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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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

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180

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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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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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