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]( . ) 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

(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

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

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

= 0.88, γ, = 2.25, α = 2/3 and p₀ = 0.01

p0 p(Y/2) p(Y)

0.01 0.656 0.0656 0.006

0.02 0.520 0.0736 0.010

0.03 0.458 0.0793 0.013

Probability of Audit

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

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]( . ) 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, 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

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 (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

Results

The level of evasion falls over time

The continued auditing is effective

This is the inverse of the probability belief

Rapid initial falls0 10 20 30 40 50 60 70 80 90 100

2800

3000

3200

3400

3600

3800

4000

4200

E

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?