REVENUE EQUALIZATION SYSTEMS IN A FEDERATION WITH TAX EVASION

Transcription

1 XXII CONFERENZA NUOVE FRONTIERE DELL INTERVENTO PUBBLICO IN UN MONDO DI INTERDIPENDENZA Pava, Unverstà, settembre 2010 REVENUE EQUALIZATION SYSTEMS IN A FEDERATION WITH TAX EVASION LISA GRAZZINI, ALESSANDRO PETRETTO socetà talana d economa pubblca dpartmento d economa pubblca e terrtorale unverstà d Pava

2 Revenue Equalzaton Systems n a Federaton wth Tax Evason Lsa Grazzn and Alessandro Petretto y 1th July 2010 Abstract We analyse how vertcal or horzontal scal equalzaton a ects the overprovson of local publc goods due to vertcal scal externalty, when there s tax evason. The regonal governments overspendng ncentve s examned both n case of a scal equalzaton based on pretax earned ncome and reported taxable ncome. Keywords: Fscal federalsm; Equalzaton; Margnal Cost of Publc Funds, Tax evason JEL Class caton: H2; H41; H71; H77. Department of Economcs, Unversty of Florence, Va delle Pandette 9, Florence, Italy. E-mal: lsa.grazzn@un.t y Department of Economcs, Unversty of Florence, Va delle Pandette 9, Florence, Italy. E-mal: alessandro.petretto@un.t 0

3 1 Introducton It s well-known n the lterature on scal federalsm that a vertcal scal externalty arsng from a two-level taxaton on the same tax base may mply overprovson of local publc goods. Local governments perceve a margnal cost of publc funds lower than the (true) socal one, and thus are subject to a sort of soft budget costrant (Dahlby (2008)). Morevoer, t has been shown that such ncentve to overprovde ncreases f an equalzaton system s appled. However, such an ncentve may change also for other reasons. For example, the ntroducton of shelterng,.e. llegal tax evason and/or legal tax avodance, may a ect the e cency of local publc good provson through ts e ects on the crteron to measure the excess burden (Chetty (2009)), and thus also the margnal cost of publc funds. Accordngly, when the e ects of equalzaton and shelterng are consdered smultaneously, one nterestng queston to rase s whether the ncentve to overprovde local publc goods wll be enforced or not..e. To analyse such an ssue, we consder a federaton where a central government s pre-commtted, t s a Stackelberg leader whle regonal governments are followers (Köthenbürger (2008a), (2008b)). Local publc expendtures are nanced through two d erent nstruments: local governments choose a surtax on the local scal base of a natonal tax, and may be enttled to receve an equalzaton grant. In partcular, we suppose that a lnear labour ncome tax s devoted to nance publc expendture, both at central and local level, so that a federal tax rate plus a local one are appled to the same bass. Further, the equalzaton system s lke that descrbed by Smart (1998), and s based on the so-called scal capacty equalzaton crteron, 1 a scheme of transfers appled n many countres as Australa, Canada, Germany, Swtzerland and now, after a recent reform, Italy too. Accordngly, regons are (partally or totally) compensated by federal revenues for the d erence between a standard level of tax revenue and the revenue regons are deemed to be able to rase f standard tax rates were appled to ther tax bass. 2 D erent spec catons of the equalzaton system (ES) are analysed n ths note: vertcal versus horzontal, and based on actual versus taxable ncome. Wth a vertcal, or gross, (horzontal, or net ) ES, poor regons, whose scal capacty s lower than the average or standard one, receve a grant from the central government (drectly from rch regons). Further, both vertcal and horzontal ES may be mplemented wth a scal capacty based on pretax earned ncome or reported taxable ncome,.e. the former net of shelterng. For nstance, art. 9(g) of the recent Italan bll n. 42/2009 on scal federalsm reform apples a horzontal ES by referrng to the comparson between the regonal per capta tax yeld and the average tax revenue over all regons. The tax consdered as a proxy of scal capacty s a regonal ncome surtax at a standardsed rate. Therefore, t seems 1 The system of equalzaton has been orgnally proposed n hs semnal work by Musgrave (1961). 2 See, n partcular, Bucovetsky and Smart (2002), Boadway et al. (2002), Barett et al. (2002), Dahlby and Warren (2003), Köthenbürger (2002), Boadway (2004), Fgueras et al. (2004), Buettner (2006), Grazzn and Petretto (2006), Smart (2007), Hndrks et al. (2008), Egger et. al. (2010). Most of these papers deals wth horzontal tax competton vs. equalzaton, whle n ths note we concentrate on vertcal tax competton. Kotsoganns (2010) deals wth both tax competton typologes vs. equalzaton. Fnally, Kotsoganns and Schwager (2008) study the mpact of equalzaton on local poltcans accountablty. 1

4 that the ES n Italy wll be horzontal and n terms of reported taxable ncome. When there are shelterng phenomena, n partcular tax evason on whch we are focusng here, t s nterestng to consder the actvty of an Authorty devoted to audtng and montorng of tax complance, and the degree of cooperaton between regonal and federal governments on runnng t. 3 Usually, both government levels partcpate to ths actvty provdng resources and agreeng on the way for sharng the clawed back tax revenue. 4 Such aspects are also analysed n the present note. Our man results are the followng. For a poor regon, a shft from a vertcal to a horzontal ES or vceversa does not change the ncentve to overprovson of a publc servce, both n the case of an ES based on pretax earned ncome and reported taxable ncome (a poor regon s always a recevng one). However, such an ncentve for a poor regon s strengthened (reduced), when an ES based on pretax earned (reported taxable) ncome s substtuted by one based on reported taxable (pretax earned) ncome, both n the case of a vertcal and a horzontal ES. For a rch regon, a shft from a vertcal (horzontal) to a horzontal (vertcal) ES ncreases (decreases) the ncentve to overprovson of a publc servce, both n the case of an ES based on pretax earned ncome and reported taxable ncome. Further, such an ncentve for a rch regon does not change when a vertcal ES based on pretax earned ncome s substtuted by one based on reported taxable ncome. Instead, n the case of a horzontal ES, a shft from one based on pretax earned (reported taxable) ncome to another based on reported taxable (pretax earned) ncome ncreases (decreases) the ncentve for a rch regon to overprovson of a publc servce. To conclude, a more e cent level of regonal publc expendtures s assocated wth a vertcal ES based on pretax earned ncome at regonal level. 5 However, such a scheme could be more demandng n terms of nformaton to be gathered. Indeed, t s known that tax records contanng data on reported taxable ncome are wdely avalable, whle gettng data on earned ncomes at regonal level s qute d cult and the use of proxy varables would be easly contrastred by local governments. Further, ths soluton s probably opposed by local poltcans who may desre to favour ther costtuences wth a generally permssve scal legslaton, and symultaneously to compensate the loss of tax revenues due to evason wth the equalzaton. The plan of the paper s as follows. In secton 2, we analyse consumers behavour wth tax evason, and we desgn the tax structure of the federaton accordng to the type of ES (vertcal versus horzontal), and the bass wth respect to whch the grant s calculated (pretax earned ncome versus reported taxable ncome). In secton 3, the ncentve to overprovde local publc goods when there s tax evason at local level s compared accordng to d erent typologes of ES. Secton 4 3 For a treatment of evason and audtng ssue n a federal context, see Cremer and Gahvar (2000), Stowhase and Traxler (2005) and Bartoln and Forllo (2009). 4 The quoted bll on scal federalsm n Italy explctely consders the possblty that a regonal agency can cooperate wth the Agenza delle Entrate, the natonal tax Authorty. For spe cc taxes, regonal Authortes may even fully substtute the Agenza delle Entrate. 5 Thus, such a soluton s contrary to the one establshed by the quoted Italan reform on scal federalsm. 2

5 contans some concludng remarks. Fnally, n the Appendx, we model the behavour of an e cent tax Authorty aganst evason, and the consequences for the e cency of local publc expendtures. 2 The model We analyse a federaton of regons,, = 1; :::; n, each wth populaton sze normalzed to unty. In each regon, consumers are mmoble, and preferences of the representatve consumer are descrbed by the followng addtvely separable utlty functon U (x ; l ; g ; G) = u (x ; l ) + b(g ) + B(G); = 1; :::; n; (1) where u (:) s a strctly quas-concave sub-utlty functon of prvate consumpton, x (taken as the numerare), and lesure, l ; and the b(g ) and B(G) functons measure the bene ts of a local publc good, g, = 1; ::n, and a federal publc good, G, respectvely. 6 Both federal and local publc goods are pure n nature, but the bene ts of the latter do not spll over across regons, whle the bene ts of the former accrue to all households rrespectve of where they lve. Both publc goods are nanced through a labour ncome tax (a pay-roll tax). Let t be the tax rate chosen by the federal government, and let, = 1; ::n, be the surtax on the regonal scal base, decded by the regonal government, wth the consoldated tax rate gven by t +, = 1; :::; n. In each regon, = 1; :::; n, Y = w L s the pretax earned ncome from labour, wth w denotng the gross wage pad by rms, and L = 1 l denotng labour. 7 Thus, the net wage rate receved by a consumer n regon obtans as fw = (1 )w, = 1; :::; n. Further, let us suppose that a tax-payer lvng n regon may evade s euros of ncome from taxaton. Thus, hs reported taxable ncome obtans as T Y = Y s. Followng the dstncton proposed by Chetty (2009), tax evason n regon mples a resource cost gven by h (s ), h 0 (:) > 0 and a transfer cost gven by z ( ; s ), > 0. 8 In our case, the resource cost functon h (s ) descrbes the cost beared by a tax Authorty whch s engaged n montorng and audtng procedures 9 and the transfer cost functon z ( ; s ) descrbes the expected prvate cost of tax evason, manly due to the rsk to be caught and to pay a ne (see the Appendx for a spec caton of these functons). The latter cost mples a transfer of resources from tax-payer to the tax Authorty. Accordngly, the budget constrant of a consumer n regon obtans as x = (1 )T Y + s z ( ; s ); = 1; :::; n: (2) Each consumer leavng n regon, = 1; :::; n, chooses lesure and how much ncome to evade by maxmsng the utlty functon n (1) subject to hs budget constrant (2). From the rst order 6 The separablty assumpton n the utlty functon mples that g, = 1; :::; n, and G do not a ect households lesure-consumpton decsons. 7 We suppose that w, = 1; :::; n, s constant, and thus t s not a ected by taxaton. 8 We also ( = 0 ( ;Y = 1, to guarantee an nteror optmum n s : 9 Actually n Chetty (2009) there s also a drect cost beared by the tax-payer, for nstance, for shftng reported money rewards to untaxable frnge bene ts n order to reduce hs taxable ncome. 3

6 condton wth respect to s, the followng standard condton n tax evason lterature obtans ; = 1; :::; n: (3) At equlbrum, the margnal prvate bene t of rasng s by 1 euro (savng euro) has to be equal to the margnal The soluton of ths maxmsaton problem mples the followng ndrect utlty functon V ( ew ; g ; G) = v ( ew ) + b(g ) + B(G); = 1; :::; n; (4) and, by usng Roy s dentty, the followng = v I T Y ; = 1; :::; n; (5) where v I = u x s the margnal utlty of ncome. Ths means that the margnal cost for the taxpayer due to the cost of tax evason, tax payment, v I T Y (see Appendx). v < 0, adds to the standard cost of the ncrease of the The structure of federal and regonal publc budget constrants depends on the agreement between federal and regonal governments on runnng the tax Authorty,.e. how the expected bene ts and costs of montorng and audtng actvty are shared between central and local governments. Moreover, the two-levels budget constrants depend on whether the adopted equalzaton scheme s vertcal or horzontal, and on whether t s based on pretax earned ncome or reported taxable ncome. Let R denote the revenue avalable for a regon, = 1; :::; n. constrant obtans as The regonal publc budget R = T Y + e + T = g ; = 1; :::; n: (6) Each regon nances a local publc good through three types of revenue: the yeld from regonal taxaton, T Y, the yeld from a federal government grant, e and the yeld from montorng actvty, T. The latter represents the fracton of the tax Authorty s budget devoted to regon, where T = z ( ; s ) h (s ) > 0 and 0 < < 1: Hence, we assume the exstence of an agreement between central and regonal governments accordng to whch each regon yelds a share of the d erence between the transfer from tax-payers and the cost of montorng and audtng. Ths dvson mght occur accordng to a poltcal deal related to the rato of the regonal tax rate over the e ectve one,.e., = 0 t > 0. 2 By denotng RF V and RH F the federal revenue wth a vertcal and a horzontal equalzaton scheme, respectvely, the federal publc budget constrant obtans as R V F = tt Y + nx X (1 k )T k k=1 k2n p e k = G; (7) 10 The condton derves from u x > 0 and envelope theorem, for whch t turns = + 1: 4

7 and R H F = tt Y + nx (1 k )T k = G: (8) k=1 A federal publc good s nanced through the revenue from taxng labour ncome, tt Y, wth nx nx T Y = T Y k plus the central government s fracton of the tax Authorty s budget, (1 k )T k, k=1 and n the case of a vertcal equalzaton scheme, mnus the sum of the grants to poor regons, P k2n p e k. The latter term does not appear n (8) because a horzontal equalzaton scheme does not mply any transfer from the federal government to regons. We are now n a poston to descrbe the structure of regonal and federal budget constrants dependng on the type of equalzaton scheme, and on the type of ncome wth respect to whch the grant s calculated. 2.1 Vertcal equalzaton on pretax earned ncome (VY) When pretax earned ncome s the bass for the equalzaton scheme, let us de ne a poor (rch) regon, f Y < ()Y, wth 2 (=2)N p, where N p denotes the set of poor regons, and Y denotes the standard tax base. Spec cally, Y s usually chosen as the average per-capta tax base, Y nx Y k =n = Y=n. Wth a vertcal equalzaton scheme, the federal government only pays grants k=1 to poor regons 2 N p. When such a scheme s based on pretax earned ncome, the equalzaton grants pad by the federal government are of the followng type k=1 e V Y 2N p = (Y Y ) > 0; (9) e V =2N Y p = 0; (10) where the parameter, 0 < 6 1, descrbes the chosen degree of equalzaton ( = 1 s the case of full equalzaton ), and denote the standard regonal tax rate. In partcular, could be a gven reference surtax rate, establshed at a federal level, or a weghted average surtax rate, nx k Y k =Y. 11 Let us de ne A Y Y, and use t nto (9). The equalzaton grant for a poor k=1 regon rewrtes as e V Y 2N p = AY Y : (11) For poor regons, ths equalzaton scheme works as a lnear (a ne) matchng grant based on (nversely correlated to) actual local tax base. Let R V Y denote the total revenue avalable for a regon, = 1; :::; n, wth a vertcal equalzaton on pretax earned ncome. By substtutng (11) nto (6), the regonal publc budget constrant obtans as R V Y 2N p = ( )T Y s + A Y + T = g ; (12) 11 Alternatvely, Y and could be nterpreted as parameters relatve to the regon wth medan ncome or the rchest one. In any case, we assume that the standard tax base and the standard tax rate are xed. Such an assumpton s n lne wth the case of a hgh number of small regons (Grazzn and Petretto 2006). 5

8 for a poor regon, and by substtutng (9) nto (6), t obtans as for a rch regon. R V Y =2N p = T Y + T = g ; (13) Let RF V Y denote the federal revenue wth a vertcal equalzaton on pretax earned ncome. By usng (11) nto (7), the federal publc budget constrant obtans as R V Y F = tt Y + nx X (1 k )T k k=1 2.2 Horzontal equalzaton on pretax earned ncome (HY) k2n p (A Y Y ) = G: (14) Wth a horzontal equalzaton scheme, poor regons receve a subsdy whle rch regons pay for them. When such a scheme s based on pretax earned ncome, the structure of the yelds s as follows wth X e HY k k2n p + X k =2N p e HY k = 0. e HY 2N p = ev 2N Y p; (15) e HY =2N p = (Y Y ) 6 0; (16) Let R HY denote the total revenue avalable for a regon, = 1; :::; n, wth a horzontal equalzaton on pretax earned ncome. Snce the grant receved by a poor regon s the same as n the case wth vertcal equalzaton based on pretax earned ncome, the regonal publc budget constrant for a poor regon s also the same,.e. R HY 2N p = RV Y 2N p = g : By substtutng (16) nto (6), the regonal publc budget constrant for a rch regon obtans as R HY =2N p = ( )T Y s + A Y + T = g : Fnally, the federal publc budget constrant s (8). 2.3 Vertcal equalzaton on reported taxable ncome (VTY) When reported taxable ncome s the bass for the equalzaton scheme, let us de ne a poor (rch) regon, f T Y < ()T Y. Wth a vertcal equalzaton scheme, the grants pad by the federal government are of the followng type e V T Y 2N p = (T Y T Y ) > 0; (17) e V =2N T Y p = 0: (18) Let us de ne A T Y T Y, and use t nto (17). The grant for a poor regon rewrtes as e V T Y 2N p = AT Y (Y s ): (19) 6

9 Gven the actual earned ncome, the grant s ncreasng wth the level of tax evason. Let R V T Y denote the total revenue avalable for a regon, = 1; :::n, wth a vertcal equalzaton on reported taxable ncome. By substtutng (19) nto (6), the regonal publc budget constrant obtans as R V T Y 2N p = ( )T Y + A T Y + T = g ; (20) for a poor regon, and by substtutng (18) nto (6), t obtans as R V T Y =2N p = T Y + T = g ; (21) for a rch regon. Thus R=2N V T Y = R V Y p =2N. p Now let RF V T Y denote the federal revenue wth a vertcal equalzaton on reported taxable ncome. By usng (19) nto (7), the federal publc budget constrant obtans as R V T Y F tt Y + nx X (1 k )T k k=1 k2n p (A T Y T Y k ) = G: (22) 2.4 Horzontal equalzaton on reported taxable ncome (HTY) Wth a horzontal equalzaton based on reported taxable ncome, the structure of the yelds s as follows wth X e HT Y k k2n p + X k =2N p e HT Y k = 0. e HT 2N Y p = ev 2N T Y p; (23) e HT Y =2N p = (T Y T Y ) 6 0; (24) Let R HT Y denote the total revenue avalable for a regon, = 1; :::; n, wth a horzontal equalzaton on reported taxable ncome. Snce the grant receved by a poor regon s the same as n the case wth vertcal equalzaton based on pretax earned ncome, the regonal publc budget constrant for a poor regon s also the same,.e. R HT Y 2N p = RV T Y 2N p = g : (25) By substtutng (24) nto (6), the regonal publc budget constrant for a rch regon obtans as R HT Y =2N p = ( )T Y + A T Y + T = g : (26) Fnally, the federal publc budget constrant s (8). 3 The overprovson of a local publc good wth d erent equalzaton schemes and tax evason We suppose that a regonal government does play a non-cooperatve game wthout takng nto account the e ects of ts scal decsons on the federal government budget constrant. In partcular, 7

10 and g are chosen n order to maxmse the welfare of a representatve consumer n regon (see (4)), gven the regonal publc sector budget constrant, and takng both federal government s and other regons scal decsons as gven. 12 On the bass of a wde agreement n the lterature, we adopt the followng De nton In a noncooperatve scal equlbrum, the ncentve to overprovde local publc servces s measured by the gap between the regonal perceved margnal cost of publc fund ( MCF ) and the socal one ( SMCF ),.e. the one perceved n a second best cooperatve equlbrum. Accordng to such a de nton, the wder s the wedge between MCF and SMCF, the hgher s the ncentve to soft budget constrant. 3.1 Benchmark case: No equalzaton and no tax evason Wthout an equalzaton scheme and tax evason, by solvng the maxmsaton problem of a regon, = 1; :::; n, the followng noncooperatve equlbrum condton obtans 13 b 0 v I = = 1 1 " = MCF ; = 1; ::n; (27) where = Y, 1 1, and ew L. Ths means that the margnal bene t of one euro nvested n the local publc good provson s equal to the regonally perceved margnal cost of t. Instead, the second best cooperatve equlbrum condton whch takes nto account the negatve tax F < 0, obtans as follows b 0 v I Y F = 1 1 " = SMCF ; = 1; ::n: (28) Ths means that the socal perceved margnal cost of publc fund, SMCF, takes nto account the fact that the true tax dstorton depends on and not only on. Thus, t s easy to check that MCF < SMCF ; = 1; ::n;.e. wthout an equalzaton scheme, the noncooperatve equlbrum results n an ncentve to overprovson. 3.2 Case wth d erent equalzaton schemes and no tax evason When an equalzaton scheme s ntroduced, the grants are as n (9) and (10) n case of a vertcal equalzaton, and as n (15) and (16) n case of a horzontal equalzaton. Wthout tax evason, let R2N V p and RH 2N p denote the total revenue avalable for a poor regon wth a vertcal and a 12 As t s well known, ths corresponds to the case when regons are scally ndependent (Köthenbürger (2008a) and (2008b)). A possble nteracton s nvestgated n Kotsoganns (2010). 13 See, for example, Dahlby (2008). 8

11 horzontal equalzaton, respectvely. By usng (9) and (15), the regonal publc budget constrant for a poor regon obtans as R V 2N p = RH 2N p = ( )Y + A Y = g : (29) Snce a rch regon does not receve any grant wth a vertcal equalzaton, (see(10)), ts publc budget constrant s the same as n the benchmark case R V =2N p = Y = g : (30) Instead, a rch regon pays a transfer (16) wth a horzontal equalzaton, and thus ts publc budget constrant obtans as R H =2N p = ( )Y + A Y = g : (31) Let MCF V and MCF H denote the margnal cost of publc fund wthout tax evason and wth a vertcal and a horzontal equalzaton, respectvely. By usng (29), t s easy to check that the followng condton for a poor regon holds MCF V 2N p = MCF H 2N p = 1 1 ( ) " < MCF < SMCF : (32) Condton (32) shows that the perceved margnal cost of publc fund s lower wth both vertcal and horzontal equalzaton than wthout an equalzaton scheme. Accordngly, the ncentve to overprovson of publc goods s strengthened when an equalzng grant s drected to a poor regon, for whch the e ectve tax rate becomes ( ). 14 Indeed, the ncrease n the regonal tax rate by a poor regon results n a decrease n the regonal ncome due to the elastcty of labour supply. However, such a decrease n regonal ncome allows to receve a greater equalzaton grant. Accordngly, the percepton of the margnal cost of taxaton decreases. By usng (30) and (31), t s easy to check that the followng condton for a rch regon holds MCF H =2N p = 1 1 ( ) " < MCF V =2N p = MCF < SMCF : (33) The result n terms of overprovson of the publc servce also apples for a rch regon n the case of horzontal equalzaton. Actually, f regon =2 N p ncreases ts tax rate, by decreasng ts ncome, t obtans to pay less for the transfer to the set of poor regons, so also ts perceved margnal cost of taxaton s lower. 3.3 Case wth d erent equalzaton schemes and tax evason Now let us ntroduce the possblty of tax evason. We wll compare the socal margnal cost of publc fund wth tax evason, denoted by SMCF S, wth the perceved margnal cost of publc fund, dependng on the type of equalzaton scheme adopted, and on the bass wth respect to whch the grant s calculated. 14 Ths ncentve to overprovson s ncreasng wth, the equalzaton rate. For a analogous statement, see Proposton 1 n Kelders and Köthenbürger (2010). 9

12 Snce the SMCF S s calculated takng nto account the sum of all regonal and federal publc budget constrants, t s easy to check that t s ndependent not only of the type of equalzaton scheme (vertcal or horzontal), but also of the bass wth respect to whch the yeld s calculated (pretax earned ncome or reported taxable ncome). Indeed, when all regonal publc budget constrants are summed up wth the federal one, postve and negatve equalzaton transfers cancel out. Thus, the socal margnal cost of publc fund obtans as 15 ew T Y SMCF S = T Y T Y 1 " T Y ; = 1; ::; n; (34) where " T ew denotes the elastcty of reported taxable ncome. Let us bre y consder the d erences wth respect to the prevous scenaro wthout tax evason. Now at the numerator of SMCF S, there s the sum of two types of margnal cost of taxaton for the tax-payer n regon : T Y In the Appendx, we show that the total cost for the tax-payer s reduced wth respect to the case of no evason f the probablty to be caught s not so hgh. Two observatons can be made for the denomnator of SMCF S. Frst, the tax dstorton s measured, not n terms of the elastcty of labour supply, but n terms of the elastcty of reported taxable ncome, whch s now consdered as the most correct method for calculatng the excess burden of ncome taxaton. 16 Second, there s the whch s postve f the margnal revenue comng from the transfer cost s hgher than the margnal cost of organzng the tax Authorty (whch s a plausble assumpton, see the Appendx, Lemma 1). Ths means that the Authorty can translate the ncrease of evason, comng from a tax rate ncrease, n an opportunty of more yeld, partally compensatng the reducton of revenue due to the taxable ncome decrease. The latter e ect s, of course, captured by the term wth the elastcty of taxable ncome n the formula The ncentve to overprovson for poor regons Wth both a vertcal and a horzontal equalzaton scheme based on pretax earned ncome, for a poor regon 2 N p, the local margnal cost of publc funds obtans as MCF2N V Y HY p = MCF2N p = T Y 1 " T Y T Y + " Y T ) : (35) Let us now compare the local margnal cost of publc fund n (35) to the socal one n (34). The numerator of the two expressons s the same, T as t captures the full mpact of taxaton for a tax-payer n regon. The denomnator s nstead d erent. In partcular, the denomnator n, represents the net gan n terms of (35) contans three terms. The rst term, T Y 1 " T Y yeld from an ncrease of regonal tax rate. The second term, " Y, represents the compensaton comng from the equalzaton scheme, measured n terms of the labour supply elastcty and pretax earned ncome. Fnally, the thrd T ) = T > 0, descrbes the mpact of 15 See the smlarty wth condton (27) n Chetty (2009), although drawn n a d erent context. 16 See Chetty (2009) and the quoted lterature. 10

13 the regonal tax rate on the share of the Authorty budget gong to regon. More precsely, the three terms underlne three types of scal externaltes due to an ncrease of regonal tax rate whch determne the d erence between the local margnal cost of publc fund and the socal one. The rst term corresponds to a tax dstorton dependng on and not only on ; the second term corresponds to the compensaton receved by regon accordng to the vertcal or horzontal equalzaton scheme, whch cancels out at socal level; and nally, the thrd term captures the fact that regon perceves only a fracton of the ncrease of tax Authorty yeld from montorng actvty. In Appendx (Lemma 2) we show the condtons accordng to whch t T (alternatvely <) the MCF tends to be greater (lower) than the SMCF: It turns out that the relatve szes of elastcty of evaded ncome w.r.t. the tax rate vs. the share of audtng costs on the totale tax Authorty s revenue are crucal. Smlarly, wth both a vertcal and a horzontal equalzaton scheme based on reported taxable ncome, for a poor regon 2 N p, the local margnal cost of publc funds obtans as MCF V T Y 2N p HT Y = MCF 2N p = T Y T Y 1 " T Y + " T Y T Y T : (36) ) By comparng the regonal margnal costs of publc fund n (36) to the ones n (35), notce that the only d erent term s the second one at the denomnator: the elastcty of labour supply tmes the pretax earned ncome, " Y, n (35) s replaced by the elastcty of reported taxable ncome tmes reported taxable ncome, " T Y T Y n (36). To conclude, for a poor regon, n the case of an equalzaton scheme based on both pretax earned ncome and reported taxable ncome, a vertcal and a horzontal equalzaton scheme provde the same ncentve to overprovde the publc servce,.e. MCF V Y 2N p MCF HT Y 2N = MCF HY p, and MCF V T Y 2N : If 2N p = p. Instead, both n the case of a vertcal and a horzontal equalzaton scheme, the ncentve to overprovde the publc servce s hgher when the equalzaton scheme s based on reported taxable ncome nstead of pretax earned ncome,.e. MCF V T Y 2N p < MCF V Y 2N p = (" T Y T Y " Y ) > under the plausble assumpton We summarze the prevous reasonngs wth the followng and MCF HT Y 2N p < MCF HY 2N p, Proposton 1 () For a poor regon, n the case of an equalzaton scheme based on both pretax earned ncome and reported taxable ncome, a shft from a vertcal to a horzontal one or vceversa does not change the ncentve to overprovson of the local publc servce. () For a poor regon, both n the case of a vertcal and a horzontal equalzaton, a shft from a scheme based on pretax earned (reported taxable) ncome to one based on reported taxable (pretax earned) ncome ncreases (decreases) the ncentve to overprovson. 17 The assumpton s sustaned by several emprcal nvestgatons n optmal ncome taxaton, where t s found that the elastcty of taxable ncome s much hgher than the labour supply elastcty. 11

14 3.3.2 The ncentve to overprovson for rch regons Wth a vertcal equalzaton scheme based on both pretax earned ncome and reported taxable ncome, the local margnal cost of publc funds, for a rch regon =2 N p, obtans as MCF V Y =2N p = MCF V T Y =2N p = T Y T Y 1 " T Y : T ) Snce a rch regon does pay nothng n case of vertcal equalzaton scheme, ts local margnal cost of publc funds does not depend on the fact that the equalzaton scheme s based on pretax earned ncome or reported taxable ncome. The local margnal cost of publc fund obtans as MCF HY =2N p = T Y 1 " T Y T Y wth a horzontal equalzaton scheme based on pretax earned ncome, and MCF HT Y + " Y T ) ; (37) =2N p = T Y T Y 1 " T Y + " T Y T Y T ; (38) ) wth a horzontal equalzaton scheme based on reported taxable ncome. Two remarks are n order. Frst, MCF=2N HY > MCF HT Y p =2N because " p Y < " T Y T Y. Second, both n the case of an equalzaton scheme based on pretax earned ncome and reported taxable ncome, the comparson between the local margnal costs of publc fund shows that MCF=2N HY < MCF V Y p =2N p because of the term " Y > 0 at the denomnator of (37), and MCF=2N HT Y < MCF V T Y p =2N because p of the term " T Y T Y > 0 at the denomnator of (38). In partcular, the tax dstorton perceved by a rch regon s lower wth a vertcal than a horzontal equalzaton scheme,.e. f a rch regon ncreases ts local tax rate, ts ncome decreases, but t obtans to pay less for the transfer to poor regons. Accordngly, a shft from a horzontal to a vertcal equalzaton scheme augments the margnal cost of publc fund, and thus reduces the gap wth respect to the socal margnal cost of publc fund. We summarze the prevous reasonngs wth the followng Proposton 2 () For a rch regon, n the case of an equalzaton scheme based on both pretax earned ncome and reported taxable ncome, a shft from a vertcal (horzontal) to a horzontal (vertcal) equalzaton scheme ncreases (decreases) the ncentve to overprovson of the local publc servce. () For a rch regon, n the case of a vertcal equalzaton, a shft from a scheme based on pretax earned ncome to one based on reported taxable ncome does not change the ncentve to overprovson. Instead, n the case of a horzontal equalzaton, a shft from a scheme based on pretax earned (reported taxable) ncome to one based on reported taxable (pretax earned) ncome ncreases (decreases) that ncentve. 12

15 4 Concluson When the central government s pre-commtted, t s well known that a vertcal scal externalty orgnated from an ncrease of a local surtax on a federal ncome tax base mples the overprovson of local publc goods. Ths s due to the fact that local governments perceve a margnal cost of publc funds lower than the (true) socal one. The ncentve to such a soft budget costrant phenomenon further ncreases f t s n charge an equalzaton system based on scal capacty, lke that one studed by Smart (1998), and now appled n many federal countres. In ths note, we have analysed how such an ncentve to overprovde local publc goods s changed when the model also allows for ncome evason. Indeed, as shown by Chetty (2009), wth tax shelterng the crteron to measure tax dstoron and excess burden must be changed n order to take nto account the elastcty of taxable ncome nstead of the elastcty of labour supply. Consequently, the formula of margnal cost of publc funds must be changed too, and ths has an mpact on the overprovson concern. In ths respect, we have shown how the local publc good overprovson phenomenon s a ected by consderng smultaneously tax evason and d erent spec catons of an equalzaton system,.e. vertcal or horzontal, and based on pre-tax earned ncome or reported taxable ncome. In terms of normatve desgn of the equalzaton system, our man result shows that a more e cent level of regonal publc expendtures s better acheved wth a vertcal equalzaton system based on pre-tax earned ncome. It should be stressed that such a normatve prescrpton may be more d cult to apply because more demandng n terms of nformatons to be gathered. Further, although the level of evason s a household s choce, t can be n uenced by regonal scal legslaton wthn whch the household makes hs choces. Indeed, the level of evason depends on local tax rates but can be also somewhat n uenced by the struggle of local governments aganst underreportng tax base. Thus, the opportunty of lmtng tax payments by local voters can be strategcally played by local poltcans to gan electoral consensus. 5 Appendx The tax Authorty cost functon can be wrtten as h (s ; ) = c [p ( )] s ; (39) where c [:] s the untary cost of audtng, as an ncreasng functon of p ( ); whch denotes the probablty that a tax-payer lvng n regon s audted, wth denotng the e ort varable measurng the x-e cency of the tax Authorty. The probablty s clearly an ncresng functon of the e ort, p 0 ( ) > 0. The transfer cost functon z ( ; s ) descrbes the expected prvate cost of tax evason. If the tax-payer has evaded and s audted, he has to pay hs tax bll on the evaded amount, s, and a ne F (s ; ). Let us suppose that the latter s lnear,.e. F (s ; ) = f s : Therefore the transfer cost obtans as the sum of the expected re-paed tax plus a ne,.e. z ( ; s ) = p ( )( s + f s ): (40) 13

16 By the envelope theorem, we (5) of the text as = p ( )s (1 + f ). Thus now we may rewrte = v I [T Y + p ( )s (1 + f )] = v I fy [1 p ( )(1 + f )] s g ; = 1; :::; n: Ths condton shows us that the tradtonal ndvdual welfare cost of a tax ncrease, v I Y, s reduced by the expected net bene t from evason, v I [1 p ( )(1 + f )] s. Therefore, f p ( ) < 1 1+f ;.e. evason s convenent (s > 0), the numerator of the margnal cost of publc funds formula wth tax evason, as for nstance (34), s reduced w.r.t. the numerator of the margnal cost of publc funds formula wthout tax evason, as for nstance (28), where there s only Y : By substtutng (39) and (40) nto the tax Authorty budget T = z ( ; s ) h (s ); we obtan: T ( ) = fp ( )(1 + f ) c [p ( )]g s : (41) If the tax Authorty s e cent n choosng the e ort level, and evason s ncreasng wth the tax rate, the followng Lemma shows that an ncrease of the local tax rate ncreases Authorty s yeld. Lemma 1 If (1 + f ) c 0 [p ( )] ; where = argmax T ( ); T ( ) 0; ( > 0: or Proof. The F.O.C. of the maxmzaton of (41) w.r.t. s as follows: where p (1 + f ) c 0 [p ( )] p 0 ( )s + fp ( )(1 + f ) c [p p 0 ( ) p s (1 + f ) c 0 [p ( )] (1 + f ) c [p ( )] p p ( ) = 0; > 0; then > 0; because s s decreasng n p for a rsk-averse tax-payer. If (1 + f ) c 0 [p ( )] ; t must be (1 + f ) c [p ( )] p ( ) ; and then T ( ) 0: Let us now compute the followng ( ) = p ( )(1 + f )s + fp ( )(1 + f ) c [p ( : (42) Thus, from (42), T ( ) 0; > 0; ( ) > 0. The followng Lemma 2 shows the condtons under whch a regonal government perceves a gan from the tax Authorty actvty lower (or hgher) than the socal one, gven that only a fracton of controllng and audtng evason goes drectly to t. Consequently, the regonal margnal cost of publc funds may be hgher (or lower) than the socal one, dependng on the elastcty of evason w.r.t. the tax rate. If s exactly equal to the rato of local tax rate on federal tax rate, and tax evason s s relatvely elastc (nelastc) w.r.t. the total tax rate ; the Lemma 2 shows that the regonally perceved MCF tends to be hgher (lower) than the socal one SMCF (the benchmark beng the share of audtng costs on the total tax Authorty s revenue). 14,

17 Lemma 2 If = ; s R c s T, T ) : Proof. It s easy to T ) = (1 0 2 t T : (43) By substtutng = by and 0 = 1; n the r.h.s. we T T from (42) and takng nto account (41), we obtan that Thus, t follows that, = p (1 + f )s = T T s = T c s = T s = 1 + > T ) : R 1. Further, References [1] Barett, C., Huber, B., Lchtblau, K. (2002), A tax on Tax Revenue: The Incentve E ects of Equalzng Transfers. Evdence from Germany, Internatonal Tax and Publc Fnance, 9, [2] Bartoln, D., Forllo, F. (2009), Central and Local Tax Enforcement, n Longobard, E., Petretto, A. (eds), Sagg d economa della tassazone, F. Angel, Mlan. [3] Boadway, R. (2004), The Theory and Practce of Equalzaton, CESfo Economc Studes, 50, [4] Boadway, R., Cu, K., Marchand, M. (2002), Equalzaton and the Decentralzaton of Revenue-Rasng n a Federaton, Journal of Publc Economc Theory, 5 (2), [5] Bucovetsky, C., Smart, M. (2002), The E cency Consequences of Local Revenue Equalzaton: Tax Competton and Tax Dstorton, CESfo Workng Paper n.767. [6] Buettner, T. (2006), The Incentve E ect of Fscal Equalzaton Transfers on Tax Polcy, Journal of Publc Economcs, 90, [7] Chetty, R. (2009), Is Taxable Income Elastcty Su cent to Calculate Deadwght Loss? The Implcatons of Evason and Avodance, Amercan Economc Journal: Economc Polcy, 2(1), [8] Cremer, H., Gahvar, F. (2000), Tax Evason, Fscal Competton and Economc Integraton, European Economc Revew, 44,

18 [9] Dahlby, B. (2008), The Margnal Cost of Publc Funds: Theory and Applcatons, The MIT Press, Cambrdge, U.S.A. [10] Dahlby, B., Warren, N. (2003), Fscal Incentve E ects of the Australan Equalzaton System, Economc Record, 79, [11] Egger, P., Köthenbürger, M., Smart, M. (2010), Does Fscal Transfers Allevate Busness Tax Competton? Evdence from Germany, Journal of Publc Economcs, 94, [12] Fgueras, C., Hndrcks, J., Myles, G. (2004), Revenue Sharng versus Expendture Sharng n a Federal System, Internatonal Tax and Publc Fnance, 11, [13] Grazzn, L., Petretto A. (2006), Vertcal Tax Competton wth Tax Sharng and Equalzaton Grants, Gornale degl Economst e Annal d Economa, 65(1), [14] Hndrks, J, Peralta, S., Weber. S. (2008), Competng n Taxes and Investment under Fscal Equalzaton, Journal of Publc Economcs, 92, [15] Kelders, C., Köthenbürger, M. (2010), Tax Incentves n Fscal Federalsm: an Integrated Perspectve, Canadan Journal of Economcs, 43 (2), [16] Köthenbürger, M. (2002), Tax Competton and Fscal Equalzaton, Internatonal Tax and Publc Fnance, 9, [17] Köthenbürger, M. (2008a), Federal Tax-Transfer Polcy and Intergovernmental Pre- Commtment, Regonal Scence and Urban economcs, 38, [18] Köthenbürger, M. (2008b), How Do Local Governments Decde on Publc Polcy n Fscal Federalsm? Tax vs Expendture Optmzaton, CESfo Workng Paper n [19] Kotsoganns, C. (2010), Federal Tax Competton and the E cency Consequences for Local Taxaton of Revenue Equalzaton, Internatonal Tax and Publc Fnance, 17, [20] Kotsoganns, C, Schwager, R. (2008), Accountablty and Fscal Equalzaton, Journal of Publc Economcs, 92, [21] Musgrave, R. A. (1961), Approaches to Fscal Theory of Poltcal Federalsm, n Buchanan J. (ed.), Publc Fnances, Needs, Sources and Utlzatons, NBER, Prnceton Unversty Press. [22] Smart, M. (1998), Taxaton and Deadweght Loss n a System of Intergovernmental Transfers, Canadan Journal of Economcs, 1, [23] Smart, M. (2007), Rasng Taxes through Equalzaton, Canadan Journal of Economcs, 40(4), [24] Stowhase, S.,Traxler, C. (2005), Tax Evason and Audtng n a Federal Economy, Internatonal Tax and Publc Fnance, 12(4),