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AN EMPIRICAL ANALYSIS OF FEDERAL INCOME TAXAUDITING AND COMPIAANCE

JEFFREY A. DUBIN* AND LOUIS L. WILDE*

ABSTRACT set and unreported income is the risky as-

This paper provides empirical evidenceset. Generally this model predicts that

on the relationship between complianceeither increases in the probability of ap-

with the Federal Income Tax and auditingprehension and conviction or the penalty

by the Internal Revenue Service. It com-for underreporting will increase compli-

bines a cross-section data set related to 1969ance, but the empirical evidence on these

individual returns assembled by the IRSeffects is both weak and scanty (see Sec-

with data taken from the Annual Reporttions 2 and 3 below). Furthermore, a strong

of the Commissioner of Internal Revenue.case can be made that IRS activity ought

We find support for an economic approachnot be taken as given, but instead be made

to tax compliance that incorporates the IRSendogenous (Graetz, Reinganum, and

as a strategic actor. Moreover, after allow-Wilde, 1986).

ing for the simultaneous determination Of The purpose of this paper is to provide

audit rates and compliance levels, we findsome empirical evidence on the relation-

significant deterrent effects of auditing onship between audits and compliance. Our

noncompliance.analysis uses in part a cross-section dataset related to 1969 individual Federal In-come Tax returns which was assembled

1. Introduction by the IRS in the seventies. This data set

DESPITE roughly fifteen years of the- includes an estimated compliance vari-

oretical work devoted to understand- able, a number of agency variables such

ing compliance with the tax laws and a as audit rates, and other demographic and

recent surge in attention paid to it by tax socio-economic variables for each of seven

policymakers and administrators, empir- audit classes, aggregated to the three-digit

ical work on tax compliance is still in its zip code level. Audit classes are defined

infancy, especially with respect to micro_ by income level (low, medium, or high) and

level studies. Yet, the "facts" of tax com- by type of return (1040 only, Schedule C

pliance are asserted routinely, almost or F present, Schedule C and F not pres-

without qualification. For example, com- ent).' We also use data taken from the

missioners of the IRS report regularly to Annual Report of the Commissioner of

Congress and the public on the size and Internal Revenue.

growth rate of the so-called "compliance Generally speaking, we find support for

gap," proponents of tax reform nearly al- an economic approach to tax compliance

ways list improved compliance as one of that incorporates the IRS as a strategic

the major benefits of lower marginal tax participant in the revenue collection pro-

rates, and even Congress acts at times as cess. In fact, in five of the seven audit

though the economics-of-crime model has classes, we find that audit rates are en-

been demonstrated to be the best repre- dogenous. After allowing for endogeneity,

sentation of the compliance problem we further observe a deterrent effect of

(Graetz and Wilde, 1985). audits in four cases.

All of this is highly problematic. The Section 2 of this paper summarizes the

basic economics-of-crime approach takes traditional decision-theoretic model of tax

the audit policies of the IRS as fixed and compliance and recent game-theoretic ex-

exogenous and models the taxpayer's tensions of it which incorporate the IRS

compliance decision as a simple portfolio into an interactive theory of auditing and

problem-reported income is the safe as- compliance. Section 3 discusses existingmicro-level studies of tax compliance.

*Califomia institute of Technology. Section 4 then describes the data set used

61

62 NATIONAL TAX JOURNAL [Vol. XLI

in this paper, Section 5 the estimation it- ity of detection and conviction increaseself, and Section 6 the results. compliance. 2

More recent theoretical innovations haveattempted to move out of the decision-

2. The Economic Theory of Tax theoretic framework characteristic of theCompliance early tax compliance literature. Of par-

ticular interest here are the principal-The contemporary revival of the eco- agent models of Border and Sobel (1985)

nomic analysis of crime began in 1968 with and Reinganum and Wilde (1985) and theBecker's classic article "Crime and Pun- game-theoretic model of Graetz, Rein-ishment: An Economic Approach." While ganum, and Wilde (1986). In both of theseBecker mentioned tax evasion as an area approaches the IRS is allowed to act stra-of application for his general model, Al- tegically, conditioning its audit rules onlingham and Sandmo (1972) and Srini- the information it receives from taxpay-vasan (1973) provided the analysis. Gen- ers. Thus the models yield predictionserally, this approach treats noncompliance about the nature of the equilibrium auditas a rational individual decision based rule used by the IRS as well as the equi-upon probabilities of detection and con- librium reporting rule used by taxpayers.viction and levels of punishment. In Al- Whether the IRS should be included aslingham and Sandmo's model, the taxpay- a strategic actor in theoretical models ofees actual income is exogenously given and tax compliance is of more than technicalknown by the taxpayer but not the IRS. interest. In assessing empirically the de-A constant proportional tax is applied to terrent effects of audits, it is criticalreported income, the amount of which is whether the IRS audit selection processchosen by the taxpayer. With some ex- turns on taxpayer compliance behavior. Ifogenous and constant probability, the it does, then any empirical specificationtaxpayer is "audited." If he or she is dis- meant to explain taxpayer compliance be-covered to be underreporting income, a havior which treats audit rates exoge-penalty proportional to the amount of un- nously may be seriously misapecified.declared income, at a rate higher than the Furthermore, an incorrect presumptionproportional tax rate, must be paid. The that probabilities of apprehension andtaxpayer chooses a level of reported in- sanctions for underreporting of income cancome so as to maximize his or her ex- be taken as given may imply unhelpfulpected utility of net wealth. policy responses. Thus, while models that

Even this simple model produces am- incorporate the IRS as a strategic playerbiguous results. For example, the effects in the tax compliance game, such asof increases in income or the tax rate on Graetz, Reinganum, and Wilde (1986),reported income depend on properties of make precise predictions about the na-the taxpayer's utility function (e.g., rela- ture of both equilibrium auditing and in-tive risk aversion). It is always the case, come reporting rules, we will focus in thishowever, that an increase in the proba- paper on the narrower questions of thebility of detection and conviction or an in- deterrent effects of audits and their en-crease in the penalty rate will increase dogeneity.compliance.

The bulk of the remainder of the the- 3. Existing Empirical Workoretical economics literature on tax com-pliance consists of extensions and refine- The primary n-deroeconomic studies ofments of Allingham and Sandmo's model. taxpayer noncompliance are due to Clot-In most cases, however, the modifications felter (1983) and Witte and Woodburyproduce more ambiguous results, not (1985). Clotfelter analyzed a data set col-fewer. For example, making labor supply lected originally as part of the 1969 IRSdecisions endogenous obviates even the Taxpayer Compliance Measurement Pro-conclusion that increases in the probabil- gram (TCMP). The TCMP consists of de-

No. 11 AUDITING AND COMPLIANCE 63

tailed audits of a stratified random sam- ing, they should be used with caution.ple of taxpayers. Each of these "line-by- There are two main problems. First, Clot-line audits" results in an amount of in- felter tries to avoid the simultaneity issuecome taxes due that is regarded by the IRS by leaving audit rates out of his model.auditor as "correct." Differences between But if audit rates affect compliance thenthe auditors' determinations and the tax- his model is still misspecified. This prob-payers' original reports are then related lem is especially acute with respect to in-to tax return characteristics in order to come since audit rates certainly responddevelop a scoring mechanism (the "Dis- to reported income, but, because mar-criminant Index Function," or "DIF") that ginal tax rates are also correlated withcan be used by the IRS to establish and income, it is likely to bias Clotfelter's es-refine its broader audit selection mecha- timates of the effects of marginal tax ratesnisms. on underreporting as well.

Normally TCMP data is aggregated in Witte and Woodbury (1985) do attemptsome fashion or another before being re- to analyze the effects of audit rates andleased to the public since the Internal sanction levels on compliance. The dataRevenue Code prohibits the IRS from re- set used by these authors is virtuallyvealing information about individual re- identical to the one we use in this paperturns. When Clotfelter wrote his paper he and is discussed in detail in the next sec-was an employee of the Treasury De- tion. It includes an estimated percentagepartment and was thus able to use the compliance variable related to 1969 re-richer return information on income and turns filed in 1970 (but not based on ac-tax deduction items as well as the esti- tual IRS audits), IRS agency variables suchmates of noncompliance contained in the as audit rates and sanction levels, and aTCMP files. He therefore focussed on the host of demographic and socio-economicrelationship between marginal tax rates variables, all aggregated to the three-digitand tax evasion for three classes of tax- zip code level. Separate equations werepayers (nonbusiness, nonfarm business, estimated by Witte and Woodbury for eachand farm). For each group he estimated a of seven audit classes, defined by incomesingle equation using Tobit maximum level (low, medium, or high) and by typelikelihood procedures. The dependent of return (1040 only, Schedule C or Fvariable was the log of underreported in- present, Schedule C and F not present),come and the independent variables in- using seemingly unrelated regression. Included a measure of the effective mar- particular, for each audit class, the esti-ginal tax rate, after-tax income, wages as mated 1969 percentage compliance vari-a proportion of adjusted gross income, in- able was regressed on a constant term andterest and dividends as a proportion of 36 explanatory variables, including auditadjusted gross income, and several socio- rates for 1967, 1968, and 1969 within thedemographic variables. The average au- audit class, and for all other audit classes,dit rate for each taxpayer class was not and other agency variables such as theincluded as an independent variable since, frequency and level of imposition of sanc-as Clotfelter put it, "the probability (of tions, both civil and criminal, and the levelaudit] for any tax return in a given class of IRS data processing efforts.is a fimetion of its reported items"; in other We discuss the 1969 IRS data set in de-words, there is a potential simultaneity tail in Section 4, but the two primaryproblem that makes it inappropriate to use problems with the Witte and Woodburyaudit rates as explanatory variables in an analysis are (1) the numerical propertiesequation meant to explain compliance with of the full 1969 data set make it undesir-the tax laws. able to regress the estimated 1969 per-

Clotfelter found that both the level of centage compliance variable on all 36 ofafter-tax income and marginal tax rates the other variables provided by the IRS,have significant negative effects on com- and (2) many of the agency variables arepliance. While these results are interest- likely to be endogenous in which case the


model used by Witte and Woodbury is also rectly related to the TCMP audits, but itmisspecified. We attempt here to correct includes all returns actually filed in cal-

3for both of these problems by using only endar year 1970 for tax year 1969.a subset of the 1969 IRS data set, aug- (ii) Audit Rates (audit): This variablementing it with additional variables, and is defined as the percent of taxpayers fil-allowing audit rates to be endogenous. ing a 1968 return in calendar year 1969

who were audited in calendar year 1968,

4. The Data for the audit class in the zip code area. Itis not the audit rate as applied to 1969

Our analysis is based on the 1969 IRS returns.data set described briefly in the last sec- The following five variables assumetion. We use seven variables from that data common values for all audit classes in aset, supplemented by two variables taken given zip code area.from the Report of the Commissioner of (iii) Unemployment Rates (uemp): TheInternal Revenue. We describe the vari- percentage of the population 16 years ofables from the 1969 IRS data set first. age and older who were unemployed in

(i) Estimated Voluntary Compliance 1970.(vcl): As we have already mentioned in (iv) Percentage Nonwhite (nw): Theour discussion of existing empirical work, percentage of the population in 1970 whoevery two or three years since 1969 the were nonwhite.IRS has conducted a special series of au- (v) Percentage Manufacturing (manuf):dits connected with the Taxpayer Com- The percentage of total employed personspliance Measurement Program (TCMP) 16 years of age and older employed inwhich are used in part to establish its au- manufacturing in 1970.dit selection mechanism. To this end, re- (vi) Age (old): The percentage of thesults of the TCMP audits are used to de- population 65 years of age and older infine a scoring rule. The scoring rule 1970.associates a number, called the DIF score, (vii) Education (hseduc): The percent-with each tax return, based on that re- age of the total population 25 years of ageturn's characteristics. A higher DIF score and older with at least 4 years of highon a given individual's return reflects a school completed in 1970.larger expected post-audit adjustment in The following two variables were takenthe tax liability owed by that individual. from the 1986 Report of the Commis-To the extent that most such adjustments sioner of the Internal Revenue. They takeare in favor of the IRS, the DIF score thus common values for all audit classes andreflects a so-called "yield criterion." all zip code areas within a state."

For each three-digit zip code and each (viii) IRS Resources (obper): The totalaudit class, vel was constructed (by the budget of all IRS district offices within aIRS) by associating with every 1969 tax state for 1968 divided by the total num-return in that zip code area and audit class, ber of returns filed in the state in 1968.the absolute value of the expected ad- (ix) Self-Employment (perself): In-juf3tment in tax liability associated with come tax not withheld and self-employ-the return's DIF score, denoted TC. For ment tax as a percentage of total individ-zip code area i and audit class j, the IRS ual income and employment tax in 1968.then defined The explanatory variables we use in our

specification of the compliance model arethe 1968 within-class audit rate (audit),

VCI,)- E SRik SR,k + E TC,k the unemployment rate (uemp), the per-k k k centage of nonwhite population (nw), the

percentage employed in manufacturingwhere SR,k is the actual self-reported tax (manuf), the percentage of the populationliability of individual k in zip code area i over 65 (old), the percentage of personsand audit class j. Thus vcl is only indi- over 25 with at least four years of high

No. 11 AUDITING AND COMPLLKNCE 65

school education (hseduc), and the per- obper, fills this role in our analysis, as iscent of collections not withheld or from described in detail in the next section.6self-employment taxes (perself).

The unemployment, manufacturing and 5. The Estimationself-employment variables are included asthey reflect opportunities to evade. The The 1969 IRS data set is a pooled cross-

nonwhite, age and education variables are section of 36 variables for seven audit

included because other studies, primarily classes. The audit classes are described in

surveys, suggest they are important.*5 Fi- Table 1. Individual observations in each

nally, we expect that audit rates and com- audit class represent aggregate values for

pliance levels are related but consider it geographic groups at the three-digit zip

fundamental to allow for the possible en- code level. Table 2 shows descriptive sta-

dogeneity of audit. Endogeneity occurs tistics for each of the nine variables de-

when elements of a taxpayer's income and scribed in Section 4, by audit class.

tax status which are known by the tax- The equation to be estimated relates

payer and observed by the IRS (but not by voluntary compliance (vcl) to 1968 audit

us) induce below average compliance and rates and the various socio-economic vari-

simultaneously induce greater audit rates. ables:

In this case, correlation between audit and vclu - oto, + oti, audit,the unobservables will lead to inconsis-tent estimates of the parameters using + ct2, uemp, + cL3. nw,ordinary least squares estimation. Con-sistent estimation then requires the use + ot4, manuf4

of an "instnnnent" which is correlated with + ot5, old, + (x6jhseduc,audit rates but not with the unobserva-bles. The IRS budget per tax return filed, + (x7,perselfj + -n,, (1)

TABLE 1

AUDIT CLASS DEFINITIONS

Number ofClass Observations Description

1 865 low-income (AGI < $10,000), nonbusiness withstandard deduction

2 856 low-income, nonbusiness, with itemized deductions.

3 858 low-income, business

4 830 medium-iricome ($10,000!5 AGI:5 $50,000), nonbusiness

5 801 medium-income ($10,000:5 AGI!@ $30,000), business

6 569 high-income (AGI Z:$50,000), nonbusiness

7 801 high-income (ACT @!$30,000), business

Total observations equal 5580. Business returns have schedule C or F present. Nonbusiness returnshave neither schedule C nor F present.


TABLE2

MEAN VALUES BY AUDrr CLASS(Standard Deviations in Parenthesis)

ClassVanable 1 2 3 4 5 6 7

vci96.57 92.63 81.55 97.05 90.78 94.41 90.58(1.36) (1. 11) (2.36) (0.35) (1.60) (1.32) (2.22)

audit 1.14 2.51 2.71 3.68 4.16 11.20 9.75(0.41) (0.74) (1.09) (1.07) (1.62) (4.36) (4.07)

uemp 2.46 2.46 2A6 2.46 2.44 2.46 2.43(0.81) (0.81) (0.80) (0.81) (0.81) (0.79) (081)

nw 9.43 9.50 9.33 9A9 9.51 10.09 954(12.03) (12.07) (11.74) (11.74) (11,62) (11.51) (11.72)

manuf 23.10 23.21 23.14 23A8 23.71 25.79 23.67(11.49) (11.45) (11.41) (11.33) (11.23) (10.77) (11.20)

old 10.55 10.55 10.60 10.49 10.58 10.03 10.57(3.18) (3.15) (3.13) (3.11) (3.14) (2.87) (3.16)

hseduc 50.91 50.98 50.80 51.40 51.52 53.16 51.38(11.55) (11.38) (11.43) (11.08) (10.84) (10.45) (10.98)

Perself 0.21 0.21 0.21 0.21 0.21 0.20 0.21(0.054) (0.054) (0.054) (0.054) (0.054) (0.049) (0.053)

obper 0.00353 0.00352 0.00352 0.00352 0.00350 0.00352 0.00349(0.00098) (0.00096) (0.00093) (0.00096) (0.00092) (0.00094) (0.00092)

where Ti. denotes a random disturbance ria of which produce observed audit ratesfor observation i within audit-class j. The and compliance levels."

coefficients, a,, are not expected to be equal Within such a simultaneous system we

across audit-classes and are not con- would ultimately like to estimate, orStrained to be so in estimation.7 "identify," both structural relationships.

Our estimation of equation (1) allows This could be done, for example, using

for the possibility that observed audit rates classical simultaneous equation estima-

and corapliance levels are the result of an tion techniques. However, these tech-

equilibrium process. On the one hand, we niques require the identification of all

hYpOthesize a deterrent effect of audits so underlying structural relationships. In our

that an increase in the audit rate will re- case, we lack the required observable fac-

sult in an increase in compliance (reflect- tors to completely specify the audit sched-ing a movement along the compliance ule. Such factors might include agencyschedule). On the other hand, we hypoth- characteristics and the political environ-

esize a yield effect of audits so that an in- ment. Nevertheless, it is possible to iden-Crease in compliance levels will result in tify the compliance schedule so long as wea decrease in the audit rate (reflecting a can find at least one observable factormovement along the audit schedule), These which affects the audit schedule indepen-two structural relationships then repre- dently of the compliance schedule. This issent a simultaneous system, the equilib- accomplished using the estimation tech-


nique known as instrumental variables.9 locates its resources, in part, on the basisAs indicated in Section 4, the variable of compliance levels. To examine this pos-

which we use to identify the compliance sibility, we have analyzed the time pathschedule is obper. In choosing this vari- of state level IRS budgets and found themable as an "instnunent," two criteria must to be independent of compliance levels;be considered. First, changes in the IRS rather they are predominately deter-state level budget per return should sys- mined by the share of total returns filed

*10

tematically affect the audit schedule. Thus, we proceed using obper as an in-While it is natural to presume that a pos- strument for audit."itive relationship exists between obper and Table 3 presents the ordinary least-audit, such a relationship can also be es- squares estimates of equation (1) by audittablished formally, as we do below. Sec- class, and Table 4 presents the instru-ond, the IRS state level budget per return mental variables estimates of these sameshould not be causally linked with com- equations. 12 At the bottom of Table 4 wepliance levels. It is very unlikely that calculate the Wald test for joint signifi-taxpayers base their decisions on infor- cance of all coefficients except the con-mation related to IRS state level budgets. stant (variable "one"). The asymptoticHowever, it is possible that the IRS al- distribution of this statistic is chi-squared

TABLE3

ORDINARY LEAST SQUARES ESTIMATION (BY AUDIT CLASS)

DEPENDENT VARIABLE IS VCL*

ClassVanable 1 2 3 4 5 6 7

one 93.97 93.20 76.70 97.41 87.90 94.72 88.98(245.83) (267.08) (109.35) (785.23) (165.00) (150.43) (109-16)

audit -0.036 0.23 0.24 -0.035 0.21 -0.071 0.039(-0.39) (5.34) (3.70) (-3.27) (7.47) (-6.34) (2.32)

uemp -0.21 -0.31 -0.70 -0.087 -0.18 -0.29 -0.68(-5.36) (-8.51) (-8.84) (-6.60) (-3.29) (4.70) (7-95)

nw -0.036 -0.020 -0.025 -0.0042 0.032 -0.016 0014(-11.36) (-7.40) (-4.08) (4.14) (7.37) (-3.25) (-209)

manuf 0.040 0.042 0.077 0.011 0.069 0.032 0.077(12.54) (14.00) (12.09) (9.78) (14.82) (5.68) (10.61)

old 0.053 -0.045 0.13 -0.0027 -0.0096 0.095 0.10(4.80) (-4.26) (5.84) (-0.73) (-0.62) (5.33) (4.15)

hseduc 0.054 0.0055 0.079 -0.00088 0.036 0.0013 0.0052(15.97) (1-80) (11.34) (-0.76) (7.02) (0.23) (0.67)

perself -3.41 -4.58 -4.88 -0.75 -5.98 -2.44 -0.67(-5.19) (-7.15) (-3.69) (-3.37) (-6.52) (-2.22) (-0.46)

Number of observafions 865 856 858 830 801 569 801Corrected R-squared 0.54 0.41 0.39 0.27 0.41 0.25 023Standard error of rcgmwion 0.92 0.96 1.93 010 122 115 1.94

*t-statistics are in parendiesis


With seven degrees of freedom (95 percent Whether audit rates should be treated ascritical level equals 2.01). In each case, the endogenous is ultimately an empirical is-overall fit of the model is impressive. In sue, but the question is amenable to a for-addition, in order to gauge the impact of mal specification test due to Hausmancolinearity in our explanatory variables, (1978). Hausman's method includes as anwe have calculated the condition number additional explanatory variable the pre-for the normalized data matrix." These dicted value of audit derived from a re-calculated condition numbers for our ex- duced form equation in which the inde-Planatory variables are well under 50 and pendent variables include those specifieddo not indicate concern for colinearity."' in (1) as well as the instruments. Haus-

Using instrumental variables to esti- man shows that endogeneity of audit ismate equation (1) allows for the simul- given by testing the significance of thistaneous determination of audit rates and additional explanatory variable. It is eas-compliance levels. However if audit rates ily demonstrated that a consistent esti-are not in fact endogenous then ordinary mate of the coefficient of audit is givenleast squares provides the most efficient by the sum of the estimated coefficient ofestimates of the compliance equation. audit and the estimated coefficient of the

TABLE4

INSTRUMENTAL VARIABLES ESTIMATION (BY AUDRF CLASS)DEPENDENT VARIABLE IS VCL*

ClassVariable 1 2 3 4 5 6 7

one 82.95 92.29 77.15 97.19 88.20 96.18 8468(13.85) (164.36) (98.87) (548.71) (134.97) (83.38) (590)

audit 6.47 0.62 -0.36 0.050 0.059 -0.22 0.66(1.85) (3.31) (-1.01) (1.02) (0.32) (-2.36) (0.32)

uemp -0.19 -0.34 -0.70 -0.090 -0.18 -0.28 -0.63(-1.85) (-8.42) (-8.43) (-6.55) (-3.25) (-3.88) (-2.93)

nw -0.12 -0.022 -0.015 -0.0047 0.034 -0.012 -0.041(-2.64) (-7.39) (-1.76) (4.19) (6.52) (-1.86) (-0.46)

manuf 0.041 0.046 0.076 0.013. 0.068 0.030 0.070(5.07) (12.58) (11.39) (7.82) (14.41) (4.71) (2.96)

old 0.13 -0.028 0,099 -0.0043 -0.014 0.11 0.066(2.60) (-2.00) (3.33) (-1.08) (-0.84) (4.91) (0.53)

hseduc 0.13 0.0065 0.10 -0.0024 0.042 0.0073 -0.020(3.05) (2.01) (6.35) (-1.62) (4.73) (0.95) (-0.24)

perself -6.44 -6.06 4.15 -0.95 -5.75 -3.82 -0.013(-2.75) (-6.27) (-2.87) (-3.70) (5.89) (-2.51) (-0.0039)

Number of observations 865 856 858 830 801 569 801Standard error of regression 2.36 0.90 1.92 0.31 1.25 1.32 3.20Chi square test forjoint sioficance 159.8 526.8 502.0 286.1 490.9 120.8 91.3

*t-statistics are in parenthesis

No. 11 AUDITING AND COMPLLKNCE 69

TABLE5

REDUCED FORM ESTIMATES (BY AUDIT CLASS)DEPENDENT VARLKBLE IS AUDM

ClassVariable 1 2 3 4 5 6 7

one 1.60 1.66 -0.079 1.58 0.98 7.11 7.12(11.77) (6.09) (-0.20) (3.86) (1.39) (2.89) (3.96)

uemp -0.0079 0.024 -0.036 -O.OD44 -0.052 0.0026 -0.067(-0.56) (0.86) (-0.89) (-0.11) (-0.76) (0.011) (0.37)

nw 0.013 0.0050 0.017 0.0032 0.016 0.029 0.043(11.86) (2.38) (5.47) (1.01) (2.98) (1.57) (3.05)

manuf 0.00011 -O.O(Y76 0.0019 -0.021 O.OOD46 -0.00095 0.0092(0.099) (-3.31) (0.57) (-6.08) (0.078) (-0.045) (0.61)

old -0.011 -0,044 -0.051 0.021 -0.030 0.064 0.057(-2.78) (-5.51) (-4.51) (1.75) (-1.55) (0.96) (1.11)

hseduc -0.013 -0.0061 0.038 0.013 0.034 0.026 0041(-10.95) (-2.54) (11 A9) (3.49) (5.30) (1.15) (2.50)

perself 0.55 4.52 1.94 3.36 2.69 -5.04 -1.34(2.28) (9.39) (2.82) (4.72) (2.28) (-1.17) (-0.42)

obper 28,19 207.03 239.22 276.11 318.09 779.64 72.56(2.03) (7.34) (5.73) (6.65) (4.43) (3.29) (-0.38)

Number of observations 865 856 858 830 801 569 801Corrected R-squamd 0.35 0.22 0.26 0.20 0.09 0.03 0.01Standard error of regression 0.33 0.66 0.94 0.95 1.53 4.30 4.06

*t-statistics are in parenthesis.

predicted audit explanatory variable." nificance of the coefficient on the pre-

To form the predicted value of audit we dicted value of audit from equation (2) asestimate the reduced form equations: estimated in equation (1). The estimated

coefficients of both audit and predictedaudit., @ 'Yii + @y?,,uemp,, audit (paudit) are presented in Table 6.

At the five percent significance level, en-• -y3j nwu + @y4,manuf, + -y,5,old, dogeneity is found in audit classes 1, 2, 3,

• -yr, hseduc, + -y7, perself@ 4, and 6.

• -y8, obper,, + t,, (2)6. Results

This equation contains the maintained Our results fall into three categories.exogenous variables, uemp, nw, manuf, The first two have to do with the nature

old, hseduc, and perself. It also includes of the IRS audit process -whether auditsthe instrumental variable obper. The re- should be treated as endogenous andsults of least squares estimation of equa- whether they have a deterrent effect ontion (2) are presented in Table 5. The noncompliance-and the third has to doHausman statistic for the endogeneity of with the nature of factors besides the au-

audit corresponds to a t-test for the sig- dit rate which influence taxpayer com-


TABLE 6

ENDOGENErrY OF AUDIT (BY AUDIT CLASS)DEPENDENT VARIABLE IS VCL*

Class

Variable 1 2 3 4 5 6 7

-0.067 0.21 0.27 -0.040 0.21 -0.067 0.040(-0.73) (4.64) (3.98) (-3.61) (7.51) (-6.04) (2.31)

paudit 6.54 OAI -0.63 0.090 -0.15 -0.15 0.63(4.87) (2.22) (-1.81) (1.85) (-0.94) (-1.87) 0.50

*OLS regression of vcl on one, audit, paudit, uemp, nw, mankf, old, hseduc, and perself. Coefficients reported are thoseOf audit and the predicted value of audit, from Table 5, paudit. t-statistics am in parenthesis.

pliance. We discuss first the endogeneity compliance, there appears to be little ad-Of the audit process. ditional information to be gleaned from

As indicated in Table 6, in five of seven the pattern of significant deterrent ef-audit classes we find the audit rate to be fects. The pattern of endogeneity of the

endogenous. Furthermore, in audit classes audit rate does, however, suggest that

1 and 2 the coefficient on audit from the different models of IRS behavior may ap-

IV estimation is positive and in audit ply to different audit classes. In particu-classes 3 and 4 it is not significantly dif- lar, for both low and middle income non-ferent from zero. In comparing these re- business audit classes, the presence of

sults with the OLS estimation given in endogenous audit rates is consistent with

Table 3, it can be seen that in two cases a simultaneous-move game-theoretic ap-

negative coefficients on audit in the OLS proach such as that described by Graetz,

estimation are eliminated by allowing for Reinganum, and Wilde (1986). But for

endogeneity (audit classes 1 and 4). Only middle income business and high income

audit class 6 (high income, nonbusiness audit classes, the results seem more con-

returns) remains an anomaly-both OLS sistent with either a random-audit model

and IV estimation yield a negative rela- of the Becker type, or, perhaps, a pre-tionship between the audit rate and com- commitment model such a,, that describedPliance in this case. by Reinganum and Wilde (1985).

Using the instrumental variable esti- Finally, we also have a number of re-mates in Table 4, we see a significant de- sults related to the other variables usedterrent effect of audits in only two of the in our specification of the audit schedule.seven audit classes, an insignificant re- We discuss next those factors besides au-lationship in four classes, and a negative dits which affect compliance, using the

relationship in one. In the two cases where results of the ordinary least squares spec-

the audit rate is found not to be endoge- ification for audit classes 5 and 7, andnous (middle and high income, nonbusi- those of the instrumental variables spec-ness returns) there is a positive (but in- ification for audit classes 1, 2, 3, 4, and 6.

significant) relationship between the audit The two variables associated with op-rate and compliance. However, using the portunities to evade operate uniformly and

ordinary least square estimates for these consistently across all audit classes: an

two audit classes, we find positive and increase in the percent employed in man-

significant relationships between audit- ufacturing or a decrease in the self-em-16

ing and compliance. ployment variable increases percentage

While we consider this to be confir- compliance in all cases except for audit

mation of the economic approach to tax class 7 for which the coeticient on the self-


employment variable is insignificant. 17 of returns. Finally, percent self-employedSimilarly, an increase in the unemploy- is positively related to equilibrium audit-ment rate uniformly decreases percent- ing for all low and middle income returnage compliance. This could be because in- classes but insignificant for upper incomedividuals "compensate" for the lower return classes.income associated with spells of unem- The mixed performance of the auditployment by understating a higher frac- equations should perhaps not be too sur-tion of their actual income (a "target-in- prising. IRS audits turn directly on thecome" theory) or because they shift to DIF score assigned to individual returns.various kinds of underground employ- The DIF score, however, depends only onment. Increases in the percentage of non- tax return characteristics. Thus there iswhites decrease compliance for all low in- no particular reason why audits shouldcome audit classes and both middle and track socioeconomic characteristics of thehigh income nonbusines-, audit classes, but population independently of the indirectincrease compliance for the middle in- effects of these characteristics on compli-come business audit class and have no ef- ance.fect on the high income business auditclass. Finally, we observe somewhat 7. Conclusion/Summaryweaker results for the education and agevariables. The latter is insignificant for Our analysis of the 1969 IRS cross-sec-both types of middle income taxpayers and tion data set has yielded a number ofhigh income business taxpayers, and is strong results. While audits have a de-positively related to compliance for others terrent effect on noncompliance, they re-(except for low income taxpayers who spond, at least for low and middle-incomeitemize-for them the age variable is nonbusiness returns, to the pattern ofnegatively related to compliance). The ed- noncompliance-the IRS seems effec-ucation variable is positively related to tively to direct its resources in these casescompliance whenever it is significant (au- to those areas in which compliance is thedit classes 1, 2, 3, and 5).18,19 worst. For middle income business and all

Our results with respect to the auditing high income returns we fail to find en-process are slightly more mixed, as one dogeneity of a type consistent with thismight expect since the reduced form es- model of IRS behavior. These results,timates represent equilibrium outcomes however, may simply reflect a uniformly(as opposed to the audit schedule itself). high level of noncompliance in these au-An increase in the district (or state) bud- dit classes which makes the DIF score aget per return generally yields more au- poor predictor of the expected return fromdits (except in audit class 7). Unemploy- an audit, at least relative to other returnsment rates have no effect on equilibrium in a given audit class. This would makeauditing, the percent employed in man- these audit classes behave in a fashionufacturing almost none (except for low inconsistent with a random audit model.come nonbusiness itemized returns and We also find that several socioeconomicmiddle income nonbusiness returns where factors, which tend to have no direct im-it is negatively related). On the other hand, pact on auditing, have dramatic effects onthe percentage of nonwhites is positively compliance. For example, increases in therelated to equilibrium auditing for five unemployment rate have significantaudit classes (1, 2, 3, 5 and 7), and age is "hidden costs" in the form of reducednegatively related to equilibrium audit- compliance levels. Increases in the per-ing for all three low income audit classes. centage of the nonwhite population alsoFurthermore, household education is neg- reduce compliance for low and middle in-atively related to equilibrium auditing for come audit classes. These kinds of resultsboth types of low income nonbusiness re are encouraging; they support the eco-turns but positively related to equilib- nomic approach to the compliance prob-rium auditing for almost all other classes lem and suggest that the payoff to im-


proved data and further analysis could be theoretical maximum of 100, its sample distribution

very high. is bounded away from this maximum by 2.5 to 8.4standard deviations. As censoring at the upper boundis unlikely, we adopt a simple linear specification for

FOOTNOTESequation (1). The use of a linear model does, as usual,require some care if extrapolations are done outside

**We thank Bill Lefbom, Chairman of the TCMP the range of the data.

committee of the IRS, for the 1969 IRS cross-section 'The audit and compliance schedules correspond to

data set. Helpful comments have been provided by the "best response" curves familiar from game-theo-

Michael Graetz, Dave Grether, Rod Kiewiet, and two retic models of tax compliance, and observed audit

,no,,ymous referees. This work was supported in part rates and compliance levels correspond to the asso-

by the National Science Foundation.ciated "Nash" equilibria (Graetz, Reinganum, and

Schedule C is for nonfarrn business income and Wilde, 1986).

schedule F is for farm business income.'Misapecification of one structural equation in a

"For a general model which incorporates labor sup system of equations may bias the estimates of all other

ply decisions see Sandmo (1981); for recent surveys of e.quations derived using classical simultaneous equa-

the literature see Witte and Woodbury (198:3) or Cow tion estimation techniques, even if the other equa-

ell (1985). tions are correctly specified, Other consistent esti-3 Details of this procedure are described in Borman mation methods, such as instrumental variables, avoid

(1978), a copy of which was provided to us by Ann this problem.

Witte. Borman gives two examples of the estimated "Using data published in The Annual Report of the

relationship between compliance levels and DEF scores Commisswner of Internal Revenue, for the years 1971-

for 1969. For audit class I (low income, nonbusiness, 1981, and excluding New York state, we find that:

standard deduction) he reports TC = 17.,lh68744 Re -0.0061 + 0.994(RFSHR)(10.0049515D'P) and for audit class 2 (low income, -SHR

nonbusiness, itemized deductions) + 0.0002(BAiVG) + 1.14(PICAP)

where BSHR is the share of total state level budgetsTC 49.4077759 + br.2348477 (DIF) in a given state in a given year, RPSHR is the one-

+ .0002691 (DIF)I. year lagged value of the share of total returns filedin the state, BANG is the one-year lagged value of

Clearly, ucl is not an ideal compliance measure. Be- average additional tax and penalty from audits for thesides combining positive and negative tax changes, it state, and PICAP is the one-year lagged value of realis itself an estimate, based on the DIF formulas, and per-capita income in the state. The correct R2 for thistherefore may be subject to measurement error. How- equation is 0.983, and the t-statiatics are respec-ever, even though measurement error in the depen tively, -8.18, 161.9, 0.50, and 7.21. In this equationdent variable may reduce the overall precision of our BANG which directly measures audit yield, is a proxyestimates, it should not itself lead to inconsistency. for non-compliance. Other related measures of non-In any event, to the extent that the DIF formulas ac- compliance produce similar results. Nevertheless, itcurately reflect noncompliance, there is potential in is important to recognize that across IRS districts, therethe 1161 IIIS data,,et to relate noncompliance to un- is still a great deal of variation in audit rates, an ob-derlying micro-economic characteristics of the tax- servation which is consistent with our hypothesizedpayer population. Furthermore, since 70 percent of the yield effect (Dubin, Graetz, and Wilde, 1987).returns selected for audit during this period were cho- "In an earlier version of this paper (Dubin andsen on the basis of their DIF score (Witte and Wood- Wilde, 1986), we used other presumably exogenousbury, 1994), the possibility of endogeneity of the au- variables such as the percentage of all returns fileddit rate must be taken seriously. that are individual returns as instruments. While of

'rhe Annual Reports are organized by IRS "dis- potential interest in providing over-identifying re-trict." New York state has four districts, and Califor- strictions, these additional instruments appeared tonia, Illinois, Ohio, Pennsylvania and Texas each have generate inconsistent estimates of the compliancetwo districts. We aggregated these to the state level equations, as was indicated by inspection of the resince we could not link three-digit zip codes to dis- duced forms for the audit equation in each class.tricts smaller than the state level. 12 Equation (1) may be estimated equation by equa-

'See Witte and Woodbury (1983) or Cowell (1985) tion, i.e. by audit-class, or in a seemingly iimlatedfor reviews of this literature which suggest that these regression system. The latter method is appropriatevariables are important. Also, note that as our data when the covariance structure of the unobservablesis segmented by audit class, which explicitly includes suggests inter-equation correlation. Using a systemincome, we did not include an income variable di- estimation method in this context however requires arectly in our model. common set of observations (or zip codes) from each

'Even though audit is based on IRS examinations audit class. This approach severely reduces the avail-performed in calendar year 1968 while vcl is an es able observations. A balanced sub-sample of the IRStimate of compliance on 1969 tax returns, there may, data requires the loss of 1611 (5580 7 -567) obser-nevertheless, exist correlation between audit and vations-over 25 percent of the sample. The effiunobservables which affect vcl. In particular, there is ciency gains from the additional observations almostlikely to be serial correlation in both compliance and surely outweigh those gained from inter equation cor-auditing behavior. relation and thus we employ a single-equation esti-

'While the voluntary compliance level (vcl) has a mation technique. With respect to pooling across au


dit classes, inferences based on the subset of common nomic variables on voluntary compliance are rela-observations lead us to reject the equality of coeffi- tively small: ranging from absolute elasticities of apcients. proximately 0.01 for Perself old and nw, 0.02 for ntanuf

"Let X be any n x p matrix, considered here to be and unemp, to 0.06 for hseduc. Similarly, the elastic-• matrix of n observations on p variables. Then X has ity of vcl with respect to audit ranges from 0.02 to• unique decomposition, X = UDV" where L7TU V7V 0.08 for the significant deterrent effects. Recalling the- I, and D is diagonal with nonnegative elements @th, definition of vcl, the magnitude of these elasticitiesk 1,2 (the singular-values of X). Note that should not be too surprising While the significancex x i@;2p' Sothat (X,X) I 2VI'.V7, _ VD Singular- of these results is necessary to demonstrate an eco-ity or near singularity in X'X manifests itself when nomic approach to tax compliance, the absolute mag-D 'is formed. Near zero elements of D will cause the nitudes involved are likely to vary with the use ofinverse of (XX) to be unstable. Belsley, Kuh, and other measures of compliance.Welsch (1980) define a condition index for the matrixX by the ratio of p_ to pm,@.For the purposes of com-paring arbitrary matrices X, Belsley, Kuh, and Welsch REFERENCESrecomniend scaling the columns so that they have unitlength. Condition numbers in the range of 50 to 100 Allingham, Michael G. and Agnar Sandmo, "Incomeindicate severe colinearity. For further details, see Tax Evasion: A Theoretical Analysis," Journal ofBelsley, Kah, and Welsch (1980). Public Economics 1 (1972):323 338.

"Me condition numbers for our data set range from Becker, Gary S., "Crime and Punishment: An Eco-33 to 39. These are based on regressions with 8 vari- nomic Approach," Journal of Political Economy 76ables and roughly 800 to 850 observations. By con- (1968):169 217.trast, the condition numbers for regressions based on Belsley, David A., Edwin Kuh, and Roy E. Welsch,all 36 variables included in the 1969 IRS data set, as Regression Diagnostics: Identifying Influential Dataused by Witte and Woodbury (1985), range from 370 and Sources of Colinearity, (New York: John Wileyto 400 (using 567 observations). The latter indicate and Sons Inc., 1980).severe iI I-conditioning (Belsley, Kuh, and Welsch, Border, Kim and Joel Sobel, "A Theory of Auditing1980) and Plunder," Social Science Working Paper no. 673,

l5Ut X ZY + V Zl@fI + Z2Y2+ v where Z, is an California Institute of Technology, May 1985,N x K, matrix of endogenous variables, Z2 is an n x forthcoming in Review of Economic Studies (1987).K2 matrix of exogenous variables, Z - [Zl:Z2] and W Borman, Scott, "Background Memo on Project 778

[Wl:Z2] is a N x (,p + K2) matrix of instruments. Regression Model: Some Pertinent In-house DataLet Pw W (W'W) "W' and M - I Pw. Then iLs on Factors Affecting Compliance," paper prepared= (Z'Z) 'Z'x and @,rv- (Z'PwZ) '(Z'Pwx). Form the for the Planning and Analysis Division of the IRSpredicted endogenous variables as V - PwZ, and the (1978).residuals from the reduced form as V MZI. Haus- Clotfelter, Charles, "Tax Evasion and Tax Rates: Anman's method focuses on the equation x ZI'YL+ Z2Y2 Analysis of Individual Returns," Review of Eco+ Va + iuo. It is straightforward to verify that ordi- nomics and Statistws 65 (1983).363 373.nary least-squares estimation of this equation is Cowell, Frank, "The Economics of Tax Evasion: Aequivalent to instumental variables. Rewriting we Survey," unpublished, London School of Economics,have, x ZI-Y@+ Z2Y2 + (Z@ Pwzl)o, + vo - Zi(-Yl 1985.+ U) + Z2Y2 + (PWZI)( ot) + vo. Thus the true coef- Dubin, Jeffrey, Michael J. Graetz, and Louis L. Wilde,ficient ^yl is the sum of the coefficients of Z, and PwV. "Are We a Nation of Tax Cheaters? New Econo

"using the notation of footnote 15, we see that the metric Evidence on Tax Compliance," Americandifference between the instrumental variables and or- Economic Review, Papers and Proceedings 77 (1987):dinary least squares covariance matrices is V(@rv) 240-245.V(@,s) - al[(ZPwZ) ' (ZZ) 'I. It follows that V(@rv) Dubin, Jeffrey and Louis L. Wilde, "An Empirical@-V (iLs) if and only if [(Z'Z) (Z'PwZ)l Z'II - Analysis of Federal Income Tax Auditing and Com-Pw]Z Z'MZ - 0. As M is idempotent this latter pliance," Social Science Working Paper 615, Octo-inequality is guaranteed. Thus ordinary least squares ber 1986.is, in general, more efficient than instrumental vari- Graetz, Michael J. and Louis L. Wilde, "The Econom-ables estimation and therefore preferable in situa- ics of Tax Compliance: Fact and Fantasy," Nationaltions where both estimators are consistent. Tax Journal 38 (1985):355 363.

"That manuf and uemp operate uniformly across Graetz, Michael J., Jennifer R. Reinganum, and Louisall seven audit classes suggests that they may in part L. Wilde, "The Tax Compliance Game: Toward anproxy regional effects. Unfortunately, the cross-see- Interactive Theory of Law Enforcement," Journaltional nature of this data set makes it impossible to of Law, Economics, and Organization 2 (1986):1-identify to what extent they do so. The data set con- 32.

"Specification Tests in Econometrics,"structed by Dubin, Graetz and Wilde (1987) should Hausman, J.,hel a rt out this issue. Econometrica 46 (1978):1251-1271.

'qhoalt age is positively related to compliance is Mason, Robert, Lyle Calvin, and G. David Faulken-consistent with Clotfelter's (1983) estimates and Spi- berry, "Knowledge, Evasion, and Public Support forcar and Lunateclt's (1076) su@ey reaulta. That com Oregon's Tax System," Survey Research Center,pliance increases with education is consistent with Oregon State University, Corvallis, Oregon, 1975.Song and Yarbrough's (1978) survey but not the work Mason, R. and H. M. Lowry, "An Estimate of Incomeof Mason and his colleagues (1975, 1981). Tax Evasion in Oregon," Survey Research Center,

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Song, Young-dahl and Tinsley E. Yarbrough, "Tax Economic Model of Tax Compliance," unpublishedEthics and Taxpayer Attitudes: A Survey," Public working paper, Wellesley College (September 1984).Administration Review 38 (1978):442-452. Witte, Ann D. and Diane P. Woodbury, "The Effect

Spicer, M. W. and S. B. Lunatedt, -Understanding Tax of Tax Laws and Tax Administration on Tax Com-Evasion," Public Finance 31 (2) (1976):295 305. pliance: The Case of the U.S. Individual Income Tax,"

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