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1 # GDP 1 GDP 1992 GDP Hamilon and Flavin (1986) Doi and Ihori(2003) (2007) 2 Bohn(1998) /GDP Bohn # 1 2 Broda and Weinsein (2005) (2007) 1

2 Hamilon and Flavin(1986) 3 (2000) Bohn 2001 Bohn Tirole(1985) Tirole Diamond (dynamic inefficiency) Tirole Tirole Tirole Tirole 3 Bohn(1998) 2

3 (Bubble Subsiuion) Tirole S (Tirole(1985) Figure 2) S b g G( ) b bˆ bˆ 2 Tirole Tirole (Golden Rule) Diamond (dynamic inefficiency) Abel e al (1989)

4 20 Tirole Tirole 5 Feldsein and Summers(1977) Bohn(1998) 4

5 Abel e al(1989) Bohn(1995) Tirole Hoshi e al(1990) Tirole 3 Tirole (overlapping generaions economy) L 6 L = ( 1+ n) L0 = (1 + n) n > 0 Y = F K, L ) Y K ( L k ( K N ) 6 GDP 5

6 Y N = f k ) 1. f (.) 3 ( f ( 0) = 0lim f '( k ) = + k 0, R W R = f '( k ) W = f ( k ) k f '( k ) W( k ) R 1 (inelasically) (limied liabiliy consrain) α 100% 1 α 100% 1 F Π 7 7 Rhee (1991) Diamond 20 6

7 (belief) q F q F +1 ( F +1 F + +1 ) j F f = ( 1+ n) i = f f ( = +, (1 + n) j ) f = ε + 1 E f f = ε + 1E f+ 1 ε +1 ε +1 + qε 1 + ( 1 q) ε 1 = E B R (2-3) R B = B. d B B ) 1 R = ( R d = p p B b (2-3) N R p (2-4) b = b. (1 + n) p p p R p p +1 (belief) q p p ( ) + 1- q p p ( ( ) ( p p ) + ( p ) p ) p =η p p ), ( p ) E ( + p =η E ( p p ) η +1 η ( p ) + qη q) η 1 ( = 7

8 λ( 0 < λ < 1) 100% 1 i f '( k ) i ( i w )(1 + r ) w 1 r ) ( + f '( k ) > 1+ r f '( k ) < 1+ r (3-1) f '( k ) = 1+ r. N w( k ) = αi N + B + F K +1 = αi N (3-2) ( 1+ n) k = w( k ) b f. w = + b + f l l r +1 8

9 1+ r Π (3-3) E ( f ) = f. 1+ n (1 + n) 2 (3-3) 1+ r (3-4) E ( f + ) = f 1+ n 1. (3-5) R E ( p p ) = 1+ r. (3-5) (2-4) 2 1+ r (3-6) E ( b + ) = b 1+ n 1. (3-7) b 0 and f 0. (aggregae bubbles) (3-8) a = b + f. 2 b f a b f a (non-sochasic) f ε + bη = f ε + bη f b + ε < ε η 0 < 1< + 0 < < 1< η 9

10 3 (3-4),(3-6),(3-8) a r + (3-9) a + = a 1+ n (3-2) (3-10) ( 1+ n) k = w( k ) a. 2 (a bubbleless equilibrium ) a = 0 a 0 a > 0 (an asympoically bubbly equilibrium) a 2 } { k, r 2 (3-11) ( 1+ n ) k = w( k ), and (3-12) 1+ r = f '( k ). 3 k, r, a } 3 (3-13) ( 1+ n) kgr = w( kgr) bgr, (3-14) + r = f '( k ), 1 GR GR (3-15) r GR = n. { GR GR GR r > n r r n n [ Tirole (1985, Proposiion 1)]. n r > (dynamically 10

11 efficien) r n (dynamically inefficien) [ Tirole (1985, Proposiion 2)] Ihori (1978) Tirole (1985) r < n Ihori (1978) (he Golden Rule) 2 f '( k ) >1+ n. 2 k k0 k r = f '( k ) 1 ( > n) r +1 i w ) ( 1 r ) i w ) ( + ( f '( k ) i ( i w )(1 + r ) λ 100% ( 1 λ) f '( k ) i (incenive compaibiliy) (4-1) ( i w( k )) (1 + r ) λ f '( k ) i. (4-1) (he borrowing consrain) 8 8 CSV(Cosly-Sae-Verificaion) CSV [ Diamond (1984)], r 11

12 (4-1) (4-2) α i w( k )) = (1 α) w( k ) ( (symmeric equilibria) (4-1) (4-2) (4-3) 1 α )(1 + r ) λf '( k ). ( 3 α + λ < 1. α (crediors) (debors) (separaion) α 1 α 0 λ λ 1 r +1 λ 0 α λ 3 12

13 (4-3) λ Proof. 1 (4-3) 1+ r f '( k ) < f '( k ) 1 α f '( k ) = 1+ r 2 { k ~, ~ r} 2 ~ ~ (4-4) ( 1+ n ) k = w( k ), and (4-5) ~ λ ~ 1+ r = f '( k ). 1 α (3-11) (4-4) 3 (3-12),(4-5) Azariadis and Smih(1993), Sakuragawa and Hamada(2001), Masuyama(2004) Bohn(1995) 13

14 (4-6) α ( i w( k )) = (1 α) w( k ) a. (4-1) (4-2) (4-1) (4-7) {( 1 α ) w( k ) a}(1 + r ) = λf '( k ){ w( k ) a}. 3 (3-9), (3-10), (4-7) ~ 3 k, a~, ~ r } 3 3 ~ ~ (4-8) ( 1+ n) k = w( k ) a~ B B { B B ~ ~ ~ (4-9) {( 1 α ) w( k ) a~ }(1 + ~ r ) = λf '( k ){ w( k ) a~ }, and (4-10) ~ r B = n. B B a f b B (belief) + f b 3 qε q) ε 1, B ( = qη q) η 1, f ε + bη = f ε + bη ( = ( 1) ε ε η + 0 < < 1< η + 0 < < 1< ε, ε, η, η } { (sunspo) + + { ε, η } f b } { ε, η f b a k f k b k Weil(1987) 1 14

15 (belief) 2 (4-5), (4-10) 3 1 (capial under-accumulaion) 5 k ~ < k ~ < B k GR W (global saddlepoin) a0 W a0 D a (infeasible) a +1 = a Tirole (1985) and Weil (1987) a +1 = a (2-5) (4-7) 2 w( k ) a (4-11) ( 1+ n){(1 α ) w( k ) a} = λf '( ){ w( k ) a} 1+ n (4-11) a = Φ k ) 2 λf '( k ) /(1 + n) + α(1 + n) b w'( k ) /( w( k ) a ) (4-12) Φ' ( k ) = > 0. 2 λf "( k ) /(1 + n) + (1 + n) αw( k ) ( w( k ) a ) ( 0 15

16 a +1 = a k +1 = k Tirole (1985) Weil (1987). 2 (a) (b) ~ r > n r~. ~ f '( k ) > 1+ n > 1+ ~ r a 0 a ~ n k ~ ~ λ ~ ~ ~ B f '( kb) > 1+ n = f '( kb) ( k B < k < kgr) 1 α (c) ~ 1 + n > f '( k ) > 1+ ~ r a 0 a ~ n k ~ ~ λ ~ ~ ~ B f '( kb) > 1+ n = f '( kb) ( kb < kgr < k ) 1 α 2 1+ n 1+ r~b n ~ r B k ~ ~ < B k ~ rb > ~ r (susainable) n > ~ r n > ~ r 1+ r~ 1+ n ~ r > n ~ r > n ~ λ ~ r f k r ~ B = '( B) 1 1 α > (3-9) 16

17 4 p b = b f = 0, R = 1+ n p (from (2-4)) R = 1 + d (5-1) p p 1+ n) (1 d ) = ( + d n) (1 + d ) ( + R 10 GDP Tirole 10 (fiscal heory of he price level) ( Woodford(1995) (2004) 17

18 6A 6B (2007) Diba and Grossman(1988)

19 GDP GDP , GDP JREIT 4 [ ] 19

20 BIS 1999? 20

21 GNP (financial repression) (2003) 3 3 ~ r > n (dynamically efficien) 21

22 4 ~ f '( k ) > 1+ n > 1+ ~ r (dynamically efficien) Proof: Q.E.D. n ~ r < ~ r < n 2(b) 4 f '( k) 1+ n r n Diamond 1 1 Diamond 22

23 ~ r < n k ~ ~ ~ ~ k ( < k ) f ( k) (1 + n) k = f ( k ) (1 + n) k 10 5 ~ n f k ) 1 ~ ~ 1 + > '( > + r k B < k ~ k B > k Producion efficiency Susainabiliy of bubbles ~ f '( k ) > 1+ r~ > 1+ n ~ f '( k ) > 1+ n > 1+ ~ r dynamically efficien infeasible dynamically efficien feasible ~ 1 + n > f '( k ) > 1+ ~ r dynamically efficien or dynamically inefficien feasible 2007, ,. 23

24 No.03-J Abel, A.B, N.G. Mankiw, L.H. Summers, R.J. Zeckhauser, 1989, Assessing dynamic efficiency: Theory and Evidence, Review of Economic Sudies 56, Azariadis, C., and B. Smih, 1993, Adverse selecion in he overlapping generaion models: The case of pure exchange, Journal of Economic Theory 60, Bohn, H., 1995, The Susainabiliy of Budge Deficis in a Sochasic Economy, Journal of Money, Credi, and Banking 27, Bohn, H., 1998, The behavior of U.S. public deb and deficis, Quarerly Journal of Economics 113, Broda, C. and D.E. Weinsein, 2005, Happy news from he dismal science: reassessing he Japanese fiscal policy and susainabiliy, in Takaoshi Io, Hugh, Parick, and David E. Weinsein eds, Reviving Japanese Economy, 39-78, MIT Press Diamond, P., 1965, Naional Deb in a Neoclassical Growh Model, American Economic Review LV, Diba, B.T. and Grossman,H.I., 1988 Explosive Raional Bubbles in Sock Prices? The American Economic Review,78, Doi, T., and T.Ihori, 2003, susainabiliy of governmen deb deficis: Including rend in local governmen finance, in N.Yoshino, S.Inukai, and N. Tamaki leds, Enhancing Marke Funcions in Japan 3-29, Keio Universiy Press. Feldsein, M., and L. Summers, 1977, Is he rae of profi falling?, Brooking Papers on Economic Aciviy Hamilon, J.D., and M.A. Flavin, 1986, On he limiaion of governmen borrowing: a framework for empirical esing, American Economic Review 76, Ihori, T., 1978, The golden rule and he role of governmen in a life cycle growh model, American Economic Review,

25 Hoshi, T. A. Kashyap and D. Scharfsein [1991], Corporae Srucure, Liquidiy, and Invesmen: Evidence from Japanese Indusrial Groups, Quarerly Journal of Economics 101: Masuyama, K., 2004, Financial marke globalizaion, symmery-breaking and endogenous inequaliy of naions, Economerica 72, Rhee, C., 1991, Dynamic Inefficiency in an Economy wih Land, Review of Economic Sudies 58, Sakuragawa, M., and K. Hamada, 2001, Capial Fligh, Norh-Souh Lending, and Sages of Economic Developmen, Inernaional Economic Review, Vol. 42, No.1, Tirole. J., 1985, Asse bubbles and overlapping generaions, Economerica 53, Weil, Philippe,. 1987, Confidence and he real value of money in an overlapping generaions economy, Quarerly Journal of Economics 102, Woodford, M., 1995, Price-level deerminacy wihou conrol of a moneary aggregae, Carnegie-Rocheser Conference Series on Public Policy 43,

27 bˆ bˆ g b s b 26

30 a a = a +1 a ~ W k k = +1 a 0 k 0 k ~ ~ B k = f ' 1 ( ~ r ) GR D G k k 27

36 f ( k) (1 + n) k k k ~ B k GR k ~ k 28

財政赤字の経済分析：中長期的視点からの考察

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