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## 3. Tax Compliance

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The Effects of Tax Noncompliance

Tax avoidance means making use of legal loopholes in the tax codes. Usually this requires costly services of specialized tax consultants and is, thus, only amenable to wealthy taxpayers. Tax avoidance encompasses making use of tax credits, itemizing expenses, making use of choosing the legal form of enterprises, choosing one’s residence, choosing one’s profession, etc.

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

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

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

Tax noncompliance imply higher taxes to secure a given tax revenue. This reinforces deadweight loss, as taxes become more distorting.

Tax noncompliance also affects tax incidence and changes tax progression. In the majority of cases it works in the direction of making the tax system less progressive (more regressive) 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.

3.1 Tax Avoidance

Assume first that income y is exogenous (or that labor supply is fixed), assume a tax schedule T(.) and assume that Θ is a legally avoided part of income which reduces the tax base. Furthermore, assume that C(Θ)is the cost of avoidance. Assume first that C(Θ) is increasing and convex, that is, additional legal reductions of the tax base require higher cost. Then the first-order condition of tax avoidance results from maximizing the next expression with respect to Θ:

This yields the first-order condition:

(1)

Thus, under a graduated (progressive) income tax the rich will avoid more taxes than the poorer taxpayers. In case of a flat tax all taxpayers declaring income above the personal allowance will avoid the same amount of income since the marginal 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.

For C(Θ) increasing and concave this implies that tax avoidance has economies of 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 it pays to avoid all taxes irrespective of the tax schedule.

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

(2)

(3)

In this model, the taxpayer decides simultaneously on his or her labor supply and the amount of labor income to be avoided from the tax base. The cost function of tax avoidance now depends on labor income and the part of it to be avoided: C(wℓ,Θ). For short, let us write C1 for ∂C/∂wℓ,C2for ∂C/∂Θ, and so on.

As tax avoidance involves cost, we have unambiguously C2>0. The sign of C1 is not clear a priori. When it is easier to avoid a given amount Θ* for higher incomes, we have C1<0; when it is more difficult, C1>0. It is plausible to assume C1<0 because Θ*/wℓ diminishes as wℓ rises and the tax authorities may more likely connive at a smaller fraction of income being avoided. If they have a closer look at higher incomes (which might be more closely checked) then C1>0 would be the appropriate assumption.

As to the second derivatives, C22>0 means that the marginal cost of tax avoidance is increasing. C11>0 holds when the “avoidance-facilitating” property of true labor income, i.e. C1, has diminishing returns. C21=C12 is crucial, as it captures the interaction between true labor income and tax avoidance. C21<0 means that higher incomes make tax avoidance less costly. This implies that Θ increases with wℓ. What is the consequence for declared income (wℓ-Θ)? Its development depends jointly on C12and C22.

Consider –C12<C22. Then the decrease of the cost of tax avoidance due to higher income is less than the increase of the cost of tax avoidance due to more avoidance. In this case, declared income (wℓ-Θ) increases with increasing true labor income wℓ.

(5)

Condition (5) is the well-known condition of our initial model: tax avoidance should be 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, -U2/U1, equals the net-of-tax wage rate. The critical aspect of this more general model is that the term (-wC1) changes the net-of-tax wage rate. When C1<0, the net-of-tax wage rate includes an implicit subsidy to working equal to (-wC1), due to the fact that working more lowers the cost of avoiding taxes by that amount. When C1>0, the net-of-tax wage rate is diminished by the waning possibility of avoiding taxes for higher incomes. A further complica-tion in this analysis comes from the fact that C1 may itself depend on ℓ, which means that the budget line in the (v,ℓ)-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 preferences which are subjective traits of the taxpayer. This makes the analysis somewhat complicated and dependent on the parameters of taxpayer reaction. For further analysis see Slemrod (2001) and, more informal, Slemrod and Yitzhaki (2002).

Tax evasion is the (illegal) attempt of a taxpayer to establish the official promise of tax equity on an individual basis.

Helmar Nahr

Taxation Economics: Short Account of Sixth Lecture

- Asymmetric information: optimum income taxation: general case (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 supply response; 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 a subsidy or an additional cost
- We started to discuss tax evasion
- Crash course on von Neumann – Morgenstern utility functions

3.2 Tax Evasion

Tax evasion means that part of the income (or of some other tax base) is not declared. It is illegal and implies, if discovered, a fine which can, in extreme cases, 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 is supposed to result from a fixed labor supply), x declared income, ta proportional tax rate, π the probability of tax audit (which will disclose true income), f the penalty rate on undeclared income (y-x), where f>t, and let U(.) denote the taxpayer’s von Neumann-Morgenstern utility function.

income if no tax audit

income in case of tax audit

(2) implies that the marginal utility of the saved expected tax from declaring no income is less than the marginal utility of the residual income after the fine in case 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 tax rate. Hence, it pays to declare less than full income. Hence, interior solutions are well 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

By decreasing absolute risk aversion we have RA(v)<RA(z). However, the sign of the bracketed expression depends on the value of f. Only if f≥1 is the derivative unambiguously positive. Note that ∂x/∂y increases as the fine f increases. The temptation to evade taxes with rising income is less the higher the fine is.

Let us now have a look at the fraction of true income declared as true income changes. We have

This shows that, as true income varies, the fraction declared increases, stays constant, 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 as absolute risk aversion is decreasing, constant, or increasing. For decreasing absolute risk aversion there is no clearcut hypothesis as to the relationship between reported income and the tax rate.

We can regard the two terms in (8) as the income effect and the substitution effect, respectively. The latter is negative, because an increase in the tax rate makes it more profitable to evade taxes on the margin. The former is positive because an increased tax rate makes the taxpayer less wealthy, which reduces both 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 always increase declared income.

Differentiating (1) with respect to the audit probability π yields

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

Yitzhaki (1974) has argued that some of the Allingham-Sandmo results are due to their assumption that their fine applies to the difference between true and declared 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 results change. Yitzhaki states the following problem: the taxpayer chooses x to maximize

Allingham and Sandmo analyze also the dynamic case: tax returns are filed at discrete times and individuals live infinitely. If tax evasion is discovered in a period, all past tax returns are corrected and the full tax amounts are charged to the 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 past evaded taxes accumulate. Once full income report has been achieved, there is no more danger of discovering the past sins of tax evasion.

Later research has endogenized labor supply into models of tax evasion. With labor 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 define a threshold value of income and a policy to audit any report below the threshold with probability π and leave all tax returns above this threshold unaudited. The probability π is chosen to be just large enough so that all taxpayers with true incomes below the threshold report honestly. All taxpayers with true incomes above the threshold report the threshold and pay taxes accordingly. Models have been proposed with a multitude of thresholds according to the various professions.

In addition to theoretical work, many field studies and experimental studies were carried out in the area of tax evasion. For a survey of this work see Andreoni, Erard, and Feinstein (1998).

3.3 Corruption and Extortion

We 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 has been tax farming: the tax inspector pays the government a fixed fee in return for the right to retain all revenue legitimately collected. This is the extreme form of 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 gets his or her reservation wage anyway – it is normalized to zero. Both I and P are risk neutral.

Stage 2: Income reporting and appeal.

- The taxpayer’s income y becomes common knowledge of the taxpayer and the tax inspector. They bargain according to a game form with two outcomes:
- they reach an agreement (x,B), such that the tax inspector I certifies to the government that the true income is x, and the taxpayer P pays him a bribe B;
- they fail to reach an agreement; I unilaterally reports z; as there is no agreement, no bribe is paid. The taxpayer P is given the opportunity to appeal 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. But appealing incurs a fixed cost for P of α≥0.

Stage 3: Audit by an honest tax attorney.

With probability π, 0<π<1, (unless it was the subject of appeal in stage 2), I’s report is audited by an honest tax attorney and P’s income is revealed for sure. π isexogenous and independent of the income reported.

We start by solving the game by P’s strategy as to whether or not to appeal when no agreement 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.

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 expected equilibrium payoffs in the event of no agreement are:

We call them disagreement payoffs.

When I and Preach 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 its distribution between I and P.

Suppose x maximizes (6). This implies

as z is also a feasible value for (6) and may be agreed upon if it maximizes S(x,y) for x=z. [This unlikely case may occur if the commission to the tax inspector 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) which makes them no worse off than under a disagreement payoff. Note that the disagreement payoffs and the possibility of appeal have no impact on the income report, but affect the negotiated bribe.

Corruption, extortion and tax evasion

Tax evasion means under-reporting of income, x(y)<y. Corruption means the payment of bribes, B(y)≠0. Hence, tax evasion and corruption may be quite different things.

Let us first exclude bargaining equilibria which ordain that income be over-stated and bribes being paid by the tax inspector to the taxpayer [this may result from rapidly increasing commission payments to the tax inspector]. The following proposition rules such cases out.

An intuitive proof of this proposition is straightforward. If not audited, the collective payment of I and P is [1-λ(x)]T(x). If this increases with reported income, then over-reporting can never maximize their surplus [(i)]. If the inspector’s commission λ(x)T(x) is increasing with the income reported, he will have to receive some bribe to agree to submit an under-report [(ii)]. The inspector’s threat in the disagreement game will not involve under-reporting because he can do better by truthful reporting [(iii)]. To tolerate tax evasion, involving a loss of commission and facing potential penalties, the inspector will need to be bribed [(iv)].

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 prevent over-reporting of income. The bribe is then a manifestation of extortion. [Reported by Jain (1997) for India and by Klitgaard (1988) for the Philippines.] This situation is characterized by

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

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

Taxation Economics: Short Account of Seventh Lecture

- We discussed the Allingham-Sandmo model of tax evasion. The first order conditions came from maximizing expected utility with respect to declared income. Then we used this condition to check how 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 about paying 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 bargaining equilibrium and the difference between corruption and extortion.

Evasion- and corruption-proof tax régimes

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

Note that the first restriction excludes tax farming [i.e., k<0] because T(0)=0 and fI(.)≥0, which imply k≥0.

If the government wants to maximize expected tax revenue, there are many tax schemes to achieve that. Suppose then that the government wants to eliminate tax evasion. A tax scheme satisfying (8) and (9) is evasion-proof if

For an intuitive proof suppose that the government has decided to use the maximum penalties (8) and (9) for misconduct. Then, if an audit discovers misreported income, I and P jointly have to pay the amount [T+fI+fP-k-λT]=y. The expected payment is thus πy. The collective payment on a truthful report is [1-λ(y)]T(y). If the tax schedule is such that [1-λ(y)]T(y)is higher than πy, it pays to report x<y instead of y. Hence, when πy<[1-λ(y)]T(y), either T(.) is too high, or π is too low. Evasion-proofness requires equality.

Second, the government‘s net receipts from a truthful report, [1-λ(y)]T(y)–k, are maximized if k=0.

Interpretation of Proposition 2: From (i) follows that πT(y)/y, i.e., the average tax rate must not be less than the probability of audit. We have also (1-π)≥λ(y), i.e., the commission rate must not exceed (1-π). Proposition 2/(i) allows a progressive tax schedule; but this requires that the commission rate λ(y) also increases 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 is needed to counter the greater incentive to evade taxes. This is attained by raising the cost to the inspector in terms of foregone commission of conniving in an under-statement of income.

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

Proposition 2/(ii) states that I’s expected payment over his reservation utility must come entirely from commission payments.

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 feasible levels. 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. A smaller audit probability requires higher fines.

Are tax schedules satisfying Proposition 2 also corruption-proof? Obviously not because the possibility of extortion means that the threat of over-reporting may enable 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., α=0, corruption-proofness follows immediately. The more realistic case is α>0. Eliminating extortion requires that the gain to I from over-reporting is outweighed by the penalty which I incurs if the over-report is discovered, i.e., if

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) with a fixed wage for inspectors and with the tax rate equal to the probability of random audit. However, the price to preclude extortion by paying no commission to tax inspectors means that one has to dispense with progressive taxes. Progression invites evasion and corruption.

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

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 from Proposition 2/(i):

This means that the decrease (x<y) [increase (x>y)] in the collective payment can be considered an implicit “penalty”. In case of over-reporting [x=z>y], it becomes a real implicit penalty. Thus, the condition in Proposition 5/(ii) requires that either punishment is so great that the inspector will never over-report or/and the cost of appealing is so low that P will choose to appeal. This condition may hold even if the fine f(z,y) decreases with over-reporting because the implicit component of the punishment increases with z and compensates for the reduction of the explicit penalty.

The proportional part in Proposition 5 is necessary to prevent extortion: The poor have little to evade. Paying inspectors a commission at low income reports does little to combat evasion but creates the possibility of extortion. Hence, no commission should be paid on low income reports.

3.4 Literature

Allingham M. andSandmo A. 1972, «Income Tax Evasion: A Theoretical Analysis», Journal of Public Economics, 1, 323-338.

Andreoni J., Erard B. and Feinstein J. 1999, «Tax Compliance», Journal of Economic Literature, 36, 818-860.

Gale W.G andHoltzblatt J. 2002, «The Role of Administrative Factors in Tax Reform: Simplicity, Compliance, and Administration», in G.R. Zodrow and P. Hindriks J., Keen, M. andMuthoo A. 1999, «Corruption, Extortion and Evasion», Journal of Public Economics, 74, 395-430.

Jain 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 21st Century, Cambridge, Cambridge University Press, 179-214.

Slemrod J.B. 1985, «An Empirical Test for Tax Evasion», The Review of Economics and Statistics 67, 232-238.

Slemrod J.B. 2001, «A General Model of the Behavioral Response to Taxation», International Tax and Public Finance 8/2, 119-128.

Slemrod J.B. and Yitzhaki S. 2002, «Tax Avoidance, Evasion, and Administration», in: A.J. Auerbach and M. Feldstein (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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