Distortionary Taxes

• 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.

Country
Australia a
France c
Japan
Korea
United Kingdom a
United States i
Central government corporate income tax rate
2
Adjusted central government corporate income tax rate
3
Sub-central government corporate income tax rate
4
Combined corporate income tax rate
5
Targeted corporate tax rates
6
30.0
34.43
30.0
25.0
30.0
35.0
30.0
34.43
27.98
25.0
30.0
32.7
11.56
2.5
6.6
30.0
34.4
39.54
27.5
30.0
39.3
Y
Y
Y
Y
Y
Y
Source: OECD Tax Database

• Corporations frequently must pay taxes on earnings. Define

• 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.
(1
  
Y t
K t
  s )
R t

1
P t

1
 
Y t
K t
(1
 s )
(1
 
)


1



1

1


 t t
I

1

1


(1
 
)

 p t
I
 p t
I
 r
 t
I

1
  t

1
 tw
• Tax Wedge, tw, is defined as the extra cost of capital beyond the interest rate
.

• 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
  t
I

1
  t

1
 I
Distortion
 r
  t
I

1
  t

1
 p
I
K
K** K *

• 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

MPK  r
  t
I

1
  t

1

2

I
K***
K**
Original
Distortion
 r
  t
I

1
  t

1
 I
 r
  t
I

1
  t

1
 p
I
K
K *

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
3,616.50 Total expenditures Total receipts
Current receipts
Capital transfer receipts
Net lending or net borrowing (-)
3,586.30
30.20 Current expenditures
Gross government investment
Other
Less: Consumption of fixed capital
-456.30
4,072.80
3,898.80
397.10
29.20
252.20
Source: BEA Table 3.1

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
Contributions for government social insurance
Income receipts on assets
Current transfer receipts
Current surplus of government enterprises\2\
2,520.70 Consumption expenditures
880.60 Current transfer payments
98.30 Interest payments\1\
102.10 Subsidies\2\
-15.40
Net government saving -312.5
Source: BEA Table 3.1
3,898.80
1,975.70
1,517.80
348.00
57.30

• Primary deficit is the difference between current government and taxes.
– Primary Deficit = G t
– TAX t
• Total Deficit is primary deficit minus interest income earned on financial wealth.
– Total Deficit = G t
– TAX t
–rB t-1

• Government Wealth Accumulates through taxes.
B t
 
) t

1

( TAX t

G t
)
• Divide each equation by 1
(1
 r ) t
B t
B t

1

1
 r
 
1
 r
 t

1

( TAX t

G t

1
 r
 t
)
 
) x t x t

1
 y t


1
  x

1
  y
0 y
1 y
2
 y
3
 
....
 t

 

0 y t
 t


0
( TAX t

G t

1
 r
 t
)

• What government deficit is necessary to keep debt to GDP ratio constant.
• DEBT t
= -B t
• Assume steady growth path, Q t
= (1+g) constant primary deficit to GDP ratio t Q
0
  r )
B

1
Y
0
 t



0
( TAX t

G t
)
Y t

1
 g
 t

1
 r
 t psy

( TAX t

G t
)
Y t
  r )
DEBT

1
Y
0
  r ) psy r
 g and

• Define dy as steady state debt to GDP ratio
DEBT
DEBT t
Y t t
 
) t

1

( G t

TAX t
)
  r )
DEBT t

1
(1

)
 t

1

( G t

TAX t
)
Y t
• Primary deficit that maintains steady state debt is dy

(1
 r )
(1
 g ) dy



( G t

TAX t
Y t
)


SUS



( G t

TAX t
Y t
)


SUS 
1

(1
 r )
(1
 g )

 dy

180
160
140
120
100
80
60
40
20
0
Au st ra lia
Fra nce
G erma ny
Ita ly
Ja pa n ep ub
Ko re a
(R lic of
)
U ni te d
Ki ng do m
U ni te d
St at es
Source:
OECD
Database

• We divide savings into 2 parts:
S
Government
+ S
Private
= S
Public Saving/Government Saving
(Budget Surplus)
Private Saving
(Household Saving)
National Saving

r
(Geometry)
S
I r*
LF*
LF

• 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 ]
S
Government

TAX

G

• 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
S
Private

DI C

 
C


• 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

r S
I
I
r** r*
LF* LF**
LF

2.8
2.4
2.0
.216
.214
.212
1.6
1.2
.210
.208
0.8
0.4
.206
.204
0.0
.202
03Q1 03Q3 04Q1 04Q3 05Q1 05Q3 06Q1
TIPS I/Y
Source: OECD
National Accounts,
St. Louis Fed Data
Base

r S
S
I
?
r** r*
LF**
LF*
LF

• 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. t



0
C t
(1
 r ) t
 t



0
Y t

TAX
(1
 r ) t t
 t



0
Y t
(1
 r ) t
 t



0
TAX t
(1
 r ) t

• For simplicity, assume that government debt is initially zero.
• Present value of taxes equal to present value of government spending t



0

TAX
1
 r t t

 t



0

1
G t
 r t

• If taxes are cut today w/o changing pv. of government spending, output

• Household budget constraint depends only on present value of government spending. t



0
C t
(1
 r ) t
 t



0
Y t
(1
 r ) t
 t



0
G t
(1
 r ) t
• 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.
– National savings unchanged.

• 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.