JOURNAL OF

N ELSEVIER Journal of Economic Psychology 16 (1995) 63-72

Tax evasion, consumption of public goods and fairness

Josef Falkinger * .1

Institute of Economics, University of Linz, Altenberger Strafle 69, A-4040 Linz-Auhof, Austria

Received 17 March 1993; accepted 31 October 1994

Abstract

This study shows that in general the impact of equity on tax evasion depends on how the taxpayer's risk aversion is affected by perceived equity. Then possible reasons are discussed why an increase in perceived equity may increase a person's risk aversion and thus lead to a decrease of evasion. An economic as well as a psychological argument are presented which can explain a positive relationship between risk aversion and equity, and thus, between evasion and inequity. The economic argument considers cases where the valuation of public output increases with income. The psychological argument is based on the hypothesis that people find evasion more blameworthy in a system which is considered to be just than in an unfair system. With such a norm an increase in equity increases the bad reputat ion or bad conscience of evaders and leads to a reduct ion of evasion.

1 . I n t r o d u c t i o n

Economic psychology and experimental economics emphasize that the perception of the fairness of the economic system plays an important role in tax-evasion behaviour. Cowell (1992) showed that the standard economic model of tax evasion does not perform very well in explaining theoretically the impact of psychological factors and social phenomena on tax evasion.

* Tel.: +43 732 2468-246; Fax: +43 732 2468-9821. 1 Some of the work for this paper was completed while the author was at the Karl-Franzens-Uni-

versit~it Graz.

0167-4870/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0167-4870(94)00038-7

64 J.. Falkinger /Journal of Economic Psychology 16 (1995) 63-72

In fact it leads to quite counterintuitive conclusions, for instance that tax evasion increases with the perceived share in publicly supplied goods or equity. To solve this puzzle the social relationships and psychological mechanisms connecting evasion behaviour with perceived fairness and equity of the political and economic system must be considered more carefully. Cowell shows that the economic analysis produces results that are in line with psychological literature and experimental evidence, if social consensus and forms of personalized inequity are properly incorporated in the economic model. If tax evasion has a direct impact on perceived equity of the system and if inequity is a bad thing, then the taxpayer will reduce evasion with perceived equity.

The purpose of this paper is to point out two further channels through which the perceived share in public consumption or perceived fairness of the political and social system affect evasion behaviour. The crucial point of both the models considered is that the risk aversion of taxpayers increases with perceived equity. In the first model, dealing with the impact of public goods consumption on tax evasion, the reason for changing risk attitudes is an economic one. If publicly supplied goods are used to produce, in combination with private consumption, a certain utility-gener- ating characteristic, then the marginal utility of income and thus the risk aversion of a taxpayer is affected by public consumption. The second model considers perceived equity and argues: If it is a social norm that evading taxes is particularly mean in a fair society, the taxpayer's inclination to bear the risk of tax evasion will decrease with equity.

Section 2 describes the basic framework and derives a general rule for determining how variations in perceived equity can affect evasion be- haviour in the standard model of tax evasion. Section 3 applies this general rule to the analysis of the relationship between tax evasion and consump- tion of publicly provided goods. Section 4 analyzes the implications of a social or moral norm that relates the gravity of the tax evasion crime to the fairness of the system in which the taxpayers lives. The results are summa- rized in Section 5.

2. The impact of equity on risk aversion and tax evasion

The standard economic model of tax evasion put forward by Allingham and Sandmo (1972) assumes that taxpayers are expected utility maximizers. In the following, I am using this model in the form presented by Cowell

J. Falkinger / Journal of Economic Psychology 16 (1995) 63-72 65

(1992) (see also Cowell, 1990). The taxpayer's preferences are represented by a concave utility function

U ( c , q ) , (1)

that is increasing in disposable income (private consumption) c and increas- 2 ing in equity measured by an index q.

Disposable income depends, on the one hand, on a person's gross income y, and the amount of concealed income e, and on the other hand, on the tax rate t and the tax enforcement system. The tax enforcement system is characterized by the probability of detection and conviction p and the surcharge s on the underpaid tax which has to be paid if a taxpayer is caught. True net income of an honest taxpayer would be c o := y - ty. If e units of income are concealed and the evader is not caught, the tax payment is reduced by the amount te. However, if the evader is detected and convicted, the full tax and a penalty ste has to be paid. Thus, the disposable income that the evader can spend on private consumption is:

c 1 = c o + te with probability 1 - p , (2)

c 2 = c o - ste with probability p. (3)

The second argument in utility function (1) is perceived equity q. It may be related to the taxpayer's perceived share in publicly provided goods or to any other indicator for the fairness and justice of the economic order. In a large economy it is plausible to assume what Cowell called self-perceived insignificance. This implies that each taxpayer assumes that her or his evasion behaviour has no impact on equity q or the factors determining q. 3 Making this assumption and using Eqs. (2) and (3), we get for a taxpayer's expected utility the expression

E U = (1 - p ) U ( c a , q ) + p U ( c 2 , q ), (4)

where E denotes the expectation operator. Differentiating (4) (after having substituted (2) and (3)) with respect to e, we obtain the first-order-condi- tion:

F ( e , q ) = (1 - P ) U c ( C o + te, q ) - p s U ~ ( c o - s t e , q ) = 0, (5)

which implicitly defines the optimal amount of evasion e * as a function of

2 Alternatively we could say that utility is decreasing with inequity measured by an index i which is the negative value of q or, more generally, inversely related to the equity index q.

3 See Falkinger (1988) for an analysis of tax evasion and equity without this assumption.

66 J. Falkinger /Journal o f Economic Psychology 16 (1995) 63-72

equity q. 4 (Partial derivatives of U are denoted by subscripts. That is, U C is a shorthand for a U / a c and so forth.) The second-order condition for a maximum requires: aF/ae < O. 5

According to the implicit function theorem, the reaction of evasion e* to changes in q can be d e t e r m i n e d by calculating ae*/aq = - (aF /aq) / (aF /ae ) . Since aF/ae < 0, according to the second-order condi- tion, we obtain:

Oe* > aF > 0 i f - - 0 . (6 )

aq < aq <

So in order to de termine the impact of equity on evasion, we must differentiate (5) with respect to q. This yields aF/aq = (1 -p )Uco(c 1, q) - psUcq(C 2, q). Using ps = (1 -p )U~(c 1, q)/Uc(c 2, q), according to (5), we conclude:

a f t 0 if S(c2, >

- - q) S(Cl,q), (7) aq < <

where S(c, q) := - Ucq(C, q)/U~(c, q). Combining the two conditions (6) and (7), we have a clear analytical

characterization of the impact of equity on evasion. The crucial criterion is if index S decreases or increases when disposable income increases from the amount c2 that is available when the evader is caught to the amount c 1 available when (s)he is not caught. The problem with this characterization is that S is not a familiar index with known economic psychological interpretation. Fortunately, it turns out that Condition (7) can be trans- lated into a condition on the familiar index of absolute risk aversion which is def ined by R(c, q):-- -Ucc(C, q)/Uc(c, q). We have: 6

aS > > - - 0 if aR/aq O. (8) Oc < <

Using this and the fact that c 2 < c t in Condition (7) and (6), we get the following result.

4 Only interior solutions are considered in this paper. Since e * = 0, for 1 - p - ps < 0, this requires that probability of detecion p and penalty rate s of the tax enforcement system fulfill the condition s < ( 1 - p ) / p .

5 Obviously, this condition is fulfilled if Ucc < O, 6By definition, aS / a c = -(UcucU c -UcqUcc) / U~ z and aR / a q = - ( U c c q U c -U~cUcq) / Uc 2. Since Ucq c

= Ucc q, if the partial derivatives exist, we have a S / a c ~ aR /aq .

J. Falkinger / Journal of Economic Psychology 16 (1995) 63-72 67

Theorem. Under the assumption of self-perceived insignificance, the amount of tax a person evades decreases (remains constant, increases) with perceived equity, if and only if the person's absolute risk aversion increases (remains constant, decreases, respectively) with perceived equity. Formally,

~e* ~_ OR ~ 0 iff O. (9)

Oq < Oq >

Before I turn to applications of this general result, I want to emphasize that the change of absolute risk aversion with (in)equity, not income, is relevant for the impact of (in)equity on tax evasion. It is a standard assumption that absolute risk aversion is a constant or decreasing function of income. I will retain this assumption in the following analysis. The important thing to be noticed is that the assumption 3R/3c < 0 puts in general no restriction on the sign of 8R/3q. Only for special types of preferences does absolute risk aversion react in the same way to changes in income as to changes in equity. In this case the above theorem predicts a counterintuitive reaction of evasion to increased equity. In general, how- ever, a person's absolute risk aversion may be positively influenced by increases in equity and negatively by increases in income. Then the predic- tion of the theorem is in line with the suggestion that evasion decreases with perceived equity (increases with perceived inequity, respectively). The next sections will show in which concrete economic situations this is to be expected.

3. Tax evasion and public output

In this section, equity is interpreted as a characteristic of the perceived exchange relationship between taxpayers and government: A person gets in return for the tax payment a certain amount of public output g. For a given amount of tax, the exchange with the government will be considered unequal by the taxpayer if (s)he gets only a small amount of g in return. A rise in g corresponds to increasing equity in the present interpretation. The question is how tax evasion reacts to changes in g. From the analysis of Section 2 we know that the impact of g on a person's risk aversion must be determined if we are to answer this question. The relationship between a person's risk aversion and consumption of public output depends on the concrete nature of the public good and the person's preferences for it. I

68 J. Falkinger /Journal of Economic Psychology 16 (1995) 63-72

will consider the following situation. The public good g produces in combination with disposable income a utility-generating characteristic z according to the household production function:

z=c'~v(g), (10)

w i t h 0 _ < a < l a n d v ' > 0 . For instance, z may be an index for the quality of life and g the public

infrastructure in the person's neighbourhood. Another instance of (10) would be the provision of public security, where z measures the character- istic security by the level of losses through crime avoided and g is the level of public security measures in the region where the taxpayer is living.

The taxpayer's utility is assumed to be a function of characteristic z and disposable income c. More specifically, I define:

U(c,g):=f(c + ez)," (11)

with f increasing ( f ' > O) and concave (f"< 0). e is a positive constant. Utility function (11) means that characteristic z fulfills the assumption that its valuation does not depend on the person's disposable income. It should also be noticed that for a = 0 and e = 1, the class of preferences specified by (10) and (11) is the same as that used in Cowell (1992). 7 So the class of preferences defined by (10) and (11) can be seen as a generalization of the preferences considered by Cowell.

If the nature of the public good and the taxpayer's preferences fall into this class, then the impact of an increase in the amount of the public good on tax evasion can easily be calculated by applying the analysis of the preceding section. Substituting (10) into (11) and differentiating (twice) with respect to c, we get for the index of absolute risk aversion (R := -Ucc/Uc):

R(c,g)=r(c+ec~'v(g))(l+eac"-'v(g))+W(c,g), (12)

with

T ( x ) : = - f " ( x ) / f ' ( x ) and W(c,g):= 1 +eotca-lu(g)

Consider first the case that a = O. It is easy to see that term W vanishes,

7 In this case, the marginal rate of substitution between c and g, Uc/Ug is equal to f ' / ( f 'v ' (g))= 1/v ' (g) . This is independent of disposable income c as required by Cowell's assumption concerning the valuation of public output (p. 533).

J. Falkinger /Journal of Economic Psychology 16 (1995) 63-72 69

and the first term of the sum at the right-hand side of Eq. (12) decreases (remains constant) with c and g if T' < 0 (if T' = 0, respectively). Thus, if constant or decreasing absolute risk aversion (that is OR/ac < 0) is re- quired, then risk aversion decreases with g also. Using g for q in Criterion (9) derived in Section 2, we can conclude that tax evasion increases with g, and decreases if the taxpayer gets a lower amount of public output, that is, if the exchange of taxes for public goods becomes less fair. This corre- sponds to the puzzle of standard tax evasion analysis discussed by Cowell.

However, if a > 0, then the first term of the sum at the right-hand side of Eq. (12) decreases with c and increases with g if T' = 0. 8 Moreover, also term W decreases with c and increases with g. 9 Thus, the assumption of decreasing absolute risk aversion is consistent with a positive impact on risk aversion of the amount of public output g. According to the theorem in Section 2, this implies that tax evasion is reduced if equity, as measured by the amount of public output that the taxpayer gets in return for the taxes, increases. It may appear to be surprising that a plausible theoretical prediction about the impact of equity on evasion results if a > 0 (instead of a = 0) is assumed. This raises the question if a > 0 is an economically meaningful assumption. Now, according to (10), 1 > a > 0 means nothing else than that the characteristic z generated by the public good g is an increasing concave function of the disposable income of the person consid- ered. 10 In other words, an increase in perceived equity of the exchange relationship between taxpayers and government has an evasion reducing effect if the value generated by the publicly supplied goods increases, at a decreasing rate, with disposable income of the taxpayer. This seems to be fairly plausible for many categories of public goods like security measures, sophisticated infrastructure and other conveniences which can be used and enjoyed somewhat more if one is rich. Only for public goods that are necessary for the fulfillment of basic needs of everybody does it appear to be plausible that the value of the produced consumption characteristic is independent of income (i.e., a = 0), so that evasion reacts in a counterintu- itive direction to changes in public output.

s For T' < 0, OR/ac < 0 and OR/Og ambiguous. For T' > 0, aR/ac ambiguous and aR/ag > O. 9To see this, divide both numera tor and denominator by et~ca-2v(g) and use e '~> 0, a < 1 and

v ' > 0 . l0 This implies that the marginal valuation of public output in terms of private consumption increases

with income. Formally, if a > 0, Ug / U c is an increasing function of c.

7 0 J. Falkinger /Journal of Economic Psychology 16 (1995) 63-72

4. Tax evasion, fairness and bad reputation or conscience

The channel through which perceived equity influenced evasion in the analysis of Section 3 was an economic one. In this section I want to consider the possibility that the impact of equity on evasion arises through a psychological mechanism. Suppose that there is a social or moral norm so that each person evading taxes has a bad reputation or simply a bad conscience. Many people think that evasion is more or less justified if the social and economic system is unfair, whereas evasion is more blameworthy if the system is considered to be fair. This implies that bad reputation or bad conscience is an increasing function of equity. Formally, we can capture this idea by specifying

k = v ( q ) , v ' > 0 , (13)

where k denotes bad reputation and q is some index measuring perceived equity. Bad reputation or bad conscience is an unpleasant thing. Thus, k enters the taxpayer's utility function as a negative term. Assuming that the marginal valuation of k is independent of a person's disposable income, we can write the utility function of a tax evader as U =f(c - k) where f is a monotonously increasing function. Substituting (13), we get

U(c,q) = f ( c - v(q)). (14)

Utility function (14) is obviously a variant of (10) and (11). Since the characteristic bad reputation or bad conscience seems to be not related to disposable income in a systematic way, I assumed a = 0 in (13) and (14). Applying the same reasoning as in Section 3, we get 1~

R ( c , q ) = T ( c - v ( q ) ) , (15)

with T = - f " / f ' . Obviously, OR/Oq = -(OR/ac)v'. Since v ' > 0, absolute risk aversion is

an increasing function of q if it decreases with disposable income c. Applying Criterion (9) of the theorem derived in Section 2, we can conclude immediately that evasion is reduced if equity increases. The intuitive reason for this result is that according to the psychological mechanism described, equity is not a good but a bad for the tax evader, since it produces bad reputation or bad conscience.

By specifying the relationship between the fairness of the system on the

11 U s e e = - 1, a = 0 i n E q . (12 ) .

J. Falkinger /Journal o f Economic Psychology 16 (1995) 63-72 71

one side and bad reputation or bad conscience on the other side in the way I did in (13) and (14), one assumes that each evader is subject to the reputation or conscience problem, regardless of the size of the evaded amount and of being caught or not. One may argue that a more plausible way to model the described psychological phenomenon would be to assume that bad reputation or bad conscience is proportional to the size of the evaded tax and arises only if the evader is caught. This means that (13) must be modified as follows

/°) k = v(q) te with probability 1 - p . p (16)

Substituting this and (2), (3), into the utility function f ( c - k), we have

E U = (1 - p ) f ( c o + te) + p f ( c o - ste - v (q) te ) . (17)

Differentiation with respect to e yields the first-order-condition

F - ( 1 - p ) f ' ( C o + t e ) - p ( s + v ( q ) ) f ' ( C o - S t e - v ( q ) t e ) = O . (18)

Implicit differentiation of (18) shows that Oe*/~q <0. 12 Thus, in this modified model we again get the result: Tax evasion decreases with equity (and increases with inequity) if some psychological mechanism is at work that relates reputation or conscience to the fairness of the system in which the taxpayer is living.

5. Conclusion

Starting from the fact that the standard economic model of tax evasion does not generally support the suggestion that a person reduces evasion if the socioeconomic system is considered to be relatively equal and fair, this study has pointed out concrete economic situations in which this suggestion /s supported by economic theory.

First, under the standard assumption of self-perceived insignificance, a general criterion for determining the impact of (in)equity on evasion was derived in Section 2. The criterion says that evasion decreases with per- ceived equity if and only if the taxpayer's risk aversion is an increasing function of equity.

12 Calculate from (18) OF/Oq = - pv ' f ' - p(s + v ) f " ( - v')te. Since f ' , v ' > 0 and f " < O, this is strictly negative. Since aF /Oe < O, Oe */Oq = - ( a F /Oq)/(OF /Oe) < O.

72 Z Falkinger/Journal of Economic Psychology 16 (1995) 63-72

Then, in Section 3 and 4, an economic and a psychological argument were provided for why risk aversion should be related to equity in such a way: In doing so only situations were considered in which the standard assumption of decreasing absolute risk aversion is fulfilled.

The economic argument was based on the notion of equity as the perceived exchange relationship between taxpayers and government (mea- sured by a person's share in public output). If the value of the consumption characteristics produced by the publicly supplied good increases, at a decreasing rate, with disposable income, then risk aversion increases with equity (and decreases with inequity) despite of the assumption that abso- lute risk aversion decreases with income. Thus, evasion decreases with the available amount of such public goods. Examples are public goods like security measures or sophisticated infrastructure which are more usable and enjoyed if income increases. For basic public goods this is less plausi- ble and increased provision may imply higher evasion.

The psychological argument considered in Section 4 said that the fair- ness of the system in which a person is living may produce bad reputation or bad conscience with evaders if people consider evasion to be more blameworthy in a just than in an unfair society. As a consequence risk aversion will increase with perceived equity so that also this psychological mechanism supports a positive relationship between the degree of inequity and the size of evasion.

Acknowledgements

I wish to thank two anonymous referees of this journal for helpful comments.

References

Allingham, M.G. and A. Sandmo, 1972. Income tax evasion: A theoretical analysis. Journal of Public Economics 1, 323-338.

Cowell, F.A., 1990. Cheating the Government. Cambridge, MA: MIT Press. Cowell, F.A, 1992. Tax evasion and inequity. Journal of Economic Psychology 13, 521-543. Falkinger, J., 1988. Tax evasion and equity: A theoretical analysis. Public Finance/Finances Publiques

43, 388-395.