harassment, corruption and tax policy

European Journal of Political EconomyŽ .Vol. 16 2000 75–94

Harassment, corruption and tax policy q

Sugata Marjit a,), Vivekananda Mukherjee b,Arijit Mukherjee c

a Centre for Studies in Social Sciences, 10 Lake Terrace, Calcutta 700 029, Indiab R.K.M. Residential College, Narendrapur, West Bengal, Pin: 743508, India

c Technische UniÕersiteit EindhoÕen, Faculteit Technologie Management, Den Dolech 2, P.O. Box513, 5600 MB EindhoÕen, Netherlands

Received 1 March 1999; received in revised form 1 April 1999; accepted 1 August 1999

Abstract

This paper introduces ‘harassment’ in a model of bribery and corruption. We character-ize the harassment equilibrium and show that taxpayers, with all possible levels of income,participate in such equilibrium. Harassment has a regressive bias. Harassment costs as suchmay not affect tax revenue. However, when the decision to file tax returns is endogenized,harassment cost can affect the filing pattern and, hence, the revenue collection. We studythe nature of the equilibrium under imperfect information when different types of taxpayersand auditors are introduced in the system. q 2000 Elsevier Science B.V. All rights reserved.

JEL classification: K42Keywords: Corruption; Harassment; Filing

q This paper was prepared for the conference on ‘‘Economic Performance, Economic Policy andPolitical Culture’’ held at Erasmus University from 3–7th February, 1999. An earlier version receivedhelpful comments from Dieter Bos, Amit Bhaduri, Kunal Sengupta, Dilip Mookherjee, Otto Swank andan anonymous referee. Sugata Marjit wishes to acknowledge CES, Munich, EPRU of CopenhagenBusiness School, SFB 303 at the University of Bonn and Chinese University of Hong Kong forfinancial support. Arijit Mukherjee acknowledges the financial support from the Netherlands Technol-

Ž .ogy Foundation STW .) Corresponding author.

0176-2680r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved.Ž .PII: S0176-2680 99 00048-8

( )S. Marjit et al.rEuropean Journal of Political Economy 16 2000 75–9476

1. Introduction

Corruption is a widely observed phenomenon. It is so pervasive that citizens inthe developing part of the world have accepted it as a social rule. This has been

Ž . Ž .clearly depicted in De Soto 1989 and in Ekpo 1979 . The UN report onŽ .‘Corruption in Government’ 1989 is also an interesting source. However,

analytical studies on corruption are limited. We believe that whatever headway hasbeen made in theoretical research on corruption, we owe it to the literature on

Ž .crime and punishment. Starting from the seminal work of Becker 1968 , severalauthors have indulged in the theoretical and empirical analysis of crime and

Ž . Ž .punishment. Lui 1985, 1986 , as well as the good survey by Becker 1993 ,provide a thorough background of the state of the literature. In general, suchliterature presumes a social structure where penalties can be enforced and there arelaw abiding public officials to execute legal mandates. Strong evidence ofcorruption at different levels of the government in most of the developing part ofthe world, however, has led to the emergence of a small but cogent literature oneconomics of corruption, which explicitly models the behavior of a corrupt law

Ž .enforcing agent. Becker and Stigler 1974 provide an elegant discussion onŽ .corruption. This line of research is represented by Rose-Ackerman 1975 , Cadot

Ž . Ž . Ž .1987 , Mookherjee and Png 1992, 1994, 1995 , Basu et al. 1992 , Besley andŽ . 1 Ž .McLaren 1993 , etc. A recent paper by Marjit and Shi 1998 discusses the

possibilities of bribery and corruption when punishments are extremely difficult toenforce. They show that high penalties almost always fail to deter crime. Thestrategic interaction between the law enforcing agent and the criminal makestandard policy prescriptions quite ineffective. Some of these issues are also

Ž . Ž .discussed in Klitgaard 1988 . In a recent paper, Mookherjee 1998 discussesincentive reforms in corrupt tax administrations.

Apart from the micro-theoretic models of bribery and corruption mentionedabove, there have been discussions on the impact of corruption on the overall

Ž .economic system. For example, Shleifer and Vishny 1993 discuss organizationof corruption and argue why bribes are more distortionary than taxation. SanteŽ .1995 develops a model of economic growth and corruption where corruptionleads to growth through the development of informal sectors. Marcouiller and

Ž .Young 1995 discuss, within a general equilibrium framework, how state keepsŽ .‘order’ and discipline in the informal black economy. Bardhan 1997 reviews

various issues on the relation between corruption and development. BanerjeeŽ .1997 offers a theory that can explain why some economic systems are moreprone to corruption than the others.

In the existing literature, corruption has been seen as a Pareto-optimum contractbetween the law enforcing agent and the criminal, where some bribes change

1 Ž .Also see Dawid and Feichtinger 1996 for a dynamic model of corruption.

( )S. Marjit et al.rEuropean Journal of Political Economy 16 2000 75–94 77

hands in exchange of some favors. In this paper, we deal with another type ofcorruption, where people are forced to pay some amount of money to the officialsto avoid harassment. Unlike the earlier type of corruption, the harassment does notgive rise to Pareto-optimum side contract. The officials use the threat of harass-ment and gain at the cost of the criminals. So, the criminals have to bear a cost tobe involved in a Pareto-improving bribery contract. The issue of harassment is notmuch discussed in the literature on corruption. An earlier paper by Mukherjee and

Ž .Marjit 1997 has presented a model of revenue-collecting agency, involvingtaxpayers and auditors, where harassment can occur. Anticipating that, the author-ity takes measures to protect the taxpayers from possible harassment caused by‘over-reporting’ their actual income. So, harassment does not occur at the equilib-rium. Here, we develop a model where harassment occurs at equilibrium. In doing

Ž .so, we use the basic framework laid out by Marjit and Mukherjee 1996 . Ourmodel is developed in the context of tax administration where the taxpayer files anincome report, and the auditor checks whether he has reported his true income ornot. The amount of tax revenue the taxpayer has to pay depends on the assessment

Ž .report submitted by the auditor. Unlike Mukherjee and Marjit 1997 , in our paper,the authority does not have any incentive scheme to induce the auditors to revealthe true information.2 The auditor uses the threat of ‘over-reporting’ to extortsome extra amount of money from the taxpayer. The taxpayer has an option ofgoing to the court against the ‘over-reporting’. But, going to the court has somestart-up costs.3 If the taxpayer does not go to court, the auditor offers to be bribedand promises to underreport his true income.4 In our paper, the corrupt auditor ifsuccessfully prosecuted of ‘harassment’ charges, does not receive any punishment.5

We now conceive the ‘harassment equilibrium’ as a situation when the taxpayerdoes not go to the court and accept the bribe offer. The threat of harassment does

2 This fits the description of the tax administration of some of the developing countries. SeeŽ .Das-Gupta and Mookerjee 1998 for a description of Indian tax administration.

3 These start-up costs may have several interpretations. For example, in the Indian legal system oneneeds to pay a fixed fee, i.e., retainer fee. Sometimes, to pursue the case, favors need to be shown at

Ž .the clerical levels. Such an idea of fixed cost occurs also in Cowell 1990 who uses the concept in adifferent context.

4 The example is not just an abstract way of theorizing our main idea, but it is drawn from ourpersonal experience confronting the tax-assessing clerks working for the municipal authority in the cityof Calcutta, known as Calcutta Corporation. Typically tax-assessing clerks visit resident premises toreport the building tax to be paid to the Corporation. After they report, one may lodge a complaint.However, it takes enormous time and energy to pursue most of these cases. The assessor usually asksfor a bribe by suggesting a possible ‘overvaluation’ of the property and consequent harassment. In thesame vein, it is also suggested that an ‘undervaluation’ would help everyone.

5 We assume this because in developing countries, punishments are difficult to enforce due tovarious reasons like union pressure and the general environment of low income, unemployment, andpoverty. It is even more difficult in a democracy because of different political pressure groups. Forexample, even an effort to compel the workers of Calcutta to come on time to their office has failedmiserably.


affect the reservation payoff of the taxpayer, who takes into account the costsassociated in proving his innocence. It also affects the bribable surplus. On theother hand, the threat of going to the court affects the auditor’s decision whetherhe uses the harassment threat or not. In the next section, we set up the model andcharacterize a ‘harassment equilibrium’. We show that the taxpayers with allpossible level of incomes participate in this equilibrium, which has a regressivebias.

Ž .In a recent paper, Das-Gupta and Mookherjee 1997 refer to the fact that oneof the major problems to the tax collection agencies in developing countries likeIndia is that a large number of potential taxpayers do not file their income report.

Ž .Virmani 1986 estimated using the 1975–1976 Indian data, that if all thenon-filers were to report their income, revenue collection would increase by 55%.We suspect that the harassment cost has a role to play in determining the filingpattern of the taxpayers, and discuss the issue in Section 3 of our paper. We alsodiscuss the effect of change in the tax rate on the filing pattern in this section. InSection 4, we introduce some honest taxpayers and two types of auditors in thesystem and allow for imperfect information. We completely characterize theequilibrium in this changed set up.6 The last section provides concluding remarks.

2. The model

The starting point of our paper is a set of potential taxpayers meeting auditorsŽ .on one-to-one basis. A taxpayer pays a proportional tax, t 0- t-1 , on his

taxable income x. So, the taxpayer has an incentive to underreport his income.Ž .Knowing this, the Revenue Collecting Authority RCA sends an auditor to assess

the taxable income of the potential taxpayer. The auditor first reports the valuationto the tax collector, who then collects the tax.7 We assume the auditor comes toknow about the true valuation of the taxpayer’s income without spending anyeffort.8 But, since the actual amount of tax revenue the taxpayer is supposed topay depends on the assessment report put forward by the auditor, the auditor

6 For a recent paper on how ‘incomplete information’ can deter crime and corruption, see Marjit etŽ .al. 2000 .

7 It is implicitly assumed that the RCA has neither time nor money to check the taxpayers. In otherwords, checking the taxpayers is infinitely costly for the RCA. So, it depends on the auditors for theassessment report.

8 This has been assumed because we want to focus on the role of the auditor as the source ofinformation. It is not important for our purpose whether the auditor is supplying a positive effort levelor not. However, if we allow for a positive effort level by the auditor, at a later stage of the paper, the

Žbribable surplus is smaller but our results remain the same since then the taxpayer has to compensateŽthe auditor for the effort he has supplied but there will definitely be a positive bribable surplus; the

auditor will ensure that by carefully choosing his effort level; see Marjit and Shi, 1998 for a..discussion .


enjoys some discretionary power either to overvalue or to undervalue the trueincome. The RCA provides no incentive for the auditor to report the true valuationof the income. Therefore, a corrupt auditor can offer to be bribed and undervaluethe taxpayer’s true income in exchange. If the taxpayer accepts the offer, he paysthe tax revenue on the undervalued income and the bribe to the auditor. Otherwise,he has to pay the tax revenue on the true valuation of his income. The other optionthat the corrupt auditor has is to overvalue the true income. In that case, thetaxpayer has to pay more than his actual tax liability. The taxpayer quite naturallydoes not want to pay the inflated amount. He has an option of going to the court toprotest against the ‘harassment’. If he can successfully prosecute the auditor, hedoes not have to pay the inflated amount. We assume there is a cost of going tocourt. If he cannot prosecute the auditor successfully, he has to pay the tax onovervalued income. The taxpayer has, however, an option of not going to thecourt. In that case, the auditor offers to be bribed and undervalues the true incomein exchange. If the taxpayer accepts the offer, he pays the tax revenue on theundervalued income and pays a bribe to the auditor. Otherwise, he has to pay therevenue on the overvalued income.

Let the overvalued and the undervalued income reports be x and x, respec-tively. These amounts depend on the true valuation of x in the following way:

x x sl x 1Ž . Ž .where, l)1 and

x x sg x 2Ž . Ž .where, 0-g-1. We suppose the higher values of x reflect more affluenttaxpayers.

If the auditor reports x instead of x and the taxpayer goes to the court seekingŽ .justice, he has to incur a cost C x , which is given by

C x saqb x 3Ž . Ž .Ž .C x contains a fixed part a which suggests no matter what the value of x is, one

has to run around and make certain number of trips to the appellate authority. AŽ .part of C x varies with x, which represents the fees needed to be paid to the

legal expert fighting for the plaintiff. We assume q is the probability of successfulprosecution, which is a parameter to the system and common knowledge.

When the auditor asks for a bribe, the amounts of bribe are represented by band b which are positive quantities. In exchange, he reports x instead of x or x.1

The model can be described as an extensive form game, as in Fig. 1.We start by solving the game following the method of backward induction. We

must first look at the bribery game when overvaluation has occurred. In this game,the taxpayer accepts a bribe offer only if:

xy tg xyb)xy tl x

or, t lyg x)b.Ž .


Fig. 1.

Since the bribe is the only source of income for the auditor, it is always in hisinterest to propose a bribe offer that is acceptable to the taxpayer. We assume that

Ž .the auditor claims a proportion of the bribable surplus t lyg x, so that,

bsu t lyg x 4Ž . Ž .

where, 0-u-1. The parameter u represents the relative bargaining strength ofthe auditor.

In endogenizing g , one has to take note of the fact that, without the possibilityof punishment of any sort, the optimal g must be zero, and with 0-u-1, thisbenefits everyone. For a meaningful determination of g , we introduce a simplenotion of punishment. For any x, the true revenue is tx and the RCA collects tg x.

Ž .Therefore, the punishment is designed over txy tg x . Suppose p is the probabil-ity that the taxpayer who has participated in the bribery game is caught.9 Then, he

9 Ž .The probability of detection p can be interpreted as the outcome of a random checkingprocedure, which the RCA can initiate at a later stage. It is possible to provide strategic foundation tothe RCA’s action of sending auditors to communicate directly with the taxpayers and then have arandomized cross check, vis-a-vis the alternative of not having the randomized check and leaveeverything for the auditors to decide. We choose to keep our focus clean and, therefore, the strategicbehavior of the RCA is kept in the background. It can be tackled in an extended model and our mainresults will go through.


has to pay a fine at the rate f , which depends on the amount of evaded income.The auditor has to pay nothing.10

Ž . Ž . XŽ .Assumption 1. f is a function of txy tg x such that f 0 s0, f txy tg x )0YŽ .and f txy tg x )0.

The taxpayer chooses g to maximize his expected payoff, which is given by:

E u sxy tg xyu t lyg xypf txy tg x . 5Ž . Ž . Ž . Ž .Suppose g

U solves the problem, which satisfies the first order condition foroptimization as follows:11

pf X txy tg U x s1yu . 6Ž . Ž .At gsg

U , by virtue of assumption 1, the second order condition for maximiza-tion is also satisfied. As a first mover in the bribery game, the auditor can solvethe taxpayer’s problem beforehand and offers to underreport x by g

U x so that thebribe offer is immediately accepted. Therefore, in the bribery game, the payoffs ofthe auditor and the taxpayer appear as:

Ž U .Auditor: u t lyg xU Ž U . Ž U .Taxpayer: xy tg xyu t lyg xypf txy tg x .

Ž .Here, we make an important observation from Eq. 6 , which we note sepa-rately as:

Ž U .Observation 1. The optimum amount of undervaluation g is independent ofthe value of l.

Now, we look at the earlier stages of the game where the auditor decideswhether to harass the taxpayer or not and the taxpayer decides given the auditor’smove whether to go to the court or not. In this part of the game, we try to specifyan equilibrium, which is defined as follows:

Definition 1. The harassment equilibrium is a Subgame Prefect Nash EquilibriumŽ .SPNE in which the auditor chooses to overvalue the taxpayer’s true income and,thereby, harass him but the taxpayer does not go to the court.

10 As opposed to the small, organized group of auditors, the large group of taxpayers is not organizedto that extent since the problem of coordination and free-riding crop up. So, the punishment schemesfor the taxpayers are easier to implement. Had we introduced punishment schemes for the auditors itcould lead to any equilibrium depending on the nature of the punishment scheme as we have in manypapers in the literature. The ‘harassment equilibrium’ occurs where punishment for the auditors isdifficult to enforce. The threat of losing a coveted job is not a ‘‘credible’’ one. If it were, we could nothave observed corruption to such an extent in the LDCs.

11 XŽ .We assume, pf tx )1yu so that the unique interior solution exists.


In doing so, we make two simplifying assumptions:

Ž .Assumption 2. The probability of successful prosecution of the corrupt auditor qis 1.

Assumption 2 implies whenever the taxpayer goes to the court following anincidence of harassment by the auditor, he achieves justice.12

Ž U .Assumption 3. aGpf txy tg x , i.e., the fixed cost of going to the court for thetaxpayer is at least as great as his expected punishment if he accepts the bribeoffer in the next stage of the game.

Here also, we follow the method of backward induction and first look at thetaxpayer’s decision regarding going to the court. If the taxpayer does not go tocourt, we know from the equilibrium of the game above that he participates in thebribery game and obtains the equilibrium payoff of that game. Since, by assump-tion 2, the value of q is 1, if he goes to the court, his payoff is as given below:

E u sxy txyayb xŽ .1

Therefore, the taxpayer does not go to the court only if:

xy tg U xyu t lygU xypf txy tg U x Gxy txyayb xŽ . Ž .

aq txqb xy 1yu gU txypf txy tg U xŽ . Ž .

or, lF . 7Ž .u tx

Ž . Ž .Since by Eq. 1 , l)1, for inequality 7 to be meaningful, it must be the caseŽ .that the right hand side RHS of the inequality is strictly greater than 1. To ensure

this, it is sufficient to show that, given the assumptions of the model, thenumerator of the fraction on the RHS of the inequality is strictly greater than thedenominator. For this to be so, it must be the case that,

aq txqb xy 1yu gU txypf txyg

U tx )u txŽ . Ž .or, aypf txyg

U tx q tx 1ygU 1yu qb x)0,� 4 � 4Ž . Ž . Ž .

which is true given assumption 3, 0-u-1, 0-gU -1 and b)0. Therefore,

there exists a value of l for which the taxpayer does not go to the court.Now, the existence of the harassment equilibrium depends on l that the auditor

chooses as an equilibrium strategy. If the auditor chooses l, such that inequalityŽ .7 is satisfied, he receives the pay-off of the bribery game described above. If he

12 The sole purpose of this assumption is to bring in analytical simplicity. Our results hold if0- q-1.


does not, he asks for a bribe from the taxpayer and undervalues his true income inexchange. In this new bribery game, the taxpayer accepts a bribe offer only if:

xy tg xyb )xy tx1

or, t 1yg x)b .Ž . 1

Ž .Therefore, now the auditor claims u proportion of the bribable surplus t 1yg x,so that,

b su t 1yg x 9Ž . Ž .1

where, 0-u-1. The description of the equilibrium of this new bribery game isŽ .the same as the earlier bribery game when harassment had occurred , except for a

Ž . Ž .change in the amount of bribe claimed, as is evident from Eqs. 4 and 9 .Let, g be the equilibrium amount of undervaluation. From observation 1, theˆ

equilibrium amount of g in the bribery game is independent of the value of l.Therefore, it must be that g

U sg . So, the payoffs of the auditor and the taxpayerˆin this new bribery game can be described as follows:

Ž U .Auditor: u t 1yg xU Ž U . Ž U .Taxpayer: xy tg xyu t 1yg xypf txyg tx

Ž .Therefore, the auditor chooses a l satisfying inequality 7 only if:

u lygU tx)u 1yg

U tx . 10Ž . Ž . Ž .Ž . Ž .Since, from Eq. 1 , inequality 10 is satisfied at all possible values of l, the

auditor chooses to harass the taxpayer as an equilibrium strategy in such a waythat the taxpayer does not go to the court and a harassment equilibrium exists.

Let the payoff of the auditor under the harassment equilibrium be representedby L, which is given as:

Lsu lygU tx 11Ž . Ž .

Since, by observation 1, gU is independent of l and L is monotonically

increasing in l, the auditor must be choosing the highest possible value of l toŽ .maximize his payoff such that inequality 7 is satisfied. The auditor’s choice of l

at the equilibrium is given by:

aq txqb xy 1yu tg U xypf txy tg U xŽ . Ž .U

l s .u tx

The above discussion allows us to state the first proposition of our model as:

Ž U .Proposition 1. If aGpf txy tg x , a harassment equilibrium exists and theauditor chooses the optimum Õalue of l as:


U txŽ . Ž .U

l s .u tx


After characterizing a harassment equilibrium for a particular value of x)0,we ask whether any taxpayer with x)0 participates in such an equilibrium or not.

Proposition 2. EÕery taxpayer with x)0 participates in the harassment equilib-rium.

Ž U . Ž .Proof. If aGpf txy tg x , inequality 8 holds and from proposition 1 we knowŽ .that the harassment equilibrium exists. Inequality 8 implies:

U Ua)pf txy tg x yx 1yu 1yg tqb .Ž . Ž . Ž .

U Ž U . Ž .Since, 0-g -1, 0- t-1, b)0 and aGpf txy tg x , inequality 8 holdsfor all x)0. Hence, the statement of the proposition follows. I

At the equilibrium, the bribable surplus generated by the taxpayer with incomeŽ U U . U Ux is given by l yg tx. Since, both l and g are functions of x, the amount

of bribable surplus may change for taxpayers with different income levels. Inproposition 3, we compare the amounts of bribable surplus generated by differentincome groups as a proportion of their income.

Proposition 3. The richer section generates proportionately less bribable surplusthan the poorer ones.

Ž U U .Proof. The bribable surplus generated by a taxpayer with income x is l yg tx.Ž U U .Therefore, the amount of bribable surplus as a proportion of income is l yg t.

Ž . UFrom Eq. 6 , we solve for the optimum g , i.e., g in terms of the parameters p,Ž .t, x and u . Since, by assumption 1, f . is continuously differentiable up to a

U Ž .second order in its argument, we can define an implicit function g x at the openneighborhood of gsg

U and the initial value of x, which is continuouslydifferentiable. Therefore, by the implicit function theorem, we have:

dgU 1yg

U

s 12Ž .d x x

which is positive since 0-gU -1, x)0.

From proposition 1 we know at the equilibrium:

aqb xq txy 1yu gU txypf txyg

U txŽ . Ž .U

l s .u tx

Therefore,

ElU y 1yu tx 1yg

U y aypf txy tg U x� 4Ž . Ž . Ž .s . 13Ž .2Ex u tx


U Ž . Ž Ž U .. Ž . Ž . Ž .Since 0-g -1, from Eq. 6 E g x r Ex s1, by assumption 1 E f r Ex )0Ž U . Ž . Ž U . Ž .and by assumption 3 aGpf txy tg x , from Eq. 13 , the sign of El r Ex is

negative. Observe,

E lU yg

U t ElU Eg U� 4Ž .

s t y t . 14Ž .Ex Ex Ex

Ž U . Ž . Ž U . Ž . Ž .Since, El r E x -0 and Eg r Ex )0 from Eq. 14 , it is clear that the signŽ �Ž U U . 4. Ž .of E l yg t r Ex is negative. Hence, the statement of the proposition

follows. I

We now compare the welfare of taxpayers in a corrupt regime vis-a-vis in anhonest regime. The question is whether all the taxpayers make a loss or only a partof them does it. Then, we try to find out which taxpayers lose more.

Proposition 4. The poorer section loses relatiÕely more in a corrupt system thanthe richer section compared to an honest system.

Proof. Let y and y be the incomes of the taxpayer in a corrupt regime and in an1 2

honest regime, respectively. That is,

y sxy tg U xyu t lU yg

U xypf txy tg U x 15Ž . Ž . Ž .1

y sxy tx2

y yy s txy 1yu gU txypf txy tg U x yu txl

U 16Ž . Ž . Ž .1 2

U Ž .Substituting the value of l from proposition 1 into Eq. 16 , we obtain:

y yy sy aqb x . 17Ž . Ž .1 2

Ž .Therefore, from Eq. 17 we can say that the taxpayer will lose under the corruptregime and the amount of loss is exactly equal to the cost of going to the courtw Ž .xfrom Eq. 3 . The amount of loss incurred by the taxpayer with income x in the

Ž .corrupt system is C x saqb x. Therefore, the amount of loss as a proportion ofincome is

C x aŽ .s qb . 18Ž .

x x

Ž . w x Ž . Ž .From Eq. 18 , since a)0 by assumption 3 , as x increases C x r x falls.Therefore, for the richer part of the population, the loss of income as a proportionof total income is less than for the poorer part of the population. Hence, thestatement of the proposition follows. I

The intuition behind proposition 4 is straight forward. Since in the harassmentgame the auditor acts as a leader, he chooses l in such a way as to push the

Ž .taxpayer down to his reservation payoff level. We shall call C x the harassmentcost. Since the harassment cost has a positive fixed component, this has a scale


effect as the value of x changes. The higher the value of x, the lower is theaverage cost of harassment. Since the marginal cost is fixed, the amount of loss ofthe richer part of the population is relatively less under the harassment equilib-rium. Before we move into the next section, we make the following significantobservation:

Ž .Observation 2. The harassment cost C x is independent of a change in the taxrate. Since the RCA’s revenue collection depends on the amount of undervaluation

Ž U . U Uin the bribery game g , and from observation 1, g is independent of l , theexistence of the harassment equilibrium does not have any added influence on theamount of revenue collected by the RCA as the tax rate changes. The harassmentcauses a pure redistribution of income from the taxpayer to the corrupt auditor.The RCA has no stake in that amount. However, it can be shown that as the taxrate rises the value of l

U falls, so that existence of the harassment equilibriummay become a problem in itself.

The harassment game described above builds on the assumption that thetaxpayer files his income report. In the next section, we set up a filing game andsee how the harassment cost affects the filing pattern of the taxpayers.

3. The filing game

In this game, the taxpayer acts as a first mover and makes the decision whetherto file his income report or not. If he files his income report, the RCA sends theauditor to assess the report filed by him and the subsequent moves take placeaccording to the game described in the previous section. So, the agents receive thepayoff of the ‘harassment equilibrium’. If he does not file his income report, hedoes not have to pay any tax revenue. If in independent investigation or throughthird party information, however, the RCA comes to know the taxpayer with

Ž . Ž .income x has not filed, a fine F x is imposed on the taxpayer where F 0 s0,XŽ .F x )0 ; xG0. We assume that the RCA can find such a non-filer with

probability k.

Ž . 13Assumption 4. The fine function F x is progressive in x.

Ž . Ž .Assumption 4 implies that the average fine rate F x r x is increasing in x andŽ .the elasticity of the fine function F x is greater than 1.

13 This is in accordance with the classical Pigouvian formula of optimal penalties for externalitycausing behavior. The Pigouvian formula requires the penalty rate to equal the harm caused, divided bythe probability of conviction, plus prosecution costs. In our case, ceteris paribus a non-filer with higherincome and higher tax liability inflicts a higher social cost than a non-filer with lower income andjustifies a progressive penalty structure for non-filing. For further discussion on Pigouvian formula, see

Ž . Ž .Polinsky and Shavell 1992 and Mookherjee and Png 1994 .


According to the description of the game, if the taxpayer files his incomereport, the harassment equilibrium occurs and he has to pay a harassment costŽ . Ž .C x apart from his stipulated tax revenue. Therefore, from Eq. 16 , the payoff of

the taxpayer can be written as:

y sxy txy aqb x . 19Ž . Ž .1

The payoff of the auditor is:

Lsu lU yg

U tx .Ž .Ž .Let the expected payoff of the taxpayer be E y if he does not file, which can be3

written as:

E y sxykF x 20Ž . Ž . Ž .3

In this situation, the auditor receives nothing. The taxpayer’s options and thecorresponding payoffs are described in Fig. 2. The taxpayer files his income reportonly if:

xy txy aqb x GxykF xŽ . Ž .

kF x yaŽ .or, bq tF

x

or, bq tFf xŽ .Ž . ŽŽ Ž . . . Ž . Ž .where f x s kF x ya rx . Observe lim f x ™y` since F 0 s0x™ 0

XŽ . Ž . XŽ .and F 0 )0. Assumption 4 implies that lim f x ™q` and f x )0.x™`

Ž . Ž .So, f x is a monotonically increasing function of x with a range y`, ` .Ž .Therefore, it must be that there exists a value of x, x such that f x sbq t. Forˆ ˆ

Fig. 2.


Ž . Ž .x-x, f x -bq t and the taxpayers do not file. If xGx, f x Gbq t and theˆ ˆ ˆ ˆtaxpayers file their income report. As a or b or both of them rises, x rises.ˆ

The above discussion leads to the next proposition:

( )Proposition 5. GiÕen the progressiÕe fine function F x , there exists a Õalue of x, x̂such that the taxpayers haÕing x-x do not file. But, the taxpayers haÕing xGxˆ ˆfile their income reports. As the fixed or the marginal component of the harass-ment cost, i.e., a or b rises, x rises.ˆ

Ž .Proposition 5 shows that if the fine function F x is progressive, the poorertaxpayers do not file their income report. It also shows how the harassment cost

Žaffects the filing pattern of the taxpayers. The higher the harassment cost i.e., the.values of a and b , the higher is the fraction of the taxpayers joining the

non-filers adversely affecting the revenue collection. Unlike observation 2, achange in the tax rate can now affect the RCA’s revenue collection, which we noteseparately as:

Observation 3. Given the harassment cost, the tax rate is the lower, the higher isthe fraction of the taxpayers filing their income report. So, there is a positive effecton the revenue collection. However, if a and b rise, lowering t may fail to affectthe revenue collection favorably.14

So far, we have restricted our attention to the case of perfect information,where it is common knowledge that all the taxpayers are corruptible. In Section 4,we relax this assumption and move into the domain of imperfect information.

4. The game with imperfect information

Here we consider the presence of some honest taxpayers in the system. Wedefine an honest taxpayer as:

Definition 2. An honest taxpayer is a person who always files his income reportand if harassed by the auditor goes to the court. He never involves himself into abribery contract.

Ž .It is common knowledge that a fraction h of taxpayers is honest. When anauditor picks up a filed income report, he does not know whether the report is

Ž .from an honest taxpayer or from a corrupt one. He believes with probability z

14 Ž .In recent times of economic reform, in India, tax rate t has been lowered considerably, but theŽ .appeal cost a has also been raised. So, the effect on filing pattern and the revenue collection is not

unambiguous.


Ž .that the report is from an honest taxpayer and with probability 1yz that it isfrom a corrupt one. The game is now described as in Fig. 3.

Observe that two types of pure strategy equilibria can occur in this game. Therecan be a pooling equilibrium when both the honest and corrupt taxpayers file theirincome reports and the auditor cannot distinguish between them. A separatingequilibrium arises when the honest taxpayer files and the corrupt taxpayer does notfile, so the auditor can distinguish between them. First, we consider the conditionsunder which a pooling equilibrium can occur.

Case 1. Pooling Equilibrium: The non-singleton information set at which theauditor moves, is on the equilibrium path. So, the auditor’s belief must followBayes’ rule. Therefore, it must be zsh. At the non-singleton information set, the

Ž . Ž .auditor could have four possible strategies: 1 harassing both the taxpayers; 2Ž .not harassing any of the taxpayers; 3 harassing the honest taxpayers and notŽ .harassing the corrupt taxpayers; and 4 not harassing the honest taxpayers and

harassing the corrupt taxpayers. If we compare the corresponding payoffs, we find

Fig. 3.


Ž . Ž .that strategies 2 and 3 are strictly dominated, but the auditor is indifferentŽ . Ž .between strategies 1 and 4 . Here, we assume there are two types of auditors as

follows.

Ž .Definition 3. A type 1 t auditor is a person who chooses to harass the taxpayer1

when according to payoff, he is indifferent between harassing and not harassingthe taxpayer.

Ž .Definition 4. A type 2 t auditor is a person who chooses not to harass the2

taxpayer when according to payoff, he is in different between harassing and notharassing the taxpayer.

We assume it is common knowledge that y fraction of the auditors are of t1Ž .type and 1yy fraction of them are of t type. Observe that for t auditors, the2 1

sequentially rational strategy is to harass both types of taxpayers. However, for t2

auditors, the sequentially rational strategy is not to harass the honest taxpayers, butto harass the corrupt taxpayers. Since an honest taxpayer always files his income

Ž .report, a pooling equilibrium occurs as a Perfect Bayesian Equilibrium PBE onlyif the corrupt taxpayer chooses to file his income report. The corrupt taxpayer

Ž .faces a t auditor with probability y and a t auditor with probability 1yy .1 2

Since with probability h he is mistaken by the t auditor as an honest taxpayer2

and is not harassed, his expected payoff is as follows:U U UE y sy xy tg xyu t lyg xypf txy tg xŽ . Ž . Ž .4

U U Uq 1yy h xy tg xyu t 1yg xypf txy tg x� 4Ž . Ž . Ž .U U Uq 1yh xy tg xyu t lyg xypf txy tg x� 4Ž . Ž . Ž .

sxy tg U xyu t lygU xypf txy tg U xŽ . Ž .

q 1yy hu t ly1 x . 21Ž . Ž . Ž .The corrupt taxpayer files his income report only if:

xykF x Fxy tg U xyu t lygU xypf txy tg U xŽ . Ž . Ž .

q 1yy hu t ly1 xŽ . Ž .or

tg U xqu t lygU xy 1yy hu t ly1 xŽ . Ž . Ž .

kGF xŽ .

skU say .Ž .1

Therefore, if kGkU a pooling equilibrium occurs.1

Case 2. Separating Equilibrium: If k-kU , the corrupt taxpayer does not file. So1

given that an income report has been filed, the auditor knows it is from an honesttaxpayer. The separating equilibrium occurs where the auditor’s belief is zs1.


The next proposition now follows as:

Proposition 6. If kGkU , pooling equilibrium occurs and if k-kU , the separating1 1

equilibrium occurs where

tg U xqu t lygU xy 1yy hu t ly1 xŽ . Ž . Ž .

Uk s .1 F xŽ .

The intuition behind proposition 6 is that, all else being constant, if theprobability of being detected for non-filing becomes too high, the corrupt tax-payer’s expected return from filing outweighs his expected return from non-filing.He then chooses to file his income report and the pooling equilibrium occurs. Inthis context, we make the following observation.

Observation 4. Under PBE, there are situations where harassment occurs and thetaxpayers go to the court. This was not possible under the benchmark modelabove. The imperfect information game is, thus, much closer to the reality.

Note that under the pooling equilibrium, both types of the auditors harass thecorrupt taxpayer and charge l in such a way that the taxpayer does not go tocourt. The corrupt taxpayer does not go to the court only if:

xy tg U xyu t lygU xypf txy tg U x q 1yy hu t ly1 xŽ . Ž . Ž . Ž .

Gxy txyayb x

which in turn implies:


U tx q 1yy hu txŽ . Ž . Ž .lF .

u tx 1y 1yy hŽ .Ž U .Since the auditor’s payoff from harassing the corrupt taxpayer u t lyg is

increasing in l, the auditor chooses the maximum possible value of l at theequilibrium. Let the equilibrium value of l be l. Therefore,


U tx q 1yy hu txŽ . Ž . Ž .ls .

u tx 1y 1yy hŽ .

Here, we make the following observation:

Observation 5. If ys1, i.e., all the auditors are t auditors, whatever the value of1Uh, lsl . Similarly, if hs0, i.e., all the taxpayers are corrupt, whatever the

Uvalue of y, lsl . Other things remaining the same, l falls as the number of t1

auditors increases and l increases as the number of honest taxpayers increases inthe system.


The intuition behind observation 5 is that the auditor charges l in such a wayas to extract the entire informational rent enjoyed by the corrupt taxpayer and

Ž .pushes him to his reservation payoff. From Eq. 21 , we note that the amount ofŽ . Ž .informational rent enjoyed by the auditor 1yy hu t ly1 x is decreasing in y

Ž .and increasing in h. As the fraction of t auditors y increases, the corrupt1

taxpayer expects a higher probability of harassment and the amount of informa-tional rent to be extracted falls. Therefore, the auditor needs to charge a lower l in

Ž .the equilibrium. Similarly, as the fraction of honest taxpayers h increases, thecorrupt taxpayer expects with higher probability that he will be mistaken for anhonest taxpayer. The amount of informational rent then increases and the auditorcharges a higher l to extract the higher amount of rent. If ys1 or, hs0, there isno informational rent left with the corrupt taxpayer. Therefore, the auditor charges

Ulsl .

5. Conclusions

In any corrupt regime, people enjoy the benefits of bypassing governmentregulations. Underreporting of income leads to tax saving, which helps both thetaxpayer and the assessing official who receives a bribe. However, this is not anunmixed blessing. In a society where corrupt officials can wield power of coercionand harassment, people are forced to pay bribes to avoid problems. Thus,corruption entails benefits as well as cost. This paper enumerates the cost andshows that the cost has a regressive bias. Among taxpayers, whoever files theirincome reports ends up paying the harassment cost and not going to the courtagainst the corrupt official. This happens in our model because the auditor canobserve the taxpayer’s income without spending any effort and acts as a perfectlydiscriminating monopolist to extract the taxpayer’s entire surplus from not goingto the court. The outcome of the model is not very satisfactory since in reality weobserve some taxpayers going to court alleging harassment. Therefore, we haveintroduced some honest taxpayers and different types of auditors in the system andhave allowed for imperfect information. In the equilibrium, we see that sometaxpayers go to court, but harassment also occurs side by side, which describesreality more closely. The auditors are still able to extract the entire surplus of thecorrupt taxpayer, but the extent of harassment at the equilibrium differs given thedistribution of the types of the auditors and the taxpayers. We show that the

Ž .harassment cost may dissuade some taxpayers from the poorer population fromparticipating in the traditional bribery game with the assessing officials. Only thericher part of society participates in the bribery game.

We have identified the parameters affecting the filing pattern of taxpayers.Given the harassment cost, an appropriate change in the tax rate can change thefiling pattern of the taxpayers drastically and can improve the revenue collection


performance of the RCA markedly. However, if the harassment cost increasessimultaneously, no amount of tax reform may bring about improved filing pattern.

Ž .We have assumed that harassment cost is partly a function of income.Likewise, some other parameters also could depend on income. For example, inthe case of bribery–collusion between the taxpayer and the auditor, the probabilityof the collusion being detected could be a function of income because the richertaxpayer can use more sophisticated methods of tax evasion or bribery. Similarly,the probability of successful prosecution of the corrupt auditor in case of thetaxpayer going to court against harassment could be an increasing function ofincome, since the richer taxpayer presumably could afford more successful andtherefore more expensive legal experts. These extensions strengthen the regressivebias of the harassment equilibrium found in this paper.

Harassment can affect efficiency.15 However, we have not modeled this aspectin this paper. We have not explored the possibility that there can be imperfectinformation about the value of the income itself. We have assumed a proportionaltax system. Having a model with a progressive tax system can also be anextension.

Another extension is to answer the following question: if everyone bears thecost due to harassment, why is there a lack of political support to remove it? Aswe have shown, poorer people do not participate in the bribery game, so that itdoes not matter to them whether harassment exists or not and, for the richerpopulation who bears the cost as a proportion of their income, it does not mattermuch. If the reduced amount of public provision is taken into consideration, sincethe richer population is less dependent on public provision, it is not an importantissue for them. The poorer population does not pay anything for the publicprovision, as it does not participate in the game. So, whatever amount of thepublic provision they obtain, they end up as net gainers and as long as there is nosignificant decline in such provision, they have no interest in supporting the causeof the richer citizens. We believe that this is the reason why harassment persists ina society.

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harassment, corruption and tax policy

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