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TAX RATES AND TAX EVASION: EVIDENCE FROM CALIFORNIAAMNESTY DATA**

STEVENE. CRANE*ANDFARROKHNOURZAD*

ABSTRACT In this paper we examinethe impactof

This paperexaminesthe effectof mar- marginal tax rates on income tax evasionginal tax rates on income tax evasion us- using data from the California Income Taxing data from the California Tax Amnesty Amnesty Program. Amnesty data repre-Program. After correcting for the selectiv- sent a new source of micro data which al-ity bias, we find that evaders respond to lows.construction of direct measures of taxhigher tax rates by increasing their eva- evasion. However, the selectivity bias in-

herent in such data requires specialsion activity. We also find that indivi,,du-als with higher levels of income tend to !conometric treatment. This involves us-evade more. Further, the absolute and rel_ !ng a maximum likelihood technique thatative sizes of both of these effects depend incorporates not only the variables influ-upon the scopeof the evasion measure used. encing the evasion decision, but also thoseFinally, evasion is generally inelastic with influencing the subsequent decision torespect to changes in both marginal tax participate in the amnesty program. Ourrates and income, with the former elastic- findings indicate that, after controlling forities tending to be larger. the effects of other relevant variables,

there is a statistically significant positiverelation from marginal tax rates to alter-

1. Introduction native measures of evasion.rMx rates have been widely recognized The remainder of this paper is orga-JL as a primary determinant of income mzed as follows. In the next section some

tax evasion. In fact, one argument in fa- general background regarding existingvor of cutting marginal tax rates has been theoretical and empirical work on the taxthat, by inducing greater income report- rate effect is provided. This is followed bying, lower rates will broaden the tax base. Section III which contains a discussion ofWhile intuitively appealing, this claim has the features of the sample data employednot been substantiated by traditional mi- in this study. In Section IV, we present acrotheoretic analyses (e.g., Allingham and description of the variables used in ourSandmo, 1972), which have generally empirical model. The estimation proce-found that consequences of a tax rate dure is outlined in Section V, followed bychange to be, a priori, indeterminate. Re- a discussion of our findings in Section VI.cent efforts to analyze this issue in a game The final section provides a summary oftheoretic context have even resulted in a this work and offers some suggestions fornegative relationship between tax rates further research.and evasion (e.g., Graetz, Reinganum, andWilde, 1986). Empirical analyses have also 11. Backgroundbeen unable to resolve this issue. Somestudies ignore the matter altogether by Since the classic work by Allingham andomitting tax rates (e.g., Witte and Wood- Sandmo (1972), the standard approach tobury, 1985). Other studies that do include analyzing the individual's evasion deci-a marginal tax rate variable obtain mixed sion has been to use a portfolio-choiceresults, ranging from no effect (e.g., framework in which the optimal level ofSlemrod, 1985) to a positive effect (e.g., evasion is obtained from maximizing ex-Clotfelter, 1983). Thus further research pected utility of income after taxes andusing alternative sources of data is war- penalties. Using this approach, four fac-ranted. tors have been commonly found to affect

*Marquette University, Milwaukee, Wisconsin the decision to evade. These are the in-53233. dividual's true income, the tax rate, the

189

190 NATIONAL TAX JOURNAL [Vol. XLIII

probability that the evader is detected, and sensus regarding the theoretical and in-the penalty rate to which detected evad- tuitive expectations about the net tax rateers are subjected. In most cases, a positive effect, one is inclined to turn to the em-relationship between the level of evasion pirical evasion literature for evidence.and the individual's true income, and Any attempt to conduct an empiricalnegative relations with both of the com- investigation of tax evasion must firstpliance policy tools are obtained. With re- overcome severe measurement difricultiesspect to the tax rate, however, most models as evasion is inherently unobservable. Ahave been unable to determine an un- variety of rather innovative approachesambiguous relation.' has been employed to deal with this prob-

This ambiguity is due to the fact that lem. Some researchers (e.g., Friedland,a change in the tax rate exerts two op- Maital, and Rutenberg, 1978; Geeroms andposing effects on the taxpayer. On the one Wilmots, 1985; Spicer and Becker, 1980)hand, an increase in the tax rate induces have designed experiments or have con-greater evasion since it increases the ducted surveys in order to generate rele-marginal return to successful evasion (the vant data. Others (e.g., Crane and Nour-substitution effect). On the other hand, by zad, 1986; Tanzi, 1983) have approachedreducing disposable income, a higher tax the problem from a macroeconomic per-rate generates an additional effect (the spective. An attempt has even been madeincome effect) which may lead to more or at developing an evasion index from theless evasion depending on the individu- distribution of tax returns across taxal's attitude towards risk. To the extent brackets (Slemrod, 1985). Only a few au-that an individual is less willing to take thors (e.g., Clotfelter, 1983; Dubin andrisk as his/her after-tax income declines, Wilde, 1988; Klepper and Nagin, 1989;he/she will be less inclined to evade taxes Witte and Woodbury, 1985) have been ablewhen the tax rate increases. Therefore, to develop direct measures that are rep-unless risk aversion increases with in- resentative of evasion behavior under ac-come, or the substitution effect is strong tual tax systems. Of these, only Clotfelterenough to dominate the income effect, one has been able to examine the issue at theobtains the counter-intuitive result that individual level.higher tax rates lead to reduced evasion, Not all empirical studies of tax evasionor that the effect is indeterminate .2 have addressed the tax rate-evasion issue

More recently, income tax evasion has (e.g., Spicer annd Lundstedt, 1976; Wittebeen examined within a game-theoretic and Woodbury, 1985). Those that haveframework which explicitly recognizes considered tax rates have obtained mixedstrategic aspects of the interaction be- results, ranging from no effect (e.g., Geer-tween the taxpayer and the tax authority oms and Wilmots, 1985; Klepper and Na-(e.g., Graetz, Reinganum, and Wilde, 1986; gin, 1989; Slemrod, 1985) to a significantReinganum and Wilde, 1986,1988). In this positive effect (e.g., Friedland, Maital, andcontext, a tax rate change generates an Rutenberg, 1978; Tanzi, 1983; and mostadditional effect through its impact on the notably, Clotfelter, 1983). Note that themarginal return to auditing. It has been one prediction that has not been sup-shown that, under some simplifying as- ported empirically is that higher taxes leadsumptions and for certain audit classes, to lower evasion. Clearly, more research,this effect dominates the conventional tax perhaps using data from alternativerate effect leading to a negative overall sources, is needed. We believe that dataimpact (Graetz, Reinganum, and Wilde, from state income tax amnesty programs1986). This result holds independently of provide a new and thus far unexploitedthe taxpayer's attitude towards risk. opportunity to search for new evidence on

It is interesting to note that the one this issue.prediction that has not been established In what follows we analyze evasion oftheoretically is the one that casual ob- state income taxes in California using dataservers expect, that higher taxes lead to from that state's tax amnesty program. Ingreater evasion. Given this lack of con- doing so, we assume that the decision to

No. 21 TAX RATES AND TAX EVASION 191

evade state income taxes is independent generating a significant amount of netof the decision to evade federal taxes. To revenue.date, no Cne has examined the possible As noted above, revenue generation wascomplications that might arise from the not the sole objective of the Californiainteraction between these two decisions Amnesty Program, as it "was also ex-in a framework which incorporates mul- pected to provide valuable information ontiple tax and enforcement systems. Con- characteristics of tax evaders and thesequently, it is not clear whether we should methods used to evade taxes," (Californiaview federal and state income tax evasion Amnesty Prog-ram, 1986, p. 5). With thisas substitute or complementary activi- in mind, the CTFB identified amnesty re-ties. Furthermore, addressing this issue turns filed by individuals who were eitherempirically would require matching in- not already known to the CTFB, or wouldformation from the individuals' federal not have been detected through normalreturns. Unfortunately, we were unable enforcement procedures. The CTFB thento gain access to these returns. drew a random sample from the amnesty

returns submitted by individuals who hadnot originally filed in the year for which

111. The California State Income Tax they claimed amnesty. Another sampleAmnesty Program was taken from the more than 7,000 re-

Following a number of other states, turns filed by those who amended their

California introduced a tax amnesty pro- original returns under the program. For

gram which ran from December 10, 1984 each of the 186 individuals in the latter3 sample, the CTFB combined the infor-to March 15, 1985. The primary purpose

mation on the amended return with rel-of this program as stated by the Califor-evant data taken from that taxpayer'snia Tax Franchise Board (CTFB) (Cali- . .

fornia Amnesty Program, 1986, p. 1) was onginal return. To ascertain the charac-

to teristics of the individuals in these sam-ples, the CTFB commissioned Sheffrin

provide a number of far-reaching enforcement tools (1985) to conduct a descriptive study.that significantly improved the state's ability to iden- Once this descriptive study was com-tify and collect tax obligations from individuals pre- pleted, the CTFB fumished us with theseviously beyond the reach of traditional enforc,eprograms. nt data. Because our objective is to conduct

econometric analysis we focus on theUnder this program, unpaid penalties and sample of individuals who filed amendedcriminal prosecution were waived for returns. This is required if we are to bequalified individuals. However, accrued consistent with standard theoretical eva-taxes and interest charges were not for- sion models which derive comparativegiven. Those eligible for amnesty in- static results for the interior solution ofcluded individuals who, for 1983 or an partial income under-reporting, and toearlier tax year, had failed to file per- avoid comer solutions of complete hon-sonal income tax returns, had filed inac- esty and dishonesty.curate returns, or were delinquent in Prior to carrying out our econometricpaying their tax liabilities. Amnesty was analysis, we examined the data for inter-not available to those already under nal consistency. This involved recalculat-criminal investigation. ing the tax bill on both the original and

There were over 145,000 returns filed amended returns of each of these 186 in-by about 85,000 individuals under this dividuals. In the process we discovered aprogram, and roughly $154 million in gross number of problem observations. Theserevenue was produced. According to CTFB were primarily missing data, obvious tax-estimates this is $34.5 million more than payer or data entry errors, inability towhat would have been collected through duplicate tax calculations, and in a fewthe traditional enforcement programs. cases no change or a drop in total tax li-Thus, in contrast to the experience of many ability. After removing the observationsother states, California was successful in with these problems, the sample size was


reduced to 123 observations. We have no mation received through the programreason to suspect these omissions bias the would be available to the IRS.sample. Of course, which figures are to be com-

Of much greater concern is the proba- pared depends upon how evasion is de-ble bias due to the self-selected nature of fined. Evasion can take place in a numberthe sample. Clearly, those evaders who of ways. An individual may choose to un-voluntarily chose to participate in the derreport his/her true income. He/she mayamnesty program may not be represen- also overstate adjustments in moving fromtative of the population of Calffomia state Total Income to Adjusted Gross Incomeincome tax evaders as a whole. Fortu- (AGI), or claim excessive deductions fromnately, while complicated, it is possible to AGI when calculating Taxable Income.deal with this type of self-selection bias Finally, once the tax liability associatedeconometrically. However, we postpone our with a given Taxable Income is deter-discussion of the appropriate estimation mined, one can claim excessive creditsprocedure until after we have described against this tax liability when calculat-our empirical model and the data to which ing his/her taxes owed.' An individualit is applied. may also choose to evade using any com-

bination of these methods.With our sample data we are able to

IV. Model Specification and construct measures for different combi-Quantification nations of these forms of evasion. One

measure, which reflects all of the aboveAs mentioned in Section II, theoretical methods of evasion, is the amount of taxes

tax evasion models generally express eva- evaded, calculated by subtracting taxession as a function of marginal tax rate, owed on the original return from taxestrue income, penalty rate, and probability owed on the amended return. An alter-of detection. Of these, the most difficult to native measure can be constructed byquantify has usually been the dependent subtracting Taxable Income on the orig-variable measuring evasion. However, our inal return from that on the amended re-amnesty dataset greatly simplifies this turn. This captures understatement of truetask. income as well as overstatement of ad-

justments and deductions. We can also

A. Measuring Evasion calculate a measure based on AdjustedGross Income by subtracting the AGI fig-

Because our sample includes informa- ure reported on the original return fromtion taken from both the original returns that on the amended return. This mea-and the amended returns filed under am- sure ignores any overstatement of deduc-nesty, construction of an evasion measure tions in moving from AGI to Taxable In-is straightforward. If we assume that the come. Finally, we can measure pureamended returns represent the "truth," we underreporting of income by subtractingcan simply compare the figures on these Total Income reported on the original re-returns with their counterparts on the turn from Total Income on the amendedoriginal returns. This is a plausible as- return.sumption since it seems unlikely that one These measures have a number of ad-who has voluntarily admitted to evading vantages. First and foremost, they are di-on a particular tax return would turn rect measures of evasion in that they arearound and file a false amended return. based on actual individual tax returns. ToThis is especially true in the case of the date, only Clotfelter's (1983) study of theCalifornia Amnesty Program, given that data from the 1969 Tax Compliance Mea-it was publicly announced that the surement Program (TCMP) has utilizedamended returns themselves may be au- such a direct measure at the individualdited, that amnesty filers would be Ragged level.' Second, unlike the TCMP figures,for future reference, and that any infor- the amnesty-based measures do not de-


pend on the auditor's ability to detect distinguish the CTFB's medium and highevasion.' Offsetting these advantages is classifications from the low. We recognizethe previously mentioned self-selection that these are less than ideal controls forproblem, which is discussed in Section V. the detection probability, but, after con-

siderable effort, we are convinced they are

B. Measuring the Determinants of the best measures available to us.'

Evasion In addition to the variables identifiedby theory, previous empirical evidence

Given our assumption that the tax- suggests that one should also control forpayer is truthful when filing under am- such taxpayer characteristics as maritalnesty, we use the information on the status and occupation. In all cases, theseamended return for some of our indepen- should reflect the conditions that existeddent variables. In particular, we use the at the time evasion took place. Therefore,total income figure on the amended re- we construct dummy variables for theseturn as our measure of true income. Sim- characteristics using information takenilarly, the true marginal tax rate (rang- from the original return.' Of course, iting from one to eleven percent) is would be desirable to include a wider rangecalculated by applying the appropriate tax of socio-demographic characteristics suchtable to the taxable income reported on as taxpayers' age, race, and the like.the amended return. However, data limitations preclude us from

As with most empirical analyses, our doing so.data place some restrictions on the extent To summarize, our empirical model ofto which we are able to directly control income tax evasion alternatively usesfor other relevant factors. The fact that Evaded Taxes (TAXGAP), Taxable In-the sample is primarily cross-sectional, come Gap (TIGAP), and Adjusted Grosscoupled with the uniformity of Califor- Income Gap (AGIGAP) as the regres-nia's penalty rate across individuals and sand.' All three regression equations useover the three-year sample period, means as primary regressors true income (Y) andthat no penalty rate can be included in marginal tax rate (MTR). Based on thethe model. On the other hand, subjective standard evasion theory we expect the in-assessment of the detection probability come variable to have a positive sign. Oncertainly varies across individuals, and it the other hand, given our earlier discus-is at least conceptually possible to have a sion of the tax rate effect, we have no signdifferent value for each individual. expectation for the tax rate variable. The

In practice, however, reliable measures regression equations also include dummyof this subjective probability are not typ- control variables for probability of detec-ically available. A connnon alternative has tion (MEDIUM, HIGH), occupation (MGR/been to use some measure of the objective PROF, SALES, CLERICAL), and maritalaudit probability as a proxy. With this in status (MS). We expect the two probabil-mind, we asked the Compliance Devel- ity variables to have negative signs sinceopment Liaison of the CTFB to provide us the omitted category represents individ-with an estimate of the probability that uals with low probability of being de-each of the original returns would have tected. We have no clear sign expecta-been audited under the audit selection tions for the other dummy variables.rules in force at the time of filing. Un-derstandably, the CTFB was not willing V. Estimation Procedureto disclose such sensitive information indetail. However, the Liaison did classify Our objective is to estimate a regres-each original return as having had a high, sion equation of the following formmedium or low probability of being au-dited under the pre-amnesty regime. yi=Xip+ui, i=1,2,...,n (1)Therefore, we control for the detectionprobability using two dummy variables to where yi is a measure of evasion, Xi is a


vector of the determinants of evasion, p though the estimates of the parameters ofis a vector of unknown parameters, and the participation function (the Ss) are un-ui is a random error term with mean zero reliable. However, given that we are in-and variance [email protected] our sample is self terested in the former set of estimates, theselected, estimating (1) using ordinary unreliability of the estimates of 8 is noleast squares (OLS) would result in biased cause for concern.estimates and therefore an alternative In order to apply this estimation pro-approach must be employed.'o cedure we need to specify the components

Correcting the selectivity bias in am- of the vector Zi. In a recent article in thisnesty data is complicated by the fact that journal, Fisher, Goddeeris, and Youngthe sample is truncated; information is (1989) suggest that the decision to partic-available on the evasion decision of those ipate in amnesty programs is influencedwho participated in the amnesty pro- by the perceived increase in the post-am-gram, but there is no information what- nesty penalty rate and probability of de-soever on nonparticipants. In this case, the tection. 12 Here, as in our evasion model,proper estimation procedure requires we focus on the latter influence since weknowledge of factors that influenced the are unable to control for the effect ofdecision of the evaders in our sample to changes in the penalty rate given that ourparticipate in the amnesty program. if sample is cross-sectional, and the highersuch factors can be identified, one can ob- post-amnesty penalty rate applied uni-tain unbiased maximum likelihood (ML) forn-ily to all individuals.estimates of the parameters of (1) using The perceived increase in the probabil-the following likelihood function (Mad- ity of detection is likely to depend upondala, 1983, pp. 266-67), what the individual can learn about the

(p/g) (y, - X,p)]/(l - P2)1/21(27r(F2)-1/2 exp (yi _ Xip)2 (2)

where Zi is a vector of factors influencing program. A good source of information isthe participation decision, 6 is a vector of the amnesty legislation itself. The Cali-unknown parameters, (D(-) is the distri- fornia Amnesty Bill stated explicitly that,bution function of the standard normal, f among other things, returns with self-em-is the correlation coefficient between u, and ployment income (Schedule C) and capi-the error term of the participation func- tal gains (Schedule D) would be targetedtion, and all other notations are as de- for intensified enforcement efforts after thefined previously." amnesty period expired. Thus regardless

The term in the large bracket is the ra- of the form of evasion, an individual whosetio of the conditional probability of par- tax return included these schedules shouldticipation in the amnesty program, given have expected to face increased scrutiny(yi - Xip), to the unconditional probabil- post amnesty." Hence it is reasonable toity of participation. The term outside of assume that evaders with incomes fromthis bracket is the density function of (yi these sources were more likely to have- Xip). Thus the bias-correction proce- participated in the program. To capturedure involves scaling the density function this effect, we create dummy variables toof (yi - Xip) using the ratio of the two reflect the presence of these two sched-probabilities as weights. This procedure ules in the individual's original return.yields unbiased estimates for the param- Other factors not directly related to theeters of the evasion model (the ps), even amnesty program could also have contrib-


uted to changes in the perceived proba- evaders with medium or high audit prob-bility of detection, thereby inducing par- abilities tend to evade less than those withticipation. A prime example would be a low probabilities. Further, as would benotice from the IRS of an impending au- expected, the coefficient of HIGH is largerdit of the federal return. It seems likely in absolute value than that of MEDIUM.that those evaders of California income However, since these estimates are nevertaxes who had recently come under in- statistically significant, not much shouldvestigation by the IRS would have ex- be made of these results.pected their probability of detection at the The marital status variable is positivestate level to have risen. In order to con- in all three equations and approaches sta-trol for this effect, we construct a dummy tistical significance at conventional levelsvariable indicating a positive response to suggesting that, other things equal, mar-an explicit question on the amended re- ried taxpayers tend to evade more. Thisturn regarding whether the participant finding is consistent with some previouswas under IRS audit at the time of filing empirical work on the evasion problemfor state amnesty. (e.g., Friedland, Maital, and Rutenberg,

To summarize, the participation deci- 1978). Finally, of the occupational clas-sion is incorporated into the likelihood sifications, only the managerial/profes-function (2) through the variables SCH- sional category has a t-ratio greater thanC, SCH-D, and IRS-AUDIT. We recognize unity in all three equations. It appears thatthat this participation function is some- in our sample either evasion does not varywhat ad hoc and that we have probably across occupations, or more detailed oc-oversimplified the complex participation cupational classifications are needed todecision. However, to date there has been capture whatever effect there may be.no formal theoretical modeling of am- Turning to the quantitative variables,nesty participation, and we are greatly we find that true income has the expectedconstrained by data availability. positive sign and is statistically signifi-

cant in all equations, a finding consistent

VI. Estimation Results with all previous empirical evasion stud-ies. More important for our purposes,

The maximum likelihood estimation however, is the fact that the marginal taxresults for each of our three measures of rate variable is positive and statisticallyevasion are presented in Table 1.1' The significant at reasonable levels of confi-top of each column of this table contains dence in all three equations. This is in linethe mean value of the dependent vari- with Clotfelter's (1983) finding, as well asable, the log of the likelihood function at with the popular contention that higherthe optimum, the calculated chi-squared tax rates lead to increased evasion. It isstatistic, and the estimated correlation also consistent with the usual microtheo-coefficient between the error terms of the retic prediction that the substitution ef-evasion and participation functions. These fect of a change in relative prices typi-are followed by the estimated parameters cally outweighs the income effect. 16

of both the evasion and participation Despite consistent results with respectfunctions (i.e., the Ps and bs in Equation to the sign and significance of income and2 above).15 tax rate across all equations, there is a

We begin our discussion of the results clear difference in the magnitudes of theseby noting that, based on the chi-squared coefficients in Equation 1 compared to thestatistics, each estimated equation is sta- other two equations. In particular, bothtistically significant. Next we consider the coefficients are markedly smaller inindividual parameter estimates associ- Equation 1, reflecting the much smallerated with the qualitative variables of the mean value of TAXGAP." This high-evasion function. The two dummy prob- lights the conceptual difference betweenability variables representing the CTFB's TAXGAP, which reflects taxes evaded, andaudit groupings have the expected nega- the other measures of evasion which rep-tive signs, which would suggest that resent understatement of various types of

196 NATIONAL TAX JOURNAL [Vol, XLIII

TABLE IMAXIMN-LIKELIHOOD ESTIMATION RESULTS

(Absolute Value of Asymptotic t-Ratios in Parentheses)

EQUATION 1 EQUATION 2 EQUATION 3TAXGAP TIGAP AGIGAP

MEAN 342.98 4265.60 4009.50LbF -924.15 -1217.26 -1216.57CHI-SQR 38.55 21.32 23.70CORR. COEF. 0.04 -0.09 0.02

TAX EVASION "RIABLES

INTERCEPT -322.78 213.02 8.31(2.00) (0.12) (0.007)

INCOME 0.002 0.018 0.018(4.25) (3.46) (3.56)

MTR 62.77 331.13 315.17(3.79) (1.85) (2.42)

MEDIUM -33.48 -402.20 -666.42(0.37) (0.41) (0.68)

HIGH -119.49 -618.60 -2222.14(0.38) (0.18) (0.64)

ms 147.78 1635.57 1901.07(1.56) (1.59) (1.96)

MGR/PROF -124.30 -1501.10 -1253.66(1.35) (1.51) (1.27)

SALES -26.52 -776.02 -2363.89(0.10) (0.27) (0.83)

CLERICAL 41.14 47.82 -761.02(0.22) (0.02) (0.38)

AMNESTY PARTICIPATION "RIABLES

INTERCEPT 4.47 5.40 4.60(0.032) (0.005) (0.003)

IRS-AUDIT -0.004 0.05 0.24(0.000) (0.000) (0.000)

SCH-C 0.24 0.14 -0.16(0.005) (0.000) (0.000)

SCH-D 0.41 -0.65 -0.23(0.003) (0.000) (0.000)


income. In light of these differences, a VII. Concluding Remarkscomparison of elasticities is more mean-ingful. This also allows us to evaluate the In this paper we have studied the be-relative effects of changes in true income havior of state income tax evaders whoand marginal tax rate on different mea- took advantage of the California Tax Am-sures of evasion. nesty Program. In the process, we have

The estimates from Table 1 are con- shown how amnesty data can be utilizedverted into elasticities using mean values to construct alternative measures of eva-and the results are reported in Table 2. sion, and have demonstrated how exist-Note that Equation I remains distinct fi-om ing econometric techniques can be used tothe other two, except that now it exhibits deal with the inherent self-selection prob-the largest relative effects with respect to lem. Our findings support the popularboth true income and marginal tax rate, contention that evaders respond to higherwhereas previously it displayed the marginal tax rates by increasing theirsmallest absolute effects. Table 2 also re- evasion activity.veals that within each equation the tax The results also confirm the theoreticalrate elasticity is considerably larger than prediction that individuals with higherthe income elasticity. However, with the levels of income tend to evade more. Fur-exception of the tax rate elasticity in ther, the absolute and relative sizes of bothEquation 1, the evasion response to these of these effects depend upon the scope oftwo variables is inelastic. The large tax the evasion measure used. In particular,rate elasticity in Equation 1 may be at- the absolute effects of income and tax ratetributable to the fact that the TAXGAP changes are larger for the income-basedreflects all types of evasion and thus cap- measures of evasion, while the relativetures the entire response to tax rate effects are larger for the tax-based mea-changes, while the other evasion measure of evasion. Finally, our results sug-sures only capture a portion of this re- gest that evasion is generally inelasticsponse. with respect to changes in both true in-

Before concluding, a few words regard- come and marginal tax rates, but that taxing the estimated parameters of the par- rate elasticities are consistently largerticipation fimction are in order. By usual than income elasticities.standards, these estimates are quite poor. Analysis of evasion using amnesty dataHowever, it is not clear what is to be made can be improved in a number of ways.of the sign, significance, or magnitude of First, more attention should be given tothese coefficients; it is normally not pos- the participation fimction, including bothsible to obtain reliable estimates for the formal modeling and use of better empir-participation parameters, even though ical counterparts for the resulting argu-their inclusion in the likelihood function ments. Second, amnesty data from othercorrects the selectivity bias. Thus the poor states should be examined to see if the re-estimates of the participation parameters sults reported here can be substantiated.need not be a serious cause for concern. Third, the sensitivity of different types of

TABLE 2ELASTICITIES OF VARIOUS MEASURES OF EVASION

WITH RESPECT TO TRUE INCOME AND MARGINAL TAX RATEEVALUATED AT MEANS

TAXGAP TIGAP AGIGAP

lyicome (Y) 0.29 0.21 0.22

Tax Rate (MTR) 1.50 0.64 0.65

198 NATIONAL TAX JOURNAL [Vol. XLHI

evasion to enforcement-related variables bias that arises from dfferent types of self-selectedshould be examined, preferably, in a model samples, along with remedial proceduressee Maddala

that incorporates a more complete treat- (1983, Ch. 9). Also see Wainer (1986), especially thecontribution by Heckman and Robb, pp. 63-107.

ment of the endogeneity problem associ- "As mentioned in note 9, we do not estimate a modelated with the detection probability. Fi- with Total Income Gap as dependent variable. This is

nally, the possible interaction between because the self-selection correction procedure would

state and federal income tax evasion be further complicated by the filet that there are manyobservations in our sample for which this variable isshould also be investigated. zero.

12They also discuss the role of personal guilt in thisdecision.

ENDNOTES "The fact that the pre-amnesty probability of beingaudited might have depended on the presence of these

**We wish to thank James morandi, Luis Reves, two schedules does not undermine our line of reason-and James Shephard of the California Tax Franchise ing. What we are arguing is that their presence in

Board for helping us gain access to the data used in one's original return has an additional effect post am-this study. The views expressed are those of the au- nesty.thom and do not necessarily reflect the views of the 14We also estimated these equations using OLS andTax Franchise Board. We would also like to aiank our obtained results that are qualitatively consistent withcolleagues at Marquette University and three anon- those reported in the text. Quantitatively, the param-ymous referees for helpftil comments. Financial sup- eter estimates for the amount of taxes evaded,

POrt from the Marquette University College of Busi- TAXG", which captures all forms of evasion, wereMiles Pi-d is gratefully acknowledged. virtually identical to the ML results. Those for the

'Other factors have also been considered in this first income-based measure, TIGAP, which ignoresframework. These include the taxpayer's labor supply overstatement of tax credits, were modestly different.decision (e.g., Sandmo, 1981) and the progressivity of In contrast, the results of the AGIGAP, which reflectsthe tax system (e.g., Marchon, 1979). The conse. only misstatement of income and ac@ustments, arequence has usually been to make the comparative notably different from the corresponding ML esti-static results even more ambiguous. mates. Evidently, the impact of the selectivity-bias

2yitzhaki (1974) showed that if taxes are propor- correction procedure used here increases as the scopetional and fines are levied on evaded taxes rather d= of the evasion measure narrows.evaded income, there would be no substitution effect. We acknowledge that applying maximum likeli-As a result, if risk aversion is decreasing with in- hood to a sample of 123 observations may not gen-come, the effect on evasion of a change in the tax rate erate the most robust results.is negative.

16 Our fmding that marginal tax rates are positivelySFor a comparative survey of the general provisions correlated with the level of evasion conflicts with the

of various states' amnesty programs see Mikesell prediction from the game-theoretic models of tax eva-(1986). sion (e.g., Graetz, Reinganum, and Wilde, 1986). This

4In addition to claiming excessive credits when cal- may be due, in part, to our crude treatment of theculating the tax bill one can understate other taxes probability of detection. On the other hand, as thesesuch as minimum tax on preference income or taxes authors have pointed out, the game-theoretic results

early withdrawals from Individual Retirement Ac- are perhaps best interpreted as applying across a nar-counts. row range of income as within a particular audit class.

50ther studies have also used TCMP data but not As a result, their theoretical predictions and our em-at the individual level (e.g., Dubin and Wilde, 1988; pirical results may not be directly comparable.Klepper and Nagin, 1989; Witte and Woodbury, 1985).

17The small mean value of TAXGAP should not be

6For more on the shortcomings of the TCMP data taken as trivial. As a point of reference, consider thatsee Graetz and Wilde (1985). the average tax liability of the 1983 state income tax

70Uraudit classification dummies serve as instru- return was $769.

mental variables for the detection probability, whichis likely to be endogenous. However, because theseProbability measures can ultimately be traced back REFERENCESto the information contained in the returns, they toomay be endogenous and, therefore, may not be good Allingham, Michael G., and Agnar Sandmo, "Incomeinstruments. Tax Evasion: A Theoretical Analysis," Journal of

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