A House Price Index Based on the SPAR

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 1960 s; 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 yields 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): value-weighted SPAR index Estimator of Dutot price index for a (fixed) stock of houses:

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

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

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):

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

Data (2) 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 ---------------------------------------------ref. month (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

Results SPAR price indexes (January 1995= 100)

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

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

Results (4) Monthly percentage index changes

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: 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