No.04-J-7 4 3 * yumi.saita@boj.or.jp ** towa.tachibana@boj.or.jp *** **** toshitaka.sekine@boj.or.jp 103-8660 30 * ** *** London School of Economics ****
: Λ y z x 4 3 / 1 (panel cointegration) Meese and Wallace (1994) Clayton (1997) (1992) (2) (2) Λ y E-mail: yumi.saita@boj.or.jp z E-mail: towa.tachibana@boj.or.jp x London School of Economics E-mail: toshitaka.sekine@boj.or.jp 1
(0) 2 3 3 (no-arbitrage condition) 4 (error correction model) 3 5 2 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 1 3 1 1 31,866 3,254 2
SNA (1997) (1999) (3) : 1990 4 3 1 (i) (ii) (2) (3) (ii) (i) SNA 6 SNA / 1 2 6 1988-89 SNA 6 SNA 2 3 1985-86 1990 25% 2 0.3% 4 1990 20% 10% 2 1 1 3 4 2 2.4% +0.2% 3.1% 4.1% 2.7% 3.9% 3 2 3
1: (1) SNA 300 275 2 225 (CY1985 = ) 175 1 125 75 1980 1990 0 (2) 300 275 2 (CY1985 = ) 225 175 1 125 75 1980 1990 0 ( ) 4
40 2: (1) (2) 60 30 40 20 30 10 0 20 10 0 10 10 20 20 1975 1980 1985 1990 1995 0 1975 1980 1985 1990 1995 0 (3) (4) 40 30 20 10 0 20 15 10 5 0 10 5 20 10 1975 1980 1985 1990 1995 0 1975 1980 1985 1990 1995 0 ( ) 5
1989 3 1990 / 3 3.1 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
3: 25 2 1995 (%) 20 15 10 5 0 5 10 15 Tokyo Osaka Fukuoka Hokkaido Aichi Kanagawa Tochigi Tottori Fukui Nagano 14.5 15.0 15.5 16.0 16.5 17.0 17.5 18.0 18.5 (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
(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. 5 1 6 (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
(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 7 8 3 (1999) (1990) τ it (i) (ii) (iii) (2) 9
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
Hadri x it x it (1/N ) N i=1 x it 47 1976 1 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: 6.59. 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: 8.70. (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: 5.96. 9 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 http://www.estima.com/procs panel.shtml 11
4: p 5.25 (1) (2) () (3) 5.1 5.00 5. 5.0 4.75 5.25 4.9 4. 4.25 5.00 4.75 4.8 4.7 4.6 4.00 4. 4.5 3.75 4.25 4.4 3. 3.25 p p * (ARIMA) p * (PF) p * (FM) 4.00 3.75 4.3 4.2 ( ) p PF (6) (PVR ) ARIMA (7) (PVR ) FM (8) ( ) / PVR (6) (7) ρ α + β =1 t (6) (7) 20.03 33.24 (8) 4 PVR 1990 / 12
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 6 5 1. r it r it 1980 2. y it y it 3. n it 1980 80 90 0 4. p s i,t 1 1 2 13
5: 0.2 p p * 0.4 p s 0.1 0.2 0.0 0.1 0.0 1970 1980 1990 0 1970 1980 1990 0 0.2 y 0.125 r 0.1 0. 0.0 0.075 1970 1980 1990 0 1970 1980 1990 0 0.02 n 0.3 c 0.01 0.2 0.1 0.00 1970 1980 1990 0 0.0 1970 1980 1990 0 0.15 NPL 0.10 0.05 1970 1980 1990 0 ( ) 14
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 1 1 1989 6. NPL i,t 1 10 1 1990 (3) II II 1992 1992 (3) 1990 1990 10 15
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) 1993 6 (1) 1990 1990 2 0-1 11 heterogeneous Pesaran and Smith (1995) Group-Mean FMOLS heterogeneity 16
2: ECM (1) (2) p it p it FY1977-FY1 FY1977-FY2 (p p ) i,t 1 0.66 (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 1 0.18 (0.06)*** 0.22 (0.05)*** c i,t 1 0.22 (0.05)*** 0.30 (0.05)*** NPL i,t 1 0.72 (0.20)*** 0.78 (0.18)*** 0.05 (0.01)*** 0.04 (0.01)*** 0.056 0.056 47 47 1,175 1,222 H β 1121.4 [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
6: 15% 10% 5% 0% -5% -10% -15% -20% -25% -30% -35% d 1993 1994 1995 1996 1997 1998 1999 0 1 2 5% 0% -5% -10% -15% -20% 1993 1994 1995 1996 1997 1998 1999 0 1 2 6% 4% 2% 0% -2% -4% -6% -8% -10% -12% 1993 1994 1995 1996 1997 1998 1999 0 1 2 18
7: 25 2 1995 (%) 20 15 10 5 0 5 10 0 5 10 15 20 (%) 1990 1990 1997 10% 1990 (i) (ii) 1990 0 0 3 19
7 1995 2 1990 PVR 1990 1990 5 1. 2. / 3. 20
(3) 21
(Panel Unit-Root Test) Hadri Fisher ADF 3 p it y it r it 1 ADF (Augmented Dicky-Fuller Test) ADF 1 p 2 2 1977-2 y 37 2 1976-1 r 0 47 1979-2 1 2 1 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 12 12 H 0 : ρ i = 0 for all i H 1 : ρ i < 0 for at least one i 22
3: ADF p p y y r r (1) -3.073* (1) -1.622 (2) -8.058** (2) -1.358 (0) -1.064 (1) -4.989** (1) -2.534 (0) -0.3 (0) -6.963** (0) -3.230* (0) -1.043 (0) -3.824** (1) -2.074 (0) -1.616 (1) -5.579** (1) -2.277 (0) -1.014 (1) -4.339** (1) -2.439 (0) -1.106 (0) -2.925 (0) -1.454 (0) -1.158 (1) -4.703** (1) -1.954 (0) -1.086 (2) -5.718** (2) -2.491 (0) -1.067 (0) -3.854** (1) -1.869 (0) -0.319 (0) -7.218** (0) -3.222* (0) -0.815 (0) -3.986** (3) -2.355 (2) -0.532 (0) -2.767 (0) -2.057 (0) -1.271 (1) -4.925** (1) -2.573 (1) -1.229 (0) -5.064** (0) -2.840 (0) -1.403 (1) -5.082** (3) -2.165 (2) -1.146 (2) -6.657** (2) -0.733 (0) -1.132 (1) -5.062** (1) -2.288 (1) -2.051 (0) -7.238** (0) -2.031 (0) -1.651 (1) -5.644** (1) -1.642 (0) -2.801 (0) -2.414 (0) -1.559 (0) -1.831 (1) -4.861** (1) -1.685 (0) -2.2 (2) -6.715** (2) -0.621 (0) -1.824 (1) -4.670** (1) -2.652 (0) -1.4 (0) -2.562 (0) -0.796 (1) -2.251 (0) -3.709* (1) -1.602 (0) -3.116* (0) -6.767** (0) -1.913 (0) -1.394 (1) -4.373** (1) -2.189 (0) -0.834 (0) -5.578** (0) -2.654 (0) -1. (1) -4.759** (1) -2.036 (0) -1.5 (1) -6.945** (1) -1.599 (0) -1.116 (1) -4.711** (1) -1.942 (0) -1.102 (2) -6.392** (2) -0.970 (0) -1.735 (1) -5.595** (1) -1.962 (0) -1.229 (1) -6.549** (1) -1.585 (0) -1.704 (1) -5.327** (1) -2.021 (0) -1.766 (0) -5.379** (0) -2.669 (0) -1.248 (1) -5.535** (1) -2.153 (1) -1.576 (0) -6.018** (0) -2.287 (0) -1.435 (1) -4.998** (3) -2.305 (2) -0.946 (2) -8.098** (2) -0.731 (0) -1.334 (1) -5.331** (3) -2.048 (1) -2.465 (1) -4.753** (1) -0.676 (0) -1.580 (1) -5.218** (1) -2.741 (1) -1.859 (2) -6.176** (2) -1.139 (0) -1.526 (1) -4.861** (2) -1.813 (1) -2.377 (1) -3.977** (1) -1.115 (0) -1.424 (1) -5.388** (3) -2.097 (2) -1.282 (0) -6.095** (0) -3.020* (0) -1.459 (1) -4.933** (2) -1.622 (1) -2.755 (3) -6.725** (3) -1.119 (0) -1.881 (1) -4.775** (1) -2.657 (0) -1.325 (2) -4.8** (2) -1.044 (0) -1.389 (1) -4.574** (2) -1.673 (2) -2.8 (2) -4.954** (2) -1.310 (0) -1.539 (1) -4.675** (3) -2.112 (2) -1.730 (0) -6.545** (0) -1.959 (0) -1.410 (1) -4.913** (1) -1.864 (1) -3.136* (0) -3.547* (0) -4.073** (0) -1.366 (1) -4.892** (1) -2.011 (1) -2.789 (1) -9.152** (1) -1.922 (0) -1.541 (1) -5.092** (3) -3.871** (2) -0.225 (0) -4.591** (0) -3.989** (0) -0.732 (0) -3.902** (1) -1.895 (0) -1.841 (0) -3.139* (0) -1.565 (0) -0.675 (1) -4.925** (1) -2.711 (1) -2.080 (0) -2.734 (0) -1.354 (0) -0.801 (1) -4.820** (1) -2.204 (0) -0.487 (0) -5.187** (0) -2.789 (0) -0.802 (1) -4.393** (3) -2.259 (3) -1.521 (1) -5.901** (1) -1.340 (0) -1.084 (1) -5.012** (1) -1.515 (0) -2.286 (0) -2.958 (0) -2.270 (0) -0.988 (1) -5.029** (1) -1.984 (2) -1.120 (2) -4.641** (2) -2.322 (0) -1.145 (1) -4.988** (1) -1.440 (0) -2.366 (0) -2.382 (0) -2.020 (0) -1.177 (1) -4.561** (1) -2.176 (0) -1.331 (0) -3.253* (0) -1.613 (0) -1.113 (1) -5.381** (1) -2.023 (0) -1.574 (2) -7.774** (2) -2.593 (0) -0.883 (1) -4.499** (1) -1.901 (0) -1.319 (0) -5.6** (0) -2.095 (0) -1.149 (1) -5.360** (1) -2.347 (1) -1.598 (0) -7.820** (0) -2.191 (0) -1.084 (1) -5.108** (1) -2.192 (2) -1.029 (0) -5.946** (0) -2.298 (0) -0.893 (1) -4.553** (1) -2.346 (3) -1.825 (3) -6.830** (3) -1.466 (0) -0.953 (0) -4.114** (1) -1.867 (0) -1.572 (3) -8.939** (3) -2.641 (0) -1.425 (1) -4.769** (1) -2.019 (0) -0.778 (0) -7.958** (0) -2.212 (0) -2.021 (1) -5.239** ( ) ( ) ADF 10% ADF-t ** * 1% 5% 23
4: (Fisher) 1 Fisher 1% 5% Fisher 1% 5% p 299.19* 319. 231.30 208.36* 231.41 187.96 y 1027.90** 238.76 195.96 165.77**.10 161.70 r 1.10 253.47 202.08 860.97** 364.59 258.19 ( 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 13 4 1 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 6. 3 5 10,000 10,000 Fisher 1% critical value 0 5% critical value 24
Hadri size Fisher Maddala and Wu (1999) Levin-Lin IPS power size 25 size size ADF Fisher 10% 20% 47 9 17 17 27 (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 97.64 82.99 5% 163.65 127.84 Bootstrap Herwartz and Reimers (2) wild bootstrap 25
τ it =. (1997) SNA 0.8 1 τ it (%) (%) (%) (%) (%) 1975 0 1.00 1.00 1.4 0.2 4 5 0 1976 0 1.00 1.00 1.4 0.2 4 5 0 1977 0 1.00 1.00 1.4 0.2 4 5 0 1978 0 1.00 1.00 1.4 0.3 4 5 0 1979 0 1.00 1.00 1.4 0.3 4 5 0 1980 0 1.00 1.00 1.4 0.3 4 5 0 1981 0 1.00 1.00 1.4 0.3 4 5 0 1982 0 1.00 1.00 1.4 0.3 4 5 0 1983 0 1.00 1.00 1.4 0.3 4 5 0 1984 0 1.00 1.00 1.4 0.3 4 5 0 1985 0 1.00 1.00 1.4 0.3 4 5 0 1986 0 1.00 1.00 1.4 0.3 4 5 0 1987 0 1.00 1.00 1.4 0.3 4 5 0 1988 0 1.00 1.00 1.4 0.3 4 5 0 1989 0 1.00 1.00 1.4 0.3 4 5 0 1990 0 1.00 1.00 1.4 0.3 4 5 0 1991 0 1.00 1.00 1.4 0.3 4 5 0 1992 0.8 1.00 1.00 1.4 0.3 4 5 0.20 1993 0.8 1.00 1.00 1.4 0.3 4 5 0.30 1994 0.8 0. 0.40 1.4 0.3 4 5 0.30 1995 0.8 0.67 0.40 1.4 0.3 4 5 0.30 1996 0.8 0. 0.40 1.4 0.3 4 5 0.15 1997 0.8 0. 0.40 1.4 0.3 4 5 0.15 1998 0 0. 0.40 1.4 0.3 4 5 0 1999 0 0. 0.33 1.4 0.3 4 5 0 0 0 0. 0.33 1.4 0.3 4 5 0 1 0 0. 0.33 1.4 0.3 4 5 0 2 0 0. 0.33 1.4 0.3 4 5 0 26
(2): pp. 99 128.. (1992): pp. 17 23,. (1997): pp. 219 247.. (2): (PVR) pp. 67 98.. (2): pp. 145 169.. (0): pp. 161 195, 10. (1990): pp. 135 163.. (1999): 2025 pp. 2 7,. (3): Working Paper 03-3. (3): 22(1), 129 156. (3): 1990 Working Paper 03-6. (1990): pp. 109 134.. (2): pp. 19 66.. (3): DP/03-2. 27
(2): pp. 195 215.. (1999):. (1997): 35 pp. 111 130. (2): pp. 28 35,. 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), 195 228. (1988b): Stock Prices, Earnings, and Expected Dividends, Journal of Finance, XLIII, 661 676. 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), 341 363. 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, 148 161. 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, 45 62. 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, 53 74. 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, 1 24. Maddala, G. S., and I.-M. Kim (1999): Unit Roots, Cointegration, and Structural Change. Cambridge University Press, Cambridge. 28
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. 631 652, 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, 245 266. Nishimura, K. G., F. Yamazaki, T. Idee, and T. Watanabe (1999): Discretionary Taxation, Excessive Price Sensitivity, and Japanese Land Prices, NBER Working Paper, No. 7254. Pedroni, P. (1999): Critical Values for Cointegration Tests in Heterogeneous Panels with Multiple Regressors, Oxford Bulletin of Economics and Statistics, 61(4), 653 670, Special Issues. (0): Fully Modified OLS for Heterogeneous Cointegrated Panels, Advances in Econometrics, 15, 93 130. (1): Purchasing Power Parity Tests in Cointegrated Panel, Review of Economics and Statistics, 83(4), 727 731. Pesaran, M. H., and R. Smith (1995): Estimating Long-Run Relationships from Dynamic Heterogeneous Panels, Journal of Econometrics, 68, 79 113. 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), 99 125. Swamy, P. A. V. B. (1970): Efficient Inference in a Random Coefficient Regression Model, Econometrica, 38(2), 311 323. 29
: 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
: Yamanashi SNA base Simple Average Weighted Average 1 Nagano 1 Gifu 1 Shizuoka 300 Aichi 1 Mie Shiga 400 Kyoto 400 Osaka 300 300 300 Hyogo Nara Wakayama 1 1 Tottori 1 Shimane Okayama 1 Hiroshima Yamaguchi Tokushima 1 1 ( ) 1985 SNA base Simple Average Weighted Average 31
: 1 Kagawa SNA base Simple Average Weighted Average 1 Ehime 1 Kochi 1 Fukuoka 1 Saga 1 Nagasaki Kumamoto 1 Oita Miyazaki 125 75 Kagoshima 1 Okinawa ( ) 1985 SNA base Simple Average Weighted Average 32