1# RECORD c7b242d28013321bceaeef0f994fd2d0dab032c02# TITLE: Implicit Prices in Urban Real Estate Valuation3# YEAR: 2013.0 VENUE: nan DOI: 10.4067/s0718-915x20130002000094# AUTHORS: J. Nuñez Tabales; F. R. Rey Carmona; J. M. C. Y. Ocerin5# PAGES: 11 CANDIDATE TABLE PAGES (1-based): [7]6# ABSTRACT: Econometric hedonic models encounter several theoretical and practical difficulties when applied to the real estate market, such as downward biases in the estimation of hedonic prices, subjective decisions in the measurement process of categorical attributes, frontier problems related to an imperfect information framework and uniequational specification. Many of these are linked to the parametric approach. Artificial Neural Networks (ANN) provide an attractive alternative: better dwelling prices estimates, avoidance of bias at different market segments, direct use of categorical data and full use of the information available. The price to be paid is the difficulties in the economic interpretation of network parameters. Nowadays, if the final objective to produce better estimates of the transaction prices, this methodology show lower errors, provided of a broad representative database of sales are recorded. A case study is presented for a medium size city in the South of Spain. Keywords: Urban Economics; Hedonic Models; Neural Networks.789===== PAGE 1 (score 2, numeric-paren 0, table-words 0, var-words 2) =====1011116 ]12Revista de la Construcción13Volumen 12 No 2 - 2013 14Precios implícitos en 15valoración inmobiliaria 16urbana17Implicit Prices in Urban 18Real Estate Valuation19Autores20NÚÑEZ TABALES, J.21University of Córdoba, Faculty of Economics22Puerta Nueva s/n, 14071, Córdoba, Spain23es2nutaj@uco.es24REY CARMONA, F.25University of Córdoba, Faculty of Economics26Puerta Nueva s/n, 14071, Córdoba, Spain27CARIDAD Y OCERIN, J. Mª.28University of Córdoba, Faculty of Economics29Puerta Nueva s/n, 14071, Córdoba, Spain30Fecha de recepción3119/6/201332Fecha de aceptación331/8/201334Código interno RDLC350146369-NUNEZ TABALE RdlC n2.indd 116379-NUNEZ TABALE RdlC n2.indd 1163820-11-13 16:383920-11-13 16:38404142===== PAGE 7 (score 29, numeric-paren 0, table-words 2, var-words 23) =====4344122 ] Revista de la Construcción45Volumen 12 No 2 - 2013 46páginas: 116 - 12647[ Núñez Tabales, J. et al ]48directly in a model. But the statistical problems like 49multicollinearity make impossible to proceed in this 50way. To tackle these difficulties, several indices have 51been built, as a way to obtain quantitative information 52from the original attributes. In the process, it has to 53be kept in mind that the interpretation of these new 54variables has to be straightforward, and that it has to 55be avoided to use complicated weights that introduce 56subjective beliefs in the indices. The indices have to 57be compatible with the consumer’s perceptions of the 58characteristics of each property.59The indices defined have been scaled to fit in the 60interval [0; 1]. Values near the upper end refer to 61optimum values in relation to higher prices, and low 62values of an index reflect lack of importance of this 63variable in the final price. These can be treated as 64numerical data in the modelling processes, as in Saura 65(1995) and Jaén and Molina (1995).66Table 2. Indexes associated to each property67Index68Variables included69Quality Index70• Age, accesses, balconies 71and terrace72External Building index73• Pavement, carpentry, 74kitchen furniture and 75reforms76Internal building index77• Pool, tennis court and 78garden79Orientation index80• Orientation of building 81and balconies82Annex index83• Garage and store room84Location index85• Location in the city and 86residents income87The conservation index reflects the general state of the 88property, at first sight. It is constructed from several 89categorical data, like the maintenance condition of the 90kitchen, baths, floor, plumbing, and electric wiring, 91if these have been updated. The complementary size 92index includes the information about some additional 93facilities, like a washing room, embedded wardrobes, 94and food storage place. The situation index reflects 95the position of the apartment or flat in the building, 96the availability of a lift, and the external views. The 97building index includes information about the quality 98of the building, its age, the entrance, and additional 99facilities like swimming pool or satellite and cable 100television. The location index includes data about the 101situation of the property in the city, the surroundings 102and the income level of the zone.103Price of transaction is the endogenous variable in 104both hedonic and NN models. The decision about the 105functional form is treated in the literature. Here is 106used a quadratic model, preferring it over the semi-107logarithmic usual transformation. The explanatory 108variables included show a high level of collinearity, 109introducing practical difficulties in the estimation 110process. Using simplicity criteria, parsimonious models 111are preferred over more complicated specifications. 112Some interactions between exogenous variables 113are considered, using quadratic forms as shown in 114formulae 1.115although the final model used is linear but for an 116interaction term. The variables finally selected to 117be included in the model are the following: size of 118the flat (in square metres, including common areas), 119age of the building, index of location (based on its 120position, characteristics of the area and income of 121the zone), index of additional facilities (as garages 122or store room), common expenses (in euros), and the 123interaction between qualities variables regarding the 124pavement condition and the external carpentry, as 125show in formulae 2.126Table 3. Hedonic model127Endogenous variable: Sales price128Variable129Coeficients130Standard 131error132t-Student133Prob.134Intercept135193.679013610237.531370.0189191380.9849139Surface1401109.95114183.6205014213.273681430.0000144Age145-1067.449146173.5725147-6.1498721480.0000149Location15064297.291515494.40315211.702321530.0000154Annexes15518458.661564572.2461574.0371111580.0001159Expenses1601296.708161105.921316212.242181630.0000164Pav xCarp1655117.270166504.052916710.152251680.0000169[1]170[2]1719-NUNEZ TABALE RdlC n2.indd 1221729-NUNEZ TABALE RdlC n2.indd 12217320-11-13 16:3817420-11-13 16:38175176177===== PAGE 8 (score 28, numeric-paren 2, table-words 9, var-words 7) =====178179páginas: 116 - 126180[ 123 181Revista de la Construcción182Volumen 12 No 2 - 2013 183[ Núñez Tabales, J. et al ]184The usual diagnostics tests have been successfully 185applied. The stability of the model is supported by 186the Chow test, and the condition index is k = 16.6, 187supporting that the multicollinearity is not worrisome. 188The goodness of fit is similar to other hedonic 189modelling, R2 = 0.7738 and the U Theil index is 0.09 190(Table 3).191NN provide a non linear alternative to estimate 192price models. The usual MLP is applied, as in several 193previous works, ad in Haykin (1999), Freeman and 194Skapura (1993) and Garcia Rubio (2004). To facilitate 195comparisons with the proposed hedonic model, the 196exogenous variables selected have been used as inputs 197to the different NN employed. Different topologies 198have been tried, with different number of hidden 199layers and neurons, as several activation functions and 200learning algorithms. Finally a 6:6-6-1:1 structured is 201selected (Figure 1), and the Trajan Software for NN 202is employed, with a lineal activation function, in the 203input, while in the other layers a sigmoid function 204is applied. The training set is composed of 80% of 205the sample, and the remaining data is used as test to 206evaluate the forecasting power. The back propagation 207method employed was limited to 5000 iterations, with 208a learning ratio of 0.1.209Figure 1. ANN 6:6-6-1:1Topology210The NN increase the determination coefficient value 211to R2 = 0.8605, higher than in the hedonic model, 212although one has to take into account the larger 213number of parameters in the network. The root mean 214square error is lower in the network (39540.36) than 215in the hedonic model (41645.43), and similar results 216are observed with other measures, at can be seen in 217the Table 4.218Table 4. Comparison of hedonic a ANN modelling219MH220NN221Determination coefficient (R2)22277,38%22386,05%224Root mean square error 225(RMSE)22641.645,4322739.540,36228Residual standard error22941.911,9123039.102,13231Mean absolute error23230.579,1823328.551,34234Mean relative error23514,45%23613,69%237The implicit prices are constant in the hedonic model, 238while in the NN, these marginal effects are non linear 239functions of the explanatory variables. To obtain the 240marginal or implicit prices, it is necessary to evaluate 241the derivatives 242 for each explanatory variable, 243it is a cumbersome process that, nevertheless, allows 244to study the evolution of the hedonic prices attributed 245to each exogenous variable. For example, to estimate 246the influence of the area upon the marginal price of 247an additional square metre.248The hedonic model shows a linear influence of area 249upon de value attribute (Figure 2), while the NN shows 250a concavity in this value. The remaining explanatory 251variables are held constant (in this case, with average 252values over the sample). An additional square metre 253in the dwelling size increases its value by over a 254thousand euros, increasing with size in the network. 255The conclusions are in line of the finding of García 256Rubio (2004) in a smaller city. The adaptability of the 257networks to the situations at both extremes of the size 258range is not possible with classical hedonic models.259Figure 2. Implicit prices (Euros) associated to the 260dwelling surface (meters)2619-NUNEZ TABALE RdlC n2.indd 1232629-NUNEZ TABALE RdlC n2.indd 12326320-11-13 16:3826420-11-13 16:38265