chapter 20 tax inefficiencies and their implications for optimal taxation jonathan gruber public...

Chapter 20Tax Inefficiencies and Their

Implications for Optimal Taxation

Jonathan GruberPublic Finance and Public Policy

Aaron S. Yelowitz - Copyright 2005 © Worth Publishers

Introduction

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.

Introduction

This lesson will illustrate how attempts to minimize 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.

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 1Figure 1.

A

D1

S1

S2

BP2 = $1.80

Q2 = 90

$0.50

Price pergallon (P)

Quantity in billionsof gallons (Q)

C

P1 = $1.50

Q1 = 100

DWL

Figure 1

The tax on gasoline shifts the supply curve.

The tax creates deadweight loss.

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.


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 2Figure 2 illustrates that deadweight loss rises with elasticities.

P

Q

P2

P1

Q1Q2

D1

S1

S2

B

A

C

DWL

P

Q

P2

P1

Q1Q2

D1

S1

S2

B

A

C

DWL

(a) Inelastic Demand (b) Elastic demand

50¢Tax

50¢Tax

Figure 2Demand is fairly inelastic,

and DWL is small.

Demand is more elastic, and DWL

is larger.


Elasticities determine tax inefficiency With inelastic demand, there is a large

change in 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.


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.

Tax avoidance in practiceTax avoidance in practice

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). Many signs are in English, with a small

amount of Thai writing!

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Deadweight loss in Thailand

Excess Burden Measurement with Demand Curves

Pounds of barley per year

Pric

e pe

r po

und

of b

arle

y

a

Db

Sb

q1q2

ih

S’b

Pb

(1 + tb)Pb g f

d

Tax revenues

Excess burden of tax

Excess burden = ½ ηPbq1tb2


Determinants of deadweight loss This formula for deadweight loss has many

important implications:

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.

DWLQ

PD 1

22


Determinants of deadweight loss 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 3Figure 3.

P

Q

P2

P1

Q1Q2

D1

S1

S2

B

A

C

S3

Q3

P3

D

E

$0.10

$0.10

Figure 3

The first $0.10 tax creates little DWL, ABC.

The next $0.10 tax creates a larger marginal DWL,

BCDE.


Determinants of deadweight loss As the tax rate doubles, from 10¢ to 20¢,

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.

Taxation and economic efficiencyDeadweight loss and the design of

efficient tax systems

The insight that deadweight loss rises with the square of the tax rate has implications for tax policy with respect to: Preexisting distortions Progressivity Tax smoothing



Preexisting distortions are market failures that are in place before any government intervention. Externalities or imperfect competition

are examples. Figure 4Figure 4 contrasts the use of a tax in a

market without any distortions and in one with positive externalities.

P

QQ1

D1

S1

S2

B

A

C

P

QQ1

D1

S1

S2

E

D

F

SMCG

H

Q0

No positive externality Positive externality

Q2 Q2

Figure 4

In a market with a preexisting distortion,

taxes can create larger (or smaller) DWL.


efficient tax systems Imposing the tax in the first market,

without 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.



This insight about deadweight loss also 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 5Figure 5 shows these cases.

Wage (W)

Hours (H)

W2=11.18

W1=10.00

H1=1,000H2=894

D1

S1

S2

B

A

C

Wage (W)

Hours (H)

W2=22.36

W1=20.00

H1=1,000H2=894

D1

S1

S2S3

W3=23.90

H3=837

E

D

F

G

I

Low Wage Workers High Wage Workers

Figure 5

DWL increases with the square of the tax rate. Smaller taxes in many

markets are better.



Under the proportional system the efficiency loss 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 1Table 1 puts actual numbers to the picture.

Table 1

Low wage workerPanel A

High wage workerPanel B

Tax Rate Below

$10,000

Tax Rate

Above $10,00

0

Hours of labor

supply

Deadweight Loss from Taxation

Hours of labor

supply

Deadweight Loss from Taxation

Total Deadweigh

t Loss

No Tax 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)

A lower proportional tax creates less DWL than the

higher progressive tax.


efficient tax systems 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.


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.

The deadweight loss ofThe deadweight loss oftaxing wireless taxing wireless communicationscommunications

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.

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Excess Burden DefinedP

ound

s of

cor

n pe

r ye

ar


E1

B1

C1

DF

A

Cb

Ca

B0

i

Effect of Tax on Consumption Bundle

Pou

nds

of c

orn

per

year


E1

B1

C1

DF

A

Cb

Ca

B0

E2

iii

G

Excess Burden of the Barley TaxP

ound

s of

cor

n pe

r ye

ar


E1

B1

C1

DF

A

Cb

Ca

B0

E2

iii

G

H

B3

M

I

Tax Revenues

Equivalent variation

Questions and Answers

If lump sum taxes are so efficient, why aren’t they widely used? Are there any results from welfare economics that would help us understand

why excess burdens arise?

c

bbc P

PMRT

c

bbbc P

PtMRS

)1(

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

X per year

PX

DX

P0

X0

c

P0 + uXb

X1

∆X

a

ExcessBurden

P0 + (uX + 1) f

X2

i

∆x

ej

h

g

MarginalExcessBurden

marginal excess burden = area fbae = 1/2∆x[uX + (uX + 1)] = ∆X

The Ramsey Rule continued

change in tax revenues = area gfih – area ibae = X2 – (X1 – X2)uX

marginal tax revenue = X1 ∆X

marginal tax revenue per additional dollar of tax revenue = ∆X/(X1 - ∆X)

marginal tax revenue per additional dollar of tax revenue for good Y = ∆Y/(Y1 - ∆Y)

To minimize overall excess burden = ∆X/(X1 - ∆X) = ∆Y/(Y1 - ∆Y)

therefore X

X

Y

Y1 1

A Reinterpretation of the Ramsey Rule

t

tX

Y

Y

X

inverse elasticity rule

t tX X Y Y

1 1

1 1( / )* ( / )*x y

x y

X Yt t

X P Y P

Optimal commodity taxationRamsey rule

The Ramsey Rule is:

It sets taxes across commodities so that the ratio of the marginal deadweight loss to marginal revenue raised is equal across commodities.

MDWL

MRi

i D


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.


measures the value of having another dollar in the government’s hands relative to the next best use in the private sector.

Smaller values of mean additional government revenues have little value relative to the value in the private market.

Optimal commodity taxationInverse elasticity rule

The inverse elasticity rule, which expresses the 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.

Optimal commodity taxationEquity implications of the

Ramsey rule Two factors must be balanced when

setting optimal commodity taxes: 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.

Thus, the government should tax all of the commodities that it is able to, but at different rates.

Price reform in PakistanPrice reform in Pakistan

An interesting application of these rules is price reform in Pakistan.

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 2Table 2.

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Table 2

Demand for Various Commodities in Pakistan

Good Subsidy

PriceElasticit

yPolicy

Change

Welfare

Gain

Include Distributional

Concerns

Wheat 40% -0.64Reduce subsidy Small

Don’t reduce subsidy

Rice 40% -2.08Reduce subsidy Large Reduce subsidy

Oil/Fat -5% -2.33Reduce

tax LargeReduce tax further

With these elasticities, the taxes and subsidies should be changed.


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.

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Deaton also found that distributional considerations 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.

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OPTIMAL INCOME TAXES

Optimal income taxation is choosing the tax rates across income groups to maximize social welfare subject to a government revenue requirement. A key concern in the analysis is vertical

equity.

Optimal income taxesA 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

above-average income. The unrealistic assumption is that total income

(labor supply) is fixed with respect to taxes.

Optimal income taxesGeneral 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.


effects The Laffer curve, which motivated the

supply-side economic policies of the Reagan presidency is shown in Figure Figure 77.

If tax rates are too high and we are on the wrong side of the Laffer curve, lowering tax rates increases revenue.

Tax rate

Tax revenues

τ*%0 100%

rightside

wrongside

Figure 7

The Laffer curve demonstrates that at some

point, tax revenue falls.


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:

Where MUi is the marginal utility of individual i, and MR is the marginal revenue from that individual.

MU

MRi

i

Optimal income taxesAn example

As with optimal commodity taxation, this outcome represents a compromise between two considerations: Vertical equity Behavior responses

Figure 8Figure 8 shows that optimal income taxation equates this ratio across individuals, leading to a higher tax rate for the rich.

Tax rate

MU/MR

10% 20%

richpoor MR

MU

MR

MUλ

Mrs. PoorMr. Rich

Figure 8

Optimal income taxation equates the ratio of (MU/MR)

across individuals.

Optimal income taxesThe structure of optimal tax rates:

Simulation exercise Simulation exercises are the numerical

simulation of 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: 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 9Figure 9.

-$11,000

-$4,200

$10,320

$34,400

$46,650

Family income

Tax payments

$32,000 $75,000 $100,000$16,364

$10,000

Figure 9

The optimal income tax schedule starts off

with a subsidy.

The average rate does not exceed 47%.

Figure 9

Optimal Tax Results

Income groups

$0To

$10K

$10KTo

$32K

$32KTo

$75K

$75Kand

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.

Optimal income taxesThe 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.

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 10Figure 10.

Labor (L)

Wage (W)

L2 L1

W1

W2

S1

D1

D2

A

C

B

Labor (L)

Wage (W)

L2 L1

W1

W2

S1

D1

D2

A

B

S2

L3

W3 D

E

F

Figure 10

Mandated benefits also shift

the supply curve.

Creating smaller DWL.


programs: The model Wages adjust by more with the tax-benefit

linkage, 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 Figure 11 shows the case of full valuation of the benefit.

Labor (L)

Wage (W)

L2 L1

W1

W2

S1

D1

D2

A

B

S2

W3

Benefits =Program cost

Figure 11

With full valuation of the benefit,

employment is not reduced and there

is no DWL.


programs: The model With full valuation, the cost of the

program is fully shifted onto workers in the form of lower wages, and there is no deadweight loss or employment reduction.


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.


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.


programs: Issues raised 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.

Recap of Tax Inefficiencies and Their Implications for

Optimal Taxation Taxation and Economic Efficiency Optimal Commodity Taxation Optimal Income Taxes Tax-Benefit Linkages and the Financing

of Social Insurance Programs

chapter 20 tax inefficiencies and their implications for optimal taxation jonathan gruber public...

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