都道府県別パネル・データを用いた均衡地価の分析: パネル共和分の応用
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1 No.04-J * yumi.saita@boj.or.jp ** towa.tachibana@boj.or.jp *** **** toshitaka.sekine@boj.or.jp * ** *** London School of Economics ****
2 : Λ y z x 4 3 / 1 (panel cointegration) Meese and Wallace (1994) Clayton (1997) (1992) (2) (2) Λ y yumi.saita@boj.or.jp z towa.tachibana@boj.or.jp x London School of Economics toshitaka.sekine@boj.or.jp 1
3 (0) (no-arbitrage condition) 4 (error correction model) i t P it p it = j i V j,t 1 j i V j,t 1 p jt. P jt i j 1 V jt P jt ,866 3,254 2
4 SNA (1997) (1999) (3) : (i) (ii) (2) (3) (ii) (i) SNA 6 SNA / SNA 6 SNA % 2 0.3% % 10% % +0.2% 3.1% 4.1% 2.7% 3.9% 3 2 3
5 1: (1) SNA (CY1985 = ) (2) (CY1985 = ) ( ) 4
6 40 2: (1) (2) (3) (4) ( ) 5
7 / PVR PVR Present Value Relation (2) PVR Y it +(P e i,t+1 P it )=r it P it, (1) Y it P e i,t+1 r it i t τ it r it = i t + τ it (1) no-arbitrage condition 1 Y it Pi,t+1 e P it (1990) (2) (1) P it = Y it + P e i,t+1 1+r it, P e i,t+1 P e i,t+2... E t t Ω t E[. Ω t ]h =1,... P e i,t+h = 6
8 3: (%) Tokyo Osaka Fukuoka Hokkaido Aichi Kanagawa Tochigi Tottori Fukui Nagano (1995 ) ( ) E t [P e i,t+h] [ { h ( P it = E t h=1 k=1 1 1+r i,t+k )} Y i,t+h + lim ( h h k=1 1 1+r i,t+k ) P i,t+h ]. (2) [ ( ) ] h 1 E t lim P i,t+h =0, h k=1 1+r i,t+k r i,t+k t r it Y it g e it 7
9 (2) P it = Y it, (3) r it git e (3) PVR (3) Meese and Wallace (1994) Clayton (1997) (1) / PVR PVR (i) (ii) (2) PVR 5 (1) PVR p it = αp e i,t+1 + βy it γr it + d t + η i + ν it. (4) p it p e it y it P it P e it Y it d t η i ν it idiosyncratic shock Campbell and Shiller (1988a,b) (1) ρ κ 6 p it ρp e i,t+1 +(1 ρ)y it r it + κ (1) P t i Y t + P e t+1 P t =1+r t. ln(1 + r t ) r t δ t =ln(y t 1 /P t )=y t 1 p t h t = ln(exp(δ t δ t+1 )+exp(δ t )) + y t, δ t δ ρ =1/(1 + exp(δ)) κ = ln(1 + exp(δ)) δ exp(δ)/(1 + exp(δ)) h t (δ t,δ t+1 ) δ t δ t+1 h t (δ, δ) 1 8
10 (4) α + β =1 γ =1 y it (3) p it = φy it ψ ln(r it g e it)+d t + η i + ν it, (5) φ = ψ =1 (4) 3.2 (Panel Cointegration Test) (i) P it (ii) Y it 7 (iii) i t (iv) τ it 8 (v) g e it 3 (vi) 1 p e i,t+1 PF Nishimura et al. (1999) ARIMA(2,1,0) 2 Hadri (0) panel unit-root test x it x it (1/N ) N i=1 x it (1999) (1990) τ it (i) (ii) (iii) (2) 9
11 1: (Hadri) 1 p 11.20** (0.00) 1.31 (0.09) y 21.06** (0.00) 1.18 (0.12) r 9.63** (0.00) 2.03* (0.02) ( 1) NPT1.3 (Chiang and Kao, 2) ( 2) ** * 1% 5% ( ) p kernel 2 Maddala and Wu (1999) 1 x it 3 1 p it y it I(1) r it 5% I(2) ADF Fisher I(1) I(1) (4) (5) Pedroni (0, 1) Group- Mean Fully Modified OLS (FMOLS) Group-Mean FMOLS (A) Within Group p WG it = p it (1/T ) T t=1 p it η i (B) FMOLS (C) (group-mean) Phillips and Hansen (1990) FMOLS Group-Mean FMOLS t (4) α t H 0 i α i =0 H 1 α i 0 (B) Within Group FMOLS H 0 H 1 i α i = α A 0α i α A t Group-Mean 12 Group-Mean FMOLS 10
12 Hadri x it x it (1/N ) N i=1 x it kernel 2 () t 7 Pedroni (1999) variance-ratio test panel ν panel/group ρ panel/group PP panel/group ADF 9 PVR (4) p it =0.85p e it +0.17y it 3.30r it, (7.26) (16.9) (6.96) (6) panel ρ: 0.88, panel PP: 4.21, panel ADF: 5.02, panel ν: 5.16, group ρ: 0.68, group PP: 4.61, group ADF: PVR (4) p it =0.88p e it +0.14y it 0.56r it, (10.9) (28.9) (4.00) (7) panel ρ: 0.83, panel PP: 3.37, panel ADF: 7.48, panel ν: 3.97, group ρ: 1.74, group PP: 2.20, group ADF: (5) p it =0.86y it 0.90 ln(r it git), e (1.82) (33.6) (8) panel ρ: 3.94, panel PP: 4.98, panel ADF: 4.06, panel ν: 2.42, group ρ: 6.15, group PP: 7.41, group ADF: panel ν panel/group ρ panel/group PP Phillips-Perron non-parametric panel/group ADF parametric (4) (5) ν it ν i,t 1 ρ ν i H 0 : ρ ν i = 1 for all i(i) panel H 1 : ρ ν i = ρν < 1 for all i (ii) group H 1 : ρ ν i < 1 for all i Pedroni (1999) Group-Mean FMOLS RATS PAN- GROUP.PRG PANCOINT.PRG panel.shtml 11
13 4: p 5.25 (1) (2) () (3) p p * (ARIMA) p * (PF) p * (FM) ( ) p PF (6) (PVR ) ARIMA (7) (PVR ) FM (8) ( ) / PVR (6) (7) ρ α + β =1 t (6) (7) (8) 4 PVR 1990 / 12
14 PVR PVR 4 ECM ECM Error Correction Model p it = θ(p p ) i,t 1 + λ z it + ε it. (9) ECM (p p ) i,t 1 z it ε it z it r it r it y it y it 3. n it p s i,t
15 5: 0.2 p p * 0.4 p s y r n 0.3 c NPL ( ) 14
16 p s it = h w i ht p ht, w i ht i h T iht h w i ht = T iht / h T iht 5. c i,t NPL i,t (3) II II (3)
17 heterogeneous heterogeneous Hsiao (1986) 11 Swamy (1970) Random Coefficients Model (9) p it = θ i (p p ) i,t 1 + λ i z it + ε it, θ i = θ + ξ i,λ i = λ + ζ i, θ λ ξ i ζ i (i) OLS (ii) θ λ efficient 2 (1) H β Random Coefficients Model 2 (2) GDP ȳ t (1) 1 5 y it GDP 2 (1) 2 (2) (1) heterogeneous Pesaran and Smith (1995) Group-Mean FMOLS heterogeneity 16
18 2: ECM (1) (2) p it p it FY1977-FY1 FY1977-FY2 (p p ) i,t (0.11)*** 0.61 (0.10)*** r it 0.46 (0.27)* 1.04 (0.32)*** y it 0.32 (0.09)*** ȳ t 0.03 (0.01)*** n it 2.47 (1.09)** 2.56 (0.91)*** p s i,t (0.06)*** 0.22 (0.05)*** c i,t (0.05)*** 0.30 (0.05)*** NPL i,t (0.20)*** 0.78 (0.18)*** 0.05 (0.01)*** 0.04 (0.01)*** ,175 1,222 H β [0.00] 1.2 [0.00] ( 1) Random Coefficients Model RATS version 5.1 SWAMY.PRG ( 2) ( ) *** ** * 1% 5% 10% ( 3) H β K(n 1) χ 2 K n [ ] p 17
19 6: 15% 10% 5% 0% -5% -10% -15% -20% -25% -30% -35% d % 0% -5% -10% -15% -20% % 4% 2% 0% -2% -4% -6% -8% -10% -12%
20 7: (%) (%) % 1990 (i) (ii)
21 PVR / 3. 20
22 (3) 21
23 (Panel Unit-Root Test) Hadri Fisher ADF 3 p it y it r it 1 ADF (Augmented Dicky-Fuller Test) ADF 1 p y r I(2) 1 I(2) 1 I(1) power Maddala and Wu (1999) (Fisher ) Fisher (i =1,..., N) x it p i x it = ρ i x i,t 1 + θ ij x i,t j + α i + ɛ it, (10) ADF ρ i p (π i ) j=1 N λ = 2 ln π i, i=1 ɛ it x it λ 2N χ 2 x it H 0 : ρ i = 0 for all i H 1 : ρ i < 0 for at least one i 22
24 3: ADF p p y y r r (1) * (1) (2) ** (2) (0) (1) ** (1) (0) -0.3 (0) ** (0) * (0) (0) ** (1) (0) (1) ** (1) (0) (1) ** (1) (0) (0) (0) (0) (1) ** (1) (0) (2) ** (2) (0) (0) ** (1) (0) (0) ** (0) * (0) (0) ** (3) (2) (0) (0) (0) (1) ** (1) (1) (0) ** (0) (0) (1) ** (3) (2) (2) ** (2) (0) (1) ** (1) (1) (0) ** (0) (0) (1) ** (1) (0) (0) (0) (0) (1) ** (1) (0) -2.2 (2) ** (2) (0) (1) ** (1) (0) -1.4 (0) (0) (1) (0) * (1) (0) * (0) ** (0) (0) (1) ** (1) (0) (0) ** (0) (0) -1. (1) ** (1) (0) -1.5 (1) ** (1) (0) (1) ** (1) (0) (2) ** (2) (0) (1) ** (1) (0) (1) ** (1) (0) (1) ** (1) (0) (0) ** (0) (0) (1) ** (1) (1) (0) ** (0) (0) (1) ** (3) (2) (2) ** (2) (0) (1) ** (3) (1) (1) ** (1) (0) (1) ** (1) (1) (2) ** (2) (0) (1) ** (2) (1) (1) ** (1) (0) (1) ** (3) (2) (0) ** (0) * (0) (1) ** (2) (1) (3) ** (3) (0) (1) ** (1) (0) (2) -4.8** (2) (0) (1) ** (2) (2) -2.8 (2) ** (2) (0) (1) ** (3) (2) (0) ** (0) (0) (1) ** (1) (1) * (0) * (0) ** (0) (1) ** (1) (1) (1) ** (1) (0) (1) ** (3) ** (2) (0) ** (0) ** (0) (0) ** (1) (0) (0) * (0) (0) (1) ** (1) (1) (0) (0) (0) (1) ** (1) (0) (0) ** (0) (0) (1) ** (3) (3) (1) ** (1) (0) (1) ** (1) (0) (0) (0) (0) (1) ** (1) (2) (2) ** (2) (0) (1) ** (1) (0) (0) (0) (0) (1) ** (1) (0) (0) * (0) (0) (1) ** (1) (0) (2) ** (2) (0) (1) ** (1) (0) (0) -5.6** (0) (0) (1) ** (1) (1) (0) ** (0) (0) (1) ** (1) (2) (0) ** (0) (0) (1) ** (1) (3) (3) ** (3) (0) (0) ** (1) (0) (3) ** (3) (0) (1) ** (1) (0) (0) ** (0) (0) (1) ** ( ) ( ) ADF 10% ADF-t ** * 1% 5% 23
25 4: (Fisher) 1 Fisher 1% 5% Fisher 1% 5% p * * y ** ** r ** ( 1) ** * 1% 5% 1% 5% critical value 10,000 Bootstrap ( 2) Ox (Doornik, 1) ɛ it Maddala and Wu (1999) χ 2 Bootstrap critical value ɛ it Bootstrap I(0) 1 I(1) IPS Im, Pesaran, and Shin (3) Levin-Lin Test Levin, Lin, and Chu (2) H 1 : ρ i = ρ<0 ρ IPS Maddala-Wu 13 Bootstrap 1. (10) 10%Fisher 2. x it = ρ 0 i x i,t 1 + ɛ 0 it ɛ0 it Maddala and Kim (1999) S 3 3. ɛ 0 it Bootstrap ɛ it 4. x it = x i,t 1 + ρ0 i x i,t 1 + ɛ it ɛ it x it x i0 x i1 x it 2 5. x it 1 Fisher ,000 10,000 Fisher 1% critical value 0 5% critical value 24
26 Hadri size Fisher Maddala and Wu (1999) Levin-Lin IPS power size 25 size size ADF Fisher 10% 20% (10) p i x it = ρ i x i,t 1 + θ ij x i,t j + α i + δ i t + ɛ it, j=1 Fisher % Bootstrap Herwartz and Reimers (2) wild bootstrap 25
27 τ it =. (1997) SNA τ it (%) (%) (%) (%) (%)
28 (2): pp (1992): pp ,. (1997): pp (2): (PVR) pp (2): pp (0): pp , 10. (1990): pp (1999): 2025 pp. 2 7,. (3): Working Paper (3): 22(1), (3): 1990 Working Paper (1990): pp (2): pp (3): DP/
29 (2): pp (1999):. (1997): 35 pp (2): pp ,. Campbell, J. Y., and R. J. Shiller (1988a): The Dividend-Price Ratio and Expectations of Future Dividends and Discount Factors, Review of Financial Studies, 1(3), (1988b): Stock Prices, Earnings, and Expected Dividends, Journal of Finance, XLIII, Chiang, M.-H., and C. Kao (2): Nonstationary Panel Time Series Using NPT 1.3 A User Guide, mimeo. Clayton, J. (1997): Are Housing Price Cycles Driven by Irrational Expectations?, Journal of Real Estate Finance and Economics, 14(3), Doornik, J. A. (1): Ox 3.0: Object-Oriented Matrix Programming Using Ox. Timberlake Consultants Press, London, fourth edn. Hadri, K. (0): Testing for Stationarity in Heterogeneous Panel Data, Econometric Journal, 3, Herwartz, H., and H.-E. Reimers (2): Testing the Purchasing Power Parity in Pooled Systems of Error Correction Models, Japan and the World Economy, 14, Hsiao, C. (1986): Analysis of Panel Data. Cambridge University Press, Cambridge. Im, K. S., M. H. Pesaran, and Y. Shin (3): Testing for Unit Roots in Heterogeneous Panels, Journal of Econometrics, 115, Levin, A., C.-F. Lin, and C.-S. J. Chu(2): Unit Root Tests in Panel Data: Asymptotic and Finite-Sample Properties, Journal of Econometrics, 108, Maddala, G. S., and I.-M. Kim (1999): Unit Roots, Cointegration, and Structural Change. Cambridge University Press, Cambridge. 28
30 Maddala, G. S., and S. Wu (1999): A Comparative Study of Unit Root Tests with Panel Data and a New Simple Test, Oxford Bulletin of Economics and Statistics, pp , Special Issue. Meese, R., and N. Wallace (1994): Testing the Present Value Relation for Housing Prices: Should I Leave My House in San Francisco?, Journal of Urban Economics, 35, Nishimura, K. G., F. Yamazaki, T. Idee, and T. Watanabe (1999): Discretionary Taxation, Excessive Price Sensitivity, and Japanese Land Prices, NBER Working Paper, No Pedroni, P. (1999): Critical Values for Cointegration Tests in Heterogeneous Panels with Multiple Regressors, Oxford Bulletin of Economics and Statistics, 61(4), , Special Issues. (0): Fully Modified OLS for Heterogeneous Cointegrated Panels, Advances in Econometrics, 15, (1): Purchasing Power Parity Tests in Cointegrated Panel, Review of Economics and Statistics, 83(4), Pesaran, M. H., and R. Smith (1995): Estimating Long-Run Relationships from Dynamic Heterogeneous Panels, Journal of Econometrics, 68, Phillips, P. C. B., and B. E. Hansen (1990): Statistical Inference in Instrumental Variables Regression with I(1) Process, Review of Economic Studies, 57(1), Swamy, P. A. V. B. (1970): Efficient Inference in a Random Coefficient Regression Model, Econometrica, 38(2),
31 : Hokkaido SNA base Simple Average Weighted Average 125 Aomori Iwate 75 Miyagi 1 Akita 1 Yamagata 1 Fukushima 1 Ibaraki 1 Tochigi 1 Gunma Saitama 300 Chiba Tokyo Kanagawa 1 Niigata 1 Toyama 1 Ishikawa 1 Fukui ( ) 1985 SNA base Simple Average Weighted Average 30
32 : Yamanashi SNA base Simple Average Weighted Average 1 Nagano 1 Gifu 1 Shizuoka 300 Aichi 1 Mie Shiga 400 Kyoto 400 Osaka Hyogo Nara Wakayama 1 1 Tottori 1 Shimane Okayama 1 Hiroshima Yamaguchi Tokushima 1 1 ( ) 1985 SNA base Simple Average Weighted Average 31
33 : 1 Kagawa SNA base Simple Average Weighted Average 1 Ehime 1 Kochi 1 Fukuoka 1 Saga 1 Nagasaki Kumamoto 1 Oita Miyazaki Kagoshima 1 Okinawa ( ) 1985 SNA base Simple Average Weighted Average 32
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