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Individual morality and reputation costs as deterrents to tax evasion
European Economic Review 33 (1989) 797-805. North-Holland
INDIVIDUAL MORALITY DETERRENTS
AND REPUTATION TO TAX EVASION*
COSTS
AS
James P.F. GORDON London School of Economics, London WC2A. UK Received May 1987, Anal version received December 1987 Empirical evidence suggestssome taxpayers never evade, evasion increases with the tax rate, and evasion decisions are interdependent. These fmdings are not easily explained by the existing theory which models evasion as an independently-made amoral gamble. This paper uses nonpecuniary costs of evasion to reconcile theory with evidence. Once individuals are assumed to differ by an honesty characteristic, taxpayers dichotomise into groups, the more honest of which responds to a tax change as the evidence suggests. A further extension is to introduce an endogenous reputation cost. This suggestsa positive relationship between the number of evaders and the tax rate.
1. Introduction
In recent years Allingham and Sandmo’s (1972) model of tax evasion has come under close empirical scrutiny, an exercise which has revealed important inconsistencies between theory and evidence. Three of these are considered here: (i) the finding that some people never evade, even when the evasion gamble is better than fair; e.g., Baldry (1986) reports the subjects of his simulation study polarising into honest and dishonest groups, behaviour not predicted by the standard theory, (ii) the finding that evasion increases with the tax rate [Clotfelter (1983), Crane and Nourzad (1986) and Poterba (1987)]; whereas the theoretical prediction with fines on tax evaded (rather than income concealed) and decreasing absolute risk aversion, is that evasion decreases with the tax rate [Yitzhaki (1974) and Christiansen (1980)]; (iii) the finding that individuals are more likely to evade once they are aware of others evading, a phenomenon which does not square with the AllinghamSandmo model where evasion reflects an independently made portfolio decision. This paper attempts to reconcile the existing theory with these three pieces of empirical evidence. It does so by modifying the standard model in a *This is a shortened version of Gordon (1987). I am indebted to Tony Atkinson, Jonathan Baldry, Frank Cowell, Mono Chatterji, Mervyn King, Ailsa Rcell, Amos Witztum and Shlomo Yitrhaki for helpful comments. All errors remain my own. 00142921/89/$3.50
a
1989, Elsevier Science Publishers B.V. (North-Holland)
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Gordon, Individual morality and reputation costs and tax evasion
straight-forward manner. The menu of costs incurred by evaders is expanded to include not only the fines payable upon detection, but also certain nonpecuniary considerations. 1 These can be interpreted in a number of ways. One possibility is that evasion generates psychic costs incurred irrespective of whether the act of evasion is observed (by the authorities or anybody else). For example, a false income declaration may induce anxiety, guilt or a reduction in self-image. This type of (private) ‘stigma’ is considered in section 2, and allows (i) and (ii) above to be explained. An alternative, but not mutually exclusive interpretation of non-pecuniary costs is as damage to reputation suffered upon detection. Section 3 extends the model of section 2 to include such social stigma, which is made endogenous by drawing on Akerlof (1980). This introduces the interdependence necessary to complete the reconciliation exercise. The model of section 3 predicts that a higher tax rate leads to a higher number of steady-state evaders and can therefore explain a positive relationship between the tax rate and tax evasion. Section 4 concludes. 2. The Allingham-Sandmo model with individual morality Assume that the individual utility function has two arguments; consumption, C, and the extent to which behaviour is honest, H. Let H= -E, where E is income concealed from the tax authorities. Preferences are represented by
u{i, I;}.
(1)
Let T be the uniform tax rate, p the probability of being detected, and s>O the surcharge levied on tax evaded, i.e., if evasion is detected, then the taxpayer with a taxable (fixed) income of Y, pays true tax liability, rY, plus srE.2 There are two states of the world, corresponding to whether or not the individual is caught, so consumption is a random variable C= Y(1 -r)+x~E,
where x= 1 with probability 1 --p, and x= --s with probability p. Only a very special form of (1) proves to be analytically tractable; in particular, the case where uCH= uHc = 0 and uHH=O. Under these assumptions (1) becomes ‘This idea was first proposed in this context by Benjamini and Maital (1985). In their model evaders incur a fixed ‘stigma’ cost which can generate corner solutions. They can thus explain the first inconsistency noted, but it is not clear that they can explain the second. 2Lcvying the fine on tax evaded - the system in the US - rather than on income concealed, implies that tax changes have only income effects. This follows Yitzhaki’s (1974) modification of the Allingham-Sandmo model.
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U(C) - vE, where vE is the private psychic cost of evasion (incurred with certainty). Essentially this is the Benjamini and Maital (1985) model with variable, rather than fixed, stigma costs. 3 Assume individuals are identical in all respects save for the honesty characteristic v, which has distribution function F(v) and support [O, VJ. Assuming that individuals are expected utility maximisers, the first order condition for an interior solution is that E[L”{C}xr]-v=O, where EC.1 is the expectations operator. The second order condition is E[U”(C}x2r2] ~0, which holds by assumption. To rule out a corner solution at E =0, it is necessary that kE(1-p-pps)rU’{Y(1-r)}>0,
(4)
where k is ECU’(C) XT] evaluated at E=O. If the evasion gamble is not better than fair, i.e., (1 -p -ps) 5 0, then k IO, and nobody evades. However, if (1 - p -ps) > 0, then k > 0, and those with v < k evade, and those with v 2 k do not. For the latter, honesty is the best policy. The observed phenomenon that some people do not evade even when the expected return is positive can therefore be easily explained.4 Also note that implicit differentiation of (3) with respect to v reveals that 8E/dv 0 if k > v > v*. Proof:
Implicitly differentiate (3) to yield
3There are theoretical arguments for either assumption. The empirical evidence about the effect of stigma on the take-up of welfare benefits supports the assumption of fixed costs [Mofhtt (1983)]. Thus, to justify the variable cost assumption, it is necessary to see evading taxes as being qualitatively different from claiming welfare (perhaps because the latter is not illegal?). 4There is an analogy with investors holding incomplete portfolios because of transactions costs, see King and Leape (1984).
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Gordon, Individual
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G/T--E[U”{C}XT(Y-xE)] - E[ U”{C)x*r*]
and reputation
costs and tax evasion
(0)
.
Consider uA and uB, such that k>u,> uB, and examine how the numerator of ($) varies under these two parameter values. Since dE/& ~0, E{u”} < E{o,}. Now decreasing absolute risk aversion implies U”‘(C) >O, so it follows from (2) that U”{CO{uA})c U”{CO{uB}} and U”{CI{u,,}} > U”(C,{u,)} where Co (C,) is consumption if evasion is undetected (detected). This implies that E[U”{C)XT( Y -xE)] will be smaller for uA than for uB. The numerator of (8) will therefore be larger for uA than for us. Since this holds for any u,, and uB, such that k > uA> uB, it follows that the numerator of (8) increases monotonically with u for all u< k. Next note from (0) that under decreasing absolute risk aversion dE/d$,,O for E-+O (since then E+O). There must therefore be some k>u*>O such that dE/d~l~=~.= 0 and the proposition then follows directly given the monotonicity of the numerator of (@).s The intuition underlying Proposition 1 is that the reduction in wealth caused by the higher tax rate has two competing effects: the conventional desire under decreasing absolute risk aversion to reduce the size of the gamble (tending to decrease evasion) and the response to the lower relative psychic cost of being dishonest (tending to increase it). For those with u < u*, the first effect dominates, and vice versa for those with k> u> u*. In effect, the latter can no longer afford to be as honest. The aggregate change by those originally evading thus depends on F(u). As to the behaviour of those with u 2 k, differentiation of (4) yields
$=(I-p-pps)[U’(
Y(1 --r))--rYYU"{
Y(1 -r)>,,
which is positive given risk aversion. The tendency for aggregate evasion to increase is reinforced by the emergence of new evaders (in particular a least honest subset of the initial non-evaders). Although this increased number of evaders is not sufficient to make the change in aggregate evasion unambiguous, the characteristics of those who respond to a tax increase as the evidence, rather than the theory, suggests, have been established. It is only large evaders who exhibit the standard portfolio response and reduce their holdings of the risky asset. Their more honest peers evade more, the higher 5Note that this does not imply that dE/Sr increases monotonically with u [since the denominator of (8). while always positive, also changes with u] but rather that the sign of ?E/Sr changes only once. There is also a result analogous to Proposition 1 for income changes. See Gordon (1987).
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Gordon, Individual morality and reputarion costs and tax evasion
tax rate making evasion less of an amoral gamble. The behaviour latter group could explain Clotfelter’s (1983) finding.
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of this
3. Taxpayer interdependence Interdependence between taxpayers can be incorporated into the model of the previous section by assuming some relationship between non-pecuniary costs and society’s attitude towards evasion. Since the individual will discern the latter from how other taxpayers behave, evasion decisions become interdependent.6 To illustrate this, assume that evasion gives rise not only to a psychic cost of uE but also to a reputation cost of WE, and that while u varies across individuals, everyone faces the same w. Moreover, the value of w is endogenous, increasing (linearly) with the extent to which the individual feels out of step with society. So w = br, where in the spirit of Akerlof (1980), b is the proportion of the population who are believed to consider evasion to be morally wrong (determined within the model), and r is a positive fixed reputation cost parameter. Non-pecuniary costs thus now include considerations of both private and social stigma, and have become partly endogenous. The individual’s maximand in period t is now E[U{ C,} -(u + b,r)E,]. In any particular time period, b is taken as given so the properties of this model are similar to those of the static version considered in section 2. The major difference is that instead of (4) the necessary condition for an interior optimum is now k-(u+b,r)>O,
(6)
where k [defined by (4)], u and r are assumed constant over time. All those with u-c k- b,r evade; all those with u > k- b,r do not. From (6) the proportion actually evading in period t is e,=F{k-b,r}.
(7)
Note that 1 -e, is what Akerlof would call the proportion of the population who obey the social custom (that evasion is wrong). However, if b,>O, those with k> II> k- b,r, will not evade, but not on account of their own consciences. Rather they are compelled to be honest by the fear of the 6Benjamini and Maital (1985) also contains an early attempt to model taxpayer interdependence [see also Schlicht (1985)]. They show that if stigma declines linearly with the number of people evading, a polar equilibrium with either zero or perfect compliance is most likely in the long run. This dramatic result reflects the ‘knife-edge’ instability of their only interior equilibrium (where evaders and non-evaders coexist). Although their model is intended to be no more than illustrative, this property is not very robust.
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reputation cost should they be detected. If actual believers are defined as those with u> k, then those with k > u > k-b,r correspond to the group in Akerlofs model who obey the social code even though they do not actually believe in it. It is the dynamic properties of the model that are of interest, so it is next necessary to specify the relationship between b, and e,, i.e., between the proportion who are thought to believe and the proportion who actually disobey. The assumption made is that in any time period, the proportion not evading in the previous period is regarded as the best indicator of society’s strength of belief’ bt=l-e,-i.
(8)
Substituting this into (7) yields a first order difference equation e,=g{e,_,}=F{k-(l-e,_&-}.
From this it can be seen that the proportion evading increases with k, the (initial) marginal benefit from evasion, and decreases with r, the reputation cost parameter. The important relationship in (9) is the positive dependence of e, on e,_ , . This implies taxpayer interdependence. The non-linear difference equation (9), possesses a myriad of possible (and plausible) solutions. The various classes of solutions, differentiated by relative magnitudes of the parameters k, V and I, and the shape of F(o), are examined in Gordon (1987). A result that emerges is the following: Proposition 2. A sufficient condition for there to be an interior solution, e*, to (9), i.e., O
(V Proof. Assume that V>r and (7) holds. Define h{e,_,}=g{e,_,}-e,_l from (9). Now h{O}=F(k-r)>O, since k-r>O, and h(l)=F(k)-l
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F(k*)
F(k)
F(k*-r)
F(k-r)
et-1
Fig. 1. Note: Arrows show stability of the system after the parameter change.
equilibrium. Next assume that T> V and (7) holds. Define I(e,} =g-‘{e,}-e,. Now I(O)=g-l(O)>0 and I(l)=g-i(l)1x0, so again there must be a point e* ~(0, 1) such that /{e*} =O, which again will be an equilibrium. The condition (t) is sufficient to ensure that evaders and non-evaders coexist in a steady-state, because it ensures that the benefits from evasion are of intermediate size. If instead k is too small (large) relative to the cost parameters, r and V then there will be a corner solution with perfect (zero) compliance. An interior equilibrium can be stable or unstable. For example, if F(u) is uniform, then differentiation of (9) yields g’{ *} =r/V,< 1 as r$ K so the two cases considered above are stable and unstable respectively. If F(o) is non-uniform multiple equilibria become possible. For further details see Gordon (1987). Baldry’s (1986) finding that some never evade can be interpreted as prima facie evidence of the existence of interior equilibria, and henceforth attention is restricted to such cases. The comparative static change of primary interest is the effect of an increased tax rate. Starting from any interior equilibrium, it can be shown that this implies a larger number evading when the system comes to rest [see Gordon (1987)]. As an illustration, consider fig. 1, which shows a unique stable interior equilibrium. It has been seen that dk/& > 0, so a higher r shifts the g(e) function up to g*{e}. By increasing k, the higher tax AA3,0008,1.
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rate reduces the relative non-pecuniary cost of evasion and it is this which facilitates the initial emergence of new evaders (the movement from A to A” in the diagram). The system is globally stable, so over time convergence to the new equilibrium occurs, with e continuing to increase as the consequent reduction in reputation costs tempts even more individuals to evade (4” to A’). A new equilibrium is established at A’, with an increased proportion of the population evading. However, for the same reason as in section 2, the effect on aggregate evasion remains ambiguous. While the amount of under-reporting by the original evaders is increased by the lower reputation cost at A’, it has been seen from Proposition 1 that the effect of the higher tax rate could go either way. Nevertheless, there are three factors tending to increase aggregate evasion here - larger numbers evading, increased evasion by all original evaders because of the lower reputation cost, and increased evasion by those with k>o>u* because of the higher tax rate, and only one working in the opposite direction - so higher aggregate evasion at A’ seems likely, if not conclusive. In any event, since a long-run increase in the numbers evading is certain, a model which recognises taxpayer interdependence is better able to explain a positive relationship between tax rates and evasion than one which does not. 4. Conclusion This paper uses non-pecuniary costs of evasion to explain two empirical findings at variance with the existing theory. In section 2, additively separable preferences, constant marginal disutility from behaving dishonestly and individuals differentiated only by an honesty characteristic, yield a model in which taxpayers dichotomise into two groups. The first consists of the more dishonest, typically all evaders, who display conventional comparative static behaviour. By contrast, the ‘honest’ group contains non-evaders and small evaders, and under decreasing absolute risk aversion, the latter evade more if the tax rate rises - the exact opposite of the standard prediction. This is a consequence of their honesty which prevents them from treating tax evasion as a simple portfolio decision. The model can therefore explain why some taxpayers refuse a favourable evasion gamble, and how a higher tax rate can increase evasion even under decreasing absolute risk aversion. Both are phenomena suggested by the evidence, but not by existing theory. In section 3 account is taken of a third empirical finding that taxpayer interdependence affects evasion behaviour. Following Akerlof (1980) part of the disutility from behaving dishonestly is endogenised as a reputation cost, and this requires the static model of section 2 to be recast in a dynamic setting. Despite the diversity of possible solutions to the model, it is found that taxpayer interdependence makes a positive relationship
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morality
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costs and tax evasion
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between evasion and the tax rate even more likely in the long run. This is because a higher tax rate increases the steady state number of evaders. References Akerlof, GA., 1980, A theory of social custom of which unemployment may be one consequence, Quarterly Journal of Economics 94, 749-795. Allingham, M.G. and A. Sandmo, 1972, Income tax evasion: A theoretical analysis, Journal of Public Economics I, 323-338. Baldry, J.C., 1986, Tax evasion is not a gamble: A report on two experiments, Economic Letters 22. 333-335. Benjamini. Y. and S. Maital. 1985, Optimal tax evasion and optimal tax evasion policy, in: W. Gartner and A. Wenig, eds., The economics of the shadow economy (Springer Verlag, Berlin) 245-264. Christiansen. V., 1980, Two comments on tax evasion, Journal of Public Economics 13, 389-393. Clotfelter, C.T., 1983, Tax evasion and tax rates: An analysis of individual returns, Review of Economics and Statistics 65, 363-373. Crane. S.E. and J. Nourzad. 1986. Inflation and tax evasion: An empirical analysis, Review of Economics and Statistics.68, no. 2, 217-223. Gordon, J.P.F., 1987, Modelling tax evasion where honesty may be the best policy, ESRC programme on taxation, incentives and the distribution of income, D.P. no. 102. King, M.A. and J.I. Leape, 1984, Wealth and portfolio composition: Theory and evidence, ESRC programme on taxation, incentives and the distribution of income, D.P. no. 68. Mollitt, R.L.. 1983, An economic model of welfare stigma, American Economic Review 73, 1023-1035. Poterba. J.M., 1987, Tax evasion and capital gains taxation, American Economic Review 77, 234-239. Schlicht, E., 1985, The shadow economy and morals: A note, in: W. Gartner and A. Wenig. eds., The economics of the shadow economy (Springer Verlag, Berlin) 265-271. Yitzhaki, S., 1974, A note on income tax evasion: A theoretical analysis, Journal of Public Economics 3.201-202.
INDIVIDUAL MORALITY DETERRENTS
AND REPUTATION TO TAX EVASION*
COSTS
AS
James P.F. GORDON London School of Economics, London WC2A. UK Received May 1987, Anal version received December 1987 Empirical evidence suggestssome taxpayers never evade, evasion increases with the tax rate, and evasion decisions are interdependent. These fmdings are not easily explained by the existing theory which models evasion as an independently-made amoral gamble. This paper uses nonpecuniary costs of evasion to reconcile theory with evidence. Once individuals are assumed to differ by an honesty characteristic, taxpayers dichotomise into groups, the more honest of which responds to a tax change as the evidence suggests. A further extension is to introduce an endogenous reputation cost. This suggestsa positive relationship between the number of evaders and the tax rate.
1. Introduction
In recent years Allingham and Sandmo’s (1972) model of tax evasion has come under close empirical scrutiny, an exercise which has revealed important inconsistencies between theory and evidence. Three of these are considered here: (i) the finding that some people never evade, even when the evasion gamble is better than fair; e.g., Baldry (1986) reports the subjects of his simulation study polarising into honest and dishonest groups, behaviour not predicted by the standard theory, (ii) the finding that evasion increases with the tax rate [Clotfelter (1983), Crane and Nourzad (1986) and Poterba (1987)]; whereas the theoretical prediction with fines on tax evaded (rather than income concealed) and decreasing absolute risk aversion, is that evasion decreases with the tax rate [Yitzhaki (1974) and Christiansen (1980)]; (iii) the finding that individuals are more likely to evade once they are aware of others evading, a phenomenon which does not square with the AllinghamSandmo model where evasion reflects an independently made portfolio decision. This paper attempts to reconcile the existing theory with these three pieces of empirical evidence. It does so by modifying the standard model in a *This is a shortened version of Gordon (1987). I am indebted to Tony Atkinson, Jonathan Baldry, Frank Cowell, Mono Chatterji, Mervyn King, Ailsa Rcell, Amos Witztum and Shlomo Yitrhaki for helpful comments. All errors remain my own. 00142921/89/$3.50
a
1989, Elsevier Science Publishers B.V. (North-Holland)
798
J.P.F.
Gordon, Individual morality and reputation costs and tax evasion
straight-forward manner. The menu of costs incurred by evaders is expanded to include not only the fines payable upon detection, but also certain nonpecuniary considerations. 1 These can be interpreted in a number of ways. One possibility is that evasion generates psychic costs incurred irrespective of whether the act of evasion is observed (by the authorities or anybody else). For example, a false income declaration may induce anxiety, guilt or a reduction in self-image. This type of (private) ‘stigma’ is considered in section 2, and allows (i) and (ii) above to be explained. An alternative, but not mutually exclusive interpretation of non-pecuniary costs is as damage to reputation suffered upon detection. Section 3 extends the model of section 2 to include such social stigma, which is made endogenous by drawing on Akerlof (1980). This introduces the interdependence necessary to complete the reconciliation exercise. The model of section 3 predicts that a higher tax rate leads to a higher number of steady-state evaders and can therefore explain a positive relationship between the tax rate and tax evasion. Section 4 concludes. 2. The Allingham-Sandmo model with individual morality Assume that the individual utility function has two arguments; consumption, C, and the extent to which behaviour is honest, H. Let H= -E, where E is income concealed from the tax authorities. Preferences are represented by
u{i, I;}.
(1)
Let T be the uniform tax rate, p the probability of being detected, and s>O the surcharge levied on tax evaded, i.e., if evasion is detected, then the taxpayer with a taxable (fixed) income of Y, pays true tax liability, rY, plus srE.2 There are two states of the world, corresponding to whether or not the individual is caught, so consumption is a random variable C= Y(1 -r)+x~E,
where x= 1 with probability 1 --p, and x= --s with probability p. Only a very special form of (1) proves to be analytically tractable; in particular, the case where uCH= uHc = 0 and uHH=O. Under these assumptions (1) becomes ‘This idea was first proposed in this context by Benjamini and Maital (1985). In their model evaders incur a fixed ‘stigma’ cost which can generate corner solutions. They can thus explain the first inconsistency noted, but it is not clear that they can explain the second. 2Lcvying the fine on tax evaded - the system in the US - rather than on income concealed, implies that tax changes have only income effects. This follows Yitzhaki’s (1974) modification of the Allingham-Sandmo model.
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U(C) - vE, where vE is the private psychic cost of evasion (incurred with certainty). Essentially this is the Benjamini and Maital (1985) model with variable, rather than fixed, stigma costs. 3 Assume individuals are identical in all respects save for the honesty characteristic v, which has distribution function F(v) and support [O, VJ. Assuming that individuals are expected utility maximisers, the first order condition for an interior solution is that E[L”{C}xr]-v=O, where EC.1 is the expectations operator. The second order condition is E[U”(C}x2r2] ~0, which holds by assumption. To rule out a corner solution at E =0, it is necessary that kE(1-p-pps)rU’{Y(1-r)}>0,
(4)
where k is ECU’(C) XT] evaluated at E=O. If the evasion gamble is not better than fair, i.e., (1 -p -ps) 5 0, then k IO, and nobody evades. However, if (1 - p -ps) > 0, then k > 0, and those with v < k evade, and those with v 2 k do not. For the latter, honesty is the best policy. The observed phenomenon that some people do not evade even when the expected return is positive can therefore be easily explained.4 Also note that implicit differentiation of (3) with respect to v reveals that 8E/dv
Implicitly differentiate (3) to yield
3There are theoretical arguments for either assumption. The empirical evidence about the effect of stigma on the take-up of welfare benefits supports the assumption of fixed costs [Mofhtt (1983)]. Thus, to justify the variable cost assumption, it is necessary to see evading taxes as being qualitatively different from claiming welfare (perhaps because the latter is not illegal?). 4There is an analogy with investors holding incomplete portfolios because of transactions costs, see King and Leape (1984).
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G/T--E[U”{C}XT(Y-xE)] - E[ U”{C)x*r*]
and reputation
costs and tax evasion
(0)
.
Consider uA and uB, such that k>u,> uB, and examine how the numerator of ($) varies under these two parameter values. Since dE/& ~0, E{u”} < E{o,}. Now decreasing absolute risk aversion implies U”‘(C) >O, so it follows from (2) that U”{CO{uA})c U”{CO{uB}} and U”{CI{u,,}} > U”(C,{u,)} where Co (C,) is consumption if evasion is undetected (detected). This implies that E[U”{C)XT( Y -xE)] will be smaller for uA than for uB. The numerator of (8) will therefore be larger for uA than for us. Since this holds for any u,, and uB, such that k > uA> uB, it follows that the numerator of (8) increases monotonically with u for all u< k. Next note from (0) that under decreasing absolute risk aversion dE/d$,,
$=(I-p-pps)[U’(
Y(1 --r))--rYYU"{
Y(1 -r)>,,
which is positive given risk aversion. The tendency for aggregate evasion to increase is reinforced by the emergence of new evaders (in particular a least honest subset of the initial non-evaders). Although this increased number of evaders is not sufficient to make the change in aggregate evasion unambiguous, the characteristics of those who respond to a tax increase as the evidence, rather than the theory, suggests, have been established. It is only large evaders who exhibit the standard portfolio response and reduce their holdings of the risky asset. Their more honest peers evade more, the higher 5Note that this does not imply that dE/Sr increases monotonically with u [since the denominator of (8). while always positive, also changes with u] but rather that the sign of ?E/Sr changes only once. There is also a result analogous to Proposition 1 for income changes. See Gordon (1987).
J.P.F.
Gordon, Individual morality and reputarion costs and tax evasion
tax rate making evasion less of an amoral gamble. The behaviour latter group could explain Clotfelter’s (1983) finding.
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of this
3. Taxpayer interdependence Interdependence between taxpayers can be incorporated into the model of the previous section by assuming some relationship between non-pecuniary costs and society’s attitude towards evasion. Since the individual will discern the latter from how other taxpayers behave, evasion decisions become interdependent.6 To illustrate this, assume that evasion gives rise not only to a psychic cost of uE but also to a reputation cost of WE, and that while u varies across individuals, everyone faces the same w. Moreover, the value of w is endogenous, increasing (linearly) with the extent to which the individual feels out of step with society. So w = br, where in the spirit of Akerlof (1980), b is the proportion of the population who are believed to consider evasion to be morally wrong (determined within the model), and r is a positive fixed reputation cost parameter. Non-pecuniary costs thus now include considerations of both private and social stigma, and have become partly endogenous. The individual’s maximand in period t is now E[U{ C,} -(u + b,r)E,]. In any particular time period, b is taken as given so the properties of this model are similar to those of the static version considered in section 2. The major difference is that instead of (4) the necessary condition for an interior optimum is now k-(u+b,r)>O,
(6)
where k [defined by (4)], u and r are assumed constant over time. All those with u-c k- b,r evade; all those with u > k- b,r do not. From (6) the proportion actually evading in period t is e,=F{k-b,r}.
(7)
Note that 1 -e, is what Akerlof would call the proportion of the population who obey the social custom (that evasion is wrong). However, if b,>O, those with k> II> k- b,r, will not evade, but not on account of their own consciences. Rather they are compelled to be honest by the fear of the 6Benjamini and Maital (1985) also contains an early attempt to model taxpayer interdependence [see also Schlicht (1985)]. They show that if stigma declines linearly with the number of people evading, a polar equilibrium with either zero or perfect compliance is most likely in the long run. This dramatic result reflects the ‘knife-edge’ instability of their only interior equilibrium (where evaders and non-evaders coexist). Although their model is intended to be no more than illustrative, this property is not very robust.
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costs and tax evasion
reputation cost should they be detected. If actual believers are defined as those with u> k, then those with k > u > k-b,r correspond to the group in Akerlofs model who obey the social code even though they do not actually believe in it. It is the dynamic properties of the model that are of interest, so it is next necessary to specify the relationship between b, and e,, i.e., between the proportion who are thought to believe and the proportion who actually disobey. The assumption made is that in any time period, the proportion not evading in the previous period is regarded as the best indicator of society’s strength of belief’ bt=l-e,-i.
(8)
Substituting this into (7) yields a first order difference equation e,=g{e,_,}=F{k-(l-e,_&-}.
From this it can be seen that the proportion evading increases with k, the (initial) marginal benefit from evasion, and decreases with r, the reputation cost parameter. The important relationship in (9) is the positive dependence of e, on e,_ , . This implies taxpayer interdependence. The non-linear difference equation (9), possesses a myriad of possible (and plausible) solutions. The various classes of solutions, differentiated by relative magnitudes of the parameters k, V and I, and the shape of F(o), are examined in Gordon (1987). A result that emerges is the following: Proposition 2. A sufficient condition for there to be an interior solution, e*, to (9), i.e., O
(V Proof. Assume that V>r and (7) holds. Define h{e,_,}=g{e,_,}-e,_l from (9). Now h{O}=F(k-r)>O, since k-r>O, and h(l)=F(k)-l
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F(k*)
F(k)
F(k*-r)
F(k-r)
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Fig. 1. Note: Arrows show stability of the system after the parameter change.
equilibrium. Next assume that T> V and (7) holds. Define I(e,} =g-‘{e,}-e,. Now I(O)=g-l(O)>0 and I(l)=g-i(l)1x0, so again there must be a point e* ~(0, 1) such that /{e*} =O, which again will be an equilibrium. The condition (t) is sufficient to ensure that evaders and non-evaders coexist in a steady-state, because it ensures that the benefits from evasion are of intermediate size. If instead k is too small (large) relative to the cost parameters, r and V then there will be a corner solution with perfect (zero) compliance. An interior equilibrium can be stable or unstable. For example, if F(u) is uniform, then differentiation of (9) yields g’{ *} =r/V,< 1 as r$ K so the two cases considered above are stable and unstable respectively. If F(o) is non-uniform multiple equilibria become possible. For further details see Gordon (1987). Baldry’s (1986) finding that some never evade can be interpreted as prima facie evidence of the existence of interior equilibria, and henceforth attention is restricted to such cases. The comparative static change of primary interest is the effect of an increased tax rate. Starting from any interior equilibrium, it can be shown that this implies a larger number evading when the system comes to rest [see Gordon (1987)]. As an illustration, consider fig. 1, which shows a unique stable interior equilibrium. It has been seen that dk/& > 0, so a higher r shifts the g(e) function up to g*{e}. By increasing k, the higher tax AA3,0008,1.
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rate reduces the relative non-pecuniary cost of evasion and it is this which facilitates the initial emergence of new evaders (the movement from A to A” in the diagram). The system is globally stable, so over time convergence to the new equilibrium occurs, with e continuing to increase as the consequent reduction in reputation costs tempts even more individuals to evade (4” to A’). A new equilibrium is established at A’, with an increased proportion of the population evading. However, for the same reason as in section 2, the effect on aggregate evasion remains ambiguous. While the amount of under-reporting by the original evaders is increased by the lower reputation cost at A’, it has been seen from Proposition 1 that the effect of the higher tax rate could go either way. Nevertheless, there are three factors tending to increase aggregate evasion here - larger numbers evading, increased evasion by all original evaders because of the lower reputation cost, and increased evasion by those with k>o>u* because of the higher tax rate, and only one working in the opposite direction - so higher aggregate evasion at A’ seems likely, if not conclusive. In any event, since a long-run increase in the numbers evading is certain, a model which recognises taxpayer interdependence is better able to explain a positive relationship between tax rates and evasion than one which does not. 4. Conclusion This paper uses non-pecuniary costs of evasion to explain two empirical findings at variance with the existing theory. In section 2, additively separable preferences, constant marginal disutility from behaving dishonestly and individuals differentiated only by an honesty characteristic, yield a model in which taxpayers dichotomise into two groups. The first consists of the more dishonest, typically all evaders, who display conventional comparative static behaviour. By contrast, the ‘honest’ group contains non-evaders and small evaders, and under decreasing absolute risk aversion, the latter evade more if the tax rate rises - the exact opposite of the standard prediction. This is a consequence of their honesty which prevents them from treating tax evasion as a simple portfolio decision. The model can therefore explain why some taxpayers refuse a favourable evasion gamble, and how a higher tax rate can increase evasion even under decreasing absolute risk aversion. Both are phenomena suggested by the evidence, but not by existing theory. In section 3 account is taken of a third empirical finding that taxpayer interdependence affects evasion behaviour. Following Akerlof (1980) part of the disutility from behaving dishonestly is endogenised as a reputation cost, and this requires the static model of section 2 to be recast in a dynamic setting. Despite the diversity of possible solutions to the model, it is found that taxpayer interdependence makes a positive relationship
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between evasion and the tax rate even more likely in the long run. This is because a higher tax rate increases the steady state number of evaders. References Akerlof, GA., 1980, A theory of social custom of which unemployment may be one consequence, Quarterly Journal of Economics 94, 749-795. Allingham, M.G. and A. Sandmo, 1972, Income tax evasion: A theoretical analysis, Journal of Public Economics I, 323-338. Baldry, J.C., 1986, Tax evasion is not a gamble: A report on two experiments, Economic Letters 22. 333-335. Benjamini. Y. and S. Maital. 1985, Optimal tax evasion and optimal tax evasion policy, in: W. Gartner and A. Wenig, eds., The economics of the shadow economy (Springer Verlag, Berlin) 245-264. Christiansen. V., 1980, Two comments on tax evasion, Journal of Public Economics 13, 389-393. Clotfelter, C.T., 1983, Tax evasion and tax rates: An analysis of individual returns, Review of Economics and Statistics 65, 363-373. Crane. S.E. and J. Nourzad. 1986. Inflation and tax evasion: An empirical analysis, Review of Economics and Statistics.68, no. 2, 217-223. Gordon, J.P.F., 1987, Modelling tax evasion where honesty may be the best policy, ESRC programme on taxation, incentives and the distribution of income, D.P. no. 102. King, M.A. and J.I. Leape, 1984, Wealth and portfolio composition: Theory and evidence, ESRC programme on taxation, incentives and the distribution of income, D.P. no. 68. Mollitt, R.L.. 1983, An economic model of welfare stigma, American Economic Review 73, 1023-1035. Poterba. J.M., 1987, Tax evasion and capital gains taxation, American Economic Review 77, 234-239. Schlicht, E., 1985, The shadow economy and morals: A note, in: W. Gartner and A. Wenig. eds., The economics of the shadow economy (Springer Verlag, Berlin) 265-271. Yitzhaki, S., 1974, A note on income tax evasion: A theoretical analysis, Journal of Public Economics 3.201-202.