Discussion Paer No. 41 Centralized and decentralized of rovision of ublic goods Janos Feidler* Klaas Staal** July 008 *Janos Feidler, University Bonn **Klaas Staal, University Bonn and IIW, Lennestr. 37, 53113 Bonn, Germany, E-mail: kstaal@uni-bonn.de Financial suort from the Deutsche Forschungsgemeinschaft through SFB/TR 15 is gratefully acknowledged. Sonderforschungsbereich/Transregio 15 www.sfbtr15.de Universität Mannheim Freie Universität Berlin Humboldt-Universität zu Berlin Ludwig-Maximilians-Universität München Rheinische Friedrich-Wilhelms-Universität Bonn Zentrum für Euroäische Wirtschaftsforschung Mannheim Seaker: Prof. Dr. Urs Schweizer Deartment of Economics University of Bonn D-53113 Bonn, Phone: +49(8) 73 90 Fax: +49 (8) 73 91
Centralized and decentralized rovision of ublic goods Janos Feidler and Klaas Staal July 3, 008 Abstract We model the trade-off between centralized and decentralized decision making over the rovision of local ublic goods. Centralized decisions are made in a legislature of locally elected reresentatives, and this creates a conflict of interest between citizens in different jurisdictions. The legislature can be self-interested or benevolent and this can result in either efficient, excessive or misallocative rovision of ublic goods. Decisions are influenced by sillover effects and differences in jurisdictional size. Furthermore, we look at the incentives for centralization. Key Words: Decentralization; Local ublic goods. JEL Numbers: H40, H70, P51. We are grateful to Michael Evers, Jürgen von Hagen, Phili Jaeschke and Tymofiy Mylovanov and articiants of resentations at the 3rd SFB / TR15 Worksho (Bonn), the BGSE Micro/Finance/Public-Finance Worksho (Bonn) and the EPCS 008 Meeting (Jena). Financial suort from the German Research Foundation through SFB / TR15 is gratefully acknowledged. University Bonn University Bonn and IIW. Address: IIW, Lennestr. 37, 53113 Bonn, Germany. E-mail: kstaal@uni-bonn.de 1
1 Introduction Centralization or decentralization of local ublic good rovision is one of the main questions in the ublic finance literature. In a country with geograhically distinct districts of different size, local ublic goods can be rovided and financed by the local governments of districts (decentralization) or rovided and financed by a central government (centralization). The citizens in a district benefit from the local ublic goods rovided in their district, but also from a ositive sillover effect from the goods rovided in the other districts. This aer studies whether centralization of decision making and which way of centralized decision making is desirable from a social welfare ersective and whether citizens actually refer centralization. Oates (197) started with the (now) standard aroach that each government maximizes the aggregate surlus of its citizens. Under decentralized decision making, this maximization is done searately for each district, while under centralized decision making this is done with a uniform ublic good level for each district. On the one hand, with decentralization the sillover effects are not taken into account and thus, there is underrovision. On the other hand, however, with centralization the uniform level does not take the differences between districts into account roerly. When there are no sillover effects, Oates Decentralization Theorem says that decentralization is desirable from a social welfare ersective. When there are sillovers, however, centralization can be desirable deending on the differences between the districts and the size of the sillover effect. Besley and Coate (003) wrote one of the first aers in which centralization does not imly that uniform levels of ublic goods have to be rovided. They argue that the assumtion of uniformity is neither emirically 1 nor theoretically satisfactory, since there is no convincing theoretical reason that a central government could not rovide different levels in districts. Therefore, they use the citizen-candidate aroach to model centralization as decision making in a legislature of locally elected reresentatives that are self-interested, arguing that this is tyically the case in centralized decision making. 1 Examles they give are federal highway sending in the U.S.A. -see Knight (00)-, federal sending on river and harbor rojects by the Army Cors of engineers -see Ferejohn (1974)- and federal sending on arks by the Deartment of the Interior. In these examles, federal sending is unequal for each district/state. See Osborne and Slivinski (1996), Besley and Coate (1997) and Coate (1997).
In the legislature, the reresentatives of each district have to make a joint decision on the levels of local ublic goods, given the different references in each district for the levels as well as the allocation of the ublic goods. Besley and Coate look at two secifications of centralized decision making in the legislature. In the first one, a minimum winning coalition 3 is formed in the legislature and reresentatives in this coalition make the decision according to their own references. This leads to misallocation as well as uncertainty in ublic good rovision, since more ublic goods are rovided to the districts whose reresentatives are in the coalition, while citizens of a district are unsure whether their reresentative will be in the minimum winning coalition. In the second secification, there is a cooerative legislature, in which the reresentatives maximize their joint surlus. This can lead to strategic delegation, since citizens of each district may elect reresentatives who demand a high level of ublic goods for their district. A major contribution of our aer is to model a benevolent legislature that maximizes the aggregate surlus of its citizens, but that is not restricted to a uniform level of ublic goods under centralized decision making. This is in shar contrast to Besley and Coate (003) where the self-interested legislature does not maximize the aggregate surlus of its citizens, but of its reresentatives. The latter imlies a dearture from the standard aroach by not only droing the assumtion of uniform levels under centralization, but also changing the objective of the legislature. Our aroach, as oosed to the others, imlies that under centralized decision making the socially otimal levels of ublic goods are rovided. Another major contribution of our aer is the study of the incentives citizens have for centralizing decision making. We find that, even though centralization leads to a bigger aggregate surlus, individuals in one of the districts might reject centralization since their ayoff would decrease, even though the gain in the other district would outweigh this loss. Furthermore, we find that in the aroach where centralized decision making obtains the socially otimal levels of ublic goods, centralization of ublic good rovision is less likely to take lace than under other aroaches. Our aer is thus closely related to Besley and Coate (003). In their aroach, individuals within as well as across districts have different references over ublic good rovision, while in our aer the key difference is 3 See Buchanan and Tullock (196), Riker (196), Ferejohn, Morris and McKelvey (1987) and Baron and Ferejohn (1989). 3
district size. A comarison of the results imlies that the difference in district size is only an imerfect roxy for differences in references. For examle, when there are only differences across districts, strategic delegation does not take lace. Another related aer is Lockwood (00), but in his aroach districts are of the same size, and local ublic good rovision is discrete. Our research also relates to aers that consider the choice between centralization and decentralization, such as Alesina and Solaore (1997, 003), Goyal and Staal (004) and Bolton and Roland (1997). Other aers also endogenize the decision for centralization, such as Bolton, Roland and Solaore (1996), Dur and Staal (008) and Ellingsen (1998), and look at districts of different size, but only in cases in which the large district dominates decision making after centralization. The rest of the aer is organized as follows. In Section we secify the ayoffs. Section 3 resents the socially otimal outcome, while Section 4 resents the outcome under the standard aroach. Section 5 discusses the aroach introduced by Besley and Coate (003) and in Section 6 we introduce our aroach in which a benevolent legislature makes decisions on ublic good rovision. In Section 7 we conclude with some more general remarks. The ublic good Assume that a country is divided into two geograhically distinct districts. Each district has a continuum of individuals, the districts i {1, } have a oulation size N 1 and N, with N 1 + N =, and without loss of generality, we assume that N 1 N. In each district, an amount g i of the ublic good is rovided and the ayoff an individual in district i gets from these ublic goods is given by (1 κ) ln(g i ) + κ ln(g i ), where the arameter κ [0, 1/] denotes the sillover effect. The higher κ, the higher the ayoff individuals get from the ublic goods rovided in the other districts. When κ = 0, individuals do not benefit from the ublic goods rovided in the other district, while when κ = 1/, individuals get the same benefit from a unit of ublic good rovided in the other district. Each individual is endowed with a single rivate good x and the roduction of the ublic goods g 1 and g requires g 1 and g units of the rivate good. In the following, we look at centralized and decentralized decision 4
making over the level of ublic good rovision. Under centralized decision making, the costs of ublic good rovision is borne by the individuals in both districts, so an individual s ayoff is given by (1 κ) ln(g i ) + κ ln(g i ) + x (g i + g i ). (1) Under decentralized decision making, individuals in each district have to bear the costs of ublic good rovision in their own district and an individual has a ayoff of (1 κ) ln(g i ) + κ ln(g i ) + x g i N i. () Finally, in the following we also look at the individual incentives for centralization of decision making. There is a referendum in each district and each individual can choose between centralization or decentralization. Centralization only takes lace when majorities in both districts refer centralized over decentralized decision making. 3 The social otimum We use the socially otimal outcome as a benchmark for comaring the results under centralized and decentralized decision making. We furthermore use social surlus to comare whether centralization of decision making is desirable, from a social welfare oint of view. When g 1 and g are the rovided levels of ublic goods, the social surlus is given by [N 1 (1 κ) + N κ] ln(g 1 ) + [N 1 κ + N (1 κ)] ln(g ) (g 1 + g ). (3) The social otimum is given by the ublic good levels ĝ 1 and ĝ that maximizes the aggregate ublic good surlus: (ĝ 1, ĝ ) = arg max g1,g = [N 1 (1 κ) + N κ] ln(g 1 ) + [N 1 κ + N (1 κ)] ln(g ) (g 1 + g ). 5
The ublic good levels that maximize aggregate ublic good surlus are calculated by taking first-order conditions and solving. This yields: ( N1 (1 κ) + N κ (ĝ 1, ĝ ) =, N ) 1κ + N (1 κ). (4) Note that when N 1 exceeds N, district 1 s level is higher for all κ < 1/. 4 The standard aroach In the standard aroach, following Oates (197), a government maximizes the aggregate ublic good surlus of its citizens. We look consecutively at decentralized and centralized decision making. Under decentralized decision making, each district has its own government, while under centralized decision making a single government reresents both districts. The section ends with a comarison of centralized and decentralized decision making. Decentralized decision making In a decentralized system each district s government chooses indeendently the district s local ublic good level. The government s objective is to maximize local ublic good surlus in its own district. Note that the chosen ublic good levels ( g1, d g) d form a Nash equilibrium. This imlies that these ublic good levels are given by the following maximization roblem: { gi d = arg max (1 κ) ln(g i ) + κ ln(g i ) g } i. (5) g i N i The ublic good levels under decentralized decision making are calculated by taking first-order conditions and solving. This yields: ( ( g d (1 1, g) d κ)n1 =, (1 κ)n ). (6) While each government maximizes the surlus of its own citizens, the local ublic good levels under non-cooerative decentralized decision making are only surlus-maximizing when there is no sillover effect. When there is a sillover effect, there is underrovision of ublic goods in both districts, and this underrovision becomes more severe when the sillover effect increases. 6
Centralized decision making In a centralized system, a uniform level of the ublic good is rovided by assumtion in each district. The government s objective is to maximize the aggregate local ublic good surlus of the citizens in both districts. This imlies that the amount of ublic goods is given by the following maximization roblem: g1 c = g c = arg max { ln(g) g}. (7) g The ublic good levels under standard centralized decision making are calculated by taking first-order conditions and solving. This yields: g c 1 = g c = 1. (8) Note that the level of local ublic goods does not deend on the size of the sillover effect. It only equals the socially otimal levels when the sillover effect is erfect (i.e. κ = 1/) or when both districts have the same size. When the sillover effect is imerfect, there is overrovision in the small district but underrovision in the big district. Comarison We first examine whether centralization of decision making is desirable from a social welfare ersective. To do so, we subtract the aggregate surlus under decentralized decision making -(3) with (6)- from the surlus under centralization -(3) with (8)-. (N i (1 κ) + N i κ) ln ((1 κ)n i ) (N i κ + N i (1 κ)) ln ((1 κ)n i ) κ (9) Centralization is thus desirable when the above difference is ositive. Note that from the results above it follows that under decentralized decision making the socially otimal levels of local ublic goods are rovided when there is no sillover effect. When the sillover effect is erfect, however, socially otimal levels are rovided under centralized decision making. Finally, the underrovision of local ublic goods under decentralized decision making increases with the size of the sillover effect, while local ublic good levels under centralized decision making do not deend on the size of the sillover effect. These observations imly the following. Proosition 1 Under the standard aroach, decentralized decision making leads to a higher local ublic good surlus when there is no sillover effect. 7
There is a value of the sillover effect such that both centralized and decentralized decision making create the same surlus, while with erfect sillovers centralized decision making leads to a higher surlus. Note that this roosition is in line with Oates Decentralization Theorem - in the absence of sillovers, decentralized decision making is otimal. An illustration of the social incentives for centralization is given in Figure 1. Now look at an individual s references over centralization of decision making. Subtracting the ayoff under decentralization -() with (6)- from the ayoff under centralization -(1) with (8)- gives the incentives of an individual to choose centralization: (1 κ) ln((1 κ)n i ) κ ln((1 κ)n i ) κ. (10) The individuals in district i thus refer centralization over decentralization if this is ositive. When 0 < N i 1 then (10) decreases with increasing N i for all 0 κ 1 and for N i = 1 it is ositive for all ossible values of κ. The individuals in district 1 thus always refer centralization of decision making. For 1 < N i, however, (10) is negative when κ = 0 and ositive for κ = 1. Individuals in district thus only refer centralization when the sillover effect is big enough. This imlies the following. Proosition Under the standard aroach, centralization only takes lace when the sillover effect exceeds a certain threshold value. An illustration of these incentives for centralizing decision making is given in Figure 1. We now comare the incentives for centralization under majority voting with the socially otimal incentives. To do so, we comare the airs of N i and κ for which (9) and (10) are ositive. To make such a comarison insightful, we have calculated for a thousand values of N the values of κ for which (9) and (10) are equal to zero. These values can be found in Figure 1, and this illustrates the following result. Proosition 3 From a social welfare ersective, individuals have insufficient incentives to centralize decision making. There is an obvious exlanation for these insufficient incentives. Under decentralized decision making, all individuals within each district obtain the same ayoff, say Ŝ1 and Ŝ, resectively, and total surlus then is N 1 Ŝ 1 + N Ŝ. 8
Centralization only takes lace if the ayoffs for both districts increase. However, when centralization only makes one ayoff higher and the other ayoff (only a bit) smaller, the latter individuals will reject centralization even though centralization could increase aggregate social welfare. We see in Figure 1 that for small values of the sillover effect, centralization is neither the majority voting outcome nor socially desirable. From a social welfare ersective, for small sillover effects it is better to have ublic good levels that deend on district size, even though there might be underrovision in the small district. For higher sillover effects, however, the underrovision becomes so severe that centralization does better, even though under centralization uniform levels have to be rovided in both districts. Under majority voting, nevertheless, individuals in the largest districts are even more reluctant to centralization, since under centralized decision making they artly have to bear the costs of the ublic goods rovided in the smaller district. Some assumtions underlying the standard aroach influence the results significantly. One is that a government chooses ublic good levels to maximize aggregate ublic good surlus, and another is that under centralized decision making uniform levels of ublic goods have to be rovided. In Section 5, we introduce elections of individuals reresenting the government, and these individuals choose ublic good levels to maximize their own surlus. This alters the first assumtion, while we also dro the assumtion of uniformity under centralized decision making. In Section 6, ublic good levels also do not need to be uniform under centralized decision making, and again there are elections of individuals reresenting the government. These individuals, however, maximize aggregate ublic good surlus, thus restoring the first-mentioned assumtion. 5 A self-interested legislature In this section we introduce elections to the model, using the citizen-candidate aroach. In this aroach, elections are organized to select an individual for a legislature (government). Elected individuals are assumed to base their decisions on their own self-interest, and a voter therefore tries to select a candidate whose self-interest is in line with the voter s interest. We first look at decentralized decision making and then at centralized decision making with a self-interested legislature. The section ends with a comarison 9
of both forms of decision making. Decentralized decision making With decentralized decision making in self-interested legislatures, individuals in each district elect a single reresentative from the district who then determines its olicy. First, simultaneous elections thus make lace in each district to determine which individuals (i.e. citizens) reresent a district. Second, the two elected individuals simultaneously but searately determine the levels of ublic goods in each district. We solve this game by backward induction. The two elected individuals of district i {1, } face the following maximization roblem: { gi d = arg max (1 κ) ln(g i ) + κ ln(g i ) g } i. (11) g i N i The ublic good levels under decentralized decision making are calculated by taking first-order conditions and solving. This yields: ( ( g d (1 1, g) d κ)n1 =, (1 κ)n ). (1) Note that in a district all citizens have the same references. Accordingly, the levels of ublic goods do not deend on which citizens are elected, and the local ublic good levels ( g d 1, g d ) are thus given by exression (1). Furthermore, it follows that decentralized decision making with self-interested legislatures yields the same outcome as in the standard aroach. Centralized decision making With centralized decision making in a selfinterested legislature, individuals in each district elect a single reresentative in a legislature, while the reresentatives in the legislature make decisions on the levels of ublic goods in each district. First, simultaneous elections thus take lace in each district to determine which individuals (i.e. citizens) reresent the district in the legislature. Each district is thus reresented by one individual from the district. Second, the legislature determines the levels of the ublic goods. We solve this game by backward induction. For this solution it is imortant how the levels of ublic goods are determined in the legislature. We use the minimum winning coalition view to model a noncooerative decision rocess in the legislature, while we also look at a cooerative decision rocess in which the reresentatives in the 10
legislature maximize their joint surlus. Under the minimum winning coalition view, a coalition that forms a majority of the reresentatives determines ublic good levels. When N 1 < N, one could argue that the reresentative of district invariably forms the winning coalition in the legislature. The decisions of the legislature would then only reflect the references of district s reresentative. The level of ublic goods rovided in district is otimal for the citizens of district, while the level of ublic goods in district 1 is only determined by the sillover effect for the individuals in district. However, we do not only evaluate the outcomes in which the reresentative of district forms the minimum winning with certainty, but also the ossibility that the reresentative of each district forms the winning coalition with a robability roortional to his district s oulation size as well as the ossibility that both reresentatives are in the minimum winning coalition with equal robability. Finally, we also look at cooerative decision making in the legislature. In this case, the reresentatives in the legislature choose a utilitarian bargaining solution, maximizing joint surlus. In a noncooerative legislature and when the reresentative from district i forms the minimum winning coalition, this reresentative faces the following maximization roblem: { ( ) g c i, g i c = arg max (1 κ) ln(g i ) + κ ln(g i ) (g } i + g i ). (13) (g i,g i ) The ublic good levels under decentralized decision making are calculated by taking first-order conditions and solving. This yields: ( ( g c (1 κ) i, g i) c =, κ ). (14) Note that in a district all citizens have the same references. Accordingly, the levels of ublic goods do not deend on which citizens are elected, and the local ublic good levels are thus given by exression (14). For an evaluation of the outcomes, however, it is imortant which individual forms the minimum winning coalition. The district whose reresentative is in the minimum winning coalition has an advantage in the sense that more ublic goods are rovided in this district, while less ublic goods are rovided 11
in the other district. Excet when sillovers are erfect, there thus is misallocation in ublic good rovision. More ublic goods than the socially otimal amount are rovided in the district whose reresentative forms the minimum winning coalition, while less ublic goods than otimal are rovided in the other district. Unless the biggest district dominates decision making, such that its reresentative always forms the minimum winning coalition, there is also uncertainty in ublic good rovision. Since it is not clear beforehand whether a reresentative is in the minimum winning coalition, it is also unclear where the highest level of the ublic good is rovided. Finally, note that the ublic good levels are only equal to the socially otimal levels when the sillover effect is erfect. In a cooerative legislature, both reresentatives face the following maximization roblem for the joint surlus. { (g1, c g) c = arg max (1 κ) ln(g i ) + κ ln(g i ) (g } i + g i ). (15) (g 1,g ) i {1,} The ublic good levels chosen by a cooerative legislature are calculated by taking first-order conditions and solving. This yields: ( 1 (g1, c g) c =, 1 ). (16) Note that in a district all citizens have the same references. Accordingly, the levels of ublic goods do not deend on which citizens are elected, and the local ublic good levels are thus given by exression (16). Furthermore, it follows that centralized decision making with self-interested legislatures yields the same outcome as in the standard aroach. Comarison Several comarisons can be made. We first comare decentralization with noncooerative as well as cooerative centralization and then cooerative with noncooerative centralization. Furthermore, we look at the incentives individuals have for centralization. As in the standard aroach, under decentralized decision making each government maximizes the surlus of its own citizens and the local ublic good levels are only surlus-maximizing when there is no sillover effect. 1
When there is a sillover effect, there is underrovision of ublic goods in both districts, and this underrovision becomes more severe when the sillover effect increases. With noncooerative as well as cooerative centralized decision making, the ublic good levels are only socially otimal when the sillover effect is erfect. These observations are reflected in the following roosition: Proosition 4 With self-interested legislatures, for noncooerative as well as cooerative centralization, it holds that decentralized decision making leads to a higher ublic good surlus when there is no sillover effect. There is a value of the sillover effect such that both centralized and decentralized decision making create the same surlus, while with erfect sillovers centralized decision making leads to a higher surlus. Note that this comarison is qualitatively the same as the comarison made for the standard aroach and that it is thus also in line with Oates Decentralization Theorem - in the absence of sillovers, decentralized decision making is otimal. The roof of Proosition 4 is in the aendix. With self-interested legislatures, the ublic good levels with decentralized as well as with cooerative centralized decision making are the same as the levels under the standard aroach. The comarison of decentralized and cooerative centralized decision making is thus analogous to the comarison resented in Section 4. From the discussion in this section it also follows that under cooerative as well as noncooerative centralized decision making individuals have fewer incentives for centralization than socially desirable. Now we turn to individual incentives for noncooerative centralization. These incentives deend on the exected ublic good surlus under centralization and thus deend on which reresentative forms the minimum winning coalition under centralization. Let Pr[i] denote the robability that the reresentative of district i forms the minimum winning coalition. Then the exected ublic good surlus of an individual in district i under centralization is Pr[i] {(1 κ) ln (g i ) + κ ln (g i )} + Pr[ i] {(1 κ) ln (g i ) + κ ln (g i )} 1 (17) with (g i, g i ) given by (14). The ublic good surlus of an individual in 13
district i under decentralized decision making is ( ) ( ) (1 κ)ni (1 κ)n i (1 κ) ln + κ ln (1 κ) (18) and an individual refers centralization when (17) is larger than (18). The individual incentives for cooerative centralization are given by subtracting the ayoff under decentralization -() with (1)- from the ayoff under centralization -(1) with (16)-. The following result is based on the above differences. Proosition 5 With a self-interested legislature, individuals only choose to centralize (cooerative or noncooerative) decision making when the sillover effect exceeds a certain threshold value. The roof of Proosition 5 is in the aendix. We now take a look at the individual incentives for noncooerative centralization. For such a comarison we should comare the airs of N i and κ for which the social surlus and the difference of (17) and (18) are ositive for the three different aroaches to forming a minimum winning coalition. To make this insightful we have calculated the values of κ for a thousand values of N, for which the social surlus and these differences are equal to zero. These values can be found in Figure. It follows that when the districts do not differ much in size -when N is close to 1- the incentives for centralization do not differ much when the minimum winning coalition is formed by the larger district either with robability 1 or with a robability equal to N. Clearly, this is due to the fact that the latter two robabilities are almost the same. When the larger district forms the minimum winning coalition with robability 1, however, individuals in the smaller district are less likely to refer centralization and centralization only occurs for larger values of the sillover effect. When there is a bigger difference in size between both districts, centralization is most likely to take lace when the larger district is in the minimum winning coalition with robability 1. In this case, the individuals always refer centralization since they dominate centralized decision making and are thus able to set ublic good levels to their own references. Moreover, the small district is so small that its individuals benefit from centralization in most cases, even though decisions are then made according to the references of individuals in the big district. When both districts are in the minimum 14
winning coalition with equal robability, the individuals in the small district refer centralization in more cases. The individuals in the large district, however, are less likely to refer centralization since it makes it ossible that ublic good levels are set according to the references of the individuals in the small district. In the aroach that we discus in this section, reresentatives in the legislature choose ublic good levels that maximize their own ayoff. In the standard aroach, however, ublic good levels are chosen to maximize the aggregate surlus of all the individuals. In the next section, we therefore change the objective of the legislature. Instead of self-interest, we then assume that reresentatives in the legislature are benevolent in the sense that they choose to maximize an aggregate surlus, as is assumed in the standard aroach. 6 A benevolent legislature In Section 5 we introduced elections in the decision making over the levels of ublic goods. Public good rovision was no longer uniform across districts, as it is in the standard aroach, and at the same time, the benevolent surlusmaximizing legislature was changed into reresentatives making decisions based on self-interest. In this section we introduce a new aroach of decision making, in which, as in the aroach with a self-interested legislature, ublic good rovision need not be uniform across districts, but the legislature is assumed to be benevolent, that is to maximize surlus. We first look at decentralized decision making and then at centralized decision making in this benevolent-legislature aroach. The section ends with a comarison of both forms of decision making. Decentralized decision making Under the benevolent-legislature aroach and with decentralized decision making, individuals in each district elect a single reresentative from the district who then determines its olicy. First, simultaneous elections thus take lace in each district to determine which individuals (i.e. citizen) reresent a district. Second, the two elected individuals simultaneously but searately determine the levels of ublic goods in each district. These levels maximize the aggregate surlus in each district. We solve this game by backward induction. The two elected individuals of 15
district i {1, } face the following maximization roblem: g d i = arg max g i {N i [(1 κ) ln(g i ) + κ ln(g i )] g i }. (19) The ublic good levels under decentralized decision making are calculated by taking first-order conditions and solving. This yields: ( ( g d (1 1, g) d κ)n1 =, (1 κ)n ). (0) Since in a district all citizens have the same references, the levels of ublic goods do not deend on which citizens are elected, and the local ublic good levels are thus indeed given by exression (0). A comarison of exressions (6), (1) and (0) reveals that, under decentralized decision making, the outcomes with a benevolent legislature are the same as with a self-interested legislature and in the standard aroach. Centralized decision making Under the benevolent-legislature aroach and with centralized decision making, individuals in each district elect a single reresentative in a legislature, while the reresentatives in the legislature make decisions on the levels of ublic goods in each district. First, simultaneous elections take lace in each district to determine which individuals (i.e. citizens) reresent the district in the legislature. Second, the legislature determines the levels of the ublic goods. The reresentatives in the legislature choose these levels such that the levels maximize the aggregate surlus of both districts, given the references revealed in the first stage. We solve this game by backward induction. The reresentatives thus face the following maximization roblem: ( ) { } g c i, g i c (g i + g i ) = arg max N i [(1 κ) ln(g i ) + κ ln(g i )] N i (g i,g i ) i {1,} (1) The ublic good levels under centralized decision making are calculated by taking first-order conditions and solving. This yields: ( (g1, c g) c N1 (1 κ) + N κ =, N 1κ + N (1 κ) ). () 16
Note that in a district all citizens have the same references. Accordingly, the levels of ublic goods do not deend on which citizens are elected, and the local ublic good levels are thus given by exression (). A comarison of (4) and () reveals that centralized decision making by a benevolent legislature leads to the socially otimal levels of ublic goods. Comarison From the results above it follows that under centralized decision making, the socially otimal levels are always rovided. Under decentralization, the otimal levels are only rovided when there is no sillover effect. These observations imly the following roosition. Proosition 6 With a benevolent legislature, centralized and decentralized decision making leads to the same surlus when there is no sillover effect, while centralized decision making leads to a higher ublic good surlus when there is a sillover effect. Again, this is similar to the results obtained for the standard aroach and with a benevolent legislature, but in an even more clear-cut way. In the absence of sillover effects, decentralization is otimal -Oates Decentralization Theorem- while with a benevolent legislature, in all other cases centralized decision making is strictly better. Now look at the individual references over centralization of decision making. Subtracting the ayoff under decentralization -() with (0)- from the ayoff under centralization -(1) with ()- gives the incentives of an individual for centralization (1 κ) ln((1 κ)n i + κn i ) + κ ln((1 κ)n i + κn i ) (1 κ) ln((1 κ)n i ) κ ln((1 κ)n i ) κ. (3) The individuals in district i thus refer centralization over decentralization if this is ositive. It is straightforward to show that this difference is ositive when both districts have the same size and that district 1, the smaller district, always refers centralization. For individuals in district, the larger district, the difference is always ositive when the sillover effect is erfect, that is when κ = 1. It is straightforward to show, however, that centralization does not always take lace under majority voting when κ < 1. Now comare the individual incentives for centralization under the standard aroach with those with a self-interested or a benevolent government. To do so, we have calculated the threshold values of κ for a thousand values 17
of N, above which centralization takes lace under majority voting. This is done for the standard aroach, giving the same outcome as with cooerative centralization in a self-interested legislature. For noncooerative centralization with a self-interested legislature, we took the minimum value of κ above which centralization takes lace. That is, for N close to 1 we took the κs when each district is in the minimum winning coalition with a robability roortional to district size, while for bigger values of N we took the the κs when the reresentative from the larger district always forms the minimum winning coalition. Figure 3 illustrates that when the difference in size between the two districts is small, centralization is most likely the majority voting outcome under the standard aroach. When the difference in district size is large, however, centralization is more likely to be the majority voting outcome under noncooerative centralization with a self-interested legislature. From this it follows that, even though centralization with a benevolent legislature would imly socially otimal levels of ublic goods, it also imlies smaller incentives for centralization. 7 Concluding remarks Public economists have extensively researched the centralized versus decentralized rovision of local ublic goods. In the standard aroach of Oates (197), albeit assuming that benevolent governments maximize aggregate welfare of their citizens, centralized rovision imlies uniform levels of ublic goods. This uniformity is a disadvantage of centralization since it revents differences between districts to be reflected in the levels of ublic goods that are rovided. In the aroach of Besley and Coate (003), citizens choose reresentatives in legislatures that make decisions on ublic good rovision. The reresentatives maximize their own surlus, instead of maximizing the aggregate surlus of the citizens. Additionally, the reresentatives can rovide different levels to each district under centralized decision making. This, however, leads to misallocation and uncertainty in ublic good rovision, since centralized decisions are assumed to be made by a minimum winning coalition of reresentatives in the legislature. The citizens are uncertain whether their reresentatives will be in this coalition, while the reresentatives in the coalition make decisions based on their own references, ignoring the 18
references in the other districts. The aroach we roose in this aer deviates in just a single way from the standard aroach. Centralized decision making is done by a benevolent legislature that maximizes the aggregate surlus, as in the standard aroach, but can rovide different ublic good levels in each district. In contrast to Besley and Coate (003), socially otimal ublic good rovision takes lace under centralization. However, centralization is not always referred by a majority of the individuals. The analysis can be extended in several imortant ways. One way is to loosen the uniform taxation assumtion. Another way is introducing transfers into the analysis. Finally, since district size is observable, the analysis oens ossibilities for emirical research on, for examle, the references of districts over centralization, given the different ways the decision-making rocess is structured after centralization. A Aendix Proof of Proosition 4. First, note that when there is no sillover effect the ublic good surlus attains the maximum ossible value under decentralization, since the ublic good levels are then socially otimal. This roves the first statement in the roosition. Likewise, when the sillover effect is erfect, with noncooerative as well as cooerative decision making the ublic good surlus attains the maximum ossible value under centralization. This roves the last statement in the roosition. The aggregate ublic goods surlus under decentralization is ( ) ( ) (N 1 (1 κ) + N κ) ln (1 κ)n1 + (N 1 κ + N (1 κ)) ln (1 κ)n (1 κ). The aggregate ublic good surlus under noncooerative centralization deends on which reresentative forms the minimum winning coalition. Let Pr[i] denote the robability that the reresentative of district i forms the 19
minimum winning coalition. The exected value of the surlus then is [ ( ) ( )] Pr[1] (N 1 (1 κ) + N κ) ln (1 κ) κ + (N 1 κ + N (1 κ)) ln + [ ( ) ( )] Pr[] (N 1 (1 κ) + N κ) ln (N 1 κ + N (1 κ)) ln (1 κ) κ. and the aggregate ublic good surlus under cooerative centralization is ( ) 1 ln. Note that the three ublic good surluses are continuous in κ. Together with the two statements mentioned at the beginning of the roof it follows that there exists a value of κ such that centralized and decentralized decision making create the same surlus. Proof of Proosition 5. When the minimum winning coalition is formed by the larger district, then the exected gain from centralizing decision making for an individual in district 1 is ( ) ( ) (1 κ)n1 N (1 κ) ln κ ln κ κ while the exected gain for an individual in district is ( ) ( ) N (1 κ)n1 (1 κ) ln κ ln κ. κ It is straightforward to show that the exected gain for an individual in district is always ositive. When κ = 0, the difference for individuals in district 1 is negative, and when κ = 1/, the gain is ositive. Since individuals in both districts have to choose to centralize, it follows that centralization only takes lace when κ exceeds a threshold value. When the minimum winning coalition is formed by each district with a robability roortional to district size, that is, with robability N 1 / for district 1 and robability N / for district, the exected gain from 0
centralization is (1 κ) ln ((1 κ)n i ) + κ ln ((1 κ)n i ) + N i ((1 κ) ln(κ) + κ ln( κ)) + N i ((1 κ) ln( κ) + κ ln(κ)) κ. It is straightforward to show that this gain is always ositive for κ = 1/. When κ is close enough to 0, however, this difference is negative, while the gain is increasing in κ. It thus follows that centralization only takes lace when κ exceeds a threshold value. When the minimum winning coalition is formed by each district with equal robability, the exected gain from centralization for an individual in district 1 is (1 κ) ln ((1 κ)n 1 ) κ ln ((1 κ)n ) + 1 ln (4κ(1 κ)) κ while the exected gain from decentralization for an individual in district is (1 κ) ln ((1 κ)n ) κ ln ((1 κ)n 1 ) + 1 ln (4κ(1 κ)) κ. For κ = 1, the exected gain from centralization is always ositive for the individuals in district 1, and this gain is increasing in κ. For κ = 0, the difference for individuals in district is negative and for κ = 1, the gain is ositive, while the difference is increasing in κ. Since individuals in both districts have to refer centralization to let centralization take lace, it follows that centralization only haens when κ exceeds a threshold value. With a cooerative legislature, the analysis is the same as in the standard aroach. References [1] Alesina, A., Solaore, E., 1997. On the number and size of nations. Quarterly Journal of Economics 11, 107-1056. [] Alesina, A., Solaore, E., 003. The size of nations. MIT Press, Cambridge, Massachusetts. 1
[3] Baron, D., 1991. Majoritarian incentives, ork barrel rograms and rocedural control. American Journal of Political Science 35 (1), 57-90. [4] Baron, D., Ferejohn, J., 1989. Bargaining in legislatures. American Political Science Review 83, 1181-106. [5] Besley, T., Coate, S., 1997. An economic model of reresentative democracy. Quarterly Journal of Economics 11 (1), 85-114. [6] Bolton, P., Roland, G., 1993. The break-u of nations: A olitical economy analysis. Quarterly Journal of Economics 11, 1057-1089. [7] Bolton, P., Roland, G., Solaore, E., 1996. Economic theories of the break-u and integration of nations. Euroean Economic Review 40, 697-705. [8] Buchanan, J., Tullock, G., 196. The Calculus of Consent. University of Michigan Press, Ann Arbor. [9] Dur, R., Staal, K., 008(Forthcoming). Local ublic good rovision, municial consolidation, and national transfers. Regional Science and Urban Economics. [10] Ellingsen, T., 1998. Externalities vs internalities: A model of olitical integration. Journal of Public Economics 68, 51-68. [11] Ferejohn, J., 1974. Pork Barrel Politics: Rivers and Harbors Legislation 1947-1968. Stanford University Press, Stanford, CA. [1] Ferejohn, J., Morris, F., McKelvey, R., 1987. Sohisticated voting and agenda indeendence in the distributive olitics setting. American Journal of Political Science 31, 167-193. [13] Goyal, S., Staal, K., 004. The olitical economy of regionalism. Euroean Economic Review 48, 563-593. [14] Lockwood, B., 00. Distributive Politics and the Benefits of Decentralization. Review of Economic Studies 69 (), 313-338. [15] Oates, W., 197. Fiscal Federalism. Harcourt Brace, New York. [16] Tiebout, C., 1956. A ure theory of local exenditures. Journal of Political Economy 64 (5), 416-44.
sillover effect centralization desirable and majority voting outcome centralization only socially desirable no centralization size district Figure 1: Individual and social incentives under the standard aroach. 3
sillover effect centralization 1 3 no centralization size district Minimum winning coalition: 1) robability ½; ) robability roortional to district size; 3) the largest district. Figure : Individual incentives with a self-interested legislature (noncooerative). 4
sillover effect centralization 1 3 no centralization size district 1) self-interested legislature (noncooerative); ) benevolent legislature; 3) standard. Figure 3: Comarison of individual incentives. 5