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