Estimating the Economic Value of Beach Nourishment

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Estimating the Economic Value of Beach Nourishment

• John Whitehead, ASU Dan Phaneuf, NCSU Chris
  Dumas, UNCW Jim Herstine, UNCW Jeff Hill, UNCW
  Bob Beurger, UNCW

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Convergent Validity of Revealed and Stated
Recreation Behavior with Quality Change A
Comparison of Multiple and Single Site Demands

• John Whitehead, ASU Dan Phaneuf, NCSU Chris
  Dumas, UNCW Jim Herstine, UNCW Jeff Hill, UNCW
  Bob Beurger, UNCW

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Beach Nourishment
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(No Transcript)
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NC Beach Nourishment 1961-2006

• Annual costs 4.37 million (2004 )
• Annual cost of nourishing all 138 miles 831
  million
• The number of NC beaches annually nourished
  ranges from one to seven (a small fraction of
  total beaches)

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Market for Beach Width?
Price
S
D
Beach Width
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Implicit Market Travel cost method
Travel cost
D
D
Trips
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Construct Validity

• The degree to which inferences can be made from
  the measures of a theoretical construct to the
  theoretical construct

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Construct validity tests

• Length of stay Loomis, ERE, 1993
• Site selection Grijalva, Berrens, Bohara and
  Shaw, AJAE, 2002
• Hurricane evacuation Whitehead, ERE, 2005

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Convergent validity

• The degree to which a measure is similar to other
  measures for which it should also be similar.

Revealed Preference
Stated Preference
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Convergent validity tests

• WTP and implicit market values Carson et al.,
  Land Econ, 1996
• RP and SP number of trips Jeon and Herriges,
  working paper, 2005

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Hypothetical bias

• Experimental WTP List and Gallet, ERE, 2001
• Experimental WTP Murphy et al. ERE, 2005
• Whitehead et al., JES, forthcoming

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A comparison of three TCM models over ?CS and ?x

• Single-site RP and SP model
• Linked multiple-site RP site-selection and trip
  frequency model
• Kuhn-Tucker RP seasonal demand system

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Issues

• Single-site models are less capable of
  incorporating substitutes
• RP data may not be able to forecast accurately
  beyond the range of historical experience
• SP data is subject to hypothetical bias

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Current Application NC Beaches
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Model 1 Single Site Model
Travel cost
D RP, SP D SP
D
D
Trips X Sxj
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Model 1 Welfare

• lnµit b0 b1p b2p b3y b4q
• b5SP ui eit
• CS per trip SP0 -x(q) x(qo)/b1
• CS CS per trip X DX

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Model 2 Linked Model

• Step 1 Discrete choice site selection model

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Step 1 Nested Logit
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Nested Logit details
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Step 2 Linked Model

• Negative binomial trip frequency model

X(IV,y,z)
IV(q)
Trips X Sxi
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Linked Model Welfare

• WTP per trip -IV(q) IV(qo)/d
• WTP WTP per trip X DX

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Model 3 Kuhn-Tucker Model
Travel costj
Dj RP Dj RP
Dj
Dj
Trips xj
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via Maximum Likelihood
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Kuhn-Tucker Model Welfare

• Welfare analysis and demand prediction in the KT
  model relies on Monte Carlo integration in which
  the unobserved heterogeneity (error) terms are
  drawn conditionally so that behavior at baseline
  travel cost and site conditions is replicated in
  the simulated outcomes. Given multiple simulated
  error vectors for each person compensating
  surplus is calculated for each error draw, and
  the average over people and draws provides an
  estimate of E(CS)
• See appendix and references for details

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Data

• 2003 Survey
• n 1000 beach goers
• n 800 with complete RP data
• n 600 with complete SP data
• n 351 with X Sxj
• Single and multi-day trips

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Sxj -X
Probit for sample selection Probit for sample selection
Variable t-value
Intercept 0.25
house 0.34
children 0.84
married 1.28
male 0.35
white -0.94
age 1.28
educ -0.12
income2 -0.98

• Mean 2.24 (n 535)
• STD 21.52
• Quantiles
• 100 260
• 95 10
• 90 3
• 10 -1
• 5 -3
• 0 -98

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Single Site Trips
RP last year 10.06
SP status quo 11.93
SP trips with improved access 15.41
SP trips with increased width 12.85
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Multiple-Site Data
Beach Trips () Width Access Park Length
Fort Macon 4.56 90 2 602 1.40
Atlantic Beach 21.08 135 19 662 4.90
Pine Knoll Shores 0.85 110 6 195 4.80
Indian Beach / S.P. 1.14 90 2 131 2.50
Emerald Isle 11.11 130 69 550 11.50
North Topsail Beach 3.42 82 42 929 9.70
Surf City 5.7 90 36 272 5.10
Topsail Beach 1.99 110 37 234 4.00
Wrightsville Beach 24.22 160 45 1479 4.50
Carolina Beach 7.98 185 26 452 2.00
Kure Beach 2.56 130 20 223 2.80
Fort Fisher 1.14 400 2 240 1.90
Caswell Beach 0.28 80 12 103 2.80
Oak Island 2.28 120 66 821 7.50
Holden Beach 3.7 90 21 200 6.80
Ocean Isle Beach 6.55 85 28 341 5.30
Sunset Beach 1.42 115 34 260 1.20
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Travel cost

• Single Site minimum distance TC 94
• Outer banks TC 203
• Mean multiple site TC 125 (n 17 351
  5967)

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Single Site Models
SP Random Effects Poisson SP Random Effects Poisson RP-SP Random Effects Poisson RP-SP Random Effects Poisson
Coeff. t-ratio Coeff. t-ratio
Constant 2.278 14.09 2.077 13.37
Own travel cost -0.011 -11.28 -0.011 -11.07
Substitute travel cost 0.004 4.13 0.004 4.14
Income 0.010 4.10 0.011 4.40
Married -0.549 -4.61 -0.526 -4.40
Stated preference 0.171 8.87
Access improvement 0.256 16.69 0.256 15.97
Increase in beach width 0.074 2.58 0.074 2.56
a 0.986 10.48 0.952 10.396
Cases 351 351 351 351
Periods 3 3 4 4
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Linked Model
Nested Logit Site Selection Nested Logit Site Selection Nested Logit Site Selection Negative Binomial Trip Frequency Negative Binomial Trip Frequency Negative Binomial Trip Frequency
Coeff. t-ratio Coeff. t-ratio
Travel cost -0.100 -25.91 Constant 2.321 16.90
Beach width 0.003 8.35 Income 0.019 6.60
Access areas 0.003 1.94 Married -0.424 -2.82
Parking spaces 0.001 17.85 Log sum 0.117 10.02
Beach length 0.020 1.94 Alpha 1.053 13.20
Inclusive Value 0.673 21.34
Sample size 5967 351
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Kuhn-Tucker Model
Model 1 Model 1 Model 2 Model 2 Model 3 Model 3
Coeff. t-ratio Coeff. t-ratio Coeff. t-ratio
Intercept -2.720 -1.17 Fixed Effects Fixed Effects Fixed Effects Fixed Effects
Married -0.028 -0.13 -0.033 -0.14 -0.034 -0.14
Translating 2.087 16.00 1.442 6.48 1.599 8.05
Access -0.004 -1.48 -0.002 -0.33 -0.007 -2.21
Length 0.011 0.71 -0.040 -1.19
Parking 0.001 10.52 0.000 1.38 0.000 1.98
Beach Width 0.001 1.55 0.002 2.06 0.003 2.71
Income -0.609 -1.52 -0.611 -1.41 -0.609 -1.40
ln(u) -0.284 -5.18 -0.195 -3.32 -0.194 -3.30
Fixed effects NO NO YES YES YES YES
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Convergent Validity
Multiple Site Multiple Site Single Site Single Site
Linked K-T SP RP-SP
?X 1.03 1.10 1.08 1.08
WTP, CS per trip 2.93 14.44 6.59 6.53
X 11.09 11.16 11.14 11.14
X WTP, CS per trip 32.49 164.65 73.41 72.74
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Policy Implications Benefits

• 1.58m households in the study region
• 64 participants
• Aggregate benefit 772 million
• The annual recreation benefit of increased width
  60 million

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Policy Implications Costs

• The annual cost to replace one foot of eroded
  beach 32,000 per mile
• 60 miles
• 100 feet
• Every 4 years
• Annual cost 48,000,000

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Net benefits

• NB 60m 48m
• NB lt 0 in linked model
• Property benefits are not included
• Environmental costs are not included

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Conclusions

• Single-site and multi-site models are
  statistically convergent valid for quality change
  not economically convergent valid
• Hypothetical bias can be adjusted with SP 0
• Joint estimation of RP and SP is not needed in
  this application
• RP data is able to forecast beyond the range of
  historical experience

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Additional Research

• Compare CS and WTP per trip
• Is it hypothetical bias?
• Consider those with mismatched trips
• Consider sample selection effects
• Compare with other multiple site models (e.g.,
  participation model)