Introduction
Chapter 20
Tax Inefficiencies and Their
Implications for Optimal Taxation
„ Markets do not take taxes lying down.
„ If there is some action that market participants can
undertake to minimize the burden of a tax, they will
do so.
„ This is true both for consumers and producers.
„ This lesson will illustrate how attempts to minimize
Jonathan Gruber
Public Finance and Public Policy
tax burdens have efficiency costs for society.
„ Since social efficiency is maximized at the
competitive equilibrium (in the absence of market
failures), taxing market participants entails
deadweight loss.
Aaron S. Yelowitz - Copyright 2005 © Worth Publishers
TAXATION AND ECONOMIC
EFFICIENCY
Graphical approach
„ We now move from discussing the effects of
taxation on equity to a discussion of its effect on
efficiency.
„ The focus therefore turns from prices to quantities.
„ Consider the impact of a 50¢ per gallon tax on the
suppliers of gasoline, illustrated in Figure 1.
1
Figure 1
Price per
gallon (P)
S2
S1
B
P2 = $1.80
DWL
P1 = $1.50
A
$0.50
The tax on gasoline shifts
the supply curve.
C
D1
Q2 = 90 Q1 = 100
Taxation and economic efficiency
Graphical approach
„ Before the tax was imposed, 100 billion gallons were
sold. Afterwards, only 90 billion gallons are sold.
„ Recall that the demand curve represents the social
marginal benefit of gasoline consumption, while the
supply curve represents the social marginal cost.
„
SMB=SMC at 100 billion gallons
„ Production less than that amount results in
deadweight loss. Beneficial trades are not made
because of the 50¢ per gallon tax.
Quantity in billions
of gallons (Q)
Taxation and economic efficiency
Elasticities determine tax inefficiency
„ The efficiency consequences would be identical
regardless of which side of the market the tax is
imposed on.
„ Just as price elasticities of supply and demand
determine the distribution of the tax burden, they
also determine the inefficiency of taxation.
„ Higher elasticities imply bigger changes in quantities,
and larger deadweight loss.
„ Figure 2 illustrates that deadweight loss rises with
elasticities.
1
Figure 2
Demand is fairly inelastic,
and DWL is small.
(a) Inelastic Demand
P
S2
Taxation and economic efficiency
Elasticities determine tax inefficiency
Demand is more elastic,
and DWL is larger.
(b) Elastic demand
P
„ With inelastic demand, there is a large change in
S2
S1
S1
B
P2
B
DWL
P1
P2
P1
A
50¢
Tax
C
DWL
A
50¢
Tax
D1
C
market prices with consumers bearing most of the
tax, but little change in quantity.
„ With more elastic demand, market prices change
more modestly and the supplier bears more of the
tax. The reduction in quantity is greater, as is the
deadweight loss triangle.
D1
Q2 Q1
Q
Q2
Q1
Q
Taxation and economic efficiency
Elasticities determine tax inefficiency
„ The inefficiency of any tax is determined by the
extent to which consumers and producers change
their behavior to avoid the tax.
„ Deadweight loss is caused by individuals and firms
making inefficient consumption and production
choices in order to avoid taxation.
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„ In reality, there are many inefficient, tax-avoiding
activities.
„ For example, the Thai government levies a tax on
signs in front of businesses, where the tax rate
depends on whether the sign is completely in Thai
(low tax), in Thai and English (medium tax), or
completely in English (high tax).
„
Deadweight loss in Thailand
Tax avoidance in practice
Many signs are in English, with a small amount of
Thai writing!
Taxation and economic efficiency
Determinants of deadweight loss
„ This formula for deadweight loss has many important
implications:
DWL = −
1
Q
× ηD × τ 2 ×
P
2
„ Deadweight loss rises with the elasticity of demand.
„ The appropriate elasticity is the Hicksian compensated
elasticity, not the Marshallian uncompensated elasticity.
„ Deadweight loss also rises with the square of the tax rate.
„ That is, larger taxes have much more DWL than smaller ones.
2
Taxation and economic efficiency
Determinants of deadweight loss
Figure 3
S3
P
„ This point about DWL rising with the square of the
tax rate can be illustrated graphically.
„ Marginal deadweight loss is the increase in
deadweight loss per unit increase in the tax.
„ See Figure 3.
3
S2
S1
D
P3
The next $0.10 tax
creates a larger marginal
DWL, BCDE.
B
P2
P1
A
The first $0.10 tax creates
little DWL, ABC.
C
$0.10
E
$0.10
D1
Q
Q3 Q2 Q1
Taxation and economic efficiency
Determinants of deadweight loss
Taxation and economic efficiency
Deadweight loss and the design of efficient tax systems
„ As the tax rate doubles, from 10¢ to 20¢, the
„ The insight that deadweight loss rises with the
deadweight loss triangle quadruples.
„ The area DBCE is three times larger than BAC.
The total deadweight loss from the 20¢ tax is DAE.
„ As the market moves farther and farther from the
competitive equilibrium, there is a widening gap
between demand and supply. The loss of these
higher surplus trades means marginal DWL gets
larger.
square of the tax rate has implications for tax policy
with respect to:
Preexisting distortions
Progressivity
„ Tax smoothing
„
„
Taxation and economic efficiency
Deadweight loss and the design of efficient tax systems
„ Preexisting distortions are market failures that are
In a market with a preexisting
distortion, taxes can create
larger (or smaller) DWL.
Figure 4
P
S2
P
S1
S2
S1
in place before any government intervention.
„
Externalities or imperfect competition are examples.
without any distortions and in one with positive
externalities.
SMC
B
„ Figure 4 contrasts the use of a tax in a market
G
E
A
D
C
F
H
D1
D1
Q2 Q1
No positive externality
Q
Q2 Q1 Q0
Q
Positive externality
3
Taxation and economic efficiency
Deadweight loss and the design of efficient tax systems
Taxation and economic efficiency
Deadweight loss and the design of efficient tax systems
„ Imposing the tax in the first market, without
„ This insight about deadweight loss also
externalities, results in a modest deadweight loss
triangle equal to BAC.
„ When an existing distortion already exists where the
firm is producing below the socially efficient level,
the deadweight loss is much higher. The marginal
deadweight loss from the same tax is now GEFH.
„ Of course, if there were negative externalities, such a
tax would actually improve efficiency.
demonstrates that a progressive tax system can be
less efficient.
„ Consider two tax systems – one a proportional 20%
payroll tax, and the other a progressive tax that
imposes a 60% rate on the rich, and a 0% rate on
the poor.
„ Figure 5 shows these cases.
DWL increases with the square of
the tax rate. Smaller taxes in
many markets are better.
Figure 5
S2
Wage (W)
S3
Wage (W)
S1
W2=11.18
S1
E
W2=22.36
A
W1=10.00
D
W1=20.00
F
C
D1
D1
I
Hours (H)
H2=894 H1=1,000
for society is the sum of two deadweight loss
triangles, BAC and EDF.
„ Under the progressive system, the efficiency loss is
the triangle GDI – that is, it adds the area GEFI but
does not include BAC.
„ Table 1 puts actual numbers to the picture.
Hours (H)
H3=837 H2=894 H1=1,000
Low Wage Workers
High Wage Workers
Taxation and economic efficiency
Deadweight loss and the design of efficient tax systems
Table 1
Low wage worker
Panel A
High wage worker
Panel B
Tax Rate
Below
$10,000
Tax Rate
Above
$10,000
Hours of
labor
supply
Deadweight
Loss from
Taxation
Hours of
labor
supply
Deadweight
Loss from
Taxation
Total
Deadweight
Loss
0
0
1000 (H1)
0
1000 (H1)
0
0
Proportional Tax
20%
20%
894 (H2)
$115.71
(area BAC)
894 (H2)
$231.42
(area EDF)
$347.13
(BAC +
EDF)
Progressive Tax
0%
60%
1000 (H1)
0
837 (H3)
$566.75
(area GDI)
$566.75
(EDF +
GEFI)
No Tax
„ Under the proportional system the efficiency loss
G
W 3=23.90
B
S2
Taxation and economic efficiency
Deadweight loss and the design of efficient tax systems
A lower proportional tax
creates less DWL than the
higher progressive tax.
„ In this case, a proportional tax is more efficient.
„ The large increase in deadweight loss arises because
the progressive tax is levied on a smaller tax base.
In order to raise the same amount of revenues on a
smaller base, the tax rate must be higher meaning a
higher marginal DWL.
„ This illustrates the larger point that the more one
loads taxes onto one source, the faster DWL rises.
The most efficient tax systems spread the burden
most broadly. Thus, a guiding principle for efficient
taxation is to create a broad and level playing field.
4
Taxation and economic efficiency
Deadweight loss and the design of efficient tax systems
„ The fact that DWL rises with the square of the tax
rate also implies that government should not raise
and lower taxes, but rather set a long-run tax rate
that will meet its budget needs on average.
„ For example, to finance a war, it is more efficient to
raise the rate by a small amount for many years,
rather than a large amount for one year (and run
deficits in the short-run).
„ This notion can be thought of as “tax smoothing,”
similar to the notion of individual consumption
smoothing.
ion The deadweight loss of
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taxing wireless communications
„ An interesting applied example computing DWL is
Hausman’s (2000) study of wireless
communications. He found that:
The federal/state tax on wireless phones was as high
as 25%.
„ There was 53¢ of DWL per $1 raised in revenue.
„ Fairly priced elastic commodity.
„ Imperfectly competitive market with high mark-ups.
„ Preexisting tax distortions.
„ Marginal DWL much higher – as high as 90¢ of
DWL per $1 raised.
„
Optimal commodity taxation
Ramsey rule
Optimal commodity taxation
„ Optimal commodity taxation is choosing tax rates
across goods to minimize the deadweight loss for a
given government revenue requirement.
„ The Ramsey Rule is:
MDWLi
λ
= λ ⇒τ =
MRi
ηD
„
„ The goal of the Ramsey Rule is to minimize
deadweight loss of a tax system while raising a fixed
amount of revenue.
„ The value of additional government revenues is
the value of having another dollar in the
government’s hands relative to its next best use in
the private sector.
It sets taxes across commodities so that the ratio of
the marginal deadweight loss to marginal revenue
raised is equal across commodities.
Optimal commodity taxation
Ramsey rule
Optimal commodity taxation
Inverse elasticity rule
„ λ measures the value of having another dollar in the
„ The inverse elasticity rule, which expresses the
government’s hands relative to the next best use in
the private sector.
„ Smaller values of λ mean additional government
revenues have little value relative to the value in the
private market.
Ramsey result in a simplified form, allows us to
relate tax policy to the elasticity of demand.
„ The government should set taxes on each
commodity inversely to the demand elasticity.
„
Less elastic items are taxed at a higher rate.
5
Optimal commodity taxation
Equity implications of the Ramsey rule
„ Two factors must be balanced when setting optimal
commodity taxes:
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Price reform in Pakistan
„ An interesting application of these rules is price
reform in Pakistan.
The elasticity rule: Tax commodities with low
elasticities.
„ The broad base rule: It is better to tax a wide variety of
goods at a lower rate, because deadweight loss
increases with the square of the tax rate.
„
„ Deaton (1997) found that the Pakastani government
was paying subsidies for wheat and rice, and was
collecting taxes on oils and fats.
„ The market conditions are summarized in Table 2.
2
„ Thus, the government should tax all of the
commodities that it is able to, but at different rates.
Table 2
Demand for Various Commodities in Pakistan
Include
Distributional
Concerns
Good
Subsidy
Price
Elasticity
Policy
Change
Welfare
Gain
Wheat
40%
-0.64
Reduce
subsidy
Small
Rice
40%
-2.08
Reduce
subsidy
Large
Reduce subsidy
Oil/Fat
-5%
-2.33
Reduce
tax
Large
Reduce tax further
Don’t reduce
subsidy
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Price reform in Pakistan
„ The subsidies generate overconsumption of wheat
and rice, and lead to particularly large efficiency
losses for rice.
„ The tax on oils/fats also generates deadweight loss.
„ Using a framework similar to Ramsey’s, Deaton
suggested a tax reform that would increase
efficiency and be revenue neutral: reduce the tax on
oils and fats, and make up for the lost tax revenues
by reducing the subsidies to rice (especially) and
wheat.
Price reform in Pakistan
OPTIMAL INCOME TAXES
„ Deaton also found that distributional considerations
„ Optimal income taxation is choosing the tax rates
might offset some of these conclusions.
„ Wheat and fats/oils were consumed quite heavily by
the poor, but rice was consumed fairly evenly
throughout the income distribution. This suggests
not to decrease the wheat subsidy on equity
grounds.
across income groups to maximize social welfare
subject to a government revenue requirement.
„
A key concern in the analysis is vertical equity.
6
Optimal income taxes
A simple example
„ Imagine we make the following assumptions:
„ Identical utility functions
„ Diminishing marginal utility of income
„ Total income is fixed
„ Utilitarian social welfare function
„ The optimal income tax system in such a case gives everyone
the same level of post-tax income.
„
„
Implies marginal tax rate of 100% for those with aboveaverage income.
The unrealistic assumption is that total income (labor supply) is
fixed with respect to taxes.
Optimal income taxes
General model with behavioral effects
„ The Laffer curve, which motivated the supply-side
Optimal income taxes
General model with behavioral effects
„ More generally, there are equity-efficiency tradeoffs.
„ Raising tax rates will likely affect the size of the tax
base. Thus, increasing the tax rate on labor income
has two effects:
„
„
Tax revenues rise for a given level of labor income.
Workers reduce their earnings, shrinking the tax
base.
„ At high tax rates, this second effect becomes
important.
Figure 7
The Laffer curve
demonstrates that at some
point, tax revenue falls.
Tax revenues
economic policies of the Reagan presidency is
shown in Figure 7.
7
„ If tax rates are too high and we are on the wrong
side of the Laffer curve, lowering tax rates increases
revenue.
right
side
0
Optimal income taxes
General model with behavioral effects
„ The goal of optimal income tax analysis is to identify a tax
schedule that maximizes social welfare, while recognizing
that raising taxes has conflicting effects on revenue.
„ The optimal tax system meet the condition that tax rates are
set across groups such that:
MU i
=λ
MRi
„ Where MUi is the marginal utility of individual i, and MR is
wrong
side
τ*%
100% Tax rate
Optimal income taxes
An example
„ As with optimal commodity taxation, this outcome
represents a compromise between two
considerations:
„
„
Vertical equity
Behavior responses
„ Figure 8 shows that optimal income taxation
equates this ratio across individuals, leading to a
higher tax rate for the rich.
the marginal revenue from that individual.
7
Optimal income taxes
The structure of optimal tax rates: Simulation exercise
Figure 8
MU/MR
„ Simulation exercises are the numerical simulation of
Mrs. Poor
Mr. Rich
⎛ MU ⎞
⎛ MU ⎞
λ =⎜
⎟ =⎜
⎟
⎝ MR ⎠poor ⎝ MR ⎠rich
economic agents’ behavior based on measured economic
parameters.
„ These are used to determine the optimal tax rates or other
parameters of interest.
„ Gruber and Saez (2000) considered a tax rate with:
„
„
„
„
Optimal income taxation
equates the ratio of
(MU/MR) across individuals.
10%
Tax rate
20%
Guaranteed income level (as with welfare)
Utilitarian SWF
Revenue neutral
Four income categories
„ They weighed the equity-efficiency implications here; their
results are presented in Figure 9.
9
Figure 9
Figure 9
Tax payments
Optimal Tax Results
$46,650
$10,320
$32K
To
$75K
$75K
and
Above
Guaranteed
income
level
Marginal Tax
Rates
68
66
56
49
$11,000
Average Tax
Rates
-161
12
40
47
Marginal rate are
higher on the poor.
$10,000
-$11,000
$10K
To
$32K
Income groups
$34,400
-$4,200
$0
To
$10K
$16,364 $32,000
$75,000
$100,000
Family income
The
Theoptimal
average
income
rate
taxdoes
schedule
not exceed
starts off
with a47%.
subsidy.
Optimal income taxes
The structure of optimal tax rates: Simulation exercise
„ Gruber and Saez (2000) found that marginal tax rates
were highest on the poor and lowest on the rich,
while average tax rates rose with income (because of
the loss of the grant).
„ Results of these sorts of exercises can be sensitive to
the formulation of the SWF.
TAX-BENEFITS LINKAGES AND THE
FINANCING OF SOCIAL INSURANCE
PROGRAMS
„ Tax-benefit linkages are direct ties between taxes
paid and benefits received.
„ Summers (1989) shows that such linkages can affect
the equity and efficiency of a tax. The link between
payroll taxes and social insurance benefits can lead
the incidence to fall more fully on workers than
might be presumed.
8
Tax-benefits linkages and the financing of
social insurance programs: The model
„ The key point of Summers’ analysis is that with
taxes alone, only the labor demand curve shifts, but
with tax-benefit linkages, the labor supply curve
shifts as well.
„ That is, workers are willing to work the same
amount of hours at a lower wage, because they get
some other benefit as well, such as workers’
compensation or health insurance.
„ This is illustrated in Figure 10.
10
Figure 10
Wage (W)
C
Creating
smaller
DWL.
S1
W1
W1
A
W2
W3
D
D1
D1
D2
L1
D2
Labor (L)
L2
L3
L1
Labor (L)
Figure 11
Wage (W)
S1
W1
A
Benefits =
Program cost
S2
W2
B
D1
W3
D2
L2
shifted onto workers in the form of lower wages,
and there is no deadweight loss or employment
reduction.
S2
B
W2
B
and employment falls by less.
„ Because of the smaller reduction in employment,
deadweight loss is smaller than with a pure tax. The
true “tax” is the difference between the statutory tax
and the employee’s valuation of the benefit.
„ Figure 11 shows the case of full valuation of the
benefit.
„ With full valuation, the cost of the program is fully
A
F
„ Wages adjust by more with the tax-benefit linkage,
Tax-benefits linkages and the financing of
social insurance programs: The model
S1
E
L2
Tax-benefits linkages and the financing of
social insurance programs: The model
Mandated benefits
also shift the
supply curve.
Wage (W)
L1
With full valuation of the
benefit, employment is
not reduced and there
is no DWL.
Labor (L)
Tax-benefits linkages and the financing of
social insurance programs: Issues raised
„ This raises some issues with tax-benefit linkages,
especially with respect to employer mandates.
„ If there is no inefficiency, why doesn’t the employer
simply provide the benefit without government
intervention?
„
Market failures, such as adverse selection, may be
present. The employer that provides a benefit such
as workers’ compensation or health insurance may
end up with high risks.
9
Tax-benefits linkages and the financing of
social insurance programs: Issues raised
„ When are there tax-benefit linkages?
„ They are strongest when taxes paid are linked directly
to a benefit for workers.
„ This generates the rise in labor supply.
„ There are a number of empirical studies that have
examined the incidence of social insurance
contributions on wages and employment.
„ Gruber (1994) examines a quasi-experiment
involving mandated maternity benefits, and finds
full wage shifting and little effect on labor supply.
10