6 Conclusion

Jan de Haan and Rens Hendriks

Previous

The simple GREG method outlined in this paper, which is based on OLS regressions of selling prices on appraisals, substantially reduces the volatility of a house price index as compared to the ratio of sample means. The SPAR index can be viewed as an estimator of the OLS GREG index (which itself is an estimator, of course) where the base period population mean of appraisals is replaced by the sample means in the base period and the comparison period. Our empirical results for the Netherlands indicate that the SPAR index is almost as efficient as the GREG index, even for small sub-populations. We have checked this by drawing a random sample of 50 observations each month from the total number of monthly sales (15,000 on average). The month-to-month changes of the SPAR index were only slightly bigger than those of the GREG.

Due to compositional change of the properties sold, the GREG (and SPAR) time series exhibit strong short-term volatility. An increase in a particular month is typically followed by a decrease in the next month. Put differently, the month-to-month changes do not tell us much about the true price change of the housing stock which, except under unusual circumstances, should behave smoothly. An improved outlier detection method might help reduce the index volatility, but the effect will probably be limited. Applying a smoothing procedure would seem to be an option. However, that will typically lead to revisions of previously published price index numbers, and the lack of revisions is one of the strenghts of the GREG and SPAR approaches. Another option would be to reduce the frequency of observation, for example to quarters, but that may be undesirable as well.

From a purely statistical point of view, in our two-variable model the variability of R 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9LqFf0x e9q8qqvqFr0dXdHiVc=bYP0xb9sq=fFfeu0RXxb9qr0dd9q8qi0lf9 Fve9Fve9vapdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamOuam aaCaaaleqabaGaaGOmaaaaaaa@3B57@  seems to be responsible for a large part of the volatility of the slope coefficient and therefore of the volatility of the price index series. Future research could focus on the relation between compositional changes in terms of the property characteristics and changes in R 2 . MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9LqFf0x e9q8qqvqFr0dXdHiVc=bYP0xb9sq=fFfeu0RXxb9qr0dd9q8qi0lf9 Fve9Fve9vapdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamOuam aaCaaaleqabaGaaGOmaaaakiaac6caaaa@3C13@  As many housing characteristics are unavailable, we cannot investigate this issue with our data. Fortunately, Statistics Netherlands has access to a data set from the largest Dutch association of real estate agents that might be useful for this purpose. This data set covers around 70% of all housing sales in the Netherlands during 1999-2008, includes many property characteristics and has been enriched with appraisal data. In the past we already used the data set to compare the SPAR index with various types of hedonic indexes.

Acknowledgements

The authors would like to thank the participants at the Economic Measurement Group Workshop, 1-3 December 2010, University of New South Wales, Sydney, Australia and the participants at an Applied Economics Seminar, 22 November 2011, University of Queensland, Brisbane, Australia for their helpful comments on preliminary versions of the paper. Comments and suggestions made by the editor and two anonymous referees also helped to improve the paper. The assistance of Erna van der Wal, who provided us with the data, is gratefully acknowledged. The views expressed in this paper are those of the authors and do not necessarily reflect the views of Statistics Netherlands.

Appendix

Approximate Standard Errors of the GREG Index

The GREG index defined by equation (3.10) in the main text is a ratio of two estimators, p ¯ ^ GREG t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9LqFf0x e9q8qqvqFr0dXdHiVc=bYP0xb9sq=fFfeu0RXxb9qr0dd9q8qi0lf9 Fve9Fve9vapdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGabmiCay aaryaajaWaa0baaSqaaiaabEeacaqGsbGaaeyraiaabEeaaeaacaWG 0baaaaaa@3F0A@  and p ¯ ^ GREG 0 ; MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9LqFf0x e9q8qqvqFr0dXdHiVc=bYP0xb9sq=fFfeu0RXxb9qr0dd9q8qi0lf9 Fve9Fve9vapdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGabmiCay aaryaajaWaa0baaSqaaiaabEeacaqGsbGaaeyraiaabEeaaeaacaaI WaaaaOGaai4oaaaa@3F94@  for brevity we delete "OLS�. Using a first-order Taylor expansion, the variance of the index can be approximated by (see e.g., Kendall and Stuart 1976)

var( P ^ GREG 0t ) [ E( p ¯ ^ GREG t ) E( p ¯ ^ GREG 0 ) ] 2 [ var( p ¯ ^ GREG t ) {E( p ¯ ^ GREG t )} 2 + var( p ¯ ^ GREG 0 ) {E( p ¯ ^ GREG 0 )} 2 + cov( p ¯ ^ GREG t , p ¯ ^ GREG 0 ) E( p ¯ ^ GREG t )E( p ¯ ^ GREG 0 ) ],       ( A.1 ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9LqFf0x e9q8qqvqFr0dXdHiVc=bYP0xb9sq=fFfeu0RXxb9qr0dd9q8qi0lf9 Fve9Fve9vapdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaciODai aacggacaGGYbGaaiikaiqadcfagaqcamaaDaaaleaacaqGhbGaaeOu aiaabweacaqGhbaabaGaaGimaiaadshaaaGccaGGPaGaeyyrIa0aam WaaeaadaWcaaqaaiaadweacaGGOaGabmiCayaaryaajaWaa0baaSqa aiaabEeacaqGsbGaaeyraiaabEeaaeaacaWG0baaaOGaaiykaaqaai aadweacaGGOaGabmiCayaaryaajaWaa0baaSqaaiaabEeacaqGsbGa aeyraiaabEeaaeaacaaIWaaaaOGaaiykaaaaaiaawUfacaGLDbaada ahaaWcbeqaaiaaikdaaaGcdaWadaqaamaalaaabaGaciODaiaacgga caGGYbGaaiikaiqadchagaqegaqcamaaDaaaleaacaqGhbGaaeOuai aabweacaqGhbaabaGaamiDaaaakiaacMcaaeaacaGG7bGaamyraiaa cIcaceWGWbGbaeHbaKaadaqhaaWcbaGaae4raiaabkfacaqGfbGaae 4raaqaaiaadshaaaGccaGGPaGaaiyFamaaCaaaleqabaGaaGOmaaaa aaGccqGHRaWkdaWcaaqaaiGacAhacaGGHbGaaiOCaiaacIcaceWGWb GbaeHbaKaadaqhaaWcbaGaae4raiaabkfacaqGfbGaae4raaqaaiaa icdaaaGccaGGPaaabaGaai4EaiaadweacaGGOaGabmiCayaaryaaja Waa0baaSqaaiaabEeacaqGsbGaaeyraiaabEeaaeaacaaIWaaaaOGa aiykaiaac2hadaahaaWcbeqaaiaaikdaaaaaaOGaey4kaSYaaSaaae aaciGGJbGaai4BaiaacAhacaGGOaGabmiCayaaryaajaWaa0baaSqa aiaabEeacaqGsbGaaeyraiaabEeaaeaacaWG0baaaOGaaiilaiqadc hagaqegaqcamaaDaaaleaacaqGhbGaaeOuaiaabweacaqGhbaabaGa aGimaaaakiaacMcaaeaacaWGfbGaaiikaiqadchagaqegaqcamaaDa aaleaacaqGhbGaaeOuaiaabweacaqGhbaabaGaamiDaaaakiaacMca caWGfbGaaiikaiqadchagaqegaqcamaaDaaaleaacaqGhbGaaeOuai aabweacaqGhbaabaGaaGimaaaakiaacMcaaaaacaGLBbGaayzxaaGa aiilaiaaxMaacaWLjaWaaeWaaeaaqaaaaaaaaaWdbiaadgeacaGGUa GaaGymaaWdaiaawIcacaGLPaaaaaa@A752@

where E( p ¯ ^ GREG t ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9LqFf0x e9q8qqvqFr0dXdHiVc=bYP0xb9sq=fFfeu0RXxb9qr0dd9q8qi0lf9 Fve9Fve9vapdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamyrai aacIcaceWGWbGbaeHbaKaadaqhaaWcbaGaae4raiaabkfacaqGfbGa ae4raaqaaiaadshaaaGccaGGPaaaaa@4137@  and E( p ¯ ^ GREG 0 ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9LqFf0x e9q8qqvqFr0dXdHiVc=bYP0xb9sq=fFfeu0RXxb9qr0dd9q8qi0lf9 Fve9Fve9vapdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamyrai aacIcaceWGWbGbaeHbaKaadaqhaaWcbaGaae4raiaabkfacaqGfbGa ae4raaqaaiaaicdaaaGccaGGPaaaaa@40F8@  denote expected values.

The covariance term in (A.1) is equal to 0 since, by assumption, the samples in periods 0 and t MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9LqFf0x e9q8qqvqFr0dXdHiVc=bYP0xb9sq=fFfeu0RXxb9qr0dd9q8qi0lf9 Fve9Fve9vapdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaamiDaa aa@3A91@  are independently drawn. Replacing the expected values in (A.1) by the estimators and subsequently taking the square root leads to the following expression for the standard error of  P ^ GREG 0t : MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9LqFf0x e9q8qqvqFr0dXdHiVc=bYP0xb9sq=fFfeu0RXxb9qr0dd9q8qi0lf9 Fve9Fve9vapdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGabmiuay aajaWaa0baaSqaaiaabEeacaqGsbGaaeyraiaabEeaaeaacaaIWaGa amiDaaaakiaacQdaaaa@4055@

se( P ^ GREG 0t ) P ^ GREG 0t [ var( p ¯ ^ GREG t ) ( p ¯ ^ GREG t ) 2 + var( p ¯ ^ GREG 0 ) ( p ¯ ^ GREG 0 ) 2 ] 1/2 .       ( A.2 ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9LqFf0x e9q8qqvqFr0dXdHiVc=bYP0xb9sq=fFfeu0RXxb9qr0dd9q8qi0lf9 Fve9Fve9vapdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaam4Cai aadwgacaGGOaGabmiuayaajaWaa0baaSqaaiaabEeacaqGsbGaaeyr aiaabEeaaeaacaaIWaGaamiDaaaakiaacMcacqGHfjcqceWGqbGbaK aadaqhaaWcbaGaae4raiaabkfacaqGfbGaae4raaqaaiaaicdacaWG 0baaaOWaamWaaeaadaWcaaqaaiGacAhacaGGHbGaaiOCaiaacIcace WGWbGbaeHbaKaadaqhaaWcbaGaae4raiaabkfacaqGfbGaae4raaqa aiaadshaaaGccaGGPaaabaGaaiikaiqadchagaqegaqcamaaDaaale aacaqGhbGaaeOuaiaabweacaqGhbaabaGaamiDaaaakiaacMcadaah aaWcbeqaaiaaikdaaaaaaOGaey4kaSYaaSaaaeaaciGG2bGaaiyyai aackhacaGGOaGabmiCayaaryaajaWaa0baaSqaaiaabEeacaqGsbGa aeyraiaabEeaaeaacaaIWaaaaOGaaiykaaqaaiaacIcaceWGWbGbae HbaKaadaqhaaWcbaGaae4raiaabkfacaqGfbGaae4raaqaaiaaicda aaGccaGGPaWaaWbaaSqabeaacaaIYaaaaaaaaOGaay5waiaaw2faam aaCaaaleqabaGaaGymaiaac+cacaaIYaaaaOGaaiOlaiaaxMaacaWL jaWaaeWaaeaaqaaaaaaaaaWdbiaadgeacaGGUaGaaGOmaaWdaiaawI cacaGLPaaaaaa@77AA@

Equation (A.2) can be estimated in practice using p ¯ ^ GREG s = α ^ s + β ^ s a ¯ 0 (s=0,t), MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9LqFf0x e9q8qqvqFr0dXdHiVc=bYP0xb9sq=fFfeu0RXxb9qr0dd9q8qi0lf9 Fve9Fve9vapdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGabmiCay aaryaajaWaa0baaSqaaiaabEeacaqGsbGaaeyraiaabEeaaeaacaWG ZbaaaOGaeyypa0JafqySdeMbaKaadaahaaWcbeqaaiaadohaaaGccq GHRaWkcuaHYoGygaqcamaaCaaaleqabaGaam4Caaaakiqadggagaqe amaaCaaaleqabaGaaGimaaaakiaacIcacaWGZbGaeyypa0JaaGimai aacYcacaWG0bGaaiykaiaacYcaaaa@4F12@  hence var( p ¯ ^ GREG s )=var( α ^ s )+ ( a ¯ 0 ) 2 var( β ^ s )+2 a ¯ 0 cov( α ^ s , β ^ s ). MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9LqFf0x e9q8qqvqFr0dXdHiVc=bYP0xb9sq=fFfeu0RXxb9qr0dd9q8qi0lf9 Fve9Fve9vapdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaciODai aacggacaGGYbGaaiikaiqadchagaqegaqcamaaDaaaleaacaqGhbGa aeOuaiaabweacaqGhbaabaGaam4CaaaakiaacMcacqGH9aqpciGG2b GaaiyyaiaackhacaGGOaGafqySdeMbaKaadaahaaWcbeqaaiaadoha aaGccaGGPaGaey4kaSIaaiikaiqadggagaqeamaaCaaaleqabaGaaG imaaaakiaacMcadaahaaWcbeqaaiaaikdaaaGcciGG2bGaaiyyaiaa ckhacaGGOaGafqOSdiMbaKaadaahaaWcbeqaaiaadohaaaGccaGGPa Gaey4kaSIaaGOmaiqadggagaqeamaaCaaaleqabaGaaGimaaaakiGa cogacaGGVbGaaiODaiaacIcacuaHXoqygaqcamaaCaaaleqabaGaam 4CaaaakiaacYcacuaHYoGygaqcamaaCaaaleqabaGaam4Caaaakiaa cMcacaGGUaaaaa@6660@  Estimates of the (co)variances are readily available in most statistical packages from the variance-covariance matrix.

Dividing (A.2) by P ^ GREG 0t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9LqFf0x e9q8qqvqFr0dXdHiVc=bYP0xb9sq=fFfeu0RXxb9qr0dd9q8qi0lf9 Fve9Fve9vapdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGabmiuay aajaWaa0baaSqaaiaabEeacaqGsbGaaeyraiaabEeaaeaacaaIWaGa amiDaaaaaaa@3F8D@  yields an expression for the relative standard error or coefficient of variation, CV( P ^ GREG 0t )=se( P ^ GREG 0t )/ P ^ GREG 0t , MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9LqFf0x e9q8qqvqFr0dXdHiVc=bYP0xb9sq=fFfeu0RXxb9qr0dd9q8qi0lf9 Fve9Fve9vapdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaam4qai aadAfacaGGOaGabmiuayaajaWaa0baaSqaaiaabEeacaqGsbGaaeyr aiaabEeaaeaacaaIWaGaamiDaaaakiaacMcacqGH9aqpcaWGZbGaam yzaiaacIcaceWGqbGbaKaadaqhaaWcbaGaae4raiaabkfacaqGfbGa ae4raaqaaiaaicdacaWG0baaaOGaaiykaiaac+caceWGqbGbaKaada qhaaWcbaGaae4raiaabkfacaqGfbGaae4raaqaaiaaicdacaWG0baa aOGaaiilaaaa@5437@  of the GREG index:

CV( P ^ GREG 0t ) [ var( p ¯ ^ GREG t ) ( p ¯ ^ GREG t ) 2 + var( p ¯ ^ GREG 0 ) ( p ¯ ^ GREG 0 ) 2 ] 1/2 = [ {CV( p ¯ ^ GREG t )} 2 + {CV( p ¯ ^ GREG 0 )} 2 ] 1/2 .       ( A.3 ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9LqFf0x e9q8qqvqFr0dXdHiVc=bYP0xb9sq=fFfeu0RXxb9qr0dd9q8qi0lf9 Fve9Fve9vapdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaam4qai aadAfacaGGOaGabmiuayaajaWaa0baaSqaaiaabEeacaqGsbGaaeyr aiaabEeaaeaacaaIWaGaamiDaaaakiaacMcacqGHfjcqdaWadaqaam aalaaabaGaciODaiaacggacaGGYbGaaiikaiqadchagaqegaqcamaa DaaaleaacaqGhbGaaeOuaiaabweacaqGhbaabaGaamiDaaaakiaacM caaeaacaGGOaGabmiCayaaryaajaWaa0baaSqaaiaabEeacaqGsbGa aeyraiaabEeaaeaacaWG0baaaOGaaiykamaaCaaaleqabaGaaGOmaa aaaaGccqGHRaWkdaWcaaqaaiGacAhacaGGHbGaaiOCaiaacIcaceWG WbGbaeHbaKaadaqhaaWcbaGaae4raiaabkfacaqGfbGaae4raaqaai aaicdaaaGccaGGPaaabaGaaiikaiqadchagaqegaqcamaaDaaaleaa caqGhbGaaeOuaiaabweacaqGhbaabaGaaGimaaaakiaacMcadaahaa WcbeqaaiaaikdaaaaaaaGccaGLBbGaayzxaaWaaWbaaSqabeaacaaI XaGaai4laiaaikdaaaGccqGH9aqpdaWadaqaaiaacUhacaWGdbGaam OvaiaacIcaceWGWbGbaeHbaKaadaqhaaWcbaGaae4raiaabkfacaqG fbGaae4raaqaaiaadshaaaGccaGGPaGaaiyFamaaCaaaleqabaGaaG OmaaaakiabgUcaRiaacUhacaWGdbGaamOvaiaacIcaceWGWbGbaeHb aKaadaqhaaWcbaGaae4raiaabkfacaqGfbGaae4raaqaaiaaicdaaa GccaGGPaGaaiyFamaaCaaaleqabaGaaGOmaaaaaOGaay5waiaaw2fa amaaCaaaleqabaGaaGymaiaac+cacaaIYaaaaOGaaiOlaiaaxMaaca WLjaWaaeWaaeaaqaaaaaaaaaWdbiaadgeacaGGUaGaaG4maaWdaiaa wIcacaGLPaaaaaa@8E40@

Of more importance is the relative standard error of the percentage change of the index, i.e., CV( P ^ GREG 0t 1)=se( P ^ GREG 0t 1)/( P ^ GREG 0t 1). MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9LqFf0x e9q8qqvqFr0dXdHiVc=bYP0xb9sq=fFfeu0RXxb9qr0dd9q8qi0lf9 Fve9Fve9vapdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaam4qai aadAfacaGGOaGabmiuayaajaWaa0baaSqaaiaabEeacaqGsbGaaeyr aiaabEeaaeaacaaIWaGaamiDaaaakiabgkHiTiaaigdacaGGPaGaey ypa0Jaam4CaiaadwgacaGGOaGabmiuayaajaWaa0baaSqaaiaabEea caqGsbGaaeyraiaabEeaaeaacaaIWaGaamiDaaaakiabgkHiTiaaig dacaGGPaGaai4laiaacIcaceWGqbGbaKaadaqhaaWcbaGaae4raiaa bkfacaqGfbGaae4raaqaaiaaicdacaWG0baaaOGaeyOeI0IaaGymai aacMcacaGGUaaaaa@5A8A@  This is generally greater than CV( P ^ GREG 0t ), MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9LqFf0x e9q8qqvqFr0dXdHiVc=bYP0xb9sq=fFfeu0RXxb9qr0dd9q8qi0lf9 Fve9Fve9vapdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaam4qai aadAfacaGGOaGabmiuayaajaWaa0baaSqaaiaabEeacaqGsbGaaeyr aiaabEeaaeaacaaIWaGaamiDaaaakiaacMcacaGGSaaaaa@4343@  given that se( P ^ GREG 0t 1)=se( P ^ GREG 0t ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9LqFf0x e9q8qqvqFr0dXdHiVc=bYP0xb9sq=fFfeu0RXxb9qr0dd9q8qi0lf9 Fve9Fve9vapdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaam4Cai aadwgacaGGOaGabmiuayaajaWaa0baaSqaaiaabEeacaqGsbGaaeyr aiaabEeaaeaacaaIWaGaamiDaaaakiabgkHiTiaaigdacaGGPaGaey ypa0Jaam4CaiaadwgacaGGOaGabmiuayaajaWaa0baaSqaaiaabEea caqGsbGaaeyraiaabEeaaeaacaaIWaGaamiDaaaakiaacMcaaaa@4EBB@  and P ^ GREG 0t 1< P ^ GREG 0t . MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9LqFf0x e9q8qqvqFr0dXdHiVc=bYP0xb9sq=fFfeu0RXxb9qr0dd9q8qi0lf9 Fve9Fve9vapdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGabmiuay aajaWaa0baaSqaaiaabEeacaqGsbGaaeyraiaabEeaaeaacaaIWaGa amiDaaaakiabgkHiTiaaigdacqGH8aapceWGqbGbaKaadaqhaaWcba Gaae4raiaabkfacaqGfbGaae4raaqaaiaaicdacaWG0baaaOGaaiOl aaaa@48F5@

If both regression lines almost pass through the origin, hence α ^ s 0(s=0,t), MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9LqFf0x e9q8qqvqFr0dXdHiVc=bYP0xb9sq=fFfeu0RXxb9qr0dd9q8qi0lf9 Fve9Fve9vapdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGafqySde MbaKaadaahaaWcbeqaaiaadohaaaGccqGHfjcqcaaIWaGaaiikaiaa dohacqGH9aqpcaaIWaGaaiilaiaadshacaGGPaGaaiilaaaa@44CC@  we have P ^ GREG 0t β ^ t / β ^ 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9LqFf0x e9q8qqvqFr0dXdHiVc=bYP0xb9sq=fFfeu0RXxb9qr0dd9q8qi0lf9 Fve9Fve9vapdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGabmiuay aajaWaa0baaSqaaiaabEeacaqGsbGaaeyraiaabEeaaeaacaaIWaGa amiDaaaakiabgwKiajqbek7aIzaajaWaaWbaaSqabeaacaWG0baaaO Gaai4laiqbek7aIzaajaWaaWbaaSqabeaacaaIWaaaaaaa@46F6@  and (A.2) simplifies to

se( P ^ GREG 0t )=se( P ^ GREG 0t 1) P ^ GREG 0t [ var( β ^ t ) ( β ^ t ) 2 + var( β ^ 0 ) ( β ^ 0 ) 2 ] 1/2 .       ( A.4 ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9LqFf0x e9q8qqvqFr0dXdHiVc=bYP0xb9sq=fFfeu0RXxb9qr0dd9q8qi0lf9 Fve9Fve9vapdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGaam4Cai aadwgacaGGOaGabmiuayaajaWaa0baaSqaaiaabEeacaqGsbGaaeyr aiaabEeaaeaacaaIWaGaamiDaaaakiaacMcacqGH9aqpcaWGZbGaam yzaiaacIcaceWGqbGbaKaadaqhaaWcbaGaae4raiaabkfacaqGfbGa ae4raaqaaiaaicdacaWG0baaaOGaeyOeI0IaaGymaiaacMcacqGHfj cqceWGqbGbaKaadaqhaaWcbaGaae4raiaabkfacaqGfbGaae4raaqa aiaaicdacaWG0baaaOWaamWaaeaadaWcaaqaaiGacAhacaGGHbGaai OCaiaacIcacuaHYoGygaqcamaaCaaaleqabaGaamiDaaaakiaacMca aeaacaGGOaGafqOSdiMbaKaadaahaaWcbeqaaiaadshaaaGccaGGPa WaaWbaaSqabeaacaaIYaaaaaaakiabgUcaRmaalaaabaGaciODaiaa cggacaGGYbGaaiikaiqbek7aIzaajaWaaWbaaSqabeaacaaIWaaaaO GaaiykaaqaaiaacIcacuaHYoGygaqcamaaCaaaleqabaGaaGimaaaa kiaacMcadaahaaWcbeqaaiaaikdaaaaaaaGccaGLBbGaayzxaaWaaW baaSqabeaacaaIXaGaai4laiaaikdaaaGccaGGUaGaaCzcaiaaxMaa daqadaqaaabaaaaaaaaapeGaamyqaiaac6cacaaI0aaapaGaayjkai aawMcaaaaa@7925@

In this particular case the GREG and SPAR indexes nearly coincide, so (A.4) also holds for the SPAR index (using P ^ SPAR 0t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9LqFf0x e9q8qqvqFr0dXdHiVc=bYP0xb9sq=fFfeu0RXxb9qr0dd9q8qi0lf9 Fve9Fve9vapdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGabmiuay aajaWaa0baaSqaaiaabofacaqGqbGaaeyqaiaabkfaaeaacaaIWaGa amiDaaaaaaa@3F9E@  rather than P ^ GREG 0t ). MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9LqFf0x e9q8qqvqFr0dXdHiVc=bYP0xb9sq=fFfeu0RXxb9qr0dd9q8qi0lf9 Fve9Fve9vapdbaqaaeGacaGaaiaabeqaamaabaabaaGcbaGabmiuay aajaWaa0baaSqaaiaabEeacaqGsbGaaeyraiaabEeaaeaacaaIWaGa amiDaaaakiaacMcacaGGUaaaaa@40F6@

References

Bailey, M.J., Muth, R.F. and Nourse, H.O. (1963). A regression method for real estate price construction. Journal of the American Statistical Association, 58, 933-942.

Beaumont, J.-F., and Alavi, A. (2004). Robust generalized regression estimation. Survey Methodology, 30, 2, 195-208.

Bourassa, S.C., Hoesli, M. and Sun, J. (2006). A simple alternative house price index method. Journal of Housing Economics, 15, 80-97.

Calhoun, C.A. (1996). OFHEO House Price Indexes: HPI Technical Description. Office of Federal Housing Enterprise Oversight, Washington, DC.

Case, K.E., and Shiller, R.J. (1987). Prices of single-family homes since 1970: New indexes for four cities. New England Economic Review, September-October, 45-56.

Case, K.E., and Shiller, R.J. (1989). The efficiency of the market for single family homes. The American Economic Review, 79, 125-137.

Cochran, W.G. (1977). Sampling Techniques, 3rd Edition, New York: John Wiley & Sons, Inc.

Cook, R.D., and Weisberg, S. (1982). Residuals and Influence in Regression, New York: Chapman and Hall.

de Haan, J. (2007). Formulae for the Variance of (Changes in) the SPAR Index. Unpublished manuscript, Statistics Netherlands, Voorburg (Dutch only; available from the author upon request).

de Haan, J. (2010). Hedonic price indexes: A comparison of imputation, time dummy and 'Re-Pricing' methods, Journal of Economics and Statistics (Jahrbucher fur Nationalokonomie und Statistik), 230, 772-791.

de Haan, J., van der Wal, E. and de Vries, P. (2009). The measurement of house prices: A review of the sale price appraisal method. Journal of Economic and Social Measurement, 34, 51-86.

de Vries, P., de Haan, J., van der Wal, E. and Mariën,G. (2009). A house price index based on the SPAR method. Journal of Housing Economics, 18, 214-223.

Diewert, W.E., de Haan, J. and Hendriks, R. (2012). The decomposition of a house price index into land and structures components: A hedonic regression approach. Econometric Reviews (forthcoming).

Diewert, W.E., Heravi, S. and Silver, M. (2009). Hedonic imputation versus time dummy hedonic indexes. In Price Index Concepts and Measurement, (Eds., W.E. Diewert, J. Greenlees and C. Hulten), NBER Studies in Income and Wealth, Chicago: Chicago University Press, 70, 161-196.

Edelstein, R.H., and Quan, D.C. (2006). How does appraisal smoothing bias real estate returns measurement? Journal of Real Estate Finance and Economics, 32, 41-60.

Eurostat (2010). Technical Manual on Owner-Occupied Housing for Harmonised Index of Consumer Prices, Version 1.9. Available at www.epp.eurostat.ec.europa.eu/portal/page/portal/hicp/documents/ Tab/Tab/03_METH-OOH-TECHMANUAL_V1-9.pdf.

Francke, M.K. (2010). Repeat sales index for thin markets: A structural time series approach. Journal of Real Estate Finance and Economics, 41, 24-52.

Geltner, D. (1996). The repeated-measures regression-based index: A better way to construct appraisal-based indexes of commercial property value. Real Estate Finance, 12, 29-35.

Gouriéroux, C., and Laferrère, A. (2009). Managing hedonic house price indexes: The french experience. Journal of Housing Economics, 18, 206-213.

Grimes, A., and Young, C. (2010). A Simple Repeat Sales House Price Index: Comparative Properties Under Alternative Data Generation Processes. Motu Working Paper 10-10, Motu Economic and Public Policy Research, New Zealand.

Hardman, M. (2011). Calculating High Frequency Australian Residential Property Price Indices. Rismark Technical Paper, available at www.rpdata.com/images/stories/content/PDFs/technical_method_ paper.pdf.

Hedlin, D., Falvey, H., Chambers, R. and Kokic, P. (2001). Does the model matter for GREG estimation? A business survey example. Journal of Official Statistics, 17, 527-544.

Hill, R.J., and Melser, D. (2008). Hedonic imputation and the price index problem: An application to housing. Economic Inquiry, 46, 593-609.

Jansen, S.J.T., de Vries, P., Coolen, H.C.C.H., Lamain, C.J.M. and Boelhouwer, P. (2008). Developing a house price index for the Netherlands: A practical application of weighted repeat sales. Journal of Real Estate Finance and Economics, 37, 163-186.

Kendall, M., and Stuart, A. (1976). The Advanced Theory of Statistics MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaacbi qcLbwaqaaaaaaaaaWdbiaa=nbiaaa@39C0@  Volume 1: Distribution Theory, 4th Edition, London: Charles Griffin & Company.

Leventis, A. (2006). Removing Appraisal Bias from a Repeat Transactions House Price Index: A Basic Approach. Paper presented at the OECD-IMF Workshop on Real Estate Price Indexes, Paris, 6-7 November 2006.

Makaronidis, A., and Hayes, K. (2006). Owner Occupied Housing for the HICP. Paper presented at the OECD-IMF Workshop on Real Estate Price Indexes, Paris, 6-7 November 2006.

Rossini, P., and Kershaw, P. (2006). Developing a Weekly Residential Price Index Using the Sales Price Appraisal Ratio. Paper presented at the twelfth Annual Pacific Rim Real Estate Society Conference, Auckland, 22-25 January 2006.

Saarnio, M. (2006). Housing Price Statistics at Statistics Finland. Paper presented at the OECD-IMF Workshop on Real Estate Price Indexes, Paris, 6-7 November 2006.

Särndal, C.-E., Swensson, B. and Wretman, J. (1992). Model Assisted Survey Sampling, New York: Springer-Verlag.

Shi, S., Young, M. and Hargreaves, B. (2009). Issues in measuring a monthly house price index in New Zealand. Journal of Housing Economics, 18, 336-350.

Statistics Netherlands (2008). Price Index Owner-occupied Existing Dwellings; Method Description. Statistics Netherlands, The Hague, available at www.cbs.nl/NR/rdonlyres/A49D8542-26EC-40FD-9093-82A519247F4B/0/MethodebeschrijvingPrijsindexBestaandeKoopwoningene.pdf.

van der Wal, E., ter Steege, D. and Kroese B. (2006). Two Ways to Construct a House Price Index for the Netherlands: The Repeat Sale and Sale Price Appraisal Ratio. Paper presented at the OECD-IMF Workshop on Real Estate Price Indexes, Paris, 6-7 November 2006.

White, H. (1980). A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica, 48, 817-838.

Previous

Report a problem on this page

Is something not working? Is there information outdated? Can't find what you're looking for?

Please contact us and let us know how we can help you.

Privacy notice

Date modified: