1# RECORD 9544f4ac839e433b51f55da090f58729fbbf99192# TITLE: A HOUSE PRICE VALUATION BASED ON THE RANDOM FOREST APPROACH: THE MASS APPRAISAL OF RESIDENTIAL PROPERTY IN SOUTH KOREA3# YEAR: 2020.0 VENUE: nan DOI: 10.3846/ijspm.2020.115444# AUTHORS: Jengei Hong; Heeyoul Choi; Woo-sung Kim5# PAGES: 13 CANDIDATE TABLE PAGES (1-based): [5, 11]6# ABSTRACT: Mass appraisal is the standardized procedure of valuing a large number of properties at the same time and is commonly used to compute real estate tax. While a hedonic pricing model based on the ordinary least squares (OLS) linear regression has been employed as the traditional method in this process, the stability and accuracy of the model remain questionable. This paper investigates the features of a house price predictor based on the Random Forest (RF) method by comparing it with that of a conventional hedonic pricing model. We used apartment transaction data from the period of 2006 to 2017 in the district of Gangnam, one of the most developed areas in South Korea. Using a data set covering 40% of all transactions in the sample area, we demonstrate that the accuracy of a machine learning-based predictor can be surprisingly high. The average of percentage deviations between the predicted and the actual market price was found to be only around 5.5% in the RF predictor, whereas it was almost 20% in the OLS-based predictor. With the RF predictor, the probability of the predicted price being within 5% of its actual market price was 72%, while only about 17.5% of the regression-based predictions fell within the same range. These results show that, in the practice of mass appraisal, the RF method may be a useful complement to the hedonic models, as it more adequately captures the complexity or non-linearity of actual housing markets.789===== PAGE 1 (score 8, numeric-paren 1, table-words 0, var-words 7) =====1011Copyright © 2020 The Author(s). Published by VGTU Press12This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unre-13stricted use, distribution, and reproduction in any medium, provided the original author and source are credited.14A HOUSE PRICE VALUATION BASED ON THE RANDOM FOREST 15APPROACH: THE MASS APPRAISAL OF RESIDENTIAL PROPERTY 16IN SOUTH KOREA17Jengei HONG 18 1, Heeyoul CHOI 19 2, Woo-sung KIM 20 1,*211 School of Management and Economics, Handong Global University, Pohang, Republic of Korea222 School of Computer Science and Electrical Engineering, Handong Global University, Pohang, Republic of Korea23Received 04 June 2019; accepted 14 October 201924Abstract. Mass appraisal is the standardized procedure of valuing a large number of properties at the same time and is 25commonly used to compute real estate tax. While a hedonic pricing model based on the ordinary least squares (OLS) lin-26ear regression has been employed as the traditional method in this process, the stability and accuracy of the model remain 27questionable. This paper investigates the features of a house price predictor based on the Random Forest (RF) method by 28comparing it with that of a conventional hedonic pricing model. We used apartment transaction data from the period of 292006 to 2017 in the district of Gangnam, one of the most developed areas in South Korea. Using a data set covering 40% 30of all transactions in the sample area, we demonstrate that the accuracy of a machine learning-based predictor can be 31surprisingly high. The average of percentage deviations between the predicted and the actual market price was found to 32be only around 5.5% in the RF predictor, whereas it was almost 20% in the OLS-based predictor. With the RF predictor, 33the probability of the predicted price being within 5% of its actual market price was 72%, while only about 17.5% of the 34regression-based predictions fell within the same range. These results show that, in the practice of mass appraisal, the RF 35method may be a useful complement to the hedonic models, as it more adequately captures the complexity or non-linearity 36of actual housing markets.37Keywords: housing price forecasting, hedonic pricing model, random forest approach, mass appraisal, apartment, machine 38learning technique.39Introduction40Mass appraisal, also called automatic valuation of real es-41tate assets, is the introduction of mathematical statistics, 42computer technology, and geographic information tech-43nology to establish a mathematical model that serves as 44a systematic appraisal of a group of real estate properties 45and reveals its market value (Zhou, Ji, Chen, & Zhang, 462018). The Basel II Accord, issued by the Basel Commit-47tee on Banking Supervision (BCBS) in 2008, states that 48“the bank is expected to monitor the value of the collateral 49on a frequent basis and at a minimum once every year. 50More frequent monitoring is suggested where the market 51is subject to significant changes in conditions. Statistical 52methods of evaluation (e.g. reference to house price in-53dices, sampling) may be used to update estimates or to 54identify collateral that may have declined in value and 55that may need re-appraisal. A qualified professional must 56evaluate the property when information indicates that the 57value of the collateral may have declined materially rela-58tive to general market prices or when a credit event, such 59as default, occurs.” As a result of this accord, the value 60of the property is appraised more frequently than before, 61which leading to an increase in costs (time and money) 62for appraisals. Thus, a stable, accurate, and fast tool for 63appraisal is needed, and the mass appraisal model may 64be a viable solution. The mass appraisal model is also 65a widely accepted tool for the valuation of property for 66the purposes of taxation or mortgage for a loan. In the 67US, the Computer Assisted Mass Appraisal (CAMA), the 68computer system and software used for mass appraisal, is 69employed nearly universally by assessors nationwide for 70tax assessment. Owing to its importance, there has been 71a rich and diverse body of work addressing the appraisal 72techniques and performance.73Traditionally, the hedonic pricing model, originat-74ing from Lancaster’s consumer theory, has been one of 75International Journal of Strategic Property Management76ISSN: 1648-715X / eISSN: 1648-9179772020 Volume 24 Issue 3: 140–15278https://doi.org/10.3846/ijspm.2020.1154479*Corresponding author. E-mail: wskim@handong.edu808182===== PAGE 5 (score 27, numeric-paren 0, table-words 2, var-words 16) =====838414485J. Hong et al. A house price valuation based on the random forest approach: the mass appraisal of residential...86Table 1. Variables used for forecasting house price87Category88Variables89Unit90Structural attributes91Elapsed year (transaction year-construction year)92Area93Floor level of a property94Heating system95year96m297floor level980 if an apartment has a central heating system. 99Otherwise, the value is set to 1100Neighborhood 101attributes102Apartment brand103Number of units in the apartment complex104Number of buildings in the apartment complex105Parking lot106Floor area ratio107Building coverage ratio108The top floor of an apartment109The lowest floor of an apartment1100 if an apartment is built by one of the ten 111highest-ranked apartment brands112Otherwise, the value is set to 1113number of units114number of buildings115number of parking spot /number of units116ratio117ratio118floor level119floor level120Locational attributes121Latitude122Longitude123Distance to national park124Distance to high school125Distance to redevelopment area126Distance to university127Distance to general hospital128Distance to museum129Distance to subway station130latitude of a property131longitude of a property132meter133meter134meter135meter136meter137meter138meter139Macro variable140Transaction period141Gross domestic product (GDP)142Annual growth rate in real GDP143Land price fluctuation rate in Seoul144Mortgage interest rate145year146billion won147%148%149%150Table 2. Descriptive statistics151Variables152Mean153Median154Standard 155deviation156Min157Max158Construction year1591992.946160199316110.27016219781632014164Area16571.56716659.9616735.049516816.78169273.83170Floor level1717.46417251735.633174−117545176Units available in the building1771724.0931789001791855.32118071815040182Number of buildings in an apartment complex18330.404184818542.8611861187124188Parking lot1891.00619011910.5911920.271934.53194Floor area ratio195252.022196224197209.46198721992435200Building coverage ratio20124.6872021920315.04620412205204206Latitude20737.49420837.4932090.012021037.46021137.533212Longitude213127.060214127.0582150.0170216127.0181217127.104218Distance to national park2191065.1472201053.208221396.08722286.1082232142.469224Distance to high school225536.979226522.609227236.37022831.8832291531.516230Distance to redevelopment area231634.044232571.583233416.60923402353,758.560236Distance to university2373,382.9762383,551.4662391272.36724024.5872417,136.498242Distance to general hospital2431,062.366244975.124245524.58524641.6332473,470.830248Distance to museum249986.1062501,032.572251373.80325287.4902533,323.865254Distance to subway station255678.640256579.455257394.34225847.4872592,559.068260GDP (billion won)261333,427262337,41126364,322264225,613265446,835266Growth rate in real GDP2673.6412683.42691.791270−1.92717.4272Land price fluctuation rate2730.06382740.01652750.319276−2.6432770.625278Mortgage interest rate2796.0502805.8832810.6022825.2632837.415284285286===== PAGE 6 (score 9, numeric-paren 0, table-words 2, var-words 5) =====287288International Journal of Strategic Property Management, 2020, 24(3): 140–152289145290longitude, and distance to nearest facilities) was calculated 291by using values obtained through the MAP open Applica-292tion Programming Interface (API).293It has been observed in previous studies that macro-294economic variables may also affect the housing market 295(Case, Quigley, & Shiller, 2005; Miller, Peng, & Sklarz, 2962011). As relevant macroeconomic factors, we consider 297the transaction period, the size of the economy (gross 298domestic product), business cycles (% growth rate in the 299real gross domestic product), land price fluctuation rate in 300Seoul, and mortgage interest rate. The values of the vari-301ables are measured for each year. The descriptive statistics 302of the data are given in Table 2. A summary of the traded 303apartment prices is shown as a histogram in Figure 2.3042. Model description3052.1. Conventional hedonic pricing model306We considered a conventional hedonic pricing model es-307timated by OLS regression. The hedonic pricing model is 308theoretically based on Lancaster (1966) and Rosen (1974). 309In Lancaster’s characteristics demand theory, consumers 310are described as deriving utility not from goods them-311selves but from their characteristics. Thus, the consump-312tion of a good can be considered the consumption of the 313composite attributes of the good. Rosen (1974) extended 314the characteristics demand theory to the hedonic pricing 315model. He suggested that the value of a good can be di-316vided into the values of its attributes. Under the assump-317tion that each attribute has a unique implicit price in an 318equilibrium market, the price of good can be interpreted 319as the sum of the attribute prices, implying that the price 320of a good can be regressed on the characteristics.321However, these theories provide little specification for 322the functional form and list of variables considered. In this 323paper, we start with the conventional assumption for the 324hedonic pricing model, which can be expressed as:325p326X327=328β + ε , 329(1)330where: p represents a n×1 vector of the natural logarithm 331of apartment prices. X is the matrix containing explana-332tory variables. b is the coefficient vector corresponding to 333X, and ε is the vector of the white-noise error.334Since the main purpose of this paper is to compare 335the performances of OLS and RF predictors, we set the 336explanatory variables considered in this hedonic pricing 337model to be the same as the variables considered in the 338RF model. However, when the hedonic pricing model 339includes time dummy variables, it is meaningless to in-340clude each macroeconomic variable, such as annual GDP 341growth rate, because the effects from those variables are 342already embedded in the coefficients of the time dummy. 343Therefore, in this paper, we set the hedonic pricing model 344to include the time dummy variable and no other macro-345economic variables, even if the RF model explicitly uses 346several macroeconomic variables.347The predictor of this OLS-based approach, ˆp , can be 348conveniently obtained from the expression as:349(350)3511352ˆ353'354'355p356X X X357X p358−359=360. 361(2)3622.2. Random forest363Decision trees (DTs) are decision support tools based on 364tree-like graph models, in which each branch represents 365a decision result on a feature and its threshold. For exam-366ple, suppose that a node has a branch based on a feature 367A with threshold T. If a new sample’s feature A is lower 368than T, then it takes the left branch; otherwise, it takes the 369right one. DTs build classification or regression models. 370For classification models, each leaf node of the tree repre-371sents a class, and classification is based on following the 372branches from the root node to a leaf node. Regression is 373based on local linear regression in the divided subspaces 374defined by leaf nodes after following the branches, as in 375classification.376To train trees, one should select one feature and one 377threshold at a time to make a branch at a node such that 378each branch has similar samples after the split. There are a 379couple of metrics, including standard deviation reduction, 380for choosing a feature for a new branch. The tree grows in 381depth by adding one new node at a time.382RF is an ensemble of DTs, which gives a prediction 383based on averaging (the case of regression) predictions 384made by each tree in the ensemble using some input data. 385Figure 3 depicts an example of RF. When given training 386data, RF runs the trees first. All of the trees in the ensem-387ble are built independently according to the algorithm as 388follows. Let P denote the set containing all predictors. A 389subset of P, randomly chosen predictors, is used to grow 390each tree on a bootstrap sample of the training data. For 391each of the bootstrap samples, an unpruned regression 392tree is grown. After a large number of trees are generated, 393predictions are averaged over the different trees.394Since RF is a decision tree-based technique, it has 395some advantages in our mass appraisal problem. In RF, 396a categorial variable with n classes is recoded into n-1 397dichotomous ones, only a fraction of which is used in 398building a tree (Antipov & Pokryshevskaya, 2012). This 399Figure 2. Histogram of traded apartment prices400401402===== PAGE 11 (score 11, numeric-paren 0, table-words 2, var-words 5) =====403404150405J. Hong et al. A house price valuation based on the random forest approach: the mass appraisal of residential...4063.3. Comparison by time period407In the previous section, we shuffled the whole sample and 408randomly selected the training sets and test sets. In doing 409so, we ignored the time order of samples. For instance, 410in that case, samples from 2016 could be trained to be 411used to appraise a property in 2010. However, in the actual 412practice of mass appraisal, the information we can access 413is usually constrained to the present and past. Therefore, 414if we use more recent information to make a less recent 415appraisal, we may overstate the model’s predictive power 416in reality. To address this problem, this section presents 417the performance of the predictors within limited time seg-418ments.419As in the previous experiments, we divided the sample 420in each time period into 90% training sets and 10% test 421sets and compared the average MAPE from 10 experi-422ments for OLS and RF predictions. Table 8 presents the 423results for each time segment, as divided into years.424We noted several features of the results. At first, the 425overall level of performance measured by MAPE is lower 426than that in the previous section. This is natural, since the 427samples for each time segment are smaller than the total 428sample. In this case, the performance of predictors inevi-429tably decreased.430Second, the performances of both predictors are un-431stable over the period. We hypothesize that this instability 432resulted from the smaller sample size and some economic 433events causing higher volatility in certain periods. From 4342006 to 2011, the housing market in Korea was impacted 435by the global housing boom-bust cycle and subsequent 436financial crisis, and the annual rate of change in apart-437ment prices was relatively more volatile than in the other 438periods. However, our data provides only the year of the 439contract, not its exact date. Hence, if the annual change in 440housing price is more severe, the importance of the un-441observable information (the exact dates of the contracts) 442becomes more important, and the predictive power of the 443models would decrease. Thus, we can expect that the aver-444age performance of both predictors is poorer from 2006 to 4452011 (see that they simultaneously reach a peak in 2011) 446than from 2012 to 2017.447Finally, we noted that the RF predictor is still more 448accurate than the OLS predictor in all individual time seg-449ments. Although the performance of the RF predictor is 450volatile, the results show that it is always stronger than 451that of OLS predictor. Roughly, it seems that the percent 452deviation rates of RF are lower than half of those of the 453OLS predictor and that the gap between the OLS and RF 454predictors is similar in the main result. Conclusively, the 455advantage of the RF predictor seems to remain even with 456a smaller data set and on different timelines.1457Conclusions458In this paper, we discussed the features of the RF predic-459tor in comparison to the conventional OLS-based predic-460tor. This paper shows that the predictive performance of a 461machine learning-based predictor can be superior to that 462of the OLS-based approach. We used apartment transac-463tion data from 2006–2017 in Gangnam, one of the most 464developed areas in Korea. We collected a data set covering 46540% of all transactions in the selected area, and the sam-466ples were randomly divided into training sets consisting 467of 90% of all transactions and test sets consisting of the 468remaining 10% of transactions. We used the averages of 10 469experiments to compare the performance measurements 470in order to eliminate the possibility that the results oc-471curred by chance.472The average percentage deviation between the pre-473dicted and actual market price was only around 5.5% for 474the machine learning predictor and almost 20% for the 475OLS-based predictor. Moreover, the probabilities that the 476RF prediction was within 3%, 5%, and 10% of the actual 477market price were 53.5%, 72%, and 90.3%, respectively, 478whereas those of the OLS-based prediction are 10.4%, 47917.4%, and 34.6%, respectively. Furthermore, we found 480that the RF predictor made fewer outlier predictions than 481the conventional hedonic pricing model. The probability 482of the RF predictions deviating more than 50% from the 483actual price was found to be only 0.5%, while that of OLS-484based predictions doing so was almost 3.8%.485The contribution of this paper can be discussed in two 486ways. From a theoretical perspective, this paper shows that 487there are significant market complexities making the value 488determination process unable to be fully accounted for in 489the simplified assumptions of the conventional hedonic 490pricing model (separability and constancy of an attribute’s 491effect on housing value). From a practical perspective, the 4921 It also implies that the superiority of the RF predictor in the 493previous section did not result from the fact that we were al-494lowed to use information from the “future”−i.e., more recent 495information for less recent appraisals.496Table 8. MAPE for each time segment (average of 10 trials)497OLS498Random Forest499200650023.113135014.574283502200750319.078255048.020659505200850618.657925078.058142508200950923.963375109.916612511201051223.4669351310.28114514201151525.5254351611.8575517201251815.286045196.439383520201352114.028135224.597863523201452414.284715255.189567526201552712.892555284.125248529201653012.965265315.764724532201753315.177135344.313319535536537===== PAGE 12 (score 14, numeric-paren 0, table-words 0, var-words 12) =====538539International Journal of Strategic Property Management, 2020, 24(3): 140–152540151541results are a demonstration that the accuracy of a machine 542learning-based mass appraisal can be surprisingly high in 543some cases (Note that the MAPE of human appraisals is 54412% in Cannon and Cole, 2011). We infer that the high 545predictive power derives from a combination of the fea-546tures of the RF model and the data set we applied.547It is important to obtain an accurate estimation of the 548value of a house whose market price is not observed in 549order to construct a reliable house price index or to con-550duct a successful mass appraisal. Traditionally, the hedonic 551pricing model has been adopted as the appraisal machine, 552but, for several reasons, the accuracy of the OLS-based 553predictor can be undermined. This paper suggests that the 554RF predictor could be a complement to this linear regres-555sion method. Its results show that there is a significant loss 556in accuracy resulting from the simplification of reality in 557the OLS-based model and that some of that loss can be 558recovered by the RF predictor. This implies that the RF 559method can more successfully track the complexity of the 560value determination process that the OLS-based models 561cannot fully capture.562Author contributions563W. Kim and J. Hong conceived the study and were respon-564sible for the design and development of the data analysis. 565W. Kim were responsible for data collection and J. Hong 566and H. Choi were responsible for data analysis and inter-567pretation.568Disclosure statement569There are no conflicts of interest.570References571Adair, A., McGreal, S., Smyth, A., Cooper, J., & Ryley, T. (2000). 572House prices and accessibility: the testing of relationships 573within the Belfast urban area. Housing Studies, 15(5), 699-574716. https://doi.org/10.1080/02673030050134565575Antipov, E. A., & Pokryshevskaya, E. B. (2012). 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