財政赤字の経済分析:中長期的視点からの考察
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2 (1982, 1996) (1997) (1977) (1990) (1996) (1997) (1996) Ihori, Doi, and Kondo (1999)
3 (1982) (1984) (1987) (1993) (1997) (1998) CAPM
4 1980 (time inconsistency) Persson, Persson and Svensson (1987) Calvo and Guidotti (1990a, 1990b) Barro (1995, 1997) (indexed bond) (nominal bond) Leeper
5 (1991) Sims (1994, 1997) Woodford (1994, 1995, 1996, 1997) Dupor (1997) Cochrane (1998a, 1998b) (the fiscal theory of the price level) = Cochrane (1998a)
6 Cochrane (1998a, 1998b) Woodford (1995) B t 1 (t) Q t (t+j)[b t (t+j) B t 1 (t+j)] = p t s t (1) j=1 B t 1 (t+j) Q t (t+j) s t (primary surplus) p t Q t (t) = 1 B t (t j) = 0 j 0 (1) (r) 1 2 3
7 Q t (t+j) = β j E t [ p t ] (2) p t+j β 1/r (2) (1) B p t = t 1 (t) (3) E t [ j=0 j 1 β j W t, j s t+j ] B t+k (t+k+j) B t+k 1 (t+k+j) B t+k+j 1 (t+k+j) W t,j k=0 W t,1 B t(t+1) B t 1 (t+1), W B t (t+1) t,0 1 W t, k, (1) (2) {s t+k 1 } k 1 {B t+k 1 (t+l)} k 1, l k (3) (3) {B t+k 1 (t+l)} k 1, l k (3)
8 (3) (3) (3) Cochrane (1998a, 1998b) B t 1 (t) Q t (t+1)b t (t+1) = p t s t (3) B t 1 (t) p t = E t j=0 β j s t+j (3') p t (1) r t+1 p t p t+1 j=1 j=1 Q t+1 (t+j)b t (t+j) Q t (t+j)b t (t+j) v t j=0 Q t (t+j)b t 1 (t+j) p t (1) v t = v t+1 r t+1 + s t (4)
9 v t 1 c t+1 = c t r t+1 c t s t+1 + v t+1 (4') c t+1 c t+1 c t
10 Leeper(1991) Woodford (1998) Leeper (1991) (m t ) money in the utility function E 0 t=0 δ t [ln(c t ) + ln(m t )] 0 < β < 1 (5) mt Mt/ pt Mt ct + Mt pt + Bt Mt 1 Bt 1 + τt = yt + + rt 1 pt pt pt (6) (6) (5)
11 M t p t (7) + B t + τ p t = g t + M t 1 B t 1 + r t p t 1 t p t gt τt = η0 + ηbt 1+ ξt (8) ξt = ρ1ξt 1 + e1t ρ1 1, e1t ~ N(0,σ1 2 ) η0, η, ρ1 bt Bt/ pt η η rt = φ0 + φπt+ µt (9) µt = ρ2µt 1 + e2t ρ2 1, e2t ~ N(0,σ2 2 ) φ0, φ, ρ2 φ φ E[e1te2t j]=0 j E[e2te1t j]=0 j Leeper
12 (1991) active passive active passive yt = ct + gt pt pt pt yt gt ct pt mt = rt rt 1 ct (10-1) rt = 1 δ Et[πt+1] πt+1 pt+1/ pt (10-2) π b ~π t πt π b ~ t bt b (6) (10) Et[ π ~ t+1 ] = φδ π ~ t +δµt (11-1) ~ b t (δ 1 η) b ~ t 1 + ~ z1 π t + ~ z2 π t 1 + ξt +z3µt + z4µt 1 = 0 (11-2)
13 Leeper (1991) (11) φδ >1 δ 1 η <1 active passive φδ <1 δ 1 η >1 passive active 4 (11) φδ >1 φδ >1 δ 1 η <1 active passive non-ricardian regime δ 1 η >1 φδ <1 δ 1 η >1 passive active Ricardian regime 4 φδ >1 δ 1 η >1 φδ <1 δ 1 η <1 Leeper (1991)
14 Cochrane (1998a) Woodford (1998) (3') (3') 5% 20% Leeper (1991) Woodford (1998) Woodford (1998) (12) (16) ~r t = ρ(vc t +sc t ) +dc t vc t-1 (12) vc t ln(v t /c t ) vc vc ln(v t /c t ) 5 Ricardian regime non-ricardian regime
15 sc t s t /c t sc sc s t /c t dc t ln(c t+1 /c t ) c ln(c t+1 /c t ) ~r t ln(r t ) r r ln(r t ) ρ (1/r t+1 )c t+1 /c t x t = Ax t 1 + e t (13) x t (vc t, sc t, dc t ) A 3 3 e t R t = φ p π t + a x t (14) π t a R t E t rt+1 ~ =R t E t π t+1 (15) ~r t =ωq t q t 1 π t (16) q t ln(q t /Q) Q Q t ω θ / rπ π π t θ B t (t+j) = θ j 1B t (t+1), j 1 Woodford (1998) (12) (4) v t s t GDP (13) VAR Leeper (1991) (8) 6 sct sct
16 (14) Leeper (1991) (9) Taylor (1993) R t = R* + φ p (π t π*) + φ y y t * y t GDP (15) (16) B t (t+j) = θ j 1B t (t+1), j 1 θ 0 θ < rπ ω <1 r t 1+ θq t p t 1 Q t 1 p t (16) (12) (15) E t π t+1 = φ p π t + (a l 0 A l 1 )x t (17) l 0 (ρ, ρ, 1) l 1 ( 1, 0, 0) (13) (17) π t = φ p π t 1 + (a l 0 A l 1 )x t + f e t (18) f [φ p ω (l 0 +ω l 1 ) ω a ](I ωa) 1 l 0 φ p < 1 (18) Woodford (1998) (18)
17 (18) (18) (18) (13) A e t (17) φ p (a l 0 A l 1 ) a (18) (18) GDP dc t vc t, sc t, (1999) 7 Cochrane (1998a)
18 (1998)
19 s t 1965 (1) (4) γ t-1 (t+j) F t (t+j) M t
20 B t 1 (t) + γ t 1 (t+j)b t 1 (t+j) F t (t+j)[b t (t+j) B t 1 (t+j)] (M t j=1 j=1 M t 1 ) = p t s t F t (t+j) F t (t+j)= F t (t+j) B t 1 (t+j)[f t (t+j)+γ t 1 (t+j)] + M t 1 j=0 v t p t B t (t+j)[f t+1 (t+j)+γ t (t+j)] + M t p r t+1 t j=1 p t+1 B t (t+j)f t (t+j) + M t j=0 15
21 (4) v t s t r t vc t, sc t ~ r t v t /c t r t s t /c t Cochrane (1998a) sc = (13) (17) ρ (1/r t+1 )c t+1 /c t 1 Cochrane (1998a) ρ = 0.99 π θ j 1 j ω 1 ω 1 θ = 0.04 ω = % 6 55% %
22 % 1980
23 VAR (13) (17) Leeper (1991) π π φ p active passive 1 φ p passive sc t vc t-1 active passive 1 active Leeper (1991) (13) (18) GDP
24 GDP 3.12% 5 (12) (18) Woodford (1998)
25 Cochrane (1998b) (1) B t 1 (t+j) = θ j B, j 0 B θ j (2) j=0 β j E t [ 1 p t+j ]B t 1 (t+j) = E t j=0 β j s t+j (19) s t p t s p (19) ps B = (1 β) β j θ j j=0 (19) ~p t p t p p, ~ s t s t s ~, B t 1 ( t + j) B t 1(t + j) θ j B s B j ~ j j ~ = (1 ) ~ j β θ E p β β θ β E s + β B ( t j) j= 0 j t t+ j j t t+ j t 1 + j= 0 j= 0 j= 0 p~ t ~ p t (1 β ) j= 0 β j θ j j= 0 j β W E ~ s j t t+ j j= 0 β j D (20) j 1 B t 1+ j
26 Bt l β k= 0 W D ~ k + Bt+ l ( t + l l j j 1 k = 0 l + 1 i= 0 j 1 θ j ) k) ( θ W, W 0 1, W 1 (θ 0 θ 1 ) i 1 θ i ) k ( θ D, D -1 1, D 0 θ 1 l i (20) (20) (1) (1) ~ B t + k ( t + m) = 0.01, 0 k m 1 (20) B t+l = 0.01β m-l-1 (20) j 1 D j-1 >0 p~ t + D -1 = 1< 0 ~ p β t+ 1
27 + (1) B t 1 (t) β j E p t [ 1 ]{B t p t (t+j) B t 1 (t+j)} = s t (1') t+j j=1 (1') B t+m 1 (t+m) β j 1 E p t [ ]{B t+m p t+m (t+m+j) B t+m 1 (t+m+j)}= s t+m t+m+j j=1 B t+m 1 (t+m) p t+m B t+m 1 (t+m) p t+m B t+m 2(t+m 1) β j 1 E p t [ ]{B t+m 1 p t+m 1 (t+m 1+j) B t+m 2 (t+m 1+j)} t+m 1+j j=1 = s t+m 1 p t+m B t+m 1 (t+m) B t+m 2 (t+m) p t+m 1 p t+m p t+k (1 k m 1) (1') B t (t+m) p t+k (0 k m 1) B t (t+m) 17 st+k >0
28 (1') p t ( ) ( ) t t ( ) t m t m ( ) Cochrane (1998b) (20) (20) 18 (18) (20)
29 (20) θ j
30 GDP (20) (20) θ j TB
31
32
33 1 Buiter (1998, 1999)
34 Ahemd, S. and J. Rogers (1995), "Government budget deficits and trade deficits: Are present value constraints satisfied in long-run data?" Journal of Monetary Economics 36, pp Barro, R.J. (1995), "Optimal debt management" National Bureau of Economic Research Working Paper No Barro, R.J. (1997), "Optimal management of indexed and nominal debt" National Bureau of Economic Research Working Paper No Buiter, W.H. (1998), "The young person s guide to neutrality, price level indeterminacy, interest rate pegs, and the fiscal theories of the price level" National Bureau of Economic Research Working Paper No Buiter, W.H. (1999), "The fallacy of the fiscal theory of the price level" Centre for Economic Policy Research Discussion Paper No Calvo, G.A. and P.E. Guidotti (1990a), "Credibility and nominal debt" IMF Staff Papers 37, pp Calvo, G.A. and P.E. Guidotti (1990b), "Indexation and maturity of government bonds: An exploratory model," in R. Dornbusch and M. Draghi eds., Public Debt Management: Theory and History, pp Cochrane, J.H. (1998a), "A frictionless view of U.S. inflation" NBER Macroeconomics Annual 1998, pp Cochrane, J.H. (1998b), "Long-term debt and optimal policy in the fiscal theory of the price level" National Bureau of Economic Research Working Paper No Dupor, B. (1997), "Exchange rates and bank notes: The fiscal theory of the price level" University of Pennsylvania. Ihori, T., T. Doi, and H. Kondo (2000), "Japanese fiscal reform: Fiscal reconstruction and fiscal policy" Japan and the World Economy, forthcoming. Leeper, E. (1991), "Equilibria under active and passive monetary policies" Journal of Monetary Economics 27, pp
35 Persson, M., T. Persson and L.E.O. Svensson (1987), "Time consistency of fiscal and monetary policy" Econometrica 55, pp Sims, C. (1994), "A simple model for the determination of the price level and the interaction of monetary and fiscal policy" Economic Theory 4, pp Sims, C. (1997), "Fiscal foundations of price stability in open economies" Yale University Working Paper. Taylor, J.B. (1993), "Discretion versus policy rules in practice" Carnegie-Rochester Conference Series on Public Policy 39, pp Woodford, M. (1994), "Monetary policy and price level determination in a cash-in-advance economy" Economic Theory 4, pp Woodford, M. (1995), "Price level determination without control of a monetary aggregate" Carnegie-Rochester Conference Series on Public Policy 43, pp1-46. Woodford, M. (1996), "Control of public debt: A requirement for price stability?" National Bureau of Economic Research Working Paper No Woodford, M. (1997), "Doing without money: Controlling inflation in a post-monetary world" National Bureau of Economic Research Working Paper No Woodford, M. (1998), Comment, NBER Macroeconomics Annual 1998, (1984), 3, pp (1993),,. (1998),, 119, pp (1982),,. (1996),,,, pp (1987),, 6, pp (1997),
36 , 48, pp (1998),, 47, pp (1999),, Keio Economic Society Discussion Paper Series No (1977),,. (1997),,. (1996),,,. (1996),,, pp47-80,. (1990),,.
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