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Behavioural and Social Explanations of Tax Evasion. Nigar Hashimzade University of Reading Gareth D. Myles University of Exeter Frank Page Indiana University Matthew Rablen Brunel University. Introduction.
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Behavioural and Social Explanations of Tax Evasion Nigar Hashimzade University of Reading Gareth D. Myles University of Exeter Frank Page Indiana University Matthew Rablen Brunel University
Introduction • An understanding of the individual tax compliance decision is important for revenue services • Their aim is to design policy instruments to reduce the tax gap • Tax evasion is an area where orthodox analysis has been challenged by behavioural economics • But what elements of behavioural economics are useful?
Introduction • The presentation presents a brief review of the "standard model" of the compliance decision • Two aspects of behavioural economics are then considered • First, the application of non-expected utility theory • Second, the role of social interaction • Networks and information exchange appear promising
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
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
Standard Model • In practice F is between 0.5 and 1 so 1/(1 + F) ≥ 1/2 • Information on p hard to obtain • In the US the proportion of individual tax returns audited was 1.7 per cent in 1997 • With these numbers p < 1/(1+F) so all US taxpayers should evade • The Taxpayer Compliance Measurement Program revealed that 40 percent of US taxpayers underpaid their taxes
Standard Model • The optimization is max{E} E[U(E)] = [1 – p]U([1 – t]Y + tE) + pU([1 – t]Y – FtE ) • So it follows that E = [1/t]f( . ) • The result that E falls as t increases is to "intuition" and has mixed empirical support • Problem of separating aggregate and individual effects • Weakness of experimental evidence • The failure of these predictions has lead to a search for alternative models
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
Non-Expected Utility • 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
Non-Expected Utility • Some of the alternatives that have been applied to the compliance decision are: • Rank Dependent Expected Utility imposes structure on the translation of probabilities • Prospect Theory translates probabilities, changes payoff functions, and uses a reference point • Non-Additive Probabilities do not require the normal linearity for aggregation for probabilities • Ambiguity permits uncertainty over the probability of outcomes
Prospect Theory • Prospect theory does three things • (i) Translates the probabilities • (ii) Assumes payoff is convex in losses and concave in gains • (iii) Payoffs are measured relative to a reference point, R
Prospect Theory • As an example consider Yaniv (1999) • Studies the consequence of paying a tax advance • This will not affect the evasion decision in an expected utility framework • It can affect the evasion decision under prospect theory through the determination of the reference point
Prospect Theory • With a tax advance of D • Use Y – D as the reference point • D – tX is the gain if evasion is successful • is the loss if evasion is unsuccessful
Prospect Theory • Observe that D – tX is achieved for sure • So write objective as • Recall that prospect theory has vconvex for losses and concave for gains • Yaniv analyzes the comparative statics of the necessary condition
Prospect Theory • Consider the power function • First assume that D > tY • The next slides illustrates VY for the parameter values Y = 1, t = 0.2, p = 0.1, F = 2, D = 0.3
Prospect Theory • For the power function we can prove: "If there is an interior solution to the first-order condition it must be a minimum" • The same comments (and result) apply to other functional forms • The assumptions of prospect theory combine to create analytical problems
Prospect Theory Two figures for D < tY β = 0.5, γ = 4 p = 0.25, F = 4 p = 0.25, F = 20
Prospect Theory • al-Nowaihi and Dhami (2007) argue that • (i) The reference point should be R = (1 – t)Y • (ii) Standard prospect theory should be used • For this objective it can be shown • A different reference point might change the result
Positive Results • One way to make progress is to assume the probability of detection depends on declared income • Within the prospect theory framework VPT = w⁺(1–p(X))v(t(Y – X)) + w⁻(p(X))v(–Ft(Y – X)) • An appropriate form of p(X) can make the objective strictly concave • Consider the power function of v( ) and p(X) = αp₀X/Y
Positive Results Probability of Audit • = 0.88, γ, = 2.25, α = 2/3 • andp₀ = 0.01
Positive Results • Now combine the Yaniv model with linear probability pL(X) = α[1 – (1-p₀)(X/Y)] • Advance payment below the true tax liability (D < tY) • t = 0.2, X/Y = 0.74, p = 0.236 • t = 0.3, X/Y = 0.50, p= 0.45 Solid: t = 0.2 Dashed: t = 0.3
Summary • Adopting non-expected utility can solve one problem • The transformation of probabilities can raise the rate of compliance • 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]f( . ) • Is a variable probability non-expected utility?
Evidence • Empirical 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
Occupational Choice • Assume that a choice is made between employment and self-employment • Employment is safe (wage is fixed) but tax cannot be evaded (UK is PAYE) • Self-employment is risky (outcome random) but permits provides opportunity to evade • Selection into self-employment is dependent on personal characteristics
Occupational Choice • A project is a pair {vb, vg} with vb < vg • 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 = b, g, Ei solves max EUi = pU((1–t)vi – FtEi) + (1–p)U((1–t) vi+tEi) • The payoff from self-employment is EUs = (1–q) EUb (Eb*) + qEUg (Eg*)
Occupational Choice • Occupational choice compares payoffs from the alternatives • Self-employment is chosen if EUs(q, vb, vg) > Ue(w) • What is the outcome in this setting? • (i) Assume CRRA utility U = Y(1–r)/(1 – r) • (ii) Assume a uniform distribution for (r, q, w)
Occupational Choice • Employment above the locus • Self-employment below the locus • The less risk-averse choose self-employment • But these people will also evade more Employed Self-employed Separation of population p = 0.5, t = 0.25, F = 0.75, vb = 0.5, vg = 2, q = 0.5
Occupational Choice E • The aggregate level of evasion can be increasing in the tax rate • This is the consequence of intensive/extensive margins • The result extends to borrowing to invest t Aggregate evasion E t With borrowing
Social Interaction • The next step is to embed occupational choice within a network model • 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
Social Interaction • A network is a symmetric matrix A of 0s and 1s (bi-directional links) • The network shown is described by 1 2 3 4
Social Interaction • Each period an action is chosen • The network is revised as a consequence of chosen actions • A random selection of meetings occur (a matrix C of 0s, 1s) • Set of permissible meetings is determined by the network (M = A.*C) • At a meeting information is exchanged • Beliefs are updated
Tax Evasion Network • There are n individuals • Individual characteristics {r, w, p, q, vb, vg} are randomly drawn at the outset • A choice is made between e and s • If s is chosen outcome b or g is randomly realised • Given the outcome evasion decision is made • Those in s are then randomly audited
Tax Evasion Network • If audited pi goes to 1 other pi decays pi=d pi, d ≤1 • Type s only meet type s • Links in network evolve as a consequence of choice • Meetings occur randomly between linked individuals • Information on p is exchanged pi = m pi + (1 – m) pj
Results • The model has been run for CRRA utility • n = 1000, t = 100 • r uniform on [0, 10], • True audit probability a= 0.05 • d= 0.95, m= 0.75 • t= 0.25, F = 1.5 p t Mean audit probability (belief)
Results r r t t Self-employed Mean risk aversion Employed Mean risk aversion
Results • The outcome is little changed if decay is increased • Figure uses d= 0.25 • The average belief about audit probability remains high p t
Results • The level of evasion falls over time • The continued auditing is effective • This is the inverse of the probability belief • Rapid initial falls E t
Conclusions (1) • Non-expected utility delivers nothing that is not given by adopting subjective probabilities in the EU model • It requires variable probability to reverse the tax result • Occupational choice selects those who will evade into situations where evasion is possible • Social interaction can lead subjective probability to differ from objective probability
Conclusions (2) • The results established by simulation • Many alternative structures are possible • What general value can be assigned? • Is it possible to “discover” anything using this analysis?