A House Price Index Based on the SPAR Method

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

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Value-Weighted SPAR Index

• Fixed sale price/appraisal ratio (base period)
• 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)

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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

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

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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

14
Results

• SPAR price indexes (January 1995 100)

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Results (2)

• SPAR and repeat-sales price indexes (January
  1995 100)

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Results (3)

• Value-weighted SPAR price index and naive index
  (January 1995 100)

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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

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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?)

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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