Transcript Lecture 22 - Nottingham

L11200 Introduction to Macroeconomics 2009/10
Lecture 22:
Public Debt I
Reading: Barro Ch.14
22 March 2010
Introduction
• Last time: effect of different forms of taxation
on real activity
– Labour income and asset income taxes both
proved ‘distortionary’
– Cost to society was lower output and income
• Today: the ‘public budget’
– Governments’ budgets and debt
Public Debt
• So far, considered how government raise
income (tax) and spend revenue
– Governments can also amass assets / incur debts
– Call the government’s budget position the ‘public
budget’
– U.K./U.S. governments currently have large public
deficits (expenditure > income) and also large
public debts.
Government Bonds
• Government can borrow by issuing ‘bonds’
– An i.o.u. from the government, bought by
households
– So households can either buy private bonds, or
government bonds
Btg  Bt  Btg
– In aggregate, Bt=0, so aggregate household bond
holdings are equal to Btg
Government Budget Constraint
• Previous government budget constraint
Gt  Vt  Tt  (M t  M t 1 ) / Pt
government spending + government transfers = tax revenue + real revenue from money
creation
• With borrowing/saving this becomes
Gt  Vt  it 1 ( B / Pt )  Tt  ( B  B ) / Pt  ( M t  M t 1 ) / Pt
g
t 1
g
t
g
t 1
spending + transfers + interest payments = tax revenue + real debt issue +real revenue from
money creation
Government Budget Constraint
• If Mt and Pt do not change over time,
simplifies to:
Gt  Vt  rt 1 ( Btg1 / P)  Tt  ( Btg  Btg1 ) / P
g
g
(
B

B
• If t
t 1 ) , government is saving, and vice-
versa
• So real government saving given by:
( Btg  Btg1 ) / P
‘National Saving’
• So saving of an economy is given by:
g
g
(
B

B
– Total private saving
t
t 1 ) / P (household
lending to other households cancels out)
– Total private capital investment K t  K t 1
g
g
– Government saving ( Bt  Bt 1 ) / P
– So government saving and private saving cancel
out (just a flow of money between the two)
Public Debt and Household Budget
• Household multiyear budget constraint:
C1  C2 / (1  r1 )  ...  (1  r0 )  ( B0 / P  K0 )  (w / P)1  L  (w / P)2  L / (1  r1 )  ...
s
1
s
2
(Vt  T1 )  (V2  T2 ) / (1  r1 )  (V3  T3 ) /[(1  r1 )  (1  r2 )]  ...
present value of consumption = value of initial assets + present value of wage incomes
+ present value of transfers net taxes
• Now add household government bond holding
C1  C2 / (1  r1 )  ...  (1  r0 )  ( B0 / P  BoG / P  K0 )  (w / P)1  L1s  (w / P)2  Ls2 / (1  r1 )  ...
(Vt  T1 )  (V2  T2 ) / (1  r1 )  (V3  T3 ) /[(1  r1 )  (1  r2 )]  ...
present value of consumption = value of initial assets + present value of wage incomes
+ present value of transfers net taxes
Government Borrowing and Taxation
• Now assume government has zero debt, and
no transfers but decides to lower taxes
without lowering spending
Gt  Vt  rt 1 ( Btg1 / P)  Tt  ( Btg  Btg1 ) / P
• With no debt or transfers, government has no
initial interest payments, so
G1  T1  ( B ) / P
g
1
Government Borrowing and Taxation
• In period 2, government repays all of its debts
G2  r  ( B1g / P)  T2  ( B2g  B1g ) / P
• For simplicity, assume borrowing was 1 unit
• So, interest due is r multiplied by ‘1’, bond to
be repaid is ‘1’:
G2  r  T2  1
• Hence:
T2  G2  1  r
Impact on households
• How does this impact on households?
C1  C2 / (1  r1 )  ...  (1  r0 )  ( B0 / P  BoG / P  K0 )  (w / P)1  L1s  (w / P)2  Ls2 / (1  r1 )  ...
(Vt  T1 )  (V2  T2 ) / (1  r1 )  (V3  T3 ) /[(1  r1 )  (1  r2 )]  ...
• T1 falls by 1, T2 rises by 1+r
• Present value  1  (1  r ) / (1  r )
 1  1
0
Decrease in year 1’s real taxes + present value of increase in year 2’s taxes
Debt Neutrality
• So effect of cutting taxes, then increasing
taxes again is 0
– Household pay lower tax in the first period
– But then have to pay higher taxes in the second
period
– No change to present value (cost of debt interest
offset by present value deduction)
Ricardian Equivalence
• This famous result is known as ‘Ricardian
Equivalence’
– Households view a cut in real taxes as equivalent
to an increase in the real budget deficit, and
hence higher future taxation
– So the real budget deficit is equivalent to the
present value of real future tax rises
Crucial Result for Public Policy
• Ricardian Equivalence implies
– Cutting taxes now to finance government
spending has no impact on the economy –
households ‘internalise the debt’ save more now
– Borrowing more now to finance government
spending has no impact on the economy –
households anticipate tax rises and save more
now
‘Fiscal Stimulus’
• No role for a fiscal stimulus
– Idea: government should borrow and spend more
now to ‘keep up demand’ during a recession
– Problem: government borrowing means future tax
rises for households
– Households anticipate this, and save more now
– Net effect (we have shown) is zero
Summary
• Government has an asset/debt position, just
like households
– Debts eventually have to be paid-off by lower
spending or more taxation
– Households know this, and offset govt activity
• Next time: intertemporal effects
– Taxes distorted output decision
– Intertemporal tax/spend policy distorts household
activity as well