Title 経済政策における時間非整合性 : 展望 Author(s) 木内, 祐輔 Citation 大阪大学経済学. 55(3) P.45-P.63 Issue Date Text Version publisher URL

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1 Title 経済政策における時間非整合性 : 展望 Author(s) 木内, 祐輔 Citation 大阪大学経済学. 55(3) P.45-P.63 Issue Date Text Version publisher URL DOI /17414 rights

2 Vol.55 No.3 December 2005 (1) (2) (3) 3 Keywords: ; ; ;. JEL Classification: E61; E62; H Kydland and Prescott (1977) 1 Fischer (1980) ykinai@js8.so-net.ne.jp 1 Stroz (1956) Kydland and Prescott (1977)

3 46 Vol.55 No.3 Fischer (1980) (1) (2) (3) (1) Chamley (1986) Judd (1985) 2 Laibson (1997) Barro (1999)

4 December (2) (2) 3 (3) (2) 3 2 Fischer (1980) Barro and Gordon (1983) Catenaro (2000) Fischer (1980) Fischer 2 benevolent Fischer 4 Fischer ; f 1 (x 1, x 2 ) + f 2 (x 1, x 2 ) ) 6 x 2 max F = f 1 (x 1, x 2 ) + f 2 (x 1, x 2 ) (1) F x 1 = f f 2 1 = 0, F x 2 = f f 2 2 = 0 (2) ( 5 Blanchard and Fischer (1989) Drazen (2000) 6

5 48 Vol.55 No.3 2 x 1 max x 2 f 2 (x 1, x 2 ) max J f 1 (x 1, g 1 ) + f 2 (x 1, x 2, g 2 ) (4) x 1,x 2 [ max max g 1,g 2 x 1,x 2 ] J g 1, g 2 (4) f 2 2 = 0 x 2 x 1 x 2 = x 2 (x 1) max x 1 f 1 (x 1, x 2 (x 1)) + f 2 (x 1, x 2 (x 1)) f f 1 2 x 2 x 1 + f 2 1 = 0 (3) 7 (2) (3) f1 1 + f 2 1 x 2 + f1 2 x + f 2 x 2 2 = 0 f 1 x 2 2 = 0 1 x 1 = x 1 (g 1, g 2 ), x 2 = x 2 (g 1, g 2 ) [ max f 1 (x g 1,g 1 (g 1, g 2 ), g 1 ) + f 2 (x 1 (g 1, g 2 ), x 2 (g 1, g 2 ), g 2 ) ] 2 (1) 1 2 g Stokey (1991)

6 December Fischer (1980) 3 Xie (1997) 9 Chamley (1986) Judd (1985) 10 9 (1989) 8 (1997) Mino (2001b) 10 Chamley (1986) Judd (1985) 0 ln c t + ln g t y t = Ak t c, k, g, τ max 0 {ln c t + ln g t }e δt dt (5) s.t. k = (1 τ t )Ak t c 1 = ln c t + ln g t + λ t {(1 τ)ak c t } λ = λ{δ (1 τ t )A} (6) c t = δk t (7) g t = τy t = τak t τ t = δ (8) 2A (6) ;

7 50 Vol.55 No.3 2 = ln(δk t ) + ln(τ t Ak t ) + φ t {(1 τ t )Ak t δk t } + π t λ t {δ (1 τ t )A} (9) φ π (6) δ τ t = ( ) (10) 2A lim π T λ T e δt e δt T (10) (8) lim π tλ t e δt = 0 (11) t (1989) V 1 (0) λ 0 = π 0 = 0 (12) 11 co-state variable π π λ λ Karp and Lee (2003) 11 V 1 ( ) Value Function (12) A.1 Xie (1997) J(k, t) value function = = 12 δj(k, t) = max {U(c) c + J k (k, t)( f (k) b(k)τ(k) c)} + J t (k, t) (13) Karp and Lee value function t k J(k, t) = W(k) + Z(t) 13 Cellini and Lambertini (2004) (1) (2) (1997) 14 Kemp, Long and Shimomura (1993) Judd (1985) 12 g t b(k) g(k, t) = b(k)τ(t) 13 Mino (2001a) 14 Tsutsui and Mino (1990) value function

8 December value function 4 2 Fischer (2005) Chari and Kehoe (1990) Fischer (1980) 16 sustainable plan Kotlikoff, Persson and Svensson (1988) 17 Bassetto (2005) Fischer (1980) 1) 16 (1986) pp Philippe and Paul (2002) Lorz (2004) 5.1

9 52 Vol.55 No.3 2) 18 Bassetto 1) R( ) 2) X 3) 1) R(X) 19 1 Bassetto 4.2 Benhabib and Rustichini (1997) 2 k t w t c t L t b t r t 18 Chari, Kehoe and Prescott (1989) 19 Bassetto Schelling timing...commitment is the choice of the strategy that the government will unconditionally follow for the remainder of its interaction with the private sector. max β t {u(c t ) v(l t )} (14) {c t,l t } t=0 s.t. r t (k t + b t ) + w t L t c t = k t+1 + b t+1 w t u (c t ) v (L t ) = 0 u (c t ) βr t+1 u (c t+1 ) = 0 (15) {r t, w t, b t } max {r t,w t,b t } β t {u(c t ) v(l t )} t=0 1) (15) 2) r t (k t + b t ) + w t L t c t = k t+1 + b t+1 (16) 3) G k t+1 + c t + G f (k t, L t ) 0 (17) Chamley (1986) Benhabib and Rustichini incentive compatibility s

10 December β t s {u(c s ) v(l s )} V D (k s, b s ) (18) t=s t 1 t t + 1 t + 2 s Kinai (2005a) Benhabib and Rustichini (1997) 1: t t + 1 Boldrin and Rustichini (2000) 2 c y t co t+1 t max u(c y t ) + βu(c0 t+1 ) (p t+1 τ t ) 21 Krusell, Quadrini and Rios-Rull (1997) 22 Breyer (1994) Galasso and Profeta (2002)

11 54 Vol.55 No.3 c y t + s t = w t (1 τ t ) c o t+1 = (1 + r t+1 )s t + p t+1 (τ t ) Majority Voting t 1 (1) t τ t (2) t + 1 ;τ t+1 t τ t τ t τ t+1 0 t 1 σ y t : [τ, τ 1,...τ t 1 ] [0, 1] σ o t : [τ, τ 1,...τ t 1 ] [0, 1] Boldrin and Rustichini 4.1 Kotlikoff et al. (1988) Majority Voting 23 Azariadis and Galasso (2002) Majority Voting Median Voter Theorem 24 Razin and Sadka (2004) Razin and Sadka Median Voter Grossman and Helpman (1998) Bassetto (1999) Renström (1996) 2 Bassetto Majority Voting Casamatta, Cremer and Pestieau (2000) Kinai (2005b) Bassetto (1999)

12 December Hassler, Storesletten and Zilibotti (2003a, b) Hassler et al. (2003a) Ramsey Allocation Hassler et al. (2003b) 5.2 Fischer (1980) 26 Persson and Tabellini (1994) Persson and Svensson (1989) Garfinkel and Lee (2000) Fischer (1980) Grossman and Helpman (1994) n i {1,..., n} U i ( ) = α i [c i1 + u(c i2 )] + (1 α i )u(g) (19)

13 56 Vol.55 No.3 2: (Garfinkel and Lee (2000) ) α (0, 1) α n i=1 U i ( ) benevolent Fischer 2 2 i 2 α α Garfinkel and Lee α Fischer time-inconsistency Fischer Fischer (1980) Boadway and Keen (1998) Batina (1999) Armenter (2004) 2 Fischer (1980) Boadway and Keen (1998) Batina (1999) Armenter (2004) Fischer (1980) 2

14 December c i n i (i = 1, 2) 1 2 3: W = λu(c 1, n 1 ) + u(c 2, n 2 ) (20) λ Armenter λ 6.2 Sato (2002) Qian and Roland (1998) 27 Qian and Roland 28 Qian and Roland (1998) Qian and Roland 27 Kornai, Maskin and Roland (2003) (2003) 28 Sato (2002) 29 Coate (1995) (2003)

15 58 Vol.55 No.3 30 vs. (Mitsui and Sato, 2001) (Köthenbürger, 2004) { }} { = }{{} + Alvarez, Kehoe and Neumeyer (2004) Lucas and Stokey (1983) Persson, Persson and Svensson (1987) 32 Dixit and Lambertini (2003) 31 Persson and Tabellini (1990) 32 Persson, Persson and Svensson (2005) Persson et al. (1987, 2005)

16 December Leeper (1991) FTPL (Fiscal Theory of Price Level) Woodford (2001) 33 (2000) 6.4 Persson and Tabellini (2004) Brender and Drazen (2004) 33 7 Lohmann (1992)

17 60 Vol.55 No.3 A A.1 (12) 3 (12) value function value function 2 { V 2 (k t ) = max (ln c t + ln g t )e δt dt, 0 } s.t. t = 0 λ 0 = V 2(k 0 ) k 0 (21) value function max π 0 V 1 (k 0,λ 0 ) 35 π 0 = V 1(k 0,λ 0 ) λ 0 = 0 (23) (12) t [0, ] π t = V 1(k t,λ t ) λ t = 0 π t Xie (1997) (11) π 0 = 0 π 0 0 costate variable { V 1 (k t,λ t ) = max (ln c t + ln g t )e δt dt, 0 } s.t. (6), (7), t = 0 π 0 = V 1(k 0,λ 0 ) λ 0 (22) π 0 k 0 Alvarez, F., P. J. Kehoe, and P. Neumeyer (2004) The Time Consistency of Optimal Monetary and Fiscal Policies. Econometrica. 72 (2), Armenter, R. (2004) Redistribution, Time-Consistent Fiscal Policy, and Representative Democracy. mimeo, Federal Reserve Bank of New York. 35 V 1 ( )

18 December Azariadis, C. and V. Galasso (2002) Fiscal Constitutions. Journal of Economic Theory. 103 (2), Barro, R. J. (1999) Ramsey Meets Laibson in the Neoclassical Growth Model. The Quarterly Journal of Economics. 114 (4), and D. B. Gordon (1983) A Positive Theory of Monetary Policy in a Natural Rate Model. Journal of Political Economy. 91 (4), Bassetto, M. (1999) Political Economy of Taxation in an Overlapping-generations Economy. Discussion Paper / Institute for Empirical Macroeconomics 133, Federal Reserve Bank of Minneapolis. (2005) Equilibrium and Government Commitment. Journal of Economic Theory. 124 (1), Batina, R. G. (1999) Tax Evasion and the Time Consistency of the Government s Income Tax Policy. Japanese Economic Review. 50 (2), Benhabib, J. and A. Rustichini (1997) Optimal Taxes without Commitment. Journal of Economic Theory. 77 (2), Blanchard, O. and S. Fischer (1989) Lectures on Macroeconomics, The MIT Press. Boadway, R. and M. Keen (1998) Evasion and Time Consistency in the Taxation of Capital Income. International Economic Review. 39 (2), Boldrin, Michele and Aldo Rustichini (2000) Political Equilibria with Social Security. Review of Economic Dynamics. 3 (1), Brender, A. and A. Drazen (2004) Political Budget Cycles in New versus Established Democracies. NBER Working Papers Breyer, F. (1994) Political Economy of Intergenerational Redistribution. European Journal of Political Economy. 10 (1), Casamatta, G., H. Cremer, and P. Pestieau (2000) The Political Economy of Social Security. Scandinavian Journal of Economics. 102 (3), Catenaro, M. (2000) Time Inconsistency: an Updated Survey of the Literature. Working Paper 29- Dicembre, University of Milan-Bicocca. Cellini, R. and L. Lambertini (2004) Time Consistent Fiscal Policies in a Ramsey Economy. Working Paper 522, Dipartimento di Scienze Economiche, Universita degli Studi di Bologna. Chamley, C. (1986) Optimal Taxation of Capital Income in General Equilibrium with Infinite Lives. Econometrica. 54 (3), Chari, V. V. and P. J. Kehoe (1990) Sustainable Plans. Journal of Political Economy. 98 (4), ,, and E. C. Prescott (1989) Time Consistency and Policy. in R. J. Barro, ed., Modern Business Cycle Theory, Cambridge, Mass: Harvard University Press, Coate, S. (1995) Altruism, the Samaritan s Dilemma and Government Transfer Policy. American Economic Review. 85 (1), Dixit, A. and L. Lambertini (2003) Interactions of Commitment and Discretion in Monetary and Fiscal Policies. American Economic Review. 93 (5), Dirazen, A. (2000) Political Economy in Macroeconomics, Princeton University Press. Fischer, S. (1980) Dynamic Inconsistency, Cooperation and the Benevolent Dissembling Government. Journal of Economic Dynamics and Control. 2 (1), Galasso, V. and P. Profeta (2002) Political Economy Models of Social Security: A Survey. European Journal of Political Economy. 18 (1), Garfinkel, M. R. and J. Lee (2000) Political Influence and the Dynamic Consistency of Policy. American Economic Review. 90 (3), Grossman, G. M. and E. Helpman (1994) Protection for Sale. American Economic Review. 84 (4), , and (1998) Intergenerational Redistribution with Short-Lived Governments. Economic Journal. 108 (127), Hassler, J., K. Storesletten, and F. Zilibotti (2003a) Democratic Public Good Provision. C.E.P.R. Discussion Papers 4044.,,and (2003b) Dynamic Political Choice in Macroeconomics. Journal of the European Economic Association.1 (2-3),

19 62 Vol.55 No.3 Judd, K. L. (1985) Redistributive Taxation in a Simple Perfect Foresight Model. Journal of Public Economics. 28 (1), Karp, L. and I. H. Lee (2003) Time-consistent Policies. Journal of Economic Theory. 112 (2), Kemp, M. C., N. V. Long, and K. Shimomura (1993) Cyclical and Noncyclical Redistributive Taxation. International Economic Review. 34 (2), Kinai, Y. (2005a) Analysis of Optimal Taxation in an OLG Model: from the Viewpoint of Time- Consistency. Discussion Papers in Economics and Business 05-04, Osaka University. (2005b) Solution Concept for Intergenerational Conflict: the Role of Inter-generational Bargaining. mimeo, Osaka University. Kornai, J., E. Maskin, and G. Roland (2003) Understanding the Soft Budget Constraint. Journal of Economic Literature. 41 (4), Köthenbürger, M. (2004) Tax Competition in a Fiscal Union with Decentralized Leadership. Journal of Urban Economics. 55 (3), Kotlikoff, L. J., T. Persson, and L. E. O. Svensson (1988) Social Contracts as Assets: A Possible Solution to the Time-Consistency Problem. American Economic Review. 78 (4), , V. Quadrini, and J.-V. Rios-Rull (1997) Politico-economic Equilibrium and Economic Growth. Journal of Economic Dynamics and Control. 21 (1), Kydland, F. E. and E. C. Prescott (1977) Rules Rather Than Discretion: The Inconsistency of Optimal Plans. Journal of Political Economy. 85 (3), Laibson, D. (1997) Golden Eggs and Hyperbolic Discounting. The Quarterly Journal of Economics. 112 (2), Leeper, E. M. (1991) Equilibria under Active and Passive Monetary and Fiscal Policies. Journal of Monetary Economics. 27 (1), Lohmann, S. (1992) Optimal Commitment in Monetary Policy: Credibility versus Flexibility. American Economic Review. 82 (1), Lorz, O. (2004) Time Consistent Optimal Redistribution Policy in an Overlapping Generations Model. Journal of Public Economic Theory. 6 (1), Lucas, R. E. and N. L. Stokey (1983) Optimal Fiscal and Monetary Policy in an Economy Without Capital. Journal of Monetary Economics. 12 (1), Mino, K. (2001a) On Time Consistency in Stackelberg Differential Games. Discussion Paper 0111, Faculty of Economics. Kobe University. (2001b) Optimal Taxation in Dynamic Economies with Increasing Returns. Japan and the World Economy. 13 (3), Mitsui, K. and M. Sato (2001) Ex ante Free Mobility, Ex post Immobility, and Time Consistency in a Federal System. Journal of Public Economics. 82 (3), Persson, M., T. Persson, and L. E. Svensson (1987) Time Consistency of Fiscal and Monetary Policy. Econometrica. 55 (6), ,, and (2005) Time Consistency of Fiscal and Monetary Policy: A Solution. National Bureau of Economic Research, Working Paper Persson, T. and G. Tabellini (1990) Macroeconomic Policy, Credibility and Politics, London, New York and Melbourne: Harwood Academic. and (1994) Representative Democracy and Capital Taxation. Journal of Public Economics. 55 (1), and (2004) Constitutional Rules and Fiscal Policy Outcomes. American Economic Review. 94 (1), and L. E. Svensson (1989) Why a Stubborn Conservative Would Run a Deficit: Policy with Time- Inconsistent Preferences. The Quarterly Journal of Economics. 104 (2), Philippe, M. and T. Paul (2002) Time-consistent Linear Taxation and Redistribution in an Overlappinggenerations Framework. Oxford Economic Papers. 54 (2), Qian, Y. and G. Roland (1998) Federalism and the Soft Budget Constraint. American Economic Review. 88 (5), Razin, A. and E. Sadka (2004) Privatizing Social Security: A Political-Economy Approach. Monetary and Economic Studies, Bark of Japan. 22 (S-1),

20 December Renström, T. I. (1996) Endogenous Taxation: an Overlapping Generations Approach. Economic Journal. 106, Sato, M. (2002) Intergovernmental Transfers, Governance Structure and Fiscal Decentralization. Japanese Economic Review. 53 (1), Stokey, N. L. (1991) Credible Public Policy. Journal of Economic Dynamics and Control. 15 (4), Stroz, R. H. (1956) Myopia and Inconsistency in Dynamic Utility Maximization. Review of Economic Studies. 23 (3), Tsutsui, S. and K. Mino (1990) Nonlinear Strategies in Dynamic Duopolistic Competition with Sticky Prices. Journal of Economic Theory. 52 (1), Woodford, M. (2001) The Taylor Rule and Optimal Monetary Policy. American Economic Review. 91 (2), (2003) (1986) (1997) (2005) 4 (1989) 5 (2000) Xie, D. (1997) On Time Inconsistency: A Technical Issue in Stackelberg Differential Games. Journal of Economic Theory. 76 (2), A Literature Survey of Time-inconsistency Problem in Economic Policy Yusuke Kinai In this paper, we survey the literature on the time-inconsistency problem, which means that, policies that were determined to be optimal at the initial point are no longer optimal later in time. Over the lact two or three decades, the issue of time-inconsistency problem in economic policy has been extensively analyzed in the context of (1) differential game, (2) commitment problem, and (3) political economy. This paper provides a survey on the time-inconsistency problem from the above three approaches and points out the problems to be analyzed in the future. Moreover, we investigate the problem s application. Keywords: Time-inconsistency; Commitment; Differential Games; Political Economy. JEL Classification: E61; E62; H21.

財政赤字の経済分析：中長期的視点からの考察

財政赤字の経済分析：中長期的視点からの考察 1998 1999 1998 1999 10 10 1999 30 (1982, 1996) (1997) (1977) (1990) (1996) (1997) (1996) Ihori, Doi, and Kondo (1999) (1982) (1984) (1987) (1993) (1997) (1998) CAPM 1980 (time inconsistency) Persson, Persson