Agent Based M odeling of Tax Evasion Behaviour

1. Agent Based Modeling of Tax Evasion Behaviour Abhishek Malik (abhim@iitk.ac.in) Instructor: Amitabh Mukherjee IIT Kanpur

2. 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.

3. 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)

4. 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.

5. 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.

6. 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.

7. Davis, Jon S., Gary Hecht, and Jon D. Perkins(2003) • 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.

8. 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.

9. 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.

10. 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).

11. Differences • Taxpayer evasion decision. • Mittone and Patelli • 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. • Davis et al. • Random threshold for risk aversion and susceptibility to evasion. • Stochastic decision process for evasion. • Bloomquist • Evasion is influenced by rate of audit and knowledge of someone close auidited. • Deterrent affects of audit. • Only Bloomquist model allows both indirect and induced effects. • Over weighting of audit probabilities. • Seen only in Bloomquist model.

12. Agent complexity. • Mittone and Patelli • Only two characteristics: decision module and utility function. • Agents live forever. • Davis et al • Agents had infinite life span with list of acquaintances, social norm, finite memory, awareness of enforcement, and in total nine attributes. • Bloomquist • 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 • Used SWARM. • Davis et al • Used Mathematica. • Bloomquist • Used NetLogo.

13. Proposal

14. Simple Model(Primary) • 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.

15. 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.

16. References • 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.