Analysing Location Attributes with a Hedonic Model

**Analysing** **Location** **Attributes** **with** a **Hedonic** **Model** for Apartment Prices in Donetsk, Ukraine159Söderberg and Janssen (2001), Gloudemans(2002), and O’Connor (2002). According toO’Connor (2002), though all three models (additive,multiplicative, and non-linear) produceexcellent results, the multiplicative model obtainsthe best results, and the hybrid modeloffers a better representation of appraisal principles.Halvorsen and Pollakowski (1981) andWilhelmsson (2002) use a flexible multi-parameterBox-Cox model to find the best-fittingtransformation. However, as a linear modeldescribes the relationships more clearly in generaland its results are easier to compare **with**the expert valuations, the focus of our attentionis on this type of model even though wecompare our results **with** results from the loglinearmodel. Hence, in our econometric modelling,two types of ordinary least square (OLS)models are specified: linear and log-linear.A useful tool to supplement regressionanalysis is GIS, which not only allows us tovisualise data, but also provides spatial analysisand additional data collection. GIS is widelyused in real estate research, particularly instudies of apartment markets (Bible and Hsieh,1999; Pavlov, 2000; Ward et al., 2002). Here,we use it mainly as a tool to estimate distances.As Wiltshaw (1996) argues, if the resultingspatial pattern is not random the conclusionsare likely to be flawed. Two types of spatialeffect exist: spatial dependency and spatial heterogeneity.However, according to De Graaff etal. (2001), due to difficulties in separating themand for other reasons they should be handledjointly. Spatial dependency in a regressionmodel can be detected **with** either the spatialweight matrix or the direct specification of thecovariance matrix (Dubin, 1998). The weightmatrix is widely applied in real estate analysis(e.g. Pace et al., 1998; Dubin et al., 1999;Wilhelmsson, 2002). We use Moran’s I, the definitionof which can be found in Dubin (1998).It is calculated **with** the row standardizedweight matrix of inverse square distances andis empirically estimated in e.g. Bogdon andCan (1997), De Graaff et al. (2001), Wilhelmsson(2002), and Wilhelmsson (2004). We measuredistances using GIS.2.2. DataThe information available is either the askingprices or the official sale prices. However,in the official register, data on apartment saleprices do not reflect realistic market prices. Asthe transaction fee depends on the official saleprice, there is a strong incentive to register alower price than the price actually paid.Real estate agencies and private personsregularly publish asking prices for apartmentsin special newspapers and magazines inDonetsk. In this paper, we use the asking priceas a dependent variable. Systematic errors inmeasuring asking price will not only affect theerror term, but will also cause bias in the estimates.Costello and Watkins (2002) highlightthat the use of asking prices, which divergefrom transaction prices by different degrees,can lead to erroneous conclusions. However,asking prices are regressed in many studiesanalysing residential market, e.g. Henneberry(1999) in Sheffield, Yang (2001) in Beijing andBjörklund and Klingborg (2005) in Sweden.Costello and Watkins (2002) call the use of askingprices an established tradition in UK housingresearch. In the current paper, it is a reasonableoption.In Donetsk, the largest number of sale proposalswas found in the newspaper Real Estatefrom Hallo! Only one issue was selected,as our research is not intended to analysemovement of prices over time. The selected issuewas published in February 2005.In Donetsk, apartments are not sold by auctionand purchasing prices are rarely higherthan asking prices. However, the opposite situationis possible, i.e. after negotiation, the purchasingprice may be lower than the askingprice. In the newspaper, the asking prices aredivided into two groups: those, for which price

160 M. Kryvobokov and M. Wilhelmssonnegotiation is possible, and those, for whichthe asking price is the final price. We selectedthe latter group for our analysis. Undoubtedly,this does not mean that all asking prices willbe equal to the sale prices in reality, but it islogical to suppose that they are closer to thesale prices than the former group. This alsoreduces the problem of a systematic measurementerror in the dependent variable. All pricesare stated in US dollars.Data include the approximate location of theapartment and internal apartment characteristics.The approximate location means a streetname and/or the nearest reference object likea shop or a crossroad. The publication of approximatelocation instead of actual addresscan be explained by two reasons. In the beginningof the selling process, real estate agenciestry to prevent direct contact between abuyer and a seller **with**out their brokerage. Thehigh crime rate is another reason why sellersdo not want to publish their precise location.As in Roseman (2002), it is important tonote that the number of rooms in an apartmentin Ukraine means bedrooms and livingrooms. Thus, a two-room apartment includesa bedroom, a living room, a kitchen, a bathroom,and a toilet. The last two items may bein separate premises or one combined, but thisinformation is not available. Two-room apartmentswere selected as typical for Donetsk andthere is generally less difference in total areaamong them compared **with** one-, three-, andfour-room apartments.Published data also include informationabout the following characteristics of apartments:floor level, number of floors in the building,existence of a wired telephone, total area,living area, existence of a balcony and/or loggia,as well as an indication of condition. Thereare seven possible conditions:1) Repair is needed;2) Satisfactory;3) Cosmetic repair is needed;4) Normal;5) Good;6) Perfect;7) “Euro-renovation.”Plastered walls and ceilings, new windows**with** plastic frames, etc., usually characterisethe seventh type. This type corresponds to“Western standard” apartments described byRoseman (2002).Only apartments in five- and nine-storeybuildings are selected in the study. These buildingsare the most typical in Donetsk and theyare located in all districts in the city. Five-storeybuildings were constructed mainly in the1950s and 1960s while nine-storey buildingsare relatively new. The latter were mainly builtin the 1970s and 1980s, up until the collapseof the USSR. In the 1990s there was only asmall amount of housing built in Donetsk,mainly elite dwellings. In recent years, manyconstruction companies have started to constructnew multifamily buildings, mainly upperclass apartments.After the review of the published informationthe apartments **with** missing data wereexcluded. Several apartments have extremelyhigh asking prices compared to similar apartmentsin the same locations. Two reasons canexplain this phenomenon. Either these apartmentshave excellent interior standards afterrepair or the sellers are asking unrealisticallyhigh prices. Apartments **with** atypical highasking prices were not included into the sample.A more sophisticated approach could beapplied, as in O’Connor (2002), where the regressionmodel was run and the records **with**the lowest and highest 2.5 percent of the estimate-to-saleratios **with**in each neighbourhoodwere removed from the sample. In this research,however, the sample is not very big,and therefore, this approach is not used.Thus, we include 325 apartments **with** askingprices in our study. Our database thus containsthe asking price, approximate location,and seven internal apartment characteristics:floor number (one to nine, because there is no

**Analysing** **Location** **Attributes** **with** a **Hedonic** **Model** for Apartment Prices in Donetsk, Ukraine161concept of ground floor in residential buildingsin Ukraine), the number of floors in the building(five or nine), telephone (1 or 0), total area(in square meters), balcony and/or loggia (1 ifthere is either a balcony or a loggia, 2 if thereare both, 0 if neither), and an indicator of condition.The variables for floor number, the numberof floors in the building, telephone, and conditiontypes can be represented as dummies. InDonetsk, the first and the top floors are usuallyconsidered the worst. First floor apartmentsare associated **with** higher risk of burglaryand noise, and top floor apartments **with**a possible poor condition of the roof (Roseman,2002 highlights the fact that repairs and maintenanceof residential buildings in Ukraine areoften lacking due to the state of municipal governmentsowning the common areas in thebuildings). For this reason we have introducedtwo dummy variables, one indicating the firstfloor (1 for the first floor, 0 for the other floors)and one the top floor (1 for the top floor, 0 forthe other floors). The expected implicit pricesare negative. We also use a dummy for thenumber of floors: 0 for older five-storey buildingsand 1 for newer nine-storey buildings. Thefive-storey buildings of the 1950s were built**with** bricks and are mostly of better qualitythan those of the 1960s built **with** pre-fabricatedconcrete panel blocks. However, data onage and material are not available. Using theworst type for condition as the default value,we have six dummies corresponding to types2 to 7.All the apartments in the sample wereplaced as points on the vector map of Donetskusing ArcView GIS (Figure 1). The map providedby the Department of Master Plan ofDonetsk contains dwelling blocks, major roads,commercial objects, water objects, green areas,etc. As the approximate location of the apartmentwas known, it was possible to recognisethe city block or, at least, the group of blocks,Figure 1. **Location** of 325 apartments **with**in the city of Donetsk

162 M. Kryvobokov and M. Wilhelmssonwhere the corresponding five-storey or ninestoreybuilding is located. We always placedthe point at the geometrical centre of the block(or of a central block, if there were several possibleblocks).The location attributes we use are:– the accessibility to the CBD;– the accessibility to the nearest secondarycentre;– the accessibility to the nearest publictransportation stop;– the accessibility to the railway station;– the accessibility to water (the river,ponds) and green area;– nuisance proximity;– prestige.Different methods can be used to recognisethe CBD. Söderberg and Janssen (2001) usedifferent locations of the CBD and select those,for which the regression result is the best.Kryvobokov (2005b) applies GIS to estimateeach block’s accessibility to all business andcommercial objects and considers the block**with** the best accessibility as the CBD. In thispaper, we do not apply any such methods. Thecentral point of the central square, usually consideredto be the centre of Donetsk, is used asthe CBD.The secondary centres are areas outside theCBD, which have relatively high concentrationsof business and commercial development,and are usually also transport junctions. Weselected secondary centres on the basis of datafrom the Department of Master Plan ofDonetsk on the centres of administrative districts;we chose additional secondary centresusing the expert approach. Again, we use thecentral points of these areas. The centres areshown in Figure 2, in which the CBD is indicatedby a point and the thirteen secondarycentres by asterisks.The contour lines for apartment askingprices are also presented in Figure 2. Theywere created **with** the Inverse DistanceFigure 2. **Location**s of the CBD, the secondary centres, the railway station,and contour lines for asking prices

**Analysing** **Location** **Attributes** **with** a **Hedonic** **Model** for Apartment Prices in Donetsk, Ukraine163Weighted method of Spatial Analyst, **with** nearest12 neighbours, power 2, and no barriers.The contour lines demonstrate that the mostexpensive apartments are situated around theCBD. At the same time, there are apartments**with** the highest condition variable, i.e. wherea “Euro-renovation” has been done, in almostall city districts. Distance from the CBD ischaracterised by a reduction in prices, thoughit differs in different directions. Thus, pricesdecrease more slowly towards the north andeast from the centre than towards the west,south and southeast. The influence of severalsecondary centres on the configuration of contourlines in Figure 2 can be noted as well.We use the city map to evaluate the variablesfor the nearest public transportation stop,the railway station, water and green area accessibility,and nuisance proximity. A publictransportation stop is the location of a stop forinner public transport: buses, trolleybuses,trams, and service routes. The main railwaystation for the regional and inter-regional railwayis considered (a “snowflake” in the northernwest in Figure 2). The water objects arethe attractive ponds and the river. Green areasare the main parks. We merge water objects**with** green areas into one variable, becausethe best parks in Donetsk are locatedclose to water. Contaminating factories andslagheaps are the objects of nuisance. As a consequenceof more than a century of coal miningactivity, which continues, there are morethan a hundred slagheaps in Donetsk. Theyare located in all districts of the city and areconsiderable sources of air pollution in the formof dust.Prestige is included as a dummy variablefor location in a prestigious area, which canbe considered as a kind of sub-market. Theseareas are mainly the city centre, and to a lesserdegree just north and east of it. In principle, itwould be possible to use income level of populationinstead of prestige, but such statisticaldata is not available. The attribute of prestigeis used in real estate literature, e.g. Sivitanidou(1995 and 1996) in regression modelling andKauko (2002) in Analytic Hierarchy Process.Distances to the CBD, a secondary centre,a public transportation stop, and the railwaystation were measured as the shortest pathsalong the road network. We measured distancesto nuisances and water (green area)along straight lines, because in these cases thephysical influence and view are important.When measuring distances to an object, e.g. toa green area, we used the nearest boundarypoint of the object. All distances were measured**with** GIS in kilometres (km) and wererounded to 0.1 km. Approximate location ofapartments leads to errors when measuringdistances. Systematic measurement errorswould create bias in the estimates. However,in our case these errors are unsystematic.3. EMPIRICAL ANALYSIS3.1. Descriptive analysisIn Table 1, we show the descriptive statisticsfor all variables. In the sample, 48 percentof the apartments are located either onthe first or on the top floor (variables Floor1and FloorT). The fact that these apartmentsare proposed for sale more often may indicatethat they are usually of lower quality thanapartments on other floors. There are 201 observationsof five-storey buildings and 124 ofnine-storey buildings (Build). Average totalarea (Area) is less than 50 square meters **with**a standard deviation as low as 6 square meters.However, this is not surprising as onlytwo-room apartments were selected. All distancevariables have high variations aroundtheir mean values. 145 apartments (45 percent)are located **with**in the prestigious area (Prest).Correlation coefficients are presented inTable 2. Among the internal apartment variables,Area and dummy for a wired phone connection(Phone) have the highest correlation

164 M. Kryvobokov and M. Wilhelmsson**with** apartment price (Price). Among the conditiondummies (Cond2 to Cond7), Cond7 hasthe highest correlation **with** Price, though inabsolute terms this relationship is weak. Alllocation variables except distance to a secondarycentre (DSCent) and to lesser degree distanceto a public transportation stop (DStop)are highly correlated **with** Price. The highestcorrelation **with** Price is observed for distanceto the CBD (DCBD) and Prest. All distancevariables, except distance to nuisance (DNuis),are negatively correlated **with** Price. Amongthe independent variables, the highest correlationis observed between DCBD and distanceto railway station (DRail) (0.70). This can beexplained by the fact that the way from theeastern part of Donetsk to the railway stationpasses through the CBD. The areas closer tothe CBD have better accessibility to water andparks; the corresponding correlation coefficientis 0.63. These two facts can explain the highpositive correlation coefficient (0.63) betweendistance to water and green area (DWater) andDRail. Naturally, DCBD and Prest are highlynegatively correlated (-0.68).3.2. Econometric analysisAs the aim of the paper is to estimate theweights of location attributes, no variableshave been excluded from the hedonic priceequation, even though the correlation betweenseveral of the independent variables is high.However, we will test for multicollinearity inregression models.As a first step in measuring the relativeimportance among the location variables,apartment prices were regressed on measuredTable 1. Descriptive statisticsVariableDescriptionMeanStandarddeviation,91MinimumMaximumPriceAskingprice, USD26,0429 1 9,00060,000Floor1Dummyfor first floor0.240.430 1FloorTDummyfor top floor0.240.430 1BuildDummyfor five-and nine-storey building0.380.490 1PhoneDummyfor phone0.800.400 1AreaTotalarea, m2486 3691BalcRankof 0 to 2 for balcony/ loggia0.870.470 2Cond2Dummyfor condition 20.190.390 1Cond3Dummyfor condition 30.050.220 1Cond4Dummyfor condition 40.230.420 1Cond5Dummyfor condition 50.310.460 1Cond6Dummyfor condition 60.070.260 1Cond7Dummyfor condition 70.060.230 1DCBDDistanceto the CBD, km5.844.720.120. 4DSCentDistanceto the nearest secondary centre, km1.851.480.19. 3DStopDistanceto the nearest stop, km0.260.160.11. 0DRailDistanceto the railway station, km9.915.120.322. 1DWaterDistanceto water (green area), km1.290.820.13. 6DNuisDistanceto the nearest nuisance, km0.970.510.12. 4PrestDummyfor prestigious area0.450.500 1

166 M. Kryvobokov and M. Wilhelmssonapartment attributes and all location attributes,denoted LIN (the linear model) andLOG (the log-linear model) in Table 3. **Model**LOG has higher adjusted R 2 than model LIN(77 percent compared to 69 percent). In bothmodels, Build, Area, Cond6, Cond7, DCBD,and Prest are statistically significant. Cond5is significant in model LIN, whereas FloorTand Phone are significant in model LOG.Where the location attributes are concerned,DWater and DNuis are significant only inmodel LIN, whereas DSCent and DRail are significantonly in model LOG. Among significantlocation attributes measured in kilometers inmodel LIN, the highest coefficients are forDNuis and DWater; the lowest is that forDCBD. At the same time the highest of thesignificant location coefficients in model LOGis that for DCBD.To investigate the existence of multicollinearity,we estimated the maximum of varianceinflationary factors (VIF) (Table 3). Theprinciple that VIF in excess of 10 (or tolerancelower than 0.10) indicates multicollinearity isusually used in the literature, see e.g. Seileret al. (2001) and Des Rosiers et al. (2001). Formodels LIN and LOG, the magnitudes of VIFare lower than the threshold that indicates noproblem **with** multicollinearity.Importantly, the values of the Moran’s I sta-Table 3. Estimated OLS results for the whole data setVariables and modelcharacteristics**Model**LIN3060.5(0.93)-1444.3(-1.69)-1570.3(-1.77)3284.0(4.75)*1311.9(1.55)478.4(7.59)*-528.5(-0.52)1312.0(1.17)1967.6(1.43)2026.7(1.75)2266.5(2.10)*4600.1(2.76)*9713.4(6.18)*Constant5Floor12FloorT0Build4Phone6Area4Balc3Cond26Cond38Cond40Cond53Cond69Cond78LOG7.97(22.13)*-0.02(-0.70)-0.06(-2.27)*0.15(6.53)*0.08(2.87)*0.65(7.24)*-0.01(-0.34)0.02(0.60)0.02(0.42)0.04(1.11)0.05(1.58)0.13(2.50)*0.30(6.08)*LINDIR5226.95(1.55)-1498.37(-1.80)-1851.60(-2.15)*3115.50(4.64)*1098.97(1.35)461.50(7.24)*-915.68(-0.92)1614.12(1.46)1990.26(1.43)2204.50(1.94)2321.35(2.17)*4615.75(2.79)*9401.38(5.79)*LOGDIR7.91-0.02-0.06(22.08)*(-0.62)(-2.13)*0.15 (6.48)*0.07 (2.61)*0.67 (7.46)*-0.07 (-0.14)0.02 (0.64)0.02(0.33)0.04 (1.25)0.06 (1.78)0.14 (2.75)*0.31 (6.36)*(continued)

**Analysing** **Location** **Attributes** **with** a **Hedonic** **Model** for Apartment Prices in Donetsk, Ukraine169Table 4. Estimated OLS results for split data setsVariables and modelcharacteristics**Model**LIN61749.3(2.21)*-7739.6(-2.28)*-2934.3(-1.48)6897.5(2.65)*-186.1(-0.06)566.0(4.80)*-2287.8(-1.08)-205.5(-0.06)1792.2(0.38)1239.5(0.38)-751.7(-0.23)9885.7(2.28)*7147.5(1.44)-6260.5(-2.55)*-1136.1(-0.28)3523.8(0.40)-5185.5(-1.84)8017.6(1.00)-4839.1(-0.83)Constant9Floor14FloorT4Build3Phone5Area2Balc5Cond26Cond33Cond47Cond55Cond68Cond74DCBD5DSCent2DStop9DRail6DWater4DNuis6Prest- -LOG9.05(7.07)*-0.20(-2.24)*-0.10(-1.84)0.16(2.22)*0.04(0.50)0.86(4.81)*-0.05(-0.80)-0.01(-0.11)0.04(0.33)0.01(0.07)-0.04(-0.43)0.22(1.85)0.15(1.17)-0.13(-2.06)*-0.12(-0.44)0.01(0.09)-0.83(-1.48)0.07(0.93)-0.12(-0.54)Observations755AdjustedR20.47.47F-value4.63.70MaxVIF8. 99.0( D Rail)( D Rail)LINDIR10514.59(3.50)*-240.10(-0.33)-987.30(-1.38)3741.82(5.77)*998.89(1.50)363.13(6.07)*-597.10(-0.86)828.44(0.77)1349.33(0.92)473.89(0.46)1899.72(1.90)2603.74(2.01)*9219.21(6.42)*-612.39(-5.64)*-794.80(-3.75)*2757.43(1.58)-217.81(-2.43)*-1442.20(-3.28)*724.51(0.99)2282.15(3.01)*57 2 00LOGDIR8.88(18.65)*-0.01(-0.22)-0.05(-1.60)0.20(7.71)*0.06(2.18)*0.43(3.53)*-0.00(-0.08)0.02(0.46)0.02(0.31)0.04(1.04)0.09(2.21)*0.12(2.25)*0.33(5.79)*-0.31(-10.65)*-0.04(-3.46)*0.01(0.54)-0.08(-3.95)*-0.04(-2.03)*0.03(1.72)0.06(2.02)*250 0.690.734 30.7436.804.03.4( D Rail)( C ond5)Note: In models LIN_Cent and LOG_Cent, Prest is equal to 1 for all apartments.

170 M. Kryvobokov and M. Wilhelmssonrespectively, both are larger than the criticalvalue of 1.57 at the 5% significance level.WSE for sub-samples in total is calculatedusing the formulam∑ (( ni− ki− 1) ⋅ SEi)WSE = i=1,m∑ ( ni− ki− 1)i=1where: n is the number of observations; k isthe number of explanatory variables; i is thecount for sub-samples; m is the number of subsamples;SE i is the standard error in the i-thsub-sample model.The results of WSE estimations are presentedand compared **with** the initial modelsin Table 5. For linear specifications, the reductionin the standard error is 17 percent,whereas for log-linear specifications it is only8 percent. According to literature review byWatkins (2001), either 5 percent or 10 percentcut off is employed **with**out a strict guidanceon the size of the reduction. In our case, thesub-market specifications in a linear form satisfyboth thresholds, while the log-linear modelssatisfy only the former one.Thus, Chow-test and WSE estimation indicatethat two delineated sub-markets are differentand cannot be described by one hedonicmodel. There are some interesting findingswhen it comes to the location variables. DCBDis the only significant location variable in modelsLIN_Cent and LOG_Cent and the coefficientfor DSCent is smaller than that for DCBD. Forthe linear model the former is 5.5 times smallerthan the latter. In models LIN_Out andLOG_Out, all the location variables exceptDStop and DNuis are significant. LIN_Out isthe only linear model where DSCent is significant.In this model, the coefficient for DSCentis higher than that for DCBD; the coefficientfor DWater is 2.4 times higher than that forDCBD. The remarkable point is the comparisonof the coefficients for DCBD in LIN_Centand LIN_Out. For central locations, it is morethan 10 times higher than that for locationsoutside the centre. At the same time, in modelLOG_Out the coefficient for DCBD is the highestamong coefficients for the location variables.For central locations, the insignificantvariables DWater and DNuis have unexpectedsigns. This might be explained by the high densityof buildings, which are barriers for theinfluence of water, green areas and nuisanceobjects.Though there are dissimilarities betweenthe linear and log-linear models concerning theimportance of secondary centres, it seems thatthese centres in Donetsk are important. Therefore,Donetsk can be considered as a nonmonocentriccity. The difference between nonmonocentricand polycentric urban models isdescribed e.g. in Sivitanidou (1997). Here wedo not investigate this difference, but concludethat a monocentric model is not appropriatefor Donetsk.Table 5. Weighted standard error tests**Model**Linear specifications:StandarderrorLIN5479LIN_Centand LIN_Out453817Log-linear specifications:LOG0.175904LOG_Centand LOG_Out0.1623338Percent reduction

**Analysing** **Location** **Attributes** **with** a **Hedonic** **Model** for Apartment Prices in Donetsk, Ukraine1714. ESTIMATION OF WEIGHTS ANDCOMPARISON WITH EXPERTVALUATIONSThe focus of the paper is on location attributesand their impact on apartment pricesin Donetsk. We can extract the relative weightsof the location variables and compare them**with** previous findings for this city. For this itis easier to use a linear model.The relative importance in linear regressionis quite often discussed in scientific literature.As the choice of one or another concept of relativeimportance often affects conclusions(Kruskal and Majors, 1989), it is important toselect a meaningful measure for our task. Itcan be the regression coefficient, the standardizedregression coefficient, the contribution toR 2 or a more complex measure (Bring, 1994;Thomas et al., 1998; Johnson, 2000; Johnsonand Lebreton, 2004).The standardized regression coefficient (orbeta coefficient) is much criticized in the statisticsliterature (e.g. Darlington, 1990; Bring,1994). This measure is a mixture of the estimatedeffect and the standard deviation, whichshould be analysed separately (King, 1986).The unstandardized regression coefficientis more appropriate for a comparison of variables,which have the same unit of measurement.We restrict the comparison of locationattributes to the distance variables, all of whichare measured in kilometres and which aretherefore comparable in nature. Thus, thoughWTP for Prest is the highest among the locationattributes, that dummy variable is notconsidered in the comparison.We suppose that the relative importance ofdistance variables estimated **with** the use ofunstandardized coefficients is transparent.Therefore, more complex measurements ofweights are not applied in this study.Among the linear models specified above itwould be better to focus on LIN_Cent andLIN_Out. However, due to the small numberof observations and only one significant locationvariable (DCBD) in LIN_Cent we only useLIN_Out. **Model** LIN is also exploited to obtainthe complete picture of the relative importanceof location attributes.In Table 6, we show the weights of significantdistance attributes calculated **with** themethod proposed in Kryvobokov (2004). Theweights are estimated on the basis of the absolutevalues of the regression coefficients, i.e.marginal WTP. Negative coefficients and theirweights are shown in grey.According to the overview of generations ofresidential property valuation methods madeby Kauko (2004), given a recent “revitalisation”of more qualitative valuation methodology, subjectivejudgement is accepted as at least asTable 6. Estimation of weights from the regression models**Location**variablesLINLIN_OutWTPWeightWTPWeightDCBD-828.210.15-612.390.20DSCentDStopDRailN/s0.00-794.800.26N/s0.00N/s0.00N/s0.00-217.810.07DWater-1702.600.32-1442.200.47DNuis2816.350.53N/s0.00Sum of absolute values 5347.161.003067.201.00Note: N/s – statistically not significant.

172 M. Kryvobokov and M. WilhelmssonTable 7. Estimation of weights from expert valuations from Kryvobokov (2005a)**Location** variablesAHPInitialweightRecalculatedweightDirect questionnaireInitialweightDCBD0.140.260.170.35DSCent0.100.190.100.21dStop0.080.150.040.08DRail0.020.040.020.04dWater0.060.110.070.15DNuis0.130.250.080.17Sum0.531.000.481.00Recalculated weightTable 8. Comparison of recalculated weightsvalid an indicator as variables based on populationcensuses, measured distances etc. Itshould be fruitful to compare the results ofexpert valuations **with** the regression outcomespresented above. **Analysing** the same housingmarket, using the same location variables andassuming that the relative importance is correctlyestimated, it is possible to compare theresults from different studies.Table 7 exhibits the weights of the locationattributes estimated for Donetsk inKryvobokov (2005a) using expert valuationmethods: the AHP and the direct questionnaire.Four groups of respondents were selected,namely valuers, realtors, urban planners,and land managers. The intention wasto select the best experts in the subject. Theseexperts evaluated the relative importance ofthe location attributes of apartments. The hypothesisthat the mean is equal to zero wasrejected for all these location variables at the5% significance level. In Table 7, the derivedweights are recalculated to include only theattributes corresponding to location variablesfrom models LIN and LIN_Out. The units ofmeasurement in the regression models and theexpert valuations are the same for the majorityof variables. The two exceptions in expertvaluation methods are the attributes for thedistance to a public transportation stop andthe distance to water and green area, whichwere measured in hundreds of meters; thereforethey are named dStop and dWater in thetables below. In order to compare weights havingthe same units of measurement we canrecalculate the weights from Table 6 as if distanceto water was measured in hundreds ofmeters. Linear models allow making such cal-**Location** LINLIN_OutAHPDirectStd.dev.- to- Max. differencevariablesquestionnaire average ratioDCBD0.220.350.260.350.220.13DSCent0.000.450.190.210.870.45dStop0.000.000.150.081.260.15DRail0.000.120.040.041.010.12dWater0.040.080.110.150.490.11DNuis0.740.000.250.171.100.74

**Analysing** **Location** **Attributes** **with** a **Hedonic** **Model** for Apartment Prices in Donetsk, Ukraine173culations. The recalculated weights from tworegression models and two expert valuationmethods are demonstrated in Table 8. Ratiosof standard deviation to average as well asmaximum differences are calculated for thesefour results.Comparison of weights in Table 8 highlightsthe following. The variables DCBD and dWaterhave the lowest standard deviation-to-averageratios and low absolute differences, i.e. maximumdifferences. According to the experts,DCBD has the highest weight (though DNuisin the AHP has almost the same magnitude).According to market valuation, either DNuisor DSCent has the highest weight. DStop (andconsequently dStop) is insignificant in the consideredhedonic models, but according to expertvaluations, dStop has weights higher thanDRail. The highest standard deviation-to-averageratios are those for dStop and DNuis thatcan be explained by zero weights in regressionresults. The same explanation is true for highabsolute differences for DNuis and DSCent.5. CONCLUSIONSOur main findings can be summarised asfollows. Each location variable is significant inat least one of the reported regression models.The only variables significant in all models aredistance to the CBD and location in a prestigiousarea. The least important location attributeis distance to a public transportationstop. The experiments **with** distance gradientsillustrated that western and northern directionsfrom the CBD are more attractive thansouthern and eastern directions. Apartmentslocated in the city centre and outside of it aredifferent sub-markets according to Chow-testsand weighted standard error estimations. Forcentrally located apartments, the only importantlocation attribute is the distance to theCBD, whereas for locations outside the citycentre the other location attributes, such asdistance to water and green area or to the nearestsecondary centre may be of more importance.The coefficient for distance to the CBDis always negative; the same is true for distanceto a secondary centre.The result of the comparison of the regressionmodels to the expert valuations includesthe following findings. According to regressionresults, distance to nuisance or to the nearestsecondary centre may be more important thanexperts supposed. Moreover, the weights ofthese attributes may be higher than that ofdistance to the CBD, which has the highestweight in expert valuations. Distance to a publictransportation stop, evaluated quite highby the experts, is not significant in hedonicmodels.Regression results concerning the accessibilityof water objects and green areas are generallysimilar to expert valuations. When thisvariable is measured **with** the same unit ofmeasurement as other location attributes (asin regression models), we see the signal thatconsumer preferences in respect to water objectsand green areas are stronger than thatin respect to the CBD and secondary centres.This signal should be accepted in context ofdevelopment policy.The specification of a model for urban landassessment in Donetsk should include all thelocation variables examined in the reportedhedonic models for apartment prices; the onlyexception might be distance to a public transportationstop. The estimation of the weightsof relative importance highlights that the attributeof distance to water and green areashould have a weight higher than the CBDaccessibility. Further research about the specificationof the model should include such itemsas distance to shops, crime rate, and trafficnoise.The fact that apartment prices can be explainedby apartment attributes and locationattributes is an indication that the Donetskapartment market is a well-functioned market.The included attributes have both signs

174 M. Kryvobokov and M. Wilhelmssonand magnitudes in line **with** results in studiescarried out in Western Europe and NorthAmerica. Furthermore, as the distances to secondarycentres are capitalised into the apartmentprices, it seems that Donetsk is a nonmonocentriccity.To detect local peculiarities, one could applyGeographically Weighted Regression (e.g.Brunsdon et al., 1996), which is becoming amore and more popular technique in real estatestudies (e.g. Borst, 2006; Des Rosiers andThériault, 2006). The application of local regressionmodelling in Donetsk merits futureresearch.AcknowledgementsThe authors thank Professors HansMattsson, Hans Lind, and Roland Anderssonat Royal Institute of Technology, Stockholm forgeneral supervision and comments. The Departmentof Master Plan of Donetsk has providedthe considerable amount of data, forwhich the authors are very grateful. The SwedishInstitute has provided finance for the researchthat is highly appreciated. We alsothank the anonymous referees for their valuableremarks and comments.REFERENCESAnselin, L. (1988) Spatial Econometrics: Methodsand **Model**s, Dordecht: Kluwer.Asabere, P. K. and Huffman, F. E. (1996) Thoroughfaresand Apartment Values. Journal of RealEstate Research, 12(1), p. 9–16.Berry, J., McGreal, S., Stevenson, S., Young, J. andWebb, J. R. (2003) Estimation of ApartmentSubmarkets in Dublin, Ireland. Journal of RealEstate Research, 25(2), p. 159–170.Bible, D. S. and Hsieh, C. (1999) Determinants ofVacant Land Values and Implications for Appraisers.The Appraisal Journal, LXVII(3),p. 264–268.Björklund, K. and Klingborg, K. (2005) Correlationbetween Negotiated Rents and NeighbourhoodQuality: A Case Study of Two Cities in Sweden.Housing Studies, 20(4), p. 627–648.Bogdon, A. S. and Can, A. (1997) Indicators of LocalHousing Affordability: Comparative andSpatial Approaches. Real Estate Economics,25(1), p. 43–80.Borst, R. A. (2006) The Comparable Sales Methodas the Basis for a Property Tax Valuation Systemand its Relationship and Comparison toGeostatistical Valuation **Model**s. Paper in theInternational congress “Advances in mass appraisalmethods”, Delft University of Technology,19 p.Boyle, M. A. and Kiel, K. A. (2001) A Survey ofHouse Price **Hedonic** Studies of the Impact ofEnvironmental Externalities. Journal of RealEstate Literature, 9(2), p. 117–144.Branas-Garza, P., Rodero Cosano, J. and Presley,J. R. (2002) The North-South divide andhouse price islands: the case of Córdoba(Spain). European Journal of Housing Policy,2(1), p. 45–63.Bring, J. (1994) How to Standardize Regression Coefficients.American Statistician, 48(3), p. 209–213.Brunsdon, C. F., Fotheringham, A. S. and Charlton,M. E. (1996) Geographically Weighted Regression:A Method for Exploring SpatialNonstationarity. Geographical Analysis, 28(4),p. 281–298.Colwell, P. F. (1990) Power Lines and Land Value.Journal of Real Estate Research, 5(1), p. 117–127.Cornia, G. C. and Slide, B. A. (2005) Property Taxationof Multifamily Housing: An EmpiricalAnalysis of Vertical and Horizontal Equity.Journal of Real Estate Research, 27(1), p. 17–46.Costello, G. and Watkins, C. (2002) Towards a Systemof Local House Price Indices. HousingStudies, 17(6), p. 857–873.Darlington, R. (1990) Regression and Linear **Model**s,New York: McGraw-Hill.De Cesare, C. M. and Ruddock, L. (1998) A NewApproach to the Analysis of Assessment Equity.Assessment Journal, 5(2), p. 57–69.De Graaff, T., Florax, R. J. G. M., Nijkamp, P. andReggiani, A. (2001) A general misspecificationtest for spatial regression model: dependence,heterogeneity, and nonlinearity. Journal of RegionalScience, 41(2), p. 255–276.

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**Analysing** **Location** **Attributes** **with** a **Hedonic** **Model** for Apartment Prices in Donetsk, Ukraine177APPENDIXSpatial Autoregressive **Model**s (SAR) and Spatial Error **Model**s (SEM)Variables andmodelcharacteristics**Model**LOGSAR8.9(9.04)*-0.0(-0.82)-0.0(-2.51)*0.1(6.11)*0.0(2.77)*0.6(6.40)*-0.0(-0.31)0.0(0.34)0.0(0.29)0.0(0.82)0.0(1.31)0.1(2.56)*0.3(5.92)*-0.1(-9.11)*-0.0(-4.26)*-0.0(-0.32)-0.0(-4.32)*-0.0(-0.36)Constant7Floor12FloorT6Build4Phone7Area0Balc1Cond21Cond32Cond43Cond55Cond62Cond70DCBD9DSCent5DStop1DRail8DWater1SEM8.15(21.76)*-0.03(-0.99)-0.06(-2.33)*0.16(6.59)*0.06(2.54)*0.60(6.25)*-0.01(-0.08)0.01(0.26)0.01(0.21)0.03(0.71)0.05(1.33)0.13(2.65)*0.30(5.83)*-0.23(-11.18)*-0.05(-4.04)*-0.01(-0.62)-0.11(-4.86)*-0.01(-0.68)LOGDIRSAR6.12(9.18)*-0.02(-0.77)-0.06(-2.41)*0.14(6.14)*0.07(2.57)*0.62(6.56)*-0.01(-0.14)0.01(0.38)0.01(0.25)0.03(0.91)0.05(1.44)0.13(2.80)*0.31(6.01)*-0.18(-7.25)*-0.04(-3.26)*-0.01(-0.22)-0.08(-3.56)*-0.01(-0.87)SEM8.09(21.74)*-0.02(-0.90)-0.05(-2.24)*0.16(6.58)*0.06(2.33)*0.61(6.44)*0.01(0.11)0.01(0.30)0.01(0.16)0.03(0.80)0.05(1.46)0.14(2.88)*0.30(5.94)*-0.21(-7.72)*-0.04(-2.84)*-0.01(-0.52)-0.10(-4.01)*-0.02(-1.27)(continued)

178 M. Kryvobokov and M. WilhelmssonVariables andmodelcharacteristics**Model**LOGSARSEMLOGDIRSARSEM(continued)DNuis0.02(1.16)0.02(1.18)Prest0.090.10(2.87)*(2.82)*N·DCBD- -S·DCBDW·DCBDρ 0.21(3.74)*λ-- -- --0.02(1.00)0.07(2.17)*0.01(0.35)-0.02(-1.00)-0.03(-1.60)0.19(3.31)*0.22-(3.32)*32250.02(0.91)0.08(2.09)*0.01(0.12)-0.04(-1.55)-0.04(-2.07)*-0.21(3.18)*32Observations32553 5AdjustedR 2 0.770.780.770.78