Tax Audit and Vertical Externalities

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1 T Audi nd Vericl Eernliies Hidey Ko Misuyoshi Yngihr Ngoy Keizi Universiy Ngoy Universiy 1. Inroducion The vericl fiscl eernliies rise when he differen levels of governmens, such s he federl nd se governmens, imposes es on he sme bse. When se increses is re, i cuses he shred bse o shrink. However, he se governmens ignore he reducion in federl revenues cused by he shrinkge effec. As resul, he se res end o be high. Bodwy nd Keen (1996) nd Dhlby (1996) consider inergovernmenl rnsfer o inernlize he vericl eernliies. They nlyze he equilibrium oucomes in federion sysem where boh he se nd federl governmens impose on he sme bse o finnce heir own public good. They conclude h he fiscl gp which represens he direcion of he rnsfer from he federl governmen o se governmen is negive. So fr, he heoreicl nlyses of compeiion wih vericl eernliies hve no ken evsion nd udi scheme ino ccoun. However, in reliy, here is evsion in he world. T udi concep cn vry beween differen forms of orgnizions nd lso beween counries. In fc, s indiced by Sowhse nd Trler (2005, p. 529) nd Bordignon, Mnsse nd Tbellini (2001, p.719), here re hree udi sysems: udi sysem implemened by boh se nd federl level; udi sysem by federl level; nd udi sysem by se level. From he sndpoin of hese, his pper incorpores evsion nd udi sysems ino vericl eernliy model by Bodwy nd Keen (1996). In he model, we focus on he quesion how he udi sysem should be implemened. By considering he udi, we cn show he following vericl fiscl eernliies which re focused on by he eising sudies. When he differen levels of governmens udi he sme bse, if se governmen increses udi ependiure, evsion decreses. The se governmens ignore he increse in he federl revenues cused by his effec, so h he se udi ependiures will be low. In his pper, we show uniry nion in which federl governmen cn choose ll governmens vribles. The uniry nion is he second-bes opimum. We compre he following hree differen sysems wih he uniry nion cse. The firs cse is decenrlizion sysem where boh he federl nd se governmens implemen udi. The second cse is sysem of udi cenrlizion where only he federl governmen implemens udi. The hird sysem is sysem of udi decenrlizion where only he se governmens implemen udi. In he firs nd hird sysems, if ren is no lloced o he federl governmen, he

2 federl opiml re nd he fiscl gp should be zero nd negive, respecively, o replice he uniry second-bes opimum. In he second cse, he federl opiml re should be negive o replice he uniry second-bes opimum. 2. Model There re idenicl k regions in federl economy nd n inhbins in ech region. Households re idenicl nd immobile mong ses. The uiliy funcion of he households is he following form: U (, l) = u(, l) + b( g) + B( G), (1) where g nd G re se nd federl public goods, respecively. We ssume h u (, l) is incresing in, decresing in l nd qusi-concve, nd b (g) nd B (G) re incresing nd concve funcions. The households re endowed wih one uni of ime nd divide heir ime beween lbor nd leisure. They ern lbor income, wl, where w nd l re wge re nd lbor supply, respecively. Per uni levied on lbor is + T, where nd T denoe se re nd federl res, respecively. The households cn evde he by filing o pr of lbor e (clled undeclred lbor ). On he oher hnd, he governmens py per cpi udi ependiures α + A o preserve bse, where nd A re per cpi udi ependiure by he se governmens nd per cpi udi ependiure by he federl governmen, respecively. In order o evde, households mus ber he coss of C ( e,, where C > 0, C > 0, C > 0, nd e ee α C eα < 0. 1 The budge consrin fced by ech household is = ( ) l + e C( e,, (2) where is prive good nd numerire. The households choose e nd l o mimize he uiliy funcion (1) subjec o budge consrin (2). Solving his problem, we obin he following firs-order condiions: u ( ) + u = 0, (3) l C e ( e, = 0. (4) From hese firs-order condiions, lbor supply funcion nd undeclred income funcion re represened by l = l( ), e = e(,. As is he cse wih Bodwy nd Keen (1996), we ssume h l ( ) > 0. 2 Undeclred income funcion hs he following properies. 1 Ce α ( e, e = > 0, eα = < 0 C ( e, C ( e, ee ee 1 Subscrips denoe pril derivives. 2 A prime denoes he derivive of funcion.

3 Subsiuing (5) nd (6) ino (1), n indirec uiliy funcion cn be represened s V v ( ),, α + b( g) + B( G. By using he envelope heorem, we ge he following resuls: ( ) ) Firms mimize profis mrginl produciviy condiion: (( ),, α ) v ( ) v (( ),, α ) (( ), α ) v, α = u l, (9) = u e, (10) = u C α. (11) f ( nl) wnl nd herefore choose lbor demnd h is given by he f ( nl) = w. Subsiuing lbor supply funcion ino his condiion, we implicily wrie he equilibrium wge re nd ren. w = f ( nl( )). (12) r ( ) = f ( nl( w )) nl( ) f ( nl( w )). (13) The rens re lloced o he federl governmen consn re θ (0,1), nd o he se governmens he re of following resul: 1 θ. Differeniing (12) nd (13) wih respec o, we obin he 2 2 n f l l w = (0,1), r (1 ) = w f n l l = < 0. (14) The se governmens collec he se revenues which consis of he, ren, nd rnsfer from he federl governmen o he se governmen S. The se governmens use he revenue for he se public good nd he se udi cos. Therefore, he se budge consrin is given by g = nl( w( ) ) ne(, + S + (1 θ ) r( ) n. (16) The federl public good nd he rnsfer beween he governmens re supplied by he federl governmens nd re finnced by he federl s revenue which consiss of he revenue nd ren. Therefore, he federl governmen s budge consrin is given by: G = kntl( w( ) ) knte(, ks + kθr( ) kna. (17) 3. Opiml policies under uniry nion In uniry nion, he federl governmen chooses, α, g, nd G o mimize socil welfre (individul uiliy). Solving his problem, we obin he necessry condiions: l e nb knb ( G) Cα = = =. (29) u l l e u neα e l e This condiions mens h he sum of he mrginl re of subsiuion beween boh he se nd federl goods nd he prive good is equl o he mrginl cos of public funds (MCPF) nd he mrginl cos of udi (MCTA) which is he cos of rising uni of revenue by incresing he

4 udi ependiure. MCPF nd MCTA re greer hn 1. (29) ogeher wih he budge consrin in (16) chrcerizes he uniry second-bes opimum. 4. Opiml policies under decenrlized sysem 4.1. The se governmen s behvior The se governmens choose, nd g o mimize he indirec uiliy funcion V subjec o (16), king s given he decision vribles of he federl governmen, T, A, S nd G. The necessry condiions of his mimizion problem re given by [( w 1) l + e] u + b g = 0, (31) C α u + b' g = 0. (32) As indiced by Appendi, we obin he following necessry condiions l e Cα nb = = l l e G G e + 1 neα + l e kn kn. (33) Compring he denominor in (29) o (33), we cn see h G nd G re imporn elemens. If G < 0 nd G < 0, hen he MCPF nd MCTA for he second bes cse is greer hn h for he se governmens under decenrlized sysem. On he oher hnd, if G > 0 nd G > 0, i led o he opposie resul. These elemens represen he effecs of he se re nd he se udi ependiure on he federl governmen revenue. The se governmens neglec hese effecs (vericl eernliies) The federl governmen s behvior In his subsecion, we consider he federl governmen behvior. The federl governmens choose T, A, S nd G o mimize he indirec uiliy funcion V subjec o (17), king ino ccoun he recion of he se governmen. The necessry condiions for his problem re wrien s follows: l e knb ( G) = nb (38) G (1 + T ) + GT l e + kn 1 knb ( G) = nb. (39) G A + (1 + A) G kn

5 ( b knb ( G) ) + nb ( G + G ) = 0 S S n. (40) The opiml federl policies re o sisfy he equions (38), (39) nd (40) simulneously. Therefore, he federl opiml re nd udi ependiure re chrcerizing by he condiions G = 0 nd G = 0. To chieve hese condiions yields h MCPF for he federl governmen is equl o h for he se governmen nd replices he second-bes opimum. From G = 0, he opiml federl is given by θr T = < 0. (41) n( w 1) l ne Subsiuing (41) ino G, he sign of G becomes negive. This mens h he decenrlized sysem cnno replice he second-bes equilibrium. Here, suppose h he federl governmen does no ge revenue from rens: θ = 0. In his cse, he federl governmen hs no revenue from nd rens. Therefore, he federl public good should be finnced by he rnsfer from he se governmens. This implies h he fiscl gp is negive. We provide he following proposiion. Proposiion 1 Under he decenrlized sysem, if he federl governmen does no ge revenue from rens, he federl governmen cn replice he second-bes. In his cse, he federl governmen se he re zero, nd herefore, he fiscl gp is negive o finnce he federl public good. 5. Alernive udi sysems 5.1. T udi cenrlizion We consider cse h only he federl governmen cn implemen udi: In his cse, α = A. Here, we ssume h he se governmens receive ccure informion bou udi from he federl governmen. In his cse, here is no soluion becuse he federl governmen only hs hree policy ools (T, A, S,G ) o in he four second-bes vribles (, α, g nd G ). Proposiion 2 Under he udi cenrlized sysem, he federl governmen cn replice he second-bes. In his cse, he federl governmen should se he re negive.

6 5.2. T udi decenrlizion We urn o show udi decenrlizion such h only he federl governmen implemen udi: in his cse, α =. In his cse, here is no soluion becuse he federl governmen only hs hree policy ools (T, S, G ) o in he four second-bes vribles (, α, g nd G ). Therefore, he udi decenrlizion cnno replice he second-bes opimum. However, if θ = 0, he udi decenrlizion cn replice he second-bes opimum. These resuls re he sme s hose under he decenrlizion sysem. 6. Conclusion In vericl eernliy models, i is ypiclly ssumed h here re no evsion nd no cos of collecion. This ssumpion does no reflec he reliies. Therefore, his pper eends he vericl eernliy model in Bodwy nd Keen (1996) by considering evsion behvior nd udi ependiure. Thereby, we obined he significn resuls relevn o policy, fiscl rnsfer policy nd udi policy. Concreely, he resuls of his pper re s follows. When he se governmens implemen udi, if ren is no lloced o he federl governmen, he federl opiml re nd he fiscl gp should be zero nd negive, respecively, o replice he uniry second-bes opimum. On he oher hnd, when only he federl governmen implemen udi, he federl opiml re should be negive o replice he uniry second-bes opimum. References Bodwy, R. nd M. Keen, (1996) Efficiency nd he opiml direcion of federl-se rnsfers, Inernionl T nd Public Finnce, 3 (2), pp Bordignon, M. P. Mnsse, nd G. Tbellini, (2001) Opiml regionl redisribuion under symmeric informion, Americn Economic Review, 91 (3), pp Cremer, H. nd F. Ghvri, (2000) T evsion, fiscl compeiion nd economic inegrion, Europen Economic Review, 44 (9), pp Dhlby, B., (1996) Fiscl eernliies nd he design of inergovernmenl grns, Inernionl T nd Public Finnce, 3 (3), pp Keen, M., (1998) Vericl eernliies in he heory of fiscl federlism, IMF Sff Ppers, 45 (3), pp Keen, M. nd C. Kosoginnis, (2002), Does federlism led o ecessively high es?, Americn Economic Review, 92, pp Sowhse, S. nd C. Trler, (2005) T evsion nd udiing in federl economy, Inernionl T nd Public Finnce, 12, pp