Craig E. Landry East Carolina University

1. Amenity Valuation in Simultaneous Hedonic Property Markets: An Exploration of Rental and Sales Markets in the Coastal Zone Craig E. Landry East Carolina University

2. Hedonic Property Price Method • Revealed preference method of non-market valuation • Use property transaction prices as signal of economic value of environmental goods and services: P = P(a) • Rosen (JPE 1974) showed how we can relate marginal implicit prices to homebuyer preferences Pa = Ua/Uq

3. Applications of Hedonic Price Method • Environmental values in exotic locations • Ski chalets, Lake retreats, Alpine villas • Beach homes • Beach erosion and beach quality • Flood & wind hazards • Coastal amenities • View • Proximity to beach • Open space • Water quality

4. Land Markets in Exotic Locations • Limited land supply • Competitive bidding for land • Sales prices adjust to reflect heterogeneity of parcels and structures • Some properties also traded in rental market • Rental prices will reflect heterogeneity • Rental income can be important source of funds for mortgage, taxes, insurance

5. Second Homes in Exotic Locations • Owner often does not occupy house year-round • May see same property traded in 2 markets • Sales market – capital asset • Rental market – pure consumption • Implications for theory of hedonic prices, statistical estimation, and welfare analysis?

6. Preview of Results • Simultaneous markets alter hedonic theory and interpretation of marginal implicit prices • Implications depend upon purpose of analysis/analytical approach utilized • Estimation of a simultaneous system of hedonic price equations improves efficiency

7. Agents in Simultaneous Markets • Suppliers—homebuilders and redevelopers • Homeowners —buyers in the sales market and suppliers in the rental market • Vacationers—buyers in the rental market

8. Assumptions • All agents take hedonic price schedules as given • Ignore seasonal variation in rental price • Asset risk factors (forest fire, avalanche, flood, erosion) will not affect rental rates • Buyers consider rental market when forming property bids • Usage for any period of time is a reasonable representation of usage patterns

9. Homeowners Max Ui(a,n,m,q) • a – vector of housing attributes • n – personal consumption of vacation property • m – rental supply of vacation property • q – numeraire subject to y + r(a)×m≥ P(a) + α(m) + τ(n) + q • y – annual income • r(a) – weekly hedonic rental price function • P(a) – annualized hedonic sales price function • α(m) – rental cost function (increasing and convex) • τ(n) – consumption cost function (e.g. travel cost) subject to T≥ m + n

10. Optimization • First-order conditions: Uq = μ [1] Ua = μ(Pa – ra×m) [2] Un – μτ'(n) – π ≤ 0, n ≥ 0, [3] [Un – μτ' (n) – π]×n = 0 Um + μ×[r(a) – α'(m)] – π ≤ 0, m ≥ 0, [4] [Um + μ×[r(a) – α'(m)] – π]×m = 0 y + r(a)×m = P(a) + α(m) + τ(n)+ q [5] T ≥ m + n π ≥ 0, [6] π ×[T – m – n] = 0

11. Optimal Housing Attributes [2] • Conventional hedonic model → marginal price equals marginal rate of substitution Pa = Ua/μ = Ua/Uq • Maintained result if m = 0 • If 0 < m < T: Pa=Ua/μ + ra×m = Ua/Uq + ra×m • If m = T: Pa= ra×T

13. Optimal Consumption [3] • Consumption depends upon the balance of marginal benefits and costs MB = Un MC(n) = μτ'(n) + π • For n = 0: MC(1) > MB • For 0 < n < T: MC(n*) = MB • For n = T: MC(T) < MB

14. Optimal Rental Supply [4] • Supply depends upon the balance of marginal benefits and costs MB = r(a) MC(m) = αm – Um /μ+ π/μ • For m = 0: MC(1) > MB • For 0 < m < T: MC(m*) = MB • For m = T: MC(T) < MB

15. $ MC r(a) MB A B m* m Figure 1: Optimal Supply in the Rental Market

16. Vacationers • Max subject to y ≥ r(a)×v + q • where v is number of rental weeks • First-order conditions imply ra= /(μ×v) • Interpretation for vacationer’s marginal WTP /μ =ra×v

17. Hedonic Price Equations • P= P(a,γ) [5] • r=r(a) [6] • Homeowner’s preferences play a role in both price schedules • Selection of rental supply (m) induces differences across the two markets • Distribution of property characteristics • Distribution of homeowners preferences

18. Data • 425 observations on properties in Dare and Brunswick counties, NC • Sales: 1979-1997 (expressed as annual expense) • Rental rates: 1998 • Observe rental supply • 29% not rented (m = 0) • 36% rented fulltime (n = 0) • Remaining 35% rented/consumed part of the year • Only 12% occupied year-round (renter or owner) • Observe housing and household attributes

20. Econometric Model • Pi(a,γ) = xi’βp + εpi [5’] • ri (a)= zi’βr + εri[6’] • Estimate likelihood function as a Bivariate Normal • Box-Cox transformation of dependent variable • Model selection in first-stage probit model

21. PROBIT SELECTION EQUATION (Pr(m>0)) • Probit regression Number of obs = 690 • LR chi2(8) = 63.71 • Prob > chi2 = 0.0000 • Log likelihood = -397.06653 Pseudo R2 = 0.0743 • ----------------------------------------------------------------------------------- • rental | Coef. Std. Err. z P>|z| • -------------+-------------------------------------------------------------------- • gradsch | -0.0958244 0.115899 -0.83 0.408 • hschool | -0.2626746 0.153001 -1.72 0.086 • retire | -0.6391054 0.1069345 -5.98 0.000 • incom98 | -0.0002414 0.0006404 -0.38 0.706 • nodare | -0.0632154 0.1286555 -0.49 0.623 • cendare | 0.4560292 0.1576279 2.89 0.004 • sodare | 0.6586108 0.351817 1.87 0.061 • nobrun | -0.233207 0.1881866 -1.24 0.215 • _cons | 0.7978059 0.1494016 5.34 0.000 • ------------------------------------------------------------------------------------

22. Results for BVN Model • Box-Cox parameter different from zero for sales model (p<0.001), not for rental model • Use semi-log form for rent • Compared to independent hedonic regressions • Overall coefficient estimates are “close” • Standard errors are generally smaller • Covariance estimate is significant (p=0.002)

23. Results of BVN Model • For significance level of 10%: • 10/14 significant coefficients in sales model • Lotsize, bedrooms, air, fireplace, multistory, age, ocean-frontage, distance from shore, distance from CBD, elevation • Yearly dummies generally statistically significant – increasing trend • 11/13 significant coefficients in rental model • Square-footage, lotsize, bedrooms, air, fireplace, garage, multistory, age, ocean-frontage, distance from shore, distance from CBD • Risk variables have no explanatory power • Coefficient on Hazard Ratio not significant (p=0.168)

24. Selected Results: BVN Model • Number of obs = 425 LR chi2(45) = 2310.85 • Log likelihood = -6268.3611 Prob > chi2 = 0.0000 • ---------------------------------------------------------------------------------------------- • | Coef. Std. Err. z P>|z| • ----------------------------------------------------------------------------------------------- • sales | • sqft | 2.28e-06 1.83e-06 1.25 0.213 • lotsize | 1.15e-06 3.88e-07 2.96 0.003 • air1 | 0.017921 0.0074215 2.41 0.016 • pur_age | -0.0008969 0.0003158 -2.84 0.005 • ocean | 0.0243136 0.0085695 2.84 0.005 • distance | -0.0000364 0.0000148 -2.46 0.014 • elev | 0.0009411 0.0004239 2.22 0.026 • -------------+-------------------------------------------------------------------------------- • rental | • sqft | 0.0000224 0.0000128 1.75 0.079 • lotsize | 0.000013 1.84e-06 7.06 0.000 • air2 | 0.2481065 0.081493 3.04 0.002 • housage | -0.0108035 0.0014259 -7.58 0.000 • ocean | 0.2565936 0.0391741 6.55 0.000 • distance | -0.0003632 0.000083 -4.38 0.000

25. Marginal Prices • Need adjustment to r(a) since it only measure peak rent • Assume 50% in pre- and post-peak periods • Assume 37% rest of year • Present means for Pa and ra • Calculate marg WTP = Ua/Uq= Pa - ra×m for each household that occupies house for some portion of year (n > 0)

26. Marginal Prices MWTP = Ua/μ= Pa - ra×m

27. Conclusions • Can improve efficiency by allowing for correlation of sales and rental prices • Interpretation of marginal sales price depends upon rental supply behavior • If household occupies and rents part-time marginal price reflects both homeowner’s and renter’s preferences and rental supply • Components of marginal price can be decomposed • Better characterization of household behavior • Applications in policy analysis

28. Extensions • Identify conditions for market equilibrium • Incorporate selection into simultaneous model • Make use of Envelope theorem result to incorporate rental supply • m(r(a),P(a),n,y) = Vr/Vy • Recover parameters of utility • Account for hazards/risk in model

29. Likelihood Function • Ir = rental indicator variable • lnL for ith observation: