Taxation 3

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3. Tax Compliance

3.1 Tax Avoidance3.2 Tax Evasion

3.3 Corruption and Extortion3.4 Literature


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The Effects of Tax NoncomplianceTax avoidance means making use of legal loopholes in the tax codes. Usuallythis requires costly services of specialized tax consultants and is, thus, onlyamenable to wealthy taxpayers. Tax avoidance encompasses making use of taxcredits, itemizing expenses, making use of choosing the legal form of enterprises, choosing ones residence, choosing ones profession, etc.

Tax evasion is the illegal concealment of parts of the tax basis, or theconcealment of taxable economic activities altogether. If it is discovered, theconvicted taxpayer has not only to pay the evaded taxes, but also a fine, or haveeven to face being sentenced to jail. Of course, if tax evasion were discoveredwith certainty, it would not occur. Rather there is a probability of less than onethat it is discovered; consequently, taxpayers strategies depend on their risk

attitudes.Corruption and extortion occurs when dishonest tax inspectors enter thescene. They need to be bribed to report understated taxes to their superiors; thisis corruption. On the other hand, they may extort taxpayers to pay them a bribeto induce them to abstain from reporting overstated taxes to their superiors; this

is extortion.


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Tax noncompliance winds up resources and causes anadditional deadweight loss of taxation.

Tax noncompliance imply higher taxes to secure a given taxrevenue. This reinforces deadweight loss, as taxes becomemore distorting.

Tax noncompliance also affects tax incidence and changes

tax progression. In the majority of cases it works in thedirection of making the tax system less progressive (moreregressive) as it benefits the upper income echelons.

Tax noncompliance may also affect occupational choice,

human capital investment, and labor supply.Tax enforcement is also a problem of law enforcement.

Hence, tax compliance is a central issue of the economics of taxation.


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3.1 Tax Avoidance Assume first that income y is exogenous (or that labor supply is fixed), assumea tax schedule T(.) and assume that is a legally avoided part of incomewhich reduces the tax base. Furthermore, assume that C() is the cost of avoidance. Assume first that C() is increasing and convex, that is, additionallegal reductions of the tax base require higher cost. Then the first-order condition of tax avoidance results from maximizing the next expression withrespect to :

This yields the first-order condition:

(1)

Thus, under a graduated (progressive) income tax the rich will avoid more taxesthan the poorer taxpayers. In case of a flat tax all taxpayers declaring incomeabove the personal allowance will avoid the same amount of income since themarginal tax rate is a constant. Hence, richer taxpayers avoid a smaller proportion of their income than the poorer taxpayers, which makes taxation in

effect more progressive than without tax avoidance.


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For C() increasing and concave this implies that tax avoidance has economiesof scale (e.g., because an efficient tax consultant may have a high fixed cost).Then marginal avoidance cost may be too high for poorer taxpayers, primarily for

a graduated income tax, but possibly also for a flat tax. For richer taxpayers itpays to avoid all taxes irrespective of the tax schedule.

Of course, such a model lacks realism. We may thus assume that C() is ogival-shaped [counter S-shaped]. This means that C() is first concave and, after apoint of inflection, convex. Under this model, it does not pay for poor taxpayers toavoid taxes, but beyond the level of income at which T(y - )=C(), all taxpayersavoid the same amount of income under a flat tax. Under a graduated(progressive) tax, the richer taxpayers avoid more income from taxation. Thisscenario seems to be the most realistic model.

(2)

(3)


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In this model, the taxpayer decides simultaneously on his or her labor supply and theamount of labor income to be avoided from the tax base. The cost function of taxavoidance now depends on labor income and the part of it to be avoided: C(w ,). For short, let us write C 1 for C/w, C 2 for C/ , and so on.

As tax avoidance involves cost, we have unambiguously C 2>0 . The sign of C 1 is notclear a priori. When it is easier to avoid a given amount * for higher incomes, wehave C 10 . It is plausible to assume C 10 would be the appropriate

assumption.

As to the second derivatives, C 22>0 means that the marginal cost of tax avoidance isincreasing. C 11>0 holds when the avoidance -facilitating property of true labor income, i.e. C 1, has diminishing returns. C 21=C 12 is crucial, as it captures theinteraction between true labor income and tax avoidance. C 21


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(4)

(5)

Condition (5) is the well-known condition of our initial model: tax avoidance shouldbe expanded until its marginal cost equals the marginal tax rate. Condition (4)corresponds to the usual one that labor supply is optimal when the marginal rate of substitution of labor for income, -U

2 /U

1, equals the net-of-tax wage rate. The critical

aspect of this more general model is that the term ( -wC 1) changes the net-of-taxwage rate. When C 10 , the net-of-tax wage rate is diminishedby the waning possibility of avoiding taxes for higher incomes. A further complica-

tion in this analysis comes from the fact that C 1 may itself depend on , whichmeans that the budget line in the ( v, )-diagram is no longer necessarily straight.

This model, therefore, combines the more technological effects of tax avoidance (of the former model) with the behavioral effects of income and labor preferenceswhich are subjective traits of the taxpayer. This makes the analysis somewhatcomplicated and dependent on the parameters of taxpayer reaction. For further analysis see Slemrod (2001) and, more informal, Slemrod and Yitzhaki (2002).


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Tax evasion is the (illegal)attempt of a taxpayer toestablish the official promise

of tax equity on an individualbasis.

Helmar Nahr


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Taxation Economics: Short Account of Sixth Lecture

Asymmetric information: optimum income taxation: generalcase (marginal tax rate lower for high population density; lower for small value of shadow price of self-selection constraint;lower for high-productivity groups; lower for higher supplyresponse; higher for higher marginal utility of consumption)

Tax noncompliance means higher excess burden of taxation Tax avoidance: marginal tax rate equal to marginal costs of

avoidance; in the more general model the impact of income on

costs of tax avoidance is also given attention: it is either asubsidy or an additional cost We started to discuss tax evasion Crash course on von Neumann Morgenstern utility functions


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3.2 Tax EvasionTax evasion means that part of the income (or of some other tax base) is notdeclared. It is illegal and implies, if discovered, a fine which can, in extremecases, also imply jail. We follow the basic paper by Allingham and Sandmo(1972).

Let y denote true income (income is supposed to be exogenously given or issupposed to result from a fixed labor supply), x declared income, t aproportional tax rate, the probability of tax audit (which will disclose trueincome), f the penalty rate on undeclared income (y-x), where f>t , and let U( .) denote the taxpayers von Neumann -Morgenstern utility function.

income if no tax audit income in case of tax audit


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(2) implies that the marginal utility of the saved expected tax from declaring noincome is less than the marginal utility of the residual income after the fine incase of tax audit. Hence, it pays to declare more income. (3) means that, at the

point where the true income is declared, the expected fine is less than the taxrate. Hence, it pays to declare less than full income. Hence, interior solutions arewell defined; we will concentrate on them in the following.

For further analysis we make use of the Arrow-Pratt risk aversion measures,absolute and relative risk aversion

!


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y and


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By decreasing absolute risk aversion we have R A(v)


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This shows that, as true income varies, the fraction declared increases, staysconstant, or decreases as relative risk aversion is an increasing, constant, or decreasing function of income.

Now differentiate (1) with respect to t . This yields

The second term is negative; the first term is positive, zero or negative according asabsolute risk aversion is decreasing, constant, or increasing. For decreasingabsolute risk aversion there is no clearcut hypothesis as to the relationship betweenreported income and the tax rate.


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We can regard the two terms in (8) as the income effect and the substitutioneffect, respectively. The latter is negative, because an increase in the tax ratemakes it more profitable to evade taxes on the margin. The former is positivebecause an increased tax rate makes the taxpayer less wealthy, which reducesboth v and z for any level of x, which, under decreasing absolute risk aversion,tends to reduce taxation; this tends to increase declared income.

Differentiating (1) with respect to the penalty rate f yields:

Both terms are positive so that an increase in the penalty rate will alwaysincrease declared income.

Differentiating (1) with respect to the audit probability yields

This derivative is positive: an increase in the audit probability increases declaredincome.


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Yitzhaki (1974) has argued that some of the Allingham-Sandmo results are due totheir assumption that their fine applies to the difference between true anddeclared income, (y-x) . However, when the fine is imposed on the evaded tax

(which is the case in most countries), then some of the Allingham-Sandmo resultschange. Yitzhaki states the following problem: the taxpayer chooses x tomaximize


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These are the effects of a more realistic penalty function.


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Allingham and Sandmo analyze also the dynamic case: tax returns are filed atdiscrete times and individuals live infinitely. If tax evasion is discovered in aperiod, all past tax returns are corrected and the full tax amounts are charged tothe taxpayer. We do not go into details. The basic result is that the optimal

strategy is to declare more and more income as time proceeds because the pastevaded taxes accumulate. Once full income report has been achieved, there is nomore danger of discovering the past sins of tax evasion.

Later research has endogenized labor supply into models of tax evasion. Withlabor supply in the model, the effects of the enforcement variable all become

ambiguous, which result from the backward bending labor supply curve.Concerning optimal audit rules, several models suggest cut-off rules, which definea threshold value of income and a policy to audit any report below the thresholdwith probability and leave all tax returns above this threshold unaudited. Theprobability is chosen to be just large enough so that all taxpayers with trueincomes below the threshold report honestly. All taxpayers with true incomesabove the threshold report the threshold and pay taxes accordingly. Models havebeen proposed with a multitude of thresholds according to the variousprofessions.

In addition to theoretical work, many field studies and experimental studies werecarried out in the area of tax evasion. For a survey of this work see Andreoni,

Erard, and Feinstein (1998).


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3.3 Corruption and ExtortionWe consider a model by Hindriks, Keen, and Muthoo (1999) of the encounter

between a taxpayer and a tax inspector, both potentially corruptible.Remark : A method of tax collection throughout most of recorded history hasbeen tax farming : the tax inspector pays the government a fixed fee in returnfor the right to retain all revenue legitimately collected. This is the extreme formof a commission for the tax inspector.

The model is a three-stage game.Stage 1 : The government announces the tax scheme, consisting of:

The government does not know y , but only its distribution; the tax inspector getshis or her reservation wage anyway it is normalized to zero. Both I and P are

risk neutral.


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Stage 2 : Income reporting and appeal.

i. The taxpayers income y becomes common knowledge of the taxpayer andthe tax inspector. They bargain according to a game form with two outcomes:

ii. they reach an agreement (x,B), such that the tax inspector I certifies to thegovernment that the true income is x , and the taxpayer P pays him a bribe B ;

iii. they fail to reach an agreement; I unilaterally reports z ; as there is noagreement, no bribe is paid. The taxpayer P is given the opportunity toappeal against the income z reported by I . Appeals are always successful:P s true income is revealed and the liability restored to the correct level. Butappealing incurs a fixed cost for P of 0 .

Stage 3 : Audit by an honest tax attorney.

With probability , 0<


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Bargaining equilibrium :

We start by solving the game by P s strategy as to whether or not to appeal when noagreement was reached. P will not appeal when

Hence it can never be in the interest of the tax inspector to over-report P s income

such that P will appeal.


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In case of no agreement the tax inspector will maximize the expected payoff such that the constraint (3) is satisfied. Call this report z . Then expectedequilibrium payoffs in the event of no agreement are:

We call them disagreement payoffs .

When I and P reach agreement , an agreement ( x,B ) is Pareto efficient if x maximizes the surplus

Note that the surplus is independent of the bribe, which simply determines itsdistribution between I and P .


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Suppose x maximizes (6). This implies

as z is also a feasible value for (6) and may be agreed upon if it maximizesS(x,y) for x =z . [This unlikely case may occur if the commission to the taxinspector is so high that it pays for him to pay a bribe to P to accept over-reporting of his income.]

Hence, (7) shows that it is always possible to find a bribe such that

for i=I,P . Both fare better than in the disagreement game.

Thus, the tax inspector and the taxpayer reach agreement on an expected

surplus-maximizing income; they report x (y) and a bribe B (y) whichmakes them no worse off than under a disagreement payoff. Note that thedisagreement payoffs and the possibility of appeal have no impact on theincome report, but affect the negotiated bribe.


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Corruption, extortion and tax evasion

Tax evasion means under-reporting of income, x (y)


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Hence, Proposition 1/(iv) shows that tax evasion implies corruption in this model.However, the converse is not true. There exist schemes for which (for some y )B (y)>0 even though x (y)=y . The reason is that a taxpayer confronted with a tax

inspector willing to over-report income will be willing to pay a bribe to preventover-reporting of income. The bribe is then a manifestation of extortion. [Reportedby Jain (1997) for India and by Klitgaard (1988) for the Philippines.] This situationis characterized by

Then we have a victim of extortion, while in the case

the taxpayer is an accomplice in evasion and corruption. [Note that victimscan emerge only if the inspector is paid a commission and if appeals aresufficiently costly to the taxpayer.]


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Taxation Economics: Short Account of Seventh Lecture

We discussed the Allingham-Sandmo model of tax evasion. Thefirst order conditions came from maximizing expected utility withrespect to declared income. Then we used this condition to checkhow declared income depends on the exogenous parameters of

this problem. Then we started to discuss corruption and extortion. A taxpayer

and a tax inspector may or may not reach agreement aboutpaying a bribe for incorrect tax reporting. There are possibilities of a master audit which reveals true income and the possibility of appeal by the taxpayer.

Furthermore, we discussed the properties of a bargainingequilibrium and the difference between corruption and extortion.


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Evasion- and corruption-proof tax rgimes

If penalties are unbound, the government can reach almost any goal . It is morerealistic to demand a limited liability constraint:

Note that the first restriction excludes tax farming [i.e., k


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For an intuitive proof suppose that the government has decided to use themaximum penalties (8) and (9) for misconduct. Then, if an audit discoversmisreported income, I and P jointly have to pay the amount [T+f I +f P-k- T ]=y . Theexpected payment is thus y. The collective payment on a truthful report is

[1- (y)]T(y). If the tax schedule is such that [1- (y)]T(y) is higher than y, it pays toreport x


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Interpretation of Proposition 2 : From (i) follows that T(y)/y , i.e., the averagetax rate must not be less than the probability of audit. We have also (1- )(y), i.e., the commission rate must not exceed (1- ). Proposition 2/(i) allows a

progressive tax schedule; but this requires that the commission rate (y) alsoincreases with the income reported:

A progressive tax schedule means that the tax saved by an under-statement of income is greater at higher incomes. Hence an increasing commission rate isneeded to counter the greater incentive to evade taxes. This is attained byraising the cost to the inspector in terms of foregone commission of connivingin an under-statement of income.

A constant commission rate requires a proportional tax schedule. [If wedispense with the assumption of a constant audit probability , then a constantcommission rate can also accommodate a progressive tax schedule if the auditprobability raises with rising income. This is often the case with the taxschemes of many countries.]

Proposition 2/(ii) states that I s expected payment over his reservation utility

must come entirely from commission payments.


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Proposition 2/(iii) states that it is only the collective fine f(x,y) that matters for evasion-proofness and revenue maximization. Surprisingly, the achievement of these objectives does not require to set penalties at their maximum feasiblelevels. It is enough that they be proportional to the extent of understatement,with the factor of proportionality being greater the less the audit probability is. Asmaller audit probability requires higher fines.

Are tax schedules satisfying Proposition 2 also corruption-proof? Obviously notbecause the possibility of extortion means that the threat of over-reporting mayenable I to extract a bribe merely to report the truth. The further requirement of corruption-proofness requires that z (y)=y .

If appeals are costless, i.e., =0 , corruption-proofness follows immediately. Themore realistic case is >0 . Eliminating extortion requires that the gain to I fromover-reporting is outweighed by the penalty which I incurs if the over-report isdiscovered, i.e., if


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Proposition 3 : A tax scheme satisfying all conditions of Proposition 2 is evasion-proof, corruption-proof, and revenue maximizing if it satisfies also condition (10).

These conditions are trivially satisfied by removing the incentive to over-report,

that is, paying no commission.

This is a tax scheme requiring a proportional tax schedule (a true flat tax) witha fixed wage for inspectors and with the tax rate equal to the probability of random audit. However, the price to preclude extortion by paying nocommission to tax inspectors means that one has to dispense with progressivetaxes. Progression invites evasion and corruption.

Can we allow for progression? In principle, this requires a two-tier taxschedule, proportional for the lower income strata, and progressive for thehigher income strata. This is stated in the next proposition.


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Interestingly enough, the fine in (ii) decreases with the extent of over-report (x>y). The fine condition can be re-written as

The first term on the left is the expected explicit penalty. The second comes fromProposition 2/(i):


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Consider

This means that the decrease (xy) ] in the collective payment

can be considered an implicit penalty. In case of over -reporting [ x=z>y ], itbecomes a real implicit penalty. Thus, the condition in Proposition 5/(ii) requiresthat either punishment is so great that the inspector will never over-reportor/and the cost of appealing is so low that P will choose to appeal. Thiscondition may hold even if the fine f(z,y) decreases with over-reporting becausethe implicit component of the punishment increases with z and compensates for the reduction of the ex plicit penalty.The proportional part in Proposition 5 is necessary to prevent extortion: Thepoor have little to evade. Paying inspectors a commission at low incomereports does little to combat evasion but creates the possibility of extortion.Hence, no commission should be paid on low income reports.


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3.4 Literature ALLINGHAM M. and S ANDMO A. 1972, Income Tax Evasion: A Theoretical Analysis,Journal of Public Economics, 1, 323-338.

ANDREONI J., E RARD B. and F EINSTEIN J. 1999, Tax Compliance, Journal of Economic Literature, 36, 818-860.G ALE W.G and H OLTZBLATT J. 2002, The Role of Administrative Factors in TaxReform: Simplicity, Compliance, and Administration, in G.R. Z ODROW and P.HINDRIKS J., K EEN , M. and M UTHOO A. 1999, Corruption, Extortion and Evasion,Journal of Public Economics, 74, 395-430.J AIN A.K. 1997, Tax Evasion, Economic Reforms and Corruption in India, Intertax 25, 18-22.KLITGAARD R. 1988, Controlling Corruption , Berkeley, University of California Press.MIESZKOWSKI (eds.) 2002, Unites States Tax Reform in the 21 st Century ,Cambridge, Cambridge University Press, 179-214.

S LEMROD J.B. 1985, An Empirical Test for Tax Evasion, The Review of Economics and Statistics 67, 232-238.S LEMROD J.B. 2001, A General Model of the Behavioral Response to Taxation,International Tax and Public Finance 8/2, 119-128.


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S LEMROD J.B. AND YITZHAKI S. 2002, Tax Avoidance, Evasion, and Administration, in: A.J. A UERBACH and M. F ELDSTEIN (eds.), Handbook of Public Economics , Volume 3, Amsterdam, Elsevier,1423-1470.YITZHAKI S. 1974, A Note on Income Tax Evasion: A Theoretical Analysis,Journal of Public Economics, 3, 201-202.

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