Public Economics

1
Chapter 16 Tax Evasion
2
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, 323338.
• Baldry, J.C. (1986) Tax evasion is not a
  gamble, Economics Letters, 22, 333335.
• Becker, G. (1968) Crime and punishment an
  economic approach, Journal of Political Economy,
  76, 169217.
• Cowell, F.A. Cheating the Government (Cambridge
  MIT Press, 1990) ISBN 0262532484 pbk.

3
Reading

• Glaeser, E.L., B. Sacerdote and J.A. Scheinkman
  (1996) Crime and social interaction, Quarterly
  Journal of Economics, 111, 506548.
• Schneider F. and D.H. Enste D.H. (2000) Shadow
  economies Size, causes, and consequences,
  Journal of Economic Literature, 38, 77114.
• Mork, K.A. (1975) Income tax evasion some
  empirical evidence, Public Finance, 30, 7076.
• Spicer, M.W. and S.B. Lundstedt (1976)
  Understanding tax evasion, Public Finance, 31,
  295305
• Challenging reading
• Bordignon, M. (1993) A fairness approach to
  income tax evasion, Journal of Public Economics,
  52, 345362.
• Cowell, F.A. and J.P.F. Gordon (1988)
  Unwillingness to pay, Journal of Public
  Economics, 36, 305321.

4
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, 132.
• Hindriks, J., M. Keen and A. Muthoo (1999)
  Corruption, extortion and evasion, Journal of
  Public Economics, 74, 395430.
• 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, 4966.
• Reinganum, J. and L. Wilde (1986) Equilibrium
  verification and reporting policies in a model of
  tax compliance, International Economics Review,
  27, 739760.
• Scotchmer, S. (1987) Audit classes and tax
  enforcement policy, American Economic Review, 77,
  229233.

5
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

6
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

7
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)

8
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

Table 16.1 Hidden Economy as of GDP, Average
Over 1990-93 Source Schneider and Enste (2000)
9
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

10
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 tY - X

11
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 - tY - FtY - X
• If income is understated the probability of being
  caught is p

12
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
• maxX EU(X) 1 pU(Ync) pU(Yc)

13
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

14
The Evasion Decision

• When X Y the income after tax is 1 - tY 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

15
The Evasion Decision

• The choice problem is shown in Fig. 16.1
• The optimal declaration achieves the highest
  indifference curve
• The taxpayer chooses to locate at the point with
  declaration X
• This is an interior point with 0 lt X lt Y
• Some tax is evaded but some income is declared

Figure 16.1 Interior choice 0 lt X lt Y
16
The Evasion Decision
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

17
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 pU'(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 lt 1/1 F

18
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

19
The Evasion Decision

• An increase in detection probability is shown in
  Fig. 16.3
• An increase in p reduces the gradient of the
  indifference curves on the 45o line
• The optimal choice moves closer to X Y
• The income declared rises so an increase in the
  detection probability reduces evasion

Figure 16.3 Increase in detection probability
20
The Evasion Decision

• A change in the fine rate affects income when
  caught evading
• An increase in F pivots the budget constraint
  around the point where X Y
• The optimal choice moves closer to honest
  declaration
• This is shown in Fig. 16.4 by the move from Xold
  to Xnew
• An increase in F reduces evasion

Figure 16.4 Increase in the fine rate
21
The Evasion Decision

• An income increase moves the budget constraint
  outward
• The optimal choice moves from Xold to Xnew in
  Fig. 16.5
• The effect depends on absolute risk aversion
  RA(Y) - U''(Y)/U'(Y)
• If RA(Y) is constant the optimal choices lie on a
  locus parallel to the 45o line
• If RA(Y) decreases with income the choice locus
  bends downward

Figure 16.5 Income increase
22
The Evasion Decision

• An increase in the tax rate moves the budget
  constraint inward as inFig. 16.6
• The outcome is not clear-cut
• If RA(Y) is decreasing a tax increase reduces tax
  evasion
• This is because the fine is Ft so an increase in
  the t raises the penalty
• This reduces income in the state in which income
  is lowest

Figure 16.6 Tax rate increase
23
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

24
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)tY X

25
Auditing and Punishment

• Differentiating with respect to p
• Differentiating with respect to F
• If pF lt1 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

26
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.

27
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

28
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

29
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 0.29
Income level -0.27
Income from wages and salaries 0.20
Table 16.3 Explanatory Factors Source Spicer
and Lundstedt (1976)
30
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

31
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

32
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

33
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

34
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

35
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

36
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( ) cE gt U(Y) where
  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

37
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.

38
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

39
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

40
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

41
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

42
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

43
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 lt Y)
• The revenue service can either audit the income
  report or not audit
• An audit costs C, C lt 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 gt C)

44
Tax Compliance Game
Figure 16.7 Compliance game
45
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 gt C
• If the revenue service audits with certainty, the
  taxpayer prefers not to evade as T F gt 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 taxpayers evasion strategy must also be
  random

46
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 eT 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)

47
Tax Compliance Game

• The equilibrium payoffs are
• u Y T, v T (C/(TF))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

48
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

49
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

50
Compliance and Social Interaction

• This is shown in Fig. 16.8
• Always move away from the intersection

Figure 16.8 Equilibrium compliance