Valuing Short Term Beach Closure in a RUM Model of Recreation

Demand Using Stated Preference Data

Stela Stefanova and George R. ParsonsCamp Resources XV

August 6 – 7, Wilmington, NC

Acknowledgements

• Funded by the National Park Service• Funded by the National Oceanic and

Atmospheric Administration’s Coastal Response Research Center at the University of New Hampshire

• Presently under consideration for a chapter in: “Preference Data for Environmental Valuation”, eds. John Whitehead, Ju-Chin Huang and Tim Haab

Outline

• Motivation• Data• Padre Island National Seashore Park• Linked Model and Welfare• Our Approach to Incorporating Delayed Trips• Coefficient and Welfare estimates• Conclusion

Motivation

• Random Utility Models (RUM) are well suited for valuing seasonal closures of sites

• However, RUM are not well suited for valuing short term closures when there is substitution across time periods within the same season

• Short term closures may have little impact on total visitation to the closed site

• People may be delaying trips, in effect substituting across time periods

Data

• 884 Texas residents living within 200 miles of the Texas Gulf Coast

• 2692 day trips taken to 65 Texas Gulf Coast beaches between May and September, 2001

• Limited choice set to beaches within 300 miles of residence

Padre Island National Seashore

• Padre Island is located near Corpus Christi, Texas.

• 66 miles along the Texas Gulf Coast

• Accessible by car, approximately 30 minutes from Corpus Christi and approximately 2.5 hours from San Antonio.

•North Beach, Malaquite Beach, South Beach, Little Shell and Big Shell Beaches, Mansfield cut

•14% of people visited Padre beaches - 394 trips

A Linked Model of Site Choice and Trip Frequency

• Step 1: Discrete choice site selection– Logit– Mixed Logit

• Step 2: Trip frequency– Negative binomial

• Bockstael, Hanemann, and Kling. 1987.• Herriges, Kling, and Phaneuf. 1999. • Parsons, Jakus, and Tomasi. 2003.

Beach Characteristics

Beach CharacteristicsNumber of

BeachesMean or % of Beaches

Beach length (miles) 5.35

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%

Lifeguards 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%

Advisory/Closure history

Beach has a recent history of closures and/or advisories

11 17%

Individual CharacteristicsVariable

Mean or % of Sample(Adjusted for Stratification)

Age 41 years

Work Fulltime 62%

Student 5%

Unemployed 5%

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 Coastal Property 7%

Three Measures of Welfare Loss• Per trip

• Per season

• Loss to trip ratio

1 1 2{ } { , }

ln ln /i tc ni i tc nix tc x tcn tci C i C C

w e e

.5 ( )c o cn n n n n nW w T w T T

1 1

/N N

n nn n

ltr W PT

Strategy for Incorporating Delayed Trips Using SP

• These welfare measures rely on RP data• Do not capture substitution across time

periods in the case of a short term closure• Survey questions offered the following

options in case of site closure – visit another site now– stay home now but visit the closed site later to

“make up” for the lost trip– stay home without making up the trip later

SP Data

Option % of SP responses

Another Beach Now 19%

Padre Later 76%

Stay Home 5%

Strategy for Incorporating Delayed Trips Using SP

Two ModelsPadre Open ModelRP data on all trips

Padre Closed Model RP data on trips to Padre is replaced with SP data * Trips to other sites assumedthe same* The scaling parameter on the SP choices relative to the RP choices vanishes in estimation. Brownstone, Bunch, and Train. 2000.

Strategy for Incorporating Delayed Trips in Welfare Measures Using SP

Padre Open (RP data) Choice set:

Conventional Approach Our ApproachPadre Closed (RP) Padre Closed (RP/SP)Choice set: Choice set: non Padre sites delayed trips to Padre Padre sites

1 2,C C C

1 2,c cC C C *1C C

1C

2C2cC

Strategy for Incorporating Delayed Trips in Welfare Measures Using SP

Padre Open (RP data)Padre Utility:

Conventional Approach Our ApproachPadre Closed (RP) Padre Closed (RP/SP)Padre Utility: Padre Utility:

0

( )oj j tc j j

oU x y tc

( )cj j tc j j

cU x y tc

Strategy for Incorporating Delayed Trips in Welfare Measures Using SP

Padre Open (RP data)Expected Utility:

Padre Closed (RP)

Padre Closed (RP/SP)

1 2

( )( )

& { } { }( ) ln e e

cj tc jj tc j

c

x y tcx y tccRP SP i C j C

E v

1

( )

{ }( ) ln e j tc jx y tcc

RP i CE v

1 2

( )( )

{ } { }( ) ln e e

oj tc jj tc j x y tcx y tco

RP i C j CE v

Strategy for Incorporating Delayed Trips in Welfare Measures Using SP

Padre Closed - Conventional Approach

Padre Closed - Accounting For Delayed Trips

( ) ( ) /c oRP RP RP tcw E v E v

& &( ) ( ) /c oRP SP RP SP RP tcw E v E v

Results LogitPADRE OPEN MODEL

Variable Mean T stat.

Travel cost -0.022 -22.28

Gulf 0.630 4.529

Restroom 0.414 4.438

Lifeguard 0.089 0.89

State park 0.321 1.224

Length 0.232 8.214

Machine clean 0.953 8.52

Vehicle free 0.852 9.087

Remote 0.118 1.142

Manual clean 0.338 3.001

Variable Mean T stat.

Concession -0.330 -3.405

Red tide -1.738 -5.342

Closure -0.526 -2.594

Padre ASC 1.477 7.683

Region 2 1.173 4.224

Region 3 2.150 4.912

Region 4 1.080 2.963

Region 5 1.606 4.843

Region 6 0.503 1.312

PADRE CLOSED MODEL

Padre ASC 1.116 9.289

Results Mixed LogitPADRE OPEN MODEL Fixed parameters Mean T stat.

Travel cost -0.027 -15.28

Restroom 0.419 4.43

Lifeguard 0.111 1.039

State park 0.374 1.398

Length 0.247 8.437

Machine clean 1.085 8.860

Manual clean 0.333 2.893

Concession -0.407 -3.906

Red tide -1.645 -4.905

Closure -0.487 -2.342

Padre ASC 1.911 8.208

Random Parameters Mean T stat. Std. Dev. T stat.

Padre Closed Std. Dev.

Gulf 0.904 2.56 0.836 1.27 0.823

Vehicle free 0.926 8.97 0.006 0.03 0.008

Remote -0.189 -1.01 1.309 3.72 1.299

Region 1 0.000 Fixed 0.000 0.00 0.009

Region 2 1.302 4.19 0.181 0.24 0.136

Region 3 2.218 4.72 0.005 0.02 0.000

Region 4 1.118 2.72 0.072 0.07 0.047

Region 5 1.747 4.58 1.644 5.09 1.704

Region 6 0.240 0.44 1.951 3.61 1.787

PADRE CLOSED MODEL

Padre ASC 1.499 10.93Unconstrained in Padre Closed

Welfare Loss for Closure of All Padre Beaches (2001$)

Logit Mixed LogitConventional approach:Per season 10.13 11.49Per trip 5.48 5.40Loss to trip ratio 70.62 80.10

Accounting for delayed trips:Per season 2.88 2.62Per trip 1.48 1.20Loss to trip ratio 83.66 76.11

Conclusion

• Included the alternative of delaying a trip in a conventional RUM

• Estimated losses are 72% to 77% lower when delayed trips are incorporated in the model

References

• Bockstael, N., W. M. Hanemann, and C. L. Kling. 1987. Estimating the Value of Water Quality Improvements in a Recreational Demand Framework. Water Resources Research 23, no. 5: 951-60.

• Parsons, G. R., P. Jakus, and T. Tomasi. 2003. A comparison of welfare estimates from four models for linking seasonal recreational trips to multinomial models of site choice,” Journal of Environmental Economics and Management 38(2): 143-157.

• Brownstone, D., D. S. Bunch, and K. Train. 2000. Joint mixed logit models of stated and revealed preferences for alternative fuel vehicles. Transportation Research Record B, 34.

Step 1: Discrete choice site selection

• Logit

1

( ) ln exp( )nS

n tc ni x ii

E v tc x

1

exp( )( )

exp( )n

tc nk x knt nkt S

tc ni x ii

tc xpr k L

tc x

Step 1: Discrete choice site selection

• Mixed logit

1 1

1( ) ln exp( )

nSRr

n tc ni x ir i

E v tc xR

( ) ( , ) ( | , )nt nkt tc x x x x xpr k L f d

1

1( ) ( )

Rr

ni nk xr

pr k LR

Step 2: Trip frequency

• Negative binomial model

( ( ) / , )n n tc nT f E v z

Pr( ) ( ) / !

where exp{ ( ( ) / ) }

n nnT un nn n

n n tc n

T u e T

E v z

Negative Binomial Results

Variable Coefficient T-Stat.

Intercept -2.96 -3.98

Iv/beta_tc 0.01 0.01

lnage 0.16 -0.10

female -0.09 -0.25

fulltime 0.15 -0.03

childdm 0.22 0.06

property 0.24 -0.03

ownboat 0.31 0.14

own pool -0.17 -0.36

ownsfcst 0.13 -0.02

spanish -0.07 -0.32

gradsch 0.46 0.17

college 0.30 0.11

high sc. -0.23 -0.42

retired -0.09 -0.41

att 0.29 0.22

Dispersion 0.30 0.25

Linked model

Welfare in linked model