九州大学学術情報リポジトリ Kyushu University Institutional Repository 構造変化と非線形性を考慮したモデルによるわが国の歳入と歳出の因果性分析 瀧本, 太郎九州大学大学院経済学研究院 坂本, 直樹東北文化学園大学総合政策学部

九州大学学術情報リポジトリ Kyushu University Institutional Repository 構造変化と非線形性を考慮したモデルによるわが国の歳入と歳出の因果性分析 瀧本, 太郎九州大学大学院経済学研究院 坂本, 直樹東北文化学園大学総合政策学部 https://doi.org/10.15017/20497 出版情報 : 經濟學研究. 78 (4), pp.111-138, 2011-12-26. 九州大学経済学会バージョン :published 権利関係 :

*1 *2 *3 DP Institutional separation Fiscal synchronization DP Spend-tax (2011) JEL classification: C32, H50, H72 Keywords: Tax-spend debate, central and local governments, ranger causality, error correction model, TAR/M-TAR model, structural breaks 1 1980 Revenue-expenditure nexus ranger Revenue-expenditure nexus Payne (2003) *1 2011 ( ) (B)(22730180) *2 6 19 1 (E-mail: takimoto@en.kyushu-u.ac.jp). *3 6 45 1 (E-mail: nsakamo@pm.tbgu.ac.jp) 1

(2011) 1955 2008 DP ranger ranger DP ranger ranger Revenue-expenditure nexus VAR 1980 Ewing et al. (2006) Young (2009) Zapf and Payne (2009) (0 ) Threshold AR model (TAR ) (0 ) Momentum-threshold model (M-TAR ) 2 Enders and Siklos (2001) Threshold Payne et al. (2008) Saunoris and Payne (2010) TAR/M-TAR (2010) SNA TAR/M-TAR TAR/M-TAR (Policymaker) ranger (2011) Zivot and Andrews (1992) regory and Hansen (1996) Enders and Siklos (2001) ranger 2 Revenue-expenditure nexus 3 4 5 2

2 4 Revenue-expenditure nexus ranger Tax-spend Spend-tax Fiscal synchronization Institutional separation 4 Tax-spend ranger Friedman (1978) Buchanan and Wagner (1977) Tax-spend Spend-tax ranger Barro (1979) Peacock and Wiseman (1979) ( ) Fiscal synchronization ranger von Furstenberg et al. (1986) Musgrave (1966) Meltzer and Richard (1981) Fiscal synchronization (2011) ranger ( ) ( ) Institutional separation ranger Baghestani and McNown (1994) ranger Wildavsky (1964, 1988) Wildavsky (1964, 1988) (Incrementalism) (1977) Revenue-expenditure nexus 1980 Payne (2003) 2002 2002 (2011) 3

Ewing et al. (2006) Revenue-expenditure nexus Bureau of Economic Analysis (BEA) 1958 1 2003 2 DP ADF/PP I(1) TAR/M-TAR TAR 5% 10% M-TAR 1% 1% M-TAR ranger ranger Payne et al. (2008) 1968 2004 NP ADF/PP/KPSS Perron (1997) I(1) regory and Hansen (1996) 1% Ewing et al. (2006) TAR/M-TAR 10% 10% ranger ranger Institutional separation Tax-spend Young (2009) Tax-spend 4

BEA 1959 3 2007 4 DP ADF/PP I(1) TAR/M-TAR Buchanan and Wagner (1977) Zapf and Payne (2009) (State and local governments) St. Louis Federal Reserve (FRED II) 1959 2005 NP ADF/PP/KPSS I(1) TAR/M-TAR 1% 10% ranger ranger ranger Spend-tax Saunoris and Payne (2010) Spendtax Fiscal synchronization Tax-spend Office for National Statistics 1955 1 2009 1 DP ADF/PP Zivot and Andrews (1992) I(1) TAR/M-TAR TAR 10% M-TAR 10% 10% M-TAR ranger ranger ( ) ( ) 5

3 3.1 1955 2008 10 1. 1: (CR) (CE1) 2. 2: (CR) ( )(CE2) 2 1 DP DP R DP CR R DP 68SNA 93SNA ( 1.01 1.08) 4 3.2 (2011) ADF/PP/KPSS 1 I(1) Zivot and Andrews (1992) ZA Zivot and Andrews (1992) 3 k A: y t = μ + θdu t (λ)+βt + αy t 1 + c j y t j + e t (1) k B: y t = μ + βt + γdtt (λ)+αy t 1 + c j y t j + e t (2) k C: y t = μ + θdu t (λ)+βt + γdt (λ)+αy t 1 + c j y t j + e t. (3) j=1 j=1 j=1 DU t (λ) = DT t (λ) = { { 1 if t>tλ 0 if t Tλ t Tλ if t>tλ 0 if t Tλ 4 (2011) 6

e t i.i.d.(0,σe) 2 T λ 15% 70% y t 1 t t t ˆα =inf λ Λ tˆα(λ) t ˆα Zivot and Andrews (1992) H 0 : α =1 Λ =[0.15, 0.85] 1 1: ( ) ZA(A) ZA(B) ZA(C) CR 1.833 1967 3.222 1982 2.931 1978 CR 5.922 a 1967 5.683 a 1970 6.293 a 1975 2 CR 7.240 a 1974 7.156 a 1965 7.542 a 1966 CE1 2.211 1969 4.723 b 1978 4.861 c 1972 CE1 6.037 a 1981 4.709 b 1971 6.142 a 1975 2 CE1 11.115 a 1975 10.636 a 1981 10.994 a 1975 CE2 2.346 1970 4.680 b 1978 4.551 1974 CE2 6.021 a 1980 4.730 b 1971 6.099 a 1979 2 CE2 8.255 a 1975 7.957 a 1981 8.251 a 1985 CR R 2.645 1967 4.222 c 1988 4.155 1987 CR R 5.460 a 1989 5.281 a 1999 5.604 a 1974 2 CR R 6.409 a 1974 6.468 a 1965 6.733 a 1966 CE1 R 1.880 1966 5.757 a 1978 5.157 b 1977 CE1 R 6.773 a 1980 5.704 a 1987 6.587 a 1980 2 CE1 R 5.501 a 1987 4.458 b 1983 5.447 b 1987 CE2 R 1.839 1966 5.270 a 1978 4.525 1977 CE2 R 7.087 a 1980 5.984 a 1987 6.924 a 1980 2 CE2 R 5.222 b 1987 3.870 1982 5.150 b 1987 CR 3.413 1978 2.920 1989 3.328 1978 CR 6.547 a 1989 6.080 a 1973 6.482 a 1989 2 CR 6.844 a 1974 6.778 a 1965 7.048 a 1967 CE1 3.156 1971 2.865 1978 3.705 1984 CE1 6.696 a 1981 5.734 a 1972 6.581 a 1981 2 CE1 7.670 a 1975 7.548 a 1983 7.601 a 1986 CE2 3.515 1984 2.633 1978 3.918 1984 CE2 6.389 a 1980 5.575 a 1972 6.329 a 1980 2 CE2 3.614 1987 3.034 1983 3.560 1987 1. 2 1 2 2. BIC 3. ZA(A) A ZA(B) B ZA(C) C 4. a, b, c 1%, 5%, 10% 5. ZA(A), ZA(B), ZA(C) Zivot and Andrews (1992) Tables 2-4 6. ZA(A) : 1%: 5.34, 5% : 4.80, 10% : 4.58. 7. ZA(B) : 1%: 4.93, 5% : 4.42, 10% : 4.11. 8. ZA(C) : 1%: 5.57, 5% : 5.08, 10% : 4.82. A I(1) 7

B (CE1), (CE2), (CR R ), (CE1 R ), (CE2 R ) 5 I(0) C (CE1) (CE1 R ) 2 I(0) A I(1) 3.3 (2011) Engle and ranger (1987) regory and Hansen (1996) (C) (C/T) (C/S) 3 (C): y 1t = μ 1 + μ 2 φ tλ + αy 2t + e t (4) + (C/T): y 1t = μ 1 + μ 2 φ tλ + βt + αy 2t + e t (5) (C/S): y 1t = μ 1 + μ 2 φ tλ + α 1 y 2t + α 2 y 2t φ tλ + e t (6) e t (0,σ 2 e) φ tλ = { 1 if t>tλ 0 if t Tλ λ Λ=[0.15, 0.85] ADF (λ) Z α (λ) Z t (λ) 3 ADF (λ) ê tλ ê t 1λ, ê t 1λ,, ê t Kλ ê t 1λ ˆρ λ t (H 0 : ρ λ =0) ADF (λ) =tˆρλ Z α (λ) Z t (λ) Z α (λ) = T (ˆρ λ 1) Z t (λ) = (ˆρ λ 1)/s.e.(ˆρ λ ) ˆρ λ 1 ADF = inf ADF (λ) λ Λ 8

Zα = inf α(λ) λ Λ Zt = inf t(λ) λ Λ regory and Hansen (1996) 2 4 9

2: ( ) (C) 1 2 CR CE1 CR CE2 ADF 3.182 3.097 3.408 3.299 1982 1982 1982 1982 1 1 1 1 Zα 15.561 14.108 16.593 15.210 1981 1981 1981 1981 Zt 2.910 2.744 3.043 2.873 1981 1981 1981 1981 + (C/T) 1 2 CR CE1 CR CE2 ADF 4.380 4.341 4.253 4.240 1982 1982 1983 1983 1 1 1 1 Zα 25.527 25.733 25.283 25.771 1983 1984 1984 1984 Zt 3.896 3.881 3.915 3.909 1984 1984 1984 1984 (C/S) 1 2 CR CE1 CR CE2 ADF 4.269 3.380 4.636 3.350 1984 1987 1985 1987 1 1 1 1 Zα 28.248 15.586 29.115 15.389 1986 1987 1985 1987 Zt 4.213 2.884 4.288 2.865 1986 1987 1985 1987 1. BIC 2. regory and Hansen (1996) Table 1 3. ADF Z t 4. Z α C: 1% : 5.13, 5% : 4.61, 10% : 4.34. C/T: 1% : 5.45, 5% : 4.99, 10% : 4.72. C/S: 1% : 5.47, 5% : 4.95, 10% : 4.68. C: 1% : 50.07, 5% : 40.48, 10% : 36.19. C/T: 1% : 57.28, 5% : 47.96, 10% : 43.22. C/S: 1% : 57.17, 5% : 47.04, 10% : 41.85. 10

3: ( ) (C) 1 2 CR R CE1 R CR R CE2 R ADF 3.442 3.212 3.594 3.329 1982 1982 1982 1982 1 1 1 1 Zα 16.240 14.042 17.249 14.782 1981 1981 1981 1983 Zt 3.007 2.740 3.127 2.810 1981 1981 1981 1983 + (C/T) 1 2 CR R CE1 R CR R CE2 R ADF 4.373 4.152 4.400 4.081 1982 1982 1995 1983 1 1 1 1 Zα 25.263 25.401 24.741 26.321 1983 1984 1984 1984 Zt 3.878 3.825 3.871 3.911 1984 1984 1984 1984 (C/S) 1 2 CR R CE1 R CR R CE2 R ADF 4.715 2.891 4.709 c 3.200 1984 1968 1984 1969 1 1 1 3 Zα 27.607 12.724 28.855 14.610 1985 1977 1985 1975 Zt 4.070 2.523 4.210 2.784 1985 1977 1985 1975 1. BIC 2. c 10% 3. regory and Hansen (1996) Table 1 4. ADF Z t 5. Z α C: 1% : 5.13, 5% : 4.61, 10% : 4.34. C/T: 1% : 5.45, 5% : 4.99, 10% : 4.72. C/S: 1% : 5.47, 5% : 4.95, 10% : 4.68. C: 1% : 50.07, 5% : 40.48, 10% : 36.19. C/T: 1% : 57.28, 5% : 47.96, 10% : 43.22. C/S: 1% : 57.17, 5% : 47.04, 10% : 41.85. 11

4: ( DP ) (C) 1 2 CR CE1 CR CE2 ADF 3.198 3.337 3.162 2.719 1975 1973 1975 1972 1 1 1 0 Zα 13.972 16.602 14.477 13.440 1974 1973 1974 1972 Zt 2.819 3.149 2.887 2.810 1973 1972 1974 1972 + (C/T) 1 2 CR CE1 CR CE2 ADF 4.599 4.021 4.757 c 4.063 1982 1973 1975 1973 1 1 1 1 Zα 23.885 21.957 23.944 23.332 1983 1972 1974 1973 Zt 3.726 3.698 3.804 3.795 1983 1972 1974 1972 (C/S) 1 2 CR CE1 CR CE2 ADF 3.072 3.391 3.052 2.728 1981 1973 1984 1967 1 1 0 1 Zα 16.530 16.685 18.024 13.366 1984 1972 1984 1972 Zt 3.122 3.135 3.271 2.744 1984 1972 1984 1972 1. BIC 2. c 10% 3. regory and Hansen (1996) Table 1 4. ADF Z t 5. Z α C: 1% : 5.13, 5% : 4.61, 10% : 4.34. C/T: 1% : 5.45, 5% : 4.99, 10% : 4.72. C/S: 1% : 5.47, 5% : 4.95, 10% : 4.68. C: 1% : 50.07, 5% : 40.48, 10% : 36.19. C/T: 1% : 57.28, 5% : 47.96, 10% : 43.22. C/S: 1% : 57.17, 5% : 47.04, 10% : 41.85. 12

2 1. 2 (C/S) (CR R ) ADF 10% 2. 2 + (C/T) ( ) DP (CR ) ADF 10% DP 3.4 Threshold TAR M-TAR 2 Enders and Siklos (2001) Threshold Chan (1993) 0 y 1t = β 0 + β 1 y 2t + e t (7) k e t = I t ρ 1 e t 1 +(1 I t )ρ 2 e t 1 + γ j e t j + ε t (8) e t i.i.d.(0,σe) ε 2 t i.i.d.(0,σε) Heaviside 2 indicator I t { 1 if e t 1 0 I t = (9) 0 if e t 1 < 0 j=1 { 1 if e t 1 0 I t = 0 if e t 1 < 0 (10) I t (9) TAR (10) M-TAR (7) (9) (10) I t (8) 2 1 ˆρ 1 ˆρ 2 t (t-max ) 1 ρ 1 = ρ 2 =0 F (Φ ) ρ 1 = ρ 2 13

F 5 t-max Φ Enders and Siklos (2001) 5 7 5: Threshold ( ) TAR 1 2 CR CE1 CR CE2 1 1 1 1 F (ρ 1 = ρ 2 =0) 4.51 4.73 4.82 4.97 max i=1,2 tˆρi 0.417 0.173 0.643 0.433 F (ρ 1 = ρ 2 ) 2.42 2.75 2.40 2.59 (1, 48) (1, 48) (1, 48) (1, 48) p 0.127 0.104 0.128 0.114 M-TAR 1 2 CR CE1 CR CE2 F (ρ 1 = ρ 2 =0) 3.20 3.21 3.61 3.60 max i=1,2 tˆρi 1.64 1.67 1.56 1.62 F (ρ 1 = ρ 2 ) 0.0863 0.0611 0.279 0.197 (1, 48) (1, 48) (1, 48) (1, 48) p 0.770 0.806 0.600 0.659 1. BIC 2. Φ t-max Enders and Siklos (2001) Tables 1-2 3. TAR ( 1 50) F (ρ 1 = ρ 2 =0) : 1%:8.67, 5% : 6.18, 10% : 5.08. max tˆρi : 1%: 2.64, 5% : 2.16, 10% : 1.92. 4. M-TAR ( 1 50) F (ρ 1 = ρ 2 =0) : 1%:9.32, 5% : 6.67, 10% : 5.56. max tˆρi : 1%: 2.57, 5% : 2.07, 10% : 1.82. 5. F (ρ 1 = ρ 2) p F 5 Ewing et al. (2006) Payne et al. (2008) 14

6: Threshold ( ) TAR 1 2 CR R CE1 R CR R CE2 R 1 1 1 1 F (ρ 1 = ρ 2 =0) 4.85 4.68 4.93 4.90 max i=1,2 tˆρi 0.397 0.282 0.658 0.448 F (ρ 1 = ρ 2 ) 2.70 2.39 2.44 2.38 (1, 48) (1, 48) (1, 48) (1, 48) p 0.107 0.129 0.125 0.130 M-TAR 1 2 CR R CE1 R CR R CE2 R F (ρ 1 = ρ 2 =0) 3.37 3.34 3.70 3.63 max i=1,2 tˆρi 1.69 1.73 1.57 1.66 F (ρ 1 = ρ 2 ) 0.0867 0.0449 0.300 0.160 (1, 48) (1, 48) (1, 48) (1, 48) p 0.770 0.833 0.586 0.691 1. BIC 2. Φ t-max Enders and Siklos (2001) Tables 1-2 3. TAR ( 1 50) F (ρ 1 = ρ 2 =0) : 1%:8.67, 5% : 6.18, 10% : 5.08. max tˆρi : 1%: 2.64, 5% : 2.16, 10% : 1.92. 4. M-TAR ( 1 50) F (ρ 1 = ρ 2 =0) : 1%:9.32, 5% : 6.67, 10% : 5.56. max tˆρi : 1%: 2.57, 5% : 2.07, 10% : 1.82. 5. F (ρ 1 = ρ 2) p F. 15

7: Threshold ( DP ) TAR 1 2 CR CE1 CR CE2 0 0 0 0 F (ρ 1 = ρ 2 =0) 3.19 1.84 2.84 1.70 max i=1,2 tˆρi 0.288 0.429 0.498 0.0934 F (ρ 1 = ρ 2 ) 1.56 1.78 0.965 0.895 (1, 50) (1, 50) (1, 50) (1, 50) p 0.217 0.188 0.331 0.349 M-TAR 1 2 CR CE1 CR CE2 F (ρ 1 = ρ 2 =0) 2.35 0.968 2.45 1.23 max i=1,2 tˆρi 1.28 0.801 1.02 0.993 F (ρ 1 = ρ 2 ) 0.00812 0.0936 0.238 0.00136 (1, 50) (1, 50) (1, 50) (1, 50) p 0.929 0.761 0.628 0.971 1. BIC 2. Φ t-max Enders and Siklos (2001) Tables 1-2 3. TAR ( 0 50) F (ρ 1 = ρ 2 =0) : 1%:8.78, 5% : 6.20, 10% : 5.09. max tˆρi : 1%: 2.58, 5% : 2.12, 10% : 1.89. 4. M-TAR ( 0 50) F (ρ 1 = ρ 2 =0) : 1%:9.50, 5% : 6.73, 10% : 5.59. max tˆρi : 1%: 2.53, 5% : 2.04, 10% : 1.79. 5. F (ρ 1 = ρ 2) p F : ρ 1 = ρ 2 =0 VAR ranger 3.5 ranger VAR (2011) 8 Wald ranger 16

8: ranger ( ) =1 =2 =3 =4 =5 Wald p- Wald p- Wald p- Wald p- Wald p- CR CE1 0.271 0.603 0.519 0.771 1.03 0.793 2.16 0.707 2.23 0.816 CE1 CR 0.0883 0.766 1.77 0.413 2.53 0.470 3.44 0.487 5.88 0.318 CR CE2 0.566 0.452 2.54 0.282 2.88 0.411 5.55 0.235 5.92 0.314 CE2 CR 0.305 0.581 1.78 0.410 3.69 0.297 4.15 0.386 4.79 0.442 CRR CE1R CRR CE2R CR CE1 CR CE2 =1 =2 =3 =4 =5 Wald p- Wald p- Wald p- Wald p- Wald p- CE1R 0.0235 0.878 0.0265 0.987 2.28 0.516 2.55 0.636 2.52 0.774 CRR 0.603 0.438 0.937 0.626 5.21 0.157 6.08 0.193 8.07 0.153 CE2R 0.192 0.661 1.44 0.487 3.91 0.271 5.32 0.256 6.01 0.305 CRR 1.20 0.273 1.15 0.564 6.54 c 0.0880 8.20 c 0.0845 8.43 0.134 =1 =2 =3 =4 =5 Wald p- Wald p- Wald p- Wald p- Wald p- CE1 0.0281 0.867 0.0194 0.990 1.76 0.623 2.24 0.692 1.98 0.851 CR 1.22 0.269 2.55 0.280 4.15 0.246 4.39 0.356 6.26 0.282 CE2 0.0426 0.837 0.540 0.763 3.19 0.363 4.91 0.296 4.89 0.429 CR 0.263 0.608 1.18 0.554 2.87 0.412 3.60 0.463 3.95 0.556 1. a, b, c 1%, 5%, 10% 2. (2011) 8 15 17

8 ( CE2 R CRR ) ranger 3 4 10% ranger 1, 2, 5 ranger DP ranger 3.6 (2011) ranger (2011) Institutional separation Institutional separation Wildavsky (1964, 1988) (2009) 4 4.1 1955 2007 ( 6 ) 10 1. : (LR) ( )(LE) 1 DP DP 6 ( ) ( ) (2011) 18

4.2 A ((1)) B ((2)) C ((3)) 3 Zivot and Andrews (1992) 9 Λ =[0.15, 0.85] 19

9: ( ) ZA(A) ZA(B) ZA(C) LR 1.749 1967 2.947 1975 2.949 1972 LR 5.592 a 1980 5.370 a 1970 6.661 a 1975 2 LR 7.242 a 1975 7.077 a 1964 7.256 a 1966 LE 1.862 1968 2.880 1975 2.607 1970 LE 5.255 b 1979 4.781 b 1970 6.091 a 1975 2 LE 11.032 a 1963 10.724 a 1964 10.932 a 1963 LR R 2.397 1967 2.491 1972 2.464 1969 LR R 6.248 a 1975 5.569 a 1984 6.285 a 1973 2 LR R 6.355 a 1973 6.078 a 1974 6.231 a 1977 LE R 0.933 1968 3.412 1972 2.979 1969 LE R 6.212 a 1973 5.531 a 1984 6.353 a 1973 2 LE R 6.314 a 1973 5.805 a 1998 6.166 a 1973 LR 2.723 1971 2.869 1999 2.969 1998 LR 6.842 a 1970 6.625 a 1998 6.802 a 1970 2 LR 10.808 a 1963 10.714 a 1971 11.039 a 1963 LE 2.452 1971 2.926 1999 2.904 1998 LE 7.307 a 1970 7.114 a 1994 7.199 a 1963 2 LE 10.692 a 1985 10.545 a 1964 10.596 a 1996 1. 2 1 2 2. BIC 3. ZA(A) A ZA(B) B ZA(C) C 4. a, b, c 1%, 5%, 10% 5. ZA(A), ZA(B), ZA(C) Zivot and Andrews (1992) Tables 2-4 6. ZA(A) : 1%: 5.34, 5% : 4.80, 10% : 4.58. 7. ZA(B) : 1%: 4.93, 5% : 4.42, 10% : 4.11. 8. ZA(C) : 1%: 5.57, 5% : 5.08, 10% : 4.82. I(0) I(1) I(1) 4.3 I(1) (2011) DP regory and Hansen (1996) C) ((4)) + (C/T) ((5)) (C/S) ((6)) 3 10 20

10: ( ) (C) DP LR LE LR R LE R LR LE ADF 3.882 3.825 3.830 3.732 5.617 a 4.065 1981 1981 1981 1981 1975 1979 1 1 1 1 1 1 Zα 24.564 24.201 23.877 23.252 27.511 22.568 1980 1980 1980 1980 1976 1978 Zt 4.255 4.187 4.174 4.056 4.243 3.723 1979 1979 1980 1980 1977 1978 + (C/T) DP LR LE LR R LE R LR LE ADF 5.630 a 5.487 a 5.653 a 5.358 b 5.226 b 4.033 1992 1992 1991 1992 1975 1979 1 1 1 1 1 1 Zα 35.878 34.598 33.600 32.100 27.264 22.940 1991 1991 1991 1991 1976 1978 Zt 5.488 a 5.360 b 5.428 b 5.210 b 4.219 3.805 1991 1991 1991 1991 1977 1978 (C/S) DP LR LE LR R LE R LR LE ADF 4.220 4.000 3.903 3.724 5.601 a 3.955 1981 1981 1993 1981 1975 1979 1 1 1 1 1 1 Zα 26.234 24.957 24.381 23.072 28.220 22.525 1980 1980 1980 1980 1976 1978 Zt 4.391 4.237 4.213 4.045 4.284 3.775 1980 1980 1980 1980 1977 1978 1. BIC 2. a, b 1%, 5% 3. regory and Hansen (1996) Table 1 4. ADF Z t C: 1% : 5.13, 5% : 4.61, 10% : 4.34. C/T: 1% : 5.45, 5% : 4.99, 10% : 4.72. C/S: 1% : 5.47, 5% : 4.95, 10% : 4.68. 5. Z α C: 1% : 50.07, 5% : 40.48, 10% : 36.19. C/T: 1% : 57.28, 5% : 47.96, 10% : 43.22. C/S: 1% : 57.17, 5% : 47.04, 10% : 41.85. 21

10 1. (C) ( ) DP (LR ) ADF 1% 2. + (C/T) ADF Zt 1% 5% 3. + (C/T) ( ) DP (LR ) ADF 5% 4. (C/S) ( ) DP (LR ) ADF 1% (C) (C/S) 2 6 1 5 + (C/T) Zα Zα 10 4.4 Threshold Enders and Siklos (2001) 0 TAR (7), (8), (9) M-TAR (7), (8), (10) 11 22

11: Threshold ( ) TAR DP LR LE LR R LE R LR LE 0 1 1 1 1 1 F (ρ 1 = ρ 2 =0) 3.30 4.33 4.35 4.32 5.81 c 5.53 c max i=1,2 tˆρi 1.44 1.67 1.69 1.63 1.86 1.52 F (ρ 1 = ρ 2 ) 0.0143 0.0285 0.0201 0.00260 0.0171 0.588 (1, 49) (1, 47) (1, 47) (1, 47) (1, 47) (1, 47) p 0.905 0.867 0.888 0.960 0.896 0.447 M-TAR DP LR LE LR R LE R LR LE F (ρ 1 = ρ 2 =0) 3.42 4.41 4.43 4.41 5.80 c 5.38 max i=1,2 tˆρi 1.00 1.41 1.42 1.42 2.17 b 1.60 F (ρ 1 = ρ 2 ) 0.225 0.164 0.155 0.145 0.00563 0.348 (1, 49) (1, 47) (1, 47) (1, 47) (1, 47) (1, 47) p 0.637 0.687 0.696 0.705 0.941 0.558 1. BIC 2. Φ t-max Enders and Siklos (2001) Tables 1-2 3. b, c 5%, 10% 4. TAR ( 0 50) F (ρ 1 = ρ 2 =0) : 1%:8.78, 5% : 6.20, 10% : 5.09. max tˆρi : 1%: 2.58, 5% : 2.12, 10% : 1.89. 5. M-TAR ( 0 50) F (ρ 1 = ρ 2 =0) : 1%:9.50, 5% : 6.73, 10% : 5.59. max tˆρi : 1%: 2.53, 5% : 2.04, 10% : 1.79. 6. TAR ( 1 50) F (ρ 1 = ρ 2 =0) : 1%:8.67, 5% : 6.18, 10% : 5.08. max tˆρi : 1%: 2.64, 5% : 2.16, 10% : 1.92. 7. M-TAR ( 1 50) F (ρ 1 = ρ 2 =0) : 1%:9.32, 5% : 6.67, 10% : 5.56. max tˆρi : 1%: 2.57, 5% : 2.07, 10% : 1.82. 8. F (ρ 1 = ρ 2) p F : ρ 1 = ρ 2 =0 Φ 1. TAR DP 10% 2. M-TAR ( ) DP (LR ) 10% t-max 5% DP 2 TAR M-TAR 2 4 DP 3 10% 5% 10% 0.18 DP 23

: ρ 1 = ρ 2 F 11 4 : ρ 1 = ρ 2 =0 t-max VAR DP 4.5 DP ranger 12 DP (2011) 24

12: ranger ( ) =1 =2 =3 =4 =5 Wald p- Wald p- Wald p- Wald p- Wald p- LR LE 1.29 0.255 4.90 c 0.0861 9.10 b 0.0280 14.0 a 0.00739 15.8 a 0.00734 LE LR 0.00795 0.929 10.9 a 0.00439 12.0 a 0.00743 13.1 b 0.0108 14.0 b 0.0154 LRR LER LR LE ˆη 1 ˆη 1 =1 =2 =3 =4 =5 Wald p- Wald p- Wald p- Wald p- Wald p- LER 1.26 0.122 1.40 0.370 4.40 0.162 6.25 0.137 6.94 0.180 LRR 0.181 0.405 2.77 0.167 3.38 0.257 8.55 c 0.0525 8.95 c 0.0847 =1 =2 =3 =4 =5 Wald p- Wald p- Wald p- Wald p- Wald p- LE 1.67 0.196 1.87 0.393 0.283 0.419 4.50 0.343 3.70 0.594 LR 9.13 a 0.00252 7.78 b 0.0204 10.7 b 0.0136 17.1 a 0.00185 20.6 a 0.000955 t p- t p- t p- t p- t p- LE 1.14 0.254 1.16 0.247 0.222 0.824 0.841 0.400 0.790 0.429 LR 3.73 a 0.000191 2.73 a 0.00626 1.92 c 0.0550 2.97 a 0.00299 3.36 a 0.000766 1. a, b, c 1%, 5%, 10% 2. (2011) 8 15 ( DP ) 25

2 5 ranger DP ranger 4 5 ranger 10% 4.6 DP DP DP (2011) (2011) Spend-tax ranger Doi and Ihori (2009) ranger ranger (2009, pp.259-264), DP DP 26

DP DP ranger ranger Fiscal synchronization (2011) Tax-spend Spend-tax DP 5 (2011) Institutional separation Fiscal synchronization DP Spend-tax DP DP Spend-tax TAR/M-TAR 0 Chan (1993) Threshold TAR/M-TAR Threshold Enders and Siklos (2001) 0 2 DP 3 27

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