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
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1 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 出版情報 : 經濟學研究. 78 (4), pp , 九州大学経済学会バージョン :published 権利関係 :
2 *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 Revenue-expenditure nexus ranger Revenue-expenditure nexus Payne (2003) * ( ) (B)( ) * ( takimoto@en.kyushu-u.ac.jp). * ( nsakamo@pm.tbgu.ac.jp) 1
3 (2011) 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
4 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) (2011) 3
5 Ewing et al. (2006) Revenue-expenditure nexus Bureau of Economic Analysis (BEA) DP ADF/PP I(1) TAR/M-TAR TAR 5% 10% M-TAR 1% 1% M-TAR ranger ranger Payne et al. (2008) 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
6 BEA 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) 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 DP ADF/PP Zivot and Andrews (1992) I(1) TAR/M-TAR TAR 10% M-TAR 10% 10% M-TAR ranger ranger ( ) ( ) 5
7 : (CR) (CE1) 2. 2: (CR) ( )(CE2) 2 1 DP DP R DP CR R DP 68SNA 93SNA ( ) (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
8 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 CR a a a CR a a a 1966 CE b c 1972 CE a b a CE a a a 1975 CE b CE a b a CE a a a 1985 CR R c CR R a a a CR R a a a 1966 CE1 R a b 1977 CE1 R a a a CE1 R a b b 1987 CE2 R a CE2 R a a a CE2 R b b 1987 CR CR a a a CR a a a 1967 CE CE a a a CE a a a 1986 CE CE a a a CE 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 ZA(A) : 1%: 5.34, 5% : 4.80, 10% : ZA(B) : 1%: 4.93, 5% : 4.42, 10% : ZA(C) : 1%: 5.57, 5% : 5.08, 10% : A I(1) 7
9 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
10 Zα = inf α(λ) λ Λ Zt = inf t(λ) λ Λ regory and Hansen (1996) 2 4 9
11 2: ( ) (C) 1 2 CR CE1 CR CE2 ADF Zα Zt (C/T) 1 2 CR CE1 CR CE2 ADF Zα Zt (C/S) 1 2 CR CE1 CR CE2 ADF Zα Zt BIC 2. regory and Hansen (1996) Table 1 3. ADF Z t 4. Z α C: 1% : 5.13, 5% : 4.61, 10% : C/T: 1% : 5.45, 5% : 4.99, 10% : C/S: 1% : 5.47, 5% : 4.95, 10% : C: 1% : 50.07, 5% : 40.48, 10% : C/T: 1% : 57.28, 5% : 47.96, 10% : C/S: 1% : 57.17, 5% : 47.04, 10% :
12 3: ( ) (C) 1 2 CR R CE1 R CR R CE2 R ADF Zα Zt (C/T) 1 2 CR R CE1 R CR R CE2 R ADF Zα Zt (C/S) 1 2 CR R CE1 R CR R CE2 R ADF c Zα Zt 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% : C/T: 1% : 5.45, 5% : 4.99, 10% : C/S: 1% : 5.47, 5% : 4.95, 10% : C: 1% : 50.07, 5% : 40.48, 10% : C/T: 1% : 57.28, 5% : 47.96, 10% : C/S: 1% : 57.17, 5% : 47.04, 10% :
13 4: ( DP ) (C) 1 2 CR CE1 CR CE2 ADF Zα Zt (C/T) 1 2 CR CE1 CR CE2 ADF c Zα Zt (C/S) 1 2 CR CE1 CR CE2 ADF Zα Zt 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% : C/T: 1% : 5.45, 5% : 4.99, 10% : C/S: 1% : 5.47, 5% : 4.95, 10% : C: 1% : 50.07, 5% : 40.48, 10% : C/T: 1% : 57.28, 5% : 47.96, 10% : C/S: 1% : 57.17, 5% : 47.04, 10% :
14 (C/S) (CR R ) ADF 10% (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
15 F 5 t-max Φ Enders and Siklos (2001) 5 7 5: Threshold ( ) TAR 1 2 CR CE1 CR CE F (ρ 1 = ρ 2 =0) max i=1,2 tˆρi F (ρ 1 = ρ 2 ) (1, 48) (1, 48) (1, 48) (1, 48) p M-TAR 1 2 CR CE1 CR CE2 F (ρ 1 = ρ 2 =0) max i=1,2 tˆρi F (ρ 1 = ρ 2 ) (1, 48) (1, 48) (1, 48) (1, 48) p BIC 2. Φ t-max Enders and Siklos (2001) Tables TAR ( 1 50) F (ρ 1 = ρ 2 =0) : 1%:8.67, 5% : 6.18, 10% : max tˆρi : 1%: 2.64, 5% : 2.16, 10% : M-TAR ( 1 50) F (ρ 1 = ρ 2 =0) : 1%:9.32, 5% : 6.67, 10% : max tˆρi : 1%: 2.57, 5% : 2.07, 10% : F (ρ 1 = ρ 2) p F 5 Ewing et al. (2006) Payne et al. (2008) 14
16 6: Threshold ( ) TAR 1 2 CR R CE1 R CR R CE2 R F (ρ 1 = ρ 2 =0) max i=1,2 tˆρi F (ρ 1 = ρ 2 ) (1, 48) (1, 48) (1, 48) (1, 48) p M-TAR 1 2 CR R CE1 R CR R CE2 R F (ρ 1 = ρ 2 =0) max i=1,2 tˆρi F (ρ 1 = ρ 2 ) (1, 48) (1, 48) (1, 48) (1, 48) p BIC 2. Φ t-max Enders and Siklos (2001) Tables TAR ( 1 50) F (ρ 1 = ρ 2 =0) : 1%:8.67, 5% : 6.18, 10% : max tˆρi : 1%: 2.64, 5% : 2.16, 10% : M-TAR ( 1 50) F (ρ 1 = ρ 2 =0) : 1%:9.32, 5% : 6.67, 10% : max tˆρi : 1%: 2.57, 5% : 2.07, 10% : F (ρ 1 = ρ 2) p F. 15
17 7: Threshold ( DP ) TAR 1 2 CR CE1 CR CE F (ρ 1 = ρ 2 =0) max i=1,2 tˆρi F (ρ 1 = ρ 2 ) (1, 50) (1, 50) (1, 50) (1, 50) p M-TAR 1 2 CR CE1 CR CE2 F (ρ 1 = ρ 2 =0) max i=1,2 tˆρi F (ρ 1 = ρ 2 ) (1, 50) (1, 50) (1, 50) (1, 50) p BIC 2. Φ t-max Enders and Siklos (2001) Tables TAR ( 0 50) F (ρ 1 = ρ 2 =0) : 1%:8.78, 5% : 6.20, 10% : max tˆρi : 1%: 2.58, 5% : 2.12, 10% : M-TAR ( 0 50) F (ρ 1 = ρ 2 =0) : 1%:9.50, 5% : 6.73, 10% : max tˆρi : 1%: 2.53, 5% : 2.04, 10% : F (ρ 1 = ρ 2) p F : ρ 1 = ρ 2 =0 VAR ranger 3.5 ranger VAR (2011) 8 Wald ranger 16
18 8: ranger ( ) =1 =2 =3 =4 =5 Wald p- Wald p- Wald p- Wald p- Wald p- CR CE CE1 CR CR CE CE2 CR CRR CE1R CRR CE2R CR CE1 CR CE2 =1 =2 =3 =4 =5 Wald p- Wald p- Wald p- Wald p- Wald p- CE1R CRR CE2R CRR c c =1 =2 =3 =4 =5 Wald p- Wald p- Wald p- Wald p- Wald p- CE CR CE CR a, b, c 1%, 5%, 10% 2. (2011)
19 8 ( CE2 R CRR ) ranger % ranger 1, 2, 5 ranger DP ranger 3.6 (2011) ranger (2011) Institutional separation Institutional separation Wildavsky (1964, 1988) (2009) ( 6 ) : (LR) ( )(LE) 1 DP DP 6 ( ) ( ) (2011) 18
20 4.2 A ((1)) B ((2)) C ((3)) 3 Zivot and Andrews (1992) 9 Λ =[0.15, 0.85] 19
21 9: ( ) ZA(A) ZA(B) ZA(C) LR LR a a a LR a a a 1966 LE LE b b a LE a a a 1963 LR R LR R a a a LR R a a a 1977 LE R LE R a a a LE R a a a 1973 LR LR a a a LR a a a 1963 LE LE a a a LE a a a 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 ZA(A) : 1%: 5.34, 5% : 4.80, 10% : ZA(B) : 1%: 4.93, 5% : 4.42, 10% : ZA(C) : 1%: 5.57, 5% : 5.08, 10% : I(0) I(1) I(1) 4.3 I(1) (2011) DP regory and Hansen (1996) C) ((4)) + (C/T) ((5)) (C/S) ((6))
22 10: ( ) (C) DP LR LE LR R LE R LR LE ADF a Zα Zt (C/T) DP LR LE LR R LE R LR LE ADF a a a b b Zα Zt a b b b (C/S) DP LR LE LR R LE R LR LE ADF a Zα Zt 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% : C/T: 1% : 5.45, 5% : 4.99, 10% : C/S: 1% : 5.47, 5% : 4.95, 10% : Z α C: 1% : 50.07, 5% : 40.48, 10% : C/T: 1% : 57.28, 5% : 47.96, 10% : C/S: 1% : 57.17, 5% : 47.04, 10% :
23 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) (C/T) Zα Zα Threshold Enders and Siklos (2001) 0 TAR (7), (8), (9) M-TAR (7), (8), (10) 11 22
24 11: Threshold ( ) TAR DP LR LE LR R LE R LR LE F (ρ 1 = ρ 2 =0) c 5.53 c max i=1,2 tˆρi F (ρ 1 = ρ 2 ) (1, 49) (1, 47) (1, 47) (1, 47) (1, 47) (1, 47) p M-TAR DP LR LE LR R LE R LR LE F (ρ 1 = ρ 2 =0) c 5.38 max i=1,2 tˆρi b 1.60 F (ρ 1 = ρ 2 ) (1, 49) (1, 47) (1, 47) (1, 47) (1, 47) (1, 47) p BIC 2. Φ t-max Enders and Siklos (2001) Tables b, c 5%, 10% 4. TAR ( 0 50) F (ρ 1 = ρ 2 =0) : 1%:8.78, 5% : 6.20, 10% : max tˆρi : 1%: 2.58, 5% : 2.12, 10% : M-TAR ( 0 50) F (ρ 1 = ρ 2 =0) : 1%:9.50, 5% : 6.73, 10% : max tˆρi : 1%: 2.53, 5% : 2.04, 10% : TAR ( 1 50) F (ρ 1 = ρ 2 =0) : 1%:8.67, 5% : 6.18, 10% : max tˆρi : 1%: 2.64, 5% : 2.16, 10% : M-TAR ( 1 50) F (ρ 1 = ρ 2 =0) : 1%:9.32, 5% : 6.67, 10% : max tˆρi : 1%: 2.57, 5% : 2.07, 10% : 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
25 : ρ 1 = ρ 2 F 11 4 : ρ 1 = ρ 2 =0 t-max VAR DP 4.5 DP ranger 12 DP (2011) 24
26 12: ranger ( ) =1 =2 =3 =4 =5 Wald p- Wald p- Wald p- Wald p- Wald p- LR LE c b a a LE LR a a b b LRR LER LR LE ˆη 1 ˆη 1 =1 =2 =3 =4 =5 Wald p- Wald p- Wald p- Wald p- Wald p- LER LRR c c =1 =2 =3 =4 =5 Wald p- Wald p- Wald p- Wald p- Wald p- LE LR 9.13 a b b a a t p- t p- t p- t p- t p- LE LR 3.73 a a c a a a, b, c 1%, 5%, 10% 2. (2011) 8 15 ( DP ) 25
27 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 ), DP DP 26
28 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
29 Baghestani, H. and McNown, R. (1994) Do revenues or expenditures respond to budgetary disequilibria?, Southern Economic Journal, 61, pp Barro, R.J. (1979) On the determination of the public debt, Journal of Political Economy, 87, pp Buchanan, J.M. and Wagner, R.W. (1977) Democracy in Deficit: The Political Legacy of Lord Keynes. New York: Academic Press. Chan, K.S. (1993) Consistency and limiting distribution of the least squares estimator of a threshold autoregressive model, The Annals of Statistics, 21, pp Doi, T. and Ihori, T. (2009) Local public finance and the soft-budget problem, in The Public Sector in Japan, edited by T. Doi and T. Ihori. Northampton, MA, US: Edward Elgar. Enders, W. and Siklos, P.L. (2001) Cointegration and threshold adjustment, Journal of Business & Economic Statistics, 19, pp Engle, R.F. and ranger, C.W.J. (1987) Cointegration and error-correction: Representation, estimation, and testing, Econometrica, 55, pp Ewing, B.T., Payne, J.E., Thompson, M.A., and Al-Zoubi, O.M. (2006) overnment expenditures and revenues: Evidence from asymmetric modeling, Southern Economic Journal, 73, pp Friedman, M. (1978) The limitation of tax limitation, Policy Review, 5, pp regory, A.W. and Hansen, B.E. (1996) Residual-based tests of cointegration in models with regime shifts, Journal of Econometrics, 70, pp Meltzer, A.H. and Richard, S.F. (1981) A rational theory of the size of government, The Journal of Political Economy, 89, pp Musgrave, R. (1966) Principles of budget determination,in Public finance: Selected readings, editedbyh. Cameron and W. Henderson. New York: Random House. Payne, J.E. (2003) A survey of the international empirical evidence on the tax-spend debate, Public Finance Review, 31, pp Payne, J.E., Mohammdai, H. and Cak, M. (2008) Turkish budget deficit sustainability and the revenueexpenditure nexus, Applied Economics, 40, pp Peacock, A.T. and Wiseman, J. (1979) Approaches to the analysis of government expenditure growth, Public Finance Quarterly, 7, pp Perron, P. (1997) Further evidence on breaking trend functions in macroeconomic variables, Journal of Econometrics, 80, pp Saunoris, J.W. and Payne, J.E. (2010) Tax more or spend less? Asymmetries in the UK revenue-expenditure nexus, Journal of Policy Modeling, 32, pp von Furstenberg,.M., reen, R.J. and Jeong, J. (1986) Tax and spend, or spend and tax?, The Review of Economics and Statistics, 68, pp Wildavsky, A. (1964) The Politics of the Budgetary Process. Boston: Little Brown and Company, inc. Wildavsky, A. (1988) The New Politics of the Budgetary Process. lenview, II: Scott, Foresman. Young, A.T. (2009) Tax-spend or fiscal illusion?, Cato Journal, 29, pp Zapf, M. and Payne, J.E. (2009) Asymmetric modelling of the revenue-expenditure nexus: Evidence from aggregate state and local government in the US, Applied Economics Letters, 16, pp Zivot, E. and Andrews, D.W.K. (1992) Further evidence on the great crash, the oil price shock, and the unit root hypothesis, Journal of Business & Economic Statistics, 10, pp (2009) : (3 ),. (2009). (2011), Discussion Paper Series No ( (1977), 66. (2010), 83, pp
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九州大学学術情報リポジトリ Kyushu University Institutional Repository 時系列区分化手法による時間変化多変量ベクトル自己回帰モデルの推定と金融政策ショック分析への応用 時永, 祥三九州大学 : 名誉教授 松野, 成悟宇部工業高等専門学校経営情報学科 : 教授 https://doi.org/10.15017/1522395 出版情報 : 經濟學研究. 82
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