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

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Lesley Bishop
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1 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

2 Beach Nourishment

NC Beach Nourishment: 1961-2006 Annual costs = $4.

3 NC Beach Nourishment: 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

4 Market for Beach Width Price S D Beach Width

5 Implicit Market: Travel cost method Travel cost D D Trips

6 Construct Validity The degree to which inferences can be made from the measures of a theoretical construct to the theoretical TCM estimate of ΔCS Market measure of ΔCS

7 Convergent validity The degree to which a measure is similar to other measures that it should also be similar to. Single-site TCM estimate of ΔCS, ΔX Multi-site TCM estimate of ΔCS, ΔX

8 A comparison of three TCM models over ΔCS and Δx Single-site revealed and stated preference model Linked multiple-site revealed preference / trip frequency model Kuhn-Tucker seasonal demand system

9 Beaches: j=17

10 Model 1: Single Site Model Travel cost D = RP, SP D = SP lnμ it = β X + u i + e it D D Trips: X = Σx j

11 Model 2: Linked Model Step 1: Discrete choice site selection model Beach Trip Bogue Banks Topsail Island New Hanover County Brunswick County 5 Beaches 3 Beaches 4 Beaches 5 Beaches

12 Step 1: Nested Logit π ni = e v ni θ m [ ] v θ θ e j [ ] v θ e θ j nj mj 1 v = α TC + β Q

13 Step 2: Linked Model Negative binomial trip frequency model IV(q) X(IV(p,q),y,z) Trips: X = Σx i

14 Model 3: Kuhn-Tucker Model Travel cost D j = RP D j = RP D j D j Trips: x j

15 via Maximum Likelihood M 1 U() = Ψ jln φjxj + θ + z ρ ρ ln lnφ ρ lnθ j j j= 1 Ψ = δ s + με μ = γ q * ln, j * 1 exp( ) = * = θ = μ j ρ

16 Data 2003 Survey n = beach goers n = 800+ with complete RP data n = 600+ with complete SP data n = 351 with X = Σx j Single and multi-day trips

17 Σx j -X Mean = 2.24 (n = 535) Variable t-value STD = Quantiles 100% = % = 10 90% = 3 10% = -1 5% = -3 0% = -98 Intercept 0.25 house 0.34 children 0.84 married 1.28 male 0.35 white age 1.28 educ income2-0.98

18 SP scenario: Increase average width by 100 feet

19 Single Site Trips RP last year SP status quo SP trips with improved access SP trips with increased width 12.85

20 Sunset Beach Multiple-Site Data Beach Trips (%) Width Access Park Length Fort Macon Atlantic Beach Pine Knoll Shores Indian Beach / S.P Emerald Isle North Topsail Beach Surf City Topsail Beach Wrightsville Beach Carolina Beach Kure Beach Fort Fisher Caswell Beach Oak Island Holden Beach Ocean Isle Beach

21 Travel cost ( ) ( ) ( ) p= 2 c d + θ w 2 d mph, Single Site minimum distance TC = $94 Outer banks TC = $203 Mean multiple site TC = $125 (n = = 5967)

22 Single Site Models SP Random Effects Poisson RP-SP Random Effects Poisson Coeff. t-ratio Coeff. t-ratio Constant Own travel cost Substitute travel cost Income Married Stated preference Access improvement Increase in beach width α Cases Periods 3 4

23 Linked Model Nested Logit Site Selection Negative Binomial Trip Frequency Coeff. t-ratio Coeff. t-ratio Travel cost Constant Beach width Income Access areas Married Parking spaces Log sum Beach length Alpha Inclusive Value Sample size

24 Kuhn-Tucker Model Model 1 Model 2 Model 3 Coeff. t-ratio Coeff. t-ratio Coeff. t-ratio Intercept Fixed Effects Fixed Effects Married Translating Access Length Parking Beach Width Income ln(u)

25 Convergent Validity Multiple Site Single Site Linked K-T SP RP-SP ΔX ΔWTP $2.93 $14.44 $6.59 $6.53 X X ΔWTP $32.49 $ $73.41 $72.74

26 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

27 Policy Implications: Costs The annual cost to replace one feet of eroded beach $32,000 per mile 60 miles 100 feet Every 4 years Annual cost $48,000,000

28 Net benefits NB = $60m $48m Property benefits are not included Environmental costs are not included

29 Additional Research Consider those with mismatched trips Consider sample selection effects Compare with other multiple site models (e.g., negative binomial) Use new measure of RP-SP travel cost

DIVISION OF COASTAL MANAGEMENT TO STUDY CURRENT LONG-TERM EROSION RATES ADJACENT TO TERMINAL GROINS

DIVISION OF COASTAL MANAGEMENT TO STUDY CURRENT LONG-TERM EROSION RATES ADJACENT TO TERMINAL GROINS North Carolina Department of Environmental Quality Division of Coastal Management February 22, 2018 N.