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Optimal Audit Policy for a Tax Evasion Network

Optimal Audit Policy for a Tax Evasion Network. Nigar Hashimzade University of Reading Gareth D. Myles University of Exeter Frank Page Indiana University Matthew Rablen Brunel University.

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Optimal Audit Policy for a Tax Evasion Network

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  1. Optimal Audit Policy for a Tax Evasion Network Nigar Hashimzade University of Reading Gareth D. Myles University of Exeter Frank Page Indiana University Matthew Rablen Brunel University The views expressed in this presentation are those of the authors and cannot be attributed to HM Revenue & Customs, HM Treasury or HM Government

  2. The Project • Financed by the HMRC/HMT/ESRC Joint Research Programme • Apply ideas from behavioural economics to study how best to encourage compliance • Focus on the effect of taxpayers possessing individual attributes and social connections • Accommodate differences in: • Preferences • Attitudes toward compliance • Opportunities for evasion

  3. Introduction The aim is to obtain insights into audit strategy Which taxpayers should be audited? To provide a flexible framework the paper combines Non-expected utility theory Social customs Occupational choice Social networks

  4. Introduction • The presentation presents a brief review of the "standard model" of evasion • This is used to motivate the application of behavioural economics • Non-expected utility • Social interaction • These are embedded within a social network • Information transmission • Attitude transmission

  5. 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

  6. 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

  7. Additional Factors • The 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

  8. 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

  9. Behavioural Approach 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

  10. Behavioural Approach A social custom is an informal rule on behaviour Additional utility if custom is followed U + S if followed, U if broken Empirical and experimental evidence on evasion is consistent with social customs The importance attached to the social custom is determined by interaction S =S(c), c= proportion following custom

  11. Individuals and Occupations There are n individuals and 3 occupations Individual characteristics {w,r, q1, q2, c; p, c} are randomly drawn at the outset A choice is made between occupation 0, 1, 2 If 1 or 2 is chosen outcome u or s is randomly realised and compliance decision is made Auditing takes place p and c are updated

  12. Occupational Choice The distinction between employment and self-employment is important for evasion Employment is safe (wage is fixed) but tax cannot be evaded (UK is PAYE) Self-employment is risky (outcome random) but provides opportunity to evade Selection into self-employment is dependent on personal characteristics

  13. Occupational Choice Self-employment is modelled as a risky project A project is a pair {ps, pu} with pu < ps An individual is described by a triple {w, r,q} Evasion level is chosen after outcome of project is known So in state i, i = u, s, Ei solves max EUi = pU((1–t) pi – ftEi) + (1–p)U((1–t)pi+tEi)

  14. Occupational Choice The payoff from self-employment is EU = (1–q) EUu (Eu*) + qEUs (Es*) Occupational choice compares payoffs from the alternatives Self-employment is chosen if EU(q, ps, pu) > U(w) The simulation has two forms of self-employment differing in risk

  15. Social Network In employment Define Expected payoff in occupation i Choose maximum of

  16. Social Network The social network governs the interaction between individuals 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

  17. Social Network 1 2 3 4 A network is a symmetric matrix A of 0s and 1s (bi-directional links) The network shown is described by

  18. Social Network • Each period an action is chosen • 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 updated • Subjective probability • Rate of compliance

  19. Beliefs If 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

  20. Social Network 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

  21. Parameter Values The model has been run for CRRA utility n = 1000 t= 0.25, f = 1.5, d = 0.75, z = 3 (x 10-5) pee = 0.1, pe1 = 0.05, pe2 = 0.05, p11 = 0.3, p12 = 0.15, p22 = 0.2 True audit probability a= 0.05

  22. Parameter Values The probability distributions are Wage w ~ U[0, 16] Risk aversion r ~ U[0, 10] Success in occupation I qi ~ U[0, 1] Initial belief pi ~ U[0, 1] Social custom ci ~ U[0, 1]

  23. Properties Relative risk aversion t Risk aversion Risk aversion differs across occupations The self-employed have lower risk aversion They will be more willing to engage in non-compliance

  24. Properties Probability t Subjective belief • 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 audit

  25. Properties Properties • The social custom is sustained • Observe the ranking by occupation • The employed learn attitude from self-employed Weight t Honesty weight

  26. Compliance Rates Occupation 2 are non-compliant They have lowest risk aversion But still place a weight on honesty Compliance can be very low in the risky occupation Proportion compliant t Compliance by occupation

  27. Analysis The model is sufficiently rich to permit a range of questions to be investigated We have considered the number of audits The type of audit strategy The choice between audit types These results are now reported

  28. 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

  29. 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? Compliance rate t

  30. 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? Revenue t

  31. Allocation of Auditing Keep number of audits constant Vary the number of audits across occupations There is an interior optimum where revenue is maximized This is almost identical to the random audit process Revenue Total Declared taxes Fines and recovered taxes No. of audits occupation 1 Allocation of auditing effort

  32. Effectiveness of Audit • Two forms of audit are possible • The light touch audit is cheaper but only uncovers a fraction of undeclared income • The deep audit is more costly but uncovers all income • Analyze the balance between the two • Taxpayers now learn about the probability of a light touch audit • The outcome is not affected by proportion • Too many “corner” solutions

  33. Conclusions Occupational choice selects those who will evade into situations where evasion is possible Social interaction causes the subjective probability to be above the objective probability A social custom raises compliance and can be sustained

  34. Conclusions Random auditing is the most successful audit method (from the set considered) Light touch audits are not effective and lead many to total non-compliance The social network provides a framework to model interesting interactions It can provide unsuspected results

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