Overlapping soft budget constraints

Journal of Urban Economics 67 (2010) 259–269

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Journal of Urban Economics www.elsevier.com/locate/jue

Overlapping soft budget constraints Marie-Laure Breuillé a, Marianne Vigneault b,* a b

EconomiX and CESAER, INRA, Bld. du Dr. Petitjean, BP 87999, 21079 Dijon Cedex, France Bishop’s University, 2600 College Street, Sherbrooke, Quebec, Canada J1M 1Z7

a r t i c l e

i n f o

Article history: Received 21 December 2008 Revised 4 September 2009 Available online 26 September 2009 JEL Classification: E62 H7

a b s t r a c t Our paper identifies a potential problem with decentralization at a time when its virtues are widely extolled. We show that responsibility for equalization at multi-levels within a decentralized federation creates an overlapping equalization policy that can worsen fiscal discipline. Contrary to Qian and Roland (1998), we also show in our set-up that fiscal competition among regional rescuers does not act as a commitment device to harden the local budget constraint. Ó 2009 Elsevier Inc. All rights reserved.

Keywords: Soft budget constraint Fiscal federalism Capital tax competition

1. Introduction To decentralize or not to decentralize? The question is not an innovative one, at least in a two-tier governmental framework. Decentralization is purported to enhance efficiency when expenditure and taxation decisions are carried out at the level that best respects citizens’ preferences (Tiebout, 1956), but only under conditions that enhance market forces (Weingast, 2009). Decentralization, however, has also been cited as a source of inefficiency when lower-level governments fail to internalize the costs or benefits that their fiscal choices impart on citizens outside of their jurisdictions. The source of inefficiency is that decentralization may encourage opportunistic behavior of lower-level governments and thus may undermine macroeconomic stability. This occurs when lower-level governments have what is called a soft budget constraint when the upper-level government is soft on enforcing its budgetary discipline and would be willing to bail out a lower-level government in the event it cannot meet its fiscal obligations. If this bail out is expected by lower-level governments then they may be induced to manipulate their access to public funds in undesirable ways. The soft budget constraint issue in fiscal federalism has recently been examined both theoretically and empirically.1 The systematic intervention from the top has been attributed by the * Corresponding author. Fax: +1 819 822 9731. E-mail addresses: [email protected] (M.-L. Breuillé), mvigneau@UBishops. ca (M. Vigneault). 1 See Kornai et al. (2003) for a discussion of the soft budget constraint problem in economics and Vigneault (2007) for a survey of the soft budget constraint problem in fiscal federalism. 0094-1190/$ - see front matter Ó 2009 Elsevier Inc. All rights reserved. doi:10.1016/j.jue.2009.09.011

theoretical literature either to the presence of interregional spillovers proportional to the size of the region (the ‘‘too big to fail” argument of Wildasin, 1997) or to an aim of equalization of marginal utilities from public good provision or private good consumption across regions (Caplan et al., 2000; Goodspeed, 2002; Köthenburger, 2004; Breuillé et al., 2006; Akai and Sato, 2008; Akai and Silva, 2009). Empirical evidence suggests that the soft budget constraint problem can be a very serious one for countries where lower-level governments have broad spending and borrowing powers and the central government has the discretionary power to intervene on their behalf (Rodden, 2002; Rodden et al., 2003; Büttner and Wildasin, 2006). The passionate debate among decentralization’s advocates and skeptics has been strikingly restricted to a vertical structure with only one layer of sub-national jurisdiction. Whether more than one layer of sub-national jurisdiction with differing responsibilities affects the advantages or disadvantages of decentralization is still an open question, especially in regard to the incentives to behave strategically. Which layer should collect which taxes? Which layer should provide which public goods? How should intergovernmental transfers be organized? On this last point, we observe in practice a large variety of intergovernmental transfer designs in countries where multiple sub-national levels exist with broad spending powers (Joumard and Kongsrud, 2003; Boadway, 2004). Whereas in some – often centralized – countries, the top level directly allocates transfers to middle and bottom levels, in some others, transfers to the bottom levels pass through the middle levels. The German intergovernmental fiscal transfer system is an example of this latter scheme whereby vertical transfers from the Bund to the Länder parallel those designed by each Land

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authority for its municipalities. These vertical transfers co-exist with horizontal transfers among the Länder governments. Our paper deals with the soft budget constraint issue in a multilevel governmental structure. We assume a multi-tier federation composed of a top layer (central or federal), an intermediate layer (provinces, states or regions) and a bottom layer (cities, municipalities or districts). In our symmetric three-layer framework, transfers are granted according to an overlapping upward equalization scheme. Each region allocates transfers to the cities located in its territory to equalize marginal utilities from the local public good provision. Then, the central government redistributes public funds across regions to equalize marginal utilities from regional public good provision. As in Goodspeed (2002), Köthenburger (2004), Breuillé et al. (2006), equalization schemes in our model constitute an incentive for higher-level governments to provide additional resources to lower-level governments ex post. This incentive limits the efficient management of lower-level jurisdictions (Weingast, 2009). In addition to overlapping equalization schemes, we consider in our model the importance of decentralized leadership vis-à-vis the higher-level governments; that is, we examine regional leadership vis-à-vis the central jurisdiction and local leadership vis-à-vis their regional and central jurisdictions. The redistributive policy is implemented ex post and is anticipated by the beneficiaries when they make their budgetary choices.2 In this setting, the intermediate layer of jurisdiction is both a ‘‘rotten kid” vis-à-vis the top layer and a ‘‘good samaritan” vis-à-vis the bottom layer. By combining these ingredients, i.e. overlapping equalization with decentralized leadership, we obtain an overlapping soft budget constraint problem. Our model of regional decentralized leadership is similar to Köthenburger (2004), with the important difference that the central transfer scheme now also depends on the regional transfer scheme (in addition to regional tax effort). Regions simultaneously choose the tax and transfer policy while fully anticipating how the top layer will respond. Unlike in Köthenburger (2004), we also have cities selecting their (non-distortive) tax policy while fully anticipating both how the regional layer will respond to local decisions and how these regional decisions will affect decisions of the central layer. The first issue examined in the paper is how the overlapping of the equalization policies affects the soft budget constraint issue in a country with decentralized leadership. We show that regional decentralization, i.e. the decentralization of responsibility to the regional governments of carrying out an equalizing transfer policy at the city level, undermines budgetary discipline in a way that worsens the soft budget constraint problem in the country. We observe a kind of snowball effect – the softer the regional budget constraint, the softer the local budget constraint – that is due to the fact that the region is even more generous towards the cities than the central government is towards the region itself. This result holds whatever the assumption on regional taxation, i.e. without regional taxation, with regional lump-sum taxation or with regional tax competition. By extension, increasing the number of layers within a decentralized structure can have a negative impact on budgetary discipline that magnifies the dangers of decentralization, to use the expression of Prud’homme (1995). The second important issue examined in the paper is whether competition among regional rescuers to attract mobile capital acts as a commitment device and hardens local budget constraints. In 2 Local and regional leaderships are particularly appropriate for characterizing the intergovernmental relationships in a bottom-up system, and even more so in a system of multiple mandates. The fact that the regional decision-maker is also a Member of Parliament enables him to expect perfectly the central reaction function. Constitutional reasons, e.g. equalization of living conditions wherever citizens are located like in Germany, or fixed rules of the equalization schemes also allow the infra-layer to anticipate the determinants of the allocation of public funds.

that sense, we challenge Qian and Roland (1998)’s result, according to which decentralization in the presence of regional competition does indeed serve to harden budget constraints at the bottommost tier. Like them, we examine a three-tier framework, but a governmental one: the bottom layer in our model is comprised of local jurisdictions, whereas in theirs it is state enterprises. Like Qian and Roland, our regional government layer competes both for mobile capital and transfers from the central government: regions compete through investment in infrastructure in Qian and Roland and through taxation on capital in our model. In addition, transfers from the central government are allocated according to a net equalization scheme which consists of self-financing region-to-region transfers in both models. Ceteris paribus, competition among regional governments to attract both capital and transfers from the upper-tier reduces the regional spending on the public good, which then raises the opportunity cost of bailout of the lower-tier. Our model is similar to that of Qian and Roland (1998) in important aspects, and yet the results arising from the two models strongly differ. Firstly, Qian and Roland ignore the impact of overlapping soft budget constraints. Qian and Roland’s analysis determines the conditions under which the budget constraint at the bottom-most tier is hard or soft by comparing the exogenous benefit of providing a bailout and the opportunity cost of doing so. Regions are confronted with a binary choice: to give a bailout equal to one or to deny a bailout. By contrast, we endogenously determine the levels of the central and regional bailouts and analyze their impact on regional and local fiscal choices. In our model, the benefit of a bailout of the local government is in the form of increased spending on the local public good, which is determined endogenously and can thus be exploited by the local government in attracting transfers from the regional government. Secondly, and contrary to Qian and Roland’s main finding, we show that tax competition among regional rescuers does not act as a commitment device to harden budget constraints at the bottom-most tier. Whether the bailout to cities is financed by a regional lump-sum tax or a distortive tax on mobile capital has no impact on the inability of the region to commit dynamically not to bail out. Our opposite result is due to the fact that tax competition externalities are perfectly internalized by regions. On the one hand, tax competition externalities on private consumption are neutralized because of the structure of the capital market. We make the standard assumption that capital is owned by the citizens of the country, whereas surprisingly there are no capital owners in Qian and Roland. Although this assumption is a common one (e.g. Köthenburger, 2004), it is not a neutral one because it implicitly implies that citizens are both the owners and users of capital. Consequently, distortive effects through the net return to capital compensate each other. On the other hand, tax competition externalities on regional public good provision are perfectly internalized because of transfers from the central government. Like in Qian and Roland, our transfers from the top are designed to equalize marginal utility from the regional public good consumption countrywide. What is left out in their analysis is that the equalization scheme implemented by the central government insulates regions from harmful tax competition (also pointed out by Köthenburger, 2004). The positive ‘‘competition for capital effect” put forward by Qian and Roland therefore vanishes in our model. The paper is organized as follows. Section 2 presents the basic model of a two-tiered equalization scheme within a three-tiered federation. Section 3 determines the benchmark outcome without decentralized leadership at the regional and local levels. Sections 4–6 all proceed to the analysis with decentralized leadership but under different assumptions regarding regional taxation. In Section 4, we exclude regional taxation to focus on the pure effect of overlapping soft budget constraints. In Section 5, regions levy a

M.-L. Breuillé, M. Vigneault / Journal of Urban Economics 67 (2010) 259–269

lump-sum tax and in Section 6 they levy a regional tax on mobile capital. We compare these two alternative settings with regional taxation to challenge Qian and Roland (1998)’s result. Concluding comments are provided in Section 7. 2. The basic model The model assumes a three-tier intergovernmental structure comprised of a central/federal government, n identical regional/ state governments indexed by i, and, within each region, m identical local/city governments indexed by j. The local government in ij finances a local public good provided in quantity g ij with a lumpsum tax, tij , levied on its immobile citizens and with a transfer from the regional government, sij . The local budget constraint is thus given by:

g ij ¼ tij þ sij :

ð1Þ

The regional government in i provides a regional public good Gi and transfers fsij gj to the cities located within the region. These expenditures are financed with a transfer from the central government, Si . The regional budget constraint is thus given by:

Gi ¼ Si 

X

sij :

ð2Þ

j

Neither cities nor regions are allowed to run a deficit in this one period model, and so public good provision is adjusted so that the budget is balanced. The central transfers are distributed according to a horizontal net equalization scheme, where transfers granted to one region are financed by contributions made by the other regions:

X

Si ¼ 0:

i

Such schemes have been introduced in several countries, e.g. Denmark and Germany (Seitz, 1999), leading at times to serious moral hazard issues. The generality of our results is not affected by the amount of resources devoted to transfers by the central government. In our decentralized three-tier architecture, no budgetary or administrative hierarchical relationship exists between the central and local jurisdictions. The representative household located in city ij derives utility from the consumption of a private good, cij , the local public good, g ij , and the regional public good, Gi , according to the function:

Uðcij ; g ij ; Gi Þ ¼ uðcij Þ þ v ðg ij Þ þ VðGi Þ;

ð3Þ

where uð:Þ, v ð:Þ, and Vð:Þ are assumed to be strictly increasing, twice differentiable, and concave. Private consumption for the representative household satisfies the budget constraint:

e K Pi cij ¼ þ q  tij ; m m

ð4Þ

e K

where m is the household’s exogenous initial capital endowment which can be invested in immobile regional firms to earn a net return q; Pmi is the household’s share of the income generated by the firm located in region i, and t ij is the local/city lump-sum tax.3 Capital is perfectly mobile and moves across regions until the same return q is earned everywhere. The firm in region i produces a homogeneous consumption good according to the production function FðK i Þ, where Fð:Þ is strictly increasing, twice differentiable and concave. The amount of capital K i borrowed by firm in i on the national market is remunerated at the gross rate r i , which, with no capital taxation, in equi3 The number of firms in each region and the number of households in each city are both normalized to one without loss of generality. Our results would be unchanged if we assumed that a unique firm is located in every city rather than in every region.

261

librium must equal the net private return q. Capital is chosen to maximize profits given by

Pi ðr i ; K i Þ ¼ FðK i Þ  r i K i : The resulting demand for capital K i ðri Þ and profit Pi ðri Þ are both decreasing functions of the interest rate ri : K 0i ðr i Þ ¼ F100 < 0 and P0i ðr i Þ ¼ K i < 0. e in the country, equilibFor the exogenous supply of capital n K rium in the capital market is such that the following condition:

X

e; K i ðri Þ ¼ n K

i

is satisfied. Before we proceed to the analysis with decentralized leadership, we first present the outcome of the three-tier architecture without decentralized leadership at the regional and local levels. This outcome will serve as a benchmark for comparison purposes to highlight the impact of overlapping soft budget constraints on the budgetary decisions at the equilibrium. 3. The overlapping HBCs benchmark In the benchmark case, the central government, the n regional governments and the m local governments simultaneously select their budgetary parameters, with each one taking as given the policy choices of the other players. Regardless of the commitment device used by the central (resp. regional) rescuer, the regional (resp. local) government does not manipulate its budgetary decisions in order to attract more transfers. The regional (resp. local) budget constraint is therefore a hard one. The transfers to regions fSi gi chosen by the central government to maximize national welfare PP i j Uðc ij ; g ij ; Gi Þ, equalize the marginal utilities from the regional public good provision; i.e. V 0 ðGi Þ ¼ V 0 ðGi Þ 8i. The transfers to cities fsij gj , chosen by each region i to maximize regional welfare P j Uðcij ; g ij ; Gi Þ, equalize the marginal utilities from the regional and local public good provision in the region; i.e. v 0 ðg i;j Þ ¼ v 0 ðg i;j Þ ¼ mV 0 ðGi Þ 8i; j. Note that in the symmetric equilibrium, Si ¼ sij ¼ 0 8i; j. Each city ij in turn chooses tij to equalize the marginal utilities for private consumption and local public good provision in order to maximize local welfare Uðcij ; g ij ; Gi Þ; i.e. u0 ðcij Þ ¼ v 0 ðg ij Þ. The outcome with overlapping hard budget constraints thus satisfies:

u0 ðcij Þ ¼ u0 ðci;j Þ ¼ u0 ðci;j Þ ¼ u0 ðci;j Þ;

ð5aÞ

¼ v 0 ðg ij Þ ¼ v 0 ðg i;j Þ ¼ v 0 ðg i;j Þ ¼ v 0 ðg i;j Þ;

ð5bÞ

¼ mV 0 ðGi Þ ¼ mV 0 ðGi Þ:

ð5cÞ

4. Overlapping SBCs without regional taxation Regions and cities are now assumed to act as Stackelberg leaders vis-à-vis the higher layer. The diagram below provides a visual description of the overlapping of the equalization policy in the three-tier country. Specifically, regional governments allocate transfers to the local governments within their region to help finance expenditures on the local public good. The central government in turn allocates transfers to the regional governments to help finance expenditures on the regional public good and on transfers to local governments. Neither the central nor the regional governments are able to commit to the level of individual transfers in advance of budgetary decisions of lower-level governments. The timing of decisions is as follows (see Fig. 1). Firstly, local governments simultaneously select their tax policy to maximize the welfare of the representative citizen residing within their city, taking into account the reaction of the regional and central governments. In doing so, they play as Nash competitors vis-à-vis each

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the central best-reply to a change in the regional policy, we differentiate the central government’s first-order conditions with respect to sij ; si;j and Si 8i; i:

Timing of decisions time 1 central jurisdiction

The central level chooses transfers {Si}i for given regions and cities' policy choices.

"

V

00

dSi 

X

Regions simultaneously choose {sij}ij for given cities' policy choices and taking into account {Si}i

m cities in each region

Cities simultaneously select {tij}ij taking into account {sij}ij and {Si}i

(j=1,..m)

Fig. 1. Timing of decisions.

other, but as Stackelberg leaders vis-à-vis the higher layers of government. Secondly, given the local budgetary decisions, the regional governments select their transfers to cities to maximize the welfare of citizens residing within their region, taking into account the reaction of the central government. Regional governments are thus Stackelberg followers vis-à-vis the local governments, Nash competitors with other regional governments and Stackelberg leaders vis-à-vis the central government. Thirdly, the central government allocates transfers to regions to maximize welfare of all citizens countrywide, for given regional and local policy choices. Finally, transfers are paid, taxes are collected, and regional and local public goods are provided as residuals of the budgetary decisions and households consume. We determine the subgameperfect equilibrium by solving the governments’ choice problems backwards; i.e. from the top to the bottom. 4.1. The central government’s problem Given the budgetary choices of regions and cities, the central government designs a transfer scheme for regions to maximize national welfare according to:

j

X

P

i Si ðsij ; si;j Þ

¼ 0 to determine that

ð7aÞ ð7bÞ

4.2. The regional government’s problem The government of region i selects its transfer scheme fsij gj to maximize the welfare of citizens within its jurisdiction. In doing so, it takes into account the central government’s reaction to its choices in the next stage of the game and takes as given the policy parameters chosen by the other regions and the cities. The problem for the regional government is thus to:

X ½uðcij Þ þ v ðg ij Þ þ mVðGi Þ;

si

j

subject to e K  tij ; m m g ij ¼ tij þ sij ; X Gi ¼ b Si  sij ;

Pi

þq

j

þq

expecting the reaction of the central government according to (7a) and (7b). The first-order condition is:

v

j

Si ¼ 0:

i

From the first-order conditions,

V 0 ðGi Þ ¼ V 0 ðGi Þ 8i; i;

8i; i;

The best-reply of central transfers fb S i ðsij ; si;j Þgi depends on regional transfer schemes s. When region i’s government increases its transfer by one dollar to any of the cities within its jurisdiction there is a reduction in funds available for the regional public good. The central government responds to this reduction by cutting all other regions’ transfers by 1n and transfers these funds to region i. Similarly, when another region increases its transfer by one dollar to any of the cities within its jurisdiction, region i’s transfer from the central government is reduced by 1n.

cij ¼

e K  t ij ; m m g ij ¼ t ij þ sij ; X sij ; Gi ¼ Si 

dsi;j

j

@b Si @b Si n1 ¼ ¼ and n @sij @si;j @b Si @b Si 1 ¼ ¼ : n @si;j @si;j

i

Pi

#

Summing, combining equations, and invoking symmetry yields:

subject to cij ¼

dSi 

X

X @Si @Si ¼ : @sij @sij i

X XX ½uðcij Þ þ v ðg ij Þ þ m VðGi Þ; i

dsij ¼ V

j

Max

S

"

00

and use the budget constraint

n regions (i=1,..n)

Max

#

ð6Þ

we see that transfers are allocated to regions so as to equalize marginal utility from the regional public good consumption countrywide which given the symmetry implies that the same amount of public good is provided in every region. This aim of equalization combined with decentralized leadership is the cause of the soft budget constraint problem at the regional level because regions take into account that the central government will respond to their budgetary choices by altering its transfers so that condition (6) holds. They can thus exploit this incentive to their advantage by strategically selecting their policy variables. To derive explicitly

0

" # @b Si þ mV  1 ¼ 0; @sij 0

ð8Þ

which determines the regional government’s reaction function f^sij ðt i1 ; . . . t im ; si Þgj . Solving the first-order condition for all regions simultaneously determines the Nash equilibrium levels of regional transfers. According to (8), each region i determines the amount of the bailout to any city ij to equalize the marginal benefit of a rise in local public good provision and the marginal cost of a reduction in regional public provision, following an increase in sij . Effects of competition for central transfers play an important role on regional choices. Combining the first-order condition (8) with the central government’s aim of equalization V 0 ðGi Þ ¼ V 0 ðGi Þ yields:

v 0 ðg ij Þ ¼ v 0 ðg i;j Þ ¼ v 0 ðg i;j Þ ¼ v 0 ðgi;j Þ;

ð9aÞ

m m ¼ V 0 ðGi Þ ¼ V 0 ðGi Þ: n n

ð9bÞ

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A comparison of the equilibrium with overlapping soft budget constraints (9) with the equilibrium with overlapping hard budget constraints (5) shows that for a number of regions n > 1 , regional decentralized leadership results in too much consumption of the local public goods and too little expenditure on the regional public good. Put differently, the regions overpay transfers to cities. Each region wants to extract as many transfers as possible from the central government and knows that the lower the regional public good, the higher the transfer from the top. The softness of the regional budget constraint leads the region to distort its budgetary choices toward more transfers to cities, reducing Gi , as soon as the cost of the bailout is not entirely born by the region itself that is for n > 1. Note also that the equilibrium with overlapping soft budget constraints (9) fails to equalize marginal utilities of consumption of the private good. We next examine the best-reply of regional transfers to the local governments’ choice of tax rate. Differentiating the first-order condition (8) yields the following system of equations in matrix form:

0

  @b Si 00 m 00 B v  @sij  1 n V B   B @ b  @@sSiji  1 mn V 00

1      1 mn V 00 C v 00 C dsij   dt ij : ¼ C A dsi;j bS i 0 v 00  @s@ i;j  1 mn V 00 



@b Si @si;j

Using Cramer’s rule gives:

b @^sij B ¼ 1 þ 2 ½1; 0; b @t ij det A b B @^si;j ¼ > 0; b @t ij det A

ð10aÞ ð10bÞ

where

#" # # " # @b Si m 00 @b Si m 00 00 v  1 v  1 V V n n @sij @si;j " # " # @b Si m 00 @ b Si m 00 V V  1 1 n n @si;j @sij " # " # @b Si m 00 00 @b Si m 00 00 00 00 ¼v v  1 vV  1 V v > 0; n n @si;j @sij " # b b ¼  @ S i  1 m v 00 V 00 > 0: B n @sij

b¼ det A

"

"

00

Ultimately, all of the policy parameters respond to a change in the local lump-sum tax tij with the aim of equalizing marginal utilities according to condition (9). A change in tij directly affects private consumption (and hence u0 ) and local public good provision (and hence v 0 ). This brings forth changes in sij and si;j (to offset the impact on the local public good provision). Then, changes in sij ; si;j elicit responses from the central government through changes in Si ; Si to keep V 0i ¼ V 0i . All of these responses serve to satisfy the aim of equalization (condition(9)) ex post. An implication we learn from (10a) is that the regional government responds to a reduction in the local government tax effort by raising its transfer, but less than one-for-one. 4.3. Implications of overlapping equalization with SBCs We can use the comparative statics of the regional government’s choice of transfers to local governments to examine in more detail the role of overlapping soft budget constraints. Recall that a local government faces a soft budget constraint when a reduction in its tax effort elicits an increase in the regional government’s @^s transfer, i.e. @tij < 0. The regional government too faces a soft budij

get constraint when an increase in its transfers to local governments elicits an increase in the central government’s transfer, i.e. @b Si > 0 8j. Consider then the following comparative static exercise: @sij 00 bþB b m V 00 v 00 @ @^sij @ @^si;j  mn v 00 V det A n ¼ ¼ 2 b b b @ S i @t ij @ S i @t ij ½det A @ @sij @ @sij     b  mn v 00 V 00 v 00 v 00  @s@ S i  1 mn v 00 V 00 i;j ¼ < 0: b ½det A2

This exercise highlights the role of overlapping transfers schemes in worsening the soft budget constraint problem in the country. The comparative static results above show that the regional government’s incentive to provide additional transfers to cities is worsened when the central government itself is victim of this incentive vis-à-vis regional governments. To summarize, Proposition 1. The softer the regional budget constraint, the softer the local budget constraint. The overlapping equalization policy worsens the soft budget constraint problem in the country, which provides a strong argument against the decentralization of local transfer policy to the regional governments. By extension, we would be able to show that the higher the number of layers, the more severe the soft budget constraint problem in the country. 4.4. The local government’s problem As first players of the game, the local governments select their lump-sum taxes to maximize the utility of citizens within their jurisdiction, while expecting the best-reply of the regional and central governments to their local choices in the next stages of the game. Thus, they take into account the subgame-perfect Nash equilibrium of the sequential game played between the central and regional levels of government. Differentiating Uðcij ; g ij ; Gi Þ w.r.t. tij , we get:

  @Uðcij ; g ij ; Gi Þ @^sij ¼ u0 þ v 0 1 þ @tij @tij "" # # " # b @ Si @^sij X @ b Si @^si;k : þ V0 1 þ 1 @sij @tij k–j @si;k @t ij Invoking symmetry, we then substitute the values for bS i @^s @^s b b ¼ @s@ i;j ¼ n1 ; @tijij ¼ 1 þ B 2 ½1; 0; @ti;j ¼ B > 0, and we n ij det b det b A A simplify as follows:

@b Si @sij

  m @Uðcij ; g ij ; Gi Þ @bs ij 1 X @^si;k ¼ u0 þ v 0 1 þ  V0 n k¼1 @t ij @t ij @tij ¼ u þ v 0

0

! b B 1 0 :  V 1 þ m b n b det A det A b B

Using the condition (9) from the regional government’s problem, i.e. v 0 ¼ mn V 0 , we obtain:

@Uðcij ; g ij ; Gi Þ 1 1 ¼ u0 þ V 0 ¼ u0 þ v 0 : n m @tij

ð11Þ

We learn from (11) the trade-off the local government faces in setting its tax level. In the particular case where m ¼ 1, only one city belongs to the region and, consequently, the soft budget constraint phenomenon plays no role. When m ¼ 1, the local government faces the standard trade-off between increasing private consumption and reducing the amount of local public good when choosing t ij so that

@Uðcij ;g ij ;Gi Þ @t ij

¼ u0 þ v 0 . Regional and local govern-

ments have the same objective to maximize the utility Uðcij ; g ij ; Gi Þ

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of the representative citizen of the unique city ij and the impact of a change in the regional transfer following a change in tij is perfectly internalized by the local government ij. By contrast, when m > 1, the local government in city ij in maximizing the welfare of its own citizens, does not take into account the negative externality it exerts on other cities when reducing its lump-sum tax tij . It thus has an incentive to set an inefficiently low tij . This negative externality clearly worsens when the number of cities increases. For m large enough, there is an incentive to lower t ij until the threshold t ij ¼ 0.4 As a consequence, the local public good is financed entirely by the regional transfer.

5.2. The regional government’s problem Working backwards, we next examine the regional government’s problem in selecting its tax and transfer policy to maximize the welfare of citizens within its region. In doing so, it takes into account the central government’s reaction to its choices and takes as given the policy choices chosen by other regions and the cities. The first-order conditions to this problem for T i and sij 8j, respectively, are:



X

0

u þ mV

j

5. Overlapping SBCs with regional lump-sum taxation

v 0 þ mV 0

We now extend the model to include the role of regional taxation in influencing the incentives for the regional government to soften local budget constraints. Specifically, region i now levies a lump-sum tax, T i , on regional citizens to help finance the transfers to cities within the region and expenditure on the regional public good. Budget constraints are thus modified as follows:

e K  T i  tij ; m m g ij ¼ t ij þ sij ; X sij ; Gi ¼ mT i þ Si  cij ¼

X

Pi

j

i

5.1. The central government’s problem As before, we determine the subgame perfect Nash equilibrium by solving the game backwards, beginning with the central government’s problem. In this extended model, the central government still sets transfers to regions so as to equalize marginal utilities from the regional public good provision, according to condition (6). The S i ðT i ; Ti ; sij ; si;j Þgi now depends best-reply5 of central transfers e both on regional lump-sum taxes T and regional transfer schemes s:

@e Si ðn  1Þm ¼ ; n @T i @e Si m ¼ ; n @T i @e Si @e Si n1 ¼ ¼ ; n @sij @si;j @e Si @e Si 1 ¼ ¼ : n @si;j @si;j

ð12aÞ ð12bÞ ð12cÞ ð12dÞ

The reaction of central transfers to an increase in the lump-sum tax of region i depends both on the size of the regional tax base, m, and the number of regions, n. When the region i’s government increases by one dollar the lump-sum tax levied on each of its citizens, ceteris paribus, the region i’s public good is overprovided in region i. Guided by the aim of equalization among regions, the central government responds by cutting the region i’s transfers in proto affect these funds portion to the regional tax base m by  ðn1Þm n to the ðn  1Þ other regions. The reaction of the central transfers to the regional transfers’ policy is unchanged from the basic model with no regional taxation.

@e Si mþ @T i !

@e Si 1 @sij

!

¼ 0;

¼ 0 8j:

Combining the first-order conditions with the central government’s aim of equalization V 0 ðGi Þ ¼ V 0 ðGi Þ yields:

u0 ðcij Þ ¼ u0 ðci;j Þ ¼ u0 ðci;j Þ ¼ u0 ðci;j Þ; ¼ v 0 ðg ij Þ ¼ v 0 ðg i;j Þ ¼ v 0 ðg i;j Þ ¼ v 0 ðg i;j Þ; m m ¼ V 0 ðGi Þ ¼ V 0 ðGi Þ: n n

þq

Si ¼ 0:

0

ð13aÞ ð13bÞ ð13cÞ

Just as for the case without regional taxation, we learn from a comparison of the equilibrium with overlapping soft budget constraints (13) with the equilibrium with overlapping hard budget constraints (5) that for a number of regions n > 1, regional decentralized leadership results in too much consumption of the local public goods and too little expenditure on the regional public good. The region therefore undertaxes its citizens and overpays transfers to cities knowing that the lower the regional public good, the higher the transfer from the top. Note that in contrast to the model without regional taxation, the addition of a lump-sum tax provides regional governments with an additional policy instrument with which to achieve the efficiency condition u0 ¼ v 0 in the allocation of private and local public good consumption. Turning now to how the regional government adjusts its policy in response to the local tax policy, we differentiate the first-order conditions to obtain6:

e B @~sij < 1; ¼ 1 þ e @tij det A e B @~si;j < 0; ¼ e @tij det A e @ Te i C < 0; ¼ e @t ij det A

ð14aÞ ð14bÞ ð14cÞ

where

e ¼  ðm  1Þ u00 v 00 m V 00 > 0; B "n # " n # " # @e Si @e Si 00 00 00 00 m 00 00 m 00 e 1 v 1 v V  V C ¼ u v v  n n @si;j @sij " # @e Si m þ  1 v 00 v 00 V 00 > 0; n @sij " # " " # e e e ¼ m þ @ S i v 00 v 00 m V 00 þ u00 v 00 v 00  @ S i  1 v 00 m V 00 det A n n @T i @si;j # " # e @ Si m   1 v 00 V 00 < 0: n @sij

4

We implicitly exclude subsidies to citizens ðt ij < 0Þ. Again, the results are obtained by differentiating the first-order condition V 0 ðG Þ ¼ V 0 ðGi Þ and using the central government’s budget constraint P i i Si ðT i ; Ti ; sij ; si;j Þ ¼ 0. Let ‘‘” be the notation used for the model with regional lump-sum taxation to differentiate from the use of the notation ‘‘^” used for the model with no regional taxation. 5

A comparison of (14) when regional governments levy a lumpsum tax to (10) when they do not is revealing. When the regional government levies a lump-sum tax, the adjustment of its transfer 6

See Appendix A for a proof of these results.

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to a change in the local lump-sum tax is greater than one-to-one, whereas it is less than one-to-one in the absence of regional taxation. The reasoning behind this has to do with the central government’s reaction to the regional government’s alteration of tax and spending policy when the local government behaves strategically by lowering its lump-sum tax. That is, a lowering of the local tax induces the regional government to raise its tax, but this, all else equal, induces the central government to lower its transfer to the regional government. To compensate for this, the regional government raises its transfer to the local government in order to induce a sufficiently large increase in the central government’s transfer.

good Gi and transfers fsij gj to the cities located within the region.7 Here, with regional capital taxation, the gross rate ri at which the amount of capital K i borrowed by the firm in i on the national market is remunerated is equal to q þ si . As shown in Section 2, the demand for capital K i ðr i Þ and profit Pi ðr i Þ are both decreasing functions of the interest rate r i . Capital moves across regions in response to tax differentials and relocates until the same post-tax return q is earned everywhere:

5.3. The local government’s problem

@q K0 1 ¼ P i 0 ¼  ; n @ si Ki

We now turn to the problem for local governments in the first stage of the game. Local governments select their lump-sum taxes to maximize the utility of citizens within their jurisdiction, while expecting the best-reply of the regional and central governments to their local choices in the later stages of the game. Differentiating Uðcij ; g ij ; Gi Þ, invoking symmetry, substituting the values for ~ @c @~s @~s e @~ Si @~ Si ¼ @s@ Si ¼ n1 , @Tij ¼ 1, @T ¼  ðn1Þm , @tij ¼ 1 þ B < 1, @ti;j ¼ n n @sij i;j i i ij ij det e A eC eB @e Ti 0 0 m 0 < 0, @tij ¼ < 0 and using u ¼ v ¼ n V from the regional det e det e A A government’s problem we obtain:

"

#





@Uðcij ; g ij ; Gi Þ @ Te i @~sij ¼ u0   1 þ v0 1 þ @tij @t ij @t ij "" # " # @~sij @ ~Si @ Te i @ ~Si 0 þV mþ þ 1 @T i @tij @sij @tij " # # " # e X @ ~Si @~si;k C 0 1 þ ¼u 1 e @si;k @tij det A k–j " # " # e e e B m C 1 m B þ V0 þ  þv 0 e e e n n det A n det A det A 1 v0 ¼ u0 þ V 0 ¼ v 0 þ < 0 for m > 1: n m For m > 1, the derivative of utility with respect to t ij being always negative, the only way to raise utility is to lower t ij until the threshold t ij ¼ 0. As a consequence, the local public good is entirely financed by transfers from the regional government. The intuition for this result is more easily understood by examining the local government’s budget constraint. For m ¼ 1, the representative citizen in ij fully bears the cost of the regional transfers so that the local lump-sum tax and the regional transfer are substitutes in financing the local public good. But when m > 1, there is clearly a preference for the local government to finance the public good solely from the regional transfer because the cost of the transfer to the city ij is partially borne by citizens residing in other cities. This negative vertical tax externality results in an incentive to the local government to reduce its tax effort as much as possible – zero in this case.

q ¼ ri  si ¼ ri  si : P e implicitly The capital market-clearing condition i K i ðri Þ ¼ n K defines the net return to capital qðsÞ, with s ¼ ðs1 ; . . . sn Þ. Differentiating the market-clearing condition yields:

@r i @q n  1 ¼1þ ¼ ; n @ si @ si

i

ð15Þ 6.1. The central government’s problem Again, we solve the game backwards, beginning with the central government’s problem. Given the budgetary choices of regions and cities, the central government designs a transfer scheme for regions to maximize national welfare according to:

X XX ½uðcij Þ þ v ðg ij Þ þ m VðGi Þ;

MaxS

i

j

In this section, we extend our model even further to allow for regional tax competition for mobile capital. Our purpose for doing so is to determine whether, in our set-up, we obtain a result similar to that in Qian and Roland (1998) such that ‘‘fiscal competition among (regional) governments under factor mobility increases the opportunity cost of bailout and thus serves as a commitment device”. Specifically, region i now levies a tax si on the capital K i invested in i to help finance the regional public

i

subject to the following constraints : e K Pi þ q  t ij ; cij ¼ m m g ij ¼ t ij þ sij ; X sij ; Gi ¼ si K i þ Si  X

j

Si ¼ 0:

i

From the first-order conditions, we obtain the same equalization condition as was found in earlier sections:

V 0 ðGi Þ ¼ V 0 ðGi Þ 8i; i;

ð16Þ

which, as we have learned previously, is the cause of the soft budget constraint problem at the regional level because regions take into account that the central government will respond to their budgetary choices by altering its transfers so that condition (16) holds. To derive explicitly the central best-reply8 to a change in the regional policy, we differentiate the central government’s first-order conditions with respect to si ; si ; sij ; si;j and Si 8i; i:

" # X @ si K i @ si K i dsi þ dsi þ dSi  dsij @ si @ si j " # X @ si K i 00 @ si K i dsi þ dsi þ dSi  dsi;j 8i; i; ¼V @ si @ si j

V 00

and use the budget constraint 6. Overlapping SBCs with regional tax competition

@r i @q 1 ¼ ¼ : n @ si @ si





X @Si @Si ¼ ; @ si @ si i



P i Si ðsi ; si ; sij ; si;j Þ ¼ 0. 

X @Sk @Si ¼ ; @ si @ si k–i



and



X @Si @Si ¼ : @sij @sij i

7 We rule out vertical tax competition, which would complicate the analysis without bringing further insights. 8 Let ‘‘” be the notation used for the model with regional capital taxation.

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Summing, combining equations, and invoking symmetry yields9:    @Si n  1 @ si K i @ si K i ¼ þ  < 0; n @ si @ si @ si    @Si 1 @ si K i @ si K i ¼ þ  > 0; @ si n @ si @ si 

ð17aÞ ð17bÞ



@Si @Si n1 ¼ ¼ n @sij @si;j 

and

ð17cÞ



@Si @Si 1 ¼ ¼ : n @si;j @si;j

ð17dÞ

  The best-reply of central transfers Si ðsi ; si ; sij ; si;j Þ depends

of a reduction in private consumption and the marginal benefit of a rise in regional public good provision, following an increase in si . According to (18b), each region i determines the amount of the transfer to any city ij to equalize the marginal benefit of a rise in local public good provision and the marginal cost of a reduction in regional public provision, following an increase in sij . Effects of tax competition and competition for central transfers play an important role on regional choices. To gain more insight into the regional governments’ incentives at the symmetric equilibrium, we simplify the first-order condition for si to yieldce:cross-ref refid="fn10">10:

h i e u0 P0i @@rsii þ @@sqi K u0 ¼  V0 ¼   m 1 þ ei þ m ð1 þ ei ÞK i þ @@ sSi i

i

both on regional tax rates s and regional transfer schemes s. Like Köthenburger (2004), a change in si exerts two opposing effects on the central transfer to region i: on the one hand, any increase in region i’s tax revenues is captured to be redistributed equally among all the regions; on the other hand, any capital outflow from region i, which increases other regions’ tax revenues, is partially compensated by contributions made by the other regions, which ensures the equalization of marginal utilities ex post. When combining these two effects, the global influence of an increase in region i’s tax effort is a reduction in region i’s central transfer, which benefits the other regions. In a standard way, the externalities linked to capital mobility across regions are perfectly internalized by the transfer scheme designed by the top layer. But unlike in Köthenburger (2004), the central transfers also react to the regional transfer policy. As we have already learned in previous sections, when region i’s government increases its transfer by one dollar to any of the cities within its jurisdiction there is a reduction in funds available for the regional public good. The central government responds to this reduction by cutting all other regions’ transfers by 1n and transfers these funds to region i. Similarly, when another region increases its transfer by one dollar to any of the cities within its jurisdiction, region i’s transfer from the central government is reduced by 1n. 6.2. The regional government’s problem Solving backwards, we next examine the problem for the regional governments. The government of region i selects its tax rate si and transfer scheme fsij gj to maximize the welfare of citizens within its jurisdiction. In doing so, it takes into account the central government’s reaction to its choices in the next stage of the game and takes as given the policy parameters chosen by the other regions and the cities. The first-order conditions are:

2 3    1 X 0 0 @ri @ q e @Si 5 0 4@ si K i ¼ 0; K þ mV =si : u Pi þ þ m j @ si @ si @ si @ si 2  3 0 4 @Si 0 =sij : v þ mV  15 ¼ 0; @sij

ð18aÞ

j

ditions for all regions simultaneously determines the Nash equilibrium levels of regional tax rates and transfers. According to (18a), each region i sets its tax rate on capital to equalize the marginal cost 9

We assume that the elasticity of the regional tax base with respect to the regional tax rate, ei , belongs to the interval [1, 0] which is in line with empirical findings (see Chirinko et al. (1999) for instance).

n 0 u; m

ð19Þ

where ei ¼ < 0 is the elasticity of capital invested in region i with respect to region i’s tax rate. Distortive effects – through the net return to capital– on private e ¼ 0 at the consumption compensate each other, i.e. P0i @@sqi þ @@sqi K symmetric equilibrium, which is due to the existence of capital endowments. Without the assumption that capital is owned by citu0 . In addiizens, the first-order condition (19) would be V 0 ¼ n1 m tion, like in Köthenburger (2004), tax competition externalities on regional public good provision are perfectly internalized by transfers from the central government. The expectation of a bailout from the central government forces each region to take into account the impact its tax policy has on other regions, and thus absorbs the distortionary effects of tax competition on regional budgetary choices. These two effects will be crucial for the analysis to follow. Combining the first-order conditions (18a) and (18b) with the central government’s aim of equalization V 0 ðGi Þ ¼ V 0 ðGi Þ yields:

u0 ðcij Þ ¼ u0 ðci;j Þ ¼ u0 ðci;j Þ ¼ u0 ðci;j Þ; ¼ v 0 ðg ij Þ ¼ v 0 ðg i;j Þ ¼ v 0 ðg i;j Þ ¼ v 0 ðg i;j Þ; m m ¼ V 0 ðGi Þ ¼ V 0 ðGi Þ: n n

ð20aÞ ð20bÞ ð20cÞ

As was true for the model with regional lump-sum taxation, a comparison of the equilibrium with overlapping soft budget constraints in the presence of regional tax competition with the equilibrium with overlapping hard budget constraints (5) shows that for a number of regions n > 1 , regional decentralized leadership results in too much consumption of the private and local public goods and too little expenditure on the regional public good. The softness of the regional budget constraint leads the region to distort its budgetary choices toward more transfers to cities and less taxes, both reducing Gi , as soon as the cost of the bailout is not entirely born by the region itself; that is for n > 1. We next examine the best-reply of regional transfers to the local governments’ choice of tax rate. Differentiating the first-order conditions and invoking symmetry yields11: 

@Sij ¼ 1 þ @tij 

which determine the regional government’s reaction functions    si ðt1 ; . . . tm ; si Þ and Sij ðt1 ; . . . tm ; si Þ . Solving the first-order con-

1 @S i eK @ si

¼

@K i si @ si K i



ð18bÞ







< 1;

ð21aÞ

det A



@Si;j ¼ @tij @ si ¼ @t ij

B

B 

< 0;

ð21bÞ

det A 

C 

< 0;

ð21cÞ

det A

h i e ¼ K i ðn1Þ  1 K e e 8i; P0 @ri þ @ q K At the symmetric given K i ¼ K i @ si @ si n  equilibrium,  h i h i n 0 @r i 0 @q @ si K i @S i 1 @ si K i n1 @ si K i 1 1 n1 1 ¼ K i and @ si þ @ si ¼ n @ si þ n @ si ¼ n K i þ n si K i @ si þ n si K i @ si ¼ n K i . 11 See Appendix B for the derivation of these results. 10

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where

2 3   @cij 4 @Si m @ s K @S i i i 00 00 00 5u00 v 00 m V 00 > 0; B¼  15u v þ V 4 n n @ si @sij @ si @ si 2 3 2  3 2  3  @S m @S m i i  15v 00 V 00  4  15v 00 V 00 5 C ¼ u00 4v 00 v 00  4 n n @si;j @sij 2  3 @Si m þ4  15v 00 v 00 V 00 > 0; n @sij 2 3 2 2  3   @ s K @S m @c @S i i ij i i 00 00 00 00 00 00 5v v 4v v  4 þ  15 V u det A ¼ 4 n @ si @ si @ si @si;j 3 2  3 m @S m i v 00 V 00  4  15v 00 V 00 5 < 0: n n @sij 2



3

Similar to the case with regional lump-sum taxation, when regional governments finance their transfers to local governments with both a distortionary tax on capital and transfers from the central government, a one unit decrease in the local lump-sum tax elicits a greater than one unit increase in the regional transfer to the local government. Ultimately, all of the policy parameters respond to a change in the local lump-sum tax t ij with the aim of equalizing marginal utilities according to condition (20). A change in tij directly affects private consumption (and hence u0 ) and local public good provision (and hence v 0 ). This brings forth changes in si (to offset the impact on private consumption) and changes in sij and si;j (to offset the impact on the local public good provision). Then, changes in si ; sij ; si;j elicit responses from the central government through changes in Si ; Si to keep V 0i ¼ V 0i . All of these responses serve to satisfy the aim of equalization (condition (20)) ex post.

consumption compensate each other, and (ii) the fact that transfers to regions are designed by the central government in a way to internalize externalities due to regional tax competition. Indeed, without the assumption that capital is owned by citizens, the first-order conu0 , and would thus differ from the firstdition (19) would be V 0 ¼ n1 m 0 n 0 order condition V ¼ m u obtained in the alternative set-up without tax competition among regional governments. In the same way, without equalization at the regional level, the first-order condition (19) would be V 0 ¼ ð1þ1ei Þm u0 , and would also differ from the first-order condition V 0 ¼ mn u0 . The positive ‘‘competition effect” put forward by Qian and Roland has thus disappeared because of the existence of both capital endowments and equalizing transfers to the regional rescuers. 6.4. Implications of overlapping equalization with SBCs We now use the comparative statics of the regional government’s choice of transfers to local governments to examine in more detail the role of overlapping soft budget constraints with regional tax competition: 



ij

00





v 00 mn V 00 det A  B @c@s    2 det A

ij







ij i

u00 v 00 mn V 00

< 0;



00 00 @ @Sij @ @Si;j u00 v 00 mn V det A  B v 00 v 00 mn V ¼  ¼ < 0;  2   @t @tij @ @@ sSii ij @ @@sSii det A    00 00 m 00 @c  u v n V þ v 00 v 00 mn V 00 det A  @ siji C u00 v 00 mn V 00 @ @ si ¼ > 0;     2 @ S i @t ij @ @s det A ij 



6.3. Comparison with Qian and Roland (1998)   From a comparison of the best-reply Sij when regional trans-

@cij

@ @Sij @ @Si;j @ si u ¼  ¼  @t @ Si @S i @t ij ij @ @s @ @s

00

@ @ si  C v 00 v 00 mn V ¼  > 0:    2 @t @ @@ sSii ij det A

j

fers are financed by a tax on mobile capital (21) with the best-reply f~sij gj when regional transfers are financed by a lump-sum tax (14), we are able to state that tax competition among regions has no impact on the opportunity cost of the regional bailout provided to   cities for the case where u00 ð~cij Þ ¼ u00 ðc ij Þ, v 00 ðg~ij Þ ¼ v 00 ðg ij Þ, 00 e 00 V ð G i Þ ¼ V ðGi Þ, which is satisfied under the assumption that the third derivative of the utility functions uð:Þ; v ð:Þ and Vð:Þ is nul. In e we can show that12: deed, using the result that det A ¼ Kmi det A 

All of the comparative static results above show that the regional government’s incentive to provide additional transfers to cities is worsened when the central government itself is victim of this incentive vis-à-vis regional governments. Thus, proposition 1 from the model without regional taxation applies just as well to this model with regional tax competition. Note that from (22) it also applies to the model with regional lump-sum taxation. 6.5. The local government’s problem

@~sij @Sij ¼ ; @t ij @tij

ð22aÞ



@~si;j @Si;j ¼ ; @t ij @tij

ð22bÞ



@ Te i K i @ si ¼ ; @t ij m @t ij

ð22cÞ

which can be summarized by the following proposition:

We now turn to the problem for local governments. As first players of the game, the local governments select their lumpsum taxes to maximize the utility of citizens within their jurisdiction, while expecting the best-reply of the regional and central governments to their local choices in the next stages of the game. Differentiating Uðcij ; g ij ; Gi Þ, invoking symmetry, substituting the  h i     @S @ Si Si  @@ssi Ki i þ @ s@isKi i , @s ¼ @s@i;j ¼ n1 , @tijij ¼ 1 þ B , values for @@ sSii ¼ n1 n n ij det A

Proposition 2. The amount of the bailout to cities is the same whether it is financed by a regional lump-sum tax or a regional tax on mobile capital. Contrary to Qian and Roland (1998), in our set-up, horizontal tax competition among the rescuers does not harden the budget constraints of the bottom-most tier. This (apparently surprising) result is explained by (i) the assumption that capital is owned by citizens, which implies that distortive effects of tax competition on private 12

See Appendix C for a proof these results.



@ S i;j @t ij



¼

B







det A

,

@ si @t ij

¼

C



, and using u ¼ v ¼ 0

0

det A

m 0 V n

from the regional gov-

ernment’s problem we obtain again:

@Uðcij ; g ij ; Gi Þ v0 ¼ v 0 þ < 0 m @tij

for m > 1:

Thus, as is true for the model with regional lump-sum taxation examined in Section 5, when m > 1, local governments still have an incentive to lower their lump-sum tax until the threshold tij ¼ 0 due to the presence of the negative tax externality.

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Note that, contrary to Qian and Roland who assume that the benefit of the bailout is a fixed/exogenous amount that the state enterprise receives, the benefit of the local bailout in our model is endogenous and increases in the marginal utility of the local public good. The local government has thus an incentive to exploit this by making the marginal utility increase very high by not supplying any local public good at all with its own taxes. They then know that the benefit of increased regional transfers will exceed the cost in terms of lower regional funds available for the regional public good. Finally, under a hard budget constraint at the regional level or 

equally in the absence of a central government (i.e. when @@sSii ¼ 0   @ Si ¼ @s@ Si ¼ 0Þ, we can show that the first-order conditions that and @s ij

i;j

determine the regional choices are as follows:

=si :

    1 X 0 0 @ri @ q e @ si K i K þ mV 0 u Pi þ ¼ 0 () u0 ¼ mV 0 ½1 þ ei ; m j @ si @ si @ si

=sij : v 0 ¼ mV 0 : @Uðc ;g ;G Þ

ij ij i For this case we have ¼ v 0 ½1 þ ei  þ vm, and there @t ij would then be two competing influences on the local government’s choice of tax policy. The first influence arises from the negative vertical tax externality described above when m > 1, which serves to reduce the local government tax effort. This influence is present regardless of whether the central government faces a hard or soft budget constraint problem, or indeed even regardless of the presence of the central government at all. The second influence is the positive horizontal tax externality arising from capital tax competition amongst regional governments. This latter effect results in lowering regional tax effort, and thus reduces the incentive of the regional government to soften the local budget constraint. Note that this tax externality effect is only important for local government incentives in the absence of the central government or if the budget constraint of the regional government is hard. Otherwise, the central government, with its transfers, negates any influence of tax competition on the regional government’s incentives. 0

would be a multi-period setting where lower-level governments have the ability to borrow as well as tax to finance their expenditures. Both theoretical and empirical analyses have examined the impact of borrowing on fiscal discipline, and have shown that it can worsen the soft budget constraint problem. Further work could also examine how the type of transfer scheme affects fiscal discipline in a multi-tier setting. In our set-up, an equalization scheme worsens the soft budget constraint problem. Would other transfers schemes have similar effects? Furthermore, do the benefits of equalization schemes in equalizing net fiscal benefits outweigh the costs in worsening strategic behavior? An important task for future work is to delve deeper in examining why the incentive for higher-level governments to provide additional transfers is strong in many federal systems. If the soft budget constraint problem is so detrimental, then why do we observe it occurring in many federations? Are there instances where welfare is improved ex ante as well as ex post when higher-level governments have the discretion to intervene on behalf of lowerlevel governments? Besfamille and Lockwood (2008) provide an analysis of when it is. They find that hard budget constraints negatively impact lower-level governments’ effort in affecting the probability that projects succeed. Future research must explore further the issue of whether hard budget constraints are necessarily indeed superior to soft ones. Acknowledgments We thank Robin Boadway who suggested this collaboration, Thiess Büttner, participants at the WZB Seminar, Public Economic Seminar CES-ENS Cachan, Seminar für Dynamische Modellierung in Munich, PET08, SBC Workshop in Osaka and PGPPE Workshop in Bonn, William Strange, and two anonymous referees for useful comments and suggestions. The financial support of the Agence Nationale de la Recherche and the Deutsche Forschungsgemeinschaft (through COMPNASTA) is acknowledged. Appendix A

7. Concluding remarks An important challenge for policymakers in achieving budgetary efficiency in multi-level fiscal systems is the design of a territorial architecture that can achieve the benefits of decentralization while avoiding its dangers. A common source of inefficiency comes from the incentive to behave strategically on the part of lower-level governments in extracting additional resources from higher-level governments. This paper has examined the soft budget constraint problem in a multi-tier federal system, and has shown that decentralized leadership in combination with overlapping equalization schemes can serve to worsen the soft budget constraint problem. In our three-tier set-up, local governments expect additional resources from their respective regional government, knowing that the central government will in turn have an incentive to respond with additional resources to the regional government. In this setting, the higher-level governments’ discretion over transfer policies can severely affect fiscal discipline in a federation. We have also shown that tax competition among regional governments to attract mobile capital has no impact on fiscal discipline because central transfers are designed to induce regional governments to internalize the externalities arising from tax competition. Our model is a simple one that is meant to highlight the role of overlapping equalization schemes in providing incentives for fiscal indiscipline. In our set-up, lower-level governments finance their expenditures through taxation and equalizing transfers from the higher-level government. An obvious extension of our model

Differentiating the FOCs w.r.t. tij ; t i;j and T i ; sij ; si;j

" # X m 00 @e Si @e Si @e Si dT i þ dsij þ dsi;j  dsij V mdT i þ n @T i @sij @si;j j ¼ u00 ½dT i  dt ij 

v

00

" m 00 @e Si @e Si @e Si ½dt ij þ dsij  ¼ V mdT i þ dT i þ dsij þ dsi;j n @T i @sij @si;j # X  dsij j

"

v

00

dsi;j

X m @e Si @e Si @e Si ¼ V 00 mdT i þ dT i þ dsij þ dsi;j  dsij n @T i @sij @si;j j

#

and simplifying it, given the symmetry, yields the following system: 0 1      @e S i m 00 @e Si @e Si 00  1 mn V 00  1 mn V 00 C B m þ @T i n V þ u @sij @si;j B C B  C      B C e e e 00 00 00 @ S @ S @ S 00 m m i i B  m þ i mV C v   1 V   1 V n n @T i n @sij @si;j B C B C      B  C @ A @e S i m 00 @e Si @e Si m 00 00 m 00  m þ @T i n V  @sij  1 n V v  @si;j  1 n V 0

dsi

1

0

u00

1

B C B C  @ dsij A ¼ @ v 00 Adt ij : dsi;j

0

We compute the reaction function with the Cramer’s rule. Q.E.D.

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M.-L. Breuillé, M. Vigneault / Journal of Urban Economics 67 (2010) 259–269

@ si ¼ @tij

Differentiating the FOCs w.r.t. t ij ; ti;j and si ; sij ; si;j : 2 3    X m 00 4@ si K i @Si @Si @Si dsi þ d si þ dsij þ dsi;j  dsij 5 V @ si @ si @sij @si;j n j   @cij dsi  dt ij ¼ u00 @ si 2    m 00 4@ si K i @Si @Si @Si 00 v ½dtij þ dsij  ¼ V d si þ dsi þ dsij þ dsi;j @ si @ si @sij @si;j n # X  dsij j

v 00 dsi;j ¼

2





   @c @ Si m 00 þ @ ½Si @ si  mn V 00  u00 @ sij  1 V n @sij i B     B   B  @@ssi K i þ @@ sS i mn V 00 v 00  @s@Siji  1 mn V 00 B i i B B      @ @S i m 00  @@ssi Ki i þ @@ sSii mn V 00  @s  1 V n ij 0 1 0 00 1 dsi u B C B C  @ dsij A ¼ @ v 00 Adt ij : @ si K i B @ si

dsi;j





@ Si @si;j

1







m 00 V n

1



0

Appendix C Substituting the values of the best-reply of the central government with regional tax competition (7) and without regional tax competition (12) in the respective best-reply of the regional government: ðm1Þ 00 u n

v 00 mn V 00

e det A

;

00 ðm1Þ @Sij K i  n u00 v 00 mn V ¼ 1 þ ;  @tij m det A   @~si;j 1 ðm  1Þ 00 00 m 00 ¼  u v V ; e n n @tij det A    @Si;j 1 Ki ðm  1Þ 00 00 m 00 ¼ v u V  ;  n n @t ij m det A e @ Te i C ; ¼ e @t ij det A



@ Te i K i @ si ¼ : @t ij m @tij

References

We compute the reaction function with the Cramer’s rule. Q.E.D.

 @es ij ¼ 1 þ @t ij



@es i;j @Si;j ¼ ; @t ij @tij

Q :E:D:

C C C @ Si m 00 C  @s  1 n V C i;j C C    A @ Si 00 m 00 v  @si;j  1 n V 

;

@es ij @Sij ¼ ; @tij @tij

X m 00 4@ si K i @Si @Si @Si dsi þ dsi þ dsij þ dsi;j  dsij 5 V @ si @ si @sij @si;j n j

0



det A 

3



C

  e i Þ ¼ V 00 ðGÞ, which and assuming u00 ð~cij Þ ¼ u00 ðc Þ, v 00 ðg~ij Þ ¼ v 00 ðg Þ, V 00 ð G i ij ij is the case for the third derivative equal to 0, we obtain  Ki e det A ¼ m det A, which as a consequence leads to:

and simplifying it, given the symmetry, yields the following system:







Appendix B

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