Tax Efficiency and Elasticity

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Tax Efficiency and Elasticity

• Professor Jane H. Leuthold
• Department of Economics
• University of Illinois at Urbana-Champaign

Econ 415 Fall 2000
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Topics for today

• Tax efficiency defined
• How is tax efficiency loss measured?
• Definition and uses of tax elasticities
• Estimating elasticities and buoyancies

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Assumption incidence of tax is fully on the buyer
Price
Demand
Supply after tax
PG
Buyers
Tax per unit
Supply before tax
P PN
Q1 Q0
Market output
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Welfare loss from a distortionary tax
Fish
E
E
I
I
Before-tax budget constraint
After-tax budget constraint
Y/P
Y/PG
Rice
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Welfare loss from a non-distortionary tax
Fish
A non-distortionary (lump-sum) tax leaves the
slope of the budget constraint unchanged.
E
Ê
I
I
Before-tax budget constraint
After-tax budget constraint
Rice
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Tax efficiency

• Taxes distort economic behavior, causing a loss
  in welfare.
• Non-distorting taxes also cause a loss in
  welfare.
• The excess burden or deadweight loss of a
  distorting tax is the extra revenue that could be
  raised with a nondistorting (lump-sum) tax that
  leaves the consumer as well off as she was with
  the distorting tax.

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Excess burden (deadweight loss) of a
distortionary tax
Fish
AB revenues from rice taxAC revenues from
lump-sum tax (equivalent variation)BC excess
burden of tax on rice
A
B
E
E
C
Ê
I
I
Before-tax budget constraint
After-tax budget constraint
Y/PG
Y/P
Rice
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Perfect complements
Fish
Revenues from rice tax equal revenues from
lump-sum tax. No excess burden.
I
E
E
I
Before-tax budget constraint
After-tax budget constraint
Rice
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Summary

• The magnitude of the excess burden depends on the
  substitution effect (movement along the
  indifference curve).
• If there is no substitution effect (perfect
  complements), there is no excess burden.
• Lump-sum taxes have no excess burden.

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Using the compensated demand curve to measure
excess burden
Price
C
Compensated demand curve
B
Supply curve after tax
PG
Tax t
Supply curve before tax
P
A
D
Excess burden of a tax on rice
Rice
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Using the ordinary demand curve to measure excess
burden
Price
Compensated demand curve (normal good)
Ordinary demand curve
Supply curve after tax
Tax t
Supply curve before tax
True excess burden of a tax on rice
Rice
Overestimated excess burden
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Calculating deadweight loss (DWL) or excess burden
Price

• EDC (?Q/Q) (P/?P)
• ?Q (?P/P) Q EDC
• ?P t
• DWL ½ (t2 /P) Q EDC ½ (t/P) (t/P) PQ EDC
  ½ r2 PQ EDC where r t/P the tax rate
• DWL increases with the square of the tax rate and
  with the compensated price elasticity of demand

DC
DWL ½ ?P ?Q
S t
?P
t
S
?Q
Rice
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Importance of compensated elasticity of demand
Price
Inelastic compensated demand curve
Elastic compensated demand curve
Supply curve after tax
Supply curve before tax
Rice
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Excess burden per dollar of tax revenue
W ½ r2 PQ EDC Tax Revenue R r PQ W/R
Efficiency loss ratio ½ r EDC
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Tax borne by the producer
Price
Supply curve
A
B
P
Demand before tax
t
PN
D
Demand after tax
W ½ r2 PQ ES
Rice
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Tax borne by both consumer and producer
Price
Supply curve
C
PG
A
E
P
B
PN
Ordinary demand curve
D
Compensated demand curve
Rice
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Tax elasticities

• Measure the responsiveness of tax revenue to
  changes in income

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Decomposition of the tax elasticity

• Decomposition by tax
• Decomposition by base and income

Tax-to-base elasticity (dT/dB) (B/T)
Base-to-income elasticity (dB/dGDP) (GDP/B)
(dT/dGDP) (GDP/T) (dT/dB) (B/T) (dB/dGDP)
(GDP/B)
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Advantage of high tax to base elasticity

• Base-to-income elasticities are largely
  determined by the way in which the structure of
  the economy changes with economic growth.
• Tax-to-base elasticities indicate revenue growth
  within control of tax authorities.
• High tax to base elasticities may be raised by an
  improvement of tax administration.

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Advantages of an elastic tax system

• Tax revenues grow proportionately faster than
  income, making it possible to fund growing
  demands for government services without
  politically sensitive tax increases. Unless tax
  rates are increased, inelastic taxes will decline
  in revenue importance in the tax system over
  time.
• An elastic tax system is a better automatic
  stabilizer than an inelastic one. Why?
• An elastic tax system is likely to be
  progressive, perhaps helping meet vertical equity
  goals.

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Tax elasticity and tax progressivity
MTR gt ATR indicates a tax is progressive.
Therefore, a progressive tax system has a tax
elasticity greater than one.
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Disadvantages of an elastic tax system

• An elastic tax system may promote too high a rate
  of government growth. Revenues that are
  available tend to be spent, perhaps unwisely.
• Revenues from an elastic tax system tend to be
  volatile, making planning difficult.
• An elastic tax system probably has high marginal
  tax rates, which in turn may suggest large excess
  burdens (deadweight losses).

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Buoyancy or elasticity?
When no attempt is made to control for
discretionary rate or base changes, then the
responsiveness of tax revenue to a change in GDP
is called tax buoyancy. When an attempt is made
to control for discretionary changes, the measure
of responsiveness is called a tax elasticity.
An elastic (buoyant) tax is one whose elasticity
(buoyancy) is greater than one.
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Discretionary and non-discretionary tax changes
Discretionary tax changes are under the control
of the tax authorities. They are due to changes
in rates, base definition, collection and
enforcement procedures. Non-discretionary
changes arise from the natural growth of the
economy.
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Estimating tax buoyancies
ln T a b ln GDP (dT/dGDP)/T b/GDP ?TY
(dT/dGDP) (GDP/T) b
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Techniques for estimating elasticities

• Data adjustment method (Prest)Adjust the data
  based on Treasury estimates of discretionary
  revenue changes
• Dummy variable method (Singer)
• D 1 in the year of discretionary tax change
  and all following yearsD 0 in all previous
  years

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Estimating tax elasticity with Singer method
ln T a b ln GDP c D where D 0 prior to
the tax change 1 following the
tax change ?TY b
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Lab 5

• Estimate tax buoyancy for your country
• Use the Singer technique to estimate the tax
  elasticity for your country

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Tax buoyancy for Egypt
  ln(T) 1.39 .883 ln (GDP) (2.42)
(37.63)   Adj R2 .985 ?TY .883  
Data 1975-97 measured in local currency units
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Forecasting future tax revenues
eTY ( change in tax revenue)/( change in
GDP) Turning this around, ( change in tax
revenue) eTY ( change in GDP)
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Next Time
Thurs Lab 5 Estimating Tax Elasticities Chat
Would you expect the elasticity of the tax
systems of less developed economies to be lower
than or greater than the elasticity of the tax
systems of developed economies? What are your
reasons for your view? Next Tues Problems of
Tax Administration and Evasion