Behavioural and Social Explanations of Tax Evasion

Nigar Hashimzade University of ReadingGareth D. Myles University of ExeterFrank Page Indiana UniversityMatthew Rablen Brunel University

Financial support from the ESRC/HMRC/HMT is gratefully acknowledged

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 Non-expected utility theory Social interaction

Standard Model

The probability of being detected is p Taxpayer chooses declaration X to maximize

expected utility

max{X} E[U(X)] = [1 – p]U(Yn) + pU(Yc) Where

Yn = Y – tX = [1 – t]Y + tE Yc = [1 – t]Y – Ft[Y – X] = [1 – t]Y – FtE

The sufficient condition for evasion to take place (X < Y) is

p < 1/[1 + F]

Standard Model

The evasion decision can be written as

max{E} E[U(E)] = [1 – p]U([1 – t]Y + tE)

+ pU([1 – t]Y – FtE ) So it follows that E = [1/t]( . ) The result that compliance rises as t increases

runs counter to "intuition" and has mixed empirical support Problem of separating aggregate and individual

effects Weakness of experimental evidence

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

Prospect Theory

Prospect theory does three things (i) Translates the probabilities

(ii) Assumes payoff is convex in losses and concave in gains

(iii) Payoffs are measured relative to a reference point, R

xvpyvpV 21

0 if 0'' ,0 if 0'' ,0' zzvzzvzv

Prospect Theory

Yaniv (1999) studies the consequence of paying a tax advance With a tax advance of D

Use Y – D as the reference point D – tX is the gain if evasion is successful is the loss if evasion is

unsuccessful

tXDDYY n XYFttXDDYY c

XYFttXD

Prospect Theory

Observe that D – tX is achieved for sure So write objective as

Recall that prospect theory has v convex for losses and concave for gains

Yaniv analyzes the comparative statics of the necessary condition

XYFtpvtXDvV Y

0'' XYFtpFtvtXDtv

Prospect Theory

Consider the power function

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

0 ,

0 ,

zz

zzzv

Prospect Theory

25.2,88.0 4,4.0

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

β = 0.5, γ = 4p = 0.25, F = 4 p = 0.25, F = 20

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

For this objective it can be shown

A different reference point might change the result

XYFtvpwXYtvpwV KT 21 1

0

t

XY

dt

dX

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

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

Solid: t = 0.2Dashed: t = 0.3

Social Interaction

Social interaction allows information to be transmitted through a network

This information affects evasion behaviour by changing beliefs

The network is determined endogenously through choices that are made

The choices are: Occupation (employed or self-employed) Level of evasion if self-employed

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, 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 – )/(1 – ) (ii) Assume a uniform distribution for (, q, w)

Occupational Choice

Employment above the locus

Self-employment below the locus

The less risk-averse choose self-employment

But these people will also evade more

Separation of populationp = 0.5, t = 0.25, F = 0.75,

vb = 0.5, vg = 2, q = 0.5

Employed

Self-employed

Occupational Choice

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

E

t

E

t

Aggregate evasion

With borrowing

Social Interaction

A network is a symmetric matrix A of 0s and 1s (bi-directional links)

The network shown is described by

0100

1010

0101

0010

A

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

{, 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 = pi, ≤ 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 = pi + (1 – ) pj

Results

The model has been run for CRRA utility

n = 1000, = 100 uniform on [0, 10], True audit probability

a = 0.05 = 0.95, = 0.75 t = 0.25, F = 1.5

0 10 20 30 40 50 60 70 80 90 1000.51

0.52

0.53

0.54

0.55

0.56

0.57

0.58

0.59

0.6

0.61

p

Mean audit probability (belief)

Results

0 10 20 30 40 50 60 70 80 90 1001.75

1.8

1.85

1.9

1.95

2

2.05

2.1

2.15

0 10 20 30 40 50 60 70 80 90 1003

3.05

3.1

3.15

3.2

3.25

3.3

3.35

3.4

EmployedMean risk aversion

Self-employedMean risk aversion

0 10 20 30 40 50 60 70 80 90 1000.34

0.36

0.38

0.4

0.42

0.44

0.46

Results

The outcome is little changed if decay is increased

Figure uses = 0.25 The average belief

about audit probability remains high

p

Conclusions

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