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2 WASEDA / REINS S&P/ I. Bailey, Muth and Nourse(1963) II. Shiller(1991) III. (Weighted Least Square Method, WLS)
3 WASEDA/CIRE All rights reserved.
4 2 S&P % 13% WASEDA/CIRE All rights reserved.
5 (de novo) % =( )/150 10% 10% 2 Geltner and Pollakowski (2006) A Set of Indexes for Trading Commercial Real Estate Based on the Real Capital Analytics Transaction Prices Database, MIT/CRE WASEDA/CIRE All rights reserved.
6 ARES J J ARES WASEDA/CIRE All rights reserved.
7 repeat-sales regression, RSR same-property price-change index. Federal Housing Finance Agency 4 Housing Price Index Office of Federal Housing Enterprise Oversight (OFHEO) WASEDA/CIRE All rights reserved.
8 7 3 Yale Shiller Case and Shiller(1987, 1989) 7 Yale Shiller MIT Geltner EU EU EU WASEDA/CIRE All rights reserved.
9 de novo WASEDA/CIRE All rights reserved.
10 4 3 M&A consistency 5 (availability) WASEDA/CIRE All rights reserved.
11 6 8 MIT WASEDA/CIRE All rights reserved.
12 n.a WASEDA/CIRE All rights reserved.
13 ( 1) = = = 1.10 (1) ( 2) = = = 1.24 (2) II. Shiller(1991) WASEDA/CIRE All rights reserved.
14 log3000 log3300 log3500 log I ( log 3300 log 3000 ) II log3500 log3500 ) b01, 0 2 b b b b12=0 b01 b02 b12 b = β 2007 β e =1.1 e 2008 = Bailey, Muth and Nourse(1963) WASEDA/CIRE All rights reserved.
15 ,0, β β β = ( 1) + β 1 = β = β = Bailey, Muth and Nourse(1963) 11 T ( ln MRt Di, t ) ln i ln Pi, t ln P 2 i, t = + 1 t= 1 ω 5 t i D, t 1 1 t ln MRt lnω i 0 ln MRt β t 0 t i t MR t βt = e 6 PB t 10 Bailey, Martin J., Muth, Richard F. and Nourse, Hugh O., A Regression Method for Real Estate Price Index Construction, Journal of the American Statistical Association, December 1963, 58, I.Bailey, Muth and Nourse(1963) WASEDA/CIRE All rights reserved.
16 P t βt β B = P e (7) B 100 ( ) 4.2 Bailey, Muth and Nourse(1963) (Arithmetic average) WASEDA/CIRE All rights reserved.
17 , 0, Case and Shiller 87 AREUEA 89 American Economic Review Shiller 91 ARS S&P 91 ARS 14 GRS 3 15 Maddla, G.S Introduction to Econometrics, 2 nd Ed. Prentice Hall 7, Green, W.H GRS VIF(Variance-Inflation Factor) WASEDA/CIRE All rights reserved.
18 Shiller(1991) 17 II Case and Shiller weighted least squares estimator (WLS) III WLS OLS 1 2 WLS Shiller, J.S.(1991) Arithmetic Repeat Sales Price Estimators, Journal of Housing Economics 1, K.Case & R.Shiller, Prices of Single Family Homes Since 1970: New Indexes for Four Cities, New England Economic Review: 45-56, Sept/Oct WASEDA/CIRE All rights reserved.
19 N H e = N + H GLS WLS,GLS GMM Bayes Goetzmann (1992) (Shrinkage Estimator) 19 Goetzmann, William.1992, The Accuracy of Real Estate Indices; Repeat Sale Estimators, Journal of Real Estate Finance and Economics, 5: ARS WASEDA/CIRE All rights reserved.
20 21 Goetzmann. and Peng 2002) MLE Peng (2002) 23 Shiller(1991,1993) GLS GMM Markov Chain Monte Carlo method, MCMC Goetzmann, William. and Liang Peng, The Bias of the RSR Estimator and the Accuracy of Some Alternatives, Real Estate Economics V30-1: Peng, Liang.2002, GMM Repeat Sales Price Indices, Real Estate Economics V30-2: WASEDA/CIRE All rights reserved.
21 4.2.4 WASEDA / REINS 10 WASEDA / REINS WASEDA/REINS / CS( ) WASEDA/REINS- ARS / CS( ) WASEDA/REINS- ARS / CS( ) WASEDA/REINS- ARS / CS( ) WASEDA/REINS- ARS / CS(GMM ) WASEDA/REINS- ARS / CS(MCMC ) WASEDA/REINS- ARS / CS(87) WASEDA/REINS- GRS / FHFA WASEDA/REINS- GRS / HKU WASEDA/REINS- GRS / MIT WASEDA/REINS- GRS ARS(Arithmetic Repeat Sales method ) GRS Geometric Repeat Sales method WASEDA/REINS I VI VII X ~ WASEDA/CIRE All rights reserved.
22 W/R W/R W/R W/R /6 1993/ /6 1994/ /6 1995/ /6 1996/ /6 1997/ /6 1998/ /6 1999/ /6 2000/ /6 2001/ /6 2002/ /6 2003/ /6 2004/ /6 2005/ /6 2006/ /6 2007/ /6 2008/ / CS( ) W/R-I / CS( ) W/R-IV / CS(GMM) W/R-V / CS(MCMC) W/R ~ / ARS W/R W/R W/R W/R W/R /6 1993/ /6 1994/ /6 1995/ /6 1996/ /6 1997/ /6 1998/ /6 1999/ /6 2000/ /6 2001/ /6 2002/ /6 2003/ /6 2004/ /6 2005/ /6 2006/ /6 2007/ /6 2008/ WASEDA/CIRE All rights reserved.
23 / CS( ) W/R- / CS(GMM) W/R-V / CS(MCMC) W/R- / FHFA W/R- / HKU W/R- / MIT W/R ~ / ARS-2 GRS-3 GRS ARS / / ( ) WASEDA/REINS- ARS GLS WASEDA/REINS- ARS GLS WASEDA/REINS- ARS GLS 2 WASEDA/REINS- ARS GLS WASEDA/REINS- ARS GMM WASEDA/REINS- ARS 0.005* MCMC WASEDA/REINS- GRS GLS WASEDA/REINS- GRS GLS 2 WASEDA/REINS- GRS OLS WASEDA/REINS- GRS Ridge *MCMC / 0.5% 2.5 2% 2% MCMC WASEDA/REINS-VI WASEDA/REINS -IV 3 1 WASEDA/REINS -II 2 WASEDA/REINS - WASEDA/REINS -V WASEDA/CIRE All rights reserved.
24 MCMC WASEDA/REINS -VI WASEDA/REINS -IV WASEDA/REINS -IV WASEDA/REINS - WASEDA/REINS -IV WASEDA/REINS- 30bps 30bps 4.3 / 2 WASEDA/REINS-I WASEDA/REINS-II 24 10bps WASEDA/CIRE All rights reserved.
25 1) ) ) 4) 5) WASEDA/CIRE All rights reserved.
26 6) 7) WASEDA/CIRE All rights reserved.
27 % % % % WASEDA/CIRE All rights reserved.
28 /6 2005/5 2007/ /6 2011/ % 13.6% -12.7% 7.0% % WASEDA/CIRE All rights reserved.
29 4 10% WASEDA/CIRE All rights reserved.
30 % +6.0% +6.8% +6.3% WASEDA/CIRE All rights reserved.
31 /6 2009/6 2009/8 2009/9 2009/6 2011/ % 8.0% 6.0% 6.8% 6.3% S&P/ S&P/ WASEDA/CIRE All rights reserved.
32 5.3.1 Standard&Poor s % WASEDA/CIRE All rights reserved.
33 Standard&Poor s Standard&Poor s WASEDA/CIRE All rights reserved.
34 5.4 Standard&Poor s % 1 1.5% % -0.35% -0.44% -0.43% 0.44% 0.43% 0.18% 0.50% 0.50% -0.20% -0.30% -0.44% -0.40% 0.55% 0.42% 0.32% 0.53% 0.54% 1.08% 0.95% 1.22% 1.21% 1.34% 1.64% 1.15% 1.04% 0.98% 0.01% 0.01% 0.01% 0.01% 0.02% 0.03% 0.01% 0.01% 0.01% -3.89% -3.21% -3.70% -3.67% -3.51% -6.25% -5.59% -2.88% -2.32% 3.24% 2.55% 3.47% 2.79% 4.12% 4.85% 5.09% 2.76% 3.01% WASEDA/CIRE All rights reserved.
35 /12-6.9% -2.2% -0.9% -1.1% -4.5% 1994/6-4.5% -5.5% -3.8% -4.7% -4.7% 1994/12-7.6% -9.6% -13.2% -9.7% -8.9% 1995/6-14.9% -13.3% -14.4% -13.3% -14.3% 1995/12-7.5% -7.2% -8.6% -9.8% -7.8% 1996/6-1.8% -0.4% -1.3% -3.4% -1.6% 1996/12 0.0% -0.2% -1.0% 2.6% 0.1% 1997/6-3.0% -3.7% -3.4% -5.8% -3.5% 1997/12-3.7% -4.2% -6.1% -5.0% -4.2% 1998/6-4.3% -6.9% -4.7% -4.7% -5.0% 1998/12-2.6% -4.1% -3.7% -2.5% -2.9% 1999/6-2.7% -1.8% -4.3% -4.2% -2.8% 1999/12-1.8% -4.2% -4.0% -3.2% -2.8% 2000/6-5.0% -3.7% -3.6% -3.0% -4.3% 2000/12-2.0% -4.8% -4.8% -6.1% -3.5% 2001/6-2.6% -3.6% -5.9% -2.3% -3.1% 2001/12-5.0% -3.7% -1.0% -3.4% -4.1% 2002/6 2.5% -1.7% -2.8% -3.8% 0.2% 2002/12-4.7% -0.9% -3.2% -0.6% -3.2% 2003/6-3.2% -4.1% 0.8% -5.9% -3.3% 2003/12-0.3% -0.9% -4.4% -0.8% -0.8% 2004/6-0.8% -1.4% -1.1% -1.9% -1.1% 2004/12-0.6% 0.7% 0.6% 1.1% -0.1% 2005/6 0.2% -2.0% -2.8% -0.9% -0.7% 2005/12 1.6% 0.5% 1.6% -1.0% 1.1% 2006/6 1.9% 2.0% -1.5% 0.0% 1.4% 2006/12 4.6% 3.2% -0.8% -0.3% 3.3% 2007/6 5.4% 2.5% 2.9% 1.9% 4.2% 2007/12 1.0% 1.6% -0.8% -4.6% 0.4% 2008/6-4.1% -1.3% -1.2% 1.2% -2.8% 2008/12-4.2% -2.7% -5.8% -3.2% -3.9% 2009/6-5.3% -4.2% -3.6% -5.9% -4.9% 2009/12 4.5% 3.8% 1.2% 2.0% 3.8% 2010/6 3.4% 0.5% 2.0% 4.2% 2.7% 2010/12-0.3% 0.8% 1.0% 2.2% 0.3% WASEDA/CIRE All rights reserved.
36 I. Bailey, Muth and Nourse(1963) Geometric average Repeat Sales regression: GRS = = = = = = = 1. Pnt n t P10 P P20 P P30 0 P32 4 P40 0 P P51 P52 y = Zγ + e ( ) WASEDA/CIRE All rights reserved.
37 y Z e y y P (n,t) (n) (t) P11 P10 P21 P20 y = P 32 P30 ( 2) P42 P40 P 52 P51 Z Z 1 1 = ( 3) Z T-1 N N T Z 1,1 0 n t Z (n,t) y Z (1 1) e P ˆ 11 + P21 + P51 P10 + P20 + ( P52 γ 2 ) ˆ γ 1 = 3 3 (. P ( ˆ ) 4) 32 + P42 + P52 P30 + P40 + P51 γ 1 ˆ γ 2 = GRS GRS WASEDA/CIRE All rights reserved.
38 1 GRS GRS 29 GRS GRS GRS WASEDA/CIRE All rights reserved.
39 II. Shiller(1991) P10 P P20 P P30 0 P32 4 P40 0 P P51 P52 Y = Xβ + U (2 1) Y X U 0 Y Y P P P P (2 2) Y 0 P (n,t) (n) (t) X 30 S&P/Case-Shiller Home Price Indices, Index Methodology, March WASEDA/CIRE All rights reserved.
40 X P11 P21 = 0 0 P P 32 P42 P 52 (2 3) X T-1 N N T X 0 n t Pn,t X (n,t) 5 P51 Y X (1) U (reciprocal) X X U consistent β = 1 ( Z X ) Z X (2 4) Z Z 1 1 Z = , 1 1 (2 5) WASEDA/CIRE All rights reserved.
41 Z X 1 X Z 1 Z N T-1 ˆ 1 P11 + P21 + P51 β1 = index1 = P ˆ 10 + P20 + β 2P52 (2 6) ˆ 1 P32 + P42 + P52 β 2 = index2 = P + P + ˆ β P ˆ β 2 P (2 6) (2 6) 31 III. (Weighted Least Square Method, WLS) n wn ˆ β ˆ β = Index 1 = Index 2 w1 P11 + w2p21 + w5p51 = w P + w P + w ˆ β P w3p32 + w4p42 + w5p52 = w P + w P + w ˆ β P , (3 1) (3 1) 31 revision error WASEDA/CIRE All rights reserved.
42 U n = e e (3 2) m( 2) m(1) em(1) n 1 em(2) n 2 2 1) 2) e = h + m nt nt n hnt n mn 2 m ~ N(0, σ ) m σ 2 m h ~ 2 N(0, σ ) h 2 2 2σ m + I nσ h In n WASEDA/CIRE All rights reserved.
43 β = ( Z Ω X ) Z Ω Y Ω Ω Ω Ωˆ ω = 1 n w n ω 1 n Ω n 32 S&P 33 S&P ( 1 ) (chain-weighting procedure) ˆ t β S&P/Case-Shiller Home Price Indices, Index Methodology, March WASEDA/CIRE All rights reserved.
44 β 1 ˆ 1 X 0 0 = P P P, ˆ β 0P ˆ β 0P = ˆ β 0P ˆ β 0P ˆ β1p , Y Z = X Z ˆ β 1 2 ˆ β = Index = w P + w + w w ˆ 3β 0P ˆ ˆ 30 + w4β 0P40 + w5β1 P P P 51 ˆ β1p ˆ0 β = 1. 0 n nτ (2, n) n t Indext = wnpn τ (1, n) / Indexτ (1, n) n t τ ( 2, n) w P τ ( 1, n) n t t WASEDA/CIRE All rights reserved.
45 3 n w 3 τ ( 1, n) τ ( 2, n) n1 τ ( 1, n) +1 τ ( 2, n) +1 n2, τ ( 1, n) +2 τ ( 2, n) +2 n waseda@cire-research.org WASEDA/CIRE All rights reserved.
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