Amenity Valuation in Simultaneous Hedonic Property Markets: An Exploration of Rental and Sales Markets in the Coastal ZoneCraig E. LandryEast Carolina University

Hedonic Property Price MethodRevealed preference method of non-market valuationUse 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 preferencesPa = Ua/Uq

Applications of Hedonic Price MethodEnvironmental values in exotic locationsSki chalets, Lake retreats, Alpine villasBeach homesBeach erosion and beach qualityFlood & wind hazardsCoastal amenities ViewProximity to beachOpen spaceWater quality

Land Markets in Exotic LocationsLimited land supplyCompetitive bidding for landSales prices adjust to reflect heterogeneity of parcels and structuresSome properties also traded in rental marketRental prices will reflect heterogeneityRental income can be important source of funds for mortgage, taxes, insurance

Second Homes in Exotic LocationsOwner often does not occupy house year-roundMay see same property traded in 2 marketsSales market capital assetRental market pure consumptionImplications for theory of hedonic prices, statistical estimation, and welfare analysis?

Preview of ResultsSimultaneous markets alter hedonic theory and interpretation of marginal implicit pricesImplications depend upon purpose of analysis/analytical approach utilizedEstimation of a simultaneous system of hedonic price equations improves efficiency

Agents in Simultaneous MarketsSuppliershomebuilders and redevelopersHomeowners buyers in the sales market and suppliers in the rental marketVacationersbuyers in the rental market

AssumptionsAll agents take hedonic price schedules as givenIgnore seasonal variation in rental priceAsset risk factors (forest fire, avalanche, flood, erosion) will not affect rental ratesBuyers consider rental market when forming property bidsUsage for any period of time is a reasonable representation of usage patterns

Homeowners Max Ui(a,n,m,q) a vector of housing attributesn personal consumption of vacation propertym rental supply of vacation propertyq numeraire subject to y + r(a)m P(a) + (m) + (n) + qy annual incomer(a) weekly hedonic rental price functionP(a) annualized hedonic sales price function(m) rental cost function (increasing and convex)(n) consumption cost function (e.g. travel cost) subject to T m + n

OptimizationFirst-order conditions:Uq = [1]

Ua = (Pa ram)[2]

Un '(n) 0, n 0,[3][Un ' (n) ]n = 0Um + [r(a) '(m)] 0, m 0, [4][Um + [r(a) '(m)] ]m = 0y + r(a)m = P(a) + (m) + (n)+ q[5]

T m + n 0,[6] [T m n] = 0

Optimal Housing Attributes [2]Conventional hedonic model marginal price equals marginal rate of substitutionPa = Ua/ = Ua/Uq Maintained result if m = 0If 0 < m < T: Pa=Ua/ + ram = Ua/Uq + ram If m = T: Pa= raT

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

Optimal Rental Supply [4]Supply depends upon the balance of marginal benefits and costs MB = r(a)MC(m) = m Um / + /

For m = 0: MC(1) > MB For 0 < m < T: MC(m*) = MB For m = T:MC(T) < MB

VacationersMax subject to y r(a)v + q where v is number of rental weeksFirst-order conditions implyra= /(v) Interpretation for vacationers marginal WTP / =rav

Hedonic Price EquationsP= P(a,)[5]r=r(a)[6]Homeowners preferences play a role in both price schedulesSelection of rental supply (m) induces differences across the two marketsDistribution of property characteristics Distribution of homeowners preferences

Data425 observations on properties in Dare and Brunswick counties, NCSales: 1979-1997 (expressed as annual expense)Rental rates: 1998Observe rental supply29% not rented (m = 0)36% rented fulltime (n = 0)Remaining 35% rented/consumed part of the yearOnly 12% occupied year-round (renter or owner)Observe housing and household attributes

Chart1

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Vacancy

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Figure 1: Property Usage

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Figure 1: Rental Supply

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Figure 2: Occupancy Count

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Figure 3: Vacancy Count

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Figure 1: Rental Supply, Occupancy, and Vacancy Counts

weeksvacantmn

0105146164

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Figure 1: Property Usage

Econometric ModelPi(a,) = xip + pi [5]ri (a)= zir + ri[6]

Estimate likelihood function as a Bivariate Normal Box-Cox transformation of dependent variableModel selection in first-stage probit model

PROBIT SELECTION EQUATION (Pr(m>0))

Probit regression Number of obs = 690 LR chi2(8) = 63.71 Prob > chi2 = 0.0000Log 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 ------------------------------------------------------------------------------------

Results for BVN ModelBox-Cox parameter different from zero for sales model (p

Results of BVN ModelFor 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, elevationYearly dummies generally statistically significant increasing trend11/13 significant coefficients in rental modelSquare-footage, lotsize, bedrooms, air, fireplace, garage, multistory, age, ocean-frontage, distance from shore, distance from CBDRisk variables have no explanatory powerCoefficient on Hazard Ratio not significant (p=0.168)

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

Marginal PricesNeed adjustment to r(a) since it only measure peak rentAssume 50% in pre- and post-peak periodsAssume 37% rest of yearPresent means for Pa and ra Calculate marg WTP = Ua/Uq= Pa - ram for each household that occupies house for some portion of year (n > 0)

Marginal PricesMWTP = Ua/= Pa - ram

ConclusionsCan improve efficiency by allowing for correlation of sales and rental pricesInterpretation of marginal sales price depends upon rental supply behaviorIf household occupies and rents part-time marginal price reflects both homeowners and renters preferences and rental supplyComponents of marginal price can be decomposedBetter characterization of household behaviorApplications in policy analysis

ExtensionsIdentify conditions for market equilibriumIncorporate selection into simultaneous modelMake use of Envelope theorem result to incorporate rental supplym(r(a),P(a),n,y) = Vr/Vy Recover parameters of utilityAccount for hazards/risk in model

Likelihood FunctionIr = rental indicator variablelnL for ith observation:

Our model differs from previous hedonic models involving rental markets. Wilman (1981) considered only the rental market, ignoring the sales market. Taylor and Smith (2000) focus on the behavior of firms that manage rental properties, providing evidence of market power. In what follows, we alter the basic hedonic property theory to reflect simultaneous markets, identify implications of such a change in model structure, and explore methods of estimation.

KEY POINT: Differential participation in the rental market alters the distribution of characteristics offered in the rental market. Also, the distribution of homeowner characteristics will differ between the two markets.

SELF-SELECTION going on in the rental market

HEDONIC PRICE FUNCTIONS depend upon available distributions of property characteristics and distributions of buyer and seller preferences.Single-family homes with a single owner (not time-share)Resource economists often interested in assessing some aspect of environmental quality in exotic locations.Examples: beaches, mountain retreats and recreational areas, properties adjacent to remote lakes, rivers, and streamsTo our knowledge this problem has not been examined.

and in some cases the rental market equation must be estimated to identify the component of preferences that the analyst is interested in.SUPPLIERS: It is common in applications of hedonic markets to take housing supply as fixed in the short run. In the long run, suppliers choose housing attributes and number of housing units supplied. HOMEOWNERS: choose the attributes of the houses they purchase and how much time to rent their property when they are not using it. Renting incurs: disutility (i.e. forgoing consumption of the property) and administrative and wear-and-tear costs that are increasing and convex.IMPORTANT: Household attributes affect not only the owners personal enjoyment of the property but also the price that the property may fetch in the rental market. The rental market rate also reflects the quantity supplied by other homeowners in the near vicinity. Some may choose not to rent their property; these households forego rental income, but maintain the option of using their vacation property at any time. Also, these households do not have to worry about administrative costs, damage, or wear-and-tear that occurs to their property when occupied by tenants. VACATIONERS: choose property attributes and the amount of time to rent the property. competitive market conditions in rental supply assumption is at odds with previous empirical work that has been done in this area

Dont examine supply behavior because this model does not offer any alteration to existing theory.Do not assume UTILITY is separable of a and m.Rental supply, m, shows up in both the utility function and the budget constraint because it determines the number of weeks the homeowners gets to occupy the property (n = 52 m), additional rental income accruing to the homeowner, as well as the costs associated with renting. Utility is increasing in q, a, and , and decreasing in m. We assume utility is separable in the numeraire and other arguments, and Uam < 0. ALPHA reflects administrative costs (largely fixed) and wear-and-tear costs (mostly variable)NOTE: Could include a in ALHPA if we think attributes affect cost. Has implications for interpretation of MARGINAL PRICES.

Set up Lagrangian expressionAssume interior solutions for a, q, and Lagrange multiplier[4] gives us back the budget constraint: nonlinear in a and mExamine [2] and [3] in more detailFor 0 < m < 52 The marginal hedonic sales price reflects not only marginal willingness to pay of the homeowner, but also marginal rental income. For m = 52, marginal sales price reflects the marginal rental price (assumed constant) scaled up to reflect the entire year. Since we are considering an annual planning period, there is no discounting in this result. This suggests that we cannot learn anything about homeowner preferences for attributes if they rent the entire year.

Note that the cost of renting reflects both administrative/wear-and-tear costs as well as the dollar value of the disutility of foregone consumption (the opportunity cost of renting). MB is assumed constantMC is increasing by strict concavity of U(.): A sufficient condition is Umm < 0 and m < 0, which is satisfied by strict concavity of the utility function. MCm = mm [Umm mUm]/ 2, so mUm > Umm is sufficient for increasing marginal cost. Note SIMULTANEITY between a-vector and m.Note SIMULTANEITY between a-vector and m.NOTE: Havent looked in detail at necessary conditions for equilibrium in these dual markets.Sales prices expressed as yearly expense using amortization formula and data on 30-year fixed mortgage rate at time of saleObservation of income, employment status, and education enable us to estimate a selection (PROBIT) equation, which is used to calculate the hazard ratio, included as a covariate in the RENTAL EQUATIONSurvey nature of data allowed for collection of housing characteristics at the time of sale and currently.

Risk variables (flood zone, erosion rate, elevation, location in CBRA) not included in rental equation

All coefficients are of expected signRisk variables (flood zone, erosion rate, elevation, location in CBRA) not included in rental equationOnly ELEVATION significant in SALES, though ER is significant in the independent SALES Box-CoxDare county dummy variable is insignificant in each model

Coefficient estimates are not directly comparable due to different functional formsOcean-frontage has large effectErosion rate is negative in sales model, but not significant

All estimates in constant 1998 dollars; Pa is measured in annual dollars; ra is measured in weekly, peak-season dollars; MWTP is only calculated for sub-sample m < 52; distances are measured in meters.