alm 1991b

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T H B WVol. 6 S. N o. 3July M l

Perspective on the ExperimentalAnalysis of T axpay er Repo rting

James Aim

University of olorado t B o u lder

T he income tax has made mo re liars o ut of the American people than golf has.Will Rogers

TAX evasion appears to be a large and grow ing problem in the United S tates. De-spite obvious difficulties in meas urement the Internal Revenue Service (1990)estimates that the tax gap, or the amou nt of u nderrepo rted federal incom e taxes,

was 83-94 bil lion in 1987, and had grow n at an annu al rate of over ten percent since1973. Such underreporting reduces the tax revenues of the federal go vern m ent affectspuhlic provision of g o o d s and services, creates misallocations in resource use, altersthe distribution of incom e in unpredictable w ay s, and increases feelings of unfair treat-ment and disrespect for the law .

The analysis of the individu al repo rting decisio n ha s taken a variety of app roach es.The underlying premise of nearly all of these appro aches, at least tho se in econo mics,has been the same: individuals pay taxes because they fear detectio n and pu nish m entThis economics-of-crime approach is based on traditional expected utility theory,which views a rational individu al as w eighing the expected u tility of benefits from suc-cessful underreporting against the uncertain prospect of detectio n and ptmis hment

This approach has generated numerous insights. ' There are however, severalfundamental problems with the existing applicatio ns of expected u tility theory to tax-

payer reporting. First although it is clear that enforcement action s affect co mpliance toa degree, it is equally clear that detection and punishment cannot explain all com idi-ance behavio r. ' T he frequency of audit in the U nited S tates has fallen to less th an one

p e r c e n t and the additio nal penalties co nstitute only a fractio n of the im paid tax liabil-ity. According to expected utility theory, most individuals should choose to under-report all of their taxes, at least on incom e not subject to third-party repo rting. How-

ever, the extent of compliance with the income tax remains relatively high, which

See Cowell (1990) for a comprehensive review of mucb of this literature.

Compliance Is defined here as reporting a income and paying aU taxes in accordance with tbe appli

cable laws, regulations, and court decisions.

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can no t be due to enforcement activities alone . Other factors must play a dom inant in the reporting decision. Indeed, the puzzle of tax compliance is why people pay tanot why they evade them. The challenge facing those who analyze the reporting dsion Is to explain these levels of com pliance, as w ell as the changes in com pliance result from policy changes.

Second, the failure of expected utility in the analysis of tax compliance reflecgrowing dissatisfaction with this approach in the analysis of individual choice ununcertainty. Numerous recent surveys (Fishburn 1988; Machina 1987, 1989; Sug1986) dociunent evidence from a variety of areas showing tha t individuals in m anycumstances do not In fact maximize expected utility. In response, alternative nexpected utility m odels of behavior have been advanced. H owever, these theories hnot yet been fully analyzed, and none have been applied to tax compliance.

In this perspective, 1 discuss and assess wh at we have learned from research oindividual taxpayer reporting decision, with a ttention to the specific evidence of Bet al. (1991h) and of Collins and Plumlee (1991) in this Fomm. I draw two general cclusions from this literature, which parallel the above problems with the econoanalysis of tax compliance. First, compliance is a com plicated decision, one that cledepends in part upon the financial incen tives facing th e taxpayer bu t one that alsopends upon other factors that have not been incorporated into the expected uttheory application. Th is deficiency renders all existing ap plications of expected uttheories in tax compliance (including my own work) incapable of explaining mucthe actual tax reporting decisions of individuals. Second, and as a consequebroader approaches to the reporting decision that encompass non-expected utitheories of behavior are nee ded .'

Still, the existing experimental analyses of taxpayer reporting decisions makcontribution to this area. For exam ple. Beck et al. (1991h) allow taxable incom e touncertain, and find that such uncertainty has significant and complex effectsreported income.^ Collins and Plumlee (1991) recognize that the probability of adepends in part on the choices of the taxpayer, and find that such audit endogenaffects the joint reporting and labor supply decision. These are important and results. Their w ork also shows that com parative statics can be usefully employed toplain the changes in the reporting decisions of individuals in response to changevarious policy p aram eters o r institutions. How ever, if the goal instead is to explain

level of compliance, then a new approach is needed that incorporates the major ments of the reporting decision in a theory that may well depart from expected uttheory; that is, existing theories of tax compliance must be modified to consider badditional elements of the tax reporting decision and alternative approaches tohavior under uncertainty. This need can be helped by various m ethods, including tof experimental economics.

The remainder of this article is structured as follows. Section I briefly revmuch of the non-experimental literature on tax compliance. Section II discusses

* Note that the foctts Is on lndividuol tax com pliance. Of perhaps equal importance is corporate compHowever, with the exception of Rice (1990). corporate compliance has received little attention.* It should be noted tha t Beck et aï 1991h) analyze taxpayer aggrassivaness, defined as a willingn

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Alm—Expérimentai Analysis of Taxpayer Reporting 579

application of experimental methods to compliance research, including tha appropriate

procedures that should he followed in experimental analysis, the results that have been

derived from previous studies, and the limitations of experimental m^hods. Section II

reviews the work of Beck et al. (1991h) and of Collins and Plumlae (1991). Section IV

presents some conclusions and obsarvations.

I. Non-Experimental Research on Tax Compliance

TTieoretiCd] Literature

The dominant approach to the analysis of taxpayer reporting follows the eco

nomics-of-crime methodology first applied to tax compliance by AlUngham and

Sandmo (1972). In this model, an individual is assumed to receive a fixed amount of

income I, and must choose how much of this income to declare to the tax authorities

and how much to underreport. The individtial pays taxes at rate t on every dollar D o

income that is declared, but pays no taxas on underreported income. However, tha individual may ba audited witii some fixed probability p; if audited, then all underre

ported income is discovered, and the individual must pay a penalty at rata / on each

dollar of deficient taxes, where f includes the unpaid taxas. If tmderreporting is de-

tected, the individual s disposable income equals:

Ic=I-tD-iï(I-D), (1

while if underreporting is not detected income is:

I«=I-tD, (2)

Expected utility theory then suggests that the individual will choose D to maximize tha

expected utility EU(I) of the evasion gamble:

EU(I)=pU(I<:)-Kl-p)U(W. (3

where utility U(I) is assumed to be a function of income. In this model, an increase in

the probability of detection p and the penalty rate / unambiguously incieasa declared

income D. An increase in the tax rata also increases reportad incoma if the

individual s preferences exhibit decreasing ahsolute risk aversion. In this case, an in

creasa in the tax rate increases the benefits of underreporting int:oma but also increases

in equal proportion tha cost of underreporting, such that the relative price of under-reporting is tinchanged. However, the higher tax rate also lowers income and increase

the individual s risk aversion, which leads to more raported income.

This basic model has baan extended to allow for diffarent settings. For exampla, tha

individual may choose declared income jointly with additional variables, such as labor

supply or income allocated to tax avoidance. Alternative tax and penalty functions can

ba introducad. The impact of complexity and uncertainty about the ralavant fiscal

parameters can ba analyzed, as can the effect of tax préparera in resolving this tmcer

tainty. Government can be allowed to spend the taxes that are collected. Hia assump

tion that the probability of detection is fixed for an individual (a random audit strategy}

There efe of course oth« approaches that do not invoke the eupKted utility hypotkesis. See Rothet a

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ca n he relaxed hy allowing the au dit agency to use information from the taxpay erstur ns in d etermining who m to select for au dit and hy examining th e interaction oftaxpayers and th e government collection agency in e game theory setting.'

Virtually all theoretical work has continued to use the expected utility m odel, anhas generated many insights, especially regarding how an individual responds

greater enforcement activities and how government can optimally choose its enfom ent strategy. However, this literatu re is in a sense too com plex. It is only in the spler models that clear-cut analytical results can be generated on the compliance im pof basic policy param eters. W hen mo re complex dimens ions of individual hehaviorintroduced, the theoretical results generally become ambiguous. It is doubtful thattheoretical analysis will yield more meaningful results in the future.'

Paradoxically, the theoretical m odels of individual ch oice are also too sim ple. Inte rna l Revenue Service (1978) has listed 64 factors that m ay affect the reporting dsions of taxpayers, hut theoretical models are capable of including only a few.

limited ability to incorporate many relevant factors or to incorporate them in a meingful way has meant that these theories are often unable to explain the level ofreporting, even wh en they are capable of explaining changes in reporting in responspolicy innovation s. In particula r, as emphasized hy Graetz and W ilde 1885) and oththese m odels generally imply that rationa l individuals shou ld pay far less in taxes tthey actually do.

In short, expected utility theory implies that individuals should pay less in tatha n they in fact d o. This result suggests that the com pliance decision m ust he affehy other factors not m entioned by expected utility theory or must he affected in wnot captured by the theory.

Empirical Literature

The obvious diffictilty in applied work is the ahsence of reliable information ondividual reporting behavior To facilitate em pirical research, the 1RS has begun to mdata available to researchers through its Taxpayer Comp liance Measurem ent Prog(TCMP), and virtually all emp irical models of com pliance in the Un ited States are baon these d ata.' For example, Clotfelter (1983), Witte and Woodhury (1985). and D uand Wilde (1988) have used different forms of these data to estimate the impacpolicy param eters (e.g., marg inal tax rates , aud it rates, and pen alty rates) upon vari

direct an d ind irect measures of tax evasion. These studies hâve found the unsurp ris

' See Roth et al . (1S89) and Cowdl (1990) for comprehensive surveys of this theoretical l iterature.

* For exam ple, Pencavei (1979,123. -24) demon strates tbat wb en labor supply is endogen ous the impareportad Inco me of cha nges in tba fíne rate and the probabil ity of detection bec om e ambiguous. H e co ncltbat the results of the exis ting literature are fragile bec au se they are generated from a set of rather napostulates.

* To i l lustrate, consid er aga in the standard expe cted util ity mo del of Allingha m and Sa nd mo (1Sup pose that the general util ity {unction U (r) i s replaced with the speci fic function ¡¡ /{i - e ) , w h ere thacript i refers to tbe state of the w or td ( i> C ,N )a nd ei sa m ea su re of the indiv idual 's constant re lat iveaverto risk Us ing the definitions of inc om e in equations 1) an d (2), the maximization in equation 3) can be s

for the optimu m am ount of reported inco me D*. Now supp ose ihet D* Is calculated for speci fic paramvalues. For exam ple, if t » 0.30, f = 2.0, p= 0. 02 , and e s 1, then an individual wi l l optimal ly report zero incBven wh en tb e pn^Hdjil ity of d etection equa ls 20 pe rço it , tbe optimal 13* is zero . Very large-^and unreali

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results that an increase in the marginal tax rate decreases reported income and that anincrease in audit rates increases reported income.

The empirical work has, however, several major weaknesses. The most trouhle-scm e is the quality of the data. Most data are from the TCMP, which contains a detaileline-by-line audit of a stratified random sample of roughly 50,000 individual tax returns

conducted on a thre&-year cycle . These audits yield an 1RS estimate of the taxpayer's true income so that a measure of individual tax evasion can he calculated. Howeveronly Clotfelter (1983) has had access to the microlevel estimates of evasion. Mostresearchers use TCMP data aggregated to the three-digit zip code level, an aggregatemeasure likely to comprise disparate elements of underreporting that refiect very dif-ferent motivational factors. TCMP data also have some well-recognized deficiencies:the audits do not detect all underreported income, nonfilers are not captured, honesterrors are not identified, final audit adjustments are not included, and there are fewnoneconomic factors to which the data can he linked. The use of TCMP data forempirical estimation of the determinants of com pliance hehavior is therefore problem-atic.

Most empirical work is also plagued by problems of endogeneity, particularly inmeasures of the audit rate. As correctly argued by Dubin and W ilde (1988), if reportedincome depends upon the probability of detection and the probability of detection alsodepends upon reported income—that is, if 1RS behavior is endogenous, so that theassumption of a random audit strategy is inappropriate—then using the audit rate as anexplanatory factor leads to simultaneity b ias. Only Dubin and Wilde (1988) and Duhinet al. 1990) consider the possible endogeneity of the audit rate in their econometric estmation: however, they use aggregate, not individual, measures of reported ncome.

To avoid the problems with the TCMP data. Crane and Nourzad 1986) examine thimpact of infiation on aggregate evasion, defined as the gap between income reportedon tax returns and income in the national income accounts. Dubin et al. 1990) estimatthe impact of audit rates on reported income of the states, with data on reported incomhy state collected from annual reports of the 1RS. By necessity, these studies focus onthe aggregate, not the individual, response.

Surveys of taxpayers have also been used to assess factors such as perceptions ofthe probability of detection, the fairness of taxation, and the re^m nsiveness of govern-ment in the respondent's reporting decis ion . Unfortunately, these surveys are also

subject to a number of m ethodological prohlems. As emphasized hy Klepper and Nagin(1989), individuals may not remember their reporting decisions, they may not respondat all, or they may not respond truthfully. Surveys are also unahle to control for manyrelevant determinants of compliance. Finally, they cannot determine the direction ofcausality between compliance and its determinants: that is, statements reg rding theunfairness of a tax may result from a rationalization of noncom pliance rather than hethe cause of noncomidiance.

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Alm—E xperimental An alysis of Taxpayer Reporting ÎS8

po ss ible to general ize beyo nd the laboratory unless on e uses neutra l instruct ioni i, s in cthe experimenter cannot contro l (or induce) the va lues that subjects assoc iate withloaded terms .

Previous Experimental Work on Taxpayer Compliance

The basic des ign of most compl iance experiments i s s imi lar . Human subjects in acontro l led laboratory are to ld that they sho uld fee l free to make as m uch inc om e as poss ible . At the heginning of each round of the experiment, each suhject i s g iven incomand must dec ide how much income to report . Taxes are paid at some rate on a l l reported, hut not on underreported, income. However , underreport ing i s discovered withsome probabi l i ty , and the subject must pay a f îne on unpaid taxes . This process irepea ted for a g iven number o f rounds . At the comple t ion o f the exper iment eachsubject i s pa id an amount (say , the accumulated earnings) that depends on his or heperformance during the experiment. Into this microeconomic system, various pol icy

changes can be introduced .In the f irst experimental s tudy of tax compl iance , Friedland et a l . (1978) examinesubject responses to changes in tax rates , penal t ies , and frequencies o f audi ts . Theyfind that an inc rea se in th e tax rate inc rea ses both the proba bil i ty of und erreporting an dthe level of underreporting, and that large fines are more effective deterrents than frequen t audi ts , a l though inc rea ses in e i ther f ines or audi t rates increa se reported in com e

A num ber of experimenta l s tudies have fo l low ed. Spicer and Becker (1980) find thaco m pl ia nc e i s lower am on g subjects w h o are to ld that the ir tax rate i s higher than thaof others , and that co m pl ia nc e i s higher am on g those w ho are to ld that the ir tax rate ilow er than others . Th ey con clud e that perception s of f isca l inequi ty affect com pl iance. In a similar vein, Becker et al . (1987) introduce a public sector transfer schemeand f ind that indiv idual compl iance dec l ines i f the subject be l ieves that he or she rece ives less than others . Spicer and Thomas (1982) f ind that the compl iance dec is ion ia ffected by the presence of uncerta in audi t probabi l i t ies , a l though the effect i s somewhat compl icated. Spicer and Hero (1985) and Webley (1987) analyze the impact oaudits on post-audi t compl iance , and f ind that subjects who have been audited repormore income. Baldry (1986) f inds that some indiv iduals do not cheat because of morarea son s. Coll in s et al . (1990) al lo w a joint cho ice of wo rk effort an d reporting, an d finthat subjects who can underreport tend to work harder than subjects who have no

opportuni ty for noncompl iance .In a ser ies o f recent pap ers , my co-authora an d I hav e exte nd ed the ana lys is o f tax

payer compl iance in several direct ions . Aim, McKee, and Beck (1990) f ind that the introduct ion o f a tax amn esty in wh ich subjec ts ca n pay prev ious ly un pa id taxes w i thoupenal ty lowers post-amnesty compl iance , a l though a wel l -des igned amnesty i s ahle toreverse Öi is dec l ine . Aim , McC lel land, and Sc hu lze (forthcoming) f ind that man y subjects overweight the low probabi l i ty of audi t , which leads them to pay more in taxethan suggested by expected ut i l i ty theory . They a lso f ind Úiat the introduction of apub l ic go od f inanced by the tax es increase s com pl ian ce . A im et aL (1991a) f iad that di

impact of taxpayer uncerta inty about the tax rate , the f ine rate , and Úu audit ratdep end s cr it i ca l ly on the presence or abs ence o f a publ i c good , W ie n subjec ts rece ive

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vote is decisive rather than close. Aim, Jackson, and McKee (forthcoming) show positive rewards to com pliant taxpaye rs have a signific ant positive affect on tax cpliance.

In total, these experimental studies suggest the following conclusions:

1. Individuals report less income as the tax rate rises.2. An increase in the penalty rate increases compliance.3 . More frequent audits encourage greater compliance.4. Many individu als overweight the probability of audit, behaving as if the pr

bility is higher tha n it actually is.5. Com pliance is reduced wh en individu als feel that they are treated unfairly

tive to others, regardless of the source of the inequity (from the tax or thependiture side).

6. The compliance decision is made jointly with the labor supply decision.7. Individuals pay more in taxes when they receive something for their tax

ments.8. Comp liance can be encouraged by rew ards as well as penalties.9. The institutions tha t determ ine the use of tax paym ents affect com pliance. I

viduals ]; ay more in taxes when faced with a public program that they seand tha t they know enjoys widespread support.

10. The introduction of unce rtain tax policies increases compliance in the absof government expenditures and decreases compliance in their presence.

11. A tax amnesty lowers post-amnesty compliance if the amnesty is not wdesigned.

12 . Some individuals pay taxes because they believe that cheating is wrong.Some of these results (a.g., the im pact of fines an d au dit rates) are similar to those foin the theoretical and empirical literatures, hut others are not (e.g., the effect ofrates), and most cannot ba derived from tha theoretical and empirical analysis of paya r reporting. As discussed later, some of these conclusions are altered hy the expm en ts of Back et al. (1991b) and of Collins and Plumlee (1991) included in th is For

Limitations o Experimental Economics

There are sound reasons for caution in intarpreting an d generalizing these exp

mental rasults. Soma early experiments did not follow some now widely accepted cadures of tha experimental paradigm, such as the use of repeated experiments naü tral instru ction s. Much work also lacks realism bacatise values of the various poparam eters do not approxim ate real-world values.

A l t h o i ^ more racent experimental rasearch has generally addressed these plems, some concerns remain, some of which are more real than others. A comm on ccism of experimental economics is that tha student subjects typically used may norepresentative of taxpayers. However, there is now much evidence that the expme ntal responses of sttidants are no different th an th e responses of other subject po(Plott 1M7),

Of more legitimate con cern , the rrau lts may wall be sansitive to the specific axpm e n U design, so that replication is cr u ci al It is also possihla that subjacts modify t

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Alm—E;q>erimentalAnalysisofTaxpay«rRsporting 585

$2 in an experiment is clearly different from a decision to report ac tual incom e on anann ual tax re turn , even if the lahoratory incentives are salient. In particular, the lahoratory setting cannot capture a catastrophic loss such as jail, and it cannot capture thesocial stigma that some surveys suggest is an important factor in taxpayer reportingTh ere is also some evidence from Wehley and Halstead 1966) that subjects may behav

differently in the laboratory than io the naturally occtirring world.In short, one must use the restilts &om lahoratory experiments with some car«

How ever, such use depends largely upon th e purpose of the experiment. According toRoth (1987), experim ents can be classified into three bro ad categories tbat dep end upo nthe dialogue in wh ich they are mean t to participate: Speaking to Theo rists includesthose expe riments designed to test well-articulated theories; Search ing for Fa cts involves experiments that examine the effects of variahles about which existing theoryhas little to say; and W hispering in the Ears of Prin ces identifies those experimentmotivated hy specific policy issues. To date, most experiments on taxpayer reportingfall into the first two categories. It is likely to he some time hefore a serious dialoguewith th e p rinces of the 1RS is established.

III. Experimental Work in this Forum

The experim ents of Beck, Davis, and Jung (BDfl and of Collins and Plumlee CP) inthis Forum exam ine different aspec ts of the taxpayer repo rting dec ision. BDj foctis ontaxpayer uncertainty ahout the true level of taxable income, while CP introdtice non-random audit selection schemes. Each study finds that reporting is affected by the specific factor introdu ced. These results are new an d impo rtant, and represent som e of the

first attempts to systematically examine these issues.The Beck, Davis, and Jung Study

Taxpay er un certainty arises hecause of imprecision and complexity in the tax codelack of uniform training and abilities among government auditors, taxpayer ignoranceof penalties or the factors that cause an audit, frequent changes in the tax code, omerely the ongoing potential for changes in the code. A growing theoretical literature(Beck and Iimg 1989; Scotchmer and Slemrod 1989) suggests that an individual whomaximizes expected utility may respond to greater uncertainty by increasing reportedincom e. There is also some anecdotal evidence that the 1RS has deliberately m aintainesome am biguity in its policies in o rder to g enerate such reactions. There is, howeverlittle evidence to support this pred iction, especially when th ere is unce rtainty ahout th elevel of taxahle income.

BDj provide th is evidence. They examine the effects of taxable income uncertaintyhy assuming that a subject does not know with certainty his or har taxable incomeRather, in the event of an aud it, a suhject's taxahle income is determined by a draw ingfrom a probahility distribution of taxable incomes in w hich possible values of taxaldeincom e range uniformly from a low to a h i ^ value.

Th e theoretical m odel of BD) is rich an d allows them to derive a num ber of specifi

hypotheses. Some of these predictions are fairiy stan dard. For example, an individual ialways predicted to increase reported incom e w hen either the probahility of detection

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or the f ine ra te incre ases , and a r isk-averse individua l is pred ic ted to incre ase repoi n c o m e w h e n t h e t a x r a t e i n c r e a s e s . Ho w e ve r , o t h e r h y p o t h e s e s a r e mo r e c o m p l i c aIn pa r t i cu la r , an inc reas e in t axab le incom e uncer ta in ty (measured by the range o fab le income in tbe un i fo rm d i s t r ibu t ion) may e i the r inc rease o r dec rease repoincom e, dep end ing u pon th e degree o f r isk ave rs ion and th e va lues of the aud i t and

ra tes . In genera l , grea ter uncer ta in ty is more l ike ly to increase repor ted incomeh i g h e r a r e t h e p r o b ab i li ty of a u d i t a n d t h e p e n a ^ .

BD) then tes t these pred ic t ions in th e labora tory . T he ir exper im enta l des ign fo llc lose ly bo th the i r theory and accep ted exper imen ta l p rocedures . Sub jec t s r ece ivecom e a t th e beg inn ing o f each rou nd an d cho ose the am oun t o f incom e to repor t. Tpay taxes on in com e tbey choose to repor t : how ever , they do no t kno w w i th ce r tathe i r t ru e t axab le incom e . If aud i ted w i th som e f ixed ran dom probab i l i ty , the actaxab le income i s de te rmined by a d rawing f rom a un i fo rm d i s t r ibu t ion , ope ra ta l ized by the use of a b ingo cage conta in ing bal ls sequent ia l ly numbered over a knrange . A low leve l o f unce r ta in ty i s r ep resen ted by a na r row range in the numbebal ls , and a b igh level of uncer ta in ty is represented by a wide range. Audi ts are demined by the ro l l of a d ie , and a penal ty is imposed on def ic ient taxes . Because ttheory sugges ts tha t a t t i tudes tow ard r isk a re an impo r tan t d e te rm inan t o f r epor t inghavior , BDJ a lso a t tempt to induce r isk neutra l i ty and r isk preference us ing the metsuggested by Berg e t a l. (1986). Severa l levels of t i e tax ra te , the f ine ra te , and th e prb i li ty o f de tec t ion a re used . The ex per im en t l a s t s 60 ro imd s .

BD J 's exp er im enta l results a re genera l ly cons is tent wi th the i r hyp othese s , a t leasthe comparat ive s ta t ics of the repor t ing decis ion . For the r isk-neutra l exper imentsincrease in the f ine ra te or the probabi l i ty of de tec t ion increases repor ted incom

chan ge in tbe t ax ra te does no t a ffec t r epor ted incom e, and an inc rease in unc e r taincreases repor ted income wben e i ther the f ine ra te or tbe probabi l i ty is increased.the r isk -averse exper imen ts , the com para t ive s ta t ic s r e su lt s a re som ewh at weaker . im pac t of th e tax ra te on reported inco m e is only m arginal ly s ignif icant , a l thoughigher tax ra te tends to increase repor ted income as predic ted . Similar ly , the ef fecuncer ta in ty on repor ted income is only marginal ly s ignif icant : again , the d i rec t iochan ge in repo r ted inco m e i s cons i s ten t w i tb the hypo thes i s (e .g ., an inc rease in unta in ty dec reases repor ted income when the t ax ra te i s low, and inc reases repor tedcome wben the t ax ra te i s h igh) .

The hypotheses on the levels of repor ted income are , however , not genera l ly vf ied by the exper imenta l resul ts . The ac tual levels of repor ted income are consis teh igher th an p red ic ted , e spec ia l ly for tbe expe r ime n ts in which r i sk ave rs ion i s induAs no ted ea r l i e r , such a re su l t i s common.

T hese results a re of con sidera ble in teres t . Th ey are wel l -grounded in (expected i ty ) theory , and they a re genera ted f rom a soun d exper im en ta l des ign . Fur the r , thresults ex pa nd considerably our exp er im enta l kno wle dge of beh aviora l responTbey conf i rm previous exper imenta l resul ts on the impact of audi t and penal ty ra tereported inc om e. Unl ike the resul ts of ear l ie r w ork, how ever , these suggest tha t th

fec t of an increase in tax ra tes may increase repor ted income, and the ef fec ts may depend upon a t t i tudes toward r i sk . Mos t impor tan t ly , the re su l t s conf i rm the theo

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witii caution. First, the theoretical and experimental results depend critically on theassum ption of a known distribution of reported incomes, and a uniform distribution isused to derive explicit theoretical solutions for reported income. However, taxpayersare unlikely to know the actual distribution of taxable incomes. Moreover, the uniformdistribution leads to some odd kinds of behavior, since subjects clearly have no incen-

tive to repo rt incom e outside the ranges of the distribution. A more realistic assum ptionmight be to have taxable incomes distributed normally around some mean level; thiswould allow an increase in uncertainty to be analyzed as a mean-preservin£ spreadwithout changing the supports of the distribution.

Second, BDJ use unrealistically high values (0.4, 0.5, and 0.9) for the probability ofaud it (BDJ also assume that the probability is fixed an d random .) These high levels maybe necessary to test the hypotheses, However, given that the percentage of tax returnsselected for audit is now less than one percen t, the levels in the experiment make it un-likely that the experimental results will generalize to actual reporting beh av ior. It

would be useful to replicate these experiments with more realistic parameter values.Third, the experimental design relies heavily upon the method of Berg et al. (1986)for inducing risk preferences. The use of this method requires that subject native preferenc es be linea r in the probabilities. M ore precisely, it requires that the independenceaxiom of expected utility theory hol ds . If this assumption does not hold, then prefer-ences cannot be induced. However, there is a growing literature that argues convinc-ingly that preferences are not in fact linear in the probabilities (see, e.g.. Machina1989).'* More generally, in their theory and inducing mechanism BDJ require that indi-viduals maximize expected utility. As discussed earlier, there is enormous evidence tothe contrary.

The maintained assumption of expected utility theory may explain the generalfailure of the experimental results to accurately p redict th e levels of reported income,even though the conditions for doing so are optimal (a.g., perfect information, non-extreme param eter values). However, the difficulties in predicting levels of com plianceshould not be surprising, since expected utility theory is often incapable of explainingtaxpayer reporting.

The Collins and Plumlee Study

The early theoretical m odels of tax compliance generally assumed that individuals

faced a fixed ra ndom probability of audit. However, this assumption ignores a centralfeature of the compliance system in the United States: each individual must submit atax return to the 1RS, each return directly conveys information to the IRS, and it is

'* It is , bow eve r, rislcy to assum e that actual audit rates are a true me asure o f tbe probability of de tection,giv en the ability of the IKS to match third-party Information reports to tax returns. Furtbermore, so me classe sof taxpayers are sub iect tom uch high ertb an average audit rates because of tbe l evel orth ena ture of lnco me s lnthese classes. Finally, the perceived audit probablUties of many taxpayers are often much greater than tbeactual rates.

The ind ep en de nc e axiom states tbat the evahiaUon of a lottery is not affected hy the replacemen t of someleme nt in the lottery with another elemen t tbat is indifferent to i t Formally, tbe lottery fx ] S preferred to th

lottery {y l if an d on ly If the com binad lottery Ix with prohab ility p, 2 with probahillty (1 -P ll is preferred to tbecombined lottery [y wi t h probabi li ty p ,zw i thp n> ba biU ty( l -p) I . I t can be shown that the independence axiomIs equivalent to the hypiHhesis tbat the individual preference function takes the expected util ity form. See

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partly o n the basis of this preliminary transm ission of information tha t the 1RS dm ines whom to select for audit. Thus, the probability of audit is neither fixed n or dom, but depends in p art upon the actions of the taxpayers.

Although recognition of this obvious feature of the com pliance gam e has been sthere are no w several theoretical analyses of the taxpayer-agency interaction (BeckJung 1989; Graetz et al. 1986; an d R einganum and Wilde 1985,1986). These studieserally find that the pre sence of strateg ic audits significantly affects individual behavIn particular, they demonstrate that the tax agency can generate greater levels oporting under a strategic audit policy than under a random audit policy.

Th e analytical results are, however, only hypotheses, and CP are the first to exine experimentally the implications of a strategic audit policy.*^ They do this hy inducing thre e audit schem es. The first is the standard random audit scheme. The secis a cutoff audit schem e, in which only those returns w ith the lowest levels of repoincome are selected for audit. The third is called a conditional audit scheme. Heprelimina ry piece of infonnation is used by the agency to classify taxpaye rs into c

gories in w hich the agency believes there are different ex ante probabilities of highecome levels; a cutoff schem e is then applied to the category with the higher ex ante of inco me. CP examine the effect of these different aud it strategies on two jointly dmined dim ensions of cho ice: the am ount of income earned (or effort) a nd the levunderreporting.

The experimental design of CP is straightforward but creative, especially inoperationaUzation of the audit sch emes. Before the start of each round, each of tenjects must earn income hy performing a decoding exercise. Subjects then chooseamount of their earnings to report as taxable income, on which they pay taxe

audited, they pay a p enalty equal to a m ultiple of the deficient tax es. Two differentrates and penalty rates are used. The three au dit schemes are designed such that thpost audit ra te is 20 perc ent for each. In the random audit scheme, two of the ten jects are random ly chosen; in the cutoff strategy, the two retu rns w ith the lowest leof reported income a re selected; in the con ditional schem e, the ten reports are firsttitioned into two groups of five on the basis of earnings in a practice round, and the two reports with the lowest levels of reported income in the high earnings cateare selected. The experiment lasts four rounds.

The experimental results of CP are broadly consistent witb their speculations

are not overly strong , especially for effort. The aud it strategy is found to have a sigcan t effect on c omp liance. The most imderreporting o ccurs with the random stratand the least with Üie conditional schem e, as expected. CP also tend to find (with snotable exceptions) that an increase in the tax rate increases underreporting, whilincrease in the penalty rate lowers un derrep orting . How ever, the results for effort sgenerally disappointing. A lthough t he au dit schem e has a significant effect on ethe results are not consistent with the expectations of C P . The effects of the taxand the penalty rate on effort are not significant.

Like those of BD{, these results are of some im portan ce, especially those rega

•• Alao, se e B eck e t al. (1991a1.

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the impact of the audit schema on tmderreporting. For the first time, ä is experl-niantal confirmation of the thaoretical speculation o n the impo rtance of äia audit pro-cess, and there is evidence that tha tax authority can indeed do hetter than a simple ran-dom audit strategy.

There are, however, reasons for some caution. First, soma results are weak andsom e are counterin tuitive. As noted, effort is little affected hy policy chang es. Even forunderreporting, the impact of the audit scheme is far from uniform. For exampla, thetwo tax/penalty combinations [low/low] and [high/high] generate roughly tha samalevel of tmd erreporting for all three au dit schem es. The impact of a penalty increase isgenerally small, and in one case an increase in the penalty actually increases tinder-raporting.

Second, despite its use in o ther experim ental studies, it is possible that the decodingexercise is not a true measure of effort. Rather, it seams more likely to indicata abil-ity, either in nate or learned. If tha decoding exercise is more acctirately seen as a tast of

innate ahility, then it is not surprising that the various policies have little impact on e ffo rt Moreover, if subjects become more skilled in decoding with m ore practice ,the n it is also not stirprising tha t effort generally increases over the four round s of theexperiment

Indeed, despite the sound theoretical reasons for analyzing tha joint effort-tinder-reporting choice, potential problems w ith decoding as a true measure of effort argu a fora replication of the experim ent in w hich income is assumed fixed. It may also ba thatthe joint choice of effort and underreporting complicates unnecessarily the stihjects'decisions.

Third, although the experimental design is generally sound, soma of its featuresraise concern. Fo r example, there are rel tively few rotmds (four) in each experim ent, andthere is some evidence that behavior changes over these rounds . The earnings of tha stib-jects seem low for the length of the exp erim ent Also, CP tise loaded instruc tions. Admit-tedly, there is some work (Aim, McClelland, an d Schulze forthcoming) that suggests tiiatthis makes no difference to the restilts . It is also evidence that economic factors cann otexplain all compliance behavior, and econo mic factors are all that neutral term s ca n in-troduce in an experiment; that is, context is important in explaining compliance he-havior, and context can be introduced only by the use of loaded terms. However, theexperimenter inevitably loses some control over preferences hy the use of loaded in-

structions. These features suggest that further replication is desirabla.Fourth, there are some aspects of strategic audits that are not captured, eiüiar by

the theoretical literature on which the experiments are based or by tha experimentsthemselves. For example, tinlika suhjects in the experiments of CP, taxpayers do notknow the RS audit se lection nila; in fact, tha RS has gone to some length to ensure thesecrecy of its rule. There is also a dynamic aspect to the 1RS audit selection that isignored in the theoiy and the experimen ts: RS discovery of underrei>orted incom e tiiisyear m ay lead to audits hoth of previotis and of future years. There are additional piecesof information that a re known by the RS and that m ay ba used in its aud it selection. Itis reasonable to assum e that the RS know s tha distrihution of incomes of all taxpayers,

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even if it does not know the income of a specific taxpayer. Such information ispresent in the experiments of C P. Finally, the theoretical and experim ental work eines only one type of interaction present in the tax com pliance game, that betweentaxpayer and th e agency, and omits the gam e among the taxpayers themselves.

Finally, and m ost importantly, as with nearly all work on taxpay er reporting, th

sults of C P show much higher levels of reporting than is predicted hy the theory. Tare som e difficulties in generating predictions , given tha t CP allow joint choice of eand underreporting and that the probability of audit is sometimes nonrandom. pose, however, that one uses the standard expected utility model in which incomfixed and audi ts are rando m. C alculations of tiie optimal level of reported incom egest that for m ost of the param eter value comb inations used by CP the level of comance shoidd be zero. The introduction of a variable labor supply complicates theseculations, hut it is possihle to show that even here com pliance shouid he at or near

IV. Summary and ConclusionsLaboratory m ethods have considerably expanded our knowledge of the taxpaye

porting dec ision. These studies have exam ined issues tha t cannot be handled fruithy theory, and hav e given information on individual behavior in areas in which reldata simply do not exist. More broadly, they have suggested new factors that slikely to affect com pliance behavior, a s well as approach es th at may prove useful ianalysis of reporting. Although experimental methods have their limitations, diffties in the theoretical and em pirical methodologies of compliance research make iperative that the potential contributions of the experimental approach he recogn

and its use he maintained.Th e work of Beck et al. (1991h) and of C ollins an d P lumlee (1991) adds to th i

cum ulating experimen tal evidence. BDJ verify their theo retical propos itions that utainty about taxable income significantly affects reported income. In particular, results suggest that uncertainty seems most likely to lower reporting, given the alevels of the various fiscal para meters . CP find tha t the nature of tha aud it scheme significant effect on tax compliance, and provide support for the common percepthat the 1RS m ay well know what it is doing in its non random selection of returns. sets of results are new and interesting.

However, as emphasized earlier, there are two major conclusions to be draw n the literature on tax compliance. First, the compliance decision depends num erous factors, includ ing but not limited to the enforcemen t activities of the gomen t. Second, the inco rporation of these factors may well require a move beyondsical expected utility theory and into theories of behavior suggested by psychologsociologists, and an thro po log ists. Un til these lessons are acted upon , I think ilikely that we will be able to explain much of the reporting decisions of taxpayerparticular, although we may continue to have some success in explaining the chain reporting behavior, we will fail to explain the level of reporting.

The major factors that must he considered in any theory of compliance are, lieve, obvious. One demonstrated factor is the threat of detection and punishm

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tion and that this probability depends in part on one's actions. Another factor is govern-

ment expenditures. Individuals may pay taxes because they value the public goods pro-

vided by government and they recognize that their taxes may be necessary to get others

to contribute to the finance of the public goods, both now and in the future. Social

norms also enter the reporting decision. Survey evidence indicates that compliance is

strongly affected by the taxpayer's commitment to the social norm of compliance, that

those who believe that others cheat are more likely to cheat themselves, and that an in-

dividual's perception of how he or she is treated relative to others affects compliance.

There are, of course, additional factors: uncertainty, the role of tax practitioners, the

process by which government decisions are made, and so on.

Incorporation of these factors in a formal theory of compliance is a difficult task. It

is a task that also is likely to require the exploration of alternative theories of hehavior

under uncertainty. It is, finally, a task in which experimental economics can play a

major role. It may not be possible to develop one theory that explains the behavior of all

individuals at all times, or even one that explains the actions of the same person at alltimes. However, until this effort is made, I think it unlikely that we will come much

closer to explaining the compliance puzzle.

There is a large literature that supports the notion that compliance depends in p art on the use of tax rev-enues. Some of this work (e.g., Isaac et al. 1985 loóles at vo lunta ^ contributions to public goods. Other work(e.g.. Aim, McClelland, and Schulzeforthc om ing) ooks directly at the impact of government expenditures oncompliance. Both strands often conclude that individusls pay more as the benefit from the ir contrihutlonsincreases. See Aim et al. (1991b) for a more detailed diacnssion.

See. for example, the studies cited in footnote 12.

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