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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 V p1 v y p 2 v x (ii) Assumes payoff is convex in losses and concave in gains v ' z 0 , v ' ' z 0 if z 0 , v ' ' z 0 if z 0 (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 Y Y c n Y D D tX Y D D tX Ft Y X Use Y – D as the reference point D – tX is the gain if evasion is successful D tX Ft Y X is the loss if evasion is unsuccessful Prospect Theory Observe that D – tX is achieved for sure So write objective as V Y v D tX pv Ft Y X Recall that prospect theory has v convex for losses and concave for gains Yaniv analyzes the comparative statics of the necessary condition tv ' D tX pFtv ' Ft Y X 0 Prospect Theory Consider the power function z , z0 vz z , z 0 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 0.6 0.3 0.4 0.2 0.2 0.1 0 0 -0.1 -0.2 0 0.2 0.4 0.6 X/W 0.8 0 . 88 , 2 . 25 1 0 0.2 0.4 0.6 X/W 0.8 0 .4 , 4 1 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 0.4 0.5 0 0 -0.4 -0.5 -0.8 -1 -1.2 -1.5 -1.6 0 0.2 0.4 0.6 X/W 0.8 1 -2 0 0.2 0.4 0.6 X/W 0.8 β = 0.5, γ = 4 p = 0.25, F = 4 p = 0.25, F = 20 1 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 V KT w1 1 p v t Y X X For this objective it can be shown dX dt w 2 p v Ft Y Y X 0 t 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 a p0 0.01 0.02 0.656 0.520 p(Y/2) p(Y) 0.0656 0.006 0.0736 0.010 0.03 0.458 0.0793 0.013 Probability of Audit = 0.88, γ, = 2.25, α = 2/3 and p₀ = 0.01 Positive Results 0 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 -0.2 -0.4 -0.6 -0.8 -1 0 0.2 0.4 0.6 X/W 0.8 Solid: t = 0.2 Dashed: t = 0.3 1 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 selfemployment 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 0.3 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 0.25 0.2 0.15 0.1 0.05 0 0 0.1 0.2 0.3 0.4 0.5 t Aggregate evasion E 2.5 2 1.5 1 0.5 0 0 0.2 0.4 0.6 With borrowing 0.8 t 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 (bidirectional links) The network shown is described by 0 1 A 0 0 1 0 0 1 1 0 0 1 0 0 1 0 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 p 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 0.61 0.6 0.59 0.58 0.57 0.56 0.55 0.54 0.53 0.52 0.51 0 10 20 30 40 50 60 70 80 90 Mean audit probability (belief) 100 t Results r r 2.15 3.4 3.35 2.1 2.05 3.3 2 3.25 1.95 3.2 1.9 3.15 1.85 3.1 1.8 3.05 1.75 0 10 20 30 40 50 60 70 80 90 100 3 0 10 20 30 40 50 60 70 80 t Self-employed Mean risk aversion 90 100 t 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 0.46 0.44 0.42 0.4 0.38 0.36 0.34 0 10 20 30 40 50 60 70 80 90 100 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 4200 4000 3800 3600 3400 3200 3000 2800 0 10 20 30 40 50 60 70 80 90 100 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?