Tax Rates and Tax Evasion: Evidence from California Amnesty Data** Stevene

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TAX RATES AND TAX EVASION: EVIDENCE FROM CALIFORNIA AMNESTY DATA** STEVENE. CRANE*ANDFARROKHNOURZAD* ABSTRACT In this paper we examinethe impactof This paperexaminesthe effectof mar- marginal tax rates on income tax evasion ginal tax rates on income tax evasion us- using data from the California Income Tax ing 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 tax higher tax rates by increasing their eva- evasion. However, the selectivity bias in- sion activity. We also find that indivi,,du- herent in such data requires special 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 that ative 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 those Finally, evasion is generally inelastic with influencing the subsequent decision to respect to changes in both marginal tax participate in the amnesty program. Our rates and income, with the former elastic- findings indicate that, after controlling for ities tending to be larger. the effects of other relevant variables, there is a statistically significant positive relation 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 existing vor of cutting marginal tax rates has been theoretical and empirical work on the tax that, by inducing greater income report- rate effect is provided. This is followed by ing, lower rates will broaden the tax base. Section III which contains a discussion of While intuitively appealing, this claim has the features of the sample data employed not been substantiated by traditional mi- in this study. In Section IV, we present a crotheoretic analyses (e.g., Allingham and description of the variables used in our Sandmo, 1972), which have generally empirical model. The estimation proce- found that consequences of a tax rate dure is outlined in Section V, followed by change 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 of theoretic context have even resulted in a this work and offers some suggestions for negative relationship between tax rates further research. and evasion (e.g., Graetz, Reinganum, and Wilde, 1986). Empirical analyses have also been unable to resolve this issue. Some 11. Background studies ignore the matter altogether by Since the classic work by Allingham and omitting tax rates (e.g., Witte and Wood- Sandmo (1972), the standard approach to bury, 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-choice results, ranging from no effect (e.g., framework in which the optimal level of Slemrod, 1985) to a positive effect (e.g., evasion is obtained from maximizing ex- Clotfelter, 1983). Thus further research pected utility of income after taxes and using 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 rate ers 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 empirical negative relations with both of the com- investigation of tax evasion must first pliance policy tools are obtained. With re- overcome severe measurement difriculties spect to the tax rate, however, most models as evasion is inherently unobservable. A have been unable to determine an un- variety of rather innovative approaches ambiguous 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 and posing 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 approached reducing disposable income, a higher tax the problem from a macroeconomic per- rate generates an additional effect (the spective. An attempt has even been made income effect) which may lead to more or at developing an evasion index from the less evasion depending on the individu- distribution of tax returns across tax al'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 and risk 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 able when 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 Clotfelter enough to dominate the income effect, one has been able to examine the issue at the obtains the counter-intuitive result that individual level. higher tax rates lead to reduced evasion, Not all empirical studies of tax evasion or 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; Witte been examined within a game-theoretic and Woodbury, 1985). Those that have framework which explicitly recognizes considered tax rates have obtained mixed strategic 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 significant Reinganum and Wilde, 1986,1988). In this positive effect (e.g., Friedland, Maital, and context, a tax rate change generates an Rutenberg, 1978; Tanzi, 1983; and most additional effect through its impact on the notably, Clotfelter, 1983). Note that the marginal 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 lead sumptions and for certain audit classes, to lower evasion. Clearly, more research, this effect dominates the conventional tax perhaps using data from alternative rate effect leading to a negative overall sources, is needed. We believe that data impact (Graetz, Reinganum, and Wilde, from state income tax amnesty programs 1986). This result holds independently of provide a new and thus far unexploited the 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 of theoretically is the one that casual ob- state income taxes in California using data servers expect, that higher taxes lead to from that state's tax amnesty program. In greater 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 net of the decision to evade federal taxes. To revenue. date, no Cne has examined the possible As noted above, revenue generation was complications that might arise from the not the sole objective of the California interaction between these two decisions Amnesty Program, as it "was also ex- in a framework which incorporates mul- pected to provide valuable information on tiple tax and enforcement systems. Con- characteristics of tax evaders and the sequently, it is not clear whether we should methods used to evade taxes," (California view federal and state income tax evasion Amnesty Prog-ram, 1986, p. 5). With this as substitute or complementary activi- in mind, the CTFB identified amnesty re- ties. Furthermore, addressing this issue turns filed by individuals who were either empirically would require matching in- not already known to the CTFB, or would formation from the individuals' federal not have been detected through normal returns. Unfortunately, we were unable enforcement procedures. The CTFB then to gain access to these returns. drew a random sample from the amnesty returns submitted by individuals who had not originally filed in the year for which 111. The California State Income Tax they claimed amnesty. Another sample Amnesty Program was taken from the more than 7,000 returns filed by those who amended their Following a number of other states, original returns under the program. For California introduced a tax amnesty pro- each of the 186 individuals in the latter gram which ran from December 10, 1984 sample, the CTFB combined the infor- to March 15, 1985. 3 The primary purpose of this program as stated by the Califor- mation on the amended return with rel- nia Tax Franchise Board (CTFB) (Cali- evant. . data taken from that taxpayer's fornia Amnesty Program, 1986, p. 1) was onginal return. To ascertain the characteristics of the individuals in these sam- to 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 these viously beyond the reach of traditional enforc,e programs. nt data. Because our objective is to conduct econometric analysis we focus on the Under this program, unpaid penalties and sample of individuals who filed amended criminal prosecution were waived for returns. This is required if we are to be qualified individuals. However, accrued consistent with standard theoretical eva- taxes and interest charges were not for- sion models which derive comparative given. Those eligible for amnesty in- static results for the interior solution of cluded individuals who, for 1983 or an partial income under-reporting, and to earlier 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 econometric paying 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 a program, and roughly $154 million in gross number of problem observations. These revenue 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 to what would have been collected through duplicate tax calculations, and in a few the 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 observations other states, California was successful in with these problems, the sample size was 192 NATIONAL TAX JOURNAL [Vol. XLIII reduced to 123 observations. We have no mation received through the program reason 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 number the 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 may amnesty program may not be represen- also overstate adjustments in moving from tative of the population of Calffomia state Total Income to Adjusted Gross Income income tax evaders as a whole. Fortu- (AGI), or claim excessive deductions from nately, while complicated, it is possible to AGI when calculating Taxable Income. deal with this type of self-selection bias Finally, once the tax liability associated econometrically. However, we postpone our with a given Taxable Income is deter- discussion of the appropriate estimation mined, one can claim excessive credits procedure 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 individual it 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 above As mentioned in Section II, theoretical methods of evasion, is the amount of taxes tax evasion models generally express eva- evaded, calculated by subtracting taxes sion as a function of marginal tax rate, owed on the original return from taxes true 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 by quantify 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 true task. income as well as overstatement of adjustments and deductions. We can also A. Measuring Evasion calculate a measure based on Adjusted Gross Income by subtracting the AGI fig- Because our sample includes informa- ure reported on the original return from tion 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 pure amended returns represent the "truth," we underreporting of income by subtracting can 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 amended original 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 are around and file a false amended return. based on actual individual tax returns. To This is especially true in the case of the date, only Clotfelter's (1983) study of the California Amnesty Program, given that data from the 1969 Tax Compliance Mea- it was publicly announced that the surement Program (TCMP) has utilized amended returns themselves may be au- such a direct measure at the individual dited, 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- No. 21 TAX RATES AND TAX EVASION 193 pend on the auditor's ability to detect distinguish the CTFB's medium and high evasion.' Offsetting these advantages is classifications from the low. We recognize the previously mentioned self-selection that these are less than ideal controls for problem, 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 identified by theory, previous empirical evidence Given our assumption that the tax- suggests that one should also control for payer is truthful when filing under am- such taxpayer characteristics as marital nesty, we use the information on the status and occupation. In all cases, these amended return for some of our indepen- should reflect the conditions that existed dent 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 these turn as our measure of true income. Sim- characteristics using information taken ilarly, the true marginal tax rate (rang- from the original return.' Of course, it ing from one to eleven percent) is would be desirable to include a wider range calculated by applying the appropriate tax of socio-demographic characteristics such table 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 of to which we are able to directly control income tax evasion alternatively uses for other relevant factors. The fact that Evaded Taxes (TAXGAP), Taxable In- the sample is primarily cross-sectional, come Gap (TIGAP), and Adjusted Gross coupled with the uniformity of Califor- Income Gap (AGIGAP) as the regres- nia's penalty rate across individuals and sand.' All three regression equations use over the three-year sample period, means as primary regressors true income (Y) and that no penalty rate can be included in marginal tax rate (MTR). Based on the the 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. On certainly 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 sign different value for each individual. expectation for the tax rate variable. The In practice, however, reliable measures regression equations also include dummy of 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 marital audit 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 since opment 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 to disclose such sensitive information in V. Estimation Procedure detail. 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 form medium or low probability of being audited under the pre-amnesty regime. yi=Xip+ui, i=1,2,...,n (1) Therefore, we control for the detection probability using two dummy variables to where yi is a measure of evasion, Xi is a 194 NATIONAL TAX JOURNAL [Vol. XLIII vector of the determinants of evasion, p though the estimates of the parameters of is 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, the selected, estimating (1) using ordinary unreliability of the estimates of 8 is no least 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 this nesty data is complicated by the fact that journal, Fisher, Goddeeris, and Young the sample is truncated; information is (1989) suggest that the decision to partic- available on the evasion decision of those ipate in amnesty programs is influenced who 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 we knowledge of factors that influenced the are unable to control for the effect of decision of the evaders in our sample to changes in the penalty rate given that our participate in the amnesty program. if sample is cross-sectional, and the higher such 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 upon dala, 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 is the 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 targeted tion, and all other notations are as de- for intensified enforcement efforts after the fined previously." amnesty period expired. Thus regardless The term in the large bracket is the ra- of the form of evasion, an individual whose tio of the conditional probability of par- tax return included these schedules should ticipation in the amnesty program, given have expected to face increased scrutiny (yi - Xip), to the unconditional probabil- post amnesty." Hence it is reasonable to ity of participation. The term outside of assume that evaders with incomes from this 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 capture dure involves scaling the density function this effect, we create dummy variables to of (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 the eters of the evasion model (the ps), even amnesty program could also have contrib- No. 21 TAX RATES AND TAX EVASION 195 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 with ticipation. A prime example would be a low probabilities. Further, as would be notice from the IRS of an impending au- expected, the coefficient of HIGH is larger dit 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 never taxes who had recently come under in- statistically significant, not much should vestigation by the IRS would have ex- be made of these results. pected their probability of detection at the The marital status variable is positive state 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 levels variable indicating a positive response to suggesting that, other things equal, mar- an explicit question on the amended re- ried taxpayers tend to evade more. This turn regarding whether the participant finding is consistent with some previous was under IRS audit at the time of filing empirical work on the evasion problem for 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 than C, SCH-D, and IRS-AUDIT. We recognize unity in all three equations. It appears that that this participation function is some- in our sample either evasion does not vary what ad hoc and that we have probably across occupations, or more detailed oc- oversimplified the complex participation cupational classifications are needed to decision. 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 expected constrained by data availability. positive sign and is statistically significant in all equations, a finding consistent with all previous empirical evasion stud- VI. Estimation Results ies. More important for our purposes, The maximum likelihood estimation however, is the fact that the marginal tax results for each of our three measures of rate variable is positive and statistically evasion 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 line the mean value of the dependent vari- with Clotfelter's (1983) finding, as well as able, the log of the likelihood function at with the popular contention that higher the optimum, the calculated chi-squared tax rates lead to increased evasion. It is statistic, 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 respect functions (i.e., the Ps and bs in Equation to the sign and significance of income and 2 above).15 tax rate across all equations, there is a We begin our discussion of the results clear difference in the magnitudes of these by noting that, based on the chi-squared coefficients in Equation 1 compared to the statistics, each estimated equation is sta- other two equations. In particular, both tistically significant. Next we consider the coefficients are markedly smaller in individual parameter estimates associ- Equation 1, reflecting the much smaller ated with the qualitative variables of the mean value of TAXGAP." This high- evasion function. The two dummy prob- lights the conceptual difference between ability variables representing the CTFB's TAXGAP, which reflects taxes evaded, and audit 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 I MAXIMN-LIKELIHOOD ESTIMATION RESULTS (Absolute Value of Asymptotic t-Ratios in Parentheses) EQUATION 1 EQUATION 2 EQUATION 3 TAXGAP TIGAP AGIGAP

MEAN 342.98 4265.60 4009.50 LbF -924.15 -1217.26 -1216.57 CHI-SQR 38.55 21.32 23.70 CORR. 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) No. 21 TAX RATES AND TAX EVASION 197 income. In light of these differences, a VII. Concluding Remarks comparison 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 who and 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 utilized verted 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 to the 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 popular both true income and marginal tax rate, contention that evaders respond to higher whereas previously it displayed the marginal tax rates by increasing their smallest absolute effects. Table 2 also re- evasion activity. veals that within each equation the tax The results also confirm the theoretical rate elasticity is considerably larger than prediction that individuals with higher the 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 both Equation 1, the evasion response to these of these effects depend upon the scope of two 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 rate tributable to the fact that the TAXGAP changes are larger for the income-based reflects all types of evasion and thus cap- measures of evasion, while the relative tures 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 inelastic sponse. with respect to changes in both true in- Before concluding, a few words regard- come and marginal tax rates, but that tax ing the estimated parameters of the par- rate elasticities are consistently larger ticipation fimction are in order. By usual than income elasticities. standards, these estimates are quite poor. Analysis of evasion using amnesty data However, 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 to these coefficients; it is normally not pos- the participation fimction, including both sible 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 other corrects 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 2 ELASTICITIES OF VARIOUS MEASURES OF EVASION WITH RESPECT TO TRUE INCOME AND MARGINAL TAX RATE EVALUATED 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-selected should be examined, preferably, in a model samples, alongwith remedial proceduressee Maddala that incorporates a more complete treat- (1983, Ch. 9). Also see Wainer (1986), especially the contribution by Heckman and Robb, pp. 63-107. ment of the endogeneity problem associ- "As mentioned in note 9, we do not estimate a model ated 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 many observations in our sample for which this variable is should also be investigated. zero. 12They also discuss the role of personal guilt in this decision. ENDNOTES "The fact that the pre-amnesty probability of being audited 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 and Tax Franchise Board. We would also like to aiank our obtained results that are qualitatively consistent with colleagues 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, were Miles 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 ignores framework. 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 reflects the tax system (e.g., Marchon, 1979). The conse. only misstatement of income and ac@ustments, are quence 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 scope tional 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 positively SFor 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 the culating the tax bill one can understate other taxes probability of detection. On the other hand, as these such 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. 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