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Fiscal Policy
Distortionary Taxes
The Data
• Information on Government Budgets is typically
available from Treasury/Finance Ministry.
– IMF Government Finance Statistics (not available on
line) collects a large amount of available data.
• Government accounts typically part of national
income and product accounts.
• Information on Taxation and Expenditure
available from OECD for rich countries.
Corporate Income Tax Rates
Central
Adjusted central
Sub-central
government
government
government
corporate income
corporate
corporate income
2
3
tax rate
income tax rate
tax rate 4
Country
Australia a
France c
Japan
Korea
United Kingdom a
United Statesi
30.0
34.43
30.0
25.0
30.0
35.0
30.0
34.43
27.98
25.0
30.0
32.7
Source: OECD Tax Database
11.56
2.5
6.6
Combined
corporate
income
tax rate 5
Targeted
corporate
tax rates 6
30.0
34.4
39.54
27.5
30.0
39.3
Y
Y
Y
Y
Y
Y
Tax Rates
•
•
•
•
Corporations frequently must
pay taxes on earnings. Define
tax rate, ( ).
Corporations also receive
deductions for costs of capital
Define deduction rates = (s)
Maximize after-tax profits
implies that after-tax marginal
product of capital = after-tax
cost of capital.
Tax Wedge, tw, is defined as
the extra cost of capital
beyond the interest rate.
(1   )
Yt
R
 (1  s ) t 1
Kt
Pt 1
Yt


Kt
 I
 1   tI1 
(1  s ) 
1  r  
 (1   )  pt
(1   ) 
 1   t 1 

 ptI   r   tI1   t 1    tw
Capital and the Tax Wedge
• An increase in the tax wedge (the excess
taxes paid on investing in capital
equipment) increases the cost of capital
and reduces optimal capital.
• The difference between the marginal
product of capital and the cost of capital is
the economic surplus value of the capital
• The value of the efficiency loss for the
economy is specified by the triangle.
MPK
 r    

Distortion
I
t 1

  t 1   tw p I

r     tI1   t 1  p I
K
K**
K*
Tax Distortions
•
The size of tax distortions grows faster than
the size of the tax rate.
–
•
•
Intuition: Diminishing Marginal Returns. Small tax
wedges eliminate only those investment projects
which are slightly more profitable than the cost of
capital. The larger the tax rate, the more valuable
will be the projects that are eliminated.
Simple models assume that distortions are
proportional to the square of the tax wedge.
Two implications
1. “Laffer Curve”
2. Tax Smoothing
 r    
MPK
I
t 1

  t 1   2tw p I
 r    
Original
Distortion
I
t 1
 r    
I
t 1

  t 1   tw p I

  t 1  p I
K
K***
K**
K*
Government Borrowing
Table 3.1. Government Receipts and Expenditures
[Billions of dollars]
Bureau of Economic Analysis
Downloaded on 10/31/2006 At 11:17:55 AM Last Revised October 27, 2006
Total receipts
3,616.50 Total expenditures
Current receipts
3,586.30
Capital transfer receipts
30.20
Current expenditures
Gross government investment
Other
Less: Consumption of fixed capital
Net lending or net borrowing (-)
-456.30
Source: BEA Table 3.1
4,072.80
3,898.80
397.10
29.20
252.20
Government Saving
Table 3.1. Government Current Receipts and Expenditures
[Billions of dollars]
Bureau of Economic Analysis
Downloaded on 10/31/2006 At 11:17:55 AM Last Revised October 27, 2006
2005
Current receipts
3,586.30
Current expenditures
Current tax receipts
2,520.70 Consumption expenditures
Contributions for government social insurance
880.60 Current transfer payments
Income receipts on assets
98.30 Interest payments\1\
Current transfer receipts
102.10 Subsidies\2\
Current surplus of government enterprises\2\
-15.40
Net government saving
Source: BEA Table 3.1
-312.5
3,898.80
1,975.70
1,517.80
348.00
57.30
Primary vs. Total Deficit
• Primary deficit is the difference between
current government and taxes.
– Primary Deficit = Gt – TAXt
• Total Deficit is primary deficit minus interest
income earned on financial wealth.
– Total Deficit = Gt – TAXt –rBt-1
Government Debt
• Government Wealth Accumulates through
Bt  (1  r ) Bt 1  (TAX t  Gt )
taxes.
• Divide each equation by (1 1r )
t
Bt
1  r 
t

Bt 1
1  r 
t 1

(TAX t  Gt )
1  r 
t
 xt  xt 1  yt 


t 0
t 0
(1  r ) B1   x1   y0  y1  y2  y3   ....   yt  
(TAX t  Gt )
1  r 
t
Sustainable Deficit
• What government deficit is necessary to keep
debt to GDP ratio constant.
• DEBTt = -Bt
• Assume steady growth path, Qt = (1+g)tQ0 and
constant primary deficit to GDP ratio
B1  (TAX t  Gt ) 1  g 
(1  r )

t
Y0
Yt
1

r
t 0
 
t
psy 
(TAX t  Gt )
Yt
 (1  r )
DEBT1
psy
 (1  r )
Y0
rg
Sustainable Deficit
• Define dy as steady state debt to GDP
ratio DEBTt  (1  r ) DEBTt 1  (Gt  TAX t )
DEBTt
DEBTt 1
(Gt  TAX t )
 (1  r )

Yt
(1  g )  Yt 1
Yt
• Primary deficit that maintains steady state
debt is
 (G  TAX ) 
(1  r )
SUS
dy 
dy  
(1  g )

 (Gt  TAX t ) 


Y
t


SUS
t
t
Yt


 (1  r ) 
 1 
dy

 (1  g ) 

Central Government Debt
(as a share of GDP)
180
160
140
120
100
80
60
40
20
0
Source:
a
Ja
(R
pa
ep
n
ub
U
ni
lic
te
of
d
)
Ki
ng
U
do
ni
m
te
d
St
at
es
ly
Ita
Ko
re
an
ce
G
er
m
an
y
Fr
Au
st
ra
lia
OECD
Database
Savings
• We divide savings
into 2 parts:
SGovernment
+
SPrivate
= S
Public Saving/Government Saving
(Budget Surplus)
Private Saving
(Household Saving)
National Saving
Competitive Market Equilibrium:
Loanable Funds Market
(Geometry)
r
S
I
r*
LF*
LF
Budget Surplus
• Economists typically distinguish between
two types of government outgoings.
– [G] Government expenditure is the purchases
of goods and services;
– [TR] Transfer payments are direct payments
to individuals for them to spend.
• Budget surplus is Taxes [TAX] net of
transfer payments less government
spending [G]
SGovernment  TAX  G
Private Saving
• Private saving is disposable income less
consumption.
– Disposable income is Income from Private
Sources plus Transfer Payments less Taxes.
– Income from Private Sources is GDP
SPrivate  DI  C  GDP  TAX  C 
Closed Economy
• In a closed economy, domestic savings is
the only source of financing for investment,
so the equilibrium real interest rate will clear
the market.
• The world economy is a closed economy.
• If we observe
– interest rates and saving/investment moving
together, then this is a shift in the demand
curve.
– Interest rates and saving/investment move in
opposite directions
Example: Investment Boom in
Japan as economy recovers
r
S
I
I´
r**
r*
LF*
LF**
LF
Rising Investment and Interest Rates
2.8
.216
2.4
.214
2.0
.212
1.6
.210
1.2
.208
Source: OECD
National Accounts,
0.8
.206
St. Louis Fed Data
Base
0.4
.204
0.0
03Q1
03Q3
04Q1
04Q3
TIPS
05Q1
I/Y
05Q3
.202
06Q1
Example: US Government runs a
deficit to finance a tax cut
r
S´
S
I
?
r**
r*
LF**
LF*
LF
Ricardian Equivalence
• Infinitely lived households choose a
consumption plan to maximize utility subject
to the PV of the consumption path being
equal to the PV of after-tax income. (for
simplicity) assumes zero initial financial
wealth.



Ct
Yt  TAX t
Yt
TAX t







t
t
t
t
(1

r
)
(1

r
)
(1

r
)
t 0
t 0
t 0
t  0 (1  r )

Government Budget Balance
• For simplicity, assume that government debt
is initially zero.
• Present value of taxes equal to present value
of government spending  TAX t  Gt


t
t
t 0 1  r 
t 0 1  r 
• If taxes are cut today w/o changing pv. of
government spending, output
Ricardian Equivalence
• Household budget constraint depends only on
present value of government spending.
C
Y
G


 (1  r )  (1  r )  (1  r )
• Timing of taxes does not matter for
consumption choice of households.
• Deficit caused by temporary tax cut w/o
changing government spending plans lead to
an increase in savings.


t
t 0

t
t
t 0
t
t
t 0
– National savings unchanged.
t
Why Not Ricardian
Equivalence?
• Myopia: Taxes in the far future may not
factor into consumption spending.
• Borrowing Constraints: Some households
spend all disposable income.
• Limited Lives: Households that die may not
care about taxes paid after their death.