the real deficit of one unit requires the government to issue one unit of real public debt at the end of year 1
Bg1 /P = 1.
22
Budget Constraints and Budget Deficits
19
Budget Constraints and Budget Deficits
A Simple Case of Ricardian Equivalence Government Budget Constraint Gt+ r·Bgt−1/P = Tt+ (Bgt−Bgt−1)/P the government starts with Bg0/P = 0. In year 1：G1 = T1 + Bg1/P
A Simple Case of Ricardian Equivalence Assume Bg2 /P = Bg3 /P = ···= 0. G2 + r·Bg1 /P = T2 + (Bg2−Bg1)/P Bg1/P = 1 and Bg2/P = 0 G2 + r = T2 − 1 T2 = G2 + 1 + r
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Budget Constraints and Budget Deficits
A Simple Case of Ricardian Equivalence r0 = r1 = r2 = ···= r . Mt, and Pt, do not change over time. Real transfers, Vt, are zero each year. the government has a given time path of purchases, Gt
1991 1059.99
1992 1282.72
1993 1540.74
1994 2286.40
1995 3300.30
1996 4361.43
1997 5508.93
1998 7765.70
1999 10542.00
2000 13674.00
2008年6月末中央财政国债总余额为52385.86亿元，控制在年 末55185.85亿元国债余额限额以内 (2008年上半年国债管理报 告)
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Budget Constraints and Budget Deficits
The Government’s Budget Constraint
Gt + Vt + it−1·(Bgt−1/ Pt ) = Tt + (Bgt − Bg t−1)/Pt + (Mt−Mt−1)/Pt
real purchases+ real transfers + real interest payments =
real national saving= Kt− Kt−1
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Budget Constraints and Budget Deficits
Household’s multiyear budget constraint
C1 + C2/(1+r1) + ···= (1+r0)·( B0/P+K0) +(w/P)1·Ls1 +(w/P)2 ·Ls2 /(1+r1)+ ··· +( V1 − T1) + ( V2 − T2)/( 1 + r1) +( V3 − T3)/[(1+ r1) ·( 1 + r2) ] + ···
17
Budget Constraints and Budget Deficits
multiyear household budget constraint with government bonds
C1 + C2/(1+r1) + ···= (1+r0)·( B0/P+Bg0/P+K0) +(w/P)1·Ls1 +(w/P)2 ·Ls2 /(1+r1) + ··· +( V1 − T1) + ( V2 − T2)/( 1 + r1) +( V3 − T3)/[(1+ r1) ·( 1 + r2) ] + ···
− (Bgt− Bgt−1)/P = Tt − 【Gt+ Vt+ rt−1·Bgt−1/P】
real government saving = real taxes− real government expenditure
13
Budget Constraints and Budget Deficits
11
Budget Constraints and Budget Deficits
The Budget Deficit
real government saving = − (Bgt − Bgt−1)/P
12
Budget Constraints and Budget Deficits
The Budget Deficit
2
3
The History of U.S. and U.K. Public Debt
4
The History of U.S. and U.K. Public Debt
5
The Data of Chine计年鉴2001年7-27)
1990 890.34
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Budget Constraints and Budget Deficits
15
Budget Constraints and Budget Deficits
Public Saving, Private Saving, and National Saving
real household saving(economy-wide) = Kt− Kt−1 + (Bgt − Bgt−1)/ P
private bonds+ government bonds Bt = 0 still holds in the aggregate. total bond holdings of all households= Bgt
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Budget Constraints and Budget Deficits
24
Budget Constraints and Budget Deficits
A Simple Case of Ricardian Equivalence If the government replaces a unit of real taxes with a unit of real budget deficit, households know that the present value of next year’s real taxes will rise by one unit. Thus, the real budget deficit is the same as a real tax in terms of the overall present value of real taxes. This finding is the simplest version of the Ricardian equivalence theorem on the public debt.
real taxes + real debt issue + real revenue from money creation
10
Budget Constraints and Budget Deficits
When nominal money, Mt, and the price level, Pt, do not change over time, the government’s budget constraint becomes. Gt+ Vt+ rt−1·Bgt−1/P = Tt+ (Bgt− Bg t−1)/P
The Budget Deficit
the government’s revenue exceeds its expenditure, and the government has a budget surplus.
the government has a balanced budget, and the government’s real saving is zero.
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Budget Constraints and Budget Deficits
A Simple Case of Ricardian Equivalence
decrease in year 1’s real taxes+ present value of increase in year 2’s taxes = −1 + ( 1 + r)/( 1 + r) = −1 + 1 =0
The Government’s Budget Constraint
Gt + Vt = Tt + ( Mt− Mt−1)/ Pt The real value of these interest payments,
it−1·(Bgt−1/Pt) adds to the government’s expenditure or uses of funds on the left-hand side of the government’s budget constraint.
25
Budget Constraints and Budget Deficits