Frank Cowell MSc Public Economics 20112 httpdarplseacukec426 Overview Introduction Basic model Policy Tax Compliance How compliance fits into public economics 2 Frank Cowell EC426 ID: 236771
Download Presentation The PPT/PDF document "Tax Compliance" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Slide1
Tax Compliance
Frank Cowell: MSc Public Economics 2011/2
http://darp.lse.ac.uk/ec426Slide2
Overview...
Introduction
Basic model
Policy
Tax Compliance
How compliance fits into public economics
2
Frank Cowell: EC426
2
Extensions
13 February 2012Slide3
Tax compliance and PE
In tax problems usually focus on margin of individual choice…
labour supply
the demand for particular consumption goods
Could consider tax-compliance analysis as just another margin
…compliance/noncompliance in reporting…work above/below groundBut: it’s related to a core problem of public economics
public goods will not be provided efficiently by private initiativeusual response is to say “let government do it”
Useful to reinterpret the basics of this type of problemprovision of collective goodspure public goods and others involving externalities
focus on relations between citizens and state13 February 2012
Frank Cowell: EC4263Slide4
Agenda
Outline main approaches to tax compliance
1 TAG
2 Strategic models
3 Social interactionConsider some important variants
public goods and the public sectorthe role of firmsAnalyse implications for policy
Literature overviews: Andreoni et al (1998)
Cowell (1990, 2004) Slemrod (2007)
Slemrod and Yitzhaki (2002)
13 February 2012Frank Cowell: EC426
4Slide5
Overview...
Introduction
Basic model
Policy
Tax Compliance
Individual behaviour and the public sector
5
Frank Cowell: EC426
5
Extensions
13 February 2012
Individual taxpayer
Multiple taxpayersSlide6
TAG model
Standard model is essentially one of
T
axpayer As
Gamblerbased on Allingham and
Sandmo (1972)The gamble involves a bet with the tax authority
Individuals make bets on whether they will be caught concealing income…or not reporting at all…or working in underground economy
Appropriateness relies on a special set of assumptions about motivation of individualsabout the way that the government is perceived
13 February 2012Frank Cowell: EC426
6Slide7
TAG: taxes, penalties, returns
Tax payer/evader has true income
y
is supposed to pay tax on all of this at rate t
chooses to conceal an amount e, pays tax on the remainderTax authority audits:
if evader is caught, pays a surcharge s on the evaded tax te
perceived probability of this happening is pParameters determine returns to evasion:consider rate of return to $1 of evasion activity...
r = – s with probability pr = 1 with probability 1 –
pexpected rate of return is 1 – p – ps Consumption (disposable income) is a function of:
income y and tax rate trandom rate of return r
evasion choice ec = [1 – t]
y + rte (a random variable)
13 February 2012Frank Cowell: EC426
7Slide8
TAG: budget constraint
A
B
c"
c'
[1
t
]
y
[1
t
st
]
y
y
[1
t
]
y
line of perfect certainty
c': consumption if not caught
B: Payoff if blatantly dishonest
c'': consumption if caught
A: Payoffs if absolutely honest
Consumption possibilities for all e
c'
= [1 –
t
]
y
+
te
if not audited / convicted
c''
= [1 –
t
]
y
–
ste
if audited and convicted
1 A cut in the surcharge rate s
2 A cut in the tax rate t
3 Increase in income y
13 February 2012
Frank Cowell: EC426
8Slide9
TAG: Preferences and beliefs
Tax payer has von-Neumann Morgenstern preferences
gets no intrinsic pleasure from evasion and feels no shame
correctly perceives probability of detection
passumes that it is exogenously given
Consumer’s welfare is expected utility of consumption:Eu(c
) = [1 – p] u(c' ) +
p u(c'' )Eu(
c) = [1 – p] u([1 – t] y +
te) + p u([1 – t] y –
ste) Cardinal utility function u has the “usual properties”:u
c(•) > 0 (first derivative)ucc(•) 0 (second derivative)
Both u and p determine shape of ICs in (c', c''
)-spacecurvature of ICs depends on risk aversion – ucc(•)/u
c(•) slope of ICs where crosses 45º line is [1 – p]/p
13 February 2012
Frank Cowell: EC4269Slide10
c
"
c
'
0
Equilibria of the tax-evader
Feasible set
A: corner solution (honesty)
B: corner solution (dishonesty)
C: Interior (partial honesty)
E: Expected payoff
B
A
E
E
(
r
u
c
(
c
))
≤
0 if
e*
= 0
E
(
r
u
c
(
c
))
≥
0 if
e*
=
y
E
(
r
u
c
(
c
))
=
0 if 0 <
e*
<
y
C
solution depends on
tax parameters
t
:= (
p, s, t
)
income
y
personal attributes
a
e*
=
e
(
t
,
y
,
a
)
13 February 2012
Frank Cowell: EC426
10Slide11
Comparative statics
Focus on the interior solution
what happens when tax / enforcement parameters change?
do this graphically or analytically
differentiate the first-order condition
E(ruc
(c)) = 0 Effect of increased p
:indifference map “rotates”for given budget constraint, tangency moves closer to AEffect of increased
s:point B moves downfor given utility function, tangency moves closer to A
Effect of increased t:assume decreasing absolute risk aversion (DARA)amount “invested” in a risky asset increases with resources
so in this model, given DARA, evasion rises with ybut this will also imply that evasion
falls with t13 February 2012
Frank Cowell: EC42611Slide12
Overview...
Introduction
Basic model
Policy
Tax Compliance
How to assemble the whole economy
12
Frank Cowell: EC426
12
Extensions
13 February 2012
Individual taxpayer
Multiple taxpayersSlide13
Forward from simple TAG model
Obvious difficulty with isolated individual model
reacts to exogenously given risk situation
no perceived effect of his behaviour on this situation
no interaction with other aspects of public sectorno interaction with other agents
Start to put this right in this section1 aggregate individual risk-taking behaviour
2 introduce public sectorThen, later in the lecture:3 focus on interaction with tax agency
4 focus on interaction amongst agents13 February 2012
Frank Cowell: EC42613Slide14
Components of model
Government budget constraint:
R ≥
`
Rrevenue actually raised ≥ required target revenueDefine economy-wide aggregates
aggregate income: Y := ∫ y dF(y
, a)aggregate nominal tax receipts: tY
aggregate “leakage” from evasion: ∫ re(t, y, a) dF
(y, a)cost of enforcing probability p across economy
F(p)Composition of revenue
R = tY t ∫ re(t,
y, a) F(
p)So budget constraint becomes tY
t ∫ re(t, y, a)
F(p)
≥`RBut this ignores how the government revenue may be used…
13 February 2012Frank Cowell: EC426
14Slide15
TAG model: Public Sector
Taxes are used to pay for a public good
z
Government budget constraint in this extended model is:
R ≥ yz
where y is the (constant) marginal rate of transformationIndividuals benefit from provision of the good
…but they prefer that someone else pay for itso there is still a motive for tax evasionand expected utility is now
Eu(c,z), where uz
(c,z) > 0FOC for an interior maximum is:
E(ruc(c,z
)) = 0essentially as beforeResponse of e in this model is much the same for some cases:Surcharge
Probability of detectionBut for the tax rate t we have new insights…
13 February 2012Frank Cowell: EC426
15Slide16
The effect of a rise in the tax rate
There are still the conventional “income” and “substitution” effects
But
t
also affects amount of public good availableIncreasing t will:
reduce private consumption cincrease availability of public good z
Desirable to increase t?depends on amount of public good already available
Expect a “hump” shape:for t close to 0 we have z close to 0: raising t is desirable
for t close to 1 we may have satiation in z: lowering t is desirable
13 February 2012Frank Cowell: EC426
16
E
u
a
t
z
>
z*
a
z
<
z*
a
“underprovision”
“overprovision” Slide17
Preferences for public and private goods
How is
z*
determined?Optimal provision uses standard
SMRS = MRT ruleBecause of the risk component general formula is unwieldySo take a simplified set of preferences
ua(c, z) = c + v
a(z)ma :=
uza(c, z)/uca(c, z) =
vza(z)m :=
Sma = MRTEvasion erodes effectiveness of tax in providing z...feeds back into effect of tax on evasion
change in (et) has sign of m – y / zt a simple criterion for determining under / over provision
13 February 2012Frank Cowell: EC426
17
c
z
slope =
mSlide18
Effect of a rise in the tax rate
If the public goods are…
under-provided
: a rise in
t increases the amount of evasionover-provided: a rise in t
decreases the amount of evasionCowell and Gordon (1988)But individuals differ in:
risk aversiontaste for public goodsincome
So, different responses:constrained by e ≤ yhigh marginal evaluation
low marginal evaluationGet a more complex relationship between t and evasion overall
te
t
ty
13 February 2012
Frank Cowell: EC426
18Slide19
Overview...
Introduction
Basic model
Policy
Tax Compliance
An alternative model of the individual agent
19
Frank Cowell: EC426
19
Extensions
13 February 2012
Firms
InteractionSlide20
Firms and non-complianceIndividuals or firms?
fine line – status of self-employed?
Two major issues in setting up the model
how to model market interaction
how to model the output decisionSeveral types of market situation captured in one modeljust need a determinate demand curve.
Output decision based on an expected-profit criterion13 February 2012
Frank Cowell: EC426
20Slide21
Firms: a model
Conventional (non strategic firm)
marginal production cost
m
demand (sales) given by x(P
)P is market priceTax
t payable on sales Firm conceals a proportion b of sales
concealment costs per unit of output G(b)Expected tax rate
p and s have same interpretation as beforeeffective tax if not caught: [1
b]teffective tax if caught: [1 + s
b]tso Et := [1
p][1 b] t + p
[1 + sb]t
Expected profits are: EP = [P
m b G
(b) [1 p][1
b] t + p [1 + s
b]t ] x(P)EP
= [P m
g(b) Et] x
(P) where g(b) :=
bG(b)
13 February 2012Frank Cowell: EC426
21Slide22
Firms: solutionMaximise
E
P
w.r.t
. b and x.From FOC for a maximum:
dg(b)
─── = [1 p
ps] t
dbmarginal concealment cost = expected return For competitive firms: P
= m + g + Et
price = expected augmented marginal costWe have a separation resultOutput and evasion decisions are taken independently
a neutrality argumentapplies to both competitive and monopolistic firmsresult depends on risk-neutrality (Lee 1998)
13 February 2012Frank Cowell: EC426
22Slide23
Firms: predictionsEffect of penalty surcharge is conventional
∂
b
/∂s
< 0∂Et/∂
s > 0∂P/∂s
> 0So is effect of detection probability ∂b/∂
p < 0∂Et/∂p > 0
∂P/∂p > 0Effect of nominal tax increase:...raises proportion not declared ∂
b/∂t > 0...may or may not raise expected tax ∂E
t/∂p K 0...raises price 0 < ∂
P/∂t <113 February 2012
Frank Cowell: EC426
23Slide24
Overview...
Introduction
Basic model
Policy
Tax Compliance
Alternative model of rational behaviour.
Climate
of evasion and social
sanction
24
Frank Cowell: EC426
24
Extensions
13 February 2012
Firms
InteractionSlide25
Strategic interaction
Based on a application of game theory
Two players: tax authority and taxpayer
Tax authority chooses whether or not to investigate
Taxpayer chooses whether or not to cheat Intuition of simple strategic model: simultaneous move
if tax authority plays “audit” best response of taxpayer is “report”if taxpayer plays “report” best response of tax authority is “not audit”
etc, etc.no equilibrium in pure strategiesIntuition of simple strategic model: leader-followerif tax authority moves first, perhaps get a simple outcome
Develop this into a richer policy model?focus on tax-collector/tax-payer interactionwhat role is there for beliefs about others’ goals and actions?can tax authority precommit to an audit strategy?
13 February 2012
Frank Cowell: EC42625Slide26
Climate: motivation
Different countries, different types of compliance behaviour?
develop a model of a compliance climate? (
Cummings, et al. 2009
)others’ evasion choices affect my evasion decision
(Fortin et al. 2007)several possible foundations…1 Symmetric consumption externality
if you evade maybe I feel less pain if caught behaving antisociallysocial stigma (Benjamini and
Maital 1985, Kim 2003)2 Technological (production) externalitythe more others evade…
…the easier to find a corrupt accountantleads to reduction in “noncompliance costs”3 May also be induced by tax authority
auditing rules may induce a perceived interdependencecreates a “co-ordination game” – Alm and Mckee (2004)
Develop the first of these variants13 February 2012
Frank Cowell: EC426
26Slide27
Climate: model background
Evasion decisions affect outcomes in two ways
each person’s outcome affected by own choices (as before)
also affected by evasion of others (independently of public goods)
Nature of the consumption externalityaggregate evasion affects utility
moral climate?Utility of an a-type is V
a(e,E) wheree
: Own evasion activity E: aggregate evasionIn principle there are two subcases:1 where aggregate E
increases utility2 where aggregate E reduces utility Focus on case 2
13 February 2012Frank Cowell: EC426
27Slide28
Interaction: model behaviour
E
V
a
(0,
E
)
Y
V
a
(
y
,
E
)
utility
aggregate evasion
The Evasion-Utility Space
Payoffs if act honestly
Payoffs if act dishonestly
Dominant behaviour
Find equilibrium…
0
•
•
min
E
= 0, max
E
=
Y
Check incentive to switch
low
E
: individual switches to 0
high
E:
individual switches to
y
E
*
•
◦
E > E
*
: switching increases
E
E < E
*
: switching decreases
E
Check stability…
Three
equilibria
:
E
= 0 (stable)
E = E
*
(unstable)
E = Y
(stable)
13 February 2012
Frank Cowell: EC426
28Slide29
Overview...
Introduction
Basic model
Policy
Tax Compliance
A utilitarian approach
29
Frank Cowell: EC426
29
Extensions
13 February 2012
Basic model & extensions
Strategic interactionSlide30
Utilitarian enforcement problem
Basic behavioural model
taxpayer maximises expected utility
E
u(
c) = Eu([1 – t] y
+ r te) y: taxable income
t: proportionate tax ratee: concealed incomer : rate of return to evasion (= – s with prob p,
1 with prob 1 – p)Outcome of basic modeldetermines optimal evasion response e* = e
(p, s, t; y, a)depends on tax parameters (p, s, t
) and personal characteristics (y, a)Welfare model Take expected utility of representative taxpayer as welfare criterion
W = [1 – p] u([1 – t] y + te
) + p u([1 – t] y – ste)
Should evasion be eliminated? t fixed : don’t eliminate evasion p fixed: eliminate evasion p, s, t all variable: no solution
13 February 2012
Frank Cowell: EC42630Slide31
Optimal degree of enforcement?
Take a standard welfare-economics approach
choose the optimal
p
, given fixed s,
tBasic utilitarian modelhomogeneous populationsimple revenue target
a type of cost-benefit approach to enforcement Individual (slightly extended)income: y =
whconsumption: c = [1 t]
y + rteleisure: ℓ = 1 h
utility: u(c, ℓ
) Government/tax authorityenforcement cost per taxpayer: f(p)
revenue requirement: `R expected revenue leakage per tax dollar: `r =1
p psbudget constraint: twh
[1 p ps]t
e(t, w)
f(p) ≥`R / nUtilitarian model, homogenous population
objective function: v(t, w) = max E
u(c, ℓ)Lagrangean: v(
t, w) + l [twh
[1 p ps]t e(t
, w) f
(p) `R / n ]
13 February 2012
Frank Cowell: EC426
31Slide32
Choosing
p
for given (
s,t
)
MC
is marginal audit cost
is monotonic increasingMB is marginal audit yields + supply side and risk effectsmay not be monotonicmay go to zero
Optimum where MB = MCfp
= [1+s]te
`r te/p
w0ℓ/p
e(t, w) + v
p/l
0
1
p
f
p
B
p
p*
Probabilities, costs and benefits
Marginal cost of audit
Marginal benefit of audit
Optimum investigation effort
13 February 2012
Frank Cowell: EC426
32Slide33
Extensions – agent interaction
Cost-benefit approach is essentially individualistic
compute MB for each agent
Social interaction models
prevent epidemics?shift the equilibrium?manipulate expectations? (
Iyer et al 2010)raise search costs?
Focus on smart use of informationrecognise that agents may have better market information than tax authority exploit information about
all agents’ behaviourExample: tax compliance by firms use of information: compare simple auditing with relative auditingrelationships amongst firms is essential to the impact of policy choice
Cournot behaviour: get effect on output as well as tax receiptscollusion amongst firms – smart auditing less effective (Bayer and Cowell 2009)
Examine smart auditing further in a reporting model13 February 2012
Frank Cowell: EC42633Slide34
Overview...
Introduction
Basic model
Policy
Tax Compliance
Strategic approach to audit policy
34
Frank Cowell: EC426
34
Extensions
13 February 2012
Basic model & extensions
Strategic interactionSlide35
Tax-payer v. Tax-collector game
Model ingredients
tax rate
t
, surcharge s, cost of audit
are exogenously determinedtax enforcement powers are delegated, like contract farming
To find a solution we need to look closely at:the structure of taxpayer population control that can be exercised by tax authority
Essence of model is taxpayer heterogeneitydiffer by income and by attitude to tax-payingauthority does not know individual taxpayer attributes and incomes...but does know distribution in the populationTake a simple 2x2 version:
type income attitude pop proportionpoor
y0 ??? a0honest rich y0 +
D y always pay a1
chancers y0 + D y cheat if can a2
13 February 2012
Frank Cowell: EC42635Slide36
A mixed-strategy approach
Each side expects the other to play probabilistically
:
tax authority investigates low incomes with probability
p
taxpayer cheats with probability pExpected net tax receipts
DT = [a1 + a
2 [1 – p] ] t Dy +
a2pp [[1 + s]t
Dy – ] – a0p
Marginal impact on receipts from increasing p is:a
2p [[1 + s]t Dy –
] – a0This is positive if
p is greater than a threshold value: a0
p > p* :=
a2 [[1+s]t
Dy – ]
13 February 2012
Frank Cowell: EC426
36Slide37
Equilibrium concepts
Taxpayers and tax agency each form beliefs about the other’s actions
Equilibrium where each adopts a consistent set of beliefs
What is the optimal “tailored” audit strategy?
Two types of relationship between taxpayer and tax authority:
tax authority precommits to a strategytax authority does not precommitsee Reinganum and Wilde (1985
, 1986)13 February 2012
Frank Cowell: EC426
37Slide38
Precommitment: policy
If the tax authority were permissive, net receipts would be low:
D
T
|p
=1,p=0 = a1
t DyIf authority can commit it ought to audit all low-income reports:
p = 0 if report is y0 + Dyp = 1 if report is
y0Tax receipts net of audit costs areDT|p
=0,p=1 = [a1 + a2]
t Dy – a0
This amounts to a “Punish the poor” policy Is this in fact optimal?viabilitycredibility
13 February 2012Frank Cowell: EC426
38Slide39
Precommitment: optimality?
Condition 1 for financial viability is:
D
T
|
p=0,p=1 ≥
DT|p=1,p
=0 [a1 + a2]
t Dy – a0
p ≥ a1t
Dya2t
Dy ≥ a0
Condition 2 for financial viability is:net return from investigating a false report must be non-negative[1 + s
] t Dy –
≥ 0Combining the two conditions[1 + s] t
Dy – ≥
[1 + s – [a2/a0
]]t Dysatisfied if audit cost is not too high and there are not too many honest people
Credibility:everyone sees that only the genuinely poor people are auditedno revenue is ever raised in equilibriumpolicy may not be credible in a repeated setting
13 February 2012Frank Cowell: EC426
39Slide40
No commitment: outline
Tax authority:
believes probability that a chancer will cheat is
p
perceived probability of catching an evader is
q := a2p
/[a0+a2
p]expected net tax receipts can be written as: a0
const +
[ p / p* - 1]
a0+a2p
p* is pivotal value of beliefChancers:believe that probability of audit is
p expected utility if cheat is: pu([1 - t
]y0 + [1-
t – st]Dy) +
[1- p]u([1 - t]y
0 + Dy)expected utility if don’t cheat is:
u([1 - t][y0 + D
y])there is a pivotal probability satisfied p*
which equates these two utilities if u is risk neutral then p*
= 1 / [1+s]Solution:tax authority’s best response given belief
p defines reaction function p(p) chancers’ best response given belief
p defines reaction function p(p) equilibrium where beliefs consistent – where reaction functions intersect
13 February 2012
Frank Cowell: EC426
40Slide41
No commitment: Solution
1
0
1
p*
p*
p
taxpayer
reaction
tax authority
reaction
p
p
(
p
)
p
(
p
)
(
p*
,
p
*)
always audit if proportion of cheats is believed high
always cheat if probability of detection is believed low
The
strategy space
Tax authority’s strategy
Chancer’s strategy
Equilibrium
p
*
=
1 / [1 +
s
]
a
0
p
*
=
a
2
[[1+
s
]
t
D
y
–
]
13 February 2012
Frank Cowell: EC426
41Slide42
How the model worksResponse to tax-enforcement parameters:
∂
p
*
/∂ > 0 ∂p*
/∂ = 0∂
p*/∂t < 0 ∂p
*/∂t ≥ 0∂p*/∂s < 0 ∂
p*/∂s < 0Changing population proportions:∂
p*/∂a0 > 0 ∂
p*/∂a0
= 0∂p*/∂a
2 < 0 ∂p*/∂a
2 = 013 February 2012
Frank Cowell: EC42642Slide43
Assessment
Compliance is a central component of public economics
Arises naturally from the issues concerning the provision of public goods
Analysed using standard microeconomic techniques
Incentives issues similar to those of labour supply
Important to model the interactions involved in evasionPerceptions of others’ behaviour may be important.
Also interaction between tax-payers and enforcement agenciesCrucial issues on policy concern the institutional background What is the nature of the optimisation problem?Is a standard reporting model appropriate?
What information should each party be assumed to have?13 February 2012
Frank Cowell: EC42643Slide44
References (1)
Allingham, M. and A. Sandmo (1972)
“Income tax evasion: a theoretical analysis,”
Journal of Public Economics,
1, 323-338Alm, J. and Mckee, M. (2004) “Tax compliance as a coordination game,” Journal of Economic Behavior & Organization
54, 297-312Andreoni, J. Erard, B. and Feinstein, J. (1998) “Tax Compliance”,
Journal of Economic Literature, 36, 818-860 *Bayer, R.-C. and Cowell, F. A. (2009)
“Tax compliance and firms' strategic interdependence,” Journal of Public Economics, 93, 1131-1143Benjamini, Y. and Maital, S. (1985) “Optimal tax evasion and optimal tax evasion policy: behavioral aspects,” in Gaertner, W. and Wenig, A. (eds) The Economics of the Shadow Economy
, Springer Verlag, BerlinCowell, F. A. (1990) Cheating the Government, MIT Press, Cambridge MA *
Cowell, F. A. (2004) “Carrots and Sticks in Enforcement” in Aaron, H. J. and Slemrod, J. (ed.) The Crisis in Tax Administration, The Brookings Institution, Washington DC, 230-275 Cowell, F. A. and Gordon, J. P. F. (1988) “Unwillingness to pay: tax evasion and public good provision,”
Journal of Public Economics, 36, 305-321Cummings, R. G., Martinez-Vazquez, J., McKee, M. and Torgler, B. (2009) Tax morale affects tax compliance: Evidence from surveys and an artefactual field experiment,
Journal of Economic Behavior and Organization, 70, 447-45713 February 2012
Frank Cowell: EC42644Slide45
References (2)
*
Fortin, B.,
Lacroix
, G. and Villeval, M.-C. (2007) “Tax evasion and social interactions,” Journal of Public Economics
, 91, 2089–2112Kim, Y. (2003) “Income distribution and equilibrium multiplicity in a stigma-based model of tax evasion”,
Journal of Public Economics, 87 1591–1616Iyer
, G.S. , Reckers, P.M.J. and Sanders, D.L. (2010) “Increasing Tax Compliance in Washington State: A Field Experiment,” National Tax Journal, 63,7-32,
Lee, K. (1998) “Tax evasion, monopoly and nonneutral profit taxes,” National Tax Journal, 51
, 333-338.Reinganum, J. F. and L. L. Wilde (1985) “Income tax compliance in a principal-agent framework,” Journal of Public Economics
, 26, 1-18.Reinganum, J. F. and L. L. Wilde (1986) “Equilibrium verification and reporting policies in a model of tax compliance,” International Economic Review,
27, 739-760. *Slemrod, J. and Yitzhaki
, S. (2002) “Tax avoidance, evasion and administration,” Handbook of Public Economics, Volume 3, pp 1423-1470, North-Holland, Elsevier
Slemrod, J. (2007) “Cheating Ourselves: The Economics of Tax Evasion,” Journal of Economic Perspectives, 21, 25-48
Slemrod, J. and Yitzhaki, S. (2002) “Tax avoidance, evasion and administration,” Handbook of Public Economics, Volume 3,
pp 1423-1470, North-Holland, Elsevier 13 February 2012
Frank Cowell: EC42645