1. 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)

2. 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)

3. 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

4. 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 registrys) sale prices p and official government appraisals a Model-based approach using appraisals as auxiliary data

5. 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 yields

6. 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:

7. Unweighted SPAR Indexes Equally-weighted arithmetic SPAR index Estimator of Carli index Violates time reversal test

8. Unweighted SPAR Indexes (2) Equally-weighted geometric SPAR index Estimator of Jevons index Satisfies all reasonable tests Bracketed factor: controls for compositional change

9. 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):

10. 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

11. 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

12. Data (2) Scatter plot and linear OLS regression line of sale prices and appraisals, January 2003 (R-squared= 0.951)

13. 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

14. Results SPAR price indexes (January 1995= 100)

15. Results (2) SPAR and repeat-sales price indexes (January 1995= 100)

16. Results (3) Value-weighted SPAR price index and naive index (January 1995= 100)

17. Results (4) Monthly percentage index changes

18. 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

19. 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?)

20. Appendix: expenditure-based interpretation Land registrys data set includes all transactions Expenditure 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 houses Value-weighted SPAR is a model-based estimator of the Paasche index