# RECORD 9544f4ac839e433b51f55da090f58729fbbf9919 # TITLE: A HOUSE PRICE VALUATION BASED ON THE RANDOM FOREST APPROACH: THE MASS APPRAISAL OF RESIDENTIAL PROPERTY IN SOUTH KOREA # YEAR: 2020.0 VENUE: nan DOI: 10.3846/ijspm.2020.11544 # AUTHORS: Jengei Hong; Heeyoul Choi; Woo-sung Kim # PAGES: 13 CANDIDATE TABLE PAGES (1-based): [5, 11] # 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. ===== PAGE 1 (score 8, numeric-paren 1, table-words 0, var-words 7) ===== Copyright © 2020 The Author(s). Published by VGTU Press This 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- stricted use, distribution, and reproduction in any medium, provided the original author and source are credited. A HOUSE PRICE VALUATION BASED ON THE RANDOM FOREST APPROACH: THE MASS APPRAISAL OF RESIDENTIAL PROPERTY IN SOUTH KOREA Jengei HONG   1, Heeyoul CHOI   2, Woo-sung KIM   1,* 1 School of Management and Economics, Handong Global University, Pohang, Republic of Korea 2 School of Computer Science and Electrical Engineering, Handong Global University, Pohang, Republic of Korea Received 04 June 2019; accepted 14 October 2019 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) lin- ear 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. Keywords: housing price forecasting, hedonic pricing model, random forest approach, mass appraisal, apartment, machine learning technique. Introduction Mass appraisal, also called automatic valuation of real es- tate assets, is the introduction of mathematical statistics, computer technology, and geographic information tech- nology to establish a mathematical model that serves as a systematic appraisal of a group of real estate properties and reveals its market value (Zhou, Ji, Chen, & Zhang, 2018). The Basel II Accord, issued by the Basel Commit- tee on Banking Supervision (BCBS) in 2008, states that “the bank is expected to monitor the value of the collateral on a frequent basis and at a minimum once every year. More frequent monitoring is suggested where the market is subject to significant changes in conditions. Statistical methods of evaluation (e.g. reference to house price in- dices, sampling) may be used to update estimates or to identify collateral that may have declined in value and that may need re-appraisal. A qualified professional must evaluate the property when information indicates that the value of the collateral may have declined materially rela- tive to general market prices or when a credit event, such as default, occurs.” As a result of this accord, the value of the property is appraised more frequently than before, which leading to an increase in costs (time and money) for appraisals. Thus, a stable, accurate, and fast tool for appraisal is needed, and the mass appraisal model may be a viable solution. The mass appraisal model is also a widely accepted tool for the valuation of property for the purposes of taxation or mortgage for a loan. In the US, the Computer Assisted Mass Appraisal (CAMA), the computer system and software used for mass appraisal, is employed nearly universally by assessors nationwide for tax assessment. Owing to its importance, there has been a rich and diverse body of work addressing the appraisal techniques and performance. Traditionally, the hedonic pricing model, originat- ing from Lancaster’s consumer theory, has been one of International Journal of Strategic Property Management ISSN: 1648-715X / eISSN: 1648-9179 2020 Volume 24 Issue 3: 140–152 https://doi.org/10.3846/ijspm.2020.11544 *Corresponding author. E-mail: wskim@handong.edu ===== PAGE 5 (score 27, numeric-paren 0, table-words 2, var-words 16) ===== 144 J. Hong et al. A house price valuation based on the random forest approach: the mass appraisal of residential... Table 1. Variables used for forecasting house price Category Variables Unit Structural attributes Elapsed year (transaction year-construction year) Area Floor level of a property Heating system year m2 floor level 0 if an apartment has a central heating system. Otherwise, the value is set to 1 Neighborhood attributes Apartment brand Number of units in the apartment complex Number of buildings in the apartment complex Parking lot Floor area ratio Building coverage ratio The top floor of an apartment The lowest floor of an apartment 0 if an apartment is built by one of the ten highest-ranked apartment brands Otherwise, the value is set to 1 number of units number of buildings number of parking spot /number of units ratio ratio floor level floor level Locational attributes Latitude Longitude Distance to national park Distance to high school Distance to redevelopment area Distance to university Distance to general hospital Distance to museum Distance to subway station latitude of a property longitude of a property meter meter meter meter meter meter meter Macro variable Transaction period Gross domestic product (GDP) Annual growth rate in real GDP Land price fluctuation rate in Seoul Mortgage interest rate year billion won % % % Table 2. Descriptive statistics Variables Mean Median Standard deviation Min Max Construction year 1992.946 1993 10.270 1978 2014 Area 71.567 59.96 35.0495 16.78 273.83 Floor level 7.464 5 5.633 −1 45 Units available in the building 1724.093 900 1855.321 7 5040 Number of buildings in an apartment complex 30.404 8 42.861 1 124 Parking lot 1.006 1 0.591 0.27 4.53 Floor area ratio 252.022 224 209.46 72 2435 Building coverage ratio 24.687 19 15.046 12 204 Latitude 37.494 37.493 0.0120 37.460 37.533 Longitude 127.060 127.058 0.0170 127.0181 127.104 Distance to national park 1065.147 1053.208 396.087 86.108 2142.469 Distance to high school 536.979 522.609 236.370 31.883 1531.516 Distance to redevelopment area 634.044 571.583 416.609 0 3,758.560 Distance to university 3,382.976 3,551.466 1272.367 24.587 7,136.498 Distance to general hospital 1,062.366 975.124 524.585 41.633 3,470.830 Distance to museum 986.106 1,032.572 373.803 87.490 3,323.865 Distance to subway station 678.640 579.455 394.342 47.487 2,559.068 GDP (billion won) 333,427 337,411 64,322 225,613 446,835 Growth rate in real GDP 3.641 3.4 1.791 −1.9 7.4 Land price fluctuation rate 0.0638 0.0165 0.319 −2.643 0.625 Mortgage interest rate 6.050 5.883 0.602 5.263 7.415 ===== PAGE 6 (score 9, numeric-paren 0, table-words 2, var-words 5) ===== International Journal of Strategic Property Management, 2020, 24(3): 140–152 145 longitude, and distance to nearest facilities) was calculated by using values obtained through the MAP open Applica- tion Programming Interface (API). It has been observed in previous studies that macro- economic variables may also affect the housing market (Case, Quigley, & Shiller, 2005; Miller, Peng, & Sklarz, 2011). As relevant macroeconomic factors, we consider the transaction period, the size of the economy (gross domestic product), business cycles (% growth rate in the real gross domestic product), land price fluctuation rate in Seoul, and mortgage interest rate. The values of the vari- ables are measured for each year. The descriptive statistics of the data are given in Table 2. A summary of the traded apartment prices is shown as a histogram in Figure 2. 2. Model description 2.1. Conventional hedonic pricing model We considered a conventional hedonic pricing model es- timated by OLS regression. The hedonic pricing model is theoretically based on Lancaster (1966) and Rosen (1974). In Lancaster’s characteristics demand theory, consumers are described as deriving utility not from goods them- selves but from their characteristics. Thus, the consump- tion of a good can be considered the consumption of the composite attributes of the good. Rosen (1974) extended the characteristics demand theory to the hedonic pricing model. He suggested that the value of a good can be di- vided into the values of its attributes. Under the assump- tion that each attribute has a unique implicit price in an equilibrium market, the price of good can be interpreted as the sum of the attribute prices, implying that the price of a good can be regressed on the characteristics. However, these theories provide little specification for the functional form and list of variables considered. In this paper, we start with the conventional assumption for the hedonic pricing model, which can be expressed as: p X = β + ε , (1) where: p represents a n×1 vector of the natural logarithm of apartment prices. X is the matrix containing explana- tory variables. b is the coefficient vector corresponding to X, and ε is the vector of the white-noise error. Since the main purpose of this paper is to compare the performances of OLS and RF predictors, we set the explanatory variables considered in this hedonic pricing model to be the same as the variables considered in the RF model. However, when the hedonic pricing model includes time dummy variables, it is meaningless to in- clude each macroeconomic variable, such as annual GDP growth rate, because the effects from those variables are already embedded in the coefficients of the time dummy. Therefore, in this paper, we set the hedonic pricing model to include the time dummy variable and no other macro- economic variables, even if the RF model explicitly uses several macroeconomic variables. The predictor of this OLS-based approach, ˆp , can be conveniently obtained from the expression as: ( ) 1 ˆ ' ' p X X X X p − = . (2) 2.2. Random forest Decision trees (DTs) are decision support tools based on tree-like graph models, in which each branch represents a decision result on a feature and its threshold. For exam- ple, suppose that a node has a branch based on a feature A with threshold T. If a new sample’s feature A is lower than T, then it takes the left branch; otherwise, it takes the right one. DTs build classification or regression models. For classification models, each leaf node of the tree repre- sents a class, and classification is based on following the branches from the root node to a leaf node. Regression is based on local linear regression in the divided subspaces defined by leaf nodes after following the branches, as in classification. To train trees, one should select one feature and one threshold at a time to make a branch at a node such that each branch has similar samples after the split. There are a couple of metrics, including standard deviation reduction, for choosing a feature for a new branch. The tree grows in depth by adding one new node at a time. RF is an ensemble of DTs, which gives a prediction based on averaging (the case of regression) predictions made by each tree in the ensemble using some input data. Figure 3 depicts an example of RF. When given training data, RF runs the trees first. All of the trees in the ensem- ble are built independently according to the algorithm as follows. Let P denote the set containing all predictors. A subset of P, randomly chosen predictors, is used to grow each tree on a bootstrap sample of the training data. For each of the bootstrap samples, an unpruned regression tree is grown. After a large number of trees are generated, predictions are averaged over the different trees. Since RF is a decision tree-based technique, it has some advantages in our mass appraisal problem. In RF, a categorial variable with n classes is recoded into n-1 dichotomous ones, only a fraction of which is used in building a tree (Antipov & Pokryshevskaya, 2012). This Figure 2. Histogram of traded apartment prices ===== PAGE 11 (score 11, numeric-paren 0, table-words 2, var-words 5) ===== 150 J. Hong et al. A house price valuation based on the random forest approach: the mass appraisal of residential... 3.3. Comparison by time period In the previous section, we shuffled the whole sample and randomly selected the training sets and test sets. In doing so, we ignored the time order of samples. For instance, in that case, samples from 2016 could be trained to be used to appraise a property in 2010. However, in the actual practice of mass appraisal, the information we can access is usually constrained to the present and past. Therefore, if we use more recent information to make a less recent appraisal, we may overstate the model’s predictive power in reality. To address this problem, this section presents the performance of the predictors within limited time seg- ments. As in the previous experiments, we divided the sample in each time period into 90% training sets and 10% test sets and compared the average MAPE from 10 experi- ments for OLS and RF predictions. Table 8 presents the results for each time segment, as divided into years. We noted several features of the results. At first, the overall level of performance measured by MAPE is lower than that in the previous section. This is natural, since the samples for each time segment are smaller than the total sample. In this case, the performance of predictors inevi- tably decreased. Second, the performances of both predictors are un- stable over the period. We hypothesize that this instability resulted from the smaller sample size and some economic events causing higher volatility in certain periods. From 2006 to 2011, the housing market in Korea was impacted by the global housing boom-bust cycle and subsequent financial crisis, and the annual rate of change in apart- ment prices was relatively more volatile than in the other periods. However, our data provides only the year of the contract, not its exact date. Hence, if the annual change in housing price is more severe, the importance of the un- observable information (the exact dates of the contracts) becomes more important, and the predictive power of the models would decrease. Thus, we can expect that the aver- age performance of both predictors is poorer from 2006 to 2011 (see that they simultaneously reach a peak in 2011) than from 2012 to 2017. Finally, we noted that the RF predictor is still more accurate than the OLS predictor in all individual time seg- ments. Although the performance of the RF predictor is volatile, the results show that it is always stronger than that of OLS predictor. Roughly, it seems that the percent deviation rates of RF are lower than half of those of the OLS predictor and that the gap between the OLS and RF predictors is similar in the main result. Conclusively, the advantage of the RF predictor seems to remain even with a smaller data set and on different timelines.1 Conclusions In this paper, we discussed the features of the RF predic- tor in comparison to the conventional OLS-based predic- tor. This paper shows that the predictive performance of a machine learning-based predictor can be superior to that of the OLS-based approach. We used apartment transac- tion data from 2006–2017 in Gangnam, one of the most developed areas in Korea. We collected a data set covering 40% of all transactions in the selected area, and the sam- ples were randomly divided into training sets consisting of 90% of all transactions and test sets consisting of the remaining 10% of transactions. We used the averages of 10 experiments to compare the performance measurements in order to eliminate the possibility that the results oc- curred by chance. The average percentage deviation between the pre- dicted and actual market price was only around 5.5% for the machine learning predictor and almost 20% for the OLS-based predictor. Moreover, the probabilities that the RF prediction was within 3%, 5%, and 10% of the actual market price were 53.5%, 72%, and 90.3%, respectively, whereas those of the OLS-based prediction are 10.4%, 17.4%, and 34.6%, respectively. Furthermore, we found that the RF predictor made fewer outlier predictions than the conventional hedonic pricing model. The probability of the RF predictions deviating more than 50% from the actual price was found to be only 0.5%, while that of OLS- based predictions doing so was almost 3.8%. The contribution of this paper can be discussed in two ways. From a theoretical perspective, this paper shows that there are significant market complexities making the value determination process unable to be fully accounted for in the simplified assumptions of the conventional hedonic pricing model (separability and constancy of an attribute’s effect on housing value). From a practical perspective, the 1 It also implies that the superiority of the RF predictor in the previous section did not result from the fact that we were al- lowed to use information from the “future”−i.e., more recent information for less recent appraisals. Table 8. MAPE for each time segment (average of 10 trials) OLS Random Forest 2006 23.11313 4.574283 2007 19.07825 8.020659 2008 18.65792 8.058142 2009 23.96337 9.916612 2010 23.46693 10.28114 2011 25.52543 11.8575 2012 15.28604 6.439383 2013 14.02813 4.597863 2014 14.28471 5.189567 2015 12.89255 4.125248 2016 12.96526 5.764724 2017 15.17713 4.313319 ===== PAGE 12 (score 14, numeric-paren 0, table-words 0, var-words 12) ===== International Journal of Strategic Property Management, 2020, 24(3): 140–152 151 results are a demonstration that the accuracy of a machine learning-based mass appraisal can be surprisingly high in some cases (Note that the MAPE of human appraisals is 12% in Cannon and Cole, 2011). We infer that the high predictive power derives from a combination of the fea- tures of the RF model and the data set we applied. It is important to obtain an accurate estimation of the value of a house whose market price is not observed in order to construct a reliable house price index or to con- duct a successful mass appraisal. Traditionally, the hedonic pricing model has been adopted as the appraisal machine, but, for several reasons, the accuracy of the OLS-based predictor can be undermined. This paper suggests that the RF predictor could be a complement to this linear regres- sion method. Its results show that there is a significant loss in accuracy resulting from the simplification of reality in the OLS-based model and that some of that loss can be recovered by the RF predictor. This implies that the RF method can more successfully track the complexity of the value determination process that the OLS-based models cannot fully capture. Author contributions W. Kim and J. Hong conceived the study and were respon- sible for the design and development of the data analysis. 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