05\va-russa-2.3.doc 21 Sptmbr 2005 Incom tax vason, socal norms and wlfar: A lnar xampl Knnth A. Krz * Jaanka Mrküll Alar Paulus Karstn Stahr Abstract: Ths papr consdrs th wlfar ffcts of tax vason n a modl wth a formal sctor and an nformal sctor. Indvduals hav dffrnt sklls or ablts, but also dffrnt atttuds toward tax vason. Th govrnmnt sks to maxmz socal wlfar whn sttng th ncom tax rat, th audtng probablty, and th fn mposd on ndvduals caught vadng taxaton. W show that n gnral t s socally optmal to allow som vason,.g. by mantanng a low audtng probablty and/or rlatvly low fns and thus mantan mploymnt n th nformal sctor. Allowng som tax vason has th potntal to rduc th xcss burdn of taxaton, whl also functonng as a socal polcy tool mprovng th lot of som lowsklld ndvduals. Kywords: H26, H21, H22. JEL classfcaton: Tax polcy, tax vason, wlfar, socal polcy. An conomy braths through ts tax loophols, Barry Bracwll-Mlns. 1 1. Introducton Th dsgn and practcal mplcaton of tax polcs ar complx ssus. Tax polcs oftn sk to addrss many objctvs ncludng ffcncy and dstrbuton and oftn also rgonal and ndustral concrns. A larg numbr of nstrumnts ar avalabl to polcymakrs. Ths nclud tax rats, xmptons and dductons, but th admnstratv ruls and procdurs nvolvd n th computaton and collcton of taxs ar qually mportant. On of th chf admnstratv chocs s whch knd of compulson to apply whn collctng taxs. Ths papr addrsss th ssu of govrnmnt polcs toward tax vason from a wlfar thortc prspctv. Our analyss s motvatd n part by th transton xprnc n th post-communst countrs. Th transton procss mant vry larg structural changs wth som ndustrs rapdly con- * Assocat Profssor, School of Publc Admnstraton, Unvrsty of Nbraska at Omaha, Omaha, USA. Ph.D. studnt, Faculty of Economcs and Busnss Admnstraton, Unvrsty of Tartu, Tartu, Estona. M.A. studnt, Faculty of Economcs and Busnss Admnstraton, Unvrsty of Tartu, Tartu, Estona. Vstng EuroFaculty Lcturr, Faculty of Economcs and Busnss Admnstraton, Unvrsty of Tartu, Tartu, Estona. 1 Ctaton from Cowll (1990, p. 195.
tractng and nw ndustrs gradually mrgng (Blanchard & Krmr 1997. Ths procss has not always procdd smoothly; rdundant workrs from dclnng ndustrs hav not always bn abl to fnd mploymnt n th xpandng ndustrs, possbly bcaus of skll msmatchs: th rdundant workrs ar not mployabl n th mrgng sctor as thy ar not suffcntly productv n ths sctors. Th rsult n many transton countrs has bn that a substantal part of th workng-ag populaton cannot fnd mploymnt n th formal part of th conomy. Th outcom s povrty and socal xcluson. On possblty of rlvng ths problms s for th dslocatd ndvduals to sk work n th nformal sctors of th conomy whr taxaton and othr forms of govrnmnt ntrvnton ar lss mportant. 2 Ths rass th quston to whch xtnt tax polcs can b usd as a socal polcy nstrumnt, allowng othrws dscouragd ndvduals to arn a lvng n th nformal part of th conomy. Th transton procss n th post-communst countrs has also nsprd our work n othr ways. As a lgacy from communsm and prhaps also th transton procss, th govrnmnt n many transton countrs s vwd upon wth skptcsm and lacks moral authorty (Prttla 1999. Many ndvduals mght fl lttl rsponsblty for th common good and thrfor rsst payng taxs. Emprcal nvstgaton of tax vason n EU countrs suggsts that th vason propnsts ar hgh although fallng n th ght East Europan countrs admttd to th EU n 2004 (Roony t al. 2004. On of th most mportant lssons concrnng polcs toward tax vason n transton countrs s that th ffct of socal norms should b takn nto account (Prttla 1999. tour rsarch contrbuts to th thortcal ltratur by consdrng th wlfar ffcts of dffrnt polcs wth rspct to tax rats, audtng schms and fns (s also th brf survy n scton 2. Our man contrbuton s to combn a sctoral approach (both formal and nformal sctors wth th mportanc of socal norms. Th da s to dvs an audtng and fn schm whch scrns taxpayrs and thus drcts taxaton toward th taxpayrs whr t s last dstortonary n th labor markt. Th sttng of tax rats for th formal part of th conomy and th audtng and fn schm taks plac smultanously. Our papr consdrs a two-sctor modl wth htrognous ndvduals. Th ndvduals dffr wth rspct to two dmnsons, havng dffrnt sklls or ablts, but also dffrnt atttuds toward tax vason. Indvduals can work thr n th formal sctor, whr labor ncom s taxd, or n th nformal sctor whr taxs ar vadd. Th govrnmnt sks to maxmz socal wlfar whn sttng th ncom tax rat, th audtng probablty and th fn mposd on ndvduals caught vadng taxaton. W show that t can b wlfar mprov- 2 Emprcal analyss skng to stmat to xtnt of povrty and socal xcluson rgularly sk to tak nto account nformal ncom sourcs. Th fndng s usually that housholds that offcally hav vry low ncom oftn hav addtonal ncom from th nformal sctor (s.g. Wallac & Harpfr 2002. 2
ng to allow som dgr of vason,.g. by mantanng a low audtng probablty or rlatvly low fns. In ths way, som taxpayrs wth low sklls wll b mployd n th nformal sctor and wll thus b abl to arn som ncom. Allowng som tax vason has th potntal to rduc th xcss burdn of taxaton, whl functonng as a socal polcy tool mprovng th lot of som low-sklld ndvduals. Th optmal dgr of tax vason dpnds on, ntr ala, th jont dstrbuton of ablts and atttuds toward tax vason, but also on th rqurd rvnu to b rasd from taxaton and fns. A low rvnu rqurmnt maks t socally optmal to allow a rlatvly larg nformal sctor by lttl audtng or low fns. Convrsly, a hgh rvnu rqurmnt mans that t s optmal to rstran th nformal sctor to a largr xtnt. Our modl s gnrally spcfd n lnar trms and should b sn as an xampl llustratng our ponts. Th lack of gnralty mght not b vry troublng as th lnar forms can b sn as lnarzatons of mor gnral functonal forms. It mght b usful to rstat what s mant by tax vason and to put t nto th broadr contxt of dffrnt atttuds toward payng taxs. Tax vason can b dfnd as th []llgal and ntntonal actons takn by ndvduals or frms to rduc thr tax paymnts (Alm 1999. In othr words, tax vason s a crmnal actvty that can b proscutd f dtctd. Thr ar othr mans of rducng th paymnt of taxs. Tax avodanc, tax mnmzaton, or tax optmzaton ar trms capturng th da that th taxpayr uss loophols, rclassfcatons, or othr mchansms to lgally rduc thr tax paymnt. Tax avodanc usually cannot b punshd although som countrs hav stpulatons outlawng som forms of tax avodanc undrtakn n bad fath. At th othr xtrm, thr ar actvts whch ar llgal n thmslvs (.g. llgal drug trad or prosttuton n som countrs and whr th omsson of tax paymnt s th consqunc of th llgal natur of th actvty. Thr ar no strct boundars btwn th catgors. In ths papr w wll us th trm tax vason n a broad sns to nclud all forms of omsson of tax paymnts, whch can b punshd f dtctd. Th rst of th papr s organzd as follows: Scton 2 provds a brf survy of rlatd ltratur. Scton 3 sts up our modl and xplans ts man mchansms. Scton 4 prsnts th qualtatv and quanttatv rsults of our modl. Scton 5 concluds and suggsts topcs for furthr rsarch. 2. Rlatd ltratur Our ltratur ovrvw s short as a numbr of hgh-qualty survys hav alrady bn wrttn (Cowll 1990, Slmrod & Ytzhak 2002, Myls 1995, Culls & Jons 1998. Prttla (1999 prsnts an ovrvw of lssons from tax thory wth rspct to tax vason n transton 3
conoms. Thr ar many ponts of dpartur for classfyng th ltratur on tax vason. On mportant dmnson s whthr th modl s of th partal qulbrum typ or whthr t s gnral qulbrum. Wthn th partal qulbrum framwork, th mportant dstncton btwn studs s whthr th study ncluds ncom as an ndognous varabl or taks t as gvn. Th acadmc study of tax vason startd wth smpl bhavoral modls of tax rportng bhavor. In th smnal study, Allngham & Sandmo (1972 modl tax rportng bhavor as a smpl cas of portfolo allocaton undr uncrtanty. In thr modl, ndvduals rcv ncom xognously and can dcd whthr to rport t or not. If thy choos not to rport th ncom, thy fac a known probablty of bng caught. If caught, thy pay a pnalty rat. In ths modl, th domnant outcom s to not rport f th probablty of bng caught or th pnalty f caught s vry low. Kolm (1973, Ytzhak (1974 and numrous othrs provdd rfnmnts to th basc rportng modl. And n a rlatd vn, Rnganum & Wld (1985, Crmr t al. (1990 and othrs analyz optmal audt stratgs gvn th ncntvs ntroducd by slf-rportng. Th structur of th rportng modls has rmand th sam throughout ths paprs, howvr, wth ncom bng drvd xognously. Th rsult of most of th portfolo modls s that ncrasng tax rats dscourag tax vason and that th optmal audtng/pnalty stratgy s a low probablty of audt coupld wth a hgh pnalty tax rat. Anothr strand of rsarch has mrgd, howvr, whch s mor ralstc and approprat for th cas of dvlopng countrs. Ths rsarch xamns th labor supply ffcts of taxaton. In dvlopng conoms, sgnfcant slack n th formal labor markt combnd wth potnt opportunts for work n th nformal or undrground labor markt may produc stuatons whr ndvduals fac labor supply dcsons that ar corrlatd wth tax rportng dcsons. In th smnal papr n ths ltratur, Sandmo (1981 bulds an analytcal modl of labor supply and taxaton wth two groups, vadrs workng n th nformal labor markt and not payng taxs, and non-vadrs workng n th formal labor markt and payng taxs. Indvduals choos to supply thr labor to th formal or nformal markt and fac a known probablty of bng caught and a known pnalty rat f caught. H fnds that th optmal tax rat to maxmz a utltaran socal wlfar functon n th fac of tax vason can b thr hghr or lowr than wthout tax vason. Th mx of ncom and substtuton ffcts along wth th proporton of vadrs dtrmns th drcton of th tax vason ffct. Addtonally h fnds that th optmal probablty of dtcton and th pnalty rat ar complx functons dpndnt not only on labor supply dcsons but also on th rsk avrson of ndvduals. Svral paprs hav followd Sandmo s ln of nqury. Espcally notabl and rlvant for our rsarch ar th paprs by Cowll (1985, Crmr & Gahvar (1994, and Fugazza & Jacqus (2003. Cowll (1985 constructs a modl whr ndvduals fac two smultanous 4
dcsons, whthr to work and what sctor to work n th formal or th nformal sctor. Indvduals rcv ncom from workng n thr sctor and from a lump-sum grant. Cowll analyzs th tax vason rspons of ths ndvduals undr four dffrnt modls, an A-S typ of modl whr total hours of labor supply ar fxd; a slf-dclard ncom modl smlar to A-S but wth flxbl total labor supply, functonal sparablty of ncom and consumpton, and qualty of wags n th formal and nformal sctors (SD modl; a modl wth tax wthholdng, havng th sam assumptons as th slf-dclard modl xcpt for th qual sctoral wag assumpton (PAYE modl; and th wthholdng modl wth rstrctons on th numbr of hours possbl to work n th formal sctor (PAYE wth rstrctons modl. Cowll fnds that n most of th cass (and wth som rlatvly wak assumptons xcpt for th PAYE wth rstrctons, vason rss wth ncrass n th formal sctor tax rat, falls wth a rs n th pnalty tax rat, falls f both rats rs, and falls as th dtcton probablty rss. Crmr & Gahvar (1994 xtnd th modl of vason and labor supply to ncorporat th possblty that ndvduals can spnd on concalmnt actvts n ordr to rduc th probablty of bng dtctd chatng on tax rportng. Thy also modl ndvduals ablts to arn wags as a contnuum, brakng wth prvous modls that assumd that ndvduals wr homognous n arnng ablty. Thy fnd that th natur of th concalmnt tchnology can affct th optmal progrssvty of th tax systm and that th optmal tax rat s lowr wth tax vason. Mor rcntly, Fugazza & Jacqus (2003 addd to th ltratur on th rlatonshp btwn tax vason and labor supply. Thy mploy a contnuous-tm matchng modl wth sarch costs. Indvduals pck whch sctor n whch thy ar gong to supply labor basd on xpctd costs and bnfts of th rlatv sctor. Th modl also allows for labor markt polcs, such as unmploymnt nsuranc and mnmum wag sttng. Thy fnd that ncrasd tax rats and ncrasd vason dtcton rats may lad to an ncras n partcpaton n th formal labor markt. Howvr, thr ar multpl qulbra possbl n th modl. Th ultmat mx of ffcts s dtrmnd by whthr th polcy nvronmnt s on of a low mploymnt qulbrum or a hgh mploymnt qulbrum and by th govrnmnt polcy toward dfcts (whthr a balancd budgt must b mantand. Thr ar rlatvly fw gnral qulbrum studs of vason. In on notabl study, Ksslman (1989 crats a gnral qulbrum modl of th labor markt wth two sctors, a formal sctor wth abov-ground actvts and an nformal sctor wth blow-ground actvts. Indvduals choos whch sctor n whch thy wll supply thr labor. Snc ths s a gnral qulbrum modl, thr ar both labor supply and labor dmand ffcts from changs n tax rats. Ths n turn affct th supply of and dmand for tax vadrs to work n th nformal 5
sctor. Ksslman fnds that th combnaton of ths ffcts producs som ntrstng rsults. Frst, changs n th tax rat ar nffctv n controllng vason on labor ncom. Scond, most of th gans to vason ar passd on to consumrs of th output of th nformal sctor through lowr prcs. Thrd, Laffr-typ ffcts ar mutd by shfts n rlatv prcs of goods n th dffrnt sctors. Th ffcts of vason on th margnal rvnu rspons to tax rat changs ar dpndnt on consumrs ablty to substtut consumpton btwn th formal and nformal sctors. So to summarz th xstng ltratur on vason, thr hav bn many dffrnt modls proposd and many dffrnt rsults producd. Som modls ndcat that vason wll rs wth ncrass n tax rats and dtcton probablts, othrs prdct th oppost rsult or ambguous rsults. Most of th modls hav bn partal qulbrum n natur and only a fw hav xplctly modld th ffcts of dffrng ncom arnng ablty. Most hav xamnd th ffcts of taxaton on vason bhavor, only brfly touchng on socal wlfar mplcatons of dffrnt polcs. In th nxt scton w buld a modl that addrsss som of ths ssus. 3. A lnar modl W hav sought to kp th tchncalts of our modl to a mnmum n ordr to focus on th dynamcs of th modl n trms of n th labor markt rspons to dffrnt tax rats and dffrnt polcs toward ndvduals ngagng n tax vason. Thr ar two sctors n th conomy: a formal or abovground sctor and an nformal or undrground sctor. Th only dffrnc btwn th two sctors s th way thy dal wth labor ncom taxaton: Indvduals workng n th prmary sctor always pay labor ncom tax as stpulatd, whl ndvduals workng n th scondary sctor do not pay labor ncom taxs xcpt f th frm or ndvdual s audtd n whch cas th labor ncom tax and a fn ar pad. It s assumd that th two sctors produc th sam output product. Th prc of th product s normalzd to 1. In ach sctor thr ar many dntcal frms ach convrtng labor nput nto output usng a constant rturn tchnology. On unt of labor s convrtd nto w unts of output, whr w > 0 s a constant. Prfct comptton n nput and output markts mpls that th pr-tax wag n ach of th two sctors s qual to th constant margnal product,.. qual to w. 6
Thr s a larg numbr, L, of ndvduals n th conomy. Each ndvdual s ndowd wth on unt of labor and dcds whthr to supply ths unt of labor to th prmary sctor, to th scondary sctor, or to b nactv. Ths dscrt choc dcson s basd on whch of th thr optons that gvs th ndvdual th hghst xpctd utlty. An ndvdual mployd n th formal or th nformal sctor ncurs a dsutlty ε from workng. Th ndvdual spcfc paramtr ε can b ntrprtd as th ndvdual s dsutlty from workng or th ffort rqurd to fulfll th rqurmnt of frms n th two sctors. 3 W wll assum that ε s contnuously dstrbutd on th ntrval [ 0, ε ], whr ε > 0 Indvduals rcv pr-tax wag w f thy supply thr unt of labor to th formal sctor. Th govrnmnt mposs a tax rat t on th labor ncom from th formal sctor wth no dductons possbl. Thus, ndvdual rcvs post-tax ncom w( 1 t and ncurs th ffort ε. Usng a smpl lnar combnaton of th two trms affctng utlty, ndvdual that chooss to work n th formal sctor has th utlty functon U = w( 1 t ε. An ndvdual supplyng ts labor unt to th nformal sctor ngags n tax vason as ths sctor by dfnton dos not pay labor taxs n th usual form. Howvr, w wll assum that th govrnmnt maks random audtng nspctons n whch th ndvdual s tru labor ncom wll b rvald. It s assumd that an ndvdual supplyng ts labor to th nformal scton has probablty ρ [0,1] of bng audtd and corrspondngly 1 ρ of avodng an audt. Addtonally, an ndvdual workng n th undrground sctor ncurs a cost of chatng,.. an xtra cost of workng n th nformal sctor nstad of n th formal sctor (or actvty. Ths xtra cost can b a physcal cost ncurrd n ordr to hd th actvts n th nformal sctor. It can also b a psychc cost rlatd to th uncrtanty whthr or not th ndvdual wll b audtd or t can b rlatd to th dscomfort from brakng ruls and chatng socty. In any cas ths subjctv cost of chatng s assumd to b ndpndnt of th amount chatd. Th chatng cost θ s assumd to b contnuously dstrbutd across th ntrval [ 0, θ ], whr θ > 0 Th chatng cost affcts th ndvdual s utlty lnarly. W wll assum that th two paramtrs ( ε, θ, whch ar spcfc to th ndvdual, ar dstrbutd accordng to th jont probablty dnsty functon g ε, θ. ( An ndvdual, who s caught workng n th nformal sctor and thus vadng taxaton, wll b taxd by th ordnary tax ratt, but wll also b subjctd to a fn calculatd as a shar F 0 of th vadd amount. Thus, th total of th tax and th fn of an ndvdual caught workng 3 A possbl ntrprtaton s th ε s th numbr of hours rqurd by th ndvdual n ordr to produc output of valu w. In acadmc crcls dffrnt ndvduals wll typcally hav to spnd a dffrnt numbr of hours n ordr to wrt a publshabl papr. 7
n th nformal sctor s w ( t + F. W wll assum that th ndvduals ar rsk nutral. Th assumptons abov mply that th xpctd utlty E[ U ] of ndvdual workng n th n- E[ U ] = (1 ρ w + ρ w(1 t F ε θ, whch can b smplfd to formal sctor s ( E[ U ] = w(1 ρ( t + F ε θ. Th trm ρ ( t + F s th total xpctd tax and fn paymnt as a fracton of th vadd amount. Havng a fully lnar modl t s convnnt to rwrt ths trm as t = ρ( t + F, whch s th xpctd (mplct tax rat f th ndvdual chooss to work n th nformal sctor. Usng ths notaton, ndvdual s xpctd utlty n cas of work n th nformal sctor s E[ U ] = w(1 t ε θ. Th rwrtng also hghlghts that although th govrnmnt can frly choos th standard tax rat t, th audtng rat ρ and th fn rat F, t s only th tax rat t and th xpctd tax rat t = ρ( t + F, whch ntrs th ndvduals xpctd utlty. Thus, th govrnmnt s choc varabls ar t and t. Indvduals who choos to b nactv and not sllng thr labor ndowmnt to th formal or th nformal sctor ar assumd to hav utlty qual to 0. Th (xpctd utlty of an ndvdual wll dpnd or th ndvdual s occupatonal choc as summarzd n (1: w(1 t ε f work n formal sctor E[ U ] = w(1 t ε θ f work n nformal sctor (1 0 f not work Each ndvdual must dcd whthr to work n th formal sctor, n th nformal sctor or whthr to stay nactv. All ndvduals ar rsk nutral so th soluton to th problm s smply th choc yldng th hghst (xpctd utlty. Thus, an ndvdual wll choos to work n th formal sctor f rwrttn as: w 1 t ε w( 1 t ε θ and w( 1 t ε 0, whch can b ( θ w( t t and ε w( 1 t (2 An ndvdual chooss to work n th formal sctor f th ndvdual s avrs to tax vason and has lttl ffort cost of workng. In spcfc, th ndvdual s chatng cost must b largr than th xpctd aftr-tax ncom gan from swtchng to th nformal sctor. In addton, th ndvdual s ffort cost of workng must b smallr than th aftr-tax ncom from workng. An ndvdual wll choos to work n th nformal sctor f and w( θ 0. A fw smplfcatons yld: 1 t ε w 1 t ε w 1 t ε θ ( < ( θ < w( t t and ε w( 1 t θ (3 8
An ndvdual works n th nformal sctor f th cost of chatng s small rlatv to th xpctd aftr-tax labor ncom and f th ffort cost of workng s rlatvly small. Notc that th scond nqualty n (3 mpls a jont rstrcton on ε and θ. Fnally, ndvduals for whom nthr (2 nor (3 s satsfd wll b thos wth a combnaton of a larg ffort cost of workng and a rlatvly hgh avrson to tax vason. Th dffrnt occupatonal rgms ar llustratd n Fgur 1. Th govrnmnt s sttng of th tax rat t and th xpctd tax rat t affcts th occupatonal choc of th ndvduals n th conomy and thus th sz of th thr sctors. Fgur 1: Rgms of work ffort and vason cost undr tax vason θ _ θ Formal sctor Inactv w(t t Informal sctor ε = w(1 t θ w(1 t _ ε ε A hghr tax rat t wll, ctrs parbus, mov popl out of th formal sctor and nto nactvty and/or nto th nformal sctor. A hghr audtng probablty or a hghr fn ladng to a hghr xpctd tax rat n th nformal sctor wll mov popl out of th nformal sctor and nto th formal sctor or nto nactvty. Clarly, ths sctoral shfts ar th sourc of mportant trad-offs n th ncom tax polcy n ths modl. Consdr Fgur 1 and assum a gvn ordnary tax rat t > 0. Clarly, th govrnmnt can altogthr lmnat th nformal sctor by sttng t = t. In ths cas th ndvdual gans nothng from workng n th nformal, but ncurs th cost of chatng. Graphcally ths shows up as th formal sctor takng up th ntr rctangl wth bas [0, w( 1 t ] and hght [0, θ ]. Th nactv ndvduals wll b thos wth th rctangl wth bas [ w( 1 t, ε ] and hght [0, θ ]. Now lowrng th xpctd tax rat to t < t has two man ffcts. Th ara of nd- 9
vduals workng n th formal sctor shrnks as ndvduals wth a low vason cost swtch from th formal to th nformal sctor. Ths s th vrtcally strpd rctangl n Fgur 1. At th sam tm ndvduals swtch from nactvty to nformal sctor as llustratd by th vrtcally strpd trangl. Ths llustrats th potntal of allowng vason as a socal polcy tool brngng popl from nactvty nto mploymnt, but also th lmtaton as ndvduals othrws workng n th formal sctor go undrground. W choos a straghtforward dfnton of th govrnmnt s problm. It s assumd that th govrnmnt sts th tax rat, t, and th xpctd tax rat undr vason, t, n ordr to maxmz a utltaran socal wlfar functon whl gnratng total rvnu from taxaton and tax audtng qual to R > 0. Th xognous rvnu rqurmnt s standard n th taxaton ltratur. max t, t θ θ = w( t t s.t. t w L w(1 t ε = 0 ( w(1 t ε θ + θ = w( t t w( t t θ = 0 w(1 t ε = 0 g( ε w(1 g( ε t θ ( w(1 t ε θ ε = 0, θ dε dθ, θ dε dθ + t w L g( ε w( t t θ = 0, θ dε dθ w(1 t θ ε = 0 g( ε, θ dε dθ = R (4 Th frst trm n th objctv dnots th total utlty attand by th ndvduals workng n th formal sctor and payng labor ncom taxaton as stpulatd. Th scond trm n th objctv dnots th total utlty of thos workng n th nformal sctor. Th nactv ndvduals hav utlty 0 and thrfor thr utlty dos not show up n th objctv. Th frst trm n th rvnu constrant dnots th tax rvnu attand from th prmary sctor, whl th scond trm dnots th rvnu from th fns admnstrd to ndvduals n th nformal sctor. Notc that w hav usd th assumpton that thr ar a larg numbr of ndvduals so that th budgt constrant can b assumd to hold dtrmnstcally. No rvnu s gnratd from th nactv ndvduals. Th govrnmnt s problm s clarly mor complx undr tax vason than othrws. Frst, th govrnmnt has two choc varabls, t and t. Scond, th utlts of ndvduals n both th formal and th nformal sctors ntr th objctv functon. W hav chosn a socal wlfar functon that wghs all ndvduals qually; ths could b modfd,.g. by wghng dffrnt ndvduals dffrntly. Thrd, th rvnu from th tax audtng fns ntrs th rvnu constrant. W hav hr assumd that tax audtng s costlss for th govrnmnt. Ths s 10
clarly an unralstc assumpton. Howvr, t s of lttl mmdat mportanc and allows us to solat th socal polcy aspct of allowng tax vason: th only rason n our modl to hav t < t n socal optmum s that t allows som ndvduals to mov from nactvty to arnng ncom (n th nformal sctor. 4. Qualtatv and quanttatv rsults Although th govrnmnt s problm s asly formulatd and ntrprtd, t s n gnral mpossbl to rach closd form solutons to th problm. Clarly any rsult wll dpnd on g( ε, θ, th jont dstrbuton of ε and θ. In ths scton w wll prov that t can b optmal for th govrnmnt to allow som tax vason and w wll thn consdr som smulaton rsults. COROLLARY 1: Assum that th jont dnsty functon g ε, θ s unform. Th maxmum rvnu 1 R = w L / ε. max 4 1 R max s attand whn t = t = 2 2 (. Th maxmum rvnu gnratd s PROOF (SKETCH: Insrt g ( ε, θ = 1/( ε θ nto th rvnu xprsson, cf. th rvnu constrant n (4: θ θ = w( t t w(1 t ε = 0 w( t t θ = 0 w(1 t θ 1 1 R = t w L dεdθ + t w L dεdθ (5 ε θ ε θ ε = 0 1 Smplfy and tak frst ordr condtons. Insrt t = t = 2 nto th rvnu xprsson n ordr to fnd R max. It s notcabl that whn th govrnmnt sts t and t to gnrat th maxmum attanabl rvnu, thn t = t and, hnc, thr s no nformal sctor. Whn t = t, all ndvduals wll work n th formal sctor to avod ncurrng th cost of chatng. COROLLARY 2: If th rqurd tax rvnu s zro,.. R = 0, thn th socally optmal tax rat and th xpctd tax rat ar dntcal and qual to zro,.. t = t = 0. PROOF: Trval as t = t = 0 rprsnts th frst bst soluton. 11
( RESULT 1: If th jont dnsty functon g ε, θ s unform and th govrnmnt s rvnu rqurmnt s abov zro but strctly postv but blow th maxmum rvnu attanabl ( < R < R, thn th socally optmal xpctd tax rat for th tax vadrs s abov zro 0 max but strctly lowr than th standard tax rat,.. 0 < t < t. PROOF (SKETCH: Assum wthout loss of gnralty that ε = 1 and θ = 1, whch mpls that g ( ε, θ = 1. Assum also that w = 1. St up th Lagrangan wth th multplr λ. Calculat / t and / t (ths rqurs n a numbr of cass th us of Lbntz rul. Th thr frst ordr condtons ar thn / t = 0, / t = 0 and / λ = 0, but ths systm s dffcult to solv. It s, howvr, straghtforward to show that s a monoton functon of t and that / > t 0 and that / t < 0 t =. Thus, / t = 0 can only b satsfd for a valu 0 t =t of t satsfyng 0 < t < t. Rfrrng to Fgur 1, Rsult 1 mght appar surprsng: whl a lowrng of th xpctd tax t from t mpls that som prvously nactv ndvduals gt mployd, a largr numbr of ndvduals swtch from th formal to th nformal sctor. Ths could rronously lad to th concluson that th losss from th largr numbr of ndvduals from th formal sctor who start vadng taxs and thus cas payng tax wll outwgh th gans to socty from addd mploymnt. Howvr, ths rasonng dos not tak nto account that th xpctd utlty ncrass not only for th ndvduals who go from nactvty to work n th nformal sctor, but also for th ndvduals who swtch from th formal to th nformal sctor. Whl optmalty rqurs t < t, t dos not mply that th optmal xpctd tax rat t s qual to or lowr than 0 whn th rvnu rqurmnt s postv. Th lowr xpctd tax rat for ndvduals n th nformal sctor mpls lowr tax rvnus whch must b countractd by a hghr standard tax rat, whch agan lads to ncrasd dadwght loss. Th balancng pont s on whr t < t but also t > 0. Ths qualtatv rsult has potntally mportant mplcatons n that t suggsts that t may b socally optmal to rtan an nformal sctor n th conomy kpt wthn bounds by th thrat of random audtng chcks. Incrasng th audtng probablty or th fn untl th pont whr t = t and th nformal sctor dsappars wll not b socally optmal at last wth a unform dstrbuton of rqurd ffort and vason costs across ndvduals. It wll b usful to larn mor about th rlatv magntuds of t and t, and also how ths chang whn.g. th rvnu rqurmnt changs. To ths nd w hav undrtakn a numbr 12
of numrcal smulatons of a dscrt vrson of th modl usng a unform jont dstrbuton functon. Th followng assumptons wr usd: Th numbr of ndvduals s L = 1000, th ndvduals ffort or dsutlty from workng s unformly dstrbutd from 1 to 100, th vason cost s unformly dstrbutd from 1 to 100, and th wag s w = 80. Th socal wlfar functon s smply th sum of th utlts of th L = 1000 ndvduals. Th maxmum tax rvnu R max s attand whn t = t = 0. 5, cf. Corollary 1 (n whch cas th socal wlfar n optmum s at ts lowst lvl. W thn smulatd th modl at varous lvls of xognous rvnu rqurmnts from R = 0 to R = Rmax n ordr to fnd th socally optmal tax rat and xpctd tax rat for ach lvl of rvnu. Th rsults ar condnsd n Fgur 2 whr th abscs axs shows th gnratd rvnu R as a fracton of R max and th ordnat axs shows th socally optmal tax rat and xpctd tax rat. Fgur 2: Optmal tax rats and xpctd tax rats at dffrnt rvnu rqurmnts 0.5 0.4 Tax rat n formal sctor Expctd tax rat n nformal sctor 0.5 0.4 0.3 0.3 0.2 0.2 0.1 0.1 0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0 Sourc: Smulatons basd on lnar modl. Th frst axs ndcats rvnu as fracton of maxmum attanabl rvnu. It follows from Fgur 2 that both th tax rat n th formal sctor and th xpctd tax rat n th nformal sctor that maxmz th utltaran socal wlfar ar monotoncally ncrasng n th rvnu rqurmnt. It s howvr notworthy that th rlaton btwn th two tax rats changs dpndng on th rvnu rqurmnt. At low lvls of rvnu, th optmal xpctd tax rat n th nformal sctor s low compard to th tax rat n th formal sctor. At hgh lvls of rvnu, howvr, th optmal xpctd tax rat s rlatvly hgh compard to th formal tax rat. Indd, th fracton of th optmal tax rats t / t dcrass monotoncally as th xognous rvnu rqurmnt ncrass. 13
Th ntuton bhnd ths rsult s straghtforward. At low lvls of rvnu, th rvnu constrant s rathr unmportant and th maxmzaton of socal wlfar can thus put rlatvly larg wght on th (sum of th ndvduals utlts. At hgh lvls of rqurd rvnu, th rvnu gnraton bcoms mor mportant and corrspondngly, th utlts of ndvduals wth hgh dsutlty from workng attan lss mportanc. At th xtrm nd whr th maxmum rvnu R max s to b gnratd, th tax rats n th two sctors ar dntcal n socal optmum. 4 Fgur 3 shows th rlatv sctoral dstrbuton of th ndvduals as a functon of th tax rat rvnu gnratd assumng that th tax rats n formal sctor and th xpctd tax rat n th nformal sctor s st optmally, cf. Fgur 2. Th shar of th total populaton workng n th formal sctor s a dcrasng functon of th tax rvnu targt. Corrspondngly th shar of th populaton bng nactv s an ncrasng functon of th rvnu gnratd. Th rsults follow partly from th fact that thr ar no ncom ffcts n our lnar modl. Th nformal sctor s ntally an ncrasng functon of rvnu but dcrass n rvnu at hghr rvnu rqurmnts as th xpctd tax rat ncrass rlatvly to th formal sctor tax rat. Fgur 3: Employmnt n th formal and nformal sctors at dffrnt rvnu rqurmnts wth optmal sttng of tax and xpctd tax rats 1 0.8 Inactvty Informal sctor Formal sctor 0.6 0.4 0.2 0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Sourc: Smulatons basd on lnar modl. Th frst axs ndcats rvnu as fracton of maxmum attanabl rvnu. 4 Our man fndng s that t can b socally optmal to hav 0 < t < t (whn th rvnu rqurmnt s abov 0 and blow R max. Notc th paralll btwn ths rsult and th dscusson of ruls vs. dscrton (Prsson & Tablln 1990. A strctly ruls-basd tax systm would thn corrspond to t = t as no xcptons ar possbl. A strctly dscrtonary tax systm would ntal t = 0 as taxpayrs would thn b abl to avod taxaton at all. Th socally optmal choc lays btwn ths xtrms. 14
Th analytcal and smulaton rsults suggst a numbr of polcy mplcatons. It nd not b optmal for a country to strv for an radcaton of th nformal sctor through vry frqunt tax audtng or svr punshmnts. Tax vason n th nformal sctor can ndd b th loophol through whch th conomy braths. Mor spcfcally, allowng tax vason allows som ndvduals wth low productvty (hgh workng dsutlty to arn a lvng by workng n th nformal sctor. In ths sns, allowng tax vason by sttng th xpctd tax rat n th nformal sctor blow th tax rat n th formal sctor can b sn as part of a socal polcy rgm. It s clar, howvr, that allowng tax vason s a rough nstrumnt wth whch to addrss socal polcy ssus. Frst, allowng tax vason only hlps thos wth low moral standards, whl thos wth hgh costs of tax vason wll rman unaffctd as thy wll stll prfr to b nactv. Scond, many ndvduals who do not nd th tax rlf but hav low costs of vason also bnft from a low xpctd tax rat n th nformal sctor, whch mpls that th formal sctor tax rat bcoms rlatvly hgh. 5 Th smulaton rsults also suggst that a country wth a low tax burdn on labor should allow a rlatvly larg xtnt of tax vason as rflctd n a rlatvly low xpctd tax rat on th nformal sctor. Convrsly, a country wth a hgh tax burdn on labor should mak sur that th nformal sctor dos not bcom nappropratly larg,.. th xpctd tax rat n th nformal sctor should b rlatvly hgh. Ths rsult mght to som xtnt b rflctd n practc; dvlopng countrs wth low tax burdns oftn allow larg nformal sctors whch ar ssntally wthout any rsk of bng subjctd to taxaton or othr knds of govrnmnt ntrfrnc. Convrsly, th hgh tax burdns n a numbr of wst Europan countrs ar accompand by strct laws concrnng taxaton and an ffctv tax admnstraton. 6 5. Fnal commnts Ths papr has focusd on th wlfar ffcts of tax vason and th govrnmnt s polcs toward vason. It was dmonstratd n a thortcal modl that th socally optmal tax polcy would prmt som tax vason as t allowd ndvduals wth hgh ffort costs to arn ncom n th nformal sctor. Allowng som tax vason thus has th potntal to rduc th xcss burdn of taxaton, whl functonng as a socal polcy tool mprovng th lot of som lowsklld ndvduals. 5 Th last pont also rass th moral quston whthr t s approprat to pursu socal polcs n such a way that only thos wth low moral standards bnft. W wll rturn to ths pont n our fnal commnts n scton 5. 6 Exprncs from a numbr of transton countrs hav also shown that th sttng of tax rats and th masurs to stm tax vason must b consdrd n tandm. Untl th prsonal ncom tax rform n Russa n 2000, hgh tax rats wr partly to blam for almost pdmc tax vason. 15
Th nsght s mportant n th contxt of post-communst transton as t ncorporats two charactrstcs of many transton countrs, namly th xstnc of larg groups wth sklls that ar badly algnd wth th rqurmnts of a modrn markt conomy and th socal norms that potntally put lttl mphass on th ndvdual s broadr soctal rsponsblts. Th nsghts from ths papr should b takn nto account whn rstructurng tax admnstraton n transton countrs: Tax audtng should not ncssarly hav as ts goal to lmnat tax vason, but should rathr sk to kp th vason wth bounds. Many transton countrs (spcally th CIS countrs hav rlatvly small publc sctors and ras lttl tax rvnu; tax vason n ths countrs mght not b a vry larg problm from th vwpont of socty. Our lnar modl s clarly smplstc n lght of th complx ssus nvolvd n th practcal dsgn and mplmntaton of tax polcs. Furthr work could consdr xtnsons of th modl that would rmov som of th rstranng assumptons. Frst, on could assum a postv audtng cost although ths assumpton would not mak much dffrnc as long as th ndvduals utlty s lnar. 7 Scond, th wag (labor productvty n th nformal sctor could (ralstcally b assumd to b lowr than n th formal sctor. Ths would mak t lss socally bnfcal to allow a larg nformal sctor. Thrd, th ndvduals could b assumd to b rsk avrs. Th rsult s that both th audtng probablty and th fn would b sparat argumnts n th ndvdual s sctoral choc and hnc also n th govrnmnt s optmzaton problm. Rsk avrson maks t lss attractv for th ndvdual to work n th nformal sctor and thus also affcts th socal dsrablty of th nformal sctor. Fourth, th socal wlfar functon could tak forms othr than th utltaran wlfar functon usd n ths papr. On possblty would b to wght ndvduals dffrntly dpndng on thr faturs: hghsklld ndvduals wth low moral standards workng n th nformal sctor could b wghtd lowr than low-sklld ndvduals workng n th nformal sctor. W ntnd to xplor som of ths xtnsons n futur paprs to broadn our undrstandng of tax vason and th govrnmnt s polcs toward tax vason. Acknowldgmnts Ths rsarch has bn supportd by grants from EuroFaculty n Rga, Latva; EuroCollg at Tartu Unvrsty, Estona; and th Unvrsty of Nbraska at Omaha, U.S.A. W would lk to 7 It s th xpctd tax rat n th nformal form that mattr for th sctoral choc of an ndvdual wth lnar utlty. Th ntroducton of audtng costs would thn only mply that th audtng probablty should b vry low and th fn vry hgh. Ths rsult s somtms summarzd as hang tax vadr wth probablty zro (Myls 1995. 16
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