Gareth D. Myles(with Nigar Hashimzade)University of Exeter and Institute for Fiscal StudiesMay 2013

Agent-Based Modelling and Tax Compliance

BACKGROUND

The economic analysis of tax compliance has two objectives1. To explain behaviour and predict

consequences

2. To design beneficial interventions Different methodologies can contribute

1. Theory2. Empirical3. Experimentation

Agent-based modelling combines methodologies

AGENT-BASED MODELLING

An agent-based model1. Creates a set of agents2. Assigns abilities, objectives, and knowledge3. Allows them to interact4. Observes the outcome

The creation and interaction takes place in a computer simulation

Parameters can be varied to test the effect on the outcome

Such models can describe natural situations or economic situations

SHEEP-WOLF PREDATION

A famous model of nature is that of sheep and wolves

Wolves and sheep wander randomly around the landscape

The wolves look for sheep to prey on Each step costs wolves energy so they

must eat sheep When they run out of energy they die The analysis simulates the evolution of

the populations

ALLINGHAM-SANDMO

The same programme can run a basic tax evasion model1. Apply the Allingham-Sandmo model of

evasion choice2. Adopt a ramdom audit strategy3. Track the degree of compliance

Policy experiments permit the effect of interventions to be judged

Provides a starting point for more detailed analysis

ALLINGHAM-SANDMO The evasion decision is a gamble since

failure to declare correctly may not be detected

The taxpayer has a fixed income level Y but declares income X, with 0 ≤ X ≤ Y

Income when not caught is Ync = Y – tX If caught a fine at rate F is levied on

the tax that has been evaded Income level when caught is Yc = [1 – t]Y – Ft[Y – X]

ALLINGHAM-SANDMO

If income is understated the probability of being caught is p

Applying expected utility theory implies the optimal declaration X solves

max{X} E[U(X)] = [1 – p]U(Ync) + pU(Yc) The model involves individual

optimisation It provides no explanation of the

income source The origin of p is not explored

LIMITATIONS

There are several limitations1. The software does not permit complex

optimisation2. The implications of the preferences do not

fit the facts3. Interventions can be more sophisticated

than random audits Use alternative software (Matlab) Appeal to recent literature on compliance The third is a current research question

IMPROVEMENTS

Current research is following two paths to construct improved models

Kim Bloomquist at the IRS is following one approach

He is using “real” data with complex tax returns and large number of agents

My research (with Hashimzade and Rablen) applies behavioural economics

We focus on individual choices and auditing rules

BLOOMQUIST

The current version of the model has 85,000 taxpayers

From a “broadly representative” county

Each submits a return that mirrors US form

The income returns are based on actual data as presented in IRS Public Use File Data manipulated in order to anonymise but

maintaining statistical properties of actual data

BLOOMQUIST

The key part of the model is reporting behaviour

There are 19 imputable items Taxpayers are grouped into four types

for each item (1) self-prepared and non-zero reported amount, (2) self-

prepared and zero reported amount, (3) paid prepared and non-zero reported amount and (4) paid prepared and zero reported amount

Random audit data is used to estimate the distribution of under-reporting for each type and item

BLOOMQUIST

A random draw then assigns under-reporting to each agent

The sum of reported income and under-reporting gives the true income of each agent

The true income remains fixed in the simulation

The ratio of reported income to true income gives a reporting ratio

Initial value is assumed optimal

BLOOMQUIST

Through the simulation the reporting ratio adjustsUp(?) following auditsDown(?) if interacting with other under-

reporting agentsUp or down according to practice of

return preparers The model user chooses the direction

and size of effects

BLOOMQUIST

The model is operational and broadly matches observed data

It can predict the effect of interventions

The future development of the model is to increase the number of agents

The aim is to model all 141 million US taxpayers

To do this some serious computing power is required

OUR APPROACH

Our research focuses on the choice behaviour behind the compliance decision

We aim to integrate the best of current theory to match evidence

The models can use artificial data or be calibrated to actual data

The ultimate aim is to permit exploration of interventions

The next sections develop the components of the model

OCCUPATIONAL CHOICE

The distinction between employment and self-employment is important for compliance

Employment is safe (wage is fixed) but tax cannot be evaded (withholding)

Self-employment is risky (outcome random) but provides opportunity to evade

Selection into self-employment is dependent on personal characteristics

OCCUPATIONAL CHOICE

Self-employment can be modelled as a risky project

An individual is described by {w, s1, s2}

The outcome of a project is siyi where yi is drawn from a lognormal distribution

Each individual compares the potential occupationsEmployment, alternative forms of self-

employment And chooses the one with the highest

expected benefit

OCCUPATIONAL CHOICE

The evasion level is chosen after income from self-employment is known

With outcome yi, amount evaded Ei solves

max EUi = pU((1–t)siyi – ftEi) + (1–p)U((1–t) siyi +tEi)

The simulation has 3 occupations Individual characteristics are randomly

drawn at the outset Incomes are realised and the compliance

decision is made Auditing and punishment take place

EVASION AND DISTRIBUTION

1000 people, 200 iterations

Characteristics drawn each iteration

Mean incomes are(h) =

12.1651 (e) = 12.8727 Gini coefficient:

G(h) = 0.3360G(e) = 0.3549

With evasion

No evasion

Lorenz Curves

EVASION AND RISK-TAKING

Distribution of Occupational Choices

No Evasion With Evasion and Auditing

EVASION AND TAX PROGRESSION

Evasion and Effective Tax Rates

Scatter Plot Histogram

Y

ETR

ETR

Observations

COMPLIANCE DECISION The Allingham-Sandmo model makes

two clear predictions1. The taxpayer evades if p < 1/[1 + F]2. The amount evaded decreases when t

increases For observed values no taxpayer will

be fully compliant The conclusion that evasion falls as t

increases runs counter to "intuition" The failure of these predictions has

lead to a search for alternative models

BEHAVIOURAL ECONOMICS

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

Both allow additional factors to be incorporated into the compliance decision

BEHAVIOURAL ECONOMICS

There are several non-expected utility models

These have the general formV = w1(p, 1 – p)v(Yc) + w2(p, 1 – p)v(Ync)

w1(p, 1 – p) and w2(p, 1 – p) are weighting functions that can depend on p and 1 – p

v( . ) is a payoff function that replaces U( . )

Different representations are special cases of this general form

BEHAVIOURAL ECONOMICS

Adopting non-expected utility can solve one problemThe weighting functions can raise the rate

of compliance We incorporate subjective probabilities

that can change through learning 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]( . )

SOCIAL INTERACTION

Tax compliance has a social aspectWe model this using a social network to

governs interaction between individuals Individuals meet with their contacts in

the networkMeetings allow exchange on beliefsThe idea is that information is

transmitted through the networkThis information affects evasion

behaviour by changing beliefs and attitudes

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

A social custom is an informal rule on behaviour

Either:Additional loss of utility if custom is brokenU if followed, U – S if broken

Or:Additional utility if custom is followedU + S if followed, U if broken

Empirical and experimental evidence on evasion is consistent with social customs

SOCIAL INTERACTION

Choose either not to evade with payoff UNE = U(Y[1 – t]) Or evade with expected payoff UE = E[U] – S(Ei, ) is the proportion of population evading A possible form is S(Ei, ) = iEic() People with high i (individual concern

about custom) will not evade Evasion increases in t for some range of i

SOCIAL INTERACTION

Each period a random selection of meetings permitted by the network occur

At a meeting information may be exchanged

Likelihood of exchange is dependent on occupation

Beliefs are updatedSubjective probability (non-expected

utility)Rate of compliance (social custom)

SOCIAL INTERACTION

The importance of social custom is also determined by interaction

It changes when there is a exchange of information

It falls if an evader is met but rises if a non-evader is met

With k as the number of previous information exchanges the process is

01 1

1

1

j

vE

it

it k

SUBJECTIVE BELIEFS

If i is audited pi goes to 1 other pi decays

Meetings occur randomly between linked individuals

The probability of information exchange pij depends on occupations

pjj > pij

Information on p is exchanged

1 1i i jt t tp p p

1,0 ,~ ddpp it

it

SIMULATION DETAILS

There are n individuals and 3 occupations

Individual characteristics {w, , q1, q2 p, } are randomly drawn at the outset A choice is made between s If 1 or 2 is chosen outcome u or s is

randomly realised and compliance decision is made

Auditing takes place then p and are updated

OUTCOME

Risk aversion differs across occupations

The self-employed have lower risk aversion

They will be more willing to engage in non-compliance

0 20 40 60 80 100 120 140 160 180 2001.5

2

2.5

3

3.5

4

4.5

5

5.5

6

6.5Risk aversion

Emp

SE1SE2

Risk aversiont

Relative risk aversion

0 10 20 30 40 50 60 70 80 90 1000

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4Subjective beliefs

Emp

SE1SE2

Total

OUTCOME

The average subjective probability exceeds objective probability

The outcome is little changed If rate of decay is

increased Belief rises to less

than 1 after auditSubjective belief

t

Probability

OUTCOME

The social custom is sustained

Observe the ranking by occupation

The employed learn from the self-employed

0 10 20 30 40 50 60 70 80 90 1000.46

0.48

0.5

0.52

0.54

0.56

0.58

0.6

0.62

0.64

0.66Honesty weight

Emp

SE1SE2

Total

Honesty weightt

Weight

OUTCOME

Occupation 2 are least compliant

They have lowest risk aversion

But still place a weight on honesty

Compliance can be very low in the risky occupation

Compliance by occupation

0 10 20 30 40 50 60 70 80 90 1000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9Compliance

SE1

SE2Total

Proportioncompliant

t

CHOICE OF AUDIT STRATEGY

Four audit strategies are analyzed: ∙ FixedProb: Random audit of the self-

employed with a fixed probability FixedNum: Audit a fixed number of

taxpayers in each occupation AlternCert: Switches audits between

occupations each period AlternRand: Randomly switches audits

between occupations

CHOICE OF AUDIT STRATEGY

Strategies have the same mean number of audits per period

The strategy FixedProb has the highest rate of compliance

FixedNum has the lowest

Is this an indication of convexity through the learning processes?

t

Compliancerate

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

1 11 21 31 41 51 61 71 81 91

FixedProb FixedNum AlternCert AlternRand

CHOICE OF AUDIT STRATEGY

The strategy FixedProb generates the highest level of revenue

FixedNum generates the lowest

Why is it not better to condition on occupation?

t

Revenue

1900

2000

2100

2200

2300

2400

2500

2600

2700

2800

1 11 21 31 41 51 61 71 81 91

FixedProb FixedNum AlternCert AlternRand

RISK-BASED AUDITING

The previous audit strategies use very limited information

The role of predictive analytics is to identify the best audit targets

We want to address two questions: Can predictive analytics raise total revenue? What are the equilibrium consequences?

Our previous model is extended to address these questions

RISK-BASED AUDITING

Audits are random for the first 50 periods The data from audits is collected and

used to run a Tobit (censored) regression Amount of non-compliance is regressed

on occupation, declaration, and audit history

The estimated equation is used to predict non-compliance

The top 5 percent are audited and audit outcomes used to update regression

The process is repeated

RISK-BASED AUDITING

Compliance Honesty Weight

(Note: SE1 and SE2 are interchanged)

RISK-BASED AUDITING

Tax and fine revenuer = 1.9343, r = 0.0298a = 2.6044, a = 0.9285

Subjective Beliefs

SUMMARY

Agent-based simulation is a modelling methodology

Each agent is given a decision rule and interact over time

Permits policy experiments to be conducted

Current models are increasing the number of agents, enhancing the choice process, and incorporating social interaction