Are Hard Budget Constraints for Sub-National GovernmentsAlwaysEfficient?

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1 Are Hard Budget Constraints for Sub-National GovernmentsAlwaysEffiient? Martin Besfamille Ben Lokwood Otober 1, 004 Abstrat In fisally deentralized ountries, sub-national governments (SNGs) may fae soft budget onstraints and onsequently invest and borrow too muh. The poliy literature laims that, with ompetitive apital markets and entral governments imposing hard budget onstraints (HBCs), ineffiient investment by SNGs should not arise. We present a model where this is not the ase: HBCs an be too "hard" and disourage investment that is soially effiient. The model ombines a dynami ommitment problem as in Kornai, Maskin and Roland (004) for entral government with a moral hazard problem between entral and SNG. The HBC over-inentivises the SNG to provide effort by penalizing it too muh for projet failure, thus leading ultimately to the possibility that soially effiient projets may not be undertaken. Keywords: Fisal federalism - Bailouts - Hard budget onstraints. We thank F. Alvarez, L. Arozamena, A. Neumeyer, A. Trannoy, I. Werning for their onstrutive suggestions and seminar partiipants at APET (Beijing, 004), CSGR (University of Warwik) and Universidad Toruato Di Tella. This paper started when M. Besfamille visited CSGR, whose hospitality and finanial support is gratefully aknowledged. Department of Eonomis, Universidad Toruato Di Tella, Ciudad Autonoma de Buenos Aires, Argentina. mbesfamille@utdt.edu CEPR and Department of Eonomis, University of Warwik, Coventry CV4 7AL, England. B.Lokwood@warwik.a.uk 1

2 1 Introdution Fisal deentralization, the alloation of tax and spending powers to lower levels of government, is now an established poliy objetive, in many developed and developing ountries. Moreover, it is atively promoted as a development strategy by organizations suh as the World Bank (Azfar et al. (001), World Bank (000)). The usual advantages that are laimed for deentralization that one an find in the literature inlude the following (Azfar et al. (001), Oates (1999)). First, deentralization is laimed to improve alloative effiieny, in the sense that the goods provided by governments in loalities will be better mathed to the preferenes of the residents of those loalities. Seond, deentralization is argued to inrease the aountability of government. There is now a growing theoretial and empirial literature 1 evaluating these laims. However, it is inreasingly laimed that one of the osts of fisal deentralization is that entral government may lose ontrol over aggregate government borrowing. In partiular, it is thought that if subnational governments (heneforth regional governments, RGs) fae soft budget onstraints, they will have an inentive to over-borrow, and/or pay insuffiient attention to the quality of the investments that their borrowing finanes. For example, Ter- Minassian, Albino-War, and Singh (004) say; "Over the last two deades, the deepening of the deentralization proess has resulted in many ountries in a signifiant inrease in subnational publi expenditure and debt." The "ommon pool" mehanism by whih over-borrowing an our has also been explored quite thoroughly in the aademi literature (for example, Wildasin (1997) and Goodspeed (00)). The ommitment of entral government (CG) to bail out RGs who annot pay reates a negative externality if - as is usual - the ost of bailout is met through inreases in taxes or redutions in spending nationally: other regions will partially finane one region s bailout. In turn, this indues exessive borrowing initially. However, in both the existing aademi and poliy literature, it is universally assumed that beause of this externality, a hard budget onstraint (HBC) for RG is always desirable. Indeed, muh of the literature is onerned with the design of institutional mehanisms that will harden the budget onstraint (Rodden, Eskeland, and Litvak (003)). It is the purpose of this paper to take issue with this presupposition; we would argue that in some irumstanes, a HBC is too "hard". 1 The theoretial literature evaluating the preferene-mathing argument inludes Alesina and Spolaore (1997), Besley and Coate (003), Ellingsen (1998), Lokwood (00), Oates (197), and Wallis and Oates (1988), while empirial ontributions are fewer, but inlude Oberholzer-Gee and Strumpf (00) and Faguet(004). Theoretial analysis of the aountability argument inludes Seabright (1996) and Bardhan and Mookherjee (1998, 000). Emprial ontributions inlude Fisman and Gatti (000), Galiani, Gertler and Shargrodsky (004), Hutter and Shah (1998), Melo and Barenstein (001), and Treisman (00). Probably the best general definition of a soft budget onstraint (SBC) is that of the survey by Kornai, Maskin and Roland (004) in the Journal of Eonomi Literature: "A budget-onstrained organization faes a hard budget onstraint (HBC) as long as it does not reeive support from other organizations to over its defiit and is obliged to redue or ease its ativity if the defiit persists. The SBC phenomenon ours if one or more supporting organizations are ready to over all or part of the defiit."

3 Our argument is the following. First, by definition 3, a HBC neessarily implies that "bad" investment projets will be terminated, when ex post, it would be desirable to ontinue them though additional finaning. Now suppose that by exerting some effort, RGs an lower the probability that projets are "bad". Then, with a HBC, RGs are over-inentivised to provide effort, as the payoff to the RG in the event of a bad projet is exessively low. Thus, effort exerted may be ineffiient. More importantly, when this is the ase, some projets will not be initiated in the firstplae,evenwhenitiseffiient to do so. So, a HBC may lead to underinvestment. In more detail, in our model, RGs have the option of hoosing to initiate a disrete projet or not. The initial ost of the projet is overed by the finanial resoures of the RG e.g. tax revenue. The projet may be good or bad. The probability that the projet is bad is determined by effort expended by regional government, one the initial investment in the projet is made. Effort may be high, in whih ase the projet is always good, or low, in whih ase the projet is bad with a positive probability. If it is good, it immediately generates a non-monetary benefit for the region greater than the ost. If it is bad, it generates no benefit unless additional resoures are invested. If these resoures are invested, the projet pays a non-monetary benefit to the region greater than the additional resoure ost, but less than the total resoure ost. Thus, there is a dynami ommitment problem. The effort of RG, and the resulting type of projet in any region (good or bad) may be observable by entral government (or CG), but is not verifiable, in the sense that entral government annot ondition any inentive sheme for RG on these variables. Our preise definition of HBC and SBC in this setting is as follows. It is assumed that at the point at whih a bad projet needs to be refinaned, neither regional nor entral government have any tax revenues available, but the RG an borrow from a ompetitive banking setor. When the loan is due for repayment, only entral government has the fisal apaity to make the repayment, by levying a national inome tax. A SBC is in plae when (i)cgallowsthergtoborrowand (ii) it is willing to repay any loans by levying an inome tax. A HBC is in plae 4 when either (i) CG forbids the RG to borrow (rules-based HBC) or (ii) the CG preommits not to repay any loans inurred by RG (market disipline HBC). In this setting, with a SBC, loal governments have insuffiient inentives to put in high effort (effort too low) for projet implementation, and also may initiate projets when it is ineffiient to do so ("too many" projets), beause the ost of refinaning a bad projet is shared with other regions though the tax system. This point is well-understood and has 3 As stressed by Kornai, Maskin and Roland (004), a dynami ommitment problem (where ex ante, bad projets are undesirable, but ex post, it is effiient to refinane them) is a neessary ondition for a SBC to be ineffiient, and thus for there to be a SBC problem in the first plae. 4 This follows Ter-Minassian (1997), who makes the distintion between a rules-based and market disipline HBCs. The first is the imposition of rules on borrowing, ranging from an outright ban on borrowing by RG, to weaker restritions, suh as borrowing only to fund investment, or imposing a maximum debt-servie to inome ratio. The seond involves giving RGs free aess to apital markets, along with preommitment by entral government not to repay any loans inurred by RGs that RGs are unable or unwilling to repay (see also Lane (1993)). 3

4 been argued formally e.g. by Wildasin (1997). Our new point, as mentioned above, is that with a HBC, loal governments have exessively strong inentives to put in high effort (effort too high), and also may not initiate projets when it is effiient to do so ("too few" projets). The reason is the following. One a projet turns out to be bad, it is ex post effiient to omplete it. But, with a HBC, the bad projet is terminated. Thus, with a HBC, the net benefit toaregionfromabadprojet is ineffiiently low. Thus, the RG government has too high an inentive to put in high effort. In turn, this implies that a projet may give the RG a negative payoff (takingintoaount the ost of effort) even when its true soial benefit is positive. This key point is made via a numerial example in the next setion. Relatedliteratureisdisussedmorefullybelow,buthereitisworthpointingoutthatour results are related to, but also distint from, the literature on rules vs. disretion 5.Inthat literature, a poliy variable an be set by government either ex ante i.e. before the realisation of some stohasti shok or ex post. An ex ante setting (a poliy rule) has the disadvantage that it annot be onditioned on the shok (lak of flexibility) but the advantage that it prevents a sub-optimal response by either the private setor or a lower level of government (preommitment). In our model, a HBC (SBC) ould be interpreted as a rule (disretion). It is ertainly true that a HBC is inflexible, as it prevents an ex post optimal response in the event of a bad shok i.e. if the projet turns out to be bad. But, the HBC does not indue an effiient response by RG - effort will generally be too high. The layout of the remainder of the paper is as follows. Setion has a numerial example. Then, Setion 3 presents the model and the effiient benhmark. Setion 4 ontains the main results, Setion 5 onsiders full entralization and deentralization as solutions, and Setion 6onludes. An Example The key point of this paper an be illustrated by a simple example. We deliberately keep the example general so as to emphasize that our point has appliations outside fisal federalism. Consider an "agent" (here, the RG) who an hoose an initial binary investment in a projet at ost 1. The agent then an hoose a low effort level (normalized to zero) or a high effort level (normalized to 1). The ost of low effort is zero to the agent, whereas the ost of high effort is 0.8. If effort is high, the projet immediately realises a benefit of with probability 1. If effort is low, the projet realises a benefit (for the agent) of with probability 0.5, and no benefit with probability 0.5. However, in this event (i.e. if the projet turns out to be "bad") if an additional investment of 1 is made, a benefit of 1.5 for the agent is then realized. The prinipal (here, the entral government) only has the role of deiding whether to allow an additional investment to be made. If he does (does not) we say that there is a soft (hard) budget onstraint. Finally, for onsisteny with the more general model that follows, 5 A paper on fisal federalism that fits muh more into the rules vs. disretion framework is Sanguinetti and Tommasi (004). See Setion 6 below. 4

5 we suppose that the ost of the additional investment is shared equally between the prinipal and agent. Consider first what the effiient investment and effort, and refinaning deision is. First, if effort is high, the payoff is. If effort is low and the projet turns out to be bad, refinaning is ex post effiient, in whih ase the expeted payoff is (1.5 1) = 1.5. So, the gain to high effort over low is 0.75, whih is less than the ost of effort. So, low effort is effiient. Given that low effort is effiient, the ex ante payoff to the projet (when the deision about initial investment is made) is 1.5, greater than the initial ost. So, initial investment in the projet is effiient. Now onsider the outome with a hard budget onstraint. First, if effort is high, the payoff is. If effort is low and the projet turns out to be bad, refinaning is impossible, in whih ase the expeted payoff is =1. So, the gain to high effort over low is 1, whih is greater than the ost of effort. So, high effort will be hosen. Given this, the ex ante payoff to the projet (when the deision about initial investment is made) is 0.8 =1., greater than the initial ost. So, initial investment in the projet will our. So, we see that a hard budget onstraint indues an effort distortion (too muh effort) beause the payoff to the "bad" projet is "too low". This is beause the HBC does not allow ontinuation of the bad projet, replaing a payoff of 0.5 with one of 0. There is also another possible onsequene of the HBC. Suppose now the initial ost of the projet inreases from 1 to 1.3. Then, it is still effiient to undertake the projet, but in equilibrium with the HBC, the projet will not be initiated, as the expeted payoff from doing so is 1. < 1.3. So, the ineffiieny generated by the HBC may be in the form of exessive effort or underfunding of projets. Note here that there is nothing unusual or pathologial about our definition of the HBC -itisexatly 6 as in Kornai, Maskin and Roland (004). Note however, that although our definition of the HBC is effetively idential to that of Kornai, Maskin and Roland (004), our findings about the eonomi onsequenes about the HBC are rather different. At the heart of their model (whih enompasses a number of speial ases already in the literature), there is a problem of hidden information; the agent has the authority to hoose projets, and he knows whih are good and whih are bad, whereas the prinipal does not. In that setting, a HBC always restores effiieny, as it deters the agent from hoosing a bad projet. By ontrast, in our model, there is a problem of hidden ation: the prinipal would like to inentivise the regional government to put in high (or low) effort in ertain situations (see Proposition 1 below), but annot offer an expliit inentive ontrat to ahieve this. The hoie of HBC or SBC is too blunt an instrument to orretly inentivise the agent. Of ourse, if the prinipal ould make expliit payments to the agent onditional on the projet outome, as in the lassial prinipal-agent literature, then effiieny ould be restored. For example, if the prinipal ould ombine the SBC with a penalty if the projet turned out to be bad, then the penalty an be set so that effort will be effiient: this is disussed in more detail below. But if payments onditional on projet outomes are possible, 6 Here, the budget-onstrained organization is regional government, and the supporting organization is entral government. 5

6 then the distintion between hard and soft budget onstraints disappears. Moreover, these payments are not observed in pratie between CG and RGs. 3 The Model 3.1 Preliminaries The model has three periods t =0, 1, and two regions, i = a, b. Eah region has a ontinuum of residents of measure 1. In the last period, eah resident derives utility from onsumption of a numeraire good, whih is produed in either region from labor input by ompetitive firms using a onstant-returns tehnology, where units are hosen so that one unit of labor produes one unit of output. So, the wage is fixedatunity. Eahresidentisendowedwith one unit of labor whih it an supply to firms in that region. Residents may also benefitfrom publi projets provided by the regional government. There are two levels of government, entral (CG) and regional (RG). There is no disounting of future payoffs. 3. The Order of Events The order of events, and relevant features of the model in more detail, are as follows. t =0 1. The entral government deides whether to set a SBC or a HBC. A SBC is in plae when (i) CG allows the RG to borrow and (ii) it is willing to repay any loans by levying an inome tax. A HBC is in plae when either (i) CG forbids the RG to borrow (rules-based HBC) or (ii) the CG preommits not to repay any loans inurred by RG (market disipline HBC). t =1 1. The regional government of i hooses whether or not to finane a projet in its region, by making an investment of of the numeraire good. Without any real loss of generality, we assume that regional government of i has an initial endowment of only, so that any additional investment will need to be externally finaned.. If the projet is initiated, the regional government exerts effort e i {0, } on its implementation. If region i exerts effort e i =, the projet will be good. If e i =0,the projet is good with probability p and bad with probability 1 p. t = 1. The projet type (good or bad) in region i is revealed to the regional government of i and the entral government. If the projet in region i is good, it generates a non-finanial benefit for all the residents of region i of b g. If the projet is bad, it generates no benefit at this date, but requires an additional input of in order to be ompleted. 6

7 . If a SBC has been set, finane is provided 7 by a ompetitive banking setor, omprising profit-maximising, risk-neutral banks, with free entry into the setor. A bank k N = {1,,..n} offers a loan to finane the projet ontinuation and demands repayment r k i. Then, ompetition among banks, plus no disounting, will ensure that r k i =. The regional government either borrows to finane ontinuation, or hooses not to ontinue with the projet. If the projet is terminated, the payoff to the projet is zero. If ontinued, the bad projet pays a non-finanial benefit for all the residents of region i of b b. If a HBC has been set, the projet is terminated. 3. If a SBC has been set, the entral government sets an inome tax at rate τ to finane the total repayment r of the loans taken out by the regional governments, if any. Following an extensive literature, the entral government is assumed to set a uniform tax rate in both regions i.e. τ = τ a = τ b. As the total tax base is simply the aggregate pre-tax wage bill of, thebudgetonstraintoftheentralgovernmentisτ = r. The timing and struture of the model are depited in Figure 1. e = b g Choie of budget onstraint regime Initial investment e = 0 p 1 p b g Refinaning Bailout No Bailout τ b b 0 Termination 0 t = 0 t = 1 t = Figure 1: Timing and struture of the model For the rest of the paper, we onentrate our attention on projets satisfying 0 < b b <<b b <b g These inequalities imply that the projets we deal with are suh that the entral government faes a dynami ommitment problem if no effort is made: that is, a bad projet is ineffiient 7 Note that with a market disipline HBC, the RGs are free to borrow from the banking setor, but the banks are unwilling to lend, as the rationally antiipate not being repaid. 7

8 ex ante, but one initiated, it is ex post effiient to refinane it. Moreover, the projet yields higher benefits if it is done with effort than if it is undertaken with no effort and refinaned. We an interpret this lower benefit as the onsequene of the delay in finishing the projet. We also assume that projets are idential between regions. By idential projets we mean: same ost, same values of benefits (b b,b g ), same ost of effort and same probability of having a bad projet after no effort. Throughout, we assume that governments are benevolent i.e. both regional and entral governments maximize the sum or average of the welfares of the residents of their jurisditions, minus the ost of effort (if any). For simpliity, we take the ost of effort e to be e itself. 3.3 Disussion There are four deisions that either level of government must make in this model: whether to finane the projet at the beginning of t = 1, the efforttobeexpendedonprojet implementation, whether to ontinue the projet (given the menu of loans on offer from the banks) and the setting of the taxes at the end of t =. In the model exposited above, we have assumed that regional governments make initial investment deisions and projet implementation and entral government authorizes the ontinuation borrowing and makes the tax deision. This desribes the situation in many ountries very well. For example, in a detailed survey of fifteen ountries, Ter-Minassian, Albino-War, and Singh (004) found that in seven of them, regional governments had (at some time) been subjet to entrally imposed fisal rules on debt, borrowing, et. So, it is a widely observed pratie for governments to onstrain the borrowing of sub-entral government: this orresponds to our definition of the HBC. Also, in most of the remaining ountries, borrowing limits of sub-national government have been ooperatively negotiated with entral government, and in many ases, enfored by market-based disipline. In our model, ex post i.e. one the projet is initiated, national and regional governments have the same preferenes vis-à-vis projet ontinuation, so ooperative bargaining (more of less however it is modelled) would lead to a deision to ontinue the projet i.e. a SBC. We all this senario divided government and it will be the fous of our analysis. Other forms of government are onsidered in Setion 6 below. 3.4 The Effiient Poliy Consider a soial planner who an make all the deisions that are above divided between the two levels of government i.e. (i) whether to undertake the projet initially; (ii) the level of effort for projet implementation in either region, and (iii) an deide whether to ontinue the bad projet after the first period or not. If ontinuation is hosen, it must be finaned by borrowing from a bank. We assume that the soial planner has the same objetive as that of entral government i.e. the sum of the welfares of the two regions, and moreover, the soial planner is assumed to fae the same informational onstraint as entral government and regional government i.e. he observes the projet quality only after effort is hosen. 8

9 Solving the soial planner s deision problem bakward, first, note that given that a bad projet annot be identified until the projet is funded and effort is exerted, ontinuation is always better, as b b >. The net soial benefit fromahighlevelofeffort in either region is therefore Wh = b g. The net soial benefit fromnoeffort depends on whether a bad projet is terminated or ontinued. So, as the projet will be ontinued, the return from a low level of effort in either region is Wl = pb g +(1 p)(b b ) Effort is optimal if Wh W l whih holds if (1 p)(b g + b b )= One an see that the threshold inreases with the ost of refinaning a bad projet. When this ost inreases, it is effiient to exert effort even for higher levels of the ost of effort. The reason is that the soial planner prefers to exert effort in order to generate a good projet and thus to prevent the seond round of finaning. Finally, we onsider the deision whether to initiate the projet. 8 Note that when : the soial planner undertakes the projet if b g, and when > : the soial planner undertakes the projet if pb g +(1 p)b b = p To summarise: Proposition 1. If min{,b g }, investment and high effort are effiient in both regions. If > and investment and low effort are effiient in both regions. Otherwise, no investment in either region is effiient. The effiient projet hoie, plus hoie of effort is depited in the following figure. b b b g * * b b * * P, e = * NP * * P, e = 0 Figure : Effiient projet and effort hoie 8 Reall that the initial investment is paid with initial resoures. 9

10 Eah point in this graph represents a projet, haraterized mainly by the values of and. To draw this figure,wehaveassumedthatpb g <b b. 9 So b b,b b. The bold line separates the parametri areas where projets are undertaken (denoted by P in the figure) or not undertaken (denoted by NP ). On the one hand, when b g < < and [,b b ], projets are not undertaken (in spite of the fat that they will be good beause effort should be made) beause their net benefit is below the opportunity ost of keeping the initial resoures that an be used for private onsumption. On the other hand, when > and [,b b ], projets are not undertaken beause the ost of two rounds of finaning is above their benefit. 4 Divided Government In this setion, we analyse the model when government is divided. At this stage, we are taking the form of the budget onstraint (hard or soft) as fixed. This generates two different games. 4.1 A Soft Budget Constraint We solve the game bakwards. We will initially assume that both regions initiate projets. The final event is that entral government sets a tax to finane total loan repayments, whih are r =(I a + I b ), where I i =1ifthe projet in region i is bad and I i =0otherwise. Realling that τ = r, we see that τ = [I a + I b ] (1) i.e. the resident of either region only pays half the ost of additional finaning of a bad projet in his region, as this ost is shared though a national tax. So, onditional on projet realizations I a,i b, the utility of a resident of region i in equilibrium is u i = (1 I i )b g + I i b b τ () ( bg = I j if e i = (1 I i )b g + I i b b [I i + I j ] if e i =0 where in the seond line, we have used the formula for τ in(1)above,andalsothefatthat I i =1is impossible if e i =. Note the fisal externality generated by the aggregate budget onstraint: u i depends negatively on the possibility of a bad projet in region j (I j =1), as eah region only bears a fration (in thisasehalf)oftheostofbailout. We are now in a position to analyse equilibrium effort hoie by eah region. Now, let u i (e i,e j ) be the expeted present value of utility to a resident of region i from hoie of effort 9 This assumption is only made for the sake of expositional purposes. Our main result does not depend upon it. 10

11 levels e i,e j {0, }. From (), it follows immediately that: u i (, ) =b g (3) u i (0, ) =pb g +(1 p)(b b ) (4) u i (, 0) = b g (1 p) (5) u i (0, 0) = p b g + p(1 p)(b g )+(1 p)p(b b )+(1 p) (b b ) (6) These an be explained as follows. First (3) follows beause if both regions hoose high effort, both projets are good and eah region gets total benefit b g and τ =0. Seond, (4) follows beause if region i puts in low effort, but region j puts in high, it gets a good projet with probability p; otherwise, with a bad projet, it gets non-peuniary benefit b b, and from (1), τ =. Third, (5) follows beause if region i putsinhigheffort, but region j puts in low effort, it gets a good projet with probability 1, but with probability 1 p the projet in region j is bad, in whih ase τ =. Fourth, (6) follows as the aforementioned possibilities an all our in this ase, plus the possibility that both projets are bad, in whih ase eah region gets net benefit b b. From these expressions, it is easily alulated that u i (, ) u i (0, ) =u i (, 0) u i (0, 0) = (1 p)(b g b b + ) So, for either region, it is a dominant strategy to put in effort in projet implementation, if (1 p)(b g b b + )=SBC and no effort otherwise, onditional on the projet having been initiated. Now we turn to the projet initiation deision. Denote by d i {0, 1} the deision adopted by the regional government of region i, where 1(0) means investment (no investment). Let v i (d i,d j ) be the expeted present value of utility to a resident of region i from hoie of investment d i,d j {0, 1}. When SBC, the government of region i antiipates that both regions will exert effort if projets are initiated. So v i (1, 1) = v i (1, 0) = b g, v i (0, 1) = v i (0, 0) = (7) These an be easily explained beause as both regions exert effort if investment is made, no bailout will be neessary and so there is no fisal externality. Therefore, from (7), we have: v i (1, 1) v i (0, 1) = v i (1, 0) v i (0, 0) = b g So, for either region is a dominant strategy to invest if b g. 11

12 Now suppose that > SBC. Now, the government of region i antiipates that both regions will exert low effort if investment is made. So v i (1, 1) = p b g + p(1 p)(b g )+(1 p)p(b b )+(1 p) (b b ) (8) v i (0, 1) = (1 p) + (9) v i (1, 0) = pb g +(1 p)(b b ) (10) v i (0, 0) = (11) These an be explained as follows. First (8) follows beause if both regions invest, they will afterwards hoose no effort. So both projets an be either good (in whih ase no bailout is needed) or bad (so a bailout is needed) ; therefore all possibilities may our. Seond, (9) follows beause if region i does not invest but region j does, region i will bear the ost of a bailout in j with probability (1 p). Third, (10) follows beause if region i invests, it gets a good projet with probability p, but with probability (1 p) the projet is bad, in whih ase a bailout will be needed. Fourth, (11) follows immediately. Therefore v i (1, 1) v i (0, 1) = v i (1, 0) v i (0, 0) = [pb g +(1 p)b b ] 3 p So, for either region is a dominant strategy to invest if [pb g +(1 p)b b ] = SBC 3 p So, we have established the following haraterization of the SBC equilibrium: Proposition. If min{ SBC,b g }, investment ours, and high effort is supplied in both regions. If > SBC and SBC investment ours, and low effortissuppliedin both regions. Otherwise, there is no investment in equilibrium in either region. The equilibrium projet hoie, plus hoie of effort is depited in the following figure. b b SBC b g P SBC, e SBC = SBC SBC NP P SBC, e SBC = 0 b b Figure 3: Equilibrium projet and effort hoie under SBC 1

13 Comparing Propositions 1 and, and in partiular, omparing ritial values, SBC and, SBC, and noting that SBC >, > SBC, we an establish the following Proposition 3. If the SBC equilibrium is ineffiient, the ineffiieny takes one of the following two forms: either (i) investments are made in equilibrium when it is ineffiient to do so; or (ii) investments are made in equilibrium and are effiient, but low effort is supplied when it is effiient to supply high effort. Thus with a SBC, ineffiieny involves either oversupply of projets, orundersupply of effort. This Proposition is most easily proved with referene to Figure 4, whih superimposes Figure 3 on Figure. b b b g SBC * SBC * C A B b b Figure 4: Ineffiienies under SBC To draw this figure,wehaveassumedthatpb g < (1 + p)b b. 10 By onstrution of the Figure 4, in regions A and B, investments are made in equilibrium when it is ineffiient to do so 11. In region C, investments are made in equilibrium and are effiient, but low effort is supplied when it is effiient to supply high effort. 4. A Hard Budget Constraint Again, we solve the game bakwards. In this ase, there is no ontinuation if a projet is bad, so no tax is set at the end of t =, i.e. τ =0. So, onditional on projet realizations 10 Again, this assumption is only made for graphial onsiderations. If pb g (1 + p)b b, the intersetion between b g and SBC is in a point above b b. In that ase, the unique differene with Figure 4 is that the size of the parametri regions A, B and C hange. 11 This result is well known and is mainly driven by the externality effet. The parametri area A represents projets that should not have been undertaken by a soial planner (beause if so, they should have been done with effort whih is soially too ostly) but are nevertheless initiated by a regional government beause they will be undertaken with no effort. The parametri area B represents projets that should not have been undertaken by a soial planner (beause if so, they should have been done with no effort and the ost of two investments is soially too ostly) but are nevertheless initiated by a regional government. 13

14 I a,i b, the utility of a resident of region i in equilibrium is ½ bg if e u i =(1 I i )b g = i = (1) (1 I i )b g if e i =0 Again, let u i (e i,e j ) be the expeted present value of utility to a resident of region i from hoie of effort levels e i,e j {0, }. From (1), we see immediately that: From (13), it is easily alulated that u i (, ) =u i (, 0) = b g,u i (0, ) =u i (0, 0) = pb g (13) u i (, ) u i (0, ) =u i (, 0) u i (0, 0) = (1 p)b g So, for either region, it is a dominant strategy to put in effort in projet implementation, if (1 p)b g = HBC and no effort otherwise. Now we turn to the investment deision. When HBC, the government of region i antiipates that both regions will exert effort if investment has ourred. So v i (1, 1) = v i (1, 0) = b g, v i (0, 1) = v i (0, 0) = Therefore, for either region is a dominant strategy to invest if b g. When > HBC, the government of region i antiipates that both regions will exert low effort. So v i (1, 1) = v i (1, 0) = pb g,v i (0, 1) = v i (0, 0) = Therefore, for either region it is a dominant strategy to invest if pb g = HBC. So, we have established the following haraterization of the HBC equilibrium: Proposition 4. If min{ HBC,b g }, investment ours, and high effort is supplied in both regions. If > HBC and HBC investment ours, and low effort is supplied in both regions. Otherwise, there is no investment in equilibrium in either region. The equilibrium projet hoie, plus hoie of effort is depited in the following figure. b b b g HBC HBC NP * HBC P HBC, e HBC = P HBC, e HBC = 0 b b Figure 5: Equilibrium projet and effort hoie under HBC 14

15 Comparing Propositions 1 and 4, and in partiular, omparing ritial values, HBC and, HBC, and noting that HBC >, < HBC, we an establish the following. Proposition 5. If the HBC equilibrium is ineffiient, the ineffiieny takes one of the following two forms: either (i) investments are not made in equilibrium when it is effiient to do so; or (ii) investments are made in equilibrium when it is effiientto doso, buthigheffort is supplied when it is effiient to supply low effort. Thus ineffiieny involves either undersupply of projets, or oversupply of effort, the reverse to the ineffiieny arising with a SBC. This Proposition is most easily proved with referene to Figure 6, whih superimposes Figure 5 on Figure. b g b b * HBC * HBC C A B b b Figure 6: Ineffiienies under HBC For the sake of graphial larity, we draw this figure assuming that HBC > b b. Again, this assumption does not hange qualitatively our results. In regions A and B of the parameter spae, investments are not made in equilibrium when it is effiient to do so. In region C of the parameter spae, investments are made in equilibrium when it is effiient to do so, but high effort is supplied when it is effiient to supply low effort. 4.3 Hard or Soft Budget Constraint? In this subsetion, we use all previous results to analyze the hoie of the entral government in the first period. At t =0, the CG deides whether to set a SBC or a HBC, omparing the expeted present value of the sums of regional welfares. The main result is as follows: Proposition 6. At t =0, the CG always hooses a regime that restores fully effiieny. But, depending on parameters, both HBC or SBC an be optimal. 15

16 The last result onfirms a interesting trade-off between hard and soft budget onstraints. Under some parametri onfigurations, hard budget onstraints help to overome the externality effet reated by bailouts. But, under other parametri onfigurations, soft budget onstraints enable the entral government to have some degree of flexibility, whih reates an option value to wait until the type of the projet is revealed. This Proposition is most easily understood using Figure 7. b g b b SBC * HBC SBC * HBC hb HBC HBC HBC sb SBC SBC b b Figure 7: Comparisons of regimes In the parametri areas without label, the entral government is indifferent between imposing a hard or a soft budget onstraint. This is not the ase for the remaining areas, where the entral government stritly prefers one regime. First, we explain the CG s hoie in the parametri areas haraterized by apital letters. On the one hand, in "HBC", the entral government alleviates the externality effet that emerges under a soft budget onstraint and that makes more projets to be ineffiiently finaned. So, by hoosing a hard budget onstraint, the projets are effiiently not initiated. On the other hand, in "SBC", the entral government prefers a soft budget onstraint beause this regime enables to ontinue bad projets for whih this deision is soially effiient. So the projets are effiiently initiated. Next we explain the CG s hoie in the parametri areas haraterized by small letters. In "hb", the entral government prefers a hard budget onstraint. In spite of the fat that under both regimes the projets are effiiently initiated, under a hard budget onstraint both regions exert effort (the soially effiient solution) and thus generate good projets. A similar reasoning applies in "sb", where the entral government prefers a soft budget onstraint beause under a hard budget onstraint both regions exert effort, whih is soially ineffiient. 16

17 Remark :Thistrade-off between HBC and SBC only emerges when moral hazard yields to an unertain outome (i.e. p>0). It is easy to verify that if p 0, then b b, SBC b b > b b 3 and HBC 0. Therefore, under that irumstanes (and realling that we have assumed that > b b ) HBC always restores fully effiieny and thus dominates. 4.4 Performane-Based Taxes for Regional Government So far, we have assumed that the projet outome is unverifiable, so that the CG annot diretly reward or penalize RGs on the basis of projet outomes. If CG ould do this, it ould ahieve the effiient outome. Speifially, it ould set a SBC ombined with regionspeifi taxesτ 1,τ at the end of period, where τ i = if the projet in i turned out to be bad. This penalty would have the dual role of repaying the loan for refinaning the projet, and inentivising RG to supply effiient effort. To put it another way, these taxes internalise the fisal externalities that arise with uniform taxation. But, in pratie, we do not observe suh taxes. Indeed, tax rates set by entral government are almost always uniform. One reason may be that projet outomes may be unverifiable (as we have assumed). Another may be that part of the role of the national tax system is to provide insurane. In any ase, our main objetive in this paper is to study the effiieny of the HBC in an environment where the SBC is ineffiient: otherwise, there is no real interest in the HBC. 5 Institutional Solutions 5.1 Centralization One possible solution is for the entral government to assume all the funtions of regional government i.e. projet initiation and the supply of effort. In our model, the entral government (given that it is benevolent, by assumption) behaves like the soial planner. So, it would seem that entralization would solve the problem studied in this paper. However, full entralization is not normally advoated as the solution to exessive subnational borrowing, beause it may entail other ineffiienies. In partiular, an argument often made is that entral government is less well-informed about regional preferenes than regional governments. This ould be introdued (for example), in our framework, by supposing at the initial investment stage, a fration λ of potential projets are worthless (type A projets), and a fration 1 λ are as desribed above (type B projets), but only regional governments know whih are whih. In this ase, entralization would involve a new ineffiieny. In that ase, depending on the parameter values, it may be better to have divided government than full entralization. 5. Deentralization We define this form of government in the natural way as one where the regional government assumes all the funtions of government i.e. projet initiation and supply of effort, as well 17

18 as the ontinuation deision, and tax powers at the end of the seond period. The regional government an now borrow, but must repay any borrowing out of an inome tax levied only on its own residents. If this tax is lump-sum, effiieny is learly restored as there is no fisal externality, and thus no SBC. The deentralized government behaves just like the soial planner. However, it is often argued that deentralization leads to other ineffiienies though failure to internalize inter-jurisditional spillovers (Oates (197)). A key example would be tax externalities between regions, whih generates ineffiient tax ompetition under deentralization. More reently, it has been argued that the presene of tax ompetition, by raising the pereived marginal ost of publi funds at the regional level an endogenously "harden" the government budget onstraint (Qian and Roland (1998)). We now show that this "hardening" of the budget onstraint an indeed our. However, inourmodel,ithastheoppositewelfareonsequenetothatfoundinqianandroland (1998). In that paper, hardening of the budget onstraint though tax ompetition was unambiguously good, as it prevented wasteful lending to state enterprises. Here, if the hardening of the budget onstraint has any effet on the equilibrium, it will be to redue welfare, as it will ause ineffiiently high effort to be supplied, with too few projets initiated as a onsequene (from Proposition 4). Thus, deentralisation may be less effiient than divided government. With fisal deentralization, ompetition in inome taxes an be introdued in a very simple and natural way in our model by allowing workers to be mobile between regions, thus generating a mobile tax base. This in turn raises the marginal ost of publi funds when only one projet is bad, as then only one region needs to set a positive tax, and pereives that in doing so, it will lose some of its tax base to the other region. This in turn makes projet ontinuation possibly undesirable from the point of view of the single region, thus endogenously "hardening" the regional budget onstraint. The details are as follows. Any resident of region i anworkeitherinregioni itself, or (at a mobility ost m) anworkinregionj. The mobility ost is uniformly distributed on [0, 1]. In eah ase, the resident of i an earn a wage (normalized to unity) in either region, minus any tax paid. Let τ a,τ b [0, 1] be the inome tax rates. Moreover, for simpliity 1, we will assume that residents of i who work in region j still enjoy the benefits of onsumption of private and publi goods in region i, and their welfare is thus taken into aount by the regional government of i. Then, the payoff of a resident of region i in period, assuming that a bad projet is refinaned, is ½ 1 τ u i (m) =b b + i if m τ i τ j (14) 1 τ j m if m<τ i τ j 1 Without this assumption, we introdue a "tax exporting" inentive for regional governments whih will tend to lower the marginal ost of publi funds, implying that in this ase, deentralization annot harden the budget onstraint. 18

19 Assume w.l.o.g. that τ i >τ j. So, from (14), the sum of utilities of all residents in region i is Z 1 0 u i (m)dm = b b +[1 (τ i τ j )](1 τ i )+ Z τ i τ j 0 (1 τ j m)dm (15) = b b +[1 (τ i τ j )](1 τ i )+(τ i τ j )(1 τ j (τ i τ j ) ) where 1 (τ i τ j ) is the fration of the population who do not move, (τ i τ j ) is the fration who do, and 1 τ i, 1 τ j m are their respetive wages net of taxes and any mobility osts. The regional government budget onstraint is therefore r i = τ i [1 (τ i τ j )] (16) where r i is any repayment to the banking setor. Note that r i =0if the projet is good, and r i = with probability 1 p if the projet is bad and is refinaned. Now onsider the refinaning deision. These deisions an now be interdependent as the tax that region i must set to over the ost of refinaning depends on the tax that region j sets. For simpliity, assume that eah region an observe not only whether its own projet is good or bad, but also whether the projet in the other region is good or bad. There are then two ases. The first is where region i has a bad projet, but region j has a good projet. In that ase, it is always optimal for j to set τ j =0. Then, i antiipates that j will set τ j =0, and thus the tax needed for refinaning is, from (16), τ i = τ>,where τ is the smaller root 13 of = τ(1 τ). Then, from (15), welfare in region i is b b +(1 τ) + τ(1 τ )=b b +1 τ(1 τ) τ = b b +1 ( + τ ) This is to be ompared to welfare of 1 without refinaning. So, the gain to refinaning the projet is b b (+ τ τ ), implying that the effetive ost of refinaning is now (+ ) >.Thus, τ / is the deadweight loss of finaning ontinuation of the projet though a distortionary tax. More preisely, τ / measures the mobility osts inurred by workers seeking to avoid the higher tax in region i. The seond ase is where both regions have bad projets. In this ase, both have the option of refinaning (say R) or terminating the projet (say T ). Then, it is easily seen that the two regions play the following matrix game, where region i hooses rows, and j hooses olumns and the payoffs are regional utilities, ignoring the onstant of 1 : i\j R T R b b, b b b b ( + τ (17) T 0,b b ( + τ 0, 0 13 In fat, τ = 1 1 4, so it must be the ase that 1 4. This reinfores the ondition <1 that must hold, in order to be viable the bad projet s refinaning. If > 1 4, refinaning is impossible if only one region has a bad projet. But the analysis of this ase is similar to the one we perform below and thus omitted from the model. 19

20 The explanation of the payoffs is as follows. If both refinane i.e. (R, R), both will set the same tax i.e. some tax τ i = τ j = τ, so from (15), regional welfare is b b +1 τ, andfrom (16), τ =. If only one region hoose to refinane, it must set a tax τ as before, whih gives apayoff of b b ( + τ ). As b b >,τ>0, if b b ( + τ ) the only weakly undominated Nash equilibrium of this game is for both regions to ontinue finaning. On the other hand, if b b < ( + τ ), (R, R) and (T, T) are both Nash equilibria. Note that (R, R) Pareto-dominates (T, T), so if players ould oordinate, they would play (R, R). However, there is no onsensus in the game-theory literature that suh oordination is possible, so we will onsider both outomes. First, if b b ( + τ ), bad projets are always refinaned, so it is lear that the outome is effiient and thus as desribed as in Proposition 1. Now onsider the ase where when 14 b b < ( + τ ). Suppose first that the "bad" equilibrium (T,T) prevails when both regions have bad projets. In this ase, there is an endogenous HBC 15 with probability 1; that is, if a region has a bad projet, it will always terminate it in equilibrium, whether the other region has a bad projet or not. Thus, the outome is exatly as in the ase with an exogenously imposed hard budget onstraint i.e. as desribed in Proposition 4. Thus, by Proposition 5, deentralisation an be ineffiient, and moreover, by the disussion in Setion 4.3, deentralisation an be less effiient than divided government with a soft budget onstraint. Now suppose that the "good" equilibrium (R, R) prevails when both regions have bad projets. Then, there is an endogenous HBC in the event that one region has a bad projet and the other a good projet. In this ase, existing propositions do not apply, and some more analysis is needed to haraterise the equilibrium. First, if both regions exert low effort, this now gives an expeted ontinuation payoff of u i (0, 0) = pb g +(1 p)p0+(1 p) (b b ) This is beause with probability (1 p)p, only one region has a bad projet, in whih ase ost of ontinuation is τ, and thus it terminates this projet; on the other hand, if both regions have bad projets, there is no termination, as the "good" equilibrium (R, R) entails that projets are refinaned. On the other hand, u i (0, ) =pb g beause in this ase, the ost of ontinuation is τ with probability 1. Finally, u i (, ) =u i (, 0) = b g beause if the projet is good, region i does not need to levy a tax and thus has no interation with the other region. From these expressions, it is easily alulated that u i (, ) u i (0, ) = (1 p)b g = HBC u i (, 0) u i (0, 0) = (1 p)b g (1 p) (b b ) = ˆ ³ Sothisaseanhappenprovidedb b < As 1 4,+ τ = We say that the HBC is endogenous here beause it is not due to expliit preommitment not to borrow, but beause borrowing is too expensive in equilibrium, beause of the deadweight loss of repayment due to tax ompetition. 0

21 Note that ˆ < HBC. So, if < ˆ, there is a unique equilibrium where both regions set e =, and if > HBC, there is a unique equilibrium where both regions set e =0. If ˆ HBC, there are two symmetri equilibria (, ) and (0, 0). Now, turn to the initial investment deision. If ˆ, the government of region i antiipates that both regions will exert effort if investment has ourred. So v i (1, 1) = v i (1, 0) = b g, v i (0, 1) = v i (0, 0) = Therefore, for either region is a dominant strategy to invest if b g. When > HBC, the government of region i antiipates that both regions will exert low effort. So, v i (1, 1) = v i (1, 0) = pb g +(1 p)p0+(1 p) (b b ) v i (0, 1) = v i (0, 0) = Therefore, for either region it is a dominant strategy to invest if pbg+(1 p) b b =ĉ. 1+(1 p) Finally, suppose that ˆ HBC. Suppose first that regions antiipate supplying high effort. Then, by the argument just given, eah will invest if b g. On the other hand, if regions antiipate supplying low effort, eah is again willing to invest if ĉ. So, we have established the following haraterization of the equilibrium with an endogenous HBC under deentralization when the good equilibrium (R, R) prevails in (17) Proposition 7. If min { ˆ, b g }, investment ours and high effort is supplied in both regions. If HBC and ĉ, investment ours and low effort is supplied in both regions. If ( ˆ, HBC ) and ĉ, multiple equilibria are possible. On the one hand, there is an equilibrium where investment ours, and low effortissuppliedinboth regions. On the other hand, there is an equilibrium where investment ours and high effort is supplied in both regions, provided b g. Otherwise, no investments are made in equilibrium. Clearly, multiple equilibria are possible here. Nevertheless, omparing with Proposition 1, the ineffiieny of the outome under deentralization is lear, as ˆ > :iftheoutome is ineffiient, it will involve either (i) too high effort, or (ii) projet not initiated when it is effiient to do so. 6 Related Literature and Conlusions 6.1 Related Literature Related literature is as follows. First, the onept of the SBC was introdued by Kornai (1980, 1986) and mainly applied to state-owned enterprises in soialist eonomies. The subsequent literature tried to analyze, in different ontexts, the reasons for the emergene of suh a problem: paternalism, politial intervention, asymmetri information and lak of ommitment, orrupt influenes, et. Dewatripont and Maskin (1995) were the first to provide 1