No. 81 PETER TUCHYŇA AND MARTIN GREGOR. Centralization Trade-off with Non-Uniform Taxes

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1 No. 81 PETER TUCHYŇA AND MARTIN GREGOR Centralization Trade-off with Non-Uniform Taxes 005

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3 Centralization Trade-off with Non-Uniform Taxes PETER TUCHYŇA #, MARTIN GREGOR Abstract When local ublic goods are rovided by a centralized authority, sillovers may be coordinated, but heterogeneity in references may be suressed. Besley and Coate (003) have already solved this classic trade-off for a uniform tax regime. Here, we extend their aroach by allowing for a non-uniform tax regime. We find that centralization with our tax system necessarily increases welfare in comarison to uniform-tax centralization. Imortantly, with non-cooerative legislators coming from homogenous districts, our centralization dominates decentralization for any degree of sillovers. In other cases, it at least imroves odds of centralization, if measured by utilitarian yardstick. Keywords: Decentralization, Local Public Goods, Distributive Politics, Political Economy JEL Classification: H40, H70, H7, P51 Acknowledgements: Any idea is contestable, so comments are more than welcome. This aer largely draws from unublished thesis Centralized or Decentralized Provision of Local Public Goods with Sillovers: Which to Choose and Under what Circumstances? written by Peter Tuchyňa. We would like to acknowledge valuable comments by František Turnovec, TEX-nical hel by Miroslav Zelený, and suort from Institutional Research Framework granted by the IES ( ). The usual caveat alies. # Ph.D. Candidate, Center for Economic Research and Graduate Education-Economics Institute, Prague. eter.tuchyna@cerge-ei.cz. Ph.D. Candidate, Institute of Economic Studies, Charles University Prague, Oletalova 6, Prague 1, , Czech Reublic. gregor@fsv.cuni.cz.

4 Contents 1 Introduction The Model 4 3 The Standard Analysis Comarative Statics A Political Economy Analysis with Two Forms of Taxation Policy Determination Under Decentralization Policy Determination Under Centralization with Two Forms of Taxation Policy Determination with Uniform Taxation Comarative Statics Policy Determination with Non-uniform Taxation Comarative Statics Centralization vs. Decentralization Homogeneous districts Heterogeneous districts Centralization with a Cooerative Legislature and Two Forms of Taxation Policy Determination with Uniform Taxation Comarative Statics Policy Determination with Non-uniform Taxation Comarative Statics Centralization vs. Decentralization Homogeneous districts Heterogeneous districts Conclusion 3 Aendix - Proofs 3 References 50 1

5 1 Introduction Centralization involves a host of trade-offs. A centralized government can exloit returns to scale in ublic goods rovision, but faces ronounced information asymmetry. Sillovers can be efficiently resolved by centralization, but centralized budget may require more distortive taxation. Also, centralization may induce higher total investment into wasteful rent-seeking activities. The case for centralization of local ublic goods is redominantly driven by cross-border sillovers. For instance, imagine maintained ski and bike routes disersed across borders, and user fees rohibitively costly to charge. Or, following an examle by Hillman (003,. 570), one community may have strict gun control laws, while a neighboring community does not; in effect, criminals can buy their guns and switch to the other community with less armed honest citizens. Interjurisdictional sillovers obviously call for centralization, since centralization involves internalization of externalities. The case may be strengthened in the resence of economies of scale in ublic good roduction (or, in tax administration, as Redoano and Scharff (004) argue). However, centralization is not costless. As Oates (197) argues, welfare loss arises if jurisdictions vary in references, and the amount of ublic good is bound to be equal across jurisdictions. The loss magnifies with increase in rice elasticity of ublic good demand. Secondly, the issue of asymmetric information is of extreme relevance here. For central authority, reliable local information is costlier to obtain. Voters observe lower yardstick cometition at the central level and, hence, have fewer oortunities to assess ublic sector erformance. Seabright (1996) builds a model caturing another imortant roblem of centralization, namely lower accountability. Centralization may decrease level of olitical cometition, roviding additional source of olitical rents. Furthermore, the roonents of FOCJ concet (Functionally Overlaing Cometing Jurisdiction), mainly Frey (1996), observe slower olicy innovation in centralized system. On the other hand, Kotsogiannis and Schwager (001) construct a model with oosite results.

6 When interest grous in jurisdictions share interests and lobbying features economies of scale, centralization may also boost rent-seeking exenditures and consequently distort market allocation (Bordignon et al. 003, Bardhan and Mookherjee 000). To be able to tackle benefits and costs of centralization, we restrict our attention to the classic trade-off between sillovers and heterogeneity. We ut aside other, albeit imortant, issues of locational choice, accountability, and incomlete information. Our aroach draws from setu of Besley and Coate (003), but we extend their aroach by introducing a non-uniform tax system. In other words, we study how centralization erforms when benefits (i.e. amounts of local ublic goods) as well as costs are non-uniform across districts. Besley and Coate (003) deart from the existing literature in emhasizing the olitical rocesses of decision making. If governments under centralized systems were allowed to allocate different levels of local ublic goods to different districts, they could resect the references of citizens in each district while otimally accounting for cross-border sillovers. This would make the centralized system referable. If there is a case for a decentralized system then, it must follow from the olitical economy considerations. Centralization has been tyically modeled as a system in which ublic sending is financed by general taxation and all jurisdictions receive a uniform level of local ublic goods. In a decentralized system local ublic goods are financed by local taxation and each district chooses its own referred level. This aroach has been adoted by Oates (197) who argued that the drawbacks of centralized and decentralized systems are uniformity in rovision and absence of reflecting the benefits going to other regions, resectively. This logic relies crucially on the assumtion that centralization rovides uniform levels of ublic goods. Besley and Coate (003) relax this assumtion and then study various forms of centralized decision making. We also relax the assumtion of olicy uniformity (i.e. uniform level of ublic goods) stiulated in Oates (197) and Musgrave (1959). To our knowledge, this assumtion may only be motivated by imlications of asymmetric information incentives between central and local authorities. Cheikbossian (000) argues that in a game layed between central olicy-maker and decentralized authorities, the latter have an incentive to reort excessive 3

7 exenditure need and low tax-aying caacity. This misinformation induces olicy uniformity. The main innovation of our aroach is to let district-secific head-tax deend on the amount of ublic good rovided in each region. The reason is that for district-uniform headtax, a marginal increase in ublic sending in one district increases average tax across all districts equally. In our tax system, the increase is not equal, but higher for the beneficiary district. This brings marginal cost of ublic good rovision closer to the marginal benefit and imroves odds for centralization comared to decentralization. For centralized legislature, we ostulate two tyes of olicy makers, non-cooerative and cooerative. We observe that cooerativeness as such cannot resolve conflict in references among the regions, since voters can insure against olicy cooerativeness by strategic delegation. Strategic delegation has origins in industrial economics (Fershtman and Judd 1987) and monetary olicy (Rogoff 1985), resulting in issues of fiscal olicy (Persson and Tabellini 1990). In our framework, a non-cooerative voter delegates a olicy maker with different concern for local ublic good than is his or her own. We thus comlement Cheikbossian (000) who describes strategic delegation in decentralization. The remainder of the aer is organized as follows. Section outlines the framework for our analysis. Section 3 rovides a brief review of the standard analysis. Section 4 resents a olitical economy analysis with two forms of taxation beginning with a centralized system based on minimum winning coalition. Section 5 continues in this direction considering a more cooerative legislature. Finally, Section 6 offers some concluding remarks. The Model There are geograhically distinct regions or districts indexed by i {1, } each oulated by a continuum of citizens with a mass of unity. The citizens are immobile between the regions. The economy contains 3 goods: a single rivate good, x, and two local ublic goods, g 1 and g, each one associated with a articular district. 1 Each citizen is endowed with some of the rivate good and throughout we will assume that the endowments are high 1 The arameters g 1 and g can be thought of as being the same ublic good rovided at different levels in each district, as further assumtions may indicate. But to make the model richer, we will assume two distinct local ublic goods such as e.g. airorts and roads each associated with a articular region. 4

8 enough for each citizen to meet their required tax obligations. To roduce one unit of either of the ublic goods requires units of the rivate good. Each citizen in district i is characterized by a ublic goods reference arameter λ. 3 The references of a tye λ citizen in district i are x + λ[(1 κ) lng i + κ ln g i ], 4 where arameter κ 0, 1/ indexes the degree of sillovers. When κ = 0, citizens consume only the ublic good in their own district, while for κ = 1/ they equally consume ublic goods in both districts. Uniform κ (across regions) means that citizens from both districts consume both ublic goods in the same roortion. 5 The range of reference tyes is 0,λ in each district. The resective median tye in district i is denoted by m i. We assume, without loss of generality, that the median citizen in district 1 is at least as ro-ublic sending as his counterart in district, i.e. m 1 m. We also assume that m 1 < λ. The latter condition will be needed in Section 5 to obtain interior solutions. Under a decentralized system, the level of ublic good in each district is chosen by the government of that district and ublic goods are financed by a uniform head tax on local residents. Thus, if district i chooses a ublic good level g i, each citizen in this district ays a tax of g i. Under a centralized system, the levels of ublic goods are determined by a government that reresents both regions. Sending is being financed by two ossible tax systems whose outcomes will be comared. The first one is a uniform head tax on all citizens; with ublic good levels (g 1,g ), this tax is (g 1 + g ). The second one is a head tax which is non-uniform across districts, but uniform for all citizens within a given region. Citizen That is, we define one unit of each of the ublic good to reresent such a quantity that costs units of the rivate good. 3 The arameter λ can be interreted as indicating the interest in ublic goods of both districts. 4 See discussion aers of Besley and Coate for more universal secifications of ublic goods references. 5 However, it could be that citizens from district 1 cared equally about the ublic goods in both districts, whereas citizens from district cared only about their own ublic good. That is to say, roortional ublic goods references κ could differ among regions. Moreover, differences among citizens from the same district could occur, i.e. a citizen could, for instance, derive benefit from both ublic goods, but his neighbor from the same district could be interested only in the ublic good rovided by his own district. We will, however, assume these sillovers to be of a urely technical nature. Moreover, we will assume them to be the same for citizens from both districts as well as for the citizens in a given region to be able to cature the fact that the resolution between centralization and decentralization deends on the degree of sillovers and the extent of heterogeneity in references for ublic goods. 5

9 of each region ays a head tax roortional to his consumtion of both ublic goods; thus, ublic good levels (g 1,g ) and degree of sillovers κ result in a head tax of g i (1 κ)+g i κ in district i. 6, 7 Our social welfare criterion for comaring the erformance of centralized and decentralized rovision of local ublic goods will be aggregate ublic goods surlus. With ublic good levels (g 1,g ), it is defined as S(g 1,g ) = [m 1 (1 κ) + m κ] ln g 1 + [m (1 κ) + m 1 κ] ln g (g 1 + g ). The surlus is a median citizens sum of marginal benefits from their consumtion of ublic goods or, more recisely, a sum of differences between median citizens utilities under the system with ublic goods and the system without ublic goods: U m1 + U m = x 1 g 1 + m 1 [(1 κ) lng 1 + κ ln g ] x 1 + x g + m [(1 κ) lng + κ ln g 1 ] x = S(g 1,g ). The surlus-maximizing ublic good levels are ( m1 (1 κ) + m κ (g 1,g ) =, m ) (1 κ) + m 1 κ. 8 This result reveals that the surlus-maximizing ublic good levels take account of the benefits received by citizens from both districts. 3 The Standard Analysis The above outlined model allows a simle exosition of the traditional analysis according to Oates (197), who influenced many ublic finance economists views on the relative merits 6 Of course, this tax system is uniform in the case when the levels of ublic goods in both districts equal. Otherwise, it is non-uniform, which is the reason we have identified it as such. 7 What is worth noting here regarding both tax systems is that uniform taxation imlies shared financing of the ublic goods whereas non-uniform tax system means that each district ays roortionally to its consumtion. If it consumes less, it ays less; if it consumes more, it ays more. 8 The vector is an interior solution of a simle maximization of function S(g 1,g ). We obtain it by taking first-order conditions, i.e. by differentiating this function w.r.t. g 1 and g and setting equal to zero. It is straightforward to verify that second-order conditions are satisfied and we leave this roof to the reader. This remark alies to all of the subsequent maximization roblems. 6

10 of centralization and decentralization. He suosed that, in a decentralized system, each district s government indeendently chooses the olicy which maximizes ublic goods surlus in the region (which is U mi, i {1, }). A air of exenditure levels (g d 1,g d ) will form a Nash equilibrium, which requires that: g d i = arg max g i {m i [(1 κ) lng i + κ ln g d i] g i }, i {1, }. Taking first order conditions yields: ( (g1,g d ) d m1 (1 κ) =, m ) (1 κ). Each region s government thus only takes into account the benefits received by his constituency and local ublic goods are surlus-maximizing only when there are no sillovers, regardless of heterogeneity in tastes. When sillovers occur, ublic goods roduction results in under-rovision in both districts and this under-rovision is increasing in the extent of sillovers. Under a centralized system, Oates assumed that the government would be restricted to rovide a uniform level of the ublic goods, denoted g c. He further assumed that exenditures would be financed by a uniform head tax, which is in the case of uniform rovision of ublic goods identical to our roosed non-uniform head tax that takes into account the roortional consumtion of both goods by citizens from each region. 9 This common level of ublic goods satisfies resulting in g c = arg max{[m 1 + m ] ln g g}, g g c = m 1 + m. The uniform level of ublic goods is indeendent of the level of sillovers and results in the surlus-maximizing level only in the case of identical districts. 10 However, when m 1 > m, centralization over-rovides ublic goods to district and under-rovides them to district 1 9 This stems from the simle fact that, with uniform rovision and identical rices of local ublic goods, (g + g) Oates head tax = g equals g(1 κ) + gκ = g. 10 Throughout the text, the hrases identical (non-identical) and homogeneous (heterogeneous) districts will indicate that the median citizens from each region have (do not have) the same ublic goods references. 7

11 excet when sillovers are maximal, i.e. κ = 1/. In this situation, citizens consume ublic goods in both districts equally which leads to uniform rovision of ublic goods in both regions. 3.1 Comarative Statics When regions are homogeneous, centralization roduces surlus maximizing ublic goods levels and dominates decentralization when sillovers are resent. 11 However, the two systems generate the same level of ublic goods surlus when sillovers do not occur (Figure 1a). S c t S c t Surlus S d Surlus S d κ κ (a) Identical districts (b) Non-identical districts Figure 1: Aggregate ublic goods surluses under decentralization (S d ) and centralization in the standard analysis (S c t). In the case of heterogeneous districts, decentralization roduces surlus maximizing ublic goods levels and dominates centralization when there are no sillovers. On the other hand, when the sillovers are maximal, centralization roduces surlus maximizing ublic goods levels and dominates decentralization. Finally, when the sillovers are somewhere in between these two olar cases, there exists a critical level of sillovers above which centralization dominates and under which decentralization is referred (Figure 1b). Proosition 1. Suose that the assumtions of the standard analysis are satisfied. Then 11 In this case, centralization has the conventional advantage of internalizing sillovers. 8

12 (i) If the regions are homogeneous and sillovers are resent (κ > 0), a centralized system roduces a higher level of surlus than does decentralization. Absent sillovers (κ = 0), the two systems generate the same level of surlus. (ii) If the districts are heterogeneous, there is a critical value of κ, greater than zero but less than 1/, such that a centralized system roduces a higher level of surlus if and only if κ exceeds this critical level. 1 According to Oates, without sillovers, a decentralized system is referred. With sillovers and homogeneous districts, a centralized system is suerior. With sillovers and heterogeneous regions, it is necessary to comare the extent of the two effects. It is often suggested that heterogeneity favors the case for decentralization. However, in our model, this does not follow. To establish such a roosition, it would be necessary to show that the critical level of sillovers is increasing in heterogeneity. But there is no guarantee that this is so. 13 Modeling the trade-off in the standard analysis relies on the assumtion of uniform exenditures in a centralized system. But this assumtion is too strong and does not corresond with emirical evidence that exenditures vary across districts in many countries. We will now relax this assumtion and model the decision making institutions which decide uon allocation of resources in both centralized and decentralized systems. 1 The roof of this as well as the other results may be found in the Aendix. 13 This may be analyzed by letting S d (κ,α) and S c t(κ,α) denote surluses under decentralization and centralization, resectively, when (m 1,m ) = (αω,(1 α)ω), where α 1/,1 measures the degree of heterogeneity between the two regions. Districts are identical when α = 1/ and become more heterogeneous when α increases. Then S c t(κ,α) = ω ln ω ω, which is indeendent of both κ and α. Therefore we can write Sc t(κ,α) = S c t. The critical value of κ, denoted κ (α), is uniquely defined by the equation S d (κ,α) = St. c To show that κ is an increasing function of α, it is necessary to show that for all α, S d (κ,α)/ α > 0. Differentiating, we obtain S d α (κ,α) = ω(1 κ)ln α 1 α + ωκ 1 α α(1 α). The first term is ositive, while the second one is negative. As sillovers increase, the first term goes to zero. Thus, it is ossible that S d (κ,α)/ α < 0. (In our secification of ublic goods references, surlus under decentralization is always decreasing in heterogeneity for all κ > 1/4. This finding makes it ossible that the critical level of sillovers is decreasing in heterogeneity, i.e. the case for centralization could be strengthened as the regions become more diverse.) 9

13 4 A Political Economy Analysis with Two Forms of Taxation 4.1 Policy Determination Under Decentralization In a decentralized system, we assume that each region elects a single reresentative from that region to choose olicy. Our model is based on the citizen-candidate aroach to olitical decision making, which has two stages. First, elections determine which citizen from each district is selected to constitute the decision making government in that district (election stage). Second, olicies are chosen simultaneously by the elected reresentatives in each district (olicy-selection stage). Using backward induction, 14 let us roceed as follows. First, we find what elected reresentatives select (stage or olicy-selection stage) and then we discuss whom citizens, considering outcomes which are subsequently selected by reresentatives, will aoint to an office (stage 1 or election stage). Beginning with stage, let the tyes of the reresentatives in district 1 and be λ 1 and λ, resectively. 15 Then the olicy outcome (g 1 (λ 1 ),g (λ )) satisfies g i (λ i ) = arg max g i {λ i [(1 κ) ln g i + κ ln g i (λ i )] g i }, for i {1, }. Solving this with first-order conditions yields ( λ1 (1 κ) (g 1 (λ 1 ),g (λ )) =, λ ) (1 κ). The level of each district s ublic goods sending is higher the stronger is the ublic good reference of its reresentative and lower the higher the level of sillovers. Now let us move to stage 1. With the reresentatives λ 1 and λ in region 1 and, resectively, a citizen of tye λ in district i will enjoy a ublic goods surlus [ U λ,i = λ (1 κ) ln λ i(1 κ) + κ ln λ ] i(1 κ) λ i (1 κ). 14 Backward induction is an iterative rocess for solving finite extensive form games. First, one determines the otimal strategy of the layer who makes the last move of the game. Then, the otimal action of the next-to-last moving layer is determined taking the last layer s action as given. The rocess continues in this way backwards in time until all layers actions have been determined. Effectively, one determines the Nash equilibrium of each subgame of the original game. 15 We assume that (i) candidates have no oortunity costs, i.e. any citizen can agree to be a candidate; and that (ii) reresentatives can only decide on the rovision of ublic goods, i.e. there are no other erquisites of the office. 10

14 These references over tyes determine citizens voting decisions. A air of reresentative tyes (λ 1,λ ) is majority referred under decentralization if, in each district i, a majority of citizens refer the tye of their reresentative to any other tye λ 0,λ, given the tye of the other district s reresentative λ i. We assume that the elected reresentatives in the two regions will be of these majority referred tyes. Further we assume that each citizen votes sincerely (according to his ublic goods references), all citizens always vote and have erfect information. Citizens references over tyes are single-eaked, 16 imlying that a air of reresentative tyes is majority referred under decentralization if and only if it is a median air; i.e. (λ 1,λ ) = (m 1,m ). This yields: Lemma 1. Suose that the assumtions of the olitical economy analysis are satisfied. Then the olicy outcome under decentralization is ( m1 (1 κ) (g 1,g ) =, m ) (1 κ). These levels of local ublic goods resect the references of the median citizen within a region, which agrees with the standard local ublic finance analysis. 4. Policy Determination Under Centralization with Two Forms of Taxation The olicy determination rocess under centralization also has two stes: an election stage; and a olicy selection stage. In the elections, one citizen from each district is chosen to serve in a common legislature. In the olicy selection stage, the legislature determines ublic goods rovision in each region. Our first method of caturing the decision making rocess in the legislature will be the minimum winning coalition view. Under this view, a coalition of justabove-50 % of the reresentatives forms to share the benefits of ublic sending among their districts. Regions whose reresentatives are outside the coalition are only allocated sending to the extent that this benefits coalition members. The logic is that, in a majority rule legislature, if there were any more than just-above-50 % of the reresentatives in the coalition 16 Given any two tyes ˆλ i and λ i such that λ i < ˆλ i < λ or λ < ˆλ i < λ i, tye λ citizens always refer tye ˆλ i citizens. 11

15 suorting the sending bill, the majority of coalition members would benefit from exelling the surlus members and further concentrating sending on their own regions. Because there are many ossible minimum winning coalitions, this view suggests that there will be uncertainty concerning the identity of the coalition that forms to determine exenditures. In our model, we may cature this uncertainty by assuming that each reresentative can be thought of as a minimum winning coalition with equal robability. Thus, again using backward induction, if the reresentatives are of tyes λ 1 and λ, the olicy outcome will be (g 1 1(λ 1 ),g 1 (λ 1 )) with robability 1/ and (g 1(λ ),g (λ )) with robability 1/, where (g i 1(λ i ),g i (λ i )) is the otimal choice of district i s reresentative Policy Determination with Uniform Taxation With uniform taxation and reresentatives of tyes λ 1 and λ, the otimal choice of district i s reresentative is { (g1(λ i i ),g(λ i i )) = arg max λ i [(1 κ) lng i + κ ln g i ] } (g i,g i ) (g i + g i ). It is straightforward to verify that ( (gi(λ i i ),g i(λ i λi (1 κ) i )) =, λ ) iκ, i {1, }. The level of ublic goods sending deends only on the decisive reresentative s reference for ublic goods and the level of sillovers. The stronger the references for ublic goods of the decisive reresentative are, the higher is the sending. Furthermore, sending for the reresentative s domestic ublic good varies inversely with sillovers while the other district s ublic good exenditures vary roortionally with sillovers. When the reresentative tyes are λ 1 and λ, a citizen of tye λ in region i obtains an exected ublic goods surlus of U λ,i = 1 { λ + λ [ (1 κ) ln λ i(1 κ) + κ ln λ iκ [ (1 κ) ln λ iκ + κ ln λ i(1 κ) ] λ i ] } λ i. Again we assume that the reresentatives will be of the majority referred tyes. A air of reresentative tyes (λ 1,λ ) is majority referred if and only if in each district i the median 1

16 tye refers λ i to any other tye λ 0,λ, given the other district s reresentative tye λ i. 17 This means that (λ 1,λ ) is majority referred if and only if it is a Nash equilibrium of the two-layer game in which each layer has strategy set 0, λ and layer i {1, } has ayoff function U mi (λ i ) = 1 [ {m i (1 κ) ln λ i(1 κ) + κ ln λ ] iκ [ + m i (1 κ) ln λ iκ + κ ln λ i(1 κ) Taking first-order conditions and solving yields (λ 1,λ ) = (m 1,m ). λ i ] } λ i. Thus, an elected air of reresentatives will be of tyes (m 1,m ) and will choose a olicy which reflects their ublic goods references. So we have: Lemma. Suose that the taxation is uniform and the assumtions of the olitical economy analysis are satisfied. Then the olicy outcome under centralization ( with a minimum winning m1 (1 κ) coalition view of the legislature is random, generating (g 1,g ) =, m ) 1κ with ( m κ robability 1/ and (g 1,g ) =, m ) (1 κ) with robability 1/. This result illuminates the main drawbacks of centralization with a minimum winning coalition legislature and uniform taxation: 1) Uncertainty: each district faces uncertainty as to the amount of ublic good that it will receive, reflecting the uncertainty in the identity of the minimum winning coalition. ) Misallocation: ublic exenditures across regions are skewed towards those inside the winning coalition. 4.. Comarative Statics The only situation in which centralization roduces the surlus maximizing level is when the districts are identical and sillovers are maximal (κ = 1/). When districts differ (m 1 > 17 If citizens of tye λ refer a tye ˆλ i candidate to a tye λ i, where ˆλ i < λ i (ˆλ i > λ i ), then so must all citizens of tyes lower (higher) than λ. This imlies that a majority of citizens in district i refer a tye ˆλ i candidate to a tye λ i candidate if and only if the median tye refers a tye ˆλ i candidate to a tye λ i candidate. 13

17 m ) and sillovers are comlete, sending is allocated equally across regions but district 1 s reresentative over-rovides local ublic goods, while district s reresentative underrovides them. While higher levels of sillovers still lead those in the minimum winning coalition to allocate ublic goods to districts outside the coalition, it is only to the extent that this benefits those inside the coalition. For low levels of sillovers, the misallocation roblem is at its worse. Public goods are over-rovided to regions in the minimum winning coalition and under-rovided to those districts that are outside the coalition, reflecting the budgetary externality created by common financing. However, this drawback is significantly suressed when the non-uniform tax system is introduced Policy Determination with Non-uniform Taxation With non-uniform taxation and reresentatives of tyes λ 1 and λ, the otimal choice of region i s reresentative is (g i 1(λ i ),g i (λ i )) = arg max (g i,g i ) {λ i[(1 κ) lng i + κ ln g i ] (g i (1 κ) + g i κ)}. It is easily checked that (g i 1(λ i ),g i (λ i )) = ( λi, λ ) i, i {1, }. As above, if the reresentative tyes are λ 1 and λ, a citizen of tye λ in district i obtains an exected ublic goods surlus of U λ,i = 1 { [ λ (1 κ) ln λ i + κ ln λ ] i [ λ i + λ (1 κ) ln λ i + κ ln λ ] } i λ i. Analogically to the case of uniform taxation, we arrive at the conclusion that an elected air of reresentatives will be of tyes (m 1,m ) and that they will choose a olicy which reflects their references. This establishes: Lemma 3. Suose that the tax system is non-uniform across districts and the assumtions of the olitical economy analysis are satisfied. Then the olicy chosen under centralized system ( with a minimum winning coalition view of the legislature is random, generating m1 (g 1,g ) =, m ) ( 1 m with robability 1/ and (g 1,g ) =, m ) with robability 1/. 14

18 Comared to the case of uniform taxation, the roblem of uncertainty remains due to the unknown identity of the coalition. However, the drawback of misallocation is significantly reduced reflecting the fact that each district is taxed according to its roortional consumtion of both local ublic goods. This suresses the incentives of the coalition members to allocate too much of the ublic goods to their districts while forgetting about the regions outside the coalition Comarative Statics The levels of ublic goods are indeendent of sillovers. They only deend on references of the decisive reresentative which then chooses uniform rovision of ublic goods. With identical reresentatives, centralization with non-uniform taxation roduces the surlus maximizing levels of local ublic goods. When m 1 exceeds m and sillovers are comlete, region 1 s reresentative over-rovides local ublic goods, while district s reresentative underrovides them. The misallocation roblem is at its worse when the sillovers are lower than comlete. The levels of ublic goods rovided are further from the otimal, aggregate surlus enhancing levels. However, the extent of these misallocations is lower than that under the centralized system with uniform taxation. 4.3 Centralization vs. Decentralization Homogeneous districts Decentralization roduces the surlus maximizing ublic goods levels only when the sillovers do not occur. We have already seen that ublic goods levels under centralization with uniform taxation are surlus maximizing when the sillovers are comlete and the districts are homogeneous. It follows that, in the case of identical districts, decentralization dominates when the sillovers are small and centralization is referred when the sillovers are large. Centralization with non-uniform taxation roduces the surlus maximizing ublic goods levels when the districts are identical. This surlus is indeendent of sillovers and is higher than the surlus under decentralization for all κ excet when the sillovers are absent. In such a case, both systems generate the surlus maximizing ublic goods levels. The next 15

19 roosition and Figure summarize these results. Proosition. Suose that the assumtions of the olitical economy analysis are satisfied, the centralized decision making relies on the minimum winning coalition, and the districts are identical. Then (i) If the taxation is uniform, there is a critical value of κ, strictly greater than 0 but less than 1/, such that a centralized system roduces a higher level of surlus if and only if κ exceeds this critical level. (ii) If the taxation is non-uniform across districts and sillovers are resent (κ > 0), a centralized system roduces a higher level of surlus than does decentralization. Absent sillovers (κ = 0), the two systems generate the same level of surlus. (iii) Surlus under centralization with non-uniform taxation equals that under the centralized system in the standard analysis for all levels of sillovers. These surluses are higher than that under centralization with uniform taxation excet when the sillovers are maximal (κ = 1/). In such a case, all three systems of centralization roduce the same ublic goods surlus. Sn c = St c Surlus S d S c u 0 κ 0.5 Figure : Aggregate ublic goods surluses under decentralization (S d ), centralization in the standard analysis (S c t) and centralization with uniform (S c u) and non-uniform (S c n) taxation in the case of identical districts. There are two comarisons which require analysis. First, comaring Proosition with its counterart in art (i) of the Proosition 1, there is one significant difference. With 16

20 identical districts, centralized system in the standard analysis is suosed to dominate decentralization for all κ > 0. However, centralization based on minimum winning coalition and uniform taxation no more dominates for low levels of sillovers, as those inside the coalition have low incentives to rovide ublic goods to the outside regions. This is further combined with the uncertain identity of the coalition. With higher sillovers, uncertainty remains but the decisive reresentatives have higher incentives to rovide more ublic goods to both districts, which increases the surlus under centralization. Thus, olitical economy analysis weakens the case for centralization when the taxation is uniform. Second, comarison of the two centralized systems under the olitical economy analysis generates a strong case for centralization with non-uniform taxation, which dominates for all κ < 1/. This is due to the effects that each taxation has on the decisions about the allocation of ublic exenditures. When the taxation is uniform, each district ays the same head-tax indeendent of the received level of ublic goods. This motivates coalition members to allocate as much as they refer to their districts. In contrast, under the centralized system with non-uniform taxation there is no such effect, as each district is taxed according to its roortional consumtion of both local ublic goods. This balances the allocated levels and centralization with non-uniform taxation significantly dominates centralization with a uniform tax system. Furthermore, the resulting surlus under centralization with non-uniform taxation is the same as under centralization in the standard analysis Heterogeneous districts When the regions are heterogeneous, centralized system with uniform taxation still dominates decentralization for high levels of sillovers and its erformance is increasing in sillovers. Thus, there is a critical value of κ under which decentralization is referred and above which centralization dominates. Centralization with non-uniform taxation is indeendent of sillovers, roduces higher level of surlus than decentralization for maximal sillovers and lower level of surlus for zero sillovers. It follows that there exists a critical value of κ above which centralized system 18 This is due to the fact that the rovision of ublic goods and the actual taxes under centralization with non-uniform taxation are the same as under the centralized system in the standard analysis. With identical districts, each reresentative would choose such uniform ublic goods levels that would be chosen by all the other reresentatives, if elected. 17

21 dominates and under which decentralization is referred. However, this critical value is lower than that in the uniform taxation case. Again, the following roosition and Figure 3 summarize these findings. Proosition 3. Suose that the assumtions of the olitical economy analysis are satisfied, the centralized decision making relies on the minimum winning coalition, and the districts are non-identical. Then (i) If the taxation is uniform, there is a critical value of κ, strictly greater than 0 but less than 1/, such that a centralized system roduces a higher level of surlus if and only if κ exceeds this critical level. This critical level is higher than that in the standard analysis. (ii) If the taxation is non-uniform across districts, there is a critical value of κ, strictly greater than 0 but less than 1/, such that a centralized system roduces a higher level of surlus if and only if κ exceeds this critical level. This critical level is higher than that in the standard analysis and lower than that under centralization with uniform taxation. (iii) Surlus under centralization in the standard analysis is higher than surluses under both centralized systems in the olitical economy analysis for all levels of sillovers. Furthermore, surlus under centralization with non-uniform taxation is higher than that under the centralized system with uniform taxation excet when the sillovers are maximal (κ = 1/). In such a case, the two systems roduce the same ublic goods surlus. As above, two juxtaositions can be observed. First, comaring Proosition 3 with its relevant counterart in art (ii) of the Proosition 1 reveals that centralization with noncooerative legislature creates even larger incongruity when the districts are heterogeneous. This exacerbated misallocation roblem combined with the ersistent drawback of uncertainty results in a weakened case for centralization comared with the centralized system in the standard analysis. However, the fundamental qualitative conclusions remain unchanged 18

22 S c t Surlus S c n S c u S d 0 κ 0.5 Figure 3: Aggregate ublic goods surluses under decentralization (S d ), centralization in the standard analysis (S c t) and centralization with uniform (S c u) and non-uniform (S c n) taxation in the case of non-identical districts. under the olitical economy analysis as under the traditional one for low sillover levels, decentralization dominates; when the sillovers are high, centralization is referred. 19 Second, comarison of the two centralized systems with different taxations remains as above. This is because the two systems surluses decrease in the same rate with increasing heterogeneity. 0 Thus, centralization with non-uniform taxation dominates centralization with uniform tax system for all κ < 1/. When sillovers are comlete, the two systems 19 What haens with both critical levels of sillovers as heterogeneity increases may be analyzed by letting S d (κ,α),s c u(κ,α) and S c n(κ,α) denote surluses under decentralization, centralization with uniform and non-uniform taxation, resectively, when (m 1,m ) = (αω,(1 α)ω), where α 1/,1 measures the degree of heterogeneity between the regions. The first critical level of κ, denoted κ 1(α), is uniquely defined by the equation S d (κ 1,α) = S c u(κ 1,α). To show that κ 1 is an increasing function of α, it is necessary to show that for all α (1/,1), S d (κ 1,α) α Sc u(κ 1,α) α > 0. Differentiating, we obtain S d (κ,α) α Sc u(κ,α) α ( 1 = ω ) κ }{{} >0 ( ln α 1 α 1 α ). α(1 α) The exression in the latter arentheses equals zero when α = 1/ and is ositive for all α in the range (1/,1). Thus, the difference is ositive for all α (1/,1) and κ 1 < 1/ which imlies that the critical level of sillovers increases with increasing heterogeneity. The second critical level of κ, denoted κ (α), is uniquely defined by the equation S d (κ,α) = Sn(κ c,α). Due to the fact that Sc u(κ,α) = Sc n(κ,α) for all κ and α, the critical level of sillovers increases with α α increasing heterogeneity for the non-uniform taxation case as well. 0 See the revious footnote. 19

23 generate the same level of surlus. This reflects the fact that, in the uniform taxation case, reresentative in the winning coalition has incentives to rovide the same level of ublic goods to both regions which corresonds to the case of non-uniform taxation. Furthermore, surlus under centralization with non-uniform taxation is lower than that under centralization in the standard analysis. In the non-uniform taxation case, increasing heterogeneity causes the otential rovisions of the two reresentatives to vary still more. This decreases the surlus under centralization with non-uniform taxation and because the surlus under centralized system in the traditional analysis is indeendent of heterogeneity, centralization with non-uniform tax system generates lower ublic goods surlus. 1 It follows that olitical economy analysis weakens the case for centralization when the taxation is nonuniform but not as considerably as in the case of a centralized system with uniform taxation. 5 Centralization with a Cooerative Legislature and Two Forms of Taxation Under the minimum winning coalition view of legislative decision-making, olicy outcomes are ex ante Pareto inefficient from the viewoint of the reresentatives. Therefore, legislators may find a way around the inefficiency created by majoritarian decision criteria and refer a less random outcome to the feast or famine imlied by the minimum winning coalition theory. The reresentatives with ower may, to a given extent, allocate benefits to those outside the coalition on the understanding that non-members would behave similarly if they were in ower. However, there are many airs of local ublic goods levels that are both efficient from the viewoint of the reresentatives and that ex ante Pareto dominate minimum winning coalition outcomes. Here we will assume the case when the reresentatives agree to the ublic goods allocation that maximizes their joint surlus, i.e. their behavior can be described by the utilitarian 1 Let St(κ,α) c and Sn(κ,α) c denote surluses under centralization in the standard analysis and with nonuniform taxation, resectively, when (m 1,m ) = (αω,(1 α)ω), where α (1/,1) measures the degree of heterogeneity. From the revious discussion we know that St c is indeendent of heterogeneity while Sn(κ,α) c = ω 1 α < 0 for all α (1/,1). This imlies that increasing heterogeneity decreases surlus α α(1 α) under centralization with non-uniform tax system which is then lower than that under a centralized system in the traditional analysis. 0

24 bargaining solution. This means that each reresentative now maximizes the same utility function as the others. They agree to form a coalition where everybody will have a weight in the decision making rocess, not just those who succeed to form a minimum winning coalition. This norm requires reresentatives to take into account the costs and benefits to their colleagues and would seem to offer centralization the best chance of dominating decentralization given our welfare criterion. But to what extent will centralization dominate decentralization will again deend on the form of taxation. 5.1 Policy Determination with Uniform Taxation With uniform taxation and reresentatives of tyes λ 1 and λ, the olicy outcome, (g 1 (λ 1,λ ), g (λ 1,λ )), will now maximize the reresentatives joint surlus given by { U λi } = i=1 i=1 { λ i [(1 κ) ln g i + κ ln g i ] } (g i + g i ). It is straightforward to show that ublic goods levels maximizing this joint surlus are ( λ1 (1 κ) + λ κ (g 1 (λ 1,λ ),g (λ 1,λ )) =, λ ) 1κ + λ (1 κ). It is clear that if both districts elected reresentatives of the median tyes, the legislature would select the surlus maximizing ublic goods levels. If the reresentative tyes are λ 1 and λ, a citizen of tye λ in district i obtains ublic goods surlus of U λ,i = λ [ (1 κ) ln λ i(1 κ) + λ i κ + κ ln λ ] i(1 κ) + λ i κ λ 1 + λ. Turning to the election stage, we again assume that the air of reresentatives will be of the majority referred tyes that is defined in the by now familiar way. The main additional comlication created by a cooerative legislature lies in finding the majority referred tyes. This is because the ublic good level for each region deends on the tye of legislator in both districts and, thereby, generates incentives for citizens in each district to delegate olicy making strategically to a reresentative with different tastes than their own. This intention arises because sincere voting becomes subotimal now. To begin with, note that a air of reresentative tyes (λ 1,λ ) is majority referred if and only if in each district i the median tye refers λ i to any other tye λ 0,λ, given 1

25 the other district s tye λ i. Thus, (λ 1,λ ) is majority referred if and only if it is a Nash equilibrium of the two layer game in which each layer has strategy set 0,λ and layer i {1, } has ayoff function [ U i (λ 1,λ ) = m i (1 κ) ln λ i(1 κ) + λ i κ + κ ln λ ] i(1 κ) + λ i κ λ 1 + λ. In this game, the district i median citizen tries to maniulate λ i so that he obtains something close to his referred olicy outcome anticiating the election outcomes in the other region and the subsequent working of the legislature. 3 He only has one degree of freedom, λ i, but two objectives, (g 1,g ). While raising λ i always leads to an increase in g i, if κ > 0 it also raises g i. To state the equilibria, define ˆκ as the solution to m 1 = ˆκ3 + (1 ˆκ) 3. m ˆκ(1 ˆκ) When the districts are identical, ˆκ = 1/. In the non-identical districts case, ˆκ < 1/. Then: Lemma 4. Suose that the tax system is uniform across districts and the assumtions of the olitical economy analysis are satisfied. Then the olicy chosen under a centralized system with a cooerative legislature is if κ < ˆκ, and if κ ˆκ. (g 1,g ) = m 1 [(1 κ) 4 k 4 ] [ (1 κ) m 1 κ m ] m 1 [(1 κ) 4 k 4 ], [ ] m1 (1 κ) κ m ( m1 (1 κ) (g 1,g ) =, m ) 1κ It can be easily seen that the cooerative legislature does not select the surlus maximizing ublic goods levels. While a cooerative legislature deals with roblems of uncertainty and misallocation that were resent in the non-cooerative legislature, a new feature emerges: If district i elects a citizen of a higher tye, then it receives more of both ublic goods. Then the same argument alies as in the footnote To ut it more rigorously, all citizens in region i now have an interest in maniulating λ i to obtain something close to their referred olicy outcome. In other words, all voters in district i have the same interest in shifting λ i according to their references and exectations of the election outcomes in the other regions and subsequent working of the legislature.

26 Strategic delegation: each district s median voter delegates olicy-making to a reresentative of different tye than median Comarative Statics When the regions are identical (m 1 = m = m), it follows from the Lemma that g 1 = g = m[(1 κ) + κ ]/. Recall that with identical districts, the surlus maximizing level of ublic goods is g 1 = g = m/. Thus, local ublic goods are over-rovided in both regions for all κ < 1/. The extent of this over-rovision is decreasing with increasing sillovers and over-rovision does not occur only when the sillovers are maximal (κ = 1/). In such a case, local ublic goods are rovided otimally. The incentives to strategically delegate can be seen most clearly in the case of zero sillovers. Then, the otimal sending levels for the median voter from region are (g 1,g ) = (0, m/). Assume for a moment that both districts elect the median tye reresentatives. This would lead to a olicy outcome (g 1,g ) = (m/,m/). But if the district elected a reresentative with a stronger taste for ublic sending, it would get more of its local ublic good with no imact on the district 1 s ublic good level. Thus, each region is drawn to elect a tye m reresentative. As sillovers increase, the otimal sending levels in the two districts for each median voter converge. Electing a reresentative with a higher reference for ublic goods sending increases sending in the other region as well. Thus, the districts elect reresentatives with references closer to their median. When the sillovers are maximal, each region elects a median tye reresentative and local ublic goods are rovided at the surlus maximizing level. With heterogeneity, an additional conflict over the level of ublic sending enters the icture, which can be seen most clearly in the case of comlete sillovers. If κ = 1/ and each region elects a reresentative of the median tye, the ublic goods levels are g 1 = g = (m 1 + m )/. This common level is too low for district 1 s median voter and too high for region s. This gives district 1 s median voter an incentive to have a higher reresentative tye to boost ublic goods sending, while region s median voter desires a reresentative with lower ublic goods references. They ull in oosite directions until 3