Chapter 16
Tax Evasion
Reading
• Essential reading
– Hindriks, J and G.D. Myles Intermediate Public Economics.
(Cambridge: MIT Press, 2005) Chapter 16.
• Further reading
– Allingham M. and A. Sandmo (1972) ‘Income tax evasion: a
theoretical analysis’, Journal of Public Economics, 1, 323—338.
– Baldry, J.C. (1986) ‘Tax evasion is not a gamble’, Economics
Letters, 22, 333—335.
– Becker, G. (1968) ‘Crime and punishment: an economic
approach’, Journal of Political Economy, 76, 169—217.
– Cowell, F.A. Cheating the Government (Cambridge: MIT Press,
1990) [ISBN 0262532484 pbk].
Reading
– Glaeser, E.L., B. Sacerdote and J.A. Scheinkman (1996) ‘Crime
and social interaction’, Quarterly Journal of Economics, 111,
506—548.
– Schneider F. and D.H. Enste D.H. (2000) ‘Shadow economies:
Size, causes, and consequences’, Journal of Economic
Literature, 38, 77—114.
– Mork, K.A. (1975) ‘Income tax evasion: some empirical
evidence’, Public Finance, 30, 70—76.
– Spicer, M.W. and S.B. Lundstedt (1976) ‘Understanding tax
evasion’, Public Finance, 31, 295—305
• Challenging reading
– Bordignon, M. (1993) ‘A fairness approach to income tax
evasion’, Journal of Public Economics, 52, 345—362.
– Cowell, F.A. and J.P.F. Gordon (1988) ‘Unwillingness to pay’,
Journal of Public Economics, 36, 305—321.
Reading
– Graetz, M., J. Reinganum and L. Wilde (1986) ‘The tax
compliance game: towards an interactive theory of law
enforcement’, Journal of Law, Economics and Organization, 2,
1—32.
– Hindriks, J., M. Keen and A. Muthoo (1999) ‘Corruption, extortion
and evasion’, Journal of Public Economics, 74, 395—430.
– Myles, G.D. and R.A. Naylor (1996) ‘A model of tax evasion with
group conformity and social customs’, European Journal of
Political Economy, 12, 49—66.
– Reinganum, J. and L. Wilde (1986) ‘Equilibrium verification and
reporting policies in a model of tax compliance’, International
Economics Review, 27, 739—760.
– Scotchmer, S. (1987) Audit classes and tax enforcement policy,
American Economic Review, 77, 229—233.
Introduction
• Tax evasion is the illegal failure to pay tax
• Tax avoidance is the reorganization of economic
activity to lower tax payment
– Tax avoidance is legal but tax evasion is not
– The borderline between avoidance and evasion is
unclear
• Estimates show evasion to be a significant
fraction of measured economic activity
• It is an important consideration for tax policy
The Extent of Evasion
• The names black, shadow or hidden economy
are used to described economic activity for
which payment is received but is not officially
declared
• Included in the hidden economy are:
– Illegal activities
– Unmeasured legal activity such as output of
smallholders
– Legal but undeclared activity
• The unmeasured economy is the shadow
economy plus activities which are economically
valuable but do not involve any transaction
The Extent of Evasion
• There are many methods for measuring the
hidden economy
• The difference between the income and
expenditure measures of national income
• Survey data directly or indirectly as an input into
an estimation procedure
• The demand for cash on the basis hidden
activity is financed by cash (monetary approach)
• The use of a basic input that is measured to
estimate true output (input approach)
The Extent of Evasion
• Table 16.1 presents
estimates of the
size of the hidden
economy
• These estimates are
subject to error
• There is a degree of
consistency
• Undeclared
economic activity is
substantial
Developing
Transition
OECD
Egypt 68-76%
Thailand 70%
Georgia 28-43%
Ukraine 28-43%
Italy 24-30%
Spain 24-30%
Mexico 40-60%
Malaysia 38-50%
Tunisia 39-45%
Hungary 20-28%
Russia 20-27%
Latvia 20-27%
Denmark 13-23%
France 13-23%
Japan 8-10%
Singapore 13%
Slovakia 9-16%
Austria 8-10%
Table 16.1: Hidden Economy as % of GDP,
Average Over 1990-93
Source: Schneider and Enste (2000)
The Evasion Decision
• The simplest model of the evasion decision
considers it to be a gamble
• If a taxpayer declares less than their true income
(or overstates deductions)
–
–
–
–
They may do so without being detected
There is also a chance that they may be caught
When they are a punishment is inflicted
Usually a fine but sometimes imprisonment
• A taxpayer has to balance these gains and
losses taking account of the chance of being
caught and the level of the punishment
The Evasion Decision
• The taxpayer has a fixed income level Y
– This income level is known to the taxpayer
– The level of income is not known to the tax collector
• The taxpayer declares a level of income X where
X≤Y
• Income is taxed at a constant rate t
• The amount of unreported income is Y – X ≥ 0
• The unpaid tax is t[Y - X]
The Evasion Decision
• If the taxpayer evades without being caught their
income is given by
Ync = Y - tX
• When the taxpayer is caught evading all income
is taxed and a fine at rate F is levied on the tax
that has been evaded.
• The income level when caught is
Yc = [1 - t]Y - Ft[Y - X]
• If income is understated the probability of being
caught is p
The Evasion Decision
• Assume that the taxpayer derives utility U(Y)
from an income Y
• After making declaration X the taxpayer obtains
– Income level Yc with probability p
– Income level Ync with probability 1 – p
• The taxpayer chooses X to maximize expected
utility
• The declaration X solves
max{X} E[U(X)] = [1 – p]U(Ync) + pU(Yc)
The Evasion Decision
• Observe that there are two states of the world.
– In one state of the world the taxpayer is not caught
evading and income is Ync
– In the other state of the world they are caught and
income is Yc
• The expected utility function describes
preferences over income levels in the two states
• The choice of X determines income in each state
• Varying X trades-off income between the states
– High X provides relatively more income in the “caught
evading” state
– Low X provides relatively more in the “not caught”
The Evasion Decision
• When X = Y the income after tax is [1 - t]Y in both
states
• When X = 0 income is [1 - t(1 + F)]Y if caught and
Y if not caught
• The options facing the taxpayer lie on the line
joining the points for X = 0 and X = Y
– This is the opportunity set of income allocations
between the two states
• The utility function provides a set of indifference
curves
– Along an indifference curve are income levels in the
two states giving equal expected utility
The Evasion Decision
• The choice problem is
Yc
shown in Fig. 16.1
• The optimal declaration
achieves the highest
indifference curve
1  t Y
• The taxpayer chooses to
locate at the point with
declaration X*
1  t 1  F Y
• This is an interior point
with 0 < X* < Y
• Some tax is evaded but
some income is declared
X Y
X*
X 0
1  t Y
Y
Figure 16.1: Interior choice:
0 < X* < Y
Y nc
The Evasion Decision
Yc
Yc
1  t Y
1  t Y
X* Y
1  t 1  F Y
1  t 1  F Y
1  t Y
a: X* Y
Y
Y nc
X* 0
1  t Y
b: X* 0
Figure 16.2: Corner solutions
• Corner solutions can also arise
• In Fig. 16.2a X* = Y so all income is declared
• In Fig. 16.2b X* = 0 so no income is declared
Y
Y nc
The Evasion Decision
• Evasion occurs when indifference curves are
steeper than the budget constraint on the 45o
line
• The indifference curves have slope
dYc/dYnc = – [1 – p]U′(Ync)/pU′(Yc)
• On the 45o line Yc = Ync so U′(Ync) = U′(Yc) implying
dYc/dYnc = – [1 – p]/p
• The slope of the budget constraint is – F
• The indifference curve is steeper than the
budget constraint on the 45o line
p < 1/[1 + F]
The Evasion Decision
• Evasion occurs if the p is small relative to F
• The condition applies to all taxpayers
• In practice F is between 0.5 and 1 so 1/(1 + F) ≥
1/2
• Information on p hard to obtain
• In the US
– The proportion of individual tax returns audited was
1.7 per cent in 1997
– The Taxpayer Compliance Measurement Program
revealed that 40 percent of US taxpayers underpaid
their taxes
– This is large but less than the model predicts
The Evasion Decision
• An increase in detection
probability is shown in
Yc
Fig. 16.3
• An increase in p reduces
the gradient of the
indifference curves on
1  t Y
the 45o line
• The optimal choice
moves closer to X = Y
1  t 1  F Y
• The income declared
rises so an increase in
the detection probability
reduces evasion
new
old
1  t Y
Y
Figure 16.3: Increase in
detection probability
Y nc
The Evasion Decision
• A change in the fine rate
affects income when
Yc
caught evading
• An increase in F pivots
the budget constraint
around the point where X
1  t Y
=Y
• The optimal choice
moves closer to honest
1  t 1  F Y
declaration
• This is shown in Fig. 16.4 1  t 1  Fˆ Y
by the move from Xold to
Xnew
• An increase in F reduces
evasion
X new
1  t Y
X old
Y
Figure 16.4: Increase in
the fine rate
Y nc
The Evasion Decision
• An income increase
moves the budget
Yc
constraint outward
• The optimal choice
moves from Xold to Xnew in
1 t Yˆ
Fig. 16.5
1  t Y
• The effect depends on
new
absolute risk aversion
old X
X
RA(Y) = - U′′(Y)/U′(Y)
1  t 1  F Yˆ
• If RA(Y) is constant the
1  t 1  F Y
optimal choices lie on a
locus parallel to the 45o
1  t Y 1 t Yˆ Y Yˆ Y nc
line
• If RA(Y) decreases with
Figure 16.5: Income increase
income the choice locus
bends downward
The Evasion Decision
• An increase in the tax
Yc
rate moves the budget
constraint inward as
inFig. 16.6
• The outcome is not clear1  t Y
cut
1 tˆY
• If RA(Y) is decreasing a
X old
tax increase reduces tax 1  t 1  F Y
X new
evasion
• This is because the fine 1  tˆ1  F Y
is Ft so an increase in
the t raises the penalty
1 tˆY 1  t Y Y
• This reduces income in
the state in which income
Figure 16.6: Tax rate increase
is lowest
Y nc
Auditing and Punishment
• The analysis of the evasion decision assumed
that the p and F were fixed
• This is satisfactory from the perspective of the
individual taxpayer
• From the government's perspective these are
choice variables that can be chosen
– The probability of detection can be raised by the
employment of additional tax inspectors
– The fine can be legislated or set by the courts
• The issues involved in the government's
decision can be analyzed
Auditing and Punishment
• An increase in either p or F will reduce the
amount of undeclared income
• Assume the government wishes to maximize
revenue
• Revenue is defined as taxes paid plus the
money received from fines
• From a taxpayer with income Y the expected
value of the revenue collected is
R = tX + p(1 + F)t[Y – X]
Auditing and Punishment
• Differentiating with respect to p
R
X
 1  F t Y  X   t 1  p  pF 
0
p
p
• Differentiating with respect to F
R
X
 ptY  X   t 1  p  pF 
0
F
F
• If pF <1 – p an increase in p or F will increase the
revenue the government receives
• p is costly, F is free
• Optimal policy is low p very high F
Auditing and Punishment
• This policy maximizes revenue not welfare
• The government may be constrained by political
factors
• The government may not be a single entity that
chooses all policy instruments
• A more convincing model would have:
– The tax rate set by central government
– The probability of detection controlled by a revenue
service
– The punishment set by the judiciary.
Auditing and Punishment
• The economics of crime views tax evasion as
just another crime
• The punishment should fit with the general
scheme of punishments
• Levels of punishment should provide incentives
that lessen the overall level of crime
– Lower punishments for less harmful rather crimes
• Tax evasion has a low punishment if viewed as
having limited harm
Evidence on Evasion
Income interval
17-20
20-25
25-30
30-35 35-40
Midpoint
18.5
22.5
27.5
32.5
37.5
Assessed income
17.5
20.6
24.2
28.7
31.7
Percentage
94.6
91.5
88.0
88.3
84.5
Table 16.2: Declaration and Income
Source: Mork (1975)
• Compares income level from interviews to income on tax
return
• Interviewees placed in income intervals based on
interview
• The percentage found by dividing the assessed income
by the midpoint of the income interval
• Declared income declines as a proportion of reported
income occurs as income rises
Evidence on Evasion
• The propensity to evade is
reduced by an increase in
the probability of detection,
age, income but increased
by an increase in perceived
inequity and number of tax
evaders known
• Extent of tax evasion
increased by inequity,
number of evaders known
and experience of previous
tax audits.
• Social variables are clearly
important
Variable
Propensity
to evade
Extent of
evasion
Inequity
0.34
0.24
Number of evaders
known
0.16
0.18
Probability of
detection
-0.17
Age
-0.29
Experience of
audits
0.22
Income level
-0.27
Income from wages
and salaries
0.20
0.29
Table 16.3: Explanatory Factors
Source: Spicer and Lundstedt (1976)
Evidence on Evasion
• Data from the US Internal Revenue Services
Taxpayer Compliance Measurement Program
survey of 1969
– Evasion increases as the marginal tax rates increases
but decreases when wages are a significant
proportion of income
• The difference between income and expenditure
figures in National Accounts support this result
• Belgian data found the converse: tax increases
lead to lower evasion
• There remains ambiguity about the tax effect
Evidence on Evasion
• Tax evasion games can be used to test evasion
behavior
• These games have shown that evasion
increases with the tax rate
• Evasion falls as the fine is increased or the
detection probability increases
• Women evade more often than men but evade
lower amounts
• Purchasers of lottery tickets were
– No more likely to evade than non-purchasers
– Evaded greater amounts when they did evade
Evidence on Evasion
• The nature of the tax evasion decision has been
tested by running two parallel experiments
– One framed as a tax evasion decision and
– The other as a simple gamble
• These experiments have the same risks and
payoffs
• For the tax evasion experiment some taxpayers
chose not to evade even when they would under
the same conditions with the gambling
experiment
• This suggests that tax evasion is more than just
a gamble
Evidence on Evasion
• There are several important lessons to be drawn
from the evidence
• The theoretical predictions are generally
supported except for the effect of the tax rate
• Tax evasion is more than the simple gamble
portrayed in the basic model
• There are attitudinal and social aspects to the
evasion decision in addition to the basic element
of risk
Effect of Honesty
• The act of tax evasion can have psychological
effects
• Taxpayers submitting incorrect returns feel
varying degrees of anxiety and regret
• The innate honesty of some taxpayers is not
captured by representing tax evasion as just a
gamble
• Non-monetary costs of detection and
punishment are not captured by preferences
defined on income alone
Effect of Honesty
• Honesty can introduced by assuming the utility
function has the form
U = U(Y) - cE
• The level of evasion is E = Y- X and c is a
measure of honesty
• The value of cE the psychological cost of
evasion
• Assume taxpayers differ in their value of c but
are identical in all other respects
• Those with high c will have a greater utility
reduction for any given level of evasion
Effect of Honesty
• Evasion occurs only if the utility gain from
evasion must exceed the utility reduction
• Let E* be the optimal level of evasion
~
~
*
• Evasion is chosen if EU( Y ) – cE > U(Y) where Y
is the random income after optimal evasion
• The population is separated into taxpayers who
do not evade (high values of c) and others who
evade (low c)
• Those who do not evade are “honest” but will
evade if the benefit is sufficiently great
Effect of Honesty
• Empirical evidence shows a positive connection
between number of tax evaders known and the
level evasion
• The evasion decision is not made in isolation but
with reference to the norms and behavior of
society
• Social norms can be incorporated as an
additional utility cost of evasion.
• This cost can be assumed an increasing function
of the proportion of taxpayers who do not evade.
Effect of Honesty
• This captures the fact that more utility will be lost
the more out of step the taxpayer is with the
remainder of society
• If evasion is chosen expected utility is
EU – m(n)
• The function m(n) is increasing in the number of
honest taxpayers, n
• This modification reinforces the separation of the
population into evaders and non-evaders
Tax Compliance Game
• A revenue service chooses the probability of
audit to maximize total revenue taking as given
the tax rate and the punishment
– The government is viewed as allocating choices to
separate agencies
• The choice of probability requires an analysis of
the interaction between the revenue service and
the taxpayers
• The revenue service reacts to income
declarations and taxpayers react to the expected
detection probability
Tax Compliance Game
• A strategy for the revenue service is the
probability with which it chooses to audit any
given value of declaration
• A strategy for a taxpayers is a choice of
declaration given the audit strategy of the
revenue service
• At a Nash equilibrium the strategy choices must
be mutually optimal
• In this game predictability in auditing cannot be
an equilibrium strategy
Tax Compliance Game
• Observe
– No auditing at all cannot be optimal because it would
mean maximal tax evasion
– Auditing of all declarations cannot be a solution
because this incurs excessive auditing costs
– A pre-specified limit on the range of declarations that
will be audited since those evading will remain
outside this limit
• To be unpredictable the audit strategy must be
random
Tax Compliance Game
• The probability of an audit should be high for an
income report that is low compared to what one
would expect from someone in that taxpayer's
occupation
• Or it should be high given the information on
previous tax returns for that taxpayer
• In either case a taxpayer should not be able to
predict if they will be audited
Tax Compliance Game
• A version of the strategic interaction is depicted in Fig.
16.7
• A taxpayer with income Y can either evade (reporting
zero income) or not (truthful income report)
• By reporting truthfully the taxpayer pays tax T to the
revenue service (with T < Y)
• The revenue service can either audit the income report
or not audit
• An audit costs C, C < T, for the revenue service to
conduct and is accurate in detecting evasion
• If the taxpayer is caught evading the tax T plus a fine F is
paid (where F > C)
Tax Compliance Game
Revenue Service
Taxpayer
Audit
No Audit
Evasion
Y T  F, T  F  C
Y, 0
No Evasion
Y T, T  C
Y T, T
Figure 16.7: Compliance game
Tax Compliance Game
• There is no pure strategy equilibrium in this tax
compliance game
– If the revenue service does not audit the taxpayer
strictly prefers evading and therefore the revenue
service is better-off auditing as T + F > C
– If the revenue service audits with certainty, the
taxpayer prefers not to evade as T + F > T, which
implies that the revenue service is better-off not
auditing
• The revenue must play a mixed strategy in
equilibrium with the audit strategy being random
• The taxpayer’s evasion strategy must also be
random
Tax Compliance Game
• Let e be the probability that the taxpayer evades, and p
the probability of audit
• In equilibrium the players must be indifferent between
their two pure strategies
• For the revenue service to be indifferent between
auditing and not auditing the cost of auditing C must
equal the expected gain in tax and fine revenue e[T + F]
• For the taxpayer to be indifferent between evading and
not evading the expected gain from evading (1 – p)T
must equal the expected penalty pF
• The equilibrium is
e* = C/(T + F), p* = T/(T + F)
Tax Compliance Game
• The equilibrium payoffs are
u* = Y – T, v* = T – (C/(T+F))T
• The taxpayer is indifferent between evading or
not evading so equilibrium payoff is equal to
truthful payoff Y – T
• This is because
– Unpaid taxes and the fine cancel out in expected
terms
– Increasing the fine does not affect the taxpayer
Tax Compliance Game
• A higher fine increases the payoff of the revenue
service since it reduces the amount of evasion
– increasing the penalty is Pareto-improving
• The equilibrium payoffs also reflect a cost of
evasion
– for any tax T paid by the taxpayer the revenue service
receives T – D
– where D = (C/(T + F))T is the deadweight loss of
evasion
• Evasion involves a deadweight loss that is
increasing with the tax rate
Compliance and Social
Interaction
• Evasion is more likely when others already
evade
• Payoff from non-compliance is increasing with
the number of non-compliers
• Aggregate compliance tendency is toward one
of the extremes
Compliance and Social
Interaction
• This is shown in Fig. 16.8
• Always move away from
the intersection
Compliance
Payoff
Non-compliance
Payoff
0
Non-compliance Rate
1
Figure 16.8: Equilibrium compliance