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Economics of taxation
dr Grzegorz Kula,
Lecture 5: Tax avoidance and tax
evasionSandmo (2005), James & Nobes (1998, ch. 2, 5)
Definitions
Tax evasion: an illegal manipulation of ones affairs in
order to reduce legally due tax.
Tax avoidance: a manipulation of ones affairs within
the law in order to reduce tax.
dr Grzegorz Kula,
Tax planning: arranging ones affairs to take advantage
of the obvious and often intended effects of tax rules
in order to maximize one’s after-tax returns.
(James and Nobes, 1998)
We usually see avoidance as an action,
which is an unintended, although legal,
consequence of tax policy.
Problems with evasion/avoidance decisions:
1. Some tax rules are not clear and there is a
possibility of different interpretations.
- Usually tax authorities have different
interpretations than tax payers.
Definitions
dr Grzegorz Kula,
interpretations than tax payers.
- Problem of arbitrariness.
2. The spirit of the law may mean something different
than the letter of the law.
- If something is allowed, should we take
advantage of it?
3. If something is an obvious mistake in legal
construction, should we use it or not?
Hypothesis:
The rich avoid and the poor evade.
• In order to legally pay lower taxes you need to
have either knowledge or advice – both are costly
Definitions
dr Grzegorz Kula,
have either knowledge or advice – both are costly
to acquire.
• If you are poor, than you have not enough income
to use the legal ways of reducing taxes.
• Tax statistics show that the rich profit more from
tax discounts and deductions than the poor.
1. High tax rates – the higher the rates, the higher the
reward from not paying taxes. The relative cost of
tax avoidance and tax evasion are getting lower.
2. Complexity of the rules and difficulty with
compliance – easier to deal with for the rich. We
The causes of tax avoidance and tax evasion
dr Grzegorz Kula,
compliance – easier to deal with for the rich. We
have to consider the marginal benefit from more
detailed taxes and marginal cost of their increasing
complexity.
3. Imprecise laws and arbitrary tax rules – often tax
rules are one step behind the economy.
4. Lack of control and problems with penalties – how
to punish tax evasion?
5. Social penalties for evasion – how society reacts to
the information that someone was evading taxes?
6. Inequity, or perceived inequality of the tax system
The causes of tax avoidance and tax evasion
dr Grzegorz Kula,
6. Inequity, or perceived inequality of the tax system
– evasion and avoidance become socially
acceptable.
• Both methods cost taxpayer’s time and money and lead
to an adjustment to his affairs which may be inefficient.
• These costs and consequences can lead to a reduction in
economic welfare.
• From the point of view of tax policy, tax avoidance and
tax evasion can render some policy actions and plans
The effects of tax avoidance and tax evasion
dr Grzegorz Kula,
tax evasion can render some policy actions and plans
ineffective.
• People may avoid and evade taxes so successfully, that
the government must increase taxes.
- Government punishes those who pay taxes, i.e. “good
citizens” – rise in avoidance and evasion.
- Government can either increase taxes again or reduce
avoidance and evasion.
The Allingham-Sandmo (A-S) model
The model shows the taxpayer at the moment of
filling in his income tax return and deciding: how
much of his income should he report and how much
should he evade.
The taxpayer’s labor supply, gross earnings and capital
income are treated as given.
dr Grzegorz Kula,
income are treated as given.
W - the gross income of the taxpayer,
t – the rate of a proportional income tax,
E – the amount of underreporting, i.e. the amount
evaded, thus the reported income is W-E.
If the tax evasion is not detected, then the net income of the taxpayer is:
(1) Y = W – t(W – E) = (1 - t)W + tE
If the evasion is discovered, he will pay the penalty rate of tax θ on the evaded amount. In such a case his net income is:
The Allingham-Sandmo (A-S) model
dr Grzegorz Kula,
net income is:
(2) Z = (1 - t)W + tE – θE = (1 - t)W – (θ – t)E
The taxpayer’s subjective probability of detection is p. He chooses the amount evaded to maximize his expected utility:
(3) V = (1 - p)U(Y) + pU(Z)Some income is known to
the tax authorities, thus we
can evade with only a part
of our income.
Utility is increasing and concave, making taxpayer risk-
averse. The first-order condition is:
(4)
or
(5)
( ) ( ) ( )( ) 0''1 =−−− tZpUtYUp θ
( )( )
( )( )
tpZU −= 1'
The Allingham-Sandmo (A-S) model
dr Grzegorz Kula,
A higher penalty rate and a higher detection probability
will discourage tax evasion.
In equation (5) the right-hand-side is a relative price of
income in the states of detection and non-
detection, which depends negatively on θ and p.
( )( )
( )( )tp
tp
YU
ZU
−−=θ
1
'
'
Lets assume that the measure of absolute risk aversion
(–U’’(.)/U’(.)) is decreasing.
Income effect is negative: higher taxes make the
taxpayer poorer and less willing to take risk.
The substitution effect increases motivation for
evasion.
The Allingham-Sandmo (A-S) model
dr Grzegorz Kula,
evasion.
The effect of the marginal tax rate on evasion can be
presented as:
(6)
where S is the substitution effect.
SW
E
t
EW
t
E +∂∂
−−−=
∂∂
1
The income effect,
which is negative if
evasion increases with
gross income.
Redefining the penalty rate to apply to evaded tax θtE
with θ > 1:
(2a) Z = (1 - t)W – (θ –1)tE
The first order condition must be rewritten:
(5a) ( )( )
( )( )1'
−−=θ
pZU
The Allingham-Sandmo (A-S) model
Then there is no
substitution effect
dr Grzegorz Kula,
The relative price of income in the two states is now
independent of t and depends only on the
probability of detection and the penalty rate.
( ) ( )1' −=
θpYU
• The substitution effect in the A-S model occurs
because the penalty rate is fixed when regular
taxes increase.
• Then the difference between the penalty rate and
the regular tax rate goes down, increasing the
The Allingham-Sandmo (A-S) model
dr Grzegorz Kula,
the regular tax rate goes down, increasing the
incentives to evade.
• The empirical evidence shows that there is a
positive connection between the marginal tax rate
and evasion.
• Therefore, maybe it is better not to transform the
original model.
An endogenous probability of detection:
• The probability function must reflect taxpayer’s beliefs
about the policy followed by the tax authorities.
• The A-S model assumes that the authorities know your
profession and the normal level of income associated
with it.
The Allingham-Sandmo (A-S) model
dr Grzegorz Kula,
with it.
• However, we may derive probability of detection from
the policy optimization of tax agency.
• The collection agency’s objective is to maximize
expected tax revenues.
• If the tax authorities can commit to an audit rule, then
there is a critical level of income, which is audited.
The model assumes that the taxpayer does in fact evade taxes, since
there was an internal solution.
Is it always optimal to move from no evasion to evasion?
According to Sandmo (p. 649) for “…some tax evasion to be optimal
from the taxpayer’s point of view, it is necessary and sufficient
condition that the expected penalty rate is less than the regular
The Allingham-Sandmo (A-S) model
dr Grzegorz Kula,
tax rate…”
In reality people evade when penalties are higher than the tax rates:
1. Different types of income are subject to different probabilities
of detection if underreported.
2. The taxpayer’s subjective probability is not necessary the same
as the actual probability.
3. There are other, non-economic reasons for not evading, which
have more social or moral character.
The theory suggest that probability of detection and the
penalty for evasion are policy substitutes:
1. High probability of detection and low penalties.
- High costs of tax administration.
2. Low probability and high penalties.
How to reduce tax evasion and tax avoidance?
dr Grzegorz Kula,
2. Low probability and high penalties.
- Low costs of tax administration.
- A horizontal equity problem: is it equitable that just a
few evaders will pay very high penalties, while the
others are left unpunished?
- We can set penalties so high that everybody would
be afraid to evade but society prefers when the
punishment fits the crime.
Alternative solutions:
• Lowering the marginal tax rates
- Depends on the substitution and income effects. If rates are
very high and the level of avoidance and evasion is also high, then
probably lowering the rates will lower incentives to avoid and
evade.
How to reduce tax evasion and tax avoidance?
dr Grzegorz Kula,
• Changing people perception of tax system and evasion
- Education, simplification of procedures, help in paying taxes.
• Tax abolitions
- Is it equitable to let some people go unpunished for breaking the
law and to expect others to pay?
- We do not know if people report the hidden incomes and
evaded taxes.
