choice set by all respondents in the sample. For example, most respondents in our sample have Padre Island sites in their choice set and have some positive probability of visiting a Padre site.12 For many people, the prob-ability of visiting a Padre site will be low (people located far from Padre Island), and their expected per-trip value for a closure will be low. For others, the probability will be high, and their expected per-trip value will be large. In any case, all trips, whether made to Padre Island or not, figure in this per-trip calculation since we average across all trips to all beaches. Clearly, how the choice set is formed originally and who is included in the choice model has a large bearing on the estimated per-trip values from a RUM model. Keeping this context in mind, our estimated values are in a range similar to those found in other RUM applications. We have listed per-trip values from four studies in table 9 for comparison. Parsons and Massey (2003) report per-trip values for the loss of individual beaches in the Mid-Atlantic. Their values range from <$0.01 to $4.85 (2008$) and apply to all trips taken by Delaware residents to beaches in Delaware and New Jer-sey. Since many of the sites in northern New Jersey are quite far away from the relevant population, mean per-trip values for these beaches are near zero. When they consider the closure of groups of beaches nearer their respondent population, losses are greater—$14.94 for the closure of the six northernmost beaches in the state and $2.94 for the closure of the eight southernmost. Unlike the other three studies in the table and our Texas application, Parsons and Massey’s sample pertains to the general population, not just identified beach-goers. Lew and Larson’s values for individual beaches range from $0.01 to $1.22 and apply to all trips taken by beachgoers in San Diego County. The Environmental Economics Research Group estimated per-trip losses at $7.49 to $15.06 for the closure of all beaches in the Tampa Bay area. It is not clear from their report how many out of the full set of 297 are closed, probably ten or more. Again, these estimates apply to the beach going popula-tion in western Florida. Finally, Hicks and Strand (2000) estimate per-trip values of $4.27 and $6.50 for closure of two separate beaches on the Chesapeake Bay. While these values tend to confirm that the general range of our per-trip estimates conforms to prior research, caution is warranted in making comparisons across studies. Values vary due to differences in the beaches areas, number of sites included in the choice sets, populations considered (all residents versus beachgoers only, nearby counties versus area extending far inland, and so forth), modeling approaches, trip cost calculation, num-ber of beaches closed, and so on. All of these features create variation in the valuation estimates. For example, concerning trip cost alone, when we estimate our model using 100%, instead of 33%, of the wage proxy, our values nearly double. Tables 7 and 8 also show our estimates in terms of per-season loss for the same set of sce-narios. As described above, these estimates account for adjustments in the total number of trips taken when there is a site closure and thereby allows for no-trip substitution. The decrease in number of trips taken to all Texas beaches drops by about 4% in the MNL model and by about 21% in MXL model when there is a closure of all Padre sites (this is adjusted for stratification). The seasonal MXL values in table 8 are nearly twice the per-trip values as expected. Mean values per season range from $84.57 for the closure of all Galveston sites, to $0.16 for the closure of Magnolia Beach only. The last column in tables 7 and 8, the aggregate seasonal loss, is the mean per-season loss times the population of Texas residents over 17 years old within 200 miles of the coast identified as beachgoers (approximately 2.5 million people). In the MXL model, aggregate seasonal (five months from May to Sep-tember) values are $73 million for the closure of all Padre Island sites and range from a high of $174 million for the closure of all Galveston beaches to a low of $340 thousand for the closure of Magnolia Beach only.

12 About 10% do not have Padre Island in their choice set and hence will have zero value for the loss of Padre sites. These respondents are averaged in our losses.


Finally, tables 7 and 8 also show our estimates as a loss-to-trip ratio computed using equation (13). This measure is useful in benefit transfer applications. When the number of displaced trips to a specific site or sites is easy to predict, as is often the case in transfers, one may seek a corresponding loss per trip to the specific site or sites. Our estimates in the MXL model give a loss-to-trip ratio of $179 for the closure of all Padre sites. The loss-to-trip ratio is higher for the loss of groups of sites (ranges from $32 to $98) versus single sites (ranges from $25 to $34), again capturing the notion that the set of available substitutes and spectrum of utilities is shrinking as the number of sites lost increases. To distinguish our loss-to-trip ratio from our per-trip value loss, note that the former applies to trips taken specifically to the site or sites of interest, and the latter applies to a trip taken to any site on the Texas coast.

Table 7Welfare Losses for Selected Scenarios using the Multinomial Logit Model (2008$)*

Beach(es) Closed Region Per-trip Per-season Loss-to-trips Aggregate Loss Loss Ratio Five-month Loss (Millions)

Padre Island Scenarios:

All 6 PI Beaches Corpus $3.44 $5.85 $58.07 $12.04

3 Northern PI Beaches Corpus 2.72 4.65 57.62 9.57

3 Southern PI Beaches Corpus 0.63 1.13 56.42 2.33

Non-Padre Island Scenarios (Most Popular Beach in Each Region):

Sea Rim State Park Sabine Pass $0.44 $0.98 $56.27 $2.02

East Beach Galveston 4.32 11.36 57.12 23.37

Surfside Beach Freeport 0.63 1.62 56.22 3.33

Magnolia Beach Port Lavaca 0.13 0.18 56.10 0.37

Rockport Beach Corpus 1.23 2.08 56.62 4.27

City of South Padre South Padre Island Beach Island 0.46 0.73 57.30 1.51

Non-Padre Island Scenarios (Entire Region):

All Beaches in Sabine Pass $1.75 $3.77 $56.88 $7.76

All Beaches in Galveston 53.09 94.57 68.04 194.46

All Beaches in Freeport 5.86 14.61 57.62 30.05

All Beaches in Port Lavaca 2.59 3.39 57.10 6.98

All Beaches in Corpus 28.94 30.39 70.38 62.49

All Beaches in South Padre Island 5.07 7.65 61.58 15.72

* Converted from 2001$ to 2008$ using the CPI reported by the Minneapolis Fed (2001$ = 177; 2008$ = 215.2).


Table 8Welfare Losses for Selected Scenarios using the Mixed Logit Model (2008$)*

Beach(es) Closed Region Per-trip Per-season Loss-to-trips Aggregate Loss Loss Ratio Five-month Loss (Millions)

Padre Island Scenarios:

All 6 PI Beaches Corpus $20.09 $35.59 $179.52 $73.19

3 Northern PI Beaches Corpus 4.53 9.03 50.95 18.56

3 Southern PI Beaches Corpus 0.23 0.50 23.60 1.02

Non-Padre Island Scenarios (Most Popular Beach in Each Region):

Sea Rim State Park Sabine Pass $0.13 $0.23 $33.84 $0.48

East Beach Galveston 2.21 5.44 25.37 11.18

Surfside Beach Freeport 0.49 1.38 27.92 2.83

Magnolia Beach Port Lavaca 0.12 0.16 26.19 0.34

Rockport Beach Corpus 0.40 0.84 26.85 1.72

City of South Padre South Padre Island 0.33 0.81 24.73 1.66Island Beach

Non-Padre Island Scenarios (Entire Region):

All Beaches in Sabine Pass $1.98 $3.39 $48.43 $6.97

All Beaches in Galveston 55.63 84.57 67.08 173.90

All Beaches in Freeport 4.54 11.46 51.54 23.57

All Beaches in Port Lavaca 1.98 2.10 32.46 4.32

All Beaches in Corpus 34.35 46.58 98.22 95.78

All Beaches in South Padre Island 5.02 8.06 54.50 16.56

* Converted from 2001$ to 2008$ using the CPI reported by the Minneapolis Fed (2001$ = 177; 2008$ = 215.2).


Tabl

e 9

Per-t

rip V

alue

s for

Bea

ch U

se fr

om D

ay T

rip T

rave

l Cos

t RU

M M

odel

s

Stud

y

B

each

es in

Cho

ice

Set

R

elev

ant P

opul

atio

n

Pe

r-trip

Val

ue

Per-t

rip V

alue

s

B

each

Clo

sure

s

as R

epor

ted

in

2008

$*

Hic

ks a

nd S

trand

(200

0)

10 b

each

es o

n th

e B

each

goer

s in

the

$2

.06

(198

4$)

$4.2

7 C

losu

re o

f one

bea

ch (B

ay R

idge

)

Che

sape

ake

Bay

C

hesa

peak

e B

ay A

rea

amon

g se

t of 1

0.

$3.1

4 (1

984$

) $6

.50

Clo

sure

of o

ne b

each

(San

dy

Po

int)

amon

g se

t of 1

0.

Envi

ronm

enta

l Eco

nom

ics

297

beac

hes i

n Fl

orid

a B

each

goer

s in

wes

tern

Flo

rida

$5.1

6–$1

0.37

$7

.49–

$15.

06

Clo

sure

of T

ampa

Bay

are

a

Res

earc

h G

roup

(199

8)

(199

4$)

be

ache

s am

ong

297

beac

hes.

Pars

ons a

nd M

asse

y (2

003)

62

bea

ches

in N

ew Je

rsey

, A

ll re

side

nts o

f the

<

$0.0

1–$3

.62

$0.0

1–$4

.85

Clo

sure

of o

ne b

each

am

ong

set o

f

Del

awar

e, M

aryl

and,

St

ate

of D

elaw

are

over

(1

997$

)

62 (r

ange

cov

ers c

losu

re o

f eac

h

and

Virg

inia

17

yea

rs o

f age

of

the

62 b

each

es in

divi

dual

ly).

$11.

14 (1

997$

) $1

4.94

A

ll no

rther

n be

ache

s in

DE,

6 be

ache

s am

ong

set o

f 62.

$2

.19

(199

7$)

$2.9

4 A

ll so

uthe

rn b

each

es in

DE,

8

beac

hes a

mon

g se

t of 6

2.

Lew

and

Lar

son

(200

5b)

31 b

each

es in

San

Die

go

Bea

chgo

ers i

n Sa

n D

iego

$0

.01–

$1.0

0 $0

.01–

$1.2

2 C

losu

re o

f one

bea

ch a

mon

g se

t of

C

ount

y C

ount

y (2

001$

)

31 (r

ange

cov

ers c

losu

re o

f eac

h

of

the

31 b

each

es in

divi

dual

ly).

* Con

verte

d us

ing

the

Min

neap

olis

Fed

CPI

con

verte

r.


Conclusions

We have demonstrated that the welfare loss associated with the closure of beaches on the Padre Island National Seashore in the event of a major incident such as an oil spill or other disruption is likely to be substantial. We estimated that a closure for an entire sea-son (May-September) generates a loss of about $70 million (2008$) in terms of consumer surplus. This value applies only to day-trips for beach recreation by Texas residents. It ig-nores overnight beach use, non-use, uses other than recreation, and day trips from out of state, so the actual losses would be larger. We also show that a similar closure of individ-ual beaches would result in aggregate losses that range from $340 thousand to over $11 million for a season and that closure of entire regions (such as the Galveston area) could be as high as $170 million (2008$). Our findings are the first estimates we are aware of for the Texas side of the Gulf Coast of Mexico. We also found that the mixed logit model works well in accounting for substitution effects among Padre sites and that estimating with mixed versus multinomial logit had a large effect on the final welfare estimates. Future applications with this data set will include incorporating the timing of trips over a season, a comparison of different mixed logit models to explore the effectiveness of these models in accounting for different patterns of substitution, and an application looking at non-monetary compensation for beach closures.

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