MPRA Muni Personl RePE Arive Imperfet etetion of Tx Evsion in Corrupt Tx Administrtion iego Esobri Te niversity of Texs - Pn Amerin 7. July 0 Online t ttp://mpr.ub.uni-muenen.de/3998/ MPRA Pper No. 3998, posted 3. June 0 6:6 TC
Imperfet etetion of Tx Evsion in Corrupt Tx Administrtion iego Esobri Tis rtile models te imperfet detetion of tx evsion motivted by te existene of orrupt tx dministrtion. Consistent wit previous literture, fines nd udit probbilities bot ve positive effet on ompline. Moreover, te model sows tt tey ve negtive effet on te bribes pid to orrupt tx offiils. More orruption dereses ompline levels, giving onest uditors inentives to work rder to detet evsion. iving inspetors sre of te deteted evsion tx frming mkes uditors work rder; owever, inresing teir wges redues teir exerted effort to disover evsion. Higer ompline n s well be ieved by iring more effiient inspetors. Keywords: Txtion, evsion, orruption Introdution Tx evsion is n importnt problem t te moment of olleting txes. For te.s., te Internl Revenue Servie estimtes tt 7% of te inome tx libility is not pid Slemrod nd Yitzki, 00. To deter txpyers from evding txes, te tx dministrtion runs osionl udits wit penlties often ssessed if te txpyer is disovered evding txes. Empiril evidene presented in Feinstein 99 sows tt udits re imperfet, wit te verge exminer's detetion rte being pproximtely 50%. However, stndrd ssumption in te tx evsion literture is tt ll tx evsion is deteted one te txpyer is udited e.g., Allingm nd Sndmo, 97; Cnder nd Wilde, 99. Lee 00 onsiders imperfet detetion by modeling te possibility tt txpyers exert ostly effort to self-insure nd redue te risk involved wen evding txes. In Lee's model te mount of evsion found in te uditing proess will depend on te txpyer's self-insurne. Te present pper follows similr rgument s in Lee 00, but imperfet detetion of evsion rises beuse te uditors re te ones wo exert ostly effort to disover evsion. A orrupt tx dministrtion is introdued to model tis imperfet tx evsion detetion nd to nlyze te effet of different uditors' remunertion lterntives on tx evsion. Beuse potentil bribes obtined troug udits re modeled s funtion of te Te utor tnks Morris Cots, Alejndro Esteller-More, Timoty ronberg, Crlos Oyrzun, Willim F. Sugrt II, Jon Strub nd Leon Tylor for teir omments. An erlier version of te pper ws presented t te Soutern Eonomis Assoition Meetings nd t te Midwest Eonomis Assoition Meetings. eprtment of Eonomis nd Finne, Te niversity of Texs - Pn Amerin, Edinburg, T 78539, Pone: 956 665-3366, Fx: 956 665-500, Emil: esobrid@utp.edu., RL: ttp://fulty.utp.edu/esobrid
mount of evsion found, orruption presents n inentive for uditors to work rder towrds disovering evsion. Consistent wit previous literture, te model finds tt fines nd udit probbilities bot ve positive effet on ompline levels. Moreover, giving te tx inspetors sre of te evsion found will inrese ompline levels, wile inresing teir lump-sum inome wge will redue it. Lower evsion levels n s well be ieved by deresing te inspetors' osts of finding evsion or by reduing orruption. Modeling tx evsion wit orrupt tx offiils is n importnt re of reser. Tnzi nd voodi 00 explin tt eonomies rterized by gret extent of orruption re rgued to be plgued by substntil tx evsion tivities s well. Cu 990 mentions tt in survey undertken by te ity government of Tipei in 98, 94% of te txpyers polled reported being led to pying bribes to orrupt tx dministrtor. Cited in Snyl, ng nd oswmi 000, Te Polie roup 985 suggests tt t lest 76% of ll Indin tx uditors re orrupt. Tere is growing literture tt onsiders te joint roles of tx evsion nd orruption. Cu 990 finds tt te fine nd te udit probbility n enourge txpyers to intensify teir bribing tivities. Cnder nd Wilde 99 find tt in te presene of orruption, udit probbilities re generlly iger, nd tt iger fines nd iger tx rtes n redue expeted government revenues. In relted pper, Hindriks, Keen nd Mutoo 999 sow tt te impt of evsion nd orruption n be regressive, nd tt induing onesty in te olletion of progressive txes n be ostly. A Lffer like bevior of overll tx revenue my rise in te model of Snyl, ng nd oswmi 000, wile more reently, Bilotk 006 onsiders tx evsion nd bribery gme, nd oerke 008 looks s ow tx evsion ffets orruption t te tx pyer firm level. 3 Two losely relted ppers re Wne 000 nd Vsin 003. As in bot of tese rtiles, we onsider two different remunertion lterntives for te tx offiils: A sre of te deteted evsion tx frming, nd wge. Wne's tx evder ooses unilterlly te mount to evde, nd is model llows for morl zrd nd dverse seletion. 4 In te urrent pper te mount of evsion omes from Ns Equlibrium, nd tere is morl zrd, but tere is no dverse seletion. Our model is similr to Vsin 003 beuse in is model tx evsion lso depends on te inspetor s efforts. However, Vsin only onsiders two levels for te inome nd two levels for te effort. Terefore, if low effort is exerted, zero evsion is found, nd if ig effort is exerted, ll evsion is found. Tis mens tt in Vsin tere is no imperfet detetion of tx evsion. In my model tere is imperfet detetion of tx evsion in te sense tt te mount of evsion disovered is ontinuous funtion of te level of effort exerted by te tx offiils. nlike tese two studies, in tis pper we llow for ontinuum in bot, inome nd effort. 3 For survey of te literture on tx evsion, see Andreoni, Errd nd Feinstein 998 nd Slemrod nd Yitzki 00. For survey on orruption, see Jin 00. 4 Tere exists te problem of morl zrd beuse te exerted effort nnot be observed. Tere exists te problem of dverse seletion beuse not ll potentil tx inspetors n be identified s being onest or disonest.
Te rest of te pper is strutured s follows. Setion explins te bevior of te txpyer, te onest nd orrupt tx uditors, nd te intertion mong gents. Setion 3 presents te bseline prmeters nd funtionl forms for te simultion. A sensitivity nlysis to poliy prmeters nd te results re presented in Setion 4. Setion 5 onludes. Te Model Te model onsiders te intertion between two gents. A rtionl txpyer tt deides ow mu of er inome to report to te tx utority, nd tx offiil tt n be of two different types: orrupt or onest. Te txpyer is onfronted wit problem of oie under risk. Se knows er inome, te tx legisltion, te penlties from evding txes, te probbility of being ugt evding txes, nd te probbility of ving orrupt tx uditor uditing er tx libilities. Te tx uditor sres te sme informtion, but ignores te txpyer's true level of inome.. Te Txpyer Te txpyer s fixed gross inome Y, nd se s to py proportionl inome tx t on delred inome. Tere is fixed probbility p of being udited by te tx dministrtion. If ugt evding txes, se s to py fine s over te unpid tx libility disovered by te uditor. If ll evsion is found by te uditor, te fine is given by sty-. Notie tt we need s for te txpyer to py t lest te evded mount ty-. A stndrd ssumption in te existing tx evsion literture is tt wen te txpyer is subjet to investigtion, te uditor gets to find te true mount of te txpyer's inome Y. 5 However, Feinstein 99 sowed tt pproximtely only one-lf of evsion is found wen tx reports re inspeted. In tis pper we llow for te mount of tx evsion found Y- to be funtion of te effort exerted by te tx offiils. Let φy,, i be te level of inome reveled in te uditing proess wen uditor i engges effort 0 i for i for te orrupt, nd i for te onest uditor. Te model does not neessrily imply tt te uditors do not know te true level of inome. A more urte interprettion of te φ funtion would be tt te uditors know te true level of inome, but tey must exert some effort to leglly justify te true level of inome given te mount of inome te txpyer s reported. One te txpyer is seleted to be udited, tere exists fixed probbility k tt te uditor is orrupt. k n be interpreted s te level of orruption in te tx dministrtion, wit k 0 wen tere is no orruption nd k wen ll tx offiils re engged in orrupt tivities. Wen udited by orrupt offiil, te txpyer is ble to espe from pying te fine if se pys lower nd lso monetry bribe. Te bribe rte b is te proportion of te fine tt te txpyer pys te orrupt offiil in order to espe from pying te full mount of te fine. It is ssumed tt if te txpyer deides to under-report er true level of inome, se will lso be willing to del wit te orrupt tx offiils. Te totl mount of te bribe is bstφy,, - wit 0 b. Te rtionl txpyer's bevior onforms te Von 5 Lee 00 presents model were te mount of evsion found depends on te txpyer's self-insurne. 3
Neumnn-Morgenstern xioms of bevior under unertinty. utility given by: Se mximizes er expeted E[ ] p Y p k Y t t bst Y,, k Y t st Y,, For nottionl onveniene define W Y t Y t bst Y,, 3 Z Y t st Y,, 4 were W is te level of disposble inome resulting wen te individul is not udited, is te level of inome resulting wen te individul is udited nd bribes orrupt tx uditor, nd Z is te level of inome wen se fes n onest uditor. If bot types of uditors exert te sme level of effort, we ve tt te txpyer will lwys be better-off if investigted by orrupt tx uditor W > > Z. However, tis my not lwys be te se sine different types my ve different inentives to work rder towrds disovering evsion. Te level of inome reveled in te uditing proess, φ, s te following properties: Y,,0 5 Y,, Y 6 Y,, i / > 0 for i, 7 i Y,, i / 0 for i, 8 i Eqution 5 implies tt wen te uditor mkes no effort i 0 for i, e finds no evsion nd te inome level reveled is just te one delred by te txpyer. Eqution 6 mens tt wen mximum effort is engged i for i, te uditor gets to know te true mount of te txpyer's inome Y. Eqution 7 indites tt iger levels of effort will enounter more evsion nd eqution 8 suggests deresing mrginl produtivity of effort. For nottionl onveniene we will just write φ i, but we sould keep in mind tt te φ funtion depends on Y nd s well. Te first nd seond-order onditions for te txpyer re respetively given by: 4
5 0 ] [ s s Z k p bs bs pk W p t E 9 < 0 ] [ Z k kb tps s s Z k p bs bs pk W p t E J 0 Assuming onvity of te utility funtion, te seond-order ondition is unmbiguously negtive wen te seond derivtive of φ i wit respet to is greter or equl to zero.. Te Tx Auditors Te model is rterized by te existene of two types of tx uditors. Te first is n onest uditor wo ooses ow mu effort to engge in finding evsion. Te seond is orrupt uditor tt ooses ow mu effort to engge in finding evsion nd bribe rte b to rge te tx evder one evsion is found. Te utility funtions tt tey mximize re respetively given by: M b stg V,, M b stb V,, were i. > 0 for i,. M is te mount of inome independent from te orruption tivity or te uditing proess. 0 < ω < is te onstnt mrginl ost of effort in terms of mrginl utility of inome nd 0 g is n exogenous sre tt te onest uditor reeives from te uditing proess. Notie tt te txpyer's delrtion is funtion of te uditors' deision vribles, so te optiml vlue of te prmeters will depend on te intertion between te gents. Te first-order onditions for te uditors re: 0 ', st N V H 3 0 ', stb N V H 4
H, b V b ' N st b 0 5 b b were te prtil derivtives of wit respet to b, nd re given in te ppendix, nd N N b,, M stg 6 b,, M stb 7 If te txpyer is udited by te orrupt tx offiil, te model ssumes tt te tx offiil rges n mount equl to sbtφ -b,, nd tells te tx dministrtion tt no evsion ws found. An interesting extension to tis model would be to follow Wne 000 nd Aoni, Amto nd Mrtin 003 nd inlude monitoring of te tx uditor bevior. Wne onsiders te possibility of n dditionl udit tt monitors te uditor s bevior. Tis udit finds weter orruption ourred or not, nd revels te true level of inome. Aoni, Amto nd Mrtin 003 onsider gme between tx uditors nd orruption monitorers wo re ssumed to be inorruptible. Wile tis would mke te model more relisti, it needs to be implemented wit dditionl ssumptions, nmely, tt te seond udit ostlessly revels te true level of inome. Tis mens tt t some point tere s to be tenology tt is not orruptible..3 Te Equilibrium Te Byesin Ns Equilibrium vlues of te endogenous vribles,, b, nd, for simultneous-move gme under ommon rtionlity setting is obtined by solving te system of non-liner equtions 9, 3, 4, nd 5. We will fous on tis Ns Equilibrium trougout te pper. Tis is te sme Equlibrium s if we llow te tx offiils to move first. However, notie tt if te txpyer moves first nd te tx uditor deides te bribe rte b one evsion is found, tere will be seond Byesin Ns Equilibrium if te uditor rges bribe rte b. Tis equilibrium is not redible beuse it relies on te myopi bevior of te txpyer. Wit non-myopi txpyer, se will forest tis b bevior nd will report er tx libilities s if tere were no orruption, even wen k 0 beuse se does not get ny benefit from being udited by orrupt offiil. In tis se orruption plys no role on ompline levels. Te only differene is tt wen udited by n onest offiil, te fine goes to te tx dministrtion, wile wen udited by orrupt offiil, te bribe equl to te fine goes to te orrupt inspetor. 3 Clibrtion nd Benmrk Prmeters Beuse of te omplexity of te first-order onditions, we will use simultions to obtin 6
n interprettion nd to nlyze te preditions of te model. In tis setion we explin ow te model will be librted to n eonomy wit inome tx tt s reltively lrge orruption nd tx evsion levels. To mke te problem more trtble for te interprettion of te ompline levels, we define te Compline Coeffiient s C.C. elred Inome/Totl Inome /Y. Notie tt - C.C. is te tx evsion rte. Moreover, notie tt given tt te uditors nd te tx pyer re representtive gents, te pyoff for te revenue servie will be proportionl to te Compline Coeffiient. Tt is, given tt te gol of te revenue servie is to ollet txes, not ollet fines or minimize te slries of te employees. 3. Agents' tility nd Reveled Level of Inome To model te gents' preferenes we ssume tt te utility funtion for bot gents, txpyer nd uditors, is given by te Constnt Reltive Risk Aversion CRRA utility YY -β /-β. Tis utility funtion ws lso used in tx evsion models in Bernsoni 998 nd Esteller-Moré 003. Te txpyer s onstnt reltive risk version given by β. Moreover, te individul is risk verse s long s β > 0, nd iger vlues of β imply iger individul s risk version. A resonble prmeter for β is.8, wi ws used in tx evsion models in Bernsoni 998 nd Esteller-Moré 003. Tis vlue ws estimted by Krni nd Smeider 990 nd Epstein 99. Te only differene between te txpyer's utility funtion nd te uditors' utility funtion is tt te uditors ve n dditionl ost of effort i ω for i, tt diretly redues utility levels, s equtions nd sow. In ddition to te gents utilities, we need te tenology to determine ow mu inome is reveled during te uditing proess. Tis is given by te φ funtion desribed in setion., wi models te mount of evsion found s funtion of te true level of inome, te delred inome, nd te level of effort exerted by te tx uditor. Equtions 5 troug 8 sow te desirble properties for te φ funtion. iven tese properties, te funtionl form tt we will use in te simultions is: Y Y Y,, i i i for i, 8 were 0 λ is mesure of te onvity of te φ funtion. Wen λ 0, we ve onstnt produtivity of effort. In ddition to omplying wit properties 5 troug 8, tis φ funtion gurntees tt te seond-order ondition in eqution 0 is unmbiguously negtive, s required. 3. Audit Probbility, Tx Rte, Fines, nd Corruption Levels One ommon problem fed by models bsed on Allingm nd Sndmo 97 is tt tey require n exess risk version to explin te observed ompline levels. Bernsoni 998 rgues tt te empiril evidene n be explined by te distintion of orders of risk version. He explins tt individuls do not ve ler ide of te udit probbilities nd 7
tey overestimte smll probbilities nd underestimte lrge probbilities. To model tis bevior e proposes using Expeted tility wit Rnk ependent Probbilities ERP in tx evsion problems bsed on Allingm nd Sndmo 97. We dopt te sme ERP nd use te trnsformtion proposed in Bernsoni 998 to work wit pereived udit probbility. 6 Tis mens tt if te tul udit probbility is 0.705%, te pereived udit probbility is 0%. We will use pereived udit probbility of p 0% for te simultions. For te tx rte we use t 5%, nd for te fine, s, wi implies 00% fine over unpid tx libilities. Finlly, for te orruption levels, Cu 990 mentions tt in survey undertken by te ity government of Tipei in 98, 94% of te txpyers polled reported being led to pying bribes to orrupt tx dministrtor. Cited in Snyl, ng nd oswmi 000, Te Polie roup 985 suggests tt t lest 76% of ll Indin tx uditors re orrupt. Tese evidene points tt te probbility of enountering orrupt tx offiil n be ig. We use vlue of s 0.4. 3.3 Benmrk Equilibrium To get te benmrk Byesin Ns Equilibrium of te model we ve to solve te system of four non-liner equtions 9, 3, 4, nd 5. Tis will give us te equilibrium inome, e, te bribe rte, b e, nd te level of effort exerted by te onest uditor, e, nd by te orrupt uditor, e. A summry of te prmeters vlues used in te librtion long wit te benmrk equilibrium is presented in Tble. In te benmrk equilibrium, te delred inome is 80.98, wi implies Compline Coeffiient of 0.8 nd tx evsion rte of 9.0%. Te equilibrium bribe rte b e is 7.88% wi mens tt for every dollr of fine, te orrupt uditor keeps 7.88 ents. Te benefit for te tx evder from enountering orrupt tx offiil is 9. ents for every dollr of fine. Te lulted effort levels re e 0.88 nd e 0.79 for te orrupt nd te onest uditors, respetively. 7 Tis mens tt te orrupt uditor works rder towrds finding evsion beuse of te dditionl benefits from keeping sre of te evsion fine for imself. 6 ERP onsiders te possibility tt indifferene urves be kinked t te ertinty point implying tt reporting te true level of inome n be optiml. Te weigting funtion used in Bernsoni 998 nd obtined by Cmerer nd Ho 994 is fp--p γ /[p γ +-p γ ] /γ, were γ 0.56. 7 Te uss ode used to solve te model is vilble from te utor upon request. Te ode uses te librry NLSYS Version 3... Te lgoritm used is line ser nd te jobin is lulted using forwrd differene. 8
Tble : Clibrtion vlues nd benmrk equilibrium Prmeter Vlue esription Clibrtion vlues p 0% Audit probbility Y 00 Inome β.8 Reltive risk version M 30 Auditor's inome t 5% Tx rte s 3 Fine k 0.4 Corruption λ Convity of φ g 0. Sre of evsion to uditors ω 0.0 Mrginl ost of effort Benmrk equilibrium C.C. e 80.98% Compline Coeffiient b e 7.88% Bribe rte e 0.88 Effort exerted by orrupt uditor e 0.79 Effort exerted by onest uditor 4 Sensitivity to Poliy Prmeters Te most ommon poliy prmeters to deter tx evsion re te udit probbility nd te fine. In tis model te tx dministrtion s five poliy prmeters under its ontrol. Besides te two trditionl udit probbility nd fine rte, te tx dministrtion n modify te sre g of te evsion fine given to te uditors, te uditors' level of inome M nd to some extent, te mrginl ost of effort ω. In tis setion we nlyze te effet of nge in e of tese prmeters nd te orruption levels k on te four endogenous vribles of te model. Te results re sown in te six pnels of Figure. 4. Audit Probbility nd te Fine Rte Pnel in Figure sows te equilibrium Compline Coeffiient, C.C., te bribe rte, b, nd te exerted efforts by te onest uditor nd te orrupt uditor for different udit probbilities. As in Allingm nd Sndmo 97, inresing te number of tx inspetions inreses ompline levels. Strting t p 0%, inresing te udit probbility s negtive impt on te levels of effort exerted by bot types of uditors. Moreover, te bribe for te orrupt offiil lso dereses. For low udit probbilities, evsion levels will be lrge, 9
mening tt te benefit from finding evsion is lso lrge. In tis se orrupt tx offiil will work rder towrds disovering evsion. However, for lrger udit probbilities evsion levels will be lower, deresing te inentives for finding evsion. Hene, for suffiiently lrge udit probbilities, onest offiil work rder tn orrupt offiils. As ompline level inreses due to iger udit probbilities, bot types of uditors will work less beuse finding evsion is not s profitble s before. Figure. Reponses to poliy prmeters. Audit probbility b Fine rte Auditor s sre d Auditor s inome e Mrginl ost of effort f Corruption level 0
Te effet of te fine rte s on te endogenous vribles is sown in Pnel b, Figure. Higer fine rtes inrese ompline levels. Consistent wit Allingm nd Sndmo 97, te udit probbility nd te fine rte re found to be substitute poliy prmeters, inditing tt by inresing ny of tese two, we n obtin lower evsion levels. As in te previous se, for low vlues of s te orrupt uditors work rder, wile onest uditors work rder for iger vlues of te fine. 4. Auditor's Sre, Inome, nd Mrginl Cost of Effort Figure, Pnel sows te equilibrium of te endogenous vribles s te uditor's sre of evsion fine nges. As we would expeted, iger sres g mke te onest uditor work rder. Te effort exerted by te orrupt tx uditor rises for reltively low vlues of g, but it is unresponsive to nges in g for reltively iger vlues of te uditor's sre. Reltively smll sres pper to be enoug to mke uditors engge in ig effort levels. Moreover, tis lso ppers to determine te spe of te ompline oeffiient sedule; inresing te sre wen it's lredy ig s negligible effet on te levels of effort exerted by te uditors nd on te ompline levels. Wen g 0, te only soure of inome for te onest uditors is M; ene, tey will not ve ny inentives to find evsion nd will exert zero effort. Terefore, s g pproes zero, te onest uditors derese teir effort to work, te bribe rte pproes to one, nd only orrupt uditors will be disovering evsion nd keeping ompline levels bove zero. In ses were te tx dministrtion does not offer inentives towrds disovering evsion in te form of g, te findings in te model will still old if we motivte te existene of non-monetry ompenstion tt reples te role of g. Honest uditors my be self motivted, or tere my exist some peer pressure to work. Te sedules of te model's endogenous vribles s te level of inome M nges re depited in Pnel d, Figure. Higer inome levels derese te mrginl utility of inome. Hene, te mrginl benefit from finding evsion is lower. As te level of inome inreses, uditors exert less effort towrds finding evsion nd te ompline oeffiient drops. Tis sows tt wen iming t reduing evsion levels using different inspetors' remunertion lterntives, it is more effetive to inrese te sre g of evsion found in te uditing proess tn to inrese level of inome M. For low vlues of M, bot types of inspetors work eqully rd. However, wen te level of M rises, te effort exerted by te onest offiil drops fster beuse te orrupt offiil reeives te dditionl inentive of iger evsion levels. Tis iger evsion levels mke orruption tivities more profitble. Moreover, prt of te drop in ompline wen M is lrger is bsorbed by te ft tt orrupt uditors now rge iger bribes, mking te effetive fine sb lrger if udited by orrupt inspetor. Even toug te tx dministrtion does not ve diret ontrol over te mrginl ost of effort ω, it my still ve vrious wys of ffeting it. Te tx dministrtion n ire more produtive inspetors, wo ve lower osts of finding evsion. Moreover, it n provide dditionl trining to existing uditors, or implement more sopistited teniques in te
uditing proess, mking finding evsion less ostly e.g., better omputers, speilized softwre. All tese potentil improvements in te inspetion proess n be summrized in one vrible, te mrginl ost of effort ω. Te effet of nges in ω on te endogenous vribles of te model is presented in Pnel e. eresing te mrginl ost of effort mkes bot types of uditors more effiient in teir inspetion tivities. Wit lower osts, bot types exert iger levels of effort, wi in turn inreses te ompline oeffiient. Wen ω 0, bot uditors will exert te mximum effort,, nd if udited, ll evsion will be found, φ Y. An interesting possibility, onsidered in Vsin 003, is tt te negotition of te bribe ours t te strt of te udit nd prior to te expenditure of ny effort by te orrupt uditor. Tis mens tt te tx evder onfesses of er tx evsion fter knowing se will be udited by orrupt offiil, nd most importntly, before ny tx evsion is found. Te ide is tt tis n potentilly inrese te net gins for te txpyer nd te uditor, beuse it voids te ostly effort on te prt of te uditor. We do not onsider tis possibility formlly. However, intuitively tere will be multiple equilibri in wi te ex-nte bribe n tke ny vlues witin rnge, b min b e b mx. If te ex-nte negotited bribe is below b min, te uditor will not ept nd will go for te udit in ser for evsion. Moreover, if it is bove b mx, ten te tx pyer will not ept nd will opt for te uditor to exert te effort. 4.3 Corruption Level To see ow te orruption level in te tx dministrtion ffets te equilibrium, Pnel f sows te sedules of te endogenous vribles s k nges. Wen te proportion of orrupt tx offiils is lrger, txpyers find evsion s suitble option beuse getting ugt by n onest offiil is less likely. Hene, evsion inreses nd finding it is esier nd more profitble for te uditors. For te onest tx offiil wo nnot nge te sre g, working rder is lwys good lterntive wit iger evsion levels. However, for te orrupt offiils wo lso ooses te bribe rte, te response is not tt simple. On te one nd, e sres te sme effet s te onest offiil; iger evsion levels s k inreses give im inentives to work rder. However, on te oter nd, wit iger evsion levels te equilibrium bribe is lso lrger. Higer bribe rtes lredy give im reltively ig inome, wi trnsltes into low mrginl utility of inome nd less inentives to work rder. Tis is te se beuse is mrginl utility of inome sould be proportionl to te mrginl ost of effort see eqution 4. An interesting point in Pnel f is te non-monotoniity of te bribe. Wen k is low, mening tt tere is smll probbility tt te tx pyer will enounter orrupt uditor, te orrupt uditor n old reltively lrge bribe rte b. Tis is beuse tis will unlikely disourge txpyers from evding. However, s te probbility of ving orrupt uditor inreses, ig bribe s greter weigt to disourge ompline; ene, te optiml bribe rte dereses. Tis is wt ppens for k below 0.. For iger orruption levels, evsion is lredy ig nd iger bribe rtes re optiml beuse tey will unlikely disourge txpyer to evde. Tis explins te inrese in b s k inreses for lredy ig levels of k.
3 Even toug k is not diretly under te tx dministrtion ontrol, tere re some tions tt n be tken to redue orruption in te dministrtion. Wen ω 0 nd k 0 we re bk to te Allingm nd Sndmo 97 nd Yitzki 974 model. 5 Conlusion Tis pper is initilly n extension of te lssi Allingm nd Sndmo 97 nd Yitzki 974 tx evsion model, were we inlude te intertion between te txpyer nd potentilly orrupt tx inspetor. A stndrd ssumption in te tx evsion literture is tt te tx uditors get to know te true level of te txpyers' txble inome during n inspetion. However, Feinstein 99 s empirilly sown tt only bout lf of te evsion is deteted in n udit. To be ble ount for tis imperfet detetion nd to nlyze different remunertion lterntives for te tx offiils, te model onsiders tt te mount of evsion found depends on ostly effort exerted by te uditors. Beuse of te omplexity of te first-order onditions tt govern te intertion mong te gents, te implitions from te model were obtined using simultions. Te existene of orruption in tx dministrtion s te following two min implitions. First, txpyers lower teir reported inome beuse orruption gives tem te opportunity to enounter orrupt offiil nd bribe im in order to espe from pying iger evsion fines. Seond, orrupt tx offiils find in orruption dditionl inentives to work rder due to te opportunity of reeiving bribes. Consistent wit previous literture, te model predits positive effet of bot, fines nd udit probbilities on ompline. Higer ompline n be ieved by giving tx inspetors sre of te evsion disovered, but inresing teir lump-sum inome will redue ompline. Finlly, iger ompline n s well be omplised by deresing inspetors' ost of finding evsion. Appendix From te Impliit Funtion Teorem: b b / / /, / / /, nd / / /. is given in eqution 9 nd sb tpks b sb tpksb Z s Z s k tp
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