tax evasion as a disciplinary mechanism for fiscal...

Published in Shibata, H., and T. Ihori (Eds.) (1998)Welfare State,Public Investment and Growth, Springer-Verlag

TAX EVASION AS A DISCIPLINARYMECHANISM FOR FISCAL POLICY *

THOMAS I. RENSTRÖM

Department of Economics, University of Birmingham, Edgbaston, Birmingham B15 2TT,UK. Email [email protected].

1. Introduction

This paper investigates the desirability of tax evasion as a mechanism for reducingthe time-inconsistency problem in fiscal policy. It endogenises the auditing ratesand punishment rates and shows that when the government cannot commit tofuture tax rates, tolerating tax evasion is optimal. The government can, bycommitting to low auditing and punishment rates, limit the effectiveness of incometaxes in the future. Furthermore we analyse establish which types of economiesthat would rely on evasion as a "disciplinary mechanism."

The contribution of the paper, apart from endogenising the enforcementsystem, is to provide answers to several issues that have been raised in the evasionliterature. We list the most important achievements of the paper below:

(1) Previous literature studying tax evasion and optimal auditingmechanisms generally concludes that maximum enforcement and consequentlyzero tax evasion are optimal (e.g. auditing everyone, or auditing very few andsetting the punishment very high). However, despite the findings of the theory,actual governments seem to tolerate tax evasion. This paper provides an answerto the following question: Why is tax evasion tolerated in equilibrium? We arguethat an optimal outcome lies between the zero and the maximum enforcement.This is so because tax evasion may act as partial solution to the time inconsistencyproblem. Infact Boadway and Keen (1998) independently reached similar

*I would like to thank Tim Besley, Torsten Persson, Peter Sinclair and Berthold

Wigger for helpful discussions and comments. Thanks are also due to participantsat the Public Economics Working Group at the Institute for Fiscal Studies,London, May 1996, and at the 53rd Congress of the International Institute ofPublic Finance, Kyoto, August 1997.

conclusions in a slightly different model than ours.1

(2) Standard models of tax evasion view the fiscal policy decision, at thetime when it is taken, as distinct from the auditing-punishment decision. Moreprecisely, when the tax system is decided upon the enforcement structure is takenas given. This reflects the idea that changing size of (or influencing) the inspectionauthority, or changing penalty structure, etc. can be done less frequently or lessrapidly than changing fiscal policy. That is, the tax system is viewed as morediscretionarythan the enforcement system. However one could criticise this viewby saying that a governmentcouldarrange differently, having a system with morediscretion in enforcement. This paper extends the standard one-period models toallow for two periods, and shows that it may actually bedesirableto operate theenforcement system under less discretion than the fiscal system, if the tax systemitself cannot be made less discretionary.

(3) As pointed out by some authors, theoretically an increase in the tax ratemay reduce the evaded amount. This may happen when the income effect (froma tax increase) makes the evader less willing to take on risk, and thereforedeclares more income (i.e. distribute consumption possibilities more evenlyaccross the risky states). However, this result depends entirely on the enforcementsystem. However, as we argue in this paper, such an enforcement system may notbe desirable. That is, it may not be optimal to operate an auditing and punishmentsystem such that when taxes are increased there is a reduction in tax evasion.Precisely because the evaded income has to increase as the tax rate increases, fortax evasion to act as a partial solution to a time-inconsistency problem. Thereforewe would expect governments to arrange their enforcement systems accordingly.

(4) One point not properly dealt with in the literature is to explain whydifferent countries experience different levels of tax evasion. Previous work saysthat different levels of the taxes or different institutional settings would cause thisdifference. This is not enough because these factors are endogenous. This papergoes behind in attempting to explaining primitives, for example the role of incomedistribution and the role of the level of aggregate income.

There are two papers, using two-period models,2 that have reached the conclusionthat some evasion may be desirable, Andreoni (1992) and Boadway and Keen(1998). The idea in Andreoni is that individuals may be credit constrained. If thegovernment can set detection probabilities and fines relatively low, so that evasionoccurs in equilibrium, individuals who evade effectively "borrow" from the

1 I was not aware that Boadway and Keen were working on this topic until MickKeen sent me their paper just before the IIPF Kyoto conference.

2 Weiss (1976) shows in a static economy that the randomisation induced byevasion may be desirable.

2

government in the first period. If an individual is caught she pays the tax (i.e. the"loan") and the fine (i.e. "interest") in the second period. In this way some evasionin equilibrium may be efficient and welfare improving. Boadway and Keen (1998)analyse a two-period economy where a representative individual is taxed on hersavings in the second period, when she also has the possibility of evading taxes.The tax receipts are used for provision of a public good. They reach theconclusion that when the government cannot commit to the future tax rateallowing some tax evasion may be optimal. The idea underlying Boadway andKeen is closest to ours.

The paper is organised as follows. Section 2 develops the basic framework of taxevasion and focuses on the evasion-concealment decision in two-class framework:self-employed and "white-market" workers. Only the self-employed can evadetaxes. Both classes are able to save. The self-employed have the possibility ofsupplying parts of their labour on the white market. The income earned on thewhite market is non-evadable.

Section 3 solves the two-period economic equilibrium. The self employedand the "white" workers decide in period one how much to consume and howmuch to save, knowing the level of enforcement and rationally expecting thegovernment’s fiscal policy decision in the second period.

In Section 4 we examine two types of governments: (a) the government isrevenue maximising, and (b) the government is majority elected. We do notexplicitly model the relative costliness of using auditing or punishment asenforcement. Therefore auditing and punishment become equivalent measures, andwe refer to them simply asenforcement. We conclude the findings in section 5.The major results of this paper are:

(1) Regardless the objective of the government, maximum enforcement isnever optimal if the government cannot commit to future taxes. Thus, tax evasionacts as a disciplinary mechanism for fiscal policy.

(2) If the government is revenue maximising and if individuals areendowed with relatively low initial wealth the government tolerates more taxevasion in equilibrium. In these economies the tax rate and the revenue are lower.

(3) If the government is majority elected and future taxes cannot becommitted to then the greater the initial wealth of the self employed, the greateris the politico-economic equilibrium enforcement rate, and the greater is thesecond-period politico-economic equilibrium tax rate.

2. The Basic Framework of Tax Evasion

In this section we develop a framework which is rich enough to capture the

3

mechanisms we think are important in determining tax evasion and that allows usto pursue general equilibrium analysis.

(1) We distinguish between two classes of individuals: self employed and"white" workers, capturing the idea that self employed (in the "grey" sector) moreeasily can evade taxes as opposed to other groups in the economy. We will stillallow individuals to differ within each class, since we would expect fiscal policyin general to depend on distributional characteristics. We will draw a sharpdistinction by assuming that tax evasion and concealment can only be undertakenby the self employed, and that no income earned by the "white" workers can beconcealed or evaded. More precisely, the self employed have the opportunity toboth hide income from the tax authorities at a cost (concealment or "laundry") andto under report the non-concealed income (evasion). Both of these choices arecontinuous.

(2) To allow for flows of labour from the grey sector into the white (andvice versa) the self employed choose the number of hours worked in their ownbusinesses and on the white market.3 This captures the idea that the tax systemoperating in the official market affects the employment in the grey sector. Whenmaking her labour allocation choice (as well as leisure) the self employed knowsthe tax rates, the auditing probability and the fines, and also takes into account heroptimal choice of income evasion and concealment.

(3) We shall always have in mind a two-period economy, where investmenthas been made in the previous period, but we solve the equilibrium recursively,starting in the second period when all capital is fixed.4 Indeed we then look at atax-evasion economy very close to Allingham and Sandmo (1972). However, theeconomy we will use here will allow for a richer characterisation due to thefollowing extensions: (i) simultaneous evasion and concealment decisions (ii)choice of hours worked on white market and in own business (iii) decreasingmarginal product of labour in own business (iv) taxation of both labour and capitalincome.5 These extended assumptions are not of crucial importance for

3 A self employed faces a concave production technology (in labour) in his ownfirm but an official after-tax market wage invariant to his labour supply.

4 The self employed may save from period one to period two, but only in his ownbusiness. By this assumption we allow the groups "grey" and "white" to beseparated. Thus the self employed have no other capital income in period two.

5 We shall abstract fromincome-source misreporting(Yaniv (1990)). It will beassumed that of whatever income is declared the authorities can perfectlydiscriminate what is due to hours worked and what is due to investment, thisautomatically rules out the possibility of misreporting thesourceof income. If wewere to study both simultaneously, the problem becomes very complex and lessintuitive. We, for example, would need a differential punishment structure,

4

establishing thebasic argument of this paper, but they offer interestingimplications for the government’s optimal level of enforcement, and predictionsof what typeof economies would suffer (or benefit!) from higher degree of taxevasion.

2.1 The Self Employed

Entrepreneurs may choose how much to work in their own firm (the "grey"market) and how much to work on the "white" market. Hours in own firm aredenoted g and on the white market asm, and total hours as =g+ m. The selfemployed has access to a constant returns-to-scale production technologyf(kg, g),where kg is the capital saved by the self employed. The self employed mayconceal some income at a costC. Denote the fraction of income that has not beenconcealed ass, so the cost of concealment isC (1-s)f(kg, g) . Of the non-concealed income the self-employed declares a fraction,α, to the tax authorities(it is assumed that the tax authorities can determine from the reported income theproportions of labour and capital income). If the tax authorities detect tax evasion(this is with probabilityp) they detect all income evaded (but not the concealedone). The monetary punishment is a fraction,π, of non-reported income. Thefiscal structure consists of a flat capital income tax (at rateθ), a flat labourincome tax (at rateτ) and a lump sum benefit,b, equal for all individuals and allstates (detected/non-detected). The consumption of the self employed if notdetected is

and if detected

(1)

Given the savings made and given the hours worked, the individual chooses how

(2)

much income to conceal and how much to report. The objective is to maximiseexpected utility

presumably convex in each source of income misreported. Otherwise we wouldhave corner solutions: the self employed would either report all income as due tocapital or all due to labour, or possibly be entirely indifferent, why no interiorsolutions exist. Since our focus is on pure evasion and one-dimensional changesin the probability/punishment structure it seems entirely reasonable to abstractfrom income source misreporting. Combining the two would indeed be aninteresting research ideaon its own, since sofar it has not been done. (Yaniv(1990) compares two cases, actually not combining them).

5

We shall make some simplifying definitions. Define a "composite" tax rate as

(3)

i.e. the effective marginal tax on income from self-employment (which of course

(4)

depends on the individual’s choice of labour supply and savings). Define the after-tax income, if all non-concealed income is declared, as

i.e. the after-tax income if the individual is not evading (only possibly concealing).

(5)

2.2 The Evasion-Concealment Decision

The decision to conceal and underreport is taken when all economic activity hasbeen undertaken, i.e. after supply of labour in own business and on the whitemarket. So taking g and m as giventhe individual choosesα and s so as tomaximise (3). The first-order conditions imply

Equation (6) is the standard Allingham and Sandmo (1972) result, the marginal

(6)

(7)

change in expected utility due to a marginal change in reported income shall bezero.6 Equation (7) tells that the marginal cost of concealment shall equal themarginal benefit, i.e. the marginal tax rate on income from self-employment.Notice that the concealment decision does not directly depend on the evasiondecision (possibly only indirectly via the labour supply decision).

2.3 The Labour Supply Decision

Given the individual’s optimal reporting strategy, the individual chooses hisoptimal occupation, i.e. the fraction of labour to devote to the white market andthe fraction to the grey market. There are two necessary conditions for an interioroptimum

6 Or in other words, the marginal utility is orthogonal to the marginal return.

6

(8)

(9)

Equation (8) tells that the official market wage (after tax) times the marginalexpected utility of consumption (evaluated at optimum evasion and concealment)equals the marginal utility from leisure. Equation (9) is the condition for selfemployment and states that the expected marginal benefit (in consumption units)from supplying labour in own business equals the marginal utility from leisure.We may further rewrite (9) by using (8) and (6) to obtain

This condition is more transparent than (9). It does not involve any marginal

(10)

utility terms and thus is a condition for efficiency in self employment. The outsideafter tax wage rate should equal the after tax marginal product of self employment(as if all income was declared) minus a term reflecting the possibility ofstrategically affecting the mixture of capital and labour income. If this latter termis zero there are no such strategic possibility and we have a very simple efficiencycondition. We see that the term is zero if the marginal (composite) tax rate onself-employment income is unaffected by the hours worked in own business. Thishappens ineither of two cases:

(a) the capital income tax equals the labour income tax in self employment:τ=θ,(b) the production function is Cobb-Douglas.

Thus, if either (a) or (b) is fulfilled the labour supply decision in own business isindependent of the evasion-concealment decisions, and thereby also independentof the auditing-punishment structure.

2.4 Tax Revenue from Self EmployedBy assuming that the auditing probability is the fraction of self employed actuallyaudited (Kolm (1973)) the tax revenues collected from the self employed are7

or after some manipulation

(11)

7 Provided that the self employed aggregate into a "representative individual", thiswill always be the case under certain conditions, see further Section 3.

7

We can verify that the tax revenues are increasing inp, the auditing rate.

(12)

3. The Two-Period Economy

3.1 AssumptionsThis section will make some simplifying assumptions in order to gain tractability.

A1 Individuals’ PreferencesIndividuals live for two periods. The utility function for each individual(regardless employed or self employed) is given by

(13)

A2 Individuals’ EarningsSelf employed choose how much to invest in their own firm, and in period 2 howmuch to work in their firm and how much to conceal and declare of their income.They face the constraints

where c=Y if not detected,Z if detected.8 The employed on the white market

(14)

(15)

constitutes the majority of the population (their fraction of the population isdenotedn>1/2. They face the constraints

whereP≡ 1+(1-θ)r andω ≡ (1-τ)w are the after-tax returns from capital and labour

(16)

(17)

respectively, andb is the lump-sum benefit. Individuals will be allowed to varyin their wage incomes (w andW).

A3 Production and Concealment Technologies in Grey MarketThe production technology in the grey market is assumed to be of the Cobb-

8 WhereY andZ are defined as in equations (1) and (2) respectively.

8

Douglas form9 and the cost of concealing grey income,Ig, is assumed to bequadratic

(18)

(19)

A4 Production Technology in the White MarketThe production technology in the white market is assumed to be linear, i.e.

(20)

A5 GovernmentThe government either

(a) maximises revenueor

(b) implements the policy resulting from majority voting.

3.2 Second Period Economic Equilibrium

Self EmployedFor log-utility the condition for optimal evasion, equation (6) becomes10

where

(21)

is defined as the tax payment if all non-concealed income is reported. It is

(22)

interesting to notice thatM/m is the ratio of after-tax income (if nothing is evaded)to tax payment (if nothing is evaded), and thus represents the inverse of"hypothetical" tax pressure. If the tax pressure is high,M/m is small and thereforeα is large, i.e. a larger proportion of income is evaded. Then, consumption if notdetected, consumption if detected, and indirect utility are

9 We have established the role of Cobb-Douglas specification in the previoussection. It will make labour supply in own business independent of the evasionand concealment decisions, even when differential taxation is allowed for.

10 Recall that we may writeY = M + (1-α)Tsf andZ = M - (1-α)πsf.

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respectively, whereΩ ≡ ln(1+π/T)+ (1-p)ln[(1-p)T/π] + plnp. M may be interpreted

(23)

as the individual’s income, to be allocated across two risky states. Because theutility function belongs to the HARA-family (Linear Risk Tolerance), theindividual allocatesconstantfractions of her income across the states (the fractionsare independent ofM).11 It should also be noted that the certainty equivalent isMeΩ, therefore we may analyze the individual’s concealment-, consumption-,labour supply-, and savings- decisions by looking at the certainty equivalent.

The quadratic cost function gives the optimal concealment decision,equation (7), as

so the concealed cost in optimum isC * = T 2/(2γ). Then

(24)

and

(25)

Finally the Cobb-Douglas specification gives the composite tax rate as

(26)

and optimal labour supply in own business, equation (10), as

(27)

Optimal labour supply on white market, equation (8), imply

(28)

where

(29)

turns out to be the after-tax return on self-employed capital.

(30)

Therefore

11 This is linear Engel curves instate space.

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It should be noticed that none of the quantities (28)-(32) are directly affected by

(31)

(32)

(33)

the auditing-punishment structure.

Employed on white marketIn the second period labour supply is chosen as

with solution

(34)

We then obtain the "white" worker’s indirect utility

(35)

whereΩw ≡ ηlnη - (1+η)ln(1+η).

(36)

Tax ReceiptsThe tax receipts,G, will be the expected collection of taxes from the selfemployed plus the collected taxes from the "white" workers

where

(37)

We shall later on takeδ as a measure oftoleranceof tax evasion.

(38)

3.3 First Period Economic Equilibrium

Self EmployedSince

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we have

(39)

(40)

Employed on white marketThe optimal savings is found as

with solution

(41)

(42)

4. Fiscal Policy

4.1 The Revenue Maximising Government: Capital-IncomeTaxation

In this section we shall assume that the government has only one fiscal instrument,the capital income tax, with the objective to maximise its tax revenues, i.e.

A5(a) GovernmentThe government maximises revenue with respect to the capital-income tax,leaving no lump-sum transfer (b=0).

The tax receipts become

We shall focus on two regimes, one in which the government credibly can

(43)

commit to future taxes, and one in which it cannot. We will examine thedesirability of tax evasion, in particular what audit rates and punishment rates thegovernment would choose. Since, within the framework outlined above, the auditrates and punishment rates are complementary instruments, and we have saidnothing about the relative costliness of using them, we shall focus on a measureof how much evasion is tolerated. As a bench mark we take the case when thegovernment does not tolerate tax evasion at all. This is the situation when eitherthe probability of detection is one or when the punishment is infinite (and

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probability of detection goes to zero), the latter case is usually referred to as whenwe "hang tax evaders with probability zero," (Kolm (1973)). In these two casesδ is zero. The following definition seems natural

Definition 1 Tax evasion is said to benot toleratedwhenδ=0. The greater valueof δ the more tax evasion istolerated.

Lemma 1 The tax receipts from self-employed when all non-concealed income isdeclared, m, is a concave function of the capital income taxθ, for 0≤θ≤2.

Proof: See the appendix.

The significance of Lemma 1 is that if all evasion is eliminated, we would expectthat there exists an interior maximum to the revenue maximising problem.However, since "white" workers’ capital income is inelastic we may have asituation where the maximising tax rate is large enough to completely discouragesavings of both groups in the first period. In such a situation the commitmentproblem is severe and no capital exists in the second period and consequentlygovernment revenue is zero. This may happen when the "white" sector is largerelative to the "grey" (whenn is large), and when capital is highly productive(when r andε are large). For example, for the self employed to save we clearlyrequireεθ<1.

Proposition 1 In a one-period economy government revenue is maximised atδ=0(i.e. when evasion is not tolerated).(a) If there is no "white" sector, the maximising tax rate is less than 100%, exceptwhen concealment is infinitely costly, then the tax rate equals 100%(b) If there is a "white" sector and concealment is infinitely costly the maximisingtax rate is greater than 100%.(c) If there is a "white" sector sufficient for maximised government revenue to begreater than zero is that r< 1, ε < 1/2, β(1+η)W≥ wL/(1-r) and

all hold.

(44)

Proof: SinceM is positive ∀ θ and independent ofδ we have mδax (1-n)(m-

δM)+nrkw = (1-n)m+nrkw. Next, maximising with respect toθ gives the first-ordercondition

(45)

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If there is no "white" savings (n=0) we havemθ θ=1<0, (when γ<∞) and byconcavity ofm(t) (Lemma 1) the value ofθ is too high. Whenγ→∞ we havemθ θ=1=0. When there is "white" savings andγ→∞, we must havemθ<0 andconsequentlyθ>1. To prove (c) we need to show that there is an interior solutionwhereθε<1 and savings are positive. Supposeθ=2 and concealment is infinitelycostly, then (45) becomes

By using (40) and (42) we have thatkw>kg at θ=2. Condition (44) is the same as

(46)

saying rg/(1-2ε)≥rn/(1-n). Then clearly (46) is negative atθ=2, thereforeθε<1.Sinceβ(1+η)W≥ wL/(1-r) white market savings are positive atθ=2 and thereforekg is also positive, and so government revenue. QED

Part (c) gives the conditions for savings being positive at interior optimum for thecapital tax. The conditions are only sufficient. If they were violated we could havea situation where the government is unable to raise any revenue at all (underdiscretionary fiscal policy).

Furthermore, we see that if capital is fixed the government cannot do better thaneliminating tax evasion.

Lemma 2 The following inequality holds(47)


We have, obviously, after-tax income (if nothing is evaded)M as a decreasingfunction of the capital taxθ: Mθ<0, but as Lemma 2 states itselasticity (inabsolute value) is always smaller than one. This is so because the individualresponds to changes in the tax by varying her labour supply.

Proposition 2 In a one-period economy the tax rate is higher whenδ=0 thanwhen evasion is tolerated (i.e. whenδ>0).

Proof: Denote asθ′ the tax rate that maximises government revenue whenδ=0,then (1-n)mθ(θ′)+nrkw=0. Denote asθ* the maximising tax rate whenδ>0, then

From the definition ofδ [equation (38)] it follows that

(48)

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Using (49) in (48) we have

(49)

By Lemma 2 we see that the right-hand side is positive and therefore (1-n)mθ(θ*)

(50)

+nrkw>0 = (1-n)mθ(θ′)+nrkw, and by concavity ofm we haveθ* < θ′.QED

Proposition 2 shows how the possibility of tax evasion limits the effectiveness ofthe capital income tax. Tax evasion lowers the value of the Laffer optimal tax rateand therefore may act as a credibility mechanism in policy making in a dynamiceconomy. But let us examine the optimal punishment and auditing rates when thegovernment isable to credibly commit to future the tax rate.

Proposition 3 When the governmentcan commit to future taxes, the governmentrevenue is maximised atδ=0, with a tax rate lower than the one in Proposition1.


Clearly, if the government can commit to future taxes it wishes to "hang evaderswith probability zero." It should be noticed that the precommitted tax rate islowerthan the one obtained in the static problem (this is due to the time-inconsistencyof optimal policy).

Proposition 4 When the governmentcannot commit to future taxes, the revenueis maximised atδ>0, i.e. evasion is tolerated.


In this case tax evasion is actuallydesirable since it acts as a credibilitymechanism for fiscal policy in the future.

Proposition 5 In economies where individuals are endowed with relatively lowinitial wealth, where the white-market return on capital is large, and where thenumber of white workers to the number of self-employed is large, the governmenttolerates more tax evasion in equilibrium.


This suggests that the time-inconsistency problem is more severe in low-incomeeconomies. When the number of individuals that cannot evade taxes is large, the

15

greater the tolerance towards evasion has to be, i.e. the more the government hasto rely on the relatively few evadors to make the tax base elastic.

4.2 The Revenue Maximising Government: Uniform IncomeTaxation

Here we shall assume that all income is taxed at a uniform rate. Still the objectiveis revenue maximisation, i.e.

A5(a′) GovernmentThe government maximises revenue with respect to a uniform income tax,leaving no lump-sum transfer (b=0).

The tax receipts are as in (37) whereθ=τ=T.

Lemma 3 The tax receipts when all non-concealed income is declared is aconcave function of the income tax T.

Proof: Follows by twice differentiating (37), whenθ=τ=T, with respect toT using(29), (30), (32), and (35). The derivative is always negative. QED

Here, because the tax is levied on labour income as well, the tax base becomesmore elastic, and therefore the tax receipts is always a concave function of theincome tax rate.

Similarly to section 4.1 we have

Proposition 6(a) In a one-period economy government revenue is maximised atδ=0 (i.e. whenevasion is not tolerated).(b) In a one-period economy the tax rate is higher whenδ=0 than when evasionis tolerated (i.e. whenδ>0).(c) When the governmentcan commit to future taxes, the government revenue ismaximised atδ=0.(c) When the governmentcannotcommit to future taxes, the revenue is maximisedat δ>0, i.e. evasion is tolerated.


The above results (section 4.1 and 4.2) were derived for therevenue maximisinggovernment. We will now turn to a rather different (and perhaps more plausible)

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objective: the government objective determined in political equilibrium.12

4.3 Endogenous Redistributive Income Taxation

Here we shall assume that all tax receipts are redistributed lump sum to all"white" workers. We analyse the case of uniform income taxation.

A5(b) GovernmentThe income tax is chosen through a majority vote in the last period, andall tax receipts are distributed lump sum to all individuals who are not selfemployed.

The political equilibrium we shall rely on, is the median-voter equilibrium.13

Proposition 7 In a one-period economy the tax rate that cannot loose undermajority rule is less than the revenue maximising tax rate. The lower the wageand the lower the capital of the median voter the higher is the tax. If alsoevadability is voted upon the outcome isδ=0 (i.e. when evasion is not toleratedin political equilibrium).


By assuming that self employed are in minority the median voter is a "white"worker. The median wishes to maximise the size of the redistribution towardsherself. The size of the redistribution is maximised when no evasion is tolerated.

Proposition 8 With precommitted enforcement, the tax rate that cannot looseunder majority rule is higher whenδ=0 than when evasion is tolerated (i.e. whenδ>0). Furthermore,(a) the less capital the median voter owns in relation to the average for whiteworkers, and(b) the less the average capital for white workers is in relation to the capital ofthe self employed, and(c) the smaller the wage of the median in relation to the mean,the higher is the tax rate.

12 Endogenous taxation.

13 We do not address the question of how the equilibrium is reached.

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The tax rate being higher when evasion is not tolerated confirms the possibilityof evasion playing a role in limiting the effectiveness of fiscal policy. The role ofredistribution is clear, the tax is greater the greater distance between the mean andthe median among the group of white workers. Also there may be redistributionfrom the self employed to the white workers.

Proposition 9 When the future tax ratecan be committed to, full enforcementcannot loose under majority rule,δ is zero. The tax rate that cannot loose undermajority rule is lower than the one in Proposition 7.


Proposition 10 When the future taxcannot be committed to,δ is positive inpolitico-economic equlibrium and the second period tax rate is lower than the onein Proposition 7.


Thus, even though evaders are in minority tax evasion is tolerated in politico-economic equilibrium.

Proposition 11 The smaller the initial wealth of the self employed, and the lessthe initial wealth of the median in relation to the mean for white workers, thelower is the politico-economic equilibrium enforcement rate.


5. Summary and Conclusions

This paper provided a theory where the size of the inspection authority and thesize of the fines evolve endogenously. We found that if a society cannot committo future taxes it may gain from committing to a small Inland Revenue Serviceand small punishments for tax evasion. The possibility of the public evading taxeslimits the effectiveness of capital taxation. By setting detection probabilities andpunishment relatively low, the government indirectly commits itself not to taxcapital income too heavily in the future. The paper analysed the factorsdetermining the level of tax evasion when taxes and enforcement are endogenous.In particular we found that societies with low level of initial wealth of the selfemployed, and more right-skewed distribution of wages, would experience a

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higher degree of tax evasion in politico-economic equilibrium.The paper contrasts sharplycommitmentversusdiscretionin fiscal policy;

either the government could commit to future policy (and maximum enforcementwas desirable) or the government could not commit to future policy (and evasionwas desirable). A natural extension of this model (which has not been undertakenyet) could be to allow for cases where the economypartially may commit tofuture taxes. We think that even in this case the tax evasion can still act as adisciplinary mechanism, but we would expect that it to be used to a lesser extent.The intuition would be that societies with more commitment in fiscal policy relyless on tax evasion and would have higher enforcement rates ceteris paribus.However, we would not expect these countries having higher taxes per se (becauseof their partial commitment).

The paper is closely linked to thestrategic-delegationliterature in theresults. In the terminology of the strategic-delegation literature the governmentcould benefit from delegating auditing and punishment decisions to a "soft" InlandRevenue Service and "soft" courts. Analogously to this literature this paper findsthat a society may benefit from making the IRS and courtsindependent(or lesssubject to government intervention). A further extension of the paper could be toallow for a rather different way of limiting the auditing authority. This could bedone by consciously appointingcorrupt officials. Then we would find that thissurely reduces the probability for a tax evader in getting fined and works in thesame way as limiting the size of the inspection authority. Thus the government inthis case would consciously allow corruption and find it desirable.

The paper studiesincome taxes, ignoringexpenditure taxes. For expendituretaxes the time-inconsistency problem is generally less severe, and there is lessgain from committing to lower rates of enforcement. Thus, we would expect VATevasion to be punished and monitored to a greater extent than income tax evasion.

We have analysed the case when the enforcement is a variable completelyfree of choice to the government. However, in some societies the enforcementmay not be a free choice variable, due to other sources of inefficiencies ortechnical problems (e.g. in developing countries) so the level of evasion may inthese cases be inexcessof what is desirable from a credibility point of view.14

We should not claim that tax evasion is the best way of solving time-inconsistency problems, other measures may be superior. However, in societieswhere these measures are not available, perhaps evasion is one of the only few"solutions."

14 For example, to operate the enforcement, punishment needs to be exercised. Inorder to do this the auditor must be able to provide evidence of evasion, whichmay be difficult in societies where collection of data is difficult or where manytransactions remain unrecorded.

19

Appendix

Proof of Lemma 1The first derivative ofm with respect toθ is

and the second derivative

(51)

which is negative as long asθ≤2. QED

(52)

Proof of Lemma 2DifferentiatingM with respect toθ gives

Premultiplying byθ (and rearranging somewhat) gives

(53)

but the term within curly brackets equalsM - [ωL + (εθ)2/(2γ)](1 + η)-1, then

(54)

or by addingM on both sides

(55)

So equivalent of provingM+θMθ>0 is to prove

(56)

The equation above is convex inθ. By evaluating at the minimum with respect

(57)

to θ it can be verified that the minimum value is positive. QED

Proof of Proposition 3Government revenue is

SinceM>0 ∀θ,kg, G is maximised atδ=0. The first-order condition forθ** to be

(58)

maximising is(59)

20

wheremθ* is short hand formθ(θ*,kg(θ*)), etc. Then clearly

Then we must haveθ*<θ′. Suppose the oppositeθ*>θ′, then we must havekg(θ*)

(60)

< kg(θ′) andkw(θ*) < kw(θ′). Then we havemθ(θ*,k(θ*)) < mθ(θ*,k(θ′)) < mθ(θ′,k(θ′)),(the first inequality follows frommθk>0 and the second bymθθ<0), andrkw(θ*) <rkw(θ′). This is a contradiction. QED

Proof of Proposition 4We solve recursively, i.e. the second period first

Necessary for optimum

(61)

or

(62)

where

(63)

Let ξ denote a parameter reflecting the desired compliance, satisfying15

(64)

and ρ′(ξ)>0, δ′(ξ)<0. This enables us to writeθ=Θ(ξ,k). Viewed from the first

(65)

periodk=k(θ), thereforek=k(Θ(ξ,k)), and we may writek=k(ξ). The first-periodproblem is

Note that (1-n)[mΘ-δΘM-δMΘ]+nrkw=0, then the necessary condition is

(66)

where functional arguments are suppressed. Sinceδξ(Θ,ξ)=0 at δ=0 we have

(67)

which is negative, sincekξg<0 andkξ

w<0. QED

(68)

15 An example is fixingπ, to say unity, and lettingξ=p.

21

Proof of Proposition 5From the proof of Proposition 4 we have

Sincemk, Mk, kξg, kξ

w andδξ are all independent of the level ofW, and thatmk, M,

(69)

Mk are positive, then ifM is large thenδ is small and vice versa.QED

Proof of Proposition 6Proposition 6 is proven in exactly the same way as Propositions 1-5.

Proof of Proposition 7Using (34) and optimising with respect toT gives16

The first term is marginal utility of consumption and is positive. Thus, at

(70)

individual i’s most preferred tax rate the following holds

By concavity ofb(T) (Lemma 3) it follows from (71) that∂T/∂ i < 0 and∂T/∂ki

(71)

< 0. Single peakedness of preferences follows by concavity ofb(T), then theMedian Voter Theorem applies. At the revenue maximising tax rateb′(T)=0, butfor any majority elected tax rateb′(T)>0, thus the majority elected tax is smaller.Finally, evasion will just redistribute from white workers to self employed, thusall white workers agree uponδ=0. QED

Proof of Proposition 8Denote as

the tax receipts collected from labour income. It is easily verified thatλ(T) is

(72)

concave inT. Denote asT′ the tax rate that maximises the median voter’s utilitywhenδ=0, then (1-n)mT(T′)+nrkw+λT(T′) = rki+wi i. Denote asT* the maximisingtax rate whenδ>0, then

16 Since optimisation also takes place overi we can, by the envelop condition,ignore the terms involving labour supply.

22

Suppose instead thatT*>T′ is true. Then by concavity (1-n)mT(T*)+nrkw+λT(T

*) <

(73)

rki+wi i, which combined with () gives

but this is a contradiction since the bracketed term can be verified to be positive.

(74)

Finally, because of concavity ofb(T) also whenδ>0, T* is greater the smallerrki

andwi i. Next, notece that

and rewrite (73)

(75)

where

(76)

SinceZT(T) > 0 the right hand side of () is large whenT* is large. Examining the

(77)

left-hand side of () proves (a)-(c). QED

Proof of Proposition 9(Scetch of proof) An individual specifying her preferred tax policy in perod 1 tobe implemented in period 2 will find it optimal to set17

For any level ofT b(T δ=0) > b(T δ>0), sinceT is precommitted to. Then white

(78)

workers would be better off atδ=0, since regardless the desicive individual therewould be greater redistribution from the self employed. QED

Proof of Proposition 10Solving recursively, i.e. the second period first, we have the first-order conditionfor the decisive individual as in (73). As in the proof of Propositon 4 letξ denotea parameter reflecting the desired compliance. Then (73) gives the optimal tax asa function ofξ, and of the capital stockski, kw, kg, i.e. T=Φ(ξ, ki, kw, kg). Viewedfrom the fist period we may writeki = ki(ξ), kw = kw(ξ) kg = kg(ξ). Then (after

17 Becasue of the envelop conditions.

23

using all envelop conditions) optimising with respect toξ in the first period givesthe first-order condition (which is very similar to (67))

Notice that by (29) and (35)∂ m/∂kg < 0 and∂ w/∂kw < 0. Sinceδξ(T,ξ)=0 atδ=0,it can be verified (by using (26) and (35)) that (79) is negative atδ=0, implyingthat compliance is too high. QED

Proof of Proposition 11(Scetch of proof) Using (79) in the same way as using (69) to prove Proposition5 establishes the result. The part concerning the distribution follows fromProposition 9, since the second period tax is greater. A greaterT in (79)establishes the result. QED

24

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tax evasion as a disciplinary mechanism for fiscal...

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