# LAGV - University of Exeter

```Behavioural and Social
Explanations of Tax Evasion
Gareth D. Myles University of Exeter
Frank Page
Indiana University
Matthew Rablen Brunel University
Introduction

An understanding of the individual tax
compliance decision is important for revenue
services
 Their aim is to design policy instruments to
reduce the tax gap
 Tax evasion is an area where orthodox
analysis has been challenged by behavioural
economics
 But what elements of behavioural economics
are useful?
Introduction





The presentation presents a brief review of the
&quot;standard model&quot; of the compliance decision
Two aspects of behavioural economics are
then considered
First, the application of non-expected utility
theory
Second, the role of social interaction
Networks and information exchange appear
promising
Standard Model

The compliance decision is a gamble on
detection
 The taxpayer has a fixed income level Y but
declares X with 0 ≤ X ≤ Y
 Income when not caught is
Yn = Y – tX = [1 – t]Y + tE
 If caught a fine at rate F is levied on the tax
Yc = [1 – t]Y – Ft[Y – X] = [1 – t]Y – FtE
Standard Model





The probability of being detected is p
If the taxpayer is an expected utility maximizer
then X solves
max{X} E[U(X)] = [1 – p]U(Yn) + pU(Yc)
Since
dYc/dYnc = – [1 – p]U′(Ync)/pU′(Yc)
The sufficient condition for evasion to take
place (X &lt; Y) is
p &lt; 1/[1 + F]
Applies to all taxpayers and is independent of
risk aversion
Standard Model





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
With these numbers p &lt; 1/(1+F) so all US
The Taxpayer Compliance Measurement
Program revealed that 40 percent of US
taxpayers underpaid their taxes
Standard Model

The optimization is
max{E} E[U(E)] = [1 – p]U([1 – t]Y + tE)
+ pU([1 – t]Y – FtE )
 So it follows that E = [1/t]f( . )
 The result that E falls as t increases is to
&quot;intuition&quot; and has mixed empirical support



Problem of separating aggregate and individual
effects
Weakness of experimental evidence
The failure of these predictions has lead to a
search for alternative models
Behavioural Approach

Behavioural economics can be seen as a
loosening of modelling restrictions
 Two different directions can be taken:
(i) Use an alternative to expected utility theory
(ii) Reconsider the context in which decisions
are taken
 The consequences of making such changes
are now considered
Non-Expected Utility





There are several non-expected utility models
These have the general form
V(X) = w1(p, 1 – p)v(Yc) + w2(p, 1 – p)v(Ync)
w1(p, 1 – p) and w2(p, 1 – p) are translations of p
and 1 – p (probability weighting functions)
v( . ) is some translation of U( . )
Different representations are special cases of
this general form
Non-Expected Utility

Some of the alternatives that have been
applied to the compliance decision are:




Rank Dependent Expected Utility imposes structure
on the translation of probabilities
Prospect Theory translates probabilities, changes
payoff functions, and uses a reference point
Non-Additive Probabilities do not require the normal
linearity for aggregation for probabilities
Ambiguity permits uncertainty over the probability
of outcomes
Prospect Theory

Prospect theory does three things
 (i) Translates the probabilities
V    p1 v  y     p 2 v  x 

(ii) Assumes payoff is convex in losses and
concave in gains
v '  z   0 , v ' '  z   0 if z  0 , v ' '  z   0 if z  0

(iii) Payoffs are measured relative to a
reference point, R
Prospect Theory

As an example consider Yaniv (1999)
 Studies the consequence of paying a tax
 This will not affect the evasion decision in an
expected utility framework
 It can affect the evasion decision under
prospect theory through the determination of
the reference point
Prospect Theory

With a tax advance of D
Y
Y
c
n
 Y  D   D  tX

 Y  D   D  tX  Ft Y  X

Use Y – D as the reference point
 D – tX is the gain if evasion is successful
 D  tX  Ft Y  X  is the loss if evasion is
unsuccessful

Prospect Theory
Observe that D – tX is achieved for sure
 So write objective as

V
Y
 v  D  tX   pv   Ft Y  X


Recall that prospect theory has v convex for
losses and concave for gains
 Yaniv analyzes the comparative statics of the
necessary condition
 tv '  D  tX   pFtv '   Ft Y  X
 
0
Prospect Theory

Consider the power function


z , z0

vz   


    z  , z  0

First assume that D &gt; tY
 The next slides illustrates VY for the parameter
values
Y = 1, t = 0.2, p = 0.1, F = 2, D = 0.3
Prospect Theory
0.6
0.3
0.4
0.2
0.2
0.1
0
0
-0.1
-0.2
0
0.2
0.4
0.6
X/W
0.8
  0 . 88 ,   2 . 25
1
0
0.2
0.4
0.6
X/W
0.8
  0 .4 ,   4
1
Prospect Theory

For the power function we can prove:
&quot;If there is an interior solution to the first-order
condition it must be a minimum&quot;
 The same comments (and result) apply to
other functional forms
 The assumptions of prospect theory combine
to create analytical problems
Prospect Theory
Two figures for D &lt; tY
0.4
0.5
0
0
-0.4
-0.5
-0.8
-1
-1.2
-1.5
-1.6
0
0.2
0.4
0.6
X/W
0.8
1
-2
0
0.2
0.4
0.6
X/W
0.8
β = 0.5, γ = 4
p = 0.25, F = 4
p = 0.25, F = 20
1
Prospect Theory

al-Nowaihi and Dhami (2007) argue that
 (i) The reference point should be R = (1 – t)Y
 (ii) Standard prospect theory should be used
V

KT
 w1 1  p v t Y  X
 X
For this objective it can be shown
dX
dt

  w 2  p v   Ft Y

Y  X
0
t
A different reference point might change the
result

Positive Results

One way to make progress is to assume the
probability of detection depends on declared
income
 Within the prospect theory framework
VPT = w⁺(1–p(X))v(t(Y – X)) + w⁻(p(X))v(–Ft(Y – X))
 An appropriate form of p(X) can make the
objective strictly concave
 Consider the power function of v( ) and
p(X) = αp₀X/Y
Positive Results
a
p0
0.01
0.02
0.656
0.520
p(Y/2) p(Y)
0.0656 0.006
0.0736 0.010
0.03
0.458
0.0793 0.013
Probability of Audit
 = 0.88, γ, = 2.25, α = 2/3
and p₀ = 0.01
Positive Results
0

Now combine the Yaniv
model with linear
probability
pL(X) = α[1 – (1-p₀)(X/Y)]
below the true tax
liability (D &lt; tY)
 t = 0.2, X/Y = 0.74, p =
0.236
 t = 0.3, X/Y = 0.50, p=
0.45
-0.2
-0.4
-0.6
-0.8
-1
0
0.2
0.4
0.6
X/W
0.8
Solid: t = 0.2
Dashed: t = 0.3
1
Summary

Adopting non-expected utility can solve one
problem


The transformation of probabilities can raise the
rate of compliance
Non-expected utility does not change the tax
effect
 Since Ync = (1– t)Y+ tE and Yc = [1 – t]Y – FtE
it follows that E = [1/t]f( . )
 Is a variable probability non-expected utility?
Evidence

Empirical evidence demonstrates a wider
range of factors may be relevant



Social groupings
Network effects
The opportunities for evasion also depend on
occupation
 Choice of occupation is determined by
individual characteristics
 We wish to explore how these factors interact
Occupational Choice

Assume that a choice is made between
employment and self-employment
 Employment is safe (wage is fixed) but tax
cannot be evaded (UK is PAYE)
 Self-employment is risky (outcome random)
but permits provides opportunity to evade
 Selection into self-employment is dependent
on personal characteristics
Occupational Choice

A project is a pair {vb, vg} with vb &lt; vg
 An individual is described by a triple {w, r, q}
 Evasion level is chosen after outcome of
project is known
 So in state i, i = b, g, Ei solves
max EUi = pU((1–t)vi – FtEi) + (1–p)U((1–t) vi+tEi)
 The payoff from self-employment is
EUs = (1–q) EUb (Eb*) + qEUg (Eg*)
Occupational Choice





Occupational choice compares payoffs from
the alternatives
Self-employment is chosen if
EUs(q, vb, vg) &gt; Ue(w)
What is the outcome in this setting?
(i) Assume CRRA utility
U = Y(1 – r)/(1 – r)
(ii) Assume a uniform distribution for (r, q, w)
Occupational Choice

Employment above
the locus
 Self-employment
below the locus
 The less risk-averse
choose selfemployment
 But these people will
Employed
Self-employed
Separation of population
p = 0.5, t = 0.25, F = 0.75,
vb = 0.5, vg = 2, q = 0.5
Occupational Choice
E 0.3

The aggregate level
of evasion can be
increasing in the tax
rate
 This is the
consequence of
intensive/extensive
margins
 The result extends to
borrowing to invest
0.25
0.2
0.15
0.1
0.05
0
0
0.1
0.2
0.3
0.4
0.5
t
Aggregate evasion
E 2.5
2
1.5
1
0.5
0
0
0.2
0.4
0.6
With borrowing
0.8
t
Social Interaction

The next step is to embed occupational choice
within a network model
 The idea is that information is transmitted
through the network
 This information affects evasion behaviour by
changing beliefs
 The network is determined endogenously
Social Interaction

A network is a
symmetric matrix A
of 0s and 1s (bidirectional links)
 The network shown
is described by
0

1

A
0

0
1
0
0
1
1
0
0
1
0

0

1

0
1
2
3
4
Social Interaction






Each period an action is chosen
The network is revised as a consequence of
chosen actions
A random selection of meetings occur (a
matrix C of 0s, 1s)
Set of permissible meetings is determined by
the network (M = A.*C)
At a meeting information is exchanged
Beliefs are updated
Tax Evasion Network






There are n individuals
Individual characteristics
{r, w, p, q, vb, vg}
are randomly drawn at the outset
A choice is made between e and s
If s is chosen outcome b or g is randomly
realised
Given the outcome evasion decision is made
Those in s are then randomly audited
Tax Evasion Network





If audited pi goes to 1 other pi decays
pi = d pi, d ≤ 1
Type s only meet type s
Links in network evolve as a consequence of
choice
individuals
Information on p is exchanged
pi = m pi + (1 – m) pj
Results






The model has been
p
run for CRRA utility
n = 1000, t = 100
r uniform on [0, 10],
True audit probability
a = 0.05
d = 0.95, m = 0.75
t = 0.25, F = 1.5
0.61
0.6
0.59
0.58
0.57
0.56
0.55
0.54
0.53
0.52
0.51
0
10
20
30
40
50
60
70
80
90
Mean audit probability (belief)
100
t
Results
r
r
2.15
3.4
3.35
2.1
2.05
3.3
2
3.25
1.95
3.2
1.9
3.15
1.85
3.1
1.8
3.05
1.75
0
10
20
30
40
50
60
70
80
90
100
3
0
10
20
30
40
50
60
70
80
t
Self-employed
Mean risk aversion
90
100
t
Employed
Mean risk aversion
Results

The outcome is little
changed if decay is
increased
 Figure uses d = 0.25
 The average belief
probability remains
high
p
0.46
0.44
0.42
0.4
0.38
0.36
0.34
0
10
20
30
40
50
60
70
80
90
100
t
Results

The level of evasion
falls over time
 The continued
auditing is effective
 This is the inverse of
the probability belief
 Rapid initial falls
E
4200
4000
3800
3600
3400
3200
3000
2800
0
10
20
30
40
50
60
70
80
90
100
t
Conclusions (1)

Non-expected utility delivers nothing that is not
given by adopting subjective probabilities in
the EU model
 It requires variable probability to reverse the
tax result
 Occupational choice selects those who will
evade into situations where evasion is
possible
 Social interaction can lead subjective
probability to differ from objective probability
Conclusions (2)

The results established by simulation
 Many alternative structures are possible
 What general value can be assigned?
 Is it possible to “discover” anything using this
analysis?
```