Journal of Publ Eonoms 80 (00) 99 9 www.elsever.nl/ loate/ eonbase When s two better than one? How federalsm mtgates and ntensfes mperfet poltal ompetton Bryan Caplan Department of Eonoms and Center for Study of Publ Choe, George Mason Unversty, Farfax, VA 030, USA Reeved February 999; reeved n revsed form February 000; aepted February 000 Abstrat The urrent paper models power-maxmzng poltans behavor subet to mperfet poltal ompetton and perfet tzen moblty. It then analyzes the welfare mplatons of federal and non-federal strutures. The model abstrats from both heterogeneous preferenes (the most ommon argument n favor of federalsm) and externaltes (the most ommon argument aganst), showng that even n ths smplfed settng federalsm has mportant welfare mplatons. There s one lass of equlbra n whh more federalsm has the purely benefal effet of offsettng mperfetons n the poltal proess. However, there s also a seond lass of equlbra n whh tzen moblty maes poltal mperfetons more severe by reatng safe dstrts for both poltal partes. 00 Elsever Sene B.V. All rghts reserved. Keywords: Optmal federalsm; Imperfet poltal ompetton; Intergovernmental ompetton JEL lassfaton: D7; H; D60. Introduton State and loal poltans fnd themselves onstraned by both polts most notably, the need to wn eletons and eonoms most notably, the opton of dssatsfed ustomers to go elsewhere wth ther human and/ or physal aptal. The welfare analyss of subetng poltans to demorat votng espeally E-mal address: baplan@gmu.edu (B. Caplan). 0047-77/ 0/ $ see front matter 00 Elsever Sene B.V. All rghts reserved. PII: S0047-77(00)0006-7
00 B. Caplan / Journal of Publ Eonoms 80 (00) 99 9 relatve to dtatorshp has been largely favorable (Wttman, 989, 995; MGure and Olson, 996). But the welfare analyss of the reloaton opton has been more equvoal. As Rose-Aerman (983) puts t, A multple-government system has lttle normatve appeal f everyone has the same tastes and nomes and f the government apparatus s ontrolled by voters. (pp. 5 6). Even when there s substantal heterogenety of tastes, ths must be weghed aganst the nablty of deentralzed governments to ope wth nterursdtonal externaltes (Gordon, 983; Donahue, 997). Inman and Rubnfeld (996) ontrast ths optmal tax aount of federalsm to the poltal eonomy vew. Whle the former treats governments as fathful agents of ther tzens, the poltal eonomy perspetve emphaszes that federalsm helps mtgate the prnpal-agent problems of demoray (Brennan and Buhanan, 980; Frey and Ehenberger, 996; Inman and Rubnfeld, 997; Qan and Wengast, 997). The urrent paper formally shows that even abstratng from heterogeneous preferenes and nterursdtonal externaltes, federalsm an both mprove and worsen the performane of demorat governments. I develop a model n whh poltans ompete eletorally wth another party wthn ther state, and ompete eonomally wth a rval government outsde ther state. As n Lndbe and Webull (987), Grossman and Helpman (996), and Dxt and Londregan (995, 996, 998a,b), eletons wor mperfetly: voters treat partes as dfferentated produts. Ths model s rh enough to generate two qute dfferent lasses of equlbra. In the frst lass, the need to eep tzens from movng away leads poltans to mprove ther poles even f they are eletorally seure. Federalsm then mtgates the mpat of the domnant party s monopoly power. In the seond lass of equlbra, however, the loyalsts of eah party tend to move to the state ther party s expeted to ontrol. Ths proess maes the poltal mperfetons n both states more severe. The next seton desrbes the players and ther obetve funtons. The thrd seton solves the model and welfare rans the possble equlbra. The fourth seton examnes the robustness of these fndngs to alternate assumptons. The ffth seton analyzes the pratal sgnfane of the results. The sxth seton onludes.. Players, preferenes, and the benhmar equlbrum There are two state governments ndexed by 5 h, (note that the nterpretaton of all varables s gven n Table ). Eah state has two ompetng poltal partes and. The players are thus four state poltal partes, plus a ontnuum of tzens whose measure Y s normalzed to. Eletons are deded by smple maorty; for smplty, ted eletons are ounted as vtores for n anddate equlbra where wns, and as vtores for n anddate equlbra where wns. Play s smultaneous, and n any Nash equlbrum:
B. Caplan / Journal of Publ Eonoms 80 (00) 99 9 0 Table Summary of the model s varables Varable Interpretaton Exogenous G * Ctzens most preferred quantty of publ goods b Utlty loss senstvty parameter for publ goods C Intensty of tzen s preferene for party Y Total populaton/ output of eonomy; normalzed to C Medan (and mean) ntensty of populaton s preferene for party B S G,G Two types of tzens most preferred quantty of publ B S goods, G. G Endogenous G Quantty of publ good n state z Indret utlty funton of tzen n state I Indator varable5 f party wns n state, 0 otherwse u,u Utlty funton of state partes, n state Y Total populaton/ output n state d Squared devaton of G * n state C The medan of the dstrbuton of C n state. All tzens must vote for ther most-preferred party n ther state.. All poltal partes must offer platforms that maxmze ther expeted utlty. 3. All tzens must resde n ther most-preferred state (f they have a hoe). If they are ndfferent between states they randomze wth equal probabltes... Ctzens Total wealth s assumed to be the same for all tzens, and s also normalzed to equal. Ctzen utlty depends upon not only onsumpton of prvate and publ goods, but also on the poltal envronment. These tastes and the per-apta budget onstrant yeld tzens ndret utlty funton, assumed to be of the followng form: z 5b(G G *) C I. () G * s tzens most-preferred per-apta sze of government; the assumpton of homogeneous poly preferenes maes the postve and negatve role of federal sm n the model learer. I s an ndator varable whh equals f party s n power n state, and 0 otherwse. C s s relatve taste for party versus party ; a tzen wll trade up to C n utlty n order to be ruled by party rather than party. C for the tzen populaton s unformly dstrbuted on the nterval
0 B. Caplan / Journal of Publ Eonoms 80 (00) 99 9 [0.5 C, 0.5 C ], where C. 0 s both the average and the medan value of C. There are a ouple ways to nterpret C. Lndbe and Webull (987) suggest that t aptures partes ontrastng and relatvely fxed ommtments to mportant non-eonom poles, suh as ther stanes on aborton and natonal defense. Whle most of the urrent paper assumes that both share the same powermaxmzng obetve, ths does not rule out the possblty of dfferent obetves along other margns. Alternately, n lne wth muh of the empral poltal sene lterature on party afflaton (e.g., Mutz and Monda, 997; Sears et al., 980; Luttbeg and Martnez, 990), C ould rredubly reflet ndvduals nherted partsan loyaltes. Just as many sports fans root for ther team even though all teams have the same obetve funton, many voters strtly prefer ther party even f t ats the same as ts ompettor. For example, Cathol voters mght ontnue votng for tradtonally preferred Demorat anddates even though platform hanges leave them somewhat deologally loser to Republans. Whle suh advantage erodes over tme, the eroson may be so gradual that for pratal purposes eah generaton of poltans treats ts level as fxed... Partes Controversy stll surrounds poltal partes obetve funtons. In Grossman and Helpman (996) and Dxt and Londregan (995, 996, 998b), poltal partes obetve s to maxmze ther votes. Dxt and Londregan s (998a) partes maxmze a weghted average of votes and an deologal soal welfare funton; Alesna and Rosenthal (995) smlarly assume that partes advane dvergent leftst and rghtst deologes subet to eletoral onstrants. In ontrast, both Brennan and Buhanan (980) and MGure and Olson (996) 3 assume they see to maxmze ther own power. Caplan (999a) presents empral evdene on the relatve merts of the deologal and power-maxmzng vews of party motvaton, fndng that both theores have some valdty. The ore of ths paper bulds on the power-maxmzng assumpton beause t maes the More mportantly, a later seton shows that the smple model s results stll hold when ompetng partes have dfferent poly obetve funtons. On the theory of poltans wth preferenes over both poles and eletoral vtory, see Wttman (983). 3 MGure and Olson s (996) self-nterested autorats maxmze ther tax revenues mnus ther expendtures; n onsequene, government unonstraned by eletons s too small. Brennan and Buhanan, however, model poltans as onstraned maxmzers of government spendng, so government spendng tends to be too large. These two approahes are probably more smlar than they appear. Dret appropraton of surplus tax revenues s normally mpermssble n demoraes; poltans therefore fae the publ-setor equvalent of rate-of-return regulaton, wth the permssble return apped at zero. The ratonal response of a self-nterested autorat or eleted powermaxmzng partes would be to elmnate monopoly profts by rasng osts.
B. Caplan / Journal of Publ Eonoms 80 (00) 99 9 03 model more tratable and the results learer: unle deologal partes, all power-maxmzng partes want to shr n the same way. Yet power-maxmzaton s not neessary for the man results: Seton 4 shows that f partes have dvergent deologes, the modfed model s nearly somorph. The power-maxmzng motve of the partes s formalzed by assumng that partes utlty nreases monotonally as the sze of government they ontrol grows: u 5 IGY, () u 5 ( I )G Y, (3) where G and G are the poltal platforms offered n state by partes and..3. The benhmar regme: poltans onstraned solely by eletons Suppose a regme has demorat eletons, but tzens and ther wealth annot move to another loalty. Eah state has demographally dental populatons of 0.5 rrespetve of poly. Ths la of moblty ould be nterpreted as a system of mmgraton ontrols, or as the result of a federal tax and grant system that leaves no nentve for reloaton at the margn. Usng (), and defnng d ; (G G *), t an be seen that tzens vote for party f bd C $bd, (4) and for party otherwse. Smlarly, the poltal partes only need to worry about beatng eah other, so () and (3) beome u 5 0.5I G, (5) u 5 0.5( I )G. (6) Gven maorty rule, t wll then not be an equlbrum for both poltal partes to offer the medan preferene. Sne by assumpton C. 0, party wns wth ertanty f t plays G *. Party wll want to eep nreasng the offered level of government untl t drves the perentage of votes t reeves down to 0.5, leavng the medan voter ndfferent: C b(d d ) 5 0. (7) Due to dsadvantaged status, n equlbrum party wll never wn. However, nether party wll have an nentve to hange ts behavor only f mnmzes s votes by mang the medan voter as well-off as possble: mn C b(d d ). (8) G
04 B. Caplan / Journal of Publ Eonoms 80 (00) 99 9 Solvng (8) reveals that s vote-maxmzng strategy s to set G 5 G *. One an fnd s best response by pluggng G 5 G * nto (7), yeldng ] C G 5 G * ]. (9) b œ In the benhmar equlbrum, then, the party wth the greater poltal advantage always wns, but s onstraned n ts hoes by the presene of the alternatve, less popular party. The dsadvantaged party offers to set the sze of government equal to tzens blss pont. The advantaged party s devaton from tzens most-preferred level s an nreasng funton of the magntude of the poltal advantage of the domnant party dvded by the loss-senstvty parameter. It goes as far as t an get away wth wthout losng offe..4. Welfare analyss of the benhmar regme Treatng C as a random varable, one an alulate total tzens expeted utlty n a gven regme. In general, E(z ) 5 YE(z ) YE(z ). (0) Usng (), defnng C as the medan value of C n state, and notng that the medan and mean value of C are equal: E(z ) 5 Y (bd C I ) Y (bd C I ). () Computng tzens expeted utlty n the benhmar regme s straghtforward. ]] G 5 G * œc/b, Y 5 0.5 and C 5C sne there s no moblty, and I 5 sne party ontrols both states. Substtutng these nto () reveals that the benhmar utlty level s 0 : S D œ ] C E(z ) 5b ] C 5 0. () b 3. Poltal equlbrum and welfare wth both moblty and votng Ths seton haraterzes the equlbra of the game wth both free eletons and unonstraned moblty, then ompares the expeted utlty of these equlbra to that of the benhmar regme. Y, C, and I beome endogenous funtons of poly, as one would expet for members of demorat federal systems. Unle the smplfed game wthout moblty, whh has the unque benhmar equlbrum, the more omplex game wth both votng and moblty an have multple equlbra. These are possble beause unrestrted movement dretly affets C, the medan of the dstrbuton of C n state, whh n turn nfluenes poltal outomes. There are four suh anddate equlbra: hi,i an equal h,, h0,0,
B. Caplan / Journal of Publ Eonoms 80 (00) 99 9 05 Table Exstene and welfare propertes of anddate equlbra Case Possble Possble good eq.? bad eq.? hi,i 5 h, Yes No hi,i 5 h0,0 Does not exst hi,i 5 h,0 or h0,; votng onstrant bnds n...... nether state Yes Yes... state but not state Yes Yes... both states Does not exst... state but not state Does not exst h,0, or h0,. Table summarzes ths seton s results, dvdng equlbra nto good equlbra where expeted utlty s wealy greater than the benhmar level, and bad equlbra where t s strtly lower. 3.. Party wns n both states: hi,i 5 h, If party s expeted to wn n both states, there s no nentve to reloate on the bass of partsan preferenes, so C 5C. Whhever state has the lower value of d aordngly gets 00% of the populaton. As n the Bertrand duopoly game, ths leaves only one Nash equlbrum n whh the rulng party n both states sets d 5 0. Both states get exatly half the populaton. To sustan ths equlbrum, both hapters of party need merely ensure that they wn eletons n both states. As shown n Seton.3, party an always wn the eleton f C. 0, so an equlbrum wth hi,i 5 h, always exsts. Expeted utlty n ths regme s learly hgher than n the benhmar ase, whh has expeted utlty of 0. Usng (): E(z ) 5 Y (bd C I ) Y (bd C I ) 5 0.5(0 C ) 0.5(0 C ) 5C. 0. (3) Hene, ths s always one of the good equlbra where moblty maes demoray wor better. Note further that there s no reason to regard ths as an unstable equlbrum, as dental ommuntes an be n a smple Tebout model wth heterogeneous tzens. In a world wth small random perturbatons, the partes would adust by amng for a larger vtory margn. 3.. Party wns n both states: hi,i 5 h0,0 If party s expeted to wn n both states, there s no nentve to reloate on the bass of partsan preferenes, so C 5C. As shown n Seton.3, ths anddate equlbrum wll not exst f C. 0.
06 B. Caplan / Journal of Publ Eonoms 80 (00) 99 9 3.3. Party wns n one state, party wns n the other: hi,i 5 h,0 or h0, The numberng of the states s arbtrary, so the equlbrum ondtons for hi,i 5 h,0 and hi,i 5 h0, are essentally dental. For smplty, then, ths seton loos only at hi,i 5 h,0, where party wns n state and party wns n state. In any equlbrum, note that tzens n state are ndfferent between votng for and when C 5 b(d d ). (4) Note further that n any equlbrum, the medan voter must wealy prefer the wnner, and losng partes platforms set the sze of government equal to G *. Usng (4) and these two fats permts the dervaton of both eletoral vtory onstrants: bd #C, (5) bd #C. (6) Ctzens are ndfferent between lvng under n state and under n state when C5 b(d d ). (7) All tzens wth C. b(d d ) strtly prefer state, and all wth C, b(d 4 d ) strtly prefer state. The fraton of tzens n eah state s thus gven by Y 5 0.5 C b(d d ), (8) Y 5 0.5 C b(d d ). (9) The demand for resdene n state s (a) an nreasng lnear funton of the mean preferene for party over party, (b) a dereasng funton of the devatons from voters blss ponts n state, and () an nreasng funton of the devatons from voters blss ponts n state. The oppostes hold for resdene n state. The medan value of C n both states an be derved from the dstrbutons mpled by (8) and (9): 0.5 C b(d d ) C 5 ]]]]]]], (0) 0.5 C b(d d ) C 5 ]]]]]]]. () 4 For purposes of later welfare analyss, note that ths means that the medan and mean values of C reman dental.
B. Caplan / Journal of Publ Eonoms 80 (00) 99 9 07 Pluggng (0) nto (5) and () nto (6) yelds s eletoral vtory onstrant n state and s orrespondng onstrant n state : bd # 0.5 C bd, () bd # 0.5 C bd. (3) To understand the welfare propertes of ths lass of equlbra, plug (8) () nto () to get an expresson for tzens expeted utlty: 0.5 C b(d d ) F H]]]]]]] JG E(z ) 5 h0.5 C b(d d ) bd whh redues to h0.5 C b(d d )[bd ], (4) E(z ) 5 0.5[b(d d )] C [b(d d )] 0.5[b(d d )] 0.5[C C 0.5]. (5) In prnple, there are four sub-ases to onsder: (a) the votng onstrant bnds n nether state; (b) the votng onstrant bnds n state but not state ; () the votng onstrant bnds n both states; (d) the votng onstrant bnds n state but not state. Smple proofs by ontradton show that sub-ases () and (d) never exst. In ontrast, t an be proven that both equlbra (a) and (b) are possble, and may be ether welfare-superor or nferor to the benhmar. All of these proofs appear n Appendx A. The remander of ths seton provdes an ntutve dsusson of equlbra (a) and (b) and ther welfare propertes, and offers some llustratve examples. The novel feature of the equlbra where hi,i 5 h,0 s that both partes smultaneously rd themselves of the most hostle elements of ther eletorates. Ths allows ether one or both partes to set per-apta government spendng at the value that maxmzes GY wthout fear of eletoral onsequenes. It remans true that rulng partes attrat more populaton and nrease ther vote share when ther poles mprove. But wth the least-frendly voters safely n the rval state, poltal ompetton beomes weaer n both ursdtons. Two opposng fores thus mae the welfare propertes of these equlbra ambguous. On the postve sde, when rules n one state and rules n the other, no one has to suffer under the rule of the party they dsle. Ths s espeally benefal for extreme partsans. On the negatve sde, when rules n one state and rules n the other, equlbrum poles tend to worsen beause poltal ompetton s weaer. Whether the postve or the negatve welfare effets matter more, as Appendx A shows, depends on parameter values.
08 B. Caplan / Journal of Publ Eonoms 80 (00) 99 9 3.3.. Votng onstrant bnds n nether state It s easest to understand the equlbrum where the votng onstrant bnds n nether state by relaxng the assumpton that C. 0 and settng C 5 0. Then eletons funton perfetly ompettvely so long as the entre eletorate or a representatve sample thereof partpates. But wth moblty, the eletorate n eah state s a self-seleted and therefore unrepresentatve sample. Voters wth postve C tend to lve n state, and voters wth negatve C tend to lve n state, so poltal ompetton beomes mperfet and poly gets worse n both states. But from the pont of vew of tzen welfare, the rual queston s: how muh worse? Mathng tzens wth ther preferred partes s learly an advantage from a welfare standpont. If poly only gets a lttle worse, then the net effet on welfare wll stll be postve. If poly gets muh worse, however, welfare falls. What then determnes how muh poly qualty deterorates? As Eq. (A.6) n Appendx A shows, when C 5 0, the unonstraned equlbrum devaton s a smple funton of two varables: the senstvty parameter b and the blss pont G *. As ether varable grows, partes departures from G * derease, so equlb- ] Œ] rum devatons from voters deal pont fall. At the rtal pont G * œb 5 / 8, the welfare osts of mperfet poltal ompetton and the welfare gans of mathng exatly balane eah other, leavng expeted utlty at the benhmar ] level. For hgher values of G * œb, welfare exeeds the benhmar level; for lower values, t falls short of t. Table 3 llustrates the fat that ths an be ether a good or a bad equlbrum. For the low values of G * and b, the equlbrum s welfare-nferor to the benhmar. For the ntermedate value shown n the table, the produt of G * and b s presely / Œ ] 8; welfare s onsequently exatly equal to the benhmar level. For onsderably larger values of the two rual parameters, welfare exeeds the benhmar level. Wth moblty hgh, and the desred level of government large to begn wth, the qualty of poly auses lttle harm ompared to the benefts of mathng. 3.3.. Votng onstrant bnds n state but not state Now tae the ase where the votng onstrant does bnd n state, but not state. As Appendx A shows, for small values of bd or large values of C, expeted utlty exeeds the benhmar level. When C taes on smaller values, welfare Table 3 Parameter values and welfare for equlbrum 3.3. * b G bd bd E(z ) 0. 0.05 0.05 0.6 0.5 0.5 0.5 0 3 0.5 0.05 0.05 0.46
B. Caplan / Journal of Publ Eonoms 80 (00) 99 9 09 Table 4 Parameter values and welfare for equlbrum 3.3. b C bd bd E(z ) 0. 0.3 0.54 0.004 6 0. 0.9 0.88 0.00 0. 0.6 0.074 0.076 6 0. 0.96 0.04 0.08 propertes depend on the sze of bd. For small values of bd, welfare exeeds the benhmar level; for large values, the benhmar s welfare superor. How an ths be nterpreted ntutvely? Usng () and (3), onsder two salent features of equlbra where the votng onstrant bnds n state but not state. Frst, the devaton n state wll be smaller than the devaton n state. If the devaton s small n state, the devaton n state must be smaller stll. Thus, when bd s small, poles must be good n both states, no one s trapped under the rule of a party they strongly dsle, and welfare n hgher than n the benhmar ase. Seond, as C nreases, summed poly devatons must delne. When C s large, good poles n state tend to ounter-balane bad poles n state. For C. 0.5, ths effet s strong enough to guarantee that welfare exeeds the benhmar level. In ontrast, when C s small and bd s large, poly wll be bad n both states, and welfare falls below the benhmar level: the soal osts of bad poly then outwegh the soal benefts of better satsfaton of onfltng party loyaltes. To llustrate these ponts, suppose we fx G * 5 0., and note how the equlbrum and ts welfare propertes hange as b and C vary (Table 4). For the smaller value, C 5 0., the welfare propertes hnge on the value of bd, whh n turn depends on b, the senstvty of utlty to devatons from G *. When b rses from to 6, the equlbrum value of bd falls, and expeted utlty rses from somewhat below the benhmar level to somewhat above. In ontrast, for the larger value, C 5 0., welfare always exeeds the benhmar level. 4. Robustness of the model The model solved n Seton 3 uses a number of non-standard assumptons. Whle these do smplfy the results, ths seton shows that the paper s entral onlusons are farly robust. They reman largely unhanged f: () there s one small-government and one bg-government party; () f there are heterogeneous deal poly ponts; (3) f there are movng osts between ursdtons; (4) f there are more than two ursdtons. The fndngs hange more f: (5) partes oordnate at the natonal level; or (6) the tmng and ommtment assumptons
0 B. Caplan / Journal of Publ Eonoms 80 (00) 99 9 hange. The followng sx setons examne how hangng one assumpton at a tme n the bas model eepng all of the others fxed alters the results. 4.. Opposng deologes In my model, both partes maxmze the sze of government. A more ommon modelng strategy, however, s to assume that partes have opposng deologes, suh as small government versus bg government. Suppose, then, that party s obetve funton s stll gven by (3), but party s utlty s an nreasng funton of the sze of the prvate setor ondtonal on holdng power: u 5 I ( G )Y. (9) Sne the rtal varable s squared equlbrum devatons from voters deal pont, a surprsng fraton of the model s results go through nearly unhanged. In the smplfed verson of the model wthout moblty, devates as far as possble from voter preferenes as t an wthout losng offe, so d remans C/b. The only dfferene s n the dreton of devaton: (9) beomes: ] C G 5 G * ]. (99) b œ For the equlbrum wth both votng and moblty, t s apparent that Eqs. (5) (3), beng symmetr wth respet to devatons from G *, do not hange. It s only neessary to remember that party devates below G *, whle devates above. Thus, the results for Setons 3. and 3. go through unhanged. The ey onlusons for Seton 3.3 are lewse robust, though the detals of the analyss 5 must be slghtly modfed. 4.. Heterogeneous poly preferenes Most models of federalsm assume that tzens have dverse tastes about poly, not a sngle shared G * as the urrent paper does. Suppose then that there are equal proportons of two types of voters, one whose most-preferred sze of government B S B S s G whle the other s s G, wth G. G. The voters are otherwse dental; n partular, for both types, the dstrbuton of C s the same. The set of equlbra of ths modfed verson of the model s omplex beause both the dstrbuton of poly preferenes as well as the dstrbuton of C are endogenous. An appendx, avalable from the author, dsusses the most straghtforward ases, and shows that wth heterogeneous preferenes there are stll good and bad equlbra. 5 An appendx, avalable from the author, provdes the spefs.
B. Caplan / Journal of Publ Eonoms 80 (00) 99 9 4.3. Movng osts and ntal tzen dstrbuton In the verson of the model n Seton, movng osts are effetvely nfnte. In Seton 3, moblty s ostless. What about ntermedate ases? An earler verson of ths paper shows that most of the results from Seton 3 persst. The man dfferene s that, wth moblty osts, nter-ursdtonal ompetton s mperfet. Even when party rules n both states, moblty annot pressure partes to offer G *. The welfare analyss s largely unhanged; the man dfferene s that t s neessary to tae aount of realzed moblty osts when alulatng the net welfare mpat of federalsm (Caplan, 999b). Wth postve moblty osts, the ntal dstrbuton of tzens begns to matter too. In general, a less-than-perfetly-evenly-dstrbuted populaton enhanes the advantages of federalsm. The dsadvantage of federalsm s that tzens wth smlar party preferenes luster together, leadng to wea poltal ompetton. If tzens wth smlar party preferenes are ntally lustered, however, the margnal dsadvantages of moblty delne and the margnal advantages nrease. In effet, f tzens luster ex ante, the relevant benhmar equlbrum s welfare level s lower, so t s more lely that the equlbrum wth moblty s welfaresuperor. 4.4. More ursdtons Inreasng the number of ursdtons, whle retanng the assumpton of ostless moblty, an yeld a frst-best outome. Wth four ursdtons, there exsts an equlbrum where party rules n two states, party rules n the other two, the equlbrum level of government n all four states s G *, and everyone lves under ther most-preferred poltal party. In general, so long as there s ostless moblty, f one party rules any two states, moblty pressures both to set the sze of government to G *. Moblty osts naturally tend to weaen ths result, as do heterogeneous poly preferenes. 4.5. Coordnaton Must the state hapters of eah party set ther platforms non-ooperatvely? Perhaps all of the branhes of party oordnate on a ommon strategy, as do the branhes of party. In the ontext of ths paper s model, there s no more reason to expet ntra-party ooperaton than nter-party ooperaton. However, ths ould hange f the natonal dmenson of ths federal system s polts were modeled more expltly. The state partes mght, for example, follow ther natonal afflates n order to get a normal level of federal grants. The equlbra where the same party runs both states then loo maredly worse: rather than ompetng n a Bertrand-le fashon, they mght not ompete at all.
B. Caplan / Journal of Publ Eonoms 80 (00) 99 9 4.6. Tmng and ommtment The model assumes that all players mae ther moves smultaneously. In ths ase, there an be no ommtment problem. Alterng ths tmng assumpton ould learly modfy the game s results, partularly f partes possess no redble ommtment tehnology. If people mae ther loaton desons frst, and partes subsequently set poly, then at the tme of deson, eletons are the only fator onstranng partes platforms. The model must then be solved by bawards nduton. Note that, n equlbrum, votng onstrants must bnd n both states, so there are only two ases that need to be analyzed. In the frst, wns n both states, and sets ]] G 5 G 5œC/b. The welfare level s no dfferent from that wthout moblty. In the seond, wns n one state, and wns n the other. In ths ase, (5) and (6) redue to: bd 5C and bd 5C. Substtutng these values nto (0) and () and solvng for C and C reveals that ths equlbrum exsts only f C 5 0. Whle the model s fndngs are defntely senstve to the tmng assumpton, movng to a repeated game struture would probably restore the relevane of the results for the smultaneous game. Gven suffently low dsount rates, the ooperatve soluton where partes mplement promses they mae pror to tzens loaton desons should be sustanable. Partes would not tae advantage of one turn s eletoral sla beause ths would redue ther state s populaton n subsequent turns. 5. Implatons for federalsm The mportane of heterogeneous preferenes as an argument for deentralzaton, and nterstate spllovers as an argument aganst, appears repeatedly n the optmal federalsm lterature. As Gordon (983) argues: There may be advantages to deentralzng government deson-mang. Loal governments, beng loser to the people, may better reflet ndvdual preferenes. The dversty of poles of loal governments allows ndvduals to move to that ommunty best refletng ther tastes. Competton among ommuntes should lead to greater effeny and nnovaton. However, ths paper has shown the many ways n whh deentralzed deson-mang an lead to neffenes, sne a loal government wll gnore the effets of ts desons on the utlty levels of nonresdents (p. 584). My model abstrats from both heterogenety and spllovers n order to fous on the nteraton between mperfet poltal ompetton and federalsm. The most
B. Caplan / Journal of Publ Eonoms 80 (00) 99 9 3 notable result s that there are good equlbra where moblty mtgates poltal mperfetons and bad equlbra where moblty ntensfes them (Table ). Even n a world where tzens poly tastes were unform and state poles affeted only resdents, federalsm s not neessarly useless or neessarly benefal. 5.. The good equlbra The ntuton behnd the good equlbra s straghtforward: f poltans tae exessve advantage of mperfet poltal ompetton, tzens leave. Powermaxmzng poltans may therefore moderate ther exesses not beause they fear eletoral defeat, but beause populaton outflows redue ther power. If poltans wn supermaortes by dong exatly what tzens want, they have an nentve to mae government bgger; f the supermaorty s ample enough, the rulng party wll even have a supermaorty at the unonstraned maxmum value of GY. At that pont there s no longer any reason to mae G larger beause t uts both the wnnng party s share of the vote and G Y. State and loal governments n federal demoraes usually fae both poltal and eonom onstrants. Ths mght ndate that onsttutonal framers thn that the good equlbra are emprally predomnant; f the framers foresee mperfet eletoral ompetton, they an mtgate t by sub-dvdng the polty. In ths ase, Brennan and Buhanan (980) are orret to argue that that nter-ursdtonal ompetton redues the power of Levathan. 5.. The bad equlbra But matters are more omplated: the nteraton of moblty and mperfet poltal ompetton an also mae the monopoly power of government greater. The underlyng ntuton s that f voters wth opposte party tastes dvde up nto ther own safe dstrts, then ompettve eletons may be absent n every state. If a poltan mplements bad poles, the frst people to ext are those who most dsle the urrent offe-holders. Ths shfts the absolute value of medan party taste C further from zero, mang worse poles eletorally sustanable. Ths s possble beause lvng under one s preferred poltal party s a prvate good, but the welfare propertes of the poltal equlbrum are a publ good. Perfet sortng of tzens aordng to the sgn of C maxmzes the realzed sum of tzens party preferenes, but at the same tme maes poly mperfetons as large as possble. The bad equlbra suggest one possble eonom nterpretaton of mahne polts (Dxt and Londregan, 996). If the Demorats ontrol the San Franso ty government, t tends to ndue out-mgraton on the part of strong Republan partsans and further ement the Demorats eletoral margn. In onsequene, not
4 B. Caplan / Journal of Publ Eonoms 80 (00) 99 9 only do the poltal mperfetons n San Franso beome more severe; at the same tme, the staunh Republans who move to Republan dstrts also exaerbate the poltal mperfetons n ther new loaltes. The bad equlbra offer a novel explanaton for why voters may smultaneously dsle numbents poles, yet ontnue to vote for them: they have self-seleted nto dstrts wth strong partsan loyaltes. Ratonal power-maxmzng poltans tae advantage of the stuaton by delberately devatng from voters poly preferenes. So long as the regnng poltans devaton from voter preferenes does not exeed the medan degree of party loyalty, the poltal mahne an stay n power ndefntely. What s partularly nterestng about the bad equlbra s that they an emerge even f C 5 0,.e. f the medan voter n the overall populaton has no party preferene whatever. If voters expet to wn n one state and n the other, t maes sense for people wth C. 0 to move to the state where rules, and for the people wth C, 0 to move to the state where rules. Imperfet poltal ompetton tself an therefore arse endogenously beause a balaned populaton tends to sub-dvde nto two mbalaned populatons. It s therefore unneessary to assume that the dstrbuton of C s sewed towards one party to generate mperfet poltal ompetton. 5.3. Interpretng the model Whle parameter values do restrt the set of possble outomes, there are stll frequently multple equlbra. Self-fulfllng expetatons sustan these equlbra: the general expetaton that party wll wn n both states maes t possble for party to atually do so; yet the expetaton that party would ontrol one state mght have made that a possblty as well. If a turn s nterpreted as a relatvely short tme perod, ths argument seems to requre an mplausbly hgh degree of nter-state moblty. Yet f the relevant turn s longer, the ompounded effet of a low annual rate of mgraton ould be appreable. The model may thus be best suted for the analyss of long-lastng state or urban poltal mahnes, where hstoral experene gves rse to voters self-fulfllng expetatons, and mgrants respond to durable poltal patterns. But a reent pee n the Eonomst (999) suggests that suh fores may wor over the medum term too. As t explans, Republan mgraton from Calforna to borderng states sne 990 s a maor fator underlyng reent trends n western states. In Calforna, the Republan party lost the governorshp, the Senate rae, all but two statewde offes and fve seats n the state Assembly. (999, p. 9) At the same tme, Calforna mgrants... have also strengthened the Republans of the Roes and turned parts of the wde-open spaes Idaho, Wyomng, Utah nto one-party states. (999, p. 30).
B. Caplan / Journal of Publ Eonoms 80 (00) 99 9 5 6. Conluson The model presented n ths paper appears to be the frst n whh tzens moblty endogenzes poltal mperfetons. It s ntended not as a substtute to but as a omplement for the more tradtonal approah to optmal federalsm (Gordon, 983), showng that there are addtonal arguments for and aganst federalsm when poltal ompetton wors mperfetly. There are good equlbra where tzen moblty dampens the mportane of mperfet poltal ompetton, and bad equlbra where tzen moblty reates safe dstrts, n whh the poltal proess s even less ompettve. There are several possble outlets for further researh buldng on ths paper s nsghts. Whle the model s relatvely smple, t shows that tzen mgraton and poltal mperfeton an nterat n sometmes unexpeted ways. These may be of some pratal mportane n understandng, for example, the reent waves of seessons and poltal and eonom unons. Sne the model an gve rse to both good and bad equlbra for the same set of parameters, further examnaton of the ondtons under whh federalsm mtgates mperfet poltal ompetton s also n order. The wdespread use of federalst nsttutons perhaps suggests that the good equlbra our most frequently. On the other hand, ontnung dssatsfaton wth the performane of government mght be a sgn that voters are stu n a bad equlbrum n whh tzen moblty has amplfed the nherent mperfetons of the poltal proess. Anowledgements I would le to than my advsor, Anne Case, as well as Igal Hendel, Davd Bradford, Robert Wllg, Harvey Rosen, Alessandro Lzzer, Gordon Dahl, Sam Peltzman, Tom Nehyba, Tyler Cowen, Bll Dens, Yesm Ylmaz, Roger Gordon, Davd Levy, Robn Hanson, two anonymous referees, and semnar partpants at Prneton and George Mason for numerous helpful omments and suggestons. Gsele Slva provded exellent researh assstane. The standard dslamer apples. Appendx A. Party wns n one state, party wns n the other: hi,i 5 h,0 or h0, Ths appendx analyzes the exstene, determnants, and welfare propertes of the equlbra dsussed n Seton 3.3.
6 B. Caplan / Journal of Publ Eonoms 80 (00) 99 9 Votng onstrant bnds n nether state Party n state maxmzes G Y subet to (8): max G h0.5 C b(d d ). (A.) G Dfferentatng (A.) and settng t equal to zero: h0.5 C b(d d ) G h b(g G *) 5 0. (A.) Implyng ]]]]]]]]] 4G * 4G * (6/b) (C/b ) d œ G 5 ]]]]]]]]]]]]. (A.3) 6 The analogous equaton for s best response s ]]]]]]]]] 4G * 4G * œ (6/b) (C/b ) d G 5 ]]]]]]]]]]]]. (A.4) 6 Consderng the speal ase where C 5 0 s suffent to show that ths equlbrum an be welfare-superor or welfare-nferor to the benhmar ase, dependng on parameter values. Then there s a smple symmetr equlbrum, where G 5 G. Usng (A.3): ]]]]]]]]]]]] 4G * 4G * (6/b) (C/b ) (G G * œ ) G 5 ]]]]]]]]]]]]]]]. (A.5) 6 Implyng ]]] G * G 5 G 5] G * ]] ]. (A.6) 4 4b œ Reall that the expeted utlty of the benhmar s 0. Usng (5), t an be seen that utlty equals the benhmar level ff [b(d d )] C [b(d d )] [b(d d )] [C C 0.5] 5 0. (A.7) If the left-hand sde of the above expresson s greater than zero, ths equlbrum s better than the benhmar; f less than zero, worse. Pluggng nto (A.7), t an be seen that expeted utlty exeeds that of the benhmar ff ]]] G * bf ] G * ]] ] G 0.5. 0, (A.8) 4 4b œ whh holds when ] Œ] G * œb. / 8. (A.9)
B. Caplan / Journal of Publ Eonoms 80 (00) 99 9 7 Votng onstrant bnds n state but not state In ths ase, (A.3) stll holds for party. Sne (3) bnds, t may be used to substtute out for party s strategy: ]]]]]]]]]]]]]]] 4G * 4G * œ (6/b) (C/b ) (/b)[0.5 C bd ] G 5]]]]]]]]]]]]]]]]]. 6 (A.0) Smplfyng: ]]]]]]] 4G * 4G * œ (/b) d G 5 ]]]]]]]]], (A.) 6 ]]]]] 6G * œ4g * (6/b) G 5 ]]]]]]]. (A.) 8 By defnton, d ; (G G *), so G G * œ4g * (6/b) d 5 F]]]]]]]]. (A.3) 8 Pluggng (A.3) ba nto s onstrant: G * œ4g * (6/b) bd 5 0.5 C b F]]]]]]]]. (A.4) G 8 To analyze welfare, reall that beause (3) bnds: b(d d ) 5 0.5 C. (A.5) Substtutng (A.5) nto (A.3) and re-arrangng terms mples [b(d d )] C [b(d d )] C C 0.5 5 0. (A.6) Note that for values of C. 0.5, the left-hand sde of (A.6) s always postve. (A.6) has two real solutons: Œ]] 8C [b(d d )] 5C 6 ]]]. (A.7) From (A.3) and (A.4), we now that G ]]]]] * œ4g * (6/b) b(d d ) 5 bf]]]]]]]] 0.5 C. (A.8) G 8 Combnng (A.7) and (A.8), and smplfyng: ]]]]] ]] G * œ4g * (6/b) 6Œ 8C bf]]]]]]]] G 5 ]]]]. (A.9) 8 4
8 B. Caplan / Journal of Publ Eonoms 80 (00) 99 9 Note, however, that the left-hand-sde of (A.9) s bounded between 0 and 0.5, whle ( Œ ]] 8C )/4. 0.5. Thus, there s only one rtal pont of nterest: bd 5 (Œ ]] 8C )/4. When ths holds wth equalty, then equlbrum 3.3. and the benhmar offer the same expeted welfare levels. It s welfare-superor to Œ]] the benhmar ff bd, ( 8C )/ 4, and welfare-nferor f bd. ( Œ]] 8C )/4. Votng onstrant bnds n both states Proof by ontradton shows ths equlbrum wll never exst. Suppose t dd: Then () and (3) both hold wth equalty. Ths mples that C 5 0, whh s a ontradton sne by assumpton C. 0. Votng onstrant bnds n state but not state Proof by ontradton shows ths equlbrum wll never exst. Suppose t dd: then () holds wth equalty, whle (3) holds as a strt nequalty. Pluggng the equalty nto the nequalty mples: bd, 0.5 C [0.5 C bd ]. Canellng terms leaves 0,C, whh s a ontradton sne C. 0. Referenes Alesna, A., Rosenthal, H., 995. Partsan Polts, Dvded Government, and the Eonomy. Cambrdge Unversty Press, New Yor. Brennan, G., Buhanan, J.M., 980. The Power to Tax: Analytal Foundatons of a Fsal Consttuton. Cambrdge Unversty Press, Cambrdge. Caplan, B., 999a. Has Levathan been bound? A theory of mperfetly onstraned government wth evdene from the States. Unpublshed manusrpt, George Mason Unversty. Caplan, B., 999b. When s two better than one? How federalsm mtgates and ntensfes mperfet poltal ompetton. Unpublshed manusrpt, George Mason Unversty. Dxt, A., Londregan, J., 995. Redstrbutve polts and eonom effeny. Ameran Poltal Sene Revew 89 (4), 856 866. Dxt, A., Londregan, J., 996. The determnants of suess of speal nterests n redstrbutve polts. Journal of Polts 58 (4), 3 55. Dxt, A., Londregan, J., 998a. Ideology, tats, and effeny n redstrbutve polts. Quarterly Journal of Eonoms 3 (), 497 59. Dxt, A., Londregan, J., 998b. Fsal federalsm and redstrbutve polts. Journal of Publ Eonoms 68 (), 53 80. Donahue, J., 997. Tebout, or not tebout? The maret metaphor and Amera s devoluton debate. Journal of Eonom Perspetves (4), 73 8. Eonomst, 999. A new Republan heartland. Eonomst, Otober 9, 9 30. Frey, B.S., Ehenberger, R., 996. To harmonze or to ompete? That s not the queston. Journal of Publ Eonoms 60 (3), 335 349. Gordon, R.H., 983. An optmal taxaton approah to fsal federalsm. Quarterly Journal of Eonoms 95 (4), 567 586. Grossman, G., Helpman, E., 996. Eletoral ompetton and speal nterest polts. Revew of Eonom Studes 63 (), 65 86.
B. Caplan / Journal of Publ Eonoms 80 (00) 99 9 9 Inman, R.P., Rubnfeld, D.L., 996. Desgnng tax poly n federalst eonomes: an overvew. Journal of Publ Eonoms 60 (3), 307 334. Inman, R.P., Rubnfeld, D.L., 997. Rethnng federalsm. Journal of Eonom Perspetves (4), 43 64. Lndbe, A., Webull, J.W., 987. Balaned-budget redstrbuton as the outome of poltal ompetton. Publ Choe 54 (3), 73 97. Luttbeg, N., Martnez, M., 990. Demograph dfferenes n opnon, 956 984. In: Long, S. (Ed.). Researh n Mropolts, Vol. 3, pp. 83 8. MGure, M.C., Olson, M., 996. The eonoms of autoray and maorty rule: the nvsble hand and the use of fore. Journal of Eonom Lterature 34 (), 7 96. Mutz, D., Monda, J., 997. Dmensons of sootrop behavor: group-based udgements of farness and well-beng. Ameran Journal of Poltal Sene 4 (), 84 308. Qan, Y., Wengast, B., 997. Federalsm as a ommtment to preservng maret nentves. Journal of Eonom Perspetves (4), 83 9. Rose-Aerman, S., 983. Tebout models and the ompettve deal: an essay on the poltal eonomy of loal government. In: Qugley, J. (Ed.). Perspetves on Loal Publ Fnane and Publ Poly, Vol.. JAI Press, Greenwh. Sears, D., Lau, R., Tyler, T., Allen, H., 980. Self-nterest vs. symbol polts n poly atttudes and presdental votng. Ameran Poltal Sene Revew 74 (3), 670 684. Wttman, D., 983. Canddate motvaton: a synthess of alternatve theores. Ameran Poltal Sene Revew 77 (), 4 57. Wttman, D., 989. Why demoraes produe effent results. Journal of Poltal Eonomy 97 (6), 395 44. Wttman, D., 995. The Myth of Demorat Falure: Why Poltal Insttutons are Effent. Unversty of Chago Press, Chago.