Week 3: The Urban Housing Market, Structures and Density.Urban HousingDallas apartment rent Hedonic equation: 1998 (Log monthly rent)Optimizing House ConfigurationOptimizing House price (P) minus construction cost (C) as a function of square feet (see Dallas results)FW Dodge data on projects tells the impact of FAR on Costs (see Dallas slide for rent impact)If each unit of floor are is unprofitable then so is land – regardless of FAR. As FAR approaches zero, land profit is zero no At “better” locations, the price of housing at any FAR is higher. This yields a substitution of capital for land and the optiBoston Back Bay Condominium Example“Optimal” Urban DesignHow does actual land use “evolve”?The spatial Pattern of Economic RedevelopmentBoston Back Bay Condominium Example (continued)Group 1 is willing to pay the most for houses near the center, but group 2 is willing to pay the most for central land (it is Examples of location and land bidding between groupsNY Land Residuals: Highest Use? (2004 Data)MIT OpenCourseWare http://ocw.mit.edu 11.433J / 15.021J Real Estate EconomicsFall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.MIT Center for Real EstateWeek 3: The Urban Housing Market, Structures and Density.• Hedonic Regression Analysis.• Shadow “prices” versus marginal costs. • Land value maximizing FAR. • FAR and Urban Redevelopment.• Land Use competition: Highest Price for Housing – versus – highest use for landMIT Center for Real EstateUrban Housing• Great diversity from historical evolution, changes in technology and tastes. • Multiple attributes to each house: size, baths, exterior material, style….location• Consumers value each of these attributes with the normal law of micro-economics: diminishing marginal utility. • Huge industry has evolved to applying statistical models to understand and predict diverse house prices:– Property Tax appraisals.– Automatic Valuation Services for lenders, brokers…MIT Center for Real EstateHedonic Regression Analysis1). Linear:R = α + β1X1+ β2X2+ β3X3+ …X’s are structural, location attributes2). Log Linear:R = e[α + β 1X1 + β 2X2 + β3X3 + …]ln(R) = α + β1X1+ β2X2+ β3X3+ …3). Log Log:R = α X1 β 1 X2 β 2 X3 β 3…ln(R) = ln(α) + β1ln(X1) + β2ln(X2) +…MIT Center for Real EstateDallas apartment rent Hedonic equation: 1998 (Log monthly rent)Regression statisticsMultiple RR SquareAdjusted R SquareStandard errorObservations0.905186720.8193630.818995670.143785767885ANOVARegressionIntercept#BED#POOLRCASECWDAPPFPDENINTLnHome$LnSAT0.011759160.171701790.008722550.022764660.01816160.021156240.007751540.016319090.00732288-0.031857480.09666656-0.087621260.095040480.64328520.04799528-0.00076159-0.57141659 0.1762321180.0049468160.0056246260.0124432050.0058392250.001954390.005337560.0015865280.0007150920.0021400120.0025567770.0016608380.0044727870.0069280090.0017843470.0053613750.019835531 0.592833 0.553311.2E-2111.04E-060.0010214.94E-058.35E-370.0024392.71E-1432.02574.888373.2858884.06046612.738293.0317617.62569910.24048-20.081.86E-241.67E-877.46E-72-44.833116.2762151.697718.533063 1.69E-170.8776490.00119 -0.9168784 -0.22595 -0.91688-0.010460.036970.6188930.083594-0.091450.086204-0.034970.0059210.0121240.002740.0179010.0093940.0091840.0052250.161192-0.027120.0089350.0590210.6676770.106487-0.083790.10713-0.028750.0087250.0205140.0127640.0244120.0269290.0363450.012220.1822120.050642-0.03496750.00592110.01212410.00273960.01790060.00939370.00918390.00522480.1611921-0.0271238-0.01045870.03696950.61889320.083594-0.09145240.0862035-3.24241-0.15395t Stat P-value Lower 95% Upper 95% Lower 95.01.31E-580018.11063Coefficients Standard error#BATHLnSQFT1/FARLnAGELnPARKdf SS MS F02230.56146.115380.020674737.8460495162.6657463000.51179581678847868Significance FResidualTotalLog/Log; Verify White Settlement, Rockwall and Ft. Worth HOME$; all observations;Figure by MIT OpenCourseWare.MIT Center for Real EstateOptimizing House Configuration• Builders and developers compare the incremental value of additional house features against their incremental cost. • Profit maximizing house: where the cost of an additional square foot, bath, fireplace falls to the marginal cost of construction. • But what about land, lot size, density or FAR? – FAR: floor area ratio (ratio of floor to land area).– Density: units per acre. – Density x unit floor area = FAR– % of lot “open” = 1-(FAR/stories) (stories>FAR)MIT Center for Real EstateOptimizing House price (P) minus construction cost (C) as a function of square feet (see Dallas results)$Size (square feet)P (size)C x SizeCΔP/ ΔSizeS*MIT Center for Real EstateFW Dodge data on projects tells the impact of FAR on Costs (see Dallas slide for rent impact)AreaUnitsStoriesSteelWoodConcreteOther/Unk196719681969197019711972197319741975 -1.149854-1.271703-1.335804-1.434557-1.479251-1.524854-1.554727-1.668757-1.7040150.01975110.019221230.02010840.10644280.02394390.0011156-0.001407 .0000897.0001058.0021155.0241704.0081667.0233001.0125935.048317.0463638.046054.0528213.040121.0399378.0434758.049658.0558866 -20.57-25.61-30.73-35.92-36.87-28.87-33.76-35.99-35.271.578.252.464.4011.3210.55-15.69 0.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.000 -1.259407 -1.0403-1.17436-1.369047-1.421029-1.512846-1.557899-1.628398-1.645005-1.759643-1.798729-.0049357.1465378.0040995.0590621.0197969.0009083-.0015827 -0.001230.29977Interval]P > t [95% Conf.Root M SEAdj R-squaredR-squaredProb > FF(44, 7659)Number of obs =M330.9507646SS1361.83364SourceModelResidualTotalLn(cost/sf)688.2451662050.07881Coef..8986097.26614031t44dfWashington, DC Apartments76597703Std. Err.0.66240.66430344.4377040.0013230.0280910.1538230.0361170.2378870.044438-1.6093-1.57787-1.46445-1.42131-1.4006-1.35627-1.250580.0140.117Figure by MIT OpenCourseWare.MIT Center for Real Estate1). P = α - βF Optimizing FARα = Price for all housing and location factors besides FARF = FARβ = marginal impact of FAR on Price per square foot.2). C = μ + τ Fμ = “baseline” cost of “stick” SFU constructionτ = marginal impact of FAR on cost per square footMIT Center for Real EstateIf each unit of floor are is unprofitable then so is land –regardless of FAR. As FAR approaches zero, land profit is zero no matter how profitable floor area.$/sq ft Floor$/sq ft LandFAR: FFAR: FConstruction Cost: CHouse Price: PFloor ProfitLand