House Prices at Different Stages of
the Buying/Selling Process
Presentation to the Ottawa Group Meeting 2011
in Wellington, New Zealand
Shimizu,C., K.Nishimura and T.Watanabe
May 5, 2011
1
Purpose of the paper
2
Key research question
Are house prices different depending on the
stages of the buying/selling process?
We address this question by comparing the distributions of prices
collected at different stages of the buying/selling process, including:
(1) initial asking prices listed on a magazine,
(2) asking prices at which an offer is made by a buyer,
(3) contract prices reported by realtors after mortgage approval,
(4) registry prices.
3
Data
4
Four prices from three datasets
Three datasets for the prices of condominiums traded in
Tokyo, 2005-2009:
Magazine dataset
This contains prices listed on “Housing Information Weekly” published
by the largest vendor of housing information
Realtor dataset
This is collected by an association of real estate agencies through the
Real Estate Information Network System (“REINS”)
Registry dataset
This is collected jointly by the Land Registry and the Ministry of Land,
Infrastructure, Transport and Tourism
Four prices:
P1 Initial asking prices from the magazine dataset
P2 Final asking prices from the magazine dataset
P3 Contract prices from the realtor dataset
P4 Registration prices from the registry dataset
5
Universe: N=360,243
P1,P2:Magazine dataset
N=155,347
N=26,496
N=14,890
N=7,551
Realtor dataset
P3 :N=122,547
N=22,613
Registry dataset
P4: N=58,949
6
Timeline of P1,P2,P3 and P4
Timing of events in real estate
transaction process
House placed on market
Real estate price information
Asking price
database
in
Magazine
(P1)
10 weeks
Offer made
Final asking price in
Magazine database
(P2)
Mortgage approved
5.5 weeks
Contracts exchanged
Completion of sale with
Land Registry or REINS
Transaction registered with
Land Registry
Transaction price in Realtor
database
(P3)
15.5 weeks
Transaction price survey
based on Land Registry
Transaction price in
Government database
(P4)
7
Price distributions
Figure 3: Price densities for P1, P2, P3, and P4
0.25
P1
P2
P3
P4
0.20
0.15
0.10
0.05
10.50
10.25
10.00
9.75
9.50
9.25
9.00
8.75
8.50
8.25
8.00
7.75
7.50
7.25
7.00
6.75
6.50
6.25
6.00
5.75
5.50
5.25
5.00
4.75
4.50
0.00
log P
8
Figure 4: Density functions for the
house attributes : Floor Space
0.30
0.25
P1&P2
0.20
P3
0.15
P4
0.10
0.05
250
240
230
220
210
200
190
180
170
160
150
140
130
120
110
100
90
80
70
60
50
40
30
20
10
0.00
square meters
9
Empirical method
10
Two methods for quality adjustment
1.
Intersection approach
• Using address information, we identify houses that are
commonly observed in two or three datasets. Then we look at
price distribution for the intersection sample.
• This idea is quite similar to the one adopted in the repeat sales
method.
2. Quantile hedonic approach
• We apply quantile hedonic regression to the raw data. Then we
use the estimated quantile coefficients and the distribution of
various house attributes to conduct quality adjustment.
• This method is proposed by Machado and Mata (2005), and
applied housing data by McMillen (2008)
11
Results1:Intersection Approach
12
Price distributions for the quality
adjusted data by the intersection
approach
Price distributions
for the raw data
0.25
0.25
P1 from the magazine dataset
P1 from the magazine dataset
P4 from the registry dataset
P4 from the registry dataset
0.20
0.20
0.15
0.15
0.10
0.10
0.05
0.05
log price
9.5
8.3
7.0
5.8
9.5
8.3
5.8
4.5
7.0
log price
4.5
0.00
0.00
13
Figure 7. Quantile-Quantile Plot
P1 vs P4
P3 vs P4
Raw
Data
Intersection
Data
14
Results2:Hedonic Approach
15
Quantile hedonic approach
θ
Qi ( p | z ) = z βi (θ )
θ
Qi ( p | z ) : θ-th quantile of
: θ ∈ (0,1)
Fi ( p | z )
βi (θ ) : the quantile regression coefficient
z : housing attributes
16
Quantile hedonic approach
Distance to the nearest station
-0.00002
-0.00004
0.02
0.05
0.08
0.11
0.14
0.17
0.2
0.23
0.26
0.29
0.32
0.35
0.38
0.41
0.44
0.47
0.5
0.53
0.56
0.59
0.62
0.65
0.68
0.71
0.74
0.77
0.8
0.83
0.86
0.89
0.92
0.95
0.98
0
P1
P2
-0.00006
-0.00008
High price
P3
P4
OLS
-0.0001
-0.00012
-0.00014
-0.00016
-0.00018
-0.0002
17
0.02
0.05
0.08
0.11
0.14
0.17
0.2
0.23
0.26
0.29
0.32
0.35
0.38
0.41
0.44
0.47
0.5
0.53
0.56
0.59
0.62
0.65
0.68
0.71
0.74
0.77
0.8
0.83
0.86
0.89
0.92
0.95
0.98
8
7.4
7.2
7
P2
6.8
6.6
-0.03
-0.035
P4
6
0
-0.01
-0.02
-0.025
P1
P3
P4
0.02
0.05
0.08
0.11
0.14
0.17
0.2
0.23
0.26
0.29
0.32
0.35
0.38
0.41
0.44
0.47
0.5
0.53
0.56
0.59
0.62
0.65
0.68
0.71
0.74
0.77
0.8
0.83
0.86
0.89
0.92
0.95
0.98
Intercept
Age of building
-0.00002
-0.00004
-0.00006
-0.00008
0.02
0.05
0.08
0.11
0.14
0.17
0.2
0.23
0.26
0.29
0.32
0.35
0.38
0.41
0.44
0.47
0.5
0.53
0.56
0.59
0.62
0.65
0.68
0.71
0.74
0.77
0.8
0.83
0.86
0.89
0.92
0.95
0.98
0.02
0.05
0.08
0.11
0.14
0.17
0.2
0.23
0.26
0.29
0.32
0.35
0.38
0.41
0.44
0.47
0.5
0.53
0.56
0.59
0.62
0.65
0.68
0.71
0.74
0.77
0.8
0.83
0.86
0.89
0.92
0.95
0.98
Quantile hedonic approach: βˆi (b)
0.02
Floor space
7.8
7.6
0.018
0.016
P1
0.014
P1
0.012
P2
P3
0.01
P3
P4
6.4
6.2
0.008
0.006
0
Distance to the nearest station
-0.005
P1
P2
P3
-0.015
P4
-0.0001
-0.00012
-0.00014
P2
-0.00016
-0.00018
-0.0002
18
Differences between price
distributions
Fi ( p | z ) → p = z βˆi (θ )
P1 : F1 ( p | z ) → p1 = z1 βˆ1 (θ )
P4 : F4 ( p | z ) → p4 = z4 βˆ4 (θ )
∞ ˆ
ˆ
F1 ( p ) ≡ ∫ −∞F1 ( p | z )u1 ( z ) dz1
Fˆ ( p ) ≡ ∫ ∞ Fˆ ( p | z )u ( z ) dz
4
−∞ 4
1
19
Decompose of distribution
• We calculate the distribution of P:
p = z ・βˆ ( b ) ,
11
1b
1
ˆ (b ) ,
β
p44 = z4・
b
4
ˆ (b )
p14 = z1・
β
b
4
(a)Coefficient differences:
p11 − p14 ,
(b)Variables differences:
p44 − p14 ,
↓
(a)+(b):Total differences:
p11 − p44 ,
20
(a) Coefficient differences
(P1)
ˆ ( b ) −・z ・βˆ ( b )
β
Coefficient differences: z1・
b
1
1b
4
Draw with
replacement :
50,000 times
βˆ1 (θ )
βˆ4 (θ )
z1
z4
21
Variables differences
(P4)
ˆ ( b ) −・z ・βˆ ( b )
β
Variables differences: z4・
b
4
1b
4
Draw with
replacement :
50,000 times
βˆ1 (θ )
βˆ4 (θ )
z1
z4
22
Total differences
(P1)
(P4)
ˆ ( b ) −・z ・βˆ ( b )
β
Total differences: z1・
b
1
4b
4
Draw with
replacement :
50,000 times
βˆ1 (θ )
βˆ4 (θ )
z1
z4
23
Figure 10: Decomposition of density
differences: P1 vs. P4
0.25
0.20
Total difference
0.15
Variables
0.10
0.05
Coefficients
-0.05
4.7
4.9
5.1
5.2
5.4
5.6
5.8
6.0
6.1
6.3
6.5
6.7
6.9
7.0
7.2
7.4
7.6
7.8
7.9
8.1
8.3
8.5
8.7
8.8
9.0
9.2
9.4
9.6
9.7
9.9
10.1
10.3
10.5
10.6
10.8
11.0
11.2
11.4
11.5
0.00
-0.10
-0.15
-0.20
24
Figure 10: Decomposition of density
differences: P2 vs. P4
0.25
0.20
0.15
0.10
Total difference
Variables
Coefficients
0.05
-0.05
4.7
4.9
5.1
5.2
5.4
5.6
5.8
6.0
6.1
6.3
6.5
6.7
6.9
7.0
7.2
7.4
7.6
7.8
7.9
8.1
8.3
8.5
8.7
8.8
9.0
9.2
9.4
9.6
9.7
9.9
10.1
10.3
10.5
10.6
10.8
11.0
11.2
11.4
11.5
0.00
-0.10
-0.15
-0.20
25
Figure 10: Decomposition of density
differences: P3 vs. P4
0.25
0.20
0.15
0.10
Total difference
Variables
Coefficients
0.05
-0.05
4.7
4.9
5.1
5.2
5.4
5.6
5.8
6.0
6.1
6.3
6.5
6.7
6.9
7.0
7.2
7.4
7.6
7.8
7.9
8.1
8.3
8.5
8.7
8.8
9.0
9.2
9.4
9.6
9.7
9.9
10.1
10.3
10.5
10.6
10.8
11.0
11.2
11.4
11.5
0.00
-0.10
-0.15
-0.20
26
Figure 7c. Quantile-Quantile Plot for Quality Adjusted Prices
P1 vs P4
P2 vs P4
P3 vs P4
27
Main findings
1. There exist substantial differences between the four
distributions of prices, as well as between the distributions of
house attributes.
2. However, once quality differences are eliminated, there
remain only small differences between the price distributions.
3. This suggests that prices collected at different stages of the
house buying/selling process are still comparable, and
therefore useful in constructing a house price index, as long as
they are quality adjusted in an appropriate way.
28
Additional question
An important question to be asked is whether
the deviations differ depending on whether the
housing market is in a downturn or in an
upturn ?
We address this question :
(1) The time series for the price ratio between P1 and P2,
(2) The time series for the interval between the time when P1 is
observed and the time when P2 is observed.
29
200910
200907
200904
200901
200810
200807
200804
200801
200710
200707
200704
200701
200610
200607
200604
0.20
200601
200510
200507
Hedonic Indices of P1 and P2
0.25
Hedonic index for P1
Hedonic index for P2
0.15
0.10
0.05
0.00
30
200910
200907
200904
200901
200810
200807
200804
200801
200710
200707
200704
200701
200610
200607
0.955
200604
200601
200510
200507
Price ratio
Price Ratio between P1 and P2
0.995
0.990
0.985
0.980
0.975
0.970
0.965
0.960
Price ratio (Left scale)
0.950
31
C1
35
0.990
40
0.985
45
0.980
50
0.975
55
0.970
60
0.965
65
0.960
Price ratio (Left scale)
70
0.955
Interval (Right scale, Inverted)
75
200910
200907
200904
200901
200810
200807
200804
200801
200710
200707
200704
200701
200610
200607
200604
200601
80
200510
0.950
Interval [days]
0.995
200507
Price ratio
Interval between P1 and P2
32
Slide 32
C1
ChihiroSHIMIZU, 30/04/2011
Additional findings
1. We saw that the hedonic index for P1 declined by more than
ten percent during the period between March 2008 and April
2009.
2. The price ratio started to decline in December 2007, three
months earlier than the hedonic index for P1, and bottomed
out in February 2009, two months earlier than the hedonic
index for P1.
3. The changes in the interval tended to precede changes in the
hedonic indices; specifically, the interval peaked in December
2008, four months before than the hedonic index for P1 hit
bottom.
33
P4
P3
P2
P1
Source: National Statistician’s Review of House Price Statistics,UK2010
34
Figure 2: Intervals between events in
the house buying/selling process
0.6000
Time lag between P1 and P2
Time lag between P1 and P3
0.5000
Time lag between P1 and P4
0.4000
0.3000
0.2000
0.1000
0.0000
0
50
100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000
days
35
Timeline of P1,P2,P3 and P4
Timing of events in real estate
transaction process
House placed on market
Real estate price information
Asking price
database
in
Magazine
(P1)
10 weeks
Offer made
Final asking price in
Magazine database
(P2)
Mortgage approved
5.5 weeks
Contracts exchanged
Completion of sale with
Land Registry or REINS
Transaction registered with
Land Registry
Transaction price in Realtor
database
(P3)
15.5 weeks
Transaction price survey
based on Land Registry
Transaction price in
Government database
(P4)
36
Figure 5: Densities for relative prices
37
Figure 4: Density functions for the
house attributes: Building Age
0.25
0.20
P1&P2
0.15
P3
0.10
P4
0.05
65
60
55
50
45
40
35
30
25
20
15
10
5
0
0.00
years
38
Quality adjustment
F1 ( p ) =
∞
∫ −∞
F1 ( p | z ) u1 ( z ) dz
F4 ( p ) = ∫ ∞−∞ F4 ( p | z ) u1 ( z ) dz
↓
[ F1 ( p | z ) − F4 ( p | z )] u1 ( z )dz
∞
+ ∫ −∞F4 ( p | z ) [u1 ( z ) − u4 ( z ) ] dz
F1 ( p ) − F4 ( p ) =
∞
∫ −∞
39
Kolmogorov-Smirnov test
D -statistic
p -value
Number of observations
Raw data
P 1 vs. P 4
0.2016
0.000
155,347 for P 1 and 58,949 for P 4
P 2 vs. P 4
0.1885
0.000
155,347 for P 2 and 58,949 for P 4
P 3 vs. P 4
0.0432
0.000
122,547 for P 3 and 58,949 for P 4
Quality adjusted by the intersection approach
P 1 vs. P 4
0.0584
0.000
14,890 for P 1 and 14,890 for P 4
P 2 vs. P 4
0.0441
0.000
14,890 for P 2 and 14,890 for P 4
P 3 vs. P 4
0.0303
0.000
22,613 for P 3 and 22,613 for P 4
40
Table 4: Goodness-of-Fit Tests
D-
p -value
Number of observations
Raw data
P 1 vs. P 4
P 2 vs. P 4
0.2016
0.000
155,347 for P 1 and
0.1885
0.000
155,347 for P 2 and
122,547 for P 3 and
0.0432
0.000
P 3 vs. P 4
Quality adjusted by the intersection approach
14,890 for P 1 and 14,890
0.0584
0.000
P 1 vs. P 4
P 2 vs. P 4
P 3 vs. P 4
0.0441
0.000
14,890 for P 2 and 14,890
0.0303
0.000
26,496 for P 3 and 26,496
Quality adjusted by the quantile hedonic approach
50,000 for P 1 and 50,000
0.0676
0.000
P 1 vs. P 4
P 2 vs. P 4
P 3 vs. P 4
0.0535
0.000
50,000 for P 2 and 50,000
0.0199
0.000
50,000 for P 3 and 50,000
41