1. Accounting for Spatial Variation of Land Prices in Hedonic Imputation House Price Indexes: A Semi- Parametric Approach Jan de Haan * and Yunlong Gong ** * Statistics Netherlands / Delft University of Technology ** Delft University of Technology SEM Conference 2015, Paris

2. 2 Outline Background A simplification of the ‘builder’s model’ –Basic ideas –Adding characteristics and linearizing the model Location and spatial variation of land prices –Two models –Semi-parametric estimation: the MWGR method Hedonic imputation price indexes Empirical results Conclusions

3. 3 Background Uniqueness of properties mainly due to location Location usually included in hedonic models at some aggregate level (postcode dummies), not at individual property level - spatial autocorrelation - location bias Land-structure split Aim of this paper Show how to account for spatial variation of land prices in hedonic house price indexes using geospatial information (longitude/latitude)

4. 4 A simplification of the ‘builder’s model’ Builder’s model (Diewert, de Haan and Hendriks, 2015): value of property is sum of value of land and value of structure: : plot size in square meters : living space in square meters : price of land per square meter : price of structure (living space) per square meter

5. 5 A simplification of the ‘builder’s model’ Potential problems No intercept (Multi)collinearity between plot size and structure size Heteroskedasticity Net depreciation Diewert, de Haan and Hendriks (2015): straight-line depreciation; adjusted value of structure : approximate age of structure in decades : depreciation rate

6. 6 A simplification of the ‘builder’s model’ Writing in linear form, using (multiplicative) dummies for age category, and reparameterizing: No restrictions on parameters Functional form is neither continuous nor smooth Adding structure characteristics (e.g. number or rooms, type of house) Only categorical variables; dummies Ignoring interaction terms and reparameterizing

7. 7 A simplification of the ‘builder’s model’ Fully linear model: Normalizing (dividing by structure size): : “normalized” property price : ratio of plot size to structure size Straightforward estimating equation (including intercept)

8. 8 Location and spatial variation of land prices Assumption: location is capitalized into price of land, not into price of structures 1) Price of land varies across postcode areas k: : price per square meter of land for area k : multiplicative dummy for k 2) Price of land varies across individual properties:

9. 9 Semi-parametric estimation Mixed Geographically Weighted Regression (MGWR) Parametric regression for estimating parameters for structure characteristics Non-parametric part (GWR) for estimating property-specific land prices Moving kernel window approach: - weighted regression on data of i and neighboring properties - decreasing function of distance to i (bi-square function) - bias-variance trade-off: choice of bandwidth using cross validation statistics

10. 10 Hedonic imputation price indexes Hedonic double imputation Laspeyres, Paasche and Fisher house price indexes, e.g. (defined on base period sample) Predicted prices: Estimated quality-adjusted prices:

11. 11 Hedonic imputation price indexes Estimated value shares for land and structures, and, sum to 1 due to double imputation E.g. Laspeyres price index for land: Big influence of properties with relatively large value shares (large plot sizes and high land prices)

12. 12 Empirical results Data set City of “A” in northeastern part of the Netherlands (population around 60,000) Annual data for 1998-2007 Total of 6,397 sales, excluding apartments and condominiums Geocoded by Statistics Netherlands Many characteristics but we only used plot size, living space, building period, type of house 57 observations removed (missing characteristics, outliers)

13. 13 Empirical results Three models estimated, separately for each year: 1) No variation in land prices (“OLS”) 2) Variation across postcodes (“OLSD”) 3) Variation across individual properties (“MGWR”) [60 neighboring properties used in MGWR estimations] According to (corrected) AICc as well as RMSE: OLSD performs better than OLS MGWR performs slightly better than OLSD for each year

14. 14 Parameter estimates for structures characteristics, 2007 OLSOLSDMGWR Intercept 1480.70*** (46.93) 1405.41*** (53.71) 1395.76*** (57.51) Building period:1960-1970 -370.48*** (25.94) -389.50*** (36.67) -309.40*** (41.75) Building period:1971-1980 -311.17*** (23.36) -261.50*** (33.96) -323.50*** (41.69) Building period:1981-1990 -232.93*** (23.37) -173.08*** (32.59) -226.14*** (42.87) Building period:1991-2000 -58.64*** (21.64) -49.34* (26.55) -115.13*** (37.26) Terrace -285.65*** (35.17) -264.34*** (35.24) -187.28*** (37.32) Corner -281.36*** (31.77) -274.54*** (31.18) -192.85*** (34.07) Semidetached -122.89** (47.96) -149.50*** (47.57) -96.93** (48.73) Duplex -151.08*** (30.60) -147.24*** (30.17) -104.56*** (31.03)

15. 15 Empirical results Intercept measures price per square meter of living space for detached houses built after 2000 (approx. EUR 1400 in 2007) Structures become less expensive as they get older Detached houses are more expensive than other types of houses All but 2 coefficients differ significantly from zero at 1% level

16. 16 (Average) estimated land prices per square meter OLSOLSDMGWR 1998 116.80131.50125.49 1999 154.64178.50167.77 2000 239.77239.41241.83 2001 214.54235.58226.79 2002 234.77245.11242.23 2003 166.07185.11172.26 2004 186.40197.19195.41 2005 226.13224.11205.89 2006 202.84195.77201.27 214.87236.73229.25

17. 17 Estimated price of land per square meter, MGWR, 2007

18. Hedonic imputation Laspeyres house price index Hardly any difference between OLSD and MGWR OLS has downward bias

19. 19 Hedonic imputation Paasche house price index OLS index upward biased

20. 20 Hedonic imputation Fisher house price index Fisher index insensitive to choice of hedonic model Official (nationwide) SPAR index rises much faster

21. 21 Hedonic imputation Fisher price indexes for land OLSD and MGWR similar but OLS very different Very volatile indexes

22. Hedonic imputation Fisher price indexes for structures Differences much smaller than for land, as expected Official construction cost index much flatter

23. 23 Empirical results Are the trends of the indexes for land and structures plausible? No benchmark available for land For structures: official (nationwide) construction cost index flattens during second half of sample period; price indexes for structures keep rising house prices were still rapidly rising while construction cost index increased by only 4.9% during 2003-2007 (CPI: 5.8%) quality change bias in construction cost index?

24. 24 Empirical results Potential causes of volatility of the land and structure indexes Small number of observations Multicollinearity Maybe not: land and structure price changes do not consistently show opposite signs; VIF for ratio of plot size to structure size is low Heteroskedasticity Yes (Breusch-Pagan test for OLS and OLSD) Limited adjustment for quality-mix changes

25. 25 Estimated value shares of land and structures, OLSD Also volatile Share of land on average 33%

26. 26 Empirical results Are the (average) estimated share of land and land price per square meter plausible? Francke and Van de Minne (2015): share of land for ‘s- Hertogenbosch – a more prosperous city than “A” – on average 0.50 (2003-2015) De Groot et al. (2015): substantial cross-city differences in the price of land in 2005, e.g. EUR 717 for Amsterdam, EUR 308 for ‘s-Hertogenbosch, EUR 184 for Leeuwarden Our estimate for “A” in 2005 of EUR 206 seems plausible

27. 27 Conclusions The linearization and ‘normalization’ of the builder’s model is useful for estimating overall house price indexes Double imputation Fisher house price index is insensitive to choice of hedonic model Postcode dummies will suffice; no need to use geocode data; see also Hill and Scholz (2014) Land and structure price indexes are volatile (which is not unexpected as we did not use any exogenous information on price change of structures) Average level of land prices seems plausible Some doubts about official SPAR house price index and construction cost index

28. 28 Future work Price per square meter of land depends on plot size: need to model nonlinear relation of plot size to structure size ratio Data for a bigger, less ‘homogeneous’ city, and longer sample period (1995-2015) More structure characteristics Smoothing?