Title: Amenity Valuation in Simultaneous Hedonic Property Markets: An Exploration of Rental and Sales Markets in the Coastal Zone
1Amenity Valuation in Simultaneous Hedonic
Property Markets An Exploration of Rental and
Sales Markets in the Coastal Zone
- Craig E. Landry
- East Carolina University
2Hedonic 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
3Applications 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
4Land 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
5Second 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?
6Preview 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
7Agents in Simultaneous Markets
- Suppliershomebuilders and redevelopers
- Homeowners buyers in the sales market and
suppliers in the rental market - Vacationersbuyers in the rental market
8Assumptions
- 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
9Homeowners
- 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) a(m) t(n) q
- y annual income
- r(a) weekly hedonic rental price function
- P(a) annualized hedonic sales price function
- a(m) rental cost function (increasing and
convex) - t(n) consumption cost function (e.g. travel
cost) - subject to T m n
10Optimization
- First-order conditions
- Uq µ 1
- Ua µ(Pa ram) 2
- Un µt'(n) p 0, n 0, 3
- Un µt' (n) pn 0
-
- Um µr(a) a'(m) p 0, m 0, 4
- Um µr(a) a'(m) pm 0
-
- y r(a)m P(a) a(m) t(n) q 5
- T m n p 0, 6
- p T m n 0
11Optimal 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 lt m lt T
- PaUa/µ ram Ua/Uq ram
- If m T
- Pa raT
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13Optimal Consumption 3
- Consumption depends upon the balance of marginal
benefits and costs - MB Un
- MC(n) µt'(n) p
- For n 0 MC(1) gt MB
- For 0 lt n lt T MC(n) MB
- For n T MC(T) lt MB
-
14Optimal Rental Supply 4
- Supply depends upon the balance of marginal
benefits and costs - MB r(a)
- MC(m) am Um /µ p/ µ
- For m 0 MC(1) gt MB
- For 0 lt m lt T MC(m) MB
- For m T MC(T) lt MB
-
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16Vacationers
- Max subject to y r(a)v q
- where v is number of rental weeks
- First-order conditions imply
- ra /(µv)
- Interpretation for vacationers marginal WTP
- /µ rav
17Hedonic Price Equations
- P P(a,?) 5
- rr(a) 6
- Homeowners 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
18Data
- 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
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20Econometric Model
- Pi(a,?) xißp epi 5
- ri (a) zißr eri 6
- Estimate likelihood function as a Bivariate
Normal - Box-Cox transformation of dependent variable
- Model selection in first-stage probit model
21PROBIT SELECTION EQUATION (Pr(mgt0))
- Probit regression
Number of obs 690 -
LR chi2(8) 63.71 -
Prob gt chi2 0.0000 - Log likelihood -397.06653
Pseudo R2 0.0743 - --------------------------------------------------
--------------------------------- - rental Coef. Std. Err. z
Pgtz - -------------------------------------------------
-------------------------------- - 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 - --------------------------------------------------
----------------------------------
22Results for BVN Model
- Box-Cox parameter different from zero for sales
model (plt0.001), 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 (p0.002)
23Results 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
(p0.168)
24Selected Results BVN Model
- Number of obs 425
LR chi2(45) 2310.85 - Log likelihood -6268.3611
Prob gt chi2 0.0000 - -------------------------------------------------
--------------------------------------------- - Coef. Std. Err.
z Pgtz - --------------------------------------------------
--------------------------------------------- - 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
25Marginal 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 - ram for each
household that occupies house for some portion of
year (n gt 0)
26Marginal Prices
Attribute Pa ra MWTP
Sqft 0.83 0.02 0.54
Lot size 0.42 0.01 0.13
Age -328.31 -11.16 -83.90
Distance to shore -13.32 -0.38 -5.11
Ocean 8,900.01 265.03 3,094.99
MWTP Ua/µ Pa - ram
27Conclusions
- 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 homeowners and
renters preferences and rental supply - Components of marginal price can be decomposed
- Better characterization of household behavior
- Applications in policy analysis
28Extensions
- 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
29Likelihood Function
- Ir rental indicator variable
- lnL for ith observation
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