AGENT BASED MODELING OF
TAX EVASION BEHAVIOUR
Abhishek Malik ([email protected])
Instructor: Amitabh Mukherjee
IIT Kanpur
INTRODUCTION TO PROBLEM
Today taxpayers see evading as a gamble or
investment with certain associated risks and
benefits.
 Taxpayers behavior is affected by many factors
like prior audit experiences, social norms,
opportunity,
observing
someone
evading,
strictness of law enforcement, etc.
 Incorporating all these factors while formulating
a policy for tax is not an easy task.
 Here agent based modeling can help predict the
affects and thus formulate appropriate policy.

PAST WORKS STUDIED AND COMPARED
“Imitative behaviour in tax evasion.” -Mittone, L.,
& Patelli, P.(2000)
 “Social Behaviors, Enforcement and Tax
Compliance Dynamics.” -Davis, Jon S., Gary
Hecht, and Jon D. Perkins(2003)
 “Multi-Agent Based Simulation of the Deterrent
Effects of Taxpayer Audits.”- Bloomquist, Kim M.
(2004)

MITTONE, L., & PATELLI, P. (2000)
Assumes three classes of taxpayers: Honest,
Imitative and Free riders, each having unique
utility function.
 Honest ones derive additional utility by paying
according to social norms of compliance.
 Free riders maximize utility by paying as little as
possible.
 Imitative ones maximize utility by paying what
others pay (population mean).
 All the three also derive utility from public goods
and services supported by tax payments.

After every period the agents must decide
whether to evade more, less or the same
 The decision is stochastic but based on whether
the calculated utility increased, decreased or
remained the same as in previous run.
 Every n period, GA (genetic algorithm) updates
the population of agents to reflect the more
successful strategies in general.
 Tax agency informs about average tax paid and
proportion of honest taxpayers (for agents to
calculate utility).
 They evaluated how the total evasion behavior
varied with initial mixture of taxpayers.

Model demonstrated that without audits tax
payments went down to zero even with initially
all honest taxpayers.
 Two audit strategies are used: uniform and tail
auditing.
 Uniform auditing resulting in all honest
population.
 In tail auditing, those with least payments were
audited.
 Tail auditing had weaker impact on compliance
as compared with uniform auditing.

DAVIS, JON S., GARY HECHT, AND JON D.
PERKINS(2003)
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Developed two models: analytical and computational.
Assumed three classes of taxpayers: honest,
susceptible and evader.
In mathematical model, audit rates had to fall to
almost nil to trigger widespread evasion in initially
honest population, and similarly in initially evaders
audit rates had to be increased very high for
compliance.
In Multi Agent Based System (MABS) taxpayers
begin as evaders or honest(by nature or as a result of
recent audit)
Honest ones become susceptible upon observation of
evasion in social network.
Susceptible agents evade if audit rate or
compliant taxpayers fall below a threshold.
 Evaders become honest if audited, but revert to
evasion upon observation of evasion in social
network.
 Assumption is that only evaders are audited.
 They created a society of 500 agents and varied
initial evaders from 10% to 50%. They ran 18
simulations with audit rates from 0.002 to 0.03 .
 100% compliance was observed for audit rates as
low as 0.03 which was different from IRS data.

BLOOMQUIST, KIM M. (2004)
He says as long as 1 – p – (p × f × d) ÷ (1 + r)t > 0 ,
taxpayer will evade.(Where d is auditor detection
rate and r is the discount rate.)
 Tax agency audits taxpayer randomly.
 Audited taxpayer becomes more risk averse by
some random amount for some specified number
of future periods.
 Agents in associated social network also become
risk averse.

SIMILARITIES
Agent interaction and tax evasion(indicating how
interaction influences evasion).
 Nature of taxpayer audits(all audits are
homogenous).
 Time intervals(each run is taken as a year).
 Model size(it was less than 1000).

DIFFERENCES

Taxpayer evasion decision.

Mittone and Patelli



Davis et al.
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Evasion is influenced by rate of audit and knowledge of
someone close auidited.
Deterrent affects of audit.


Random threshold for risk aversion and susceptibility to
evasion.
Stochastic decision process for evasion.
Bloomquist


Assume agents to be rational and consistent in calculating
utility.
GA makes agents switch to one of three utility functions based
on their success history.
Only Bloomquist model allows both indirect and induced
effects.
Over weighting of audit probabilities.

Seen only in Bloomquist model.

Agent complexity.

Mittone and Patelli



Davis et al

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Agents had infinite life span with list of acquaintances, social norm,
finite memory, awareness of enforcement, and in total nine attributes.
Bloomquist

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Only two characteristics: decision module and utility function.
Agents live forever.
Had twenty nine different attributes like age, life span, risk aversion,
memory for income, under reporting and audits, and many others.
Implementation.

Mittone and Patelli


Davis et al
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Used SWARM.
Used Mathematica.
Bloomquist

Used NetLogo.
PROPOSAL
I would like to start with a simple model of taxpayers with honesty varying
randomly and perfect audits.
I plan to develop the model using NetLogo or Repast and Ascape(these are
available freely on the web).
I will then calibrate or in other words modify model to give results similar to
real world using database available.
I plan to increase the complexity of the system and then calibrate at each
improvement with corresponding database result.
SIMPLE MODEL(PRIMARY)
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Agents will be assigned a honesty and risk aversion
level distributed between minimum(initially 0) and 1.
Perceived social norm according to social network will
be the perceived percentage of honest ones.
A function of honesty, risk aversion and social norms
can be set for decision to evade or not and also how
much to hide if to evade.
Certain thresholds (can be chosen initially, and
updated later according to the model) below which
agent will evade and hide accordingly with difference
in threshold and value of above function.
Audits will be done on agents randomly selected from
those with least payments, and a few from middle
level of payments also.
Audit will increase the perceived social norm value
thus increasing the above mentioned function value.
A FEW PLANNED IMPROVEMENTS
Varying incomes levels for agents, and also
income variation with time.
 Agents will have different levels of visible and
invisible incomes.
 Incorporating a few irrational agents into the
system.
 Different tax rates for different levels of income.
 Corruption in audits.
 Different classes of taxpayers(salaried ones and
the business class).
 Variable size of social network for each agent and
enforcement awareness indicators.
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REFERENCES
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Bloomquist, Kim M. “A Comparison of Agent-Based Models
of Income Tax Evasion.” Social Science Computer Review
24 No. 4 Winter, 2006): 411-25.(and references cited
therein)
Bloomquist, Kim M. “Multi-Agent Based Simulation of the
Deterrent Effects of Taxpayer Audits.” Paper presented at
the 97th Annual Conference of the National Tax
Association, Minneapolis, MN, November, 2004. (and
references cited therein)
Davis, Jon S., Gary Hecht, and Jon D. Perkins. “Social
Behaviors, Enforcement and Tax Compliance Dynamics.”
Accounting Review 78 No. 1 January, 2003): 39-69.
Mittone, L., & Patelli, P. (2000). “Imitative behaviour in tax
evasion.” In B. Stefansson & F. Luna (Eds.), Economic
simulations in swarm: Agent-based modelling and object
oriented programming (pp. 133-158) Amsterdam: Kluwer.