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1 3 23 4

... 1 2... 3 3... 6 4... 10 4.1... 10 4.2... 14 4.2.1... 14 4.2.2... 16 4.2.3... 17 4.2.4 WASEDA / REINS... 19 4.3... 22 5... 25 5.1... 25 5.2... 26 5.3 S&P/... 29 5.4... 32 5.5... 32 5.6... 33 I. Bailey, Muth and Nourse(1963)... 34 II. Shiller(1991)... 37 III. (Weighted Least Square Method, WLS)... 39... 41

1 2008 3 90 1 2009-1 - WASEDA/CIRE All rights reserved.

2 S&P500 2006 75% 13% 1995 2008-2 - WASEDA/CIRE All rights reserved.

(de novo) 2 2 150 165 10% =(165-150)/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. - 3 - WASEDA/CIRE All rights reserved.

ARES J J ARES 2002 4 3 3-4 - WASEDA/CIRE All rights reserved.

repeat-sales regression, RSR same-property price-change index. Federal Housing Finance Agency 4 Housing Price Index 5 6 4 Office of Federal Housing Enterprise Oversight (OFHEO) 5 6-5 - WASEDA/CIRE All rights reserved.

7 3 Yale Shiller 1991 1993 Case and Shiller(1987, 1989) 7 Yale Shiller MIT Geltner EU EU EU - 6 - WASEDA/CIRE All rights reserved.

de novo 1 1 2 2009 3 6-7 - WASEDA/CIRE All rights reserved.

4 3 M&A consistency 5 (availability) - 8 - WASEDA/CIRE All rights reserved.

6 8 MIT 8 2-9 - WASEDA/CIRE All rights reserved.

4 4.1 1 4.1.1 4.1.1 0 n.a. 1 5 1 6 4.1.1-10 - WASEDA/CIRE All rights reserved.

4.1.1 9 4.1.2 20+ 30+ 42+ 68 160 1( 1) = = = 1.10 (1) 18+ 27+ 40+ 60 145 22+ 34+ 62 118 2 ( 2) = = = 1.24 (2) 18+ 27+ 50 95 4.1.2 2 4.1.3 2006 2008 2007 2008 4.1.3 2006 2007 2008 3000 3300 3500 3500 9.1.2 II. Shiller(1991) - 11 - WASEDA/CIRE All rights reserved.

2006 4.1.4 4.1.4 0 1 2 log3000 log3300 log3500 log3500 4.1.4 I 2 0.095( log 3300 log 3000 ) II 1 2 0 log3500 log3500 ) 4.1.5 4.1.5 0 1 2 0 0.095 0 0 4.1.5 4.1.5 4.1.5 0 1 b01, 0 2 b02 1 2 b12 4.1.5 b02 0.095 b12=0 b01 b02 b12 b01 0.095 0 1 0.095 1 1 0 0.095=0.095 2 2 0.095 0 0.095 β 2007 β e =1.1 e 2008 =1. 1 3 100 1 110 2 110 1 10 2 0 Bailey, Muth and Nourse(1963) - 12 - WASEDA/CIRE All rights reserved.

1 2 10 1,0,1 3 0 1 1 4.1.6 4.1.6 2007 2008 0 1 1 1 2007 2007 2008 2008 4.1.5 4.1.6 β β 2007 2007 0 + β 2008 1 = 0.095 ( 1) + β 1 = 0 2008 4 β = 0. 2007 095 β = 0. 2008 095 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 2 1 0 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, 933-42. 11 I.Bailey, Muth and Nourse(1963) - 13 - WASEDA/CIRE All rights reserved.

P t βt β B = P e (7) B 100 ( ) 4.2 Bailey, Muth and Nourse(1963) 2 4.2.1 2 1 0 1 3 (Arithmetic average) - 14 - WASEDA/CIRE All rights reserved.

12 13 2 2 1, 0, 1 3 0 1 14 0 1 15 16 0 1 2 12 13 Case and Shiller 87 AREUEA 89 American Economic Review 2 89 87 Shiller 91 ARS S&P 91 ARS 14 GRS 3 15 Maddla, G.S. 1992. Introduction to Econometrics, 2 nd Ed. Prentice Hall 7, Green, W.H.1997. 16 GRS VIF(Variance-Inflation Factor) 2009-15 - WASEDA/CIRE All rights reserved.

Shiller(1991) 17 II 4.2.2 Case and Shiller 1987 18 weighted least squares estimator (WLS) III WLS OLS 1 2 WLS 1 2 17 Shiller, J.S.(1991) Arithmetic Repeat Sales Price Estimators, Journal of Housing Economics 1, 110-126. 18 K.Case & R.Shiller, Prices of Single Family Homes Since 1970: New Indexes for Four Cities, New England Economic Review: 45-56, Sept/Oct 1987. - 16 - WASEDA/CIRE All rights reserved.

N H e = N + H GLS 4.2.3 WLS,GLS GMM Bayes Goetzmann (1992) 19 20 (Shrinkage Estimator) 19 Goetzmann, William.1992, The Accuracy of Real Estate Indices; Repeat Sale Estimators, Journal of Real Estate Finance and Economics, 5:5-53 20 ARS - 17 - WASEDA/CIRE All rights reserved.

21 Goetzmann. and Peng 2002) 22 0 1 MLE Peng (2002) 23 Shiller(1991,1993) GLS GMM Markov Chain Monte Carlo method, MCMC 21 2005 22 Goetzmann, William. and Liang Peng, 2002. The Bias of the RSR Estimator and the Accuracy of Some Alternatives, Real Estate Economics V30-1:13-39. 23 Peng, Liang.2002, GMM Repeat Sales Price Indices, Real Estate Economics V30-2:239-261. - 18 - WASEDA/CIRE All rights reserved.

4.2.4 WASEDA / REINS 10 WASEDA / REINS 4.2.4 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 10 4.2.4 6 I VI VII X 4 4.2.5 4.2.6 1993 6 ~2008 12-19 - WASEDA/CIRE All rights reserved.

240 220 200 180 W/R W/R W/R W/R 160 140 120 100 80 1993/6 1993/12 1994/6 1994/12 1995/6 1995/12 1996/6 1996/12 1997/6 1997/12 1998/6 1998/12 1999/6 1999/12 2000/6 2000/12 2001/6 2001/12 2002/6 2002/12 2003/6 2003/12 2004/6 2004/12 2005/6 2005/12 2006/6 2006/12 2007/6 2007/12 2008/6 2008/12 2003 10 / CS( ) W/R-I / CS( ) W/R-IV / CS(GMM) W/R-V / CS(MCMC) W/R- 1993 6 ~2008 12 4.2.5 / ARS 240 220 200 180 W/R W/R W/R W/R W/R 160 140 120 100 80 1993/6 1993/12 1994/6 1994/12 1995/6 1995/12 1996/6 1996/12 1997/6 1997/12 1998/6 1998/12 1999/6 1999/12 2000/6 2000/12 2001/6 2001/12 2002/6 2002/12 2003/6 2003/12 2004/6 2004/12 2005/6 2005/12 2006/6 2006/12 2007/6 2007/12 2008/6 2008/12-20 - WASEDA/CIRE All rights reserved.

2003 10 / CS( ) W/R- / CS(GMM) W/R-V / CS(MCMC) W/R- / FHFA W/R- / HKU W/R- / MIT W/R- 1993 6 ~2008 12 4.2.6 / ARS-2 GRS-3 GRS ARS 4.2.7 10 / 4.2.7 / ( ) WASEDA/REINS- ARS 0.015 GLS WASEDA/REINS- ARS 0.013 GLS WASEDA/REINS- ARS 0.013 GLS 2 WASEDA/REINS- ARS 0.010 GLS WASEDA/REINS- ARS 0.013 GMM WASEDA/REINS- ARS 0.005* MCMC WASEDA/REINS- GRS 0.025 GLS WASEDA/REINS- GRS 0.025 GLS 2 WASEDA/REINS- GRS 0.025 OLS WASEDA/REINS- GRS 0.023 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 3-21 - WASEDA/CIRE All rights reserved.

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 24-22 - WASEDA/CIRE All rights reserved.

1) 6 25 2) 1993 1993 3) 4) 5) 25-23 - WASEDA/CIRE All rights reserved.

6) 7) - 24 - WASEDA/CIRE All rights reserved.

5 4 5.1 2011 2 26 +2.5% 2010 2 13 5.1.1 1993 6 2005 2 59.5% 2005 2 2007 10 +13.6% 2010 5.1.1 0% 5.1.1 26-25 - WASEDA/CIRE All rights reserved.

5.1.2 1993/6 2005/5 2007/10 2009/6 2011/2 194.30 78.65 89.32 77.94 83.36-59.5% 13.6% -12.7% 7.0% 2011 2 83.36 2008 9 83.64 2009 6 77.94 +7% 5.1.2 2007 10 2009 6 5.1.3 5.1.3 2000 5.2 5.2.1 2006 5.2.2-26 - WASEDA/CIRE All rights reserved.

4 10% 5.2.1-27 - WASEDA/CIRE All rights reserved.

5.2.2 2000 2009 2011 2 +8.0% +6.0% +6.8% +6.3% 5.2.3 2010 2-28 - WASEDA/CIRE All rights reserved.

77.94 81.12 77.68 68.73 67.44 2009/6 2009/6 2009/8 2009/9 2009/6 2011/2 83.36 87.59 82.37 73.43 71.69 7.0% 8.0% 6.0% 6.8% 6.3% 5.2.3 5.3 S&P/ 27 5.3.1 2006 7 2007 11 2009 4 2009 6 27 S&P/ 10-29 - WASEDA/CIRE All rights reserved.

5.3.1 Standard&Poor s 2006 5.3.2 5.3.3 2010 2 2010 6 5% 2010 11-30 - WASEDA/CIRE All rights reserved.

Standard&Poor s 5.3.2 Standard&Poor s 5.3.3-31 - WASEDA/CIRE All rights reserved.

5.4 Standard&Poor s 5.4 5.5 0.3 0.5% 1 1.5% 5.5. 1995 1 2011 1-0.29% -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% 192 192 192 192 192 192 192 192 192-32 - WASEDA/CIRE All rights reserved.

5.6 1993/12-6.9% -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% - 33 - WASEDA/CIRE All rights reserved.

I. Bailey, Muth and Nourse(1963) Geometric average Repeat Sales regression: GRS = = = = = = = 1. Pnt n t 1. 5 2 2 3 0 0 5 1 3 4 2 1 2 0 1. 0 1 2 1 P10 P11 0 2 P20 P21 0 3 P30 0 P32 4 P40 0 P42 5 0 P51 P52 y = Zγ + e ( ) - 34 - WASEDA/CIRE All rights reserved.

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 = 0 0 1 0 0 1 1 1 ( 3) Z T-1 N N T Z 1,1 0 n t 1 2 1 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 = 3 3 28 GRS GRS 28-35 - WASEDA/CIRE All rights reserved.

1 GRS GRS 29 GRS GRS GRS 29-36 - WASEDA/CIRE All rights reserved.

II. Shiller(1991) 1. 30 1. 0 1 2 1 P10 P11 0 2 P20 P21 0 3 P30 0 P32 4 P40 0 P42 5 0 P51 P52 Y = Xβ + U (2 1) Y X U 0 Y Y P P P P 0 10 20 30 40 (2 2) Y 0 P (n,t) (n) (t) X 30 S&P/Case-Shiller Home Price Indices, Index Methodology, March 2008-37 - WASEDA/CIRE All rights reserved.

X P11 P21 = 0 0 P 51 0 0 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 = 0 0 1 0 0 1, 1 1 (2 5) - 38 - WASEDA/CIRE All rights reserved.

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 30 40 1 51 1 ˆ β 2 P 52 5 2 (2 6) (2 6) 31 III. (Weighted Least Square Method, WLS) n wn ˆ β ˆ β 1 1 1 2 = Index 1 = Index 2 w1 P11 + w2p21 + w5p51 = w P + w P + w ˆ β P 1 3 10 30 2 4 20 w3p32 + w4p42 + w5p52 = w P + w P + w ˆ β P 40 5 5 2 1 52 51, (3 1) (3 1) 31 revision error - 39 - WASEDA/CIRE All rights reserved.

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 - 40 - WASEDA/CIRE All rights reserved.

β = 1 1 1 ( 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 2000 1 100.0 ( 1 ) (chain-weighting procedure) ˆ t β 32 33 S&P/Case-Shiller Home Price Indices, Index Methodology, March 2008-41 - WASEDA/CIRE All rights reserved.

β 1 ˆ 1 X 0 0 = P P P, ˆ β 0P ˆ β 0P = ˆ β 0P ˆ β 0P ˆ β1p 10 40 51, 20 32 Y Z 30 42 52 0 0 = 1 1 1 X Z ˆ β 1 2 ˆ β = Index = w P + w + w 1 3 32 4 42 5 52 2 2 w ˆ 3β 0P ˆ ˆ 30 + w4β 0P40 + w5β1 P P P 51 ˆ β1p51 5 1 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 - 42 - WASEDA/CIRE All rights reserved.

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 n3 103-0027 1-4-1 5 E-mail waseda@cire-research.org - 43 - WASEDA/CIRE All rights reserved.