1
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)
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 registryrecords 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 period sample: Imputing predicted base period prices for into
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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):
value-weighted SPAR index
Estimator of Dutot price index for a (fixed) stock of houses:
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Unweighted SPAR Indexes
Equally-weighted arithmetic SPAR index
• Estimator of Carli index
• Violates time reversal test
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Unweighted SPAR Indexes (2)
Equally-weighted geometric SPAR index
• Estimator of Jevons index
• Satisfies all ‘reasonable’ tests• Bracketed factor: controls for compositional change
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Unweighted Geometric SPAR and Hedonics
If appraisals were based on semi-log hedonic model
estimated on base period sale prices, then geometric SPAR would be
WLS time dummy index (observations weighted by reciprocal of sample sizes):
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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
Number of sales for second-hand houses
5.000
7.000
9.000
11.000
13.000
15.000
17.000
19.000
21.000
23.000
25.000
1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006
Data (2)
Scatter plot and linear OLS regression line of sale prices and appraisals, January 2003 (R-squared= 0.951)
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Data (3)
Comparison of sale prices and appraisals in appraisal reference months-------------------------------------------------------------------------------------------
ref. month
(1000€) (1000€) 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
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Results
SPAR price indexes (January 1995= 100)
100
120
140
160
180
200
220
240
260
280
1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006
value-w eighted SPAR unw eighted arithmetic SPAR
unw eighted geometric SPAR
Results (2)
SPAR and repeat-sales price indexes (January 1995= 100)
100
120
140
160
180
200
220
240
260
280
300
1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006
repeat sales unw eighted geometric SPAR unw eighted geometric SPAR RS
Results (3)
Value-weighted SPAR price index and ‘naive’ index (January 1995= 100)
100
120
140
160
180
200
220
240
260
280
1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006
value-w eighted SPAR naive (arithmetic mean)
Results (4)
Monthly percentage index changes
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-2
-1
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1
2
3
4
5
6
1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006
repeat sales value-w eighted SPAR
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 equally-weighted 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 transactionsExpenditure perspective: is not a sample (hence, no sampling variance and sample selection bias), and
is the (single) imputation Paasche price index for all purchases of second-hand housesValue-weighted SPAR
is a model-based estimator of the Paasche index
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