# RECORD 09caaf09cd085f29d8f22c8f28dd86b492ec121d
# TITLE: ESTABLISHING DYNAMIC IMPACT FUNCTION FOR HOUSE PRICING BASED ON SURRENDING MULTI-ATTRIBUTES: EVIDENCE FROM TAIPEI CITY, TAIWAN
# YEAR: 2020.0  VENUE: nan  DOI: 10.3846/ijspm.2020.11096
# AUTHORS: Jieh-Haur Chen; Li-Ren Yang; V. T. Azzizi; Eric-Liluan Chu; Hsi-Hsien Wei
# PAGES: 11  CANDIDATE TABLE PAGES (1-based): [6, 7, 9]
# ABSTRACT: The objective of the research is aimed for a solution that is to establish the dynamic impact function of surrounding multi-attribute for house pricing. It is also able to measure the ripple effect and allows the hedonic parameter estimates to vary from point-to-point. A comprehensive literature review is carried out to obtain an adequate theoretical basis for the corresponding hypothesis and concepts. The proposed dynamic impact function for multiattributes is then constructed based on the characteristics of surrounding facilities. Adopting the convenience sampling criteria of 95% confidence level on the data sampling and 10% limit of error in a 5−95% proportion, we collect the empirical data of 39 yearly house sales in the investigated urban areas of Taipei city focusing on housing prices and then utilize them for evaluating and adjusting the function. The actual house price and that of proposed function affected by Mass Rapid Transit (MRT) stations are analysed, resulting in the correlation coefficient at 0.946 (single attribute) and 0.944 (multi-attribute), respectively. The findings support that proposed function can highly represent the house pricing pattern and be an accurate tool for appraisers.


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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.
ESTABLISHING DYNAMIC IMPACT FUNCTION FOR HOUSE PRICING 
BASED ON SURRENDING MULTI-ATTRIBUTES:  
EVIDENCE FROM TAIPEI CITY, TAIWAN
Jieh-Haur CHEN1,*, Li-Ren YANG2, Vidya Trisandin AZZIZI1, Eric CHU1, Hsi-Hsien WEI3
1 Department of Civil Engineering, National Central University, Jhongli, Taiwan
2 Department of Business Administration, Tamkang University, Tamsui, Taiwan
3 Department of Building and Real Estate, The Hong Kong Polytechnic University, Hong Kong, PR China
Received 10 September 2018; accepted 05 August 2019
Abstract. The objective of the research is aimed for a solution that is to establish the dynamic impact function of surround-
ing multi-attribute for house pricing. It is also able to measure the ripple effect and allows the hedonic parameter estimates 
to vary from point-to-point. A comprehensive literature review is carried out to obtain an adequate theoretical basis for the 
corresponding hypothesis and concepts. The proposed dynamic impact function for multi- attributes is then constructed 
based on the characteristics of surrounding facilities. Adopting the convenience sampling criteria of 95% confidence level 
on the data sampling and 10% limit of error in a 5−95% proportion, we collect the empirical data of 39 yearly house sales 
in the investigated urban areas of Taipei city focusing on housing prices and then utilize them for evaluating and adjusting 
the function. The actual house price and that of proposed function affected by Mass Rapid Transit (MRT) stations are ana-
lysed, resulting in the correlation coefficient at 0.946 (single attribute) and 0.944 (multi-attribute), respectively. The find-
ings support that proposed function can highly represent the house pricing pattern and be an accurate tool for appraisers.
Keywords: house pricing theory, impact function, multi-attribute, financial engineering, property management.
Introduction
Over the last few years, the Taiwan government has ap-
plied a new policy regarding property tax within the real 
estate domain which has had a considerable impact on 
the Taiwan real estate market. The possible turnover index 
for the period from 2003 to 2005 had dropped from its 
original peak of 136.77 to 121.38. Furthermore, because 
of this property tax, some construction companies are re-
luctant to build new properties (Bahmani-Oskooee & Wu, 
2018). Even the ones that have already started a project 
may be reluctant to complete it, because after completion, 
the contractor has to bear a huge tax burden even prior 
selling it. These circumstances have caused many investors 
to withdraw from the real estate market. The proportion 
of customers who buy their own homes or their own real 
estate has increased. The Ministry of the Interior’s real es-
tate platform has identified the following trend: the rate 
for residential demand for the first half year was 43%. 
The change of housing demand accounted for 42%, with 
an increase of 4.7% in the second half of the year. This 
was the highest within the last five years, previously the 
rate had never gone above 4% (Bahmani-Oskooee & Wu, 
2018). Consumers choosing self-built real estate take into 
account various factors such as the quality of housing, the 
surroundings, parking, traffic convenience, and so on. De-
spite the fact that accurate appraisals and consideration of 
impact factors have helped to improve consumer aware-
ness of real estate prices, it is still difficult for them to 
assess the impact of different factors on real estate prices. 
There has been little on the accurate assessment of the 
impact of real estate impact factors, therefore consumers 
do not have any basis of reference to follow.
The rational and effective allocation of information as 
well as resource integration has only been used by real 
estate producers for determination of prices. Consumers 
and government departments also need to pursue this 
goal. Rosen introduced the Hedonic price theory in 1974, 
which became the main method to solve the pricing prob-
lem with a wide range of applications. In addition to its 
application in real estate analysis, it is also used in agricul-
tural land use analysis, agricultural marketing, video game 
marketing, industrial product marketing, environmental 
International Journal of Strategic Property Management
ISSN: 1648-715X / eISSN: 1648-9179
2020 Volume 24 Issue 2: 119–129
https://doi.org/10.3846/ijspm.2020.11096
*Corresponding author. E-mail: jhchen@ncu.edu.tw


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124
J.-H. Chen et al. Establishing dynamic impact function for house pricing based on surrending...
The value of α is always positive, because in house 
price convergence, the value of the house price is always 
greater than zero.
4. Implementation and discussion
The research has provided a solution that is to establish the 
dynamic impact function of surrounding multi-attribute for 
house pricing. It is also able to measure the ripple effect and 
allows the hedonic parameter estimates to vary from point-
to-point. Thus, there are two implementations to evaluate 
the proposed function f(x). The first one is to evaluate the 
proposed function using a single main facility that affects 
house prices. The other one is for multi-attributes (main 
facilities). The following conditions must be met: (1) there 
must be no other major impact factor affecting housing 
prices in the MRT area; (2) the main impact on housing 
prices in the area is proximity to MRT facilities; (3) there 
are no other MRT stations within a investigated range, so it 
is clear which MRT station acts as the main facility that af-
fects house prices. After determining the area, the real estate 
locations are chosen using the Ministry of Interior real estate 
network transaction price inquiry service. The real estate is 
selected according to the following conditions, being similar 
in: (1) age; (2) size; (3) quality; and (4) terms of the reputa-
tion of the construction company that develops the real es-
tate. After the selection of real estate cases around the MRT 
station, information regarding location of the transaction, 
real estate area, transaction price, price per unit, room and 
housekeeping patterns, as well as floor height is obtained 
using the Ministry of Interior real estate transaction data 
base. Other real estate related information is obtained using 
Google earth, such as date, house age, the time it takes for 
the house to be sold, access to parking, number of floors, 
and real estate category. Analysis of position, distance from 
the MRT station, as well as status quo is carried out using 
GIS and survey data. For the feature price impact function 
affected by a single and multiple factors (numbers of MRT 
stations), we conduct 4 case studies: Beitou MRT station 
(single factor), Jingmei MRT (single factor), Houshanpi-
Kunyang MRT (2 factors), Dongmen-Zhongxiao-Xinsheng 
MRT (3 factors) stations in the investigated area based on 
convenient sampling. The prices of total 138 housing units 
sold in 2009 around investigated MRT stations are selected, 
which satisfies 95% confidence level on the data sampling 
and 5% limit of error in a 10–90% proportion (Chen & Hsu, 
2008; Chen, Yang, Su, & Lin, 2010). The observations cover 
house sold data in the investigated area in a limited time pe-
riod (May, 2009) in 2009. This can minimize the impact by 
force majeure such domestic macro-economy, global trade 
volatility, and major disasters. The reason to use past data is 
due to the data/case sensitivity themselves. It may influence 
house transactions/price if revealing latest information. For 
Case Study 1 and 2, they can be inferred as the significant 
factor because there are no other factors that affect the price 
of housing in the surrounding area. Beitou MRT station is 
located in the Taipei north region approximately 6 km away 
from downtown center and Jingmei MRT station is in the 
south side of the city, also approximately 6 km away from 
downtown center. For Case Study 3 and 4, Houshanpi-Ku-
nyang MRT stations (2 factors) are approximate 1 km away 
from the main shopping district of Taipei and Dongmen-
Zhongxiao-Xinsheng MRT stations (3 factors) are right at 
the most prosperous center of the city.
The chosen housing units sold from 3 to 7 years old are 
all located in the investigated regions. None of the chosen 
apartment buildings had first-floor storefronts, and the se-
lected units are located on the 2nd to 10th floors. Each unit 
is between 30 and 60 pings (100 to 200 meter2) in area. It 
can be seen that the theoretical house price curve is similar 
to the actual house price curve, and shows the same trend. 
The correlation between the two lines is analyzed using 
the distance between the actual housing unit and the MRT 
station. The CORREL (array1, array2) function in Micro-
soft Excel allows users to calculate correlation coefficient r 
by inserting the real price data and estimated price by the 
proposed function. The value of the correlation is between 
1 and −1. The closer to 1 the greater the correlation, the 
higher the degree of similarity between the two curves, im-
plying that the proposed function can be applied in prac-
tice. By inserting the dynamic impact function (Equation 
15), the actual house price and the theoretical house price 
are analysed using the CORREL function in Microsoft Ex-
cel. Tables 1−3 show that all of their correlation coefficients 
r > 0.9 (0.946, 0.981, and 0.944 respectively).
Table 1. The actual distance and case prices affected by a single 
impact factor (Beitou MRT station, Taipei)
Observation
Distance 
(m)
Actual  
house price  
(million NTD/m2)
Predicted house 
price (million 
NTD/m2)
1
70
14.92
15.11
2
110
16.12
16.26
3
145
16.64
16.64
4
196
16.61
16.64
5
234
15.97
15.23
6
300
15.40
13.94
7
314
14.24
13.77
8
314
14.15
13.77
9
336
13.65
13.55
10
364
13.50
13.32
11
400
13.18
13.10
12
445
12.61
12.88
13
454
12.49
12.85
14
513
12.32
12.65
15
568
12.62
12.51
16
653
12.57
12.35
17
679
11.77
12.31
18
694
10.85
12.29
Correlation coefficient r = 0.946


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International Journal of Strategic Property Management, 2020, 24(2): 119–129
125
Table 2. The actual distance and case prices affected by a single 
impact factor (Jingmei MRT station, Taipei)
Observation
Distance 
from 
Jingmei 
MRT 
station 
(m)
Actual  
house price 
(million NTD/m2)
Predicted house 
price (million 
NTD/m2)
1
191
12.30
12.30
2
203
12.22
12.22
3
247
11.93
11.93
4
270
11.31
9.95
5
272
11.42
11.31
6
274
11.06
11.42
7
301
9.83
8.85
8
307
9.45
9.45
9
311
8.92
8.92
10
316
8.89
8.62
11
327
8.76
8.49
12
346
8.75
8.49
13
351
8.74
8.48
14
355
8.65
8.39
15
358
8.59
8.16
16
375
8.26
7.85
17
398
8.24
7.83
18
403
8.06
7.66
19
425
8.06
7.66
20
511
8.02
7.62
21
528
7.92
7.53
22
550
7.90
7.51
23
554
7.79
7.79
24
557
7.77
7.77
25
558
7.76
7.76
26
559
7.74
7.74
27
561
7.69
7.69
28
570
7.64
7.64
29
588
7.62
7.62
30
593
7.54
7.54
31
604
7.47
7.47
32
633
7.46
7.46
33
723
7.39
7.39
34
745
7.38
7.38
35
813
7.35
7.35
36
830
7.30
7.30
37
834
7.26
7.26
38
840
7.24
7.24
39
847
7.23
7.23
40
849
7.22
7.22
Correlation coefficient r = 0.981
Table 3. Actual distance and case prices affected by multiple 
impact factors (2 factors)
Observation
Distance 
from 
Houshanpi 
MRT 
station 
(m)
Distance 
from 
Kunyang 
MRT 
station 
(m)
Actual 
house 
price 
($million 
NTD/m2)
Predicted 
house 
price 
($million 
NTD/m2)
1
1
1399
12.21
12.25
2
28
1373
12.73
12.72
3
66
1334
13.08
13.52
4
79
1321
13.79
13.79
5
248
1153
14.50
14.49
6
255
1145
14.46
14.49
7
263
1137
13.90
14.30
8
325
1075
13.23
13.27
9
431
969
12.70
12.59
10
431
969
12.64
12.59
11
525
875
11.33
12.31
12
665
735
11.57
11.50
13
831
569
14.44
13.67
14
861
539
14.39
14.05
15
900
500
14.82
14.82
16
965
435
14.67
14.82
17
970
430
13.69
14.82
18
1003
398
14.30
14.82
19
1188
213
14.12
14.54
20
1241
159
14.14
14.37
21
1395
5
13.28
13.75
Correlation coefficient r = 0.944
Figures 2−4 illustrate the fitting between actual and 
predicting house sold price. For Case study 1, the pres-
ence of a park (Chengde Park) increases the quality of 
life in the surrounding area, making house prices higher 
than the theoretical curve, as indicated by results obtained 
after a field visit. It can be seen that the theoretical house 
price curve is similar to the actual house price curve, 
and shows the same trend. Accordingly, the findings in-
dicate that it is the facility characteristics which affect 
the level of housing prices. It can be seen that there is 
a convergence of housing prices in the same area. For 3 
or more attributes, assuming that there are N MRT sta-
tions affecting the same area, the dynamic function gives 
( )
( )
( )
( )
( )
( )
( )
( )
1
2
3
1
2
3
,
,
,
,
N
N
f
x
f
x
f
x
f
x f
x
f
x
f
x
f
x
…
…
. 
Thus, N-1 should be summed and deducted from α. The 
aggregate is as formulated follows:
( )
(
)
1
N
i
i
f
x
N

−
−
α


∑
.	
(16)


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126
J.-H. Chen et al. Establishing dynamic impact function for house pricing based on surrending...
Actual price 
Theoretical 
house price 
Price/ping 
Price (in 
10.000 
NTD) 
Distance from MRT station 
60.00
50.00
40.00
30.00
20.00
10.00
0.00
0 
200 
400 
600 
800   (m)
Figure 2. Comparison between theoretical and actual house price curve influenced by single 
factor (Beitou MRT station, Taipei)
Figure 3. Comparison between theoretical and actual house price curve influenced by single 
factor (Jingmei MRT station, Taipei)
0 
500 
1000 
1500   (m)
Price/ping 
Price (in 
10.000 
NTD) 
Distance from MRT station 
Actual price 
Theoretical 
house price 
60.00
50.00
40.00
30.00
20.00
10.00
0.00
Figure 4. Comparison between theoretical and actual house price curve influenced by 
multiple factors (2 factors)


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International Journal of Strategic Property Management, 2020, 24(2): 119–129
127
For example, if there are three MRT stations in the 
investigation area, 3^N types of function combination 
should be taken into consideration since each MRT sta-
tion has a combination of three dynamic functions. As a 
result, for Case Study 4 with 3 attributes (3 MRT stations), 
the resulting correlation coefficient is r = 0.912 still highly 
matching to the real housing price as shown in Table 4 
and Figure 5.
Figure 5 exhibits several peaks for the house price due 
to more attributes that can influence house price such as 
shopping malls, parks, stadiums, and schools. The dy-
namic impact function of surrounding multi-attributes for 
house pricing is then evaluated and ready for both further 
academic study and practical use.
Conclusions
This is an academic study focused on the construction of a 
dynamic impact function of surrounding multi-attributes 
for house pricing. This paper discusses not only real estate 
characteristics regarding distance effects but practical ap-
plications for improving appraisal accuracy. The analysis 
from the empirical implementation is carried out in order 
Table 4. Actual distance and case prices affected by multiple impact factors (3 factors)
Observation (59 in total)
Shortest distance to 
the closest MRT (m)
Longest distance to 
the farthest MRT 
(m)
Actual house price 
($million NTD/m2)
Predicted house 
price ($million 
NTD/m2)
1 (Shortest distance)
62
907
14.62
14.62
52 (Longest distance)
751
1073
12.72
11.44
15 (Highest actual price)
211
847
15.76
14.97
20 (Highest predicted price)
321
866
15.75
15.75
57 (Lowest actual price)
368
745
10.40
10.40
6 (Lowest predicted price)
141
901
10.65
10.33
Average
391
818
13.10
12.92
Standard Deviation
202
245
1.31
1.37
Correlation coefficient r = 0.912
to test its impact on real estate pricing, to examine the real 
estate impact curve interpretation ability, and finally to 
apply the results to verify accuracy for the function. The 
implementation using empirical data is one of the contri-
butions demonstrating the feasibility of the proposed func-
tion. In addition, the function is verified by empirical cases 
and the results can enhance appraisal accuracy, real estate 
market development, and strategies in the future. From the 
findings of correlation coefficient r = 0.944 and 0.946 for a 
single and multi-attributes, respectively, we can convey that 
the proposed function is an effective method to express 
(1) the ripple effects by multi-attributes to the target house 
price, (2) a dynamic distance pattern to the house price. 
It, thus, gives appraisers an accurate model for estimating 
house prices. This study differs from the previous studies 
in that the relationship between the proximity to the facil-
ity and the real estate price is presented in the form of a 
mathematical function with high accuracy. A thorough un-
derstanding of real estate appraisal and related knowledge 
can help across the field. As a result, the implementation of 
the proposed model can be used to establish different vari-
ables such as distance factors and proximity to “YIMBY” 
facilities in the field of selected location.
Figure 5. Comparison between theoretical and actual house price curve influenced 
by multiple factors (3 factors)


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128
J.-H. Chen et al. Establishing dynamic impact function for house pricing based on surrending...
The findings explain real estate price well in a math-
ematical way based on distance; however, the model may 
be not applicable when other factors are out of current 
consideration or assumptions such as economic impact, 
political impact, force majeure, and long-run period. For 
example, economic status may be changed dramatically in 
a developing country. Political or unforeseen impact may 
create temporarily deviation in the investigated region. 
Any period longer than one year may also cause price 
escalation/de-escalation due to inflation/disinflation. The 
follow-up study is encouraged to deal with time integrated 
with macroeconomic issues that may lead practitioners to 
a different level of dynamic prediction model for real es-
tate pricing.
Acknowledgements
This work was partly supported by the Ministry of Sci-
ence and Technology (MOST), Taiwan, for promoting 
academic excellent of universities under grant numbers 
of MOST-106-2221-E-008-020-MY2.
Disclosure statement
All authors do not have any competing financial, profes-
sional, or personal interests from other parties.
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