THE IMPACT OF LUXURY HOUSING ON NEIGHBORHOOD HOUSING PRICES IN TAIPEI CITY
1Professor, Department of Real Estate Management, National Pingtung University, Taiwan No. 51, Mingsheng East Road, Pingtung, Taiwan
2Associate professor, Department of Public Finance and Tax Administration, National Taipei University of Business, Taiwan
3Associate professor, Department of Computer Science and Information Engineering, National Pingtung University, Taiwan
4Department of Real Estate Management, National Pingtung University, Taiwan No. 51, Mingsheng East Road, Pingtung, Taiwan
ABSTRACT
This study investigated whether a decision to construct luxury housing can help increase neighborhood housing prices. The difference-in-difference method was used in the analysis. Housing transaction data from 2008 to 2011 were used in the analysis. According to the empirical results, after eliminating the common growth in prices (10.6%) between the neighborhood in which luxury housing was to be built and the other non-luxury neighborhood, the real gap in the housing prices caused by the luxury housing was 11.2%. This suggests that luxury housing has spillover effects on neighborhood housing prices and, specifically, can help to increase neighborhood housing prices. Furthermore, the results showed that housing prices in the neighborhood in which the luxury housing was to be built were inversely proportional to the distance from the luxury housing.
Keywords:Luxury housing Difference-in-difference method Housing price Spillover effects Geographic information system Taipei City.
ARTICLE HISTORY: Received:9 May 2018. Revised:3 August 2018. Accepted:7 September 2018. Published:30 October 2018.
Contribution/ Originality:This suggests that luxury housing has spillover effects on neighborhood housing prices and, specifically, can help to increase neighborhood housing prices. Furthermore, the results showed that housing prices in the neighborhood in which the luxury housing was to be built were inversely proportional to the distance from the luxury housing.
In  recent years, Taiwan’s real estate market has been dominated by high-priced housing  products, which are advertised as being  built with the highest quality building materials and  equipment in the best locations, with large floor areas, good planning and  strong management. Moreover,  due to the intense competition  of the housing  sales market, numerous luxury housing development  projects are currently in progress. Thus, the effects of such luxury housing have become a  focus of concern. With regard to high-priced housing, the Taipei City Revenue Service defines a house with a total transaction price  above 80 million NTD  as a “senior house,” which would more  commonly be described as luxury housing. According  to Lin and Jou (2005 ) luxury housing refers to houses  with exceptional landscapes,  locations and other rare space-related resources, or houses with a high total price, high floor area,  high quality facilities and high profile. Almatarneh (2013 
) suggested that real estate developers distinguish between luxury housing and general  housing through their advertisements of various housing characteristics, such  as design, planning, and architectural concepts, thereby further strengthening  the position of luxury housing in  the minds of the public. The unique and  irreplaceable features of luxury housing units have  a very important impact on the real estate market.
The  choice of a good living environment depends not only on the characteristics of  the home itself, but also on the characteristics of the given neighborhood  residential environment. DiPasquale and Wheaton (1996 ) indicated that when the appearance of a  residential area becomes more beautiful, the quality of life in that  neighborhood will become more attractive, resulting in positive spillover effects on neighborhood housing prices. Bourassa et al. (2004 
) proposed that attractive buildings increase the value of the real estate  in the surrounding neighborhoods, and that attractive luxury housing may also  attract more residents, including those  with high incomes, as well as members of the political and business elite with high socioeconomic statuses. Moreover, people may  select their places of residence to maintain their images by getting close to  people with high incomes and social statuses (Cialdini et al., 1976 
). Ooi and Le (2013 
)  argued that both newly developed buildings and luxury housing may have positive  external effects or spillover effects  on neighborhood housing.  The architectural style of  luxury housing is generally different from that of general buildings.  In addition to their innovative and stylish appearances, luxury housing units may  create price spillover effects through the beautification of the neighborhood environment and  high sales prices, thereby affecting the average neighborhood housing price.
This study aims to investigate whether luxury housing has such spillover effects on neighborhood housing prices. It adopts the difference-in-difference method (DD) to analyze the impact of luxury housing on neighborhood housing prices before and after the obtainment of a construction license. This method can accurately estimate the impact of a single event on two groups. After eliminating the common growth trend of the treatment group and the control group, as well as other unobserved influential factors, the real impact of luxury housing buildings on neighborhood housing prices can be more effectively estimated.
The purposes of this study are: (1) to discuss the differences in housing prices between a neighborhood in which luxury housing is to be built and another, non-luxury neighborhood before the announcement of luxury housing construction, as well as the differences in neighborhood housing prices after the announcement of luxury housing construction; that is, to determine whether luxury housing spillover effects have a greater impact on the neighborhood housing prices in which the luxury housing is actually built than on the prices in other neighborhoods; and (2) to determine whether, after a decision to construct luxury housing has been made, there are different impacts on neighborhood housing prices based on the distance from the luxury housing. If the impact of the luxury housing on neighborhood housing price decreases with increasing distance from the luxury housing, it means that the luxury housing spillover effects will decrease over increasing distances from the luxury housing.
The impact of luxury housing on neighborhood  housing prices can be explained by spillover effects and amenity effects. The  quality of a living environment depends not only on the characteristics of a  home itself, but also on the characteristics of the given neighborhood  residential environment. Boyle and Kiel (2001 )  proposed that environmental externalities such  as a neighborhood’s air quality, water quality, and unpopular land use are  likely to affect neighborhood housing prices. Des Rosiers et al. (2002 
) found that beautification  of landscaped curbs will  increase neighborhood real  estate prices by about 4.4%. Bourassa et al. (2004 
)  argued that attractive buildings can increase neighborhood real estate prices by about 37%  and that the unique and attractive improvements in a neighborhood can increase neighborhood real estate prices by about 27%.  In contrast, the prices of housing in neighborhoods of poorer  environmental quality can be reduced by 51%.
The  prices of houses in a neighborhood with luxury housing are affected by that luxury housing  because people are attracted by things of value higher than their intrinsic  value and seek associate themselves with them. (Cialdini et al.,  1976 )  called this effect the basking in reflected  glory (BIRGing) effect, arguing that people associate with successful people to  create a positive self-image and better evaluations from others. According to Tesser (1988 
)  when people become closer to outstanding or  superior people, they feel honored with improved self-evaluations. Similarly, luxury housing will also attract  those with high socio-economic status to live in a given neighborhood 5  neighborhood effect (DiPasquale and Wheaton, 1996 
; O’Sullivan, 2000 
).
According to a review of the literature on empirical estimation methods, in the past, the hedonic price method was generally used for estimating the impact of improved neighborhood environment quality on housing prices. However, in recent years, where the occurrence of a specific event has improved the quality of a specific neighborhood environment to affect the neighborhood housing price, the estimation of cause and effect has typically been accomplished by using the difference-in-difference method. The advantage of the method is that it can review the impact of the announcement of a specific policy or the construction of a specific building on the neighborhood.
Kiel and McClain (1995 ) explored the  impact of the establishment of waste incineration plants on the price of the  housing in the North Andover area by setting the announcement times for the  establishment of the incineration plants from 1979 to 1980 and comparing the housing prices as  of 1978 and 1981. Residential  housing outside of the perimeter of 3 miles from the incineration plants was the control group, while  houses within the perimeter of 3 miles from the incineration plants were  regarded as the treatment group. The  research findings suggested that the difference-in-difference price was 11,863.9 USD. 
Kavetsos (2012 )  analyzed the effect of the announcement of hosting the Olympic Games on London  housing prices by using five regions hosting Olympic events as the treatment group  and the rest of the regions of London as the control group. The results,  estimated by using the  difference-in-difference method, indicated that the housing prices  in the five administrative regions (Greenwich, Hackney, Newham, Tower Hamlets, and Waltham Forest) increased  by 2.1%  to 3.3%  after the announcement. 
Dehring et al. (2007 )  explored the impact of the announcement that a new stadium would be constructed  on the local housing prices in Dallas-Fort  Worth. The sample data included the residential housing sales  data for Dallas  and Arlington  from January 2004 to March  2005. The  difference-in-difference method was adopted to analyze the impact of  the announcement of building a new stadium on local housing prices. The research  findings suggested that the average housing price decreased by 1.5% after the announcement that a new stadiums would be  built as the tax burden on the local community was increased to subsidize the  construction. Therefore, the local housing prices dropped in the short term. 
Dubé et al. (2011 ) applied the difference-in-difference  method to estimate of the impact of rapid bus transit service in Quebec on residential housing prices,  finding that the residential housing prices did not change significantly. Heintzelman (2010 
) employed the difference-in-difference  method in the analysis of CPA (community  preservation act) implementation in communities across Massachusetts on  local real estate prices by using communities implementing CPA as the treatment group  and communities not implementing CPA as the  control group. According to the estimation results, the local real  estate prices decreased by about 1.5% after the implementation of CPA. Compared to many previous  research methods such as the hedonic  price method, the difference-in-difference  method can eliminate the possible interference of unobserved factors on housing prices to avoid estimation  bias, and thus demonstrate the real impact on neighborhood housing prices. 
The difference-in-difference method  is a research method now widely used in the field of micro econometrics. The method assumes that  the treatment group and the control group are the groups that will be compared  both before and after a policy change, where the treatment group is the group affected by  the policy change and the control group  is a group not affected by the policy change. The purpose of using the method  is to evaluate the impact of the policy. Through time delineation, that is, by  examining certain periods before and after the occurrence of the specific event or policy announcement,  as well as by comparing the differences between the control group and the treatment group.  An analysis that uses the  difference-in-difference method can effectively control for any systematic differences  caused by potential selection bias (Wooldridge, 2009 ).
The  estimation of luxury housing  spillover effects can be made by comparing the differences in housing  prices of a control group  and a treatment group  after the occurrence of a specific event, namely, the obtainment of a construction license  for the luxury housing. In  general, real estate developers can legally sell housing  products after obtaining the relevant  construction license, and can thus pre-sell the housing products before the  completion of construction. Such a pre-sales method is very common in Asian  countries and regions. Lai et al. (2004 ) and Munneke et al. (2011 
)  used the time of obtaining the construction license as the delineation  benchmark. This study also used the date on which the official construction  license for the luxury housing in  question was obtained as the time at which the decision to construct the luxury housing was made. With regards  to studies classifying the treatment group  and the control group  by distance, Liang (2009 
) and Dempsey and Plantinga (2013 
)  classified the groups according to a radius of 500 meters; Voicu and Been (2008 
)  compared the housing prices in the research rea of a radius between 500 feet and 1000 feet (about 150~300 meters). This study  classified houses located within the radius of 500 meters from the luxury housing as the treatment group and those outside the  radius of 500 meters from the luxury housing as the control group in order to  discuss the differences in the impact on housing prices in terms of the distance from the luxury housing. The settings of  the empirical model used are  shown as follows in Eq. (1):
In order to analyze whether the housing prices of sub-samples within the treatment group were different due to their different distances from the luxury housing, samples within the treatment group were divided in terms of their distances from the luxury housing as follows: distances within 100 meters, distances of 100 meters to 300 meters, distances of 300 meters to 500 meters.
Ihlanfeldt (2007 ), Matthews and Turnbull (2007 
) and Andersson et al. (2010 
)  divided the residential housing attributes into basic attributes, including the hedonic price variables in the unit of  household or building, and housing neighborhood environmental attributes, including environmental factors and the accessibility  of public transport  facilities. This study used the basic hedonic attributes as the internal attributes. Secondly, this study used Arc GIS software 10.1 to compute the nearest  distances of the houses to the neighborhood  environment attributes (e.g., MRT station, railway station, primary school, junior  high school)  as the external housing attributes.  Thirdly, this  study also explored the difference-in-difference  attributes. The definitions of various variables are shown below in Table 1. 
This  study used the natural logarithm of the housing transaction total price as the dependent variable ( In PRICE ). Cohen and Coughlin (2008 ), Kavetsos (2012 
) and Gibbons et al. (2013 
)  argued that the total transaction price as the dependent variable has more complete  economic implications as compared to the dependent variable of the transaction  unit price in representing the housing price. Moreover, many scholars,  including Sirmans et al. (2005 
), Lipscomb and Farmer (2005 
) and Zietz et al. (2008 
) have suggested that the logarithm of dependent variable  price has been confirmed to be able to reduce the data heterogeneity and avoid  the estimation by using the quantile  regression approach. As such, this study adopted the log-linear function type as the  regression model.  
The  residential area ( AREA ) is the actual registered area of the housing subject  and is a continuous variable. In  general, under the same assumed conditions, if the area is greater, the housing price will be higher. McMillen and Redfearn (2010 ), Landry and Jahan-Parvar (2011 
) and Abbott and Klaiber (2011 
)  found that residential area  has a positive impact on housing price. The  housing age ( AGE ) refers to the number of years since the year that  construction of the building was completed to the year of the transaction. It  is also a continuous variable, and directly reflects the depreciation and  replacement cost. Under the same assumed conditions, if the housing age is older, the facilities  and building materials will deteriorate over time, resulting in a reduced housing price. Osland (2010 
), Carrillo (2012 
) and Bin and Landry (2013 
)  argued that housing age and housing  price were negatively correlated. It is expected that housing age has a negative impact on housing price. However, the  depreciation due to housing age  does not occur in a rigid linear fashion as the depreciation is faster in the  beginning. If the regression model adopts the variable of housing age only, only the linear change caused  by housing age is observed. Therefore, the addition of the variable of housing age squared ( AGES) is used to observe the non-linear change of  depreciation. Kadish and Netusil (2012 
) and Bin and Landry (2013 
)  argued that housing age squared and  housing price were positively correlated. It is expected that housing age squared has a positive impact on housing price.  
The  number of rooms (ROOM ) is related to the internal layout of the housing  subject. It is a continuous variable. If the residential  area remains unchanged, a greater number of rooms results in a  higher likelihood of using the internal space. Sirmans et al. (2005 ), Hansen et al. (2006 
), McMillen and Redfearn (2010) and Araya and Iturra (2013 
)  suggested that number of rooms and  housing price were positively correlated. It is expected that the number of rooms has a positive  impact on housing price. The  number of living rooms (LIVEROOM) is related to the internal layout of the housing  subject measured by the unit of living rooms. It is a continuous variable. When the number of living rooms  is greater, it means the area of the house is larger, and the price of the  house will be higher. This attribute  will be directly reflected in the house purchasing cost. Hong and Lin (1999 
) and Huang et al. (2010 
)  found that the housing price would be higher if the number of living rooms was  larger, indicating  that the number of living rooms and housing price were positively correlated. It is expected  that the number of living rooms  has a positive impact on housing price. The  number of bathrooms ( BATH ) is also related to the internal layout of the housing  subject. It is also a continuous variable. According to a review of previous  studies on price models, it is generally accepted that the number of bathrooms  has a positive impact on housing price (Anselin and Lozano-Gracia, 2008 
; McMillen and  Redfearn, 2010 
; Baltagi and Bresson, 2011 
) . It  is expected  that the number of bathrooms has a positive impact on housing price. 
The  residential floor refers to the  floor of the housing subject. It is set as a dummy variable. FLOOR1  means that the  house is located on the first floor; otherwise, it is set as 0. Alternatively, FLOOR4  means that the  house is located on the fourth floor; otherwise, it is set as 0. Houses on the  first floor can usually be used as shops or for other commercial purposes, and  thus there will be an effect of increasing the housing price. Therefore, it is  expected that being located on the first floor has a positive impact on housing price. As for houses on  the fourth floor, the pronunciation of the number “four” sounds similar to the  word for “death” in Chinese, so people in Taiwan are generally less willing to  live on the fourth floor. Therefore, the utility ratio of the fourth floor is generally lower (Yang and Su, 2011 ). Lin et al. (2011 
)  argued that a location on the fourth floor thus has a negative impact on real  estate price. It is expected, then, that a location on the  fourth floor  has a negative impact on housing price.
 This  study uses data from residential samples including buildings and apartments. In general, a building of six or more  floors with elevators is regarded as a building while a building of five or  fewer floors without elevators is regarded as an apartment. The housing type (TYPE) is set as a dummy variable. It is set as 1 for a  building and 0 for an apartment. The building and apartment are common types of  condominium housing in Taiwan. In recent years, most of the newly built  buildings have steel structures. In contrast, apartments generally do not have  steel structures. Moreover, apartments usually have only four or five floors.  Buildings have more than six floors and also have elevators. Therefore, the  construction costs of buildings are higher than those apartments (Lin and Ma, 2012 ). It is expected that prices of buildings are higher.  
Concerning the distance to MRT station variable, this  study considered MRT stations in Taipei City. Since the MRT was put into  service, the cost of commuting time has been reduced and the accessibility of neighborhoods has been improved, making urban  life more convenient and better; hence, MRT may have a significant impact on housing  price. Ahlfeldt and Maennig (2010 )  found that increasing the distance to an MRT station may lead to a reduced housing price. It is expected that the nearest distance to an MRT station has a negative impact on housing  price. Regarding the distance to a railway station (TRAIN) variable, this study considered several railway stations including Taipei Station, Wanha Station, Songshan  Station, and Nangang Station. As a transportation node, a railway station can promote the  development of commercial activities in the surrounding areas, and living  facilities closer to railway stations  are more numerous and convenient. Gibbons et al. (2014 
)  found that the distance to a railway station is inversely proportional to housing price. It is expected  that the nearest distance to a railway  station has a negative impact on housing price. In  terms of the distance to school ( PRIM  , JUIN  ) variables, the schools considered in this study  included primary schools and junior high schools. As schools provide living  and recreational space for residents, and provide families with children  convenient and safe access to education, the distance to a school is regarded  as one of the major factors to consider in purchasing a house. Gibbons et al. (2014 
)  found that a housing price would be higher if it was closer to a school, as  they were negatively correlated. It  is expected  that the distance to a school has a negative impact on housing price. 
As for the time when the luxury housing construction license was obtained ( TIME  ) variable, the sample period of this study was  from January 1, 2008, to  December 31, 2011. The sample data were divided into samples from before a construction license was obtained and samples  from after a construction  license was obtained by the benchmark period for obtaining such construction  licenses of July to December, 2010. It is a dummy variable. The  value of the variable for samples during the period from January 1, 2008, to June 30, 2010  (that is, before a license was obtained) is set as 0, while the value of the  variable for samples during  the period from January 1, 2011, to  December 31, 2011 (that is, after a license was obtained) is set as 1. The  appearance of luxury housing is more  attractive than that of general housing, and it can beautify the surrounding  environment; therefore, it can improve the quality of a neighborhood  environment to make the neighborhood more attractive (O’Sullivan, 2000 ). In addition, it can attract people  of high social and economic status to move in. As a result, regular people and  investors may follow the lead of celebrities or others of high socioeconomic  status in choosing to live in the neighborhood or invest in the area. People may also have higher  self-evaluations if they live in a neighborhood with luxury housing (Cialdini et al., 1976 
; Tesser, 1988 
) resulting in increased  housing prices for the whole community. It  is thus expected  that obtaining a  construction license for luxury housing has a positive impact on housing prices. 
The luxury housing neighborhood  (TREAT) variable refers  to the number of houses that are really located in the radius of the luxury housing. It is a dummy variable. If the  sample is located within the radius of the luxury housing (the treatment group),  the value is set as 1; otherwise (the control group), it is set as 0. This study sought to explore the  difference between samples within the radius of 500 meters from the luxury housing and samples outside the radius  of 500 meters from the luxury housing in terms of housing price. The  development of luxury housing may result in positive spillover effects on a  neighborhood. Bourassa et al. (2004 )  argued that attractive buildings can increase neighborhood housing prices. The neighborhood  environment can improve the neighborhood quietness and comfort to create a positive impact on  neighborhood housing prices. In addition, based on the social  attributes of Taiwanese society and the extent to which Taiwanese people  typically seek to bask in the glory of the high status people and positive  events of a neighborhood, it is expected that neighborhood luxury housing has a positive impact on  housing price. The time of obtaining construction license × luxury housing neighborhood ( TIME * TREAT ) variable is an interactive variable referring to the  interaction between the time of obtaining the construction license and being in the neighborhood of luxury housing. After obtaining the construction license, if a  house is located in the luxury housing neighborhood, luxury housing can  beautify the neighborhood environment to improve the neighborhood environmental quality. Moreover,  the architectural design of luxury housing can improve the neighborhood housing  landscape to result in a positive impact on the neighborhood. Ooi and Le (2013 
)  explored the impact of new development projects on neighborhood housing prices. Kavetsos (2012 
)  discussed the impact of newly built Olympic stadiums on neighborhood housing prices. Both of those  studies applied the difference-in-difference method and predicted that newly  developed or newly built buildings have a positive impact on neighborhood  housing prices. It is expected that the time to obtain the construction license × luxury housing  neighborhood has a positive impact on housing price. 
In this study, the residential transaction data source used was the “Taiwan Real Estate Transaction Bulletin” published by the Giga House website of the Taiwan Real Estate Transaction Center (Taiwan Real Estate Portal). The data period was from January 1, 2008, to December 31, 2011. Focusing on Taipei City, this study obtained a total of 10,930 samples. Taiwan Real Estate Portal started to provide a transaction information query service in 2005. The data were collected from well-known real estate agencies in Taiwan including Sinyi Realty, Pacific Realtor, Century 21 Real Estate LLC, Chinatrust Real Estate, H&B Real Estate, Dafengfu Real Estate, Good Morning Rehouse, ERA Taiwan Master Franchise, Ever Spring Real Estate, and Chiau Mau Realty, and the data were about transactions with a guarantee of performance. This study obtained the transaction data regarding buildings and apartments from the bulletin, including housing attributes such as the housing transaction price, floor area, housing age, and number of floors. As the data from the website were not limited only to housing transaction data, this study eliminated any data regarding non-residential housing transactions including transactions involving land, parking spaces, factories, offices, and stores, as well as any samples with incomplete information. This study eliminated the top and bottom 5% of samples of housing prices in various administrative regions to avoid the effect of outliers on the statistical computational results. Finally, 8,871 samples were used for the empirical analysis. According to luxury housing standards set by the Taipei City Revenue Service and the central bank of Taiwan,1 -- that is, independent building, luxurious appearance, great location, good landscape, few households on each floor, parking space for each household, strict security and comprehensive management -- the total price of such a house should be 80 million NTD and above, and the unit price of each ping should be 1 million NTD and above. After cross-validation, this study collected real cases of luxury housing in Taipei City. During the sampling period from July to December 2010, the luxury housing cases with construction licenses were selected as the samples in this study. The five cases of luxury housing for this study were located in various districts of Taipei City, including the Zhongzheng, Songshan, and Da’an districts. The sources of the data on the luxury housing cases included the Ministry of Interior real estate transaction price query service website, the official websites of various construction companies and other housing information websites on the Internet.2
Table-1. Variable Descriptions
According to the descriptive statistics in Table 2, the average housing price was 13.978 million NTD. The average residential area (AREA ) was 31.63 ping (1 ping equals 35.58 sq. ft.). The average housing age ( AGE ) was 20.86 years. The average number of rooms ( ROOM ) was 2.47 rooms. The average number of living rooms ( LIVEROOM ) was 1.77 rooms. The average number of bathrooms ( BATH ) was 1.48 rooms. The residential floor being on the first floor ( FLOOR1 ) accounted for 6.0% of the sample houses, the residential floor being on the fourth floor ( FLOOR4 ) accounted for 21.0%, and the residential floor being on the other floors accounted for 73.0%. Regarding housing types ( TYPE ), buildings accounted for 56.0%, while apartments accounted for 44.0%. The average nearest distance to an MRT station ( MRT ) was 588.55 meters. The average distance to the nearest railway station ( TRAIN ) was 3,713 meters. The average distance to the nearest primary school ( PRIME ) was 401.92 meters. The average distance to the nearest junior high school ( JUNI ) was 586.60 meters.
Table-2. Descriptive statistics (N=8,871)
Regarding basic housing properties, the residential area estimation coefficient was 0.017, having reached the 1% significance level. This means that if the residential area is increased by 1 ping, the housing price will increase by 1.7%. The housing age estimation coefficient was -0.016, having reached the 1% significance level. This means that if the housing age is increased by one year, then the housing price will decrease by 1.6%. Its square estimation coefficient was 0.001, having reached the 1% significance level. This means that an older housing age can result in a lower housing price. However, the decrease is at the marginal decrease state. The number of rooms’ estimation coefficient was 0.027, having reached the 1% significance level. This means that an increase of one room can result in an increase of the housing price by 2.7%. The number of living rooms estimation coefficient was 0.082, having reached the 1% significance level. This means that an increase of one living room can result in an increase of housing price by 8.2%. The number of bathrooms estimation coefficient was 0.136, having reached the 1% significance level. This means that an increase of one bathroom would result in a housing price increase of 13.6%. The Floor1 estimation coefficient was 0.175, and the Floor4 estimation coefficient was -0.069, having reached the 1% significance level. This means that the price of Floor1 was higher than the average price for the rest of the floors by about 17.5%, while the price of Floor4 was lower than the average price for the rest of the floors by about 6.9%. The housing type estimation coefficient was 0.253, having reached the 1% significance level. This means the average building housing price was higher than the average apartment housing price by about 25.3%.
Regarding neighborhood environment attributes, the variable of distance to an MRT station estimation coefficient was -2.604e-5, having reached the 1% significance level. This suggests that an increase in the distance to an MRT station by 1 meter would result in a housing price reduction by about 0.026%. The distance to a railway station estimation coefficient was -2.408e-5, having reached the 1% significance level. This suggests that an increase in the distance to a railway station by 1 meter would result in a housing price reduction by about 0.024%. The distance to a primary school estimation coefficient was -8.204e-5, having reached the 1% significance level. This suggests that an increase in the distance to a primary school by 1 meter would result in a housing price reduction by about 0.082%. The distance to a junior high school estimation coefficient was -8.360e-5, having reached the 1% significance level. This suggests that increase in the distance to a junior high school by one 1 meter would result in a housing price reduction by about 0.083%.
Regarding difference-in-difference attributes, the estimation coefficient of the variable of when the luxury housing construction license was obtained was 0.202, having reached the 1% significance level. This means that housing prices were higher by about 20.2% after obtaining the luxury housing construction license. The estimation coefficient of the variable of luxury housing neighborhood was 0.101, having reached the 1% significance level. This suggests that housing prices in the luxury housing neighborhood were higher by 10.1%. The estimation value of the difference-in-difference was 0.106, having reached the 1% significance level. This suggests that the luxury housing (after obtaining the construction license) had positive spillover effects on neighborhood house prices by about 10.6%.
Model 3 categorizes samples in the luxury housing neighborhood  (the treatment group)  into three groups, including samples within the  distance of 100 meters, samples between the distances of  100 meters and 300 meters, and samples between  the distances of 300 meters  and 500 meters, to test whether the impact of luxury housing varies with increasing distance  from the luxury housing. The GLS  regression results are as shown in Model 3,  and its F statistic value was 765.499, having reached the 1% significance level,  whilewas 65.0%. The estimation  results of the coefficients of variables of the basic housing properties and  neighborhood environment attributes were  not significantly different from those of Model 2. 
Regarding the interactive items of difference-in-difference, the estimation coefficients of the samples of 100 meters, 100 meters to 300 meters and 300 meters to 500 meters after obtaining the construction license were 0.490, 0.182 and 0.047 respectively. This suggests that the spillover effects of luxury housing after obtaining the construction license will increase the housing prices in general. However, the effects will gradually decrease over greater distances from 49.0% to 18.2% to 4.7%. Moreover, the effect in the case of samples at distances from the luxury housing in the range from 300 meters to 500 meters did not reach the level of significance.
The focus of a DD study is (interaction term coefficient). However, to make the  estimation more efficient and avoid the possible selection error, covariates  can be added. The covariates are selected according to the hedonic model, and  the empirical results seem to be in line with prediction results.  
 According  to the difference-in-difference  attribute regression results, the time to obtain the luxury housing construction license, luxury housing neighborhood, and time  to obtain the luxury housing  construction license × luxury housing neighborhood had  significant and positive impacts on housing prices, as expected. The time to obtain the luxury housing construction license  had a positive and significant impact on housing prices. Its estimation coefficient was about 0.202, suggesting that housing  price after obtaining luxury housing  construction license were increased by about 20.2%. The luxury housing had a positive impact on neighborhood housing prices. Its  estimation coefficient was about 0.101, suggesting that the housing prices in the neighborhood of the luxury housing increased by 10.1%. The  interactive term of the time to obtain luxury housing construction license and luxury housing neighborhood had  a positive and significant impact on housing prices. The estimation coefficient was about 0.106, suggesting that the  difference in the time to obtain construction license and luxury housing neighborhood and non-luxury housing neighborhood  spatial difference was  approximately 10.6%. The results are in line with the findings by Bourassa et al. (2004 ), Kavetsos (2012 
) and Ooi and Le (2013 
). Newly built or attractive  buildings with positive effects on a neighborhood can improve that neighborhood’s environmental quality and comfort to  facilitate the increase in neighborhood  housing prices. The  luxury housing can significantly beautify the surrounding environment and  maintain tidiness, so that it can help improve the neighborhood’s environmental  quality. 
According to GLS estimation results, the difference-in-difference coefficients B1 ,    B2  ,  B3 and were obtained.  According to the descriptions of Hill et al. (2011 
) about difference-in-difference, changes in luxury housing after  obtaining the construction license, luxury housing neighborhood and non-luxury  housing neighborhood housing prices can be determined. Figure 1 suggests that the luxury housing  neighborhood (the treatment group) housing prices will be higher than those of  the non-luxury housing neighborhood (the control group). Moreover, regardless of construction  decisions, there was a common trend that housing prices were increased over time. If the two  increase at the same rate, after the construction decision, the neighborhood (the treatment  group) housing prices will increase more rapidly than the housing prices of the  non-luxury housing neighborhood (i.e., greater than the original trend). The interactive term  estimated by using the difference-in-difference method 
could  be used to calculate the housing price difference  before and after obtaining the construction license.  To get the difference  in the impact of luxury housing, we need to convert the estimation coefficient  by using log-linear  function type for computation to get more accurate results.  
The log-linear function estimated coefficients can roughly compute and illustrate the percentage of change in a dependent variable caused by  each unit of independent variable. The method is fast and  easy. To more accurately illustrate the regression coefficients estimated by  using the log-linear function, the regression  coefficients can be input intoBy multiplying the value  and the average housing price of the sample data, this paper computed the real change in housing  prices caused by each unit of change in an independent variable. The computation of the log-linear function is as shown in Table  4. The intercept, TIME  ,   TREAT   ,     TIME*TREAT  GLS estimated coefficients were  
 .
with the average sample housing price, we obtained 460.3, 312.7, 148.5 and 156.2, respectively. This suggests that the intercept is the starting price without the influence of any other variables. The basic housing price is about 4.603 million NTD. In the case of the control group, after obtaining the construction license, the housing prices increased by 3.127 million NTD. Housing prices in the neighborhood of the luxury housing before obtaining the construction license were higher by about 1.485 million NTD. The difference before and after getting the construction license and the luxury housing neighborhood and non-luxury housing neighborhood difference, that is, the difference-in-difference housing price, was about 1.562 million NTD.
Figure-1. difference-in-difference estimation results
Table-4. Log-liner function conversion
Note: the value in the brackets refers to the price of converted result percentage multiplied by sample average housing price measured by the unit of NTD (10, 000).
This study applied the difference-in-difference method by the time to obtain luxury housing constructio
 Kiel and McClain (1995 ), Dehring et al. (2007 
) and Ooi and Le (2013 
), Bourassa et al. (2004 
)  argued that attractive buildings can increase neighborhood housing prices.  However, empirically,  they only estimated the impact of buildings on neighborhood housing prices without  deducting the location difference caused by time trends and geographic space  from the estimation results, and  thus may have overestimated the impact of such buildings. The difference-in-difference method  applied in this study can explore the impacts of differences caused by the  occurrence of an event and by geographic space on housing prices. Through the  interactive variables of time and space -- that is, the interactive term of the  time to obtain the luxury housing construction  license and luxury housing  neighborhood -- this study was able to provide more accurate  estimation results. 
According to the empirical results of this study, the housing price difference caused by the time to obtain the construction license and distance to the luxury housing was about 1.56 million NTD, suggesting that obtaining a construction license has a real impact on luxury housing neighborhood housing prices. That is, the average housing price increases by about 1.56 million NTD after obtaining a construction license. This paper further categorized the treatment group samples into those within 100 meters, those between 100 meters and 300 meters and those between 300 meters and 500 meters for estimation. The results suggested that housing prices increase in inverse proportion to the distance from the luxury housing neighborhood.
Due to the limitation of data processing, this study only measured the nearest linear distance of a given house from the relevant public facilities without considering the real geographical environment (e.g., rivers and slopes) and urban road planning. If the real distances from the houses to the public facilities can be measured and the above geographic environment and urban roads can be considered in a follow-up study, then housing prices can be more accurately and realistically estimated.
| Funding: This study received no specific financial support. | 
| Competing Interests: The authors declare that they have no competing interests. | 
| Contributors/Acknowledgement: All authors contributed equally to the conception and design of the study. | 
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