Hedonisk prismodell
Föreläsning Lund, 21 februari 2013
Mats Wilhelmsson
Centrum för bank och finans (KTH)
Institutet för bostadsforskning (Uppsala universitet)
1
21 februari 2013

Förmiddag


Föreläsning två artiklar
Eftermiddag
Presentation av fem artiklar
 Två grupper

2
(1) Varför använda sig av
hedonisk metodik?
Värdera kostnader och nyttigheter
 Alla varor och nyttigheter har inte ett
(explicit) pris. Vi måste skatta ett
(implicit) pris
 Två metoder


”revealed preference” metod
• fastighetsmarknaden

”stated preference” metod
• frågeformulär
3
(2) Varför använda sig av
hedonisk metodik?
Som värderingsmodell
 Vi önskar ta fram ett förväntat pris på
en fastighet mha historisk
prisinformation.
4
(3) Varför använda sig av
hedonisk metodik?

Skatta prisutvecklingen på
bostadsmarknaden mha historisk
prisinformation
www.valueguard.se
5
6
Gemensamt
Regressionsanalys
 Kontrollera för att fastigheter

ser olika ut
 ligger på olika platser
 har sålts vid olika tidpunkter

7
Prisvariation i rummet



8
Varför varierar fastighetspriser i rummet?
 Dvs. hur kan vi förklara priset om vi använder oss av
tvärsnittsdata?
Egenskaper
 Fastighetsknutna
• Storlek, kvalitet, ålder
 Områdesknutna (läget, läget, läget)
• Positiva och negativa externa effekter
• Förekomst av kollektiva varor
• Segmenterad marknad
Relationen mellan fastighetens pris och fastighetens
egenskaper skattas mha den sk hedoniska
regressionen.
Den hedoniska regressionen



Den hedoniska regressionsmodellen är
baserad på den hedoniska värdemodellen
där vi antar att fastighetens pris är en
funktion av fastighetens egenskaper.
Den hedoniska regressionen kontrollerar för
skillnader i egenskaper mellan fastigheter
genom att sätta ett värde på dessa
skillnader.
Dvs. vi skattar implicita (hedoniska) priser
på egenskaperna.

9
Haas (1922), Court (1937) och Rosen (1974)
Den hedoniska
regressionsmodellen
Price P(Z )      1F  2O  3T  

Egenskaper(Z)
Fastighetsknutna(F)
 Områdesknutna (O)
 Tidsbundna (T)

10
Den hedoniska teorin
max u(y,z i )
s.t. I  Py y  P( zi )
FOC
u zi MU zi
P
 p zi 

 i
zi
u y MU y
Skattade parametrar (koefficienter) i den hedoniska ekvationen är
lika med den marginella betalningsviljan , dvs. de hedoniska
priserna är lika med hur mycket vi är villiga att offra av andra
varor för 11
att få egenskaperna.
Den hedoniska teorin


Första steget: estimera P(Z)
Andra steget: estimera Zi  g ( Pz , I ,...)
i
Price

Det andra steget ger oss


Egenpriselasticitet
Inkomstelasticitet
z
12
När är den använd?

Värdering/fastighetstaxering

Ersättning

Skatta betalningsviljan på egenskaper

Områdesegenskaper
• Golfbanor, högspänningsledningar, sjöutsikt,
detaljplaner, närhet till vägar (buller) etc

Fastighetsegenskaper
• Storlek, kvalitet, antal rum

13
Tiden
• Indexkonstruktion
Artikel 1:
“The Impact of Traffic Noise on the
Values of Single-family Houses”





14
Buller är något man är tar hänsyn till i planering av
bostäder och infrastruktur.
Buller är ett av de miljöproblem som är högst rankat i
samhället.
Trafik är den vanligaste källan till buller.
Nästan 1,6 miljoner människor i Sverige är påverkade
av buller i sin hem. Knappt 20% av dessa bor i
bostäder där bullernivån är mer än 65 dBA.
“The objective of the paper is to provide an empirical
analysis of the impact traffic noise have on the values
of single-family houses.”
Buller och störning

















15
0 decibel gränsen för vad ett friskt öra kan uppfatta
10 decibel mänsklig andning på 3 meters avstånd
20 decibel viskningar
50 decibel kraftigt regn
60 decibel normalt samtal
70 decibel vältrafikerad gata på 5 meters avstånd
75 decibel tvättmaskin
80 decibel dammsugare på 1 meters avstånd
85 decibel stadstrafik
90 decibel hårtork, gräsklippare
100 decibel traktor, slagborr på 2 meters avstånd
110 decibel konsert, motorsåg på 1 meters avstånd
120 decibel ambulans, knall från åska
130 decibel gränsen för smärta
140 decibel fyrverkeri, gevärsskott på 1 meters avstånd
150 decibel jetmotor på 30 meters avstånd, kan orsaka fysisk skada
200 decibel människor kan dö
Design av studien







16
Under antagandet att negativa externa effekter
kapitaliseras i fastighetspriserna så har jag använt en
hedonisk modell.
Mikrostudie (area 300 x 300 meter)
Förort till Stockholm (Bromma)
1986-1995
Närhet till en större väg (Bergslagsvägen)
Ungefär 300 fastigheter har sålts under perioden av
totalt 1000 (vissa har sålts flera gånger)
 (30% omsättning på 10 år)
Resultat: Närhet till genomfartsvägen kapitaliseras i
fastighetspriserna upp till 30 %.
300 meter
1000 meter
17
NA
SA
Oberoende variabler
18
Bullervariabeln
valuation
positive effects
net valuation
100
0
meter
1
300
other negative effects
traffic noise
-200
19
Ekonometrisk analys

Modelspecifikation
Price = b0 + b1. living area + b2. lot size + b3.
age + b4. quality + b5. corner + b6. park + b7.
FPI + b8. HV + b9. BBV + b10. VV + b11. SA +
b12. SAliving area + b13. SAquality + b14.
SAnoise + b15. SAlot size + b16. noise + b17.
Noiseexp + ei

20
Log-linjär specification
Resultat
21
Resultat
SEK
1200000
1000000
800000
600000
400000
200000
0
dBA
50
52
22
54
56
58
60
62
64
66
68
70
72
74
76
78
80
Sammanfattning




23
Bullereffekten är stor.
Statistiskt och ekonomiskt signifikant
Den empiriska analysen tyder på att i
genomsnitt så minskar värdet på en
fastighet med 0,6% per decibel eller med
hela 30% om vi jämför en fastighet som är
utsatt för buller med en som inte är det.
Den samhällsekonomisk nyttan att slippa
buller värdera till 8000 kronor per person
och år vid ljudnivåer över 72 dBA.
Artikel 2:
The Impact of Crime on Apartment
Prices: Evidence of Stockholm,
Sweden
Vania Ceccato and Mats Wilhelmsson
Royal Institute of Technology
Stockholm, Sweden
24
Crime rates, Stockholm
25000
4500
Total crime
4000
Crime per 100.000 inhabitants
20000
3500
Vandalism
3000
15000
2500
Thefts
2000
10000
1500
Violent crime
1000
Robbery
Residential burglary
500
5000
0
0
1997
25
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
Residential burglary, 2008
26
Introduction



27
Researchers have long suggested that high
crime levels make communities decline.
This decline may translate into an
increasing desire to move, weaker
attachments of residents and lower house
values.
This is because buyers are willing to pay
more for living in neighbourhoods with lower
crime rates or, alternatively, buyers expects
discounts for purchasing properties in
neighbourhoods with higher crime rates.
Introduction

International literature, that is heavily based
on North American and British evidence,
shows somewhat inconclusive findings.

Little empirical evidence exists under the
Swedish conditions.

This study aims at assessing the impact of
crime on apartment prices using Stockholm
City as study area.
28
Contributions

This analysis explores a set of land use attributes
created by spatial techniques in hedonic pricing
modelling.

If a low crime area is surrounded by high crime,
then criminogenic conditions at that area may be
underestimated because of the high levels of
crime in neighbouring zones.
 GIS and spatial statistics techniques are used to
tackle this problem, so the neighbourhood
structure is added to the model to capture crime
conditions at each unit of analysis but also in its
neighbouring units.
29
Theory and empirical
findings

The effect of crime on housing prices is well documented.




Evidence from the last three decades confirmed that crime had a
significant impact on house prices (Hellman and Naroff, 1979,
Rizzo, 1979, Dubin and Goodman, 1982, Clark and Cosgrove,
1990, Feinberg and Nickerson, 2002, Titta et al., 2006, Munroe,
2007).
In the UK, the effect of crime on property prices does not seem the
same across crime types.
In Gibbons (2004) residential burglary had no measurable impact
on prices, but criminal damage did affect negatively housing prices.

30
Since the seminal work by Thaler (1978) showing that property crime
reduces house values by approximately three percent, studies have
shown evidence of similar effect.
One explanation for this is that vandalism, graffiti and other forms of
criminal damage motivate fear of crime in the community and may be
taken as signals or symptoms of community instability and
neighbourhood deterioration in general, pulling housing prices down.
Our hypotheses
1.
2.
3.
4.
Crime impacts negatively on apartment
prices after controlling for attributes of the
property and neighbourhood characteristics.
Different types of crimes affect property
values differently.
The price of an apartment is dependent on
the crime levels at its location as well as the
crime levels in the surrounding areas.
Parameter heterogeneity in crime effects on
apartment
prices.
31
Estimation approach





32
OLS (benchmark model)
Spatial dependency (spatial lag and error model)
 A binary weight matrix based on shared common
boundaries was created to represent the spatial
arrangement of the city.
Endogeneity (instrument variable approach)
 The causal relationship between apartment prices
and crime seems to go in both directions.
 Areas with high apartment prices may attract burglars
and therefore will the number of burglaries be high in
high priced neighborhoods.
Different aspects of crime
Parameter heterogeneity (in space)
Spatial dependency
Pris=100
Fel=-50
Pris=200
Fel=50
”Bästa gissning”=150
Spatial dependency

Omitted variables
$100
$200
”Best guess”=100 and 200
Instrument variable approach
(according to Wikipedia)


IV methods allow consistent estimation when the
explanatory variables are correlated with the error terms.
In attempting to estimate the causal effect of some
variable x on another y, an instrument is a third variable
z which affects y only through z's effect on x.
y  a  bx  e
1 x  c0  c1 z  u
2 y  a  bxˆ  e
5 Models
y  1 x   2C   3WC  
y  1 xˆ   2C   3WC  
1
2
xˆ  z
y  1 xˆ   2C   3WC  Wy  
y  1 xˆ   2C   3WC  
3
4
5
36
  W  
y  1 xˆ   2C   3WC   4CI  CN  
  W  
The data

Apartment prices (arm-length)
9622 transaction, 2008
The capital of Sweden - Stockholm

Property attributes




Location attribute


Total crime rate, robbery, vandalism, violence, burglary, shoplifting,
drugs, theft, theft of cars, theft from cars, assault.
Instrument variable

37
Distance to CBD, distance to water, subway station, commuting train
station, highway, main street.
Crime data


Living area, no. of rooms, monthly fee, age, elevator, balcony, floor
Homicide
Location attributes
Sold apartments in relation to water bodies, buffer of 100
meters (red), 300 meters (orange) and 300 meters (yellow).
38
Location attributes
Sold apartments in relation to subway stations, buffer of 100
meters (red), 300 meters (orange) and 300 meters (yellow).
39
Descriptive statistics
Average
Crime
Robbery
Vandalism
Violence
Burglary
Shoplifting
Drugs
Theft
Theft of cars
Theft from cars
Assault
40
Crime rate per 10,000 inhabitants
Robbery per 10,000 inhabitants
Vandalism per square meter of area
Outdoor violence per 10,000
inhabitants
Residential burglary per 10,000
inhabitants
Shoplifting per 10,000 inhabitants
Drug related crimes per 10,000
inhabitants
Theft per square meter of area
Theft of cars per square meter of area
Theft from cars per square meter of
area
Assaults per 10,000 inhabitants
7963.494
93.776
4.306
281.5881
Standard
deviation
254881.1
3141.251
5.158
8905.225
51.481
92.930
1880.947
434.534
95930.84
13668.88
8.715
.406
1.053
11.222
.304
.786
188.569
5988.247
The hedonic equation –
property attributes
OLS
OLS & Instrumental
Lag & Instrumental
Error & Instrumental
Coefficient t-values Coefficient t-values Coefficient z-values Coefficient z-values
.7043
53.37
.7054
53.19
.5919
53.64
.6360
65.91
.1889
15.85
.1878
15.68
.2013
20.66
.1898
22.73
-.1195
-18.97
-.1194
-.18.95
-.0723
-14.05
-.0513
-11.07
.1938
13.58
.1931
13.52
.1213
10.42
.0603
4.98
.1142
13.35
.1119
12.47
.1169
15.98
.0240
2.85
-.0277
-3.00
-.0277
-3.00
.0282
3.74
-.0073
-.85
-.2044
.01
-.2047
-18.12
-.1030
-11.11
-.0631
-5.80
-.1729
.01
-.1739
-13.74
-.1149
-11.10
-.1194
-8.78
.1117
4.77
.1157
4.83
.0674
3.46
.1134
5.50
-.0389
-4.69
-.0392
-4.68
-.0493
-7.22
-.0301
-4.51
.0164
9.10
.0163
9.07
.0158
10.81
.0157
12.31
-.0103
-.98
-.0101
-.957
-.0028
-.33
.0038
.53
-.0084
-1.04
-.0086
-1.07
-.0139
-2.16
-.0049
-.87
-.0345
-4.65
-.0345
-4.64
-.0292
-4.83
-.0216
-4.36
.0245
3.56
.0243
3.54
.0224
4.01
.0289
6.21
Area
Room
Fee
Age1
Age2
Age3
Age4
Age5
New
Elev
Elev*floor
Balc
Elev*Balc
First
Top
Small differences between OLS, IV and the spatial models.
41
The hedonic equation –
Location attributes
OLS
OLS & Instrumental
Lag & Instrumental
Error & Instrumental
Coefficient t-values Coefficient t-values Coefficient z-values Coefficient z-values
.1054
9.33
.1051
9.30
.0398
4.32
.0335
2.31
.0218
2.48
.0202
2.63
.0210
2.88
.0117
.92
.1005
12.84
.1010
12.87
.0609
9.49
.0721
5.95
.0186
1.89
.0210
2.04
.0047
.57
.0207
1.66
.0451
6.25
.0461
6.29
.0294
4.93
.0265
2.70
.0305
3.85
.0318
3.94
.0323
4.92
-.0070
-.56
-.0236
-.71
-.0230
-.69
-.0351
-1.31
-.0223
-.97
-.0725
-3.64
-.0734
-3.68
-.0737
-4.55
-.0334
-.16
.0292
2.23
.0315
2.35
.0338
3.10
-.0029
-.13
-.0986
-2.98
-.0976
-2.95
-.0637
-2.37
-.0325
-.97
.0116
0.80
.0122
.84
.0272
2.30
-.0032
-.16
.0326
3.28
.0304
2.94
.0214
2.55
-.0022
-.13
.0159
2.25
.0164
2.31
-.0001
-.1708
.0010
.12
.0493
5.81
.0481
5.60
.0362
5.18
.0479
4.22
-.0835
-8.84
-.0818
-8.46
-.0481
-6.10
.0058
.41
-.3599
-70.43
-.3600
-70.43
-.1926
-38.82
-.2630
-23.82
Water100
Water300
Water500
Sub100
Sub300
Sub500
Train100
Train300
Train500
Road100
Road300
Road500
Main100
Main300
Main500
Distance
42
Effect of seaview
Effect of subway
30%
12%
Water100
Water300
Sub100
Water500
25%
10%
20%
8%
15%
6%
10%
4%
5%
2%
Sub300
Sub500
0%
0%
OLS
IV
SAR
OLS
SEM
IV
SAR
SEM
Effect of main street
Effect of highway
6%
6%
4%
4%
Main100
Main300
Main500
2%
2%
0%
0%
OLS
OLS
IV
SAR
SEM
-2%
-2%
-4%
-4%
-6%
-8%
-6%
43
-8%
Road100
Road300
Road500
-10%
IV
SAR
SEM
The hedonic equation –
Crime variables
Total crime
W_tot crime
W_Y
Lambda
R-square
Adj R-square
AIC
Moran’s I
OLS
OLS & Instrumental
Lag & Instrumental
Error & Instrumental
Coefficient t-values Coefficient t-values Coefficient z-values Coefficient z-values
.0011
.20
-.0089
-.79
.0068
.74
-.0418
-2.79
-.0479
-6.61
-.0455
-8.53
-.0314
-7.24
-.0229
-2.71
.4936
64.68
.8024
104.31
.7674
.7675
.8453
.8850
.7662
.7662
863
863
-2348
-4026
.50
0.50
-
If total crime increase by 1 percent, apartment
prices are expected to fall by 0.04 percent.
44
If total crime in the surrounding areas increase by
1 percent, prices are expected to fall by 0.02
percent.
Different measures of crime
Robbery
Coefficient
OLS
Error
-.0049
-.0037
(-.45)
(-2.43)
-.0470
-.0028
(-15.7)
(-4.64)
-
Robbery
W_Robbery
Vandalism
Vandalism
Coefficient
OLS
Error
-
-.0340
(-2.27)
-.0.184
(-4.83)
Burglary
Coefficient
OLS
Error
-
Assault
Coefficient
OLS
Error
-
-
-
-
-
-
-
-
-
-
-
W_Vandalism
-
Burglary
-
-.0058
(-2.80)
.0035
(4.32)
-
W_Burglary
-
-
Assault
-
-
W_Assault
-
-
-.1468
(-2.14)
-.0514
(-13.27)
-.2110
(-2.16)
-.0044
(-5.16)
.0013
(.0923)
-.0358
(-13.05)
-.0503
(-2.45)
-.0213
(-3.80)
Theft
W_Theft
R-square
AIC
Moran’s I on
residuals
45
.7720
691
0.49
.8848
-4036
.7662
914
0.50
Theft
Coefficient
OLS
Error
-
.8854
-4035
.7702
762
0.50
.8849
-4041
.7700
768
0.49
.8457
-4030
If burglary increases by 1 percent, apartment
prices are expected to fall by 0.21 percent.
-.0792
(-6.20)
.0442
(9.74)
.7681
843
0.50
-.0563
(-3.26)
.0832
(8.92)
.8854
-4094
Parameter heterogeneity
Burglary
W_Burglary
Burglary *Inner
Burglary *North
Adj R-square
R-square
AIC
Moran’s I
46
Inside inner circle
Coefficient
OLS
Error
-.3730
-.2487
(-5.43)
(-2.59)
-.0358
-.0345
(-9.31)
(-4.27)
.2500
.1093
(9.92)
(3.79)
. 7893
.7880
1.35
0.47
.8857
-4246
North
Coefficient
OLS
-.2002
(-3.00)
-.0372
(-9.61)
.0300
(1.41)
.7870
.7857
97.8
0.47
Error
-.1836
(-1.92)
-.0353
(-4.33)
-.0270
(-.85)
.8857
-4233
Inside inner circle and north
Coefficient
OLS
Error
-.3716
-.2353
(-5.38)
(-2.45)
-.0357
-.0345
(-9.26)
(-4.26)
.2508
.1159
(9.81)
(3.97)
-.0040
-.0392
(-.19)
(-1.45)
. 7893
.7880
.8857
3.32
-4246
0.48
Conclusion





Findings indicate that if total crime increase by 1 percent, apartment
prices are expected to fall by 0.04 percent.
Different from what was initially hypothesized, residential burglary (and
not vandalism) seems to have the largest effect on property values.
If residential burglary increases by 1 percent, apartment prices are
expected to fall by 0.21 percent. It seems that the expected ‘visual
effect’ vandalism has on people’s perception of an area is not strong
enough to affect property prices in the case of Stockholm.
Results show that magnitude of the effect of residential burglary on
apartment prices is highest in the northern part of Stockholm than in the
South. Apartments in inner city areas are also less discounted than the
ones located of the central areas.
One of the most important results of this research is the indication that
price of an apartment is dependent on the crime levels at its location as
well as the crime levels in the surrounding areas, regardless crime type.
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