Transcript A House Price Index Based on the SPAR Method Paul de Vries (OTB Research Institute) Jan de Haan (Statistics Netherlands) Gust Mariën (OTB.

A House Price Index Based on the SPAR Method
Paul de Vries (OTB Research Institute)
Jan de Haan (Statistics Netherlands)
Gust Mariën (OTB Research Institute)
Erna van der Wal (Statistics Netherlands)
1
Outline
• Background
• Sale Price Appraisal Ratio (SPAR) method
• Value-weighted SPAR index
• Unweighted SPAR indexes
• Unweighted geometric SPAR and hedonics
• Data
• Results
• Conclusions
• Publication and future work
• (Appendix)
Background
Owner-occupied housing currently excluded from HICP
Eurostat pilot study: net acquisitions approach
(newly-built houses and second-hand houses purchased from
outside household sector)
This paper: price index for housing stock
Dutch land registry
records sale prices (second-hand houses only) and limited
number of attributes (postal code, type of dwelling);
published monthly repeat-sales index until January 2008
Sale Price Appraisal Ratio Method
Bourassa et al. (Journal of Housing Economics, 2006):
“ …. the advantages and the relatively limited drawbacks of the
SPAR method make it an ideal candidate for use by government
agencies in developing house price indexes.”
• Used in new Zealand since early 1960s; also in Sweden and
Denmark
• Promising results in Australia (Rossini and Kershaw, 2006)
• Based on (land registry’s) sale prices p and official government
appraisals a
• Model-based approach using appraisals as auxiliary data
Value-Weighted SPAR Index
1.Fixed sale price/appraisal ratio (base period)
2.Random sampling from (fixed) housing stock
Linear regression model, no intercept term. Estimation on base
ˆ i0  ˆ ( S 0 )ai0
period sample: p
Imputing predicted base period prices for
PˆWt 
t
t
p
/
n
 i
iS t
0
t
ˆ
p
/
n
 i
iS t
yields
t
t
p
(
S
)
ˆ
P 
ˆ ( S 0 )a 0 ( S t )
t
W
iSt
into
Value-Weighted SPAR Index (2)
Normalisation (dividing the imputation index by base period value
to obtain an index that is equal to 1 during base period):
PˆWt ( S )
p t (S t ) / a 0 (S t )  a 0 (S 0 )  p t (S t )
 0 0
 0 t  0 0
0
0
p (S ) / a (S )  a (S )  p (S )
value-weighted SPAR index
Estimator of Dutot price index for a (fixed) stock of houses:
t


p
0
i
t


p
pi

i 

0 
pi 
iU 0

t
iU 0
PW 


0
0
 pi
 pi
iU 0
iU 0
t
0
p
/
N
 i
t
0
p
(
U
)
iU
 0 0
0
0
 pi / N p (U )
0
iU 0
Unweighted SPAR Indexes
Equally-weighted arithmetic SPAR index
t
PˆUA
(S )
 pit 
t  a 0 
iS  i 

 pi0 
1
 0 
0 
n iS 0  ai 
1
nt
• Estimator of Carli index
t
PUA
 pit
0  p 0
iU 
i

N0




• Violates time reversal test
Unweighted SPAR Indexes (2)
Equally-weighted geometric SPAR index
1
Pˆ
t
G(S )
 p  nt
t  a   a~ 0 (S 0 ) 
 iS   1   ~ 0 t 
a (S ) 
 pi0  n0 
0  a 0 
iS  i 
t
i
0
i
~
p t (S t )
~
p 0 (S 0 )
• Estimator of Jevons index
1
t
PUG
 pit  N 0
   0 
iU 0  p i 
• Satisfies all ‘reasonable’ tests
• Bracketed factor: controls for compositional change
Unweighted Geometric SPAR and Hedonics
If appraisals were based on semi-log hedonic model
ln p    k 1  k0 xik   i0
0
i
0
K
estimated on base period sale prices, then geometric SPAR would be
PˆGt ( S )
 K ˆ0 0

0
t
 exp   k ( S )[ xk ( S )  xk ( S )]
 k 1

~
p t (S t )
~
p 0 (S 0 )
WLS time dummy index (observations weighted by reciprocal of
sample sizes):
K ~
~t
0
t 
PTD  exp   k [ xk ( S )  xk ( S )]
 k 1

~p ( S t )
~p ( S 0 )
Unweighted Geometric SPAR and Hedonics (2)
If appraisals were based on semi-log hedonic model:
• similarity between geometric SPAR and bilateral time dummy
index
• time dummy index probably more efficient due to pooling data
• multi-period time dummy index even more efficient but suffers
from ‘revision’
In general: stochastic indexes (including time dummy indexes,
repeat sales indexes) violate ‘temporal fixity’
Data
• Monthly sale prices (land registry): January 1995 – May 2006
• Official appraisals (municipalities): January 1995, January 1999,
January 2003
25.000
23.000
21.000
19.000
17.000
15.000
13.000
11.000
9.000
7.000
5.000
1995
1996
1997
1998
1999
2000
2001
2002
Number of sales for second-hand houses
2003
2004
2005
2006
Data (2)
1000
900
800
700
Sale price
600
500
400
300
200
100
0
0
100
200
300
400
500 600
Appraisal
700
800
900
1000
Scatter plot and linear OLS regression line of sale prices and
appraisals, January 2003 (R-squared= 0.951)
Data (3)
Comparison of sale prices and appraisals in appraisal reference
months
------------------------------------------------------------------------------------------0
0
0
0
0
0
p
(
S
)
ref. month
p (S ) a (S )
pi0 / ai0
(1000€)
(1000€)
a 0 ( S 0 ) mean stand. dev.
------------------------------------------------------------------------------------------January 1995
90.5
87.6
1.033
1.044 0.162
January 1999
130.5
133.9
0.975
0.976 0.114
January 2003
200.2
202.7
0.988
0.991 0.107
-------------------------------------------------------------------------------------------
Appraisals tend to approximate sale prices increasingly better:
• mean value of sale price/appraisal ratios approaches 1
• standard deviation becomes smaller
Results
280
260
240
220
200
180
160
140
120
100
1995
1996
1997
1998
1999
2000
value-w eighted SPAR
2001
2002
2003
2004
2005
unw eighted arithmetic SPAR
unw eighted geometric SPAR
SPAR price indexes (January 1995= 100)
2006
Results (2)
300
280
260
240
220
200
180
160
140
120
100
1995
1996
1997
repeat sales
1998
1999
2000
2001
unw eighted geometric SPAR
2002
2003
2004
2005
2006
unw eighted geometric SPAR RS
SPAR and repeat-sales price indexes (January 1995= 100)
Results (3)
280
260
240
220
200
180
160
140
120
100
1995
1996
1997
1998
1999
2000
value-w eighted SPAR
2001
2002
2003
2004
2005
2006
naive (arithmetic mean)
Value-weighted SPAR price index and ‘naive’ index (January
1995= 100)
Results (4)
6
5
4
3
2
1
0
-1
-2
-3
1995
1996
1997
1998
1999
2000
repeat sales
2001
2002
2003
value-w eighted SPAR
Monthly percentage index changes
2004
2005
2006
Conclusions
SPAR and repeat sales indexes
• control for compositional change (based on matched pairs)
• suffer from sample selection bias
• do not adjust for quality change
Stratified ‘naive’ index
• controls to some extent for compositional change and selection bias
Empirical results
• Small difference between value-weighted (arithmetic) and equallyweighted geometric SPAR index
• Repeat-sales index upward biased
• Volatility of SPAR index less than volatility of repeat-sales index but
still substantial
Publication and Future Work
Statistics Netherlands and Land Registry Office publish (stratified)
value-weighted SPAR indexes as from January 2008
Stratification and re-weighting for two reasons:
• relax basic assumption (fixed sale price/appraisal ratio)
• compute ‘Laspeyres-type’ indexes at upper level (fixed weights)
Future work:
• Estimation of standard errors
• Construction of annually-chained SPAR index (adjusting for
quality change?)
Appendix: expenditure-based interpretation
Land registry’s data set includes all transactions
Expenditure perspective: S t is not a sample (hence, no sampling
variance and sample selection bias), and
PˆPt ( E ) 
t
p
 i
iS t
0
ˆ
p
 i
iS t
is the (single) imputation Paasche price index for all purchases of
second-hand houses
Value-weighted SPAR
  ai0   pit
 0  t
PˆWt ( S )   iS 0  iS 0
ai  ai

 iS 0  iS t
is a model-based estimator of the Paasche index