LAGV - University of Exeter
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Transcript LAGV - University of Exeter
Behavioural and Social
Explanations of Tax Evasion
Nigar Hashimzade University of Reading
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
"standard model" 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
evaded so income is
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 < Y) is
p < 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 < 1/(1+F) so all US
taxpayers should evade
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
"intuition" 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
advance
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 , z0
vz
z , z 0
First assume that D > 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:
"If there is an interior solution to the first-order
condition it must be a minimum"
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 < 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)]
Advance payment
below the true tax
liability (D < 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 < 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) > 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
also evade more
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
through choices that are made
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
Meetings occur randomly between linked
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
about audit
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?