1# RECORD bbc85c0376ef4c6974813a189124a407086844782# TITLE: PRICE CHANGES OF REPEAT-SALES HOUSES IN KAOHSIUNG CITY: ANALYSES BASED ON HIERARCHICAL LINEAR GROWTH MODELS3# YEAR: 2023.0 VENUE: International Journal of Strategic Property Management DOI: 10.3846/ijspm.2023.199354# AUTHORS: Chun-Chang Lee; Yu-Chen Wang; Chih-Min Liang; Zheng Yu5# PAGES: 14 CANDIDATE TABLE PAGES (1-based): [9, 11]6# ABSTRACT: This study adopts the hierarchical linear growth modeling approach to analyze the differences in the changes of repeat-sales house prices in Kaohsiung City from 2012 to 2020. The Level 1 time-varying factors include house age and the time of repeat-sales; the Level 2 factors include house attributes such as house area, house type, and house location. Based on the results of the null model, the estimated variance is 0.42816, with a 1% level of significance. This shows that significant differences exist in the mean repeat-sales prices between houses. The interclass correlation coefficient is 91.65%, showing that the interclass variation and intraclass variation of the mean repeat-sales prices are 91.65% and 8.35%, respectively. The estimation results of the non-randomly varying slope model indicate that the sales time and sales time squared significantly affect repeat-sales prices. The annual growth rate and quadratic growth of sales prices do not differ by house type (luxury condominiums and apartment buildings) but are affected by house area and house location. The effect of house age on repeat-sales prices is moderated by house area, house type, and house location.789===== PAGE 1 (score 14, numeric-paren 1, table-words 2, var-words 9) =====1011Copyright © 2023 The Author(s). Published by Vilnius Gediminas Technical University12This 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.14Introduction15On August 1, 2012, Taiwan began to implement a real 16estate actual price registration scheme. Before this, the 17previous sales prices of a new or pre-owned house had 18remained unavailable to housebuyers. However, the actual 19price registration scheme is unable to present the repeat-20sales prices of the same house at different points in time. 21Therefore, the actual price registration scheme does not 22reveal whether changes in the price of a single house over 23time are in line with market conditions.24The repeat-sales model was first proposed by Bailey 25et al. (1963) and was later reinterpreted and applied by 26Case and Shiller (1987). This model centers on analyzing 27the selling price of a single house at different points in 28time; it is generally used to formulate a real estate prop-29erty price index. The interference of external factors can 30be reduced by observing the same property at different pe-31riods, assuming that the structural, material, and external 32quality of the property remains unchanged. By combin-33ing the repeat-sales approach with weighted indices and 34the hedonic price model, Shiller (1991) examined house 35International Journal of Strategic Property Management36ISSN: 1648-715X / eISSN: 1648-9179372023 Volume 27 Issue 5: 290–30338https://doi.org/10.3846/ijspm.2023.1993539*Corresponding author. E-mail: lcc@mail.nptu.edu.tw40PRICE CHANGES OF REPEAT-SALES HOUSES IN KAOHSIUNG CITY: 41ANALYSES BASED ON HIERARCHICAL LINEAR GROWTH MODELS42Chun-Chang LEE1,*, Yu-Chen WANG1, Chih-Min LIANG2, Zheng YU3431 Department of Real Estate Management, National Pingtung University, Pingtung City, Taiwan442 Department of Public Finance and Tax Administration, National Taipei University of Business, Taipei City, Taiwan453 Department of Land Economics, National Chengchi University, Taipei City, Taiwan46Received 18 January 2023; accepted 7 September 202347Abstract. This study adopts the hierarchical linear growth modeling approach to analyze the differences in the changes of 48repeat-sales house prices in Kaohsiung City from 2012 to 2020. The Level 1 time-varying factors include house age and 49the time of repeat-sales; the Level 2 factors include house attributes such as house area, house type, and house location. 50Based on the results of the null model, the estimated variance is 0.42816, with a 1% level of significance. This shows that 51significant differences exist in the mean repeat-sales prices between houses. The interclass correlation coefficient is 91.65%, 52showing that the interclass variation and intraclass variation of the mean repeat-sales prices are 91.65% and 8.35%, respec-53tively. The estimation results of the non-randomly varying slope model indicate that the sales time and sales time squared 54significantly affect repeat-sales prices. The annual growth rate and quadratic growth of sales prices do not differ by house 55type (luxury condominiums and apartment buildings) but are affected by house area and house location. The effect of 56house age on repeat-sales prices is moderated by house area, house type, and house location.57Keywords: hierarchical linear growth modeling, repeat-sales, house prices, house area, house type, house location.58price indices in Atlanta, Chicago, Dallas, and San Francis-59co from 1970 to 1986. Clapp and Giaccotto (1998) wrote 60that the repeat-sales model increases the precision validity 61of the standard error in an estimator indicator. Recently, 62Beltrán et al. (2019) adopted the repeat-sales model to an-63alyze the effects of flooding in England on property prices. 64The results show that property prices in completely inun-65dated areas fell by 21%, although this reduction was only 66significant within five years. On the other hand, the effects 67of flooding on lower-priced houses lasted for 6 to 7 years. 68Ryu and Song (2020) applied the repeat-sales model to 69exploring the price of office spaces in Seoul. According to 70their results, the price of office spaces per 3.3 m2 per year 71has risen continuously by 12% from 2000 to 2019.72However, many studies have analyzed the factors af-73fecting house prices using the hedonic price model (Ros-74en, 1974; Nelson & Schumaker, 2001; Umanailo et al., 752019). Hox (1995) uniquely pointed out that estimating 76different levels of characteristic variables at the same in-77dividual level will lead to fallacies in statistical inference. 78Giuliano et al. (2010) suggest that hierarchical linear mod-79eling (HLM) can control the variation in research data 808182===== PAGE 9 (score 40, numeric-paren 2, table-words 16, var-words 3) =====838429885C.-C. Lee et al. Price changes of repeat-sales houses in Kaohsiung city: analyses based on hierarchical...86transferred house area among the 3,167 pieces of data is 87125.079 m2 (SD = 60.879 m2); houses located in the sub-88urbs accounted for 8.6% (273 pieces) of the sample, while 89houses located in the CBD accounted for 91.4% (2,894 90pieces) of the sample; condominiums, luxury condomini-91ums, and apartment buildings accounted for 20.1% (637 92pieces), 10.3% (325 pieces), and 69.6% (2,205), respectively.93In the same data period, there were 136,913 pieces of 94single sales data, and the mean house area was 134.48 m2 95while the mean house age was 19.95 years. In terms of 96house type, condominiums, luxury condominiums, and 97apartment buildings accounted for 19.3%, 9.1%, and 9871.6%, respectively. In terms of location, houses in the 99suburbs accounted for 9.1% while houses in the CBD ac-100counted for 90.9%. The house attribute statistics did not 101vary greatly between the two samples.1024. Empirical results and analysis1034.1. Null model104A null model was developed for this study to check for sig-105nificant differences between the mean sales price of each 106house, as well as to examine the extent to which the vari-107ation in house prices is caused by variation between the 108houses. The estimation results obtained through HLM6.08 109software are presented in Table 4.110As shown in Table 4, the estimated coefficient of the 111grand mean of the first sales price of each house (b00) is 1126.132 and attains a 1% level of significance. In terms of 113random effects, the variance in Level 2 derived from the 114restricted maximum likelihood approach is 0.428, with 115a chi-square value of 80,509; it attains a 1% level of sig-116nificance. This suggests that the mean house prices differ 117significantly. To understand whether the empirical results 118can be estimated through the HLGM approach, we first 119computed the intraclass correlation coefficient (ICC). The 120ICC was determined to be 0.91648, indicating that the in-121terclass variance and intraclass variance of the repeat-sales 122prices account for 91.65% and 8.35% of the total variance 123respectively. In other words, the variance between the 124sales prices of a single house at different sales times ac-125counts for 8.35% of the total variance. Therefore, it is suit-126able to use the HLGM approach for subsequent analysis.1274.2. Non-randomly varying slope model128The empirical results of the non-randomly varying slope 129model are presented in Table 5. In terms of fixed effects, 130the estimated coefficient of the grand mean of the first 131sales price of each house (b00) is 6.0497, attaining a 1% 132level of significance. The estimated coefficient of house 133area (b01) is 0.0088, attaining a 1% level of significance, 134which suggests that every 1-m2 increase in house area in-135creases the sales price by 0.88% (converted using (eb –1) 136hereafter). The estimated coefficients of the two house 137types (b02 and b03) are 0.2395 and 0.4180, respectively, 138and both attain a 1% level of significance. This suggests 139that luxury condominiums and apartment buildings are 14027.06% and 51.89% more expensive, respectively, than 141condominiums. The estimated coefficient of house loca-142tion is 0.5478, attaining a 1% level of significance. This 143shows that houses in the CBD are 72.94% more expensive 144than those in the suburbs. Arribas et al. (2016) have dem-145onstrated that, regardless of the regression model used 146for estimation, house attributes significantly affect sales 147prices. Therefore, the results of our study align with those 148of Arribas et al. (2016).149Thhe estimated coefficient of the time of repeat-sales 150(b10) is 0.0382, attaining a 1% level of significance. This 151shows that the price of a house has grown annually by 1523.89% from 2012 onwards. The estimated coefficient of the 153time of repeat-sales squared (b20) is –0.0035, attaining a 1545% level of significance. This suggests that the curve of 155the quadratic growth of house prices in Kaoshiung City 156opens downward and that the growth rate of house prices 157gradually falls over time. In other words, an increase in 158the repeat-sales time increases the sales price of a house, 159and the margin diminishes with the sales time. In terms 160of moderating effects, the estimated interaction coef-161ficient between house area and the time of repeat-sales 162(b11) is –0.0005 and attains a 5% level of significance. The 163interaction coefficient between house area and the time of 164repeat-sales squared (b21) is 0.0001, attaining a 1% level 165of significance. These findings indicate that an increase 166in house area reduces the growth rate of sales prices and 167that the quadratic growth gradually reduces over time. The 168estimated interaction coefficients between the two house 169types (Type1 and Type2) and the time of repeat-sales (b12 170Table 4. Analysis results of the null model171Fixed effects172Coefficient173Standard error174t-ratio175p-value176Grand mean of the first sales price of 177each house b00 1786.13171790.0118180516.4581810.001***182Random effects183Variance184Degree of freedom185Chi-square186p-value187Level 2 t00188Interclass variance1890.42821903,16619180,509.9151920.001***193Level 1 s2194Intraclass variance1950.0394196Deviance1977,354.474198Number of estimated parameters1992200Note: *** denotes p < 0.01. Standard errors are presented as robust standard errors.201202203===== PAGE 10 (score 19, numeric-paren 0, table-words 6, var-words 6) =====204205International Journal of Strategic Property Management, 2023, 27(5): 290–303206299207and b13) are 0.0049 and 0.0381, respectively, and do not 208attain a level of significance; the estimated interaction co-209efficients between the two house types and the time of 210repeat-sales squared (b22 and b23) are 0.0002 and –0.0025, 211respectively, and also do not attain a level of significance. 212These findings indicate that the growth rate and quadratic 213growth (changes in the growth rate over time) of house 214prices are not moderated by house type. In other words, 215the annual growth in house prices do not differ by house 216types. The estimated interaction coefficient between house 217location and the time of repeat-sales (b14) is –0.1335, at-218taining a 1% level of significance; the interaction coef-219ficient between house area and the time of repeat-sales 220squared (b24) is 0.0182, attaining a 5% level of signifi-221cance. These findings indicate that the growth rate and 222quadratic growth (changes in the growth rate over time) 223of house prices are moderated by house location. Houses 224in the CBD have a lower growth rate than those in the 225suburbs. Melser (2017) has demonstrated that houses in 226suburbs have a higher price appreciation than houses in 227the city center. Locational differences will diminish the 228differences in the growth rates of house prices over time.229The estimated coefficient of house age (b30) is –0.0211 230and attains a 1% level of significance; the estimated coeffi-231cient of house age squared (b40) is 0.0005 and attains a 1% 232level of significance. This shows that an increase in house 233age reduces the sales price, and that the decrease becomes 234more gradual with decreasing house age. Soltani et al. 235(2021) show that house age has the most substantial effect 236on sales prices, compared to other house attributes. Shi-237mizu et al. (2010) concur that sales prices change over time 238and that such changes also vary continuously over time. 239Lyndsey et al. (2020) report that an increase in house age 240has diminishing effects on the sales prices of older houses 241and those suitable for redevelopment. In terms of moder-242ating effects, the estimated interaction coefficient between 243house area and house age (b31) is 0.0001, attaining a 1% 244level of significance; the interaction coefficient between 245house area and house age squared (b41) is 0.000002, at-246taining a 10% level of significance. These findings indicate 247that an increase in house area and house age will reduce 248the decrease in sales prices, and that the depreciation in 249sales prices accelerates with increasing house age. The es-250timated interaction coefficients between Type1 houses and 251house age (b32) and house age squared (b42) are 0.0342 252and –0.0008, attain levels of significance of 10% and 5%, 253respectively. This suggests that, compared to condomini-254ums, the decrease in the prices of luxury condominiums 255is smaller when the house age is higher, while the rate of 256depreciation falls with an increasing house age. The esti-257mated interaction coefficients between Type2 houses and 258house age (b33) and house age squared (b43) are 0.0278 259and –0.0012, attaining levels of significance of 5% and 1%, 260respectively. This suggests that, compared to condomini-261ums, the decrease in the prices of apartment buildings is 262smaller when the house age is higher, while the rate of 263depreciation falls with increasing house age. The estimated 264interaction coefficient between house location and house 265age (b34) is 0.0279 and attains a 1% level of significance; 266the interaction coefficient between house location and 267house age squared (b44) is –0.0008 and attains a 1% level 268of significance. These findings indicate that, compared to 269houses in suburbs, an increase in house age will reduce the 270decrease in the prices of houses in the CBD, while the de-271preciation diminishes with increasing house age. Xu et al. 272(2018) have found that the added value of older houses in 273Beijing between 2005 and 2012 stems from the land itself 274rather than buildings on the land, while the price growth 275rate and quadratic growth are affected by house location. 276Liou et al. (2016) report that, between 2004 and 2012, the 277annual quadratic growth of house prices in Taipei City 278was faster than that of houses in New Taipei City. These 279findings demonstrate that the quadratic growth of house 280prices is affected by house location.281In terms of random effects, p0i is a Level 2 variable 282used to interpret p0i based on the three Level 2 charac-283teristics (i.e., house area, house type, and house location). 284r0i is the error term with an estimated variance (t00) of 2850.0727 that has a significance of 1%. Therefore, p0i remains 286random even after controlling for the effects of the three 287Level 2 variables on house prices. In other words, other 288house attribute variables affect house prices.289We apply the HLGM approach to analyze repeat-sales 290data. Our empirical results suggest that the annual growth 291rate and quadratic growth of sales prices do not differ by 292house type. The effects of house age and the time of re-293peat-sales on sales prices are affected by house location 294and house area. Thus, the annual growth rate and qua-295dratic growth of repeat-sales prices are affected by house 296location and house area. Controlling for the effects of the 297Level 2 variables (house area, house type, and house loca-298tion) and a Level 1 variable (house age) on sales prices will 299reduce the random component of the initial price (p0i). 300Lastly, given that area is a continuous variable and its 301moderating effects cannot be plotted easily, and house 302type (Type1, Type2) did not significantly influence the re-303lationship between the time variables and house price, we 304did not plot the effects of these variables. We only plotted 305the effects of house location on sales time and price; house 306type and location affected the relationship between house 307age and price (see Figures 3 to 5).308Figure 3. The moderating effects of house location on the 309relationship between house price and sales time310311312===== PAGE 11 (score 43, numeric-paren 22, table-words 5, var-words 1) =====313314300315C.-C. Lee et al. Price changes of repeat-sales houses in Kaohsiung city: analyses based on hierarchical...316Figure 4. The moderating effects of house type on the 317relationship between house price and age318Figure 5. The confounding effects of house location on the 319relationship between house price and age320Table 5. Analysis results of the non-randomly varying slope model321Fixed effects322Coefficient323Standard error324t-ratio325p-value326Grand mean of the first sales price of 327each house 328b003296.04973300.0186331325.7303320.001***333 334Area 335b01336 337Type1 338b02339 340Type2 341b03342 343Location b043440.00883450.23953460.41803470.54783480.00033490.09073500.06983510.057135231.0993532.6413545.9873559.5913560.001***3570.009***3580.001***3590.001***360Time – T 361b10362 363Area 364b11365 366Type1 367b12368 369Type2 370b13371 372Location b143730.0382374–0.00053750.00493760.0381377–0.13353780.00903790.00023800.03363810.02823820.04363834.260384–2.2223850.1463861.350387–3.0603880.001***3890.026**3900.8843910.1773920.003***393(Time – T)2 394b20395 396Area 397b21398 399Type1 400b22401 402Type2 403b23404 405Location b24406–0.00354070.00014080.0020409–0.00254100.01824110.00144120.000044130.00504140.00424150.0072416–2.5424173.3584180.411419–0.5784202.4994210.011**4220.001***4230.6814240.5634250.013**426Age 427 428b30429 430Area 431b31432 433Type1 434b32435 436Type2 437b33438 439Location b34440–0.02114410.00014420.03424430.02784440.02794450.00304460.000034470.01794480.01134490.0052450–7.0904513.2714521.9104532.4594545.2864550.001***4560.001***4570.056*4580.014**4590.001***460Age2 461 462b40463 464Area 465b41466 467Type1 468b42469 470Type2 471b43472 473Location b444740.00054750.000002476–0.0008477–0.0012478–0.00084790.000074800.0000014810.00034820.00024830.00014846.9254851.858486–2.450487–5.912488–5.2474890.001***4900.063*4910.015**4920.001***4930.001***494Variance495Degree of freedom496Chi-square497p-value498Level 2 t00499Interclass variance5000.07275013,16250217,543.42505030.001***504Level 1 s2505Intraclass variance5060.0369507Deviance5082,305.7188509Number of estimated 510parameters5112512Note: *** denotes p < 0.01; ** denotes p < 0.05; * denotes p < 0.1. Standard errors are presented as robust standard errors.513514515===== PAGE 12 (score 15, numeric-paren 0, table-words 3, var-words 7) =====516517International Journal of Strategic Property Management, 2023, 27(5): 290–303518301519Conclusions and recommendations520This study focuses on changes in the repeat-sales prices 521of houses over time in Kaohsiung City. The empirical re-522sults suggest that the HLGM approach is a feasible means 523of exploring house price changes. Notwithstanding the 524wide availability of other options, examining changes in 525the sales prices of houses over time through ANOVA can 526only reveal relative changes in the sales prices between 527houses; it is unable to directly estimate changes in the sales 528prices of houses. Moreover, ANOVA does not account for 529measurement errors–nor does it include variables at the 530aggregate level (Level 2) for estimation (Lee et al., 2013). 531Arribas et al. (2016) demonstrate that the variance of each 532coefficient in HLGM is always smaller than those in OLS. 533This is because the lower estimation efficiency of OLS will 534result in a higher variance than that from HLGM. Fur-535thermore, HLGM can also calculate the interclass vari-536ance, as well as the ratio of the intraclass variance to the 537total variance (i.e., the ICC). OLS, on the other hand, can 538only derive the variance between the horizontal intraclass 539residuals. Not only is HLGM able to estimate changes in 540the growth curve of each housing transaction at different 541points in time, it can also examine the differences between 542individual-level data, which facilitates investigations into 543how house attributes affect changes in sales prices (Hsieh, 5442015). After analyzing the advantages and drawbacks of 545each approach, showing that the HLGM approach is the 546appropriate method to examinine repeated observations in 547housing transactions over time. It can analyze the curves 548of the growth rate and quadratic growth of sales prices 549while elucidating how house attributes affect changes in 550the growth rate and quadratic growth of sales prices.551According to the empirical results of the null model, 552the interclass error attained significance, suggesting that 553major differences exist in the mean house prices in this 554study, with an ICC of 91.65%. This means that the dif-555ferences in housing prices caused by different house at-556tributes accounted for 91.65% of the variance in the re-557peat-sales data. The differences in housing prices of the 558same house caused by different sales periods accounted 559for 8.38% of the variance. This result cannot be obtained 560through a single-level repeat-sales model. The non-ran-561domly varying slope model results indicate that the annual 562growth rate and quadratic growth of sales prices failed to 563attain significance in terms of the interaction coefficient 564between sales time and house type. This suggests that the 565effects of sales time on sales prices do not differ by house 566type. House area and house location moderate the effects 567of sales time on sales prices (i.e., both variables affect the 568growth rate and quadratic growth). The interaction coef-569ficients between house area, house type, and house loca-570tion are all significant, which implies that all three vari-571ables moderate the effects of house age on sales prices. 572This finding shows that in repeat-sales data, the growth 573rate and the changes in the growth rate of the price of the 574same house are influenced by house area and house loca-575tion. This result cannot be obtained through a single-level 576repeat-sales model. The empirical evidence demonstrates 577that house attributes are an important factor and modera-578tor of the dynamic changes in repeat-sale house prices.579The current repeat-sales approach suffers from con-580ventional drawbacks, such as small sample sizes and sam-581ple selection bias (Guo et al., 2014). We recommend that 582future studies perform HLGM analyses using panel data-583based analytical methods. From July 1, 2021, onwards, 584house numbers must be disclosed on the actual price 585registration system. This measure would assist future re-586searchers in performing accurate validations and would 587reduce the need to compare and analyze repeat-sales data. 588Additionally, house price indices can be developed using 589the HLGM approach.590References591Aiken, L. S., & West, S. G. (1991). Multiple regression: testing and 592interpreting interactions. Sage Publications Ltd.593Anthony, O. A. (2018). Construction and application of property 594price indices. 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