Chapter 7 Tax Compliance and Evasion I. What is Special about Tax Evasion? Why tax evasion differs from other forms of economic crime?

First, tax evasion is a fraud that is committed against a very special economic agent: the government. The government is special in that it has the power to set and to enforce some of the rules of the game by which economic relationships are supposed to abide. It sets the structure and the level of taxes. It also has ultimate control over the mechanism used to enforce the payment of taxes and over the structure of penalties for offenders. It combines the roles of rulemaker, victim, and umpire.

Second is due to the delicate interplay of information among those involved in the underground economy (evaders, investigators, and the government). The government’s awareness of the scope for evasion, and its (imperfect) knowledge of how the tax-evading sector operator can play a crucial role in determining the structure of taxation.

Third, there is a special relationship between tax evasion and certain other topic central to the study of public economics. The precise form that economic crimes take ─ tax evasion, fiddling government controls, smuggling trading on black markets ─ will differ according to the type of society, the economic structure, and the legal system.

In short, the issue of evasion is, unlike other illegal activities, inseparably bound up with the instruments of fiscal control that the government attempts to use in carrying out its economic policy. II. What Is Tax Evasion? Can the concept of “evasion” be usefully distinguished from “tax avoidance” or “tax planning”? The usual answers fall roughly into three categories: Legalistic The distinction between evasion and avoidance can be taken as purely a

question of legal boundaries: Evasion is outside the law; avoidance is not. Moralistic It is sometimes argued that certain types of avoidance are just as morally

wrong as evasion and therefore should be treated the same as evasion for the purposes of analysis.

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Agnostic “Evasion” and “avoidance” are merely two arbitrary segments of a continuum that stretches from innocent tax planning to outrageous fraud.

The above classifications touch the issue as to what of well-designed tax policy ought to be in a sense that all taxpayers should be treated equally under the same tax policy. The economic approach to the whole issue of tax evasion is founded on the analysis of the behavior of individual tax evaders. The way in which the individual perceives his economic opportunities to be affected by the tax code and by the instruments of tax enforcement is particularly relevant. The system of taxation and its enforcement many induce the taxpayer to conceal or misrepresent some of his activities. By themselves such concealment and misrepresentation do not constitute evasion; in fact, the state may actually acquiesce in such apparent deviousness.

However, the taxpayer may perceive certain choices with regard to tax declaration, financial transactions, or economic activity to be potentially costly in that they are subject to the threat of exposure and penalty. If so, then this perception will influence such choices, hence influencing the response of the economy as a whole to the fact of evasion and the apparatus of control.

We can see that “evasion” activities typically involve the individual taxpayer either in making decisions under uncertainty (concerning his eventual liability to taxes and penalties) or in trying to eliminate that uncertainty by more thorough concealment. “Tax planning” implies certainty on the part of the taxpayer at the time when he makes his decisions about the deployment of his assets and his report to the tax authority. “Avoidance” is essentially similar to this but may also involve an attempt to frustrate the intention of the tax low by such deployment. In some cases the success of such attempts may depend on the rulings of tax administrators; in others the legislature or the judiciary may respond to such frustrated intentions by changing or clarifying the law.

Whereas the law attempts to make distinctions on the basis of entitlement, the appropriate distinction from the viewpoint of economic analysis is one of function. The law attempts to specify the portion of your resources to which the state is entitled; evasion is a violation of that entitlement. How the law places such entitlement in principle may correspond to economic function. In practice, the scope of the economic problem of tax evasion is likely to be broader than the boundaries set by the legal definition. III. What Is the Underground (Black) Economy?

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Everyone knows that there is the underground economy. But what constitutes a sensible definition of the economic reality of the underground economy is far from self-evident.

Let’s examine figure Y, a rough schematic depiction of the relationship among different types of economic transaction. Figure 1 The Scope of the Underground Economy

α

ⅠⅠ Ⅱ Ⅲ

β δ εγ

Ⅰ: total production Ⅱ: officially defined production Ⅲ: the underground economy α: housework, do-it-yourself work and voluntary organizations β: legal official production, private and public sectors, γ: the underground economy allowed for in official accounts, δ: the underground economy not allowed for in official accounts, ε: benefit fraud and tax evasion outside the production sector.

IV. Empirical Evidence of Tax Evasion

The importance of developing a theoretical understanding of tax evasion can only be assessed by estimating the actual extent of evasion. If such evasion constitutes a significant activity within the economy, then a theory of evasion is of potential use in designing structures that minimize evasion at least cost and ensuring that policies are optimal given that evasion occurs.

Due to its very nature, the measurement of tax evasion and unreported economic activity is fraught with difficulty and uncertainty. By definition, tax evasion is not measured in official

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statistics. Then how to measure it? The expenditure-income discrepancy method (1) Rey (1965) calculates 52.46 % of actual sales tax revenue was evasion. His method is to

identify consumption and GNP, and estimate the amount which should be paid and compare it with what is actually paid.

(2) Pissarides and Weber (1989) employ data from the 1982 U.K. Family Expenditure Survey. By assuming that income and expenditure are reported accurately by employees whose employer filed their income report, an estimate of the expenditure function for these households then gives the true relation between income and expenditure. Observing the expenditure of other households permits an estimate to be made of their income and, consequently, their tax evasion. They find that the unobserved economy is 5.5% of GNP in U.K..

(3) Feige and McGee (1983) finds 10% of GDP for Sweden. The monetary aggregate method (4) Gutmann (1977) is based on the observation that transactions in the underground

economy are invariably financed by cash rather than cheque or credit. Gutmann uses the growth of currency in circulation relative to demand deposits as an indirect measure of unobserved activity. He finds 10 % of legal measured activity.

(5) Feige (1979) uses the observation that total economic activity, including both the measured and unmeasured sectors, is equal to the price level times transactions. An estimate of the unmeasured sector is then provided by the ration of the value of measured income to that of transactions. The major difficulty of this approach is determining the number of transactions that actually occur. Feige achieved this by using data on the life-span in months of bank notes in circulation relative to the number of times it is expected each note can be used. The estimate of the unmeasured sector in 1976 was 22% of GNP, and in 1978 was 33% GNP (U.S.A.). For U.K., Feige (1981) estimated 15% of GNP in 1979 (U.K.).

V. The Tax Compliance Measurement Program U.S. Internal Revenue Service provides detailed data on audit and prosecution rates, severity of sentences, income sources, regions, and the demographic and social classification of taxpayers.

Findings

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(1) Evasion behavior varies considerably by income type and population group. Clotfelter (1983) Review of Economic and Statistics, 65, 363-73.

(2) Disposable income and enforcement parameters have the expected effects on evasion behavior. Witte and Woodbury (1985) National Tax Journal 38, 1-13, Alexander and Feinstein (1987) mimeo.

(3) Evasion increases with the tax rate

VI. The Basic Model Idea: Tax evasion is treated as a simple form of gambling. Rational gamblers take fewer

risks if the odds are worsened; therefore, simple adjustments to enforcement parameters have the desired effect. Rich gamblers (evaders) stake more than those of modest mean — the reckless more than the cautions.

Drawback: The evidence suggests that evasion rise with the tax rate, in contrast to the results of the basic model.

Figure 2 Payoffs to Evasion

If not caught

If caught

A

y DeclaredIncome

evasion0

C’’

y

C’

(1-t)y

(1-t-ts)y

DisposableIncome

e

Taxpayer has to decide whether to attempt to evade paying tax and, if so, how much to evade.

Once the decision to evade has been taken, one of two possible states of the world must obtain: Either the taxpayer escapes detection and enjoys a consumption level c’, or he is caught, convicted and punished, in which case his consumption is c’’. If he chooses to be perfectly honest, then c’’=c’.

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Assumptions:

A1. The taxpayer has a fixed gross income y which is liable to tax. A2. There is a proportional income tax at rate t. A3(a). There is a fixed probability p that tax evasion will be discovered and punished. A3(b). The tax in any income found to have been concealed from the authorities is subject to

surcharge at a rate s.

It will be convenient to refer to the collection τ=τ(p,s,t) as the tax-enforcement parameters. A4. The taxpayer has a von Neumann-Morgenstern utility function that is concave in

consumption. It may be written )''()'()1()'','( cpUcUpccU +−= where U is a

concave cardinal utility function. Maximization problem of U(c’,c’’) with the budget constraint rteytc +−= )1( where r is the

rate of return to a dollar of evaded tax and is defined as

⎩⎨⎧−

= y probabilit with

1y probabilit with 1 ps-p

r

The first-order condition is given,

0)'(')1()''(')1( =−−− cUpcUsp (1)

The second-order condition is

[ ] 0)''('')1()'('')1( 2 ≤−+−= cpUscUptK (2)

where , 0'>U 0'' <U For tax evasion to take place, (1) must have evasion e>0. Totally differentiating (1) with respect to (y-e), the declared income, and p and rearranging

gives

0)'(')''(')1()(>

+−−=

∂−∂

KcUcUs

pey

(3)

An increase in the probability of detection raises the level of income declared and reduces

evasion.

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0)''('')1()''(')(>

−−−=

∂−∂

KecUspcpU

sey τ

(4)

An increase in the fine leads to a reduction in the level of tax evasion.

[ ]K

cseRcRcReycUpey AAA )''()]'()''()[()'(']1[)( +−−−=

∂−∂τ

(5)

where )(')('')( XUXUXRA −= is the Arrow-Pratt measure of absolute risk aversion. Since , for an increase in the tax rate to increase the level of income declared, it is sufficient that . Thus if absolute risk aversion decreases as income

increases, higher tax rates will lead to greater income declarations and a reduction in evasion.

0>AR0)'()''( >− cRcR AA

This result has provoked considerable discussion since it runs counter to the intuitive expectation that an increase in tax rate should provide a greater incentive to evade.

[ ][ ])'()''()''(

)'()''()''()(cRcRcstR

cRcRcstRy

ey

AAA

AAA

−−−−

−=∂−∂

τ (6)

The condition and τ<1, 0)'()''( >− cRcR AA 1)( <∂−∂ yey and hence declared

income rises less fast than actual income implying that tax evasion rises with income.

VII. The More Practical Model for Tax Authority The tax authority wants to uncover as much evasion as possible with limited time constraint. Once the authority decides to investigate a certain agent with a certain period of time, then it needs to decide the procedure as to which item to investigate. Mathematical method of this issue is given by Makino (1976).

The authority spends Ni days for declared income i. The probability of evasion exists is pi.

The date required to uncover evasion is Ti which follows the cumulative distribution fi(t). The evasion amount is Ai. Unintentional evasion can be uncovered with t days for sure, it amounts

to . )1( ti

ieB γ−−

Expected evasion Ci is given

∫ −−+=Ni N

iiiiiiieiBdttfPAC

0 )()( γ (7)

The tax authority’s problem is then to solve,

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∑ ∑= =

=n

i

n

iii MNC

1 1 )constant( subject to max (8)

As usual, we can define the Lagrangean equation,

∑ ∑= =

⎟⎠

⎞⎜⎝

⎛−+=

n

i

n

iii MNCU

1 1 λ (9)

The first-order condition with respect to Ni is

),21( 0)( n,,ieBNfPA tt Niiiiii L==++ − λγ γ (10)

The cumulative distribution function fi(τ) is empirically closer to exponential function. Average date the tax authority spends would be 2-3 days for lower income class and 5-6 days for higher income class.

VIII. The Procedure to Investigate

The probability to discover evasion in between t and tt ∆+ , given the fact the authority can not discover until t,λ(t) is defined as

∫−= t

dttf

tft

0 )(1

)()(λ (11)

Evasion rate for item Si at t corresponding toλ(t) is defined as

AdttfP

tfPt t

ti

iii

∫−=

0 )(1

)()(α (12)

Intentional evasion rate for item Si at t is

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ti

ttt

tit

tt

eBt

eBeBt γγγ

γβ −−∆+−

→∆=

∆−−−

=]1[]1[lim)(

)(

0 (13)

For all i (i=1,2,…l), evasion rate at t=0

iii BAfP γ+)0( (14)

should be calculated and order by size. The maximum item is Sj, then Sk, …. We start investigate Sj.

We investigate Sj for t days without success. Evasion rate at t is

)()( tt jj βα + (15)

Sk at t=0,

)0()0( kk βα + (16)

If [ ] [ ])0()0()()( kkjj tt βαβα +≤+ , then the item should be moved from j to k.

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References Books Cowell, F.A. (1990) Cheating the Government: the Economics of Evasion, MIT Press. Myles, G.D. (1995) Public Economics, Cambridge University Press, Chap. 12. Papers Alexander, C. and Feinstein, J.S. (1987) “A Microeconometric Analysis of Income Tax

Evasion”, mimeo, MIT. Clotfelter, C.T. (1983) “Tax Evasion and Tax Rates: An Analysis of Individual Returns”, Review

of Economic and Statistics, 65, 363-73. Erard, B. (1997) “Self-selection with Measurement Errors: A Microeconometric Analysis of the

Decision to Seek Tax Assistance and Its Implications for Tax Compliance”, Journal of Econometrics, 81, 319-56.

Feige, E.L. (1979) “How Big Is the Irregular Economy?”, Challenge, 5-13. Feige, E.L. and McGee, R.T. (1983) “Sweden’s Laffer Curve: Taxation and the Unobserved

Economy”, Scandinavian Journal of Economics, 85, 499-519. Gutmann, P.M. (1977) “The Subterranean Economy”, Financial Analysts Journal, 26-8. Makino, I. (1976) “Detection Procedure of Tax Evasion”, Mathematical Seminar, July (in

Japanese). Pissarides, C.A. and Weber, G. (1989) “An Expenditure-Based Estimate of Britains’ Black

Economy”, Journal of Public Economics, 39, 17-32. Rey, M. (1965) “Estimating Tax Evasions: the Example of the Italian General Sales Tax”,

Public Finance, 20, 366-92. Slemrod, J. and Sorum, N. (1984) “The Compliance Cost of the U.S. Individual Income Tax

System”, National Tax Journal, 37, 461-74. Witte, A.D. and Woodbury, D.F. (1985) “The Effect of Tax Laws and Tax Administration on Tax

Compliance: The Case of the U.S. Individual Income Tax”, National Tax Journal 38, 1-13.

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