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Fiscal decentralization with regional redistribution and risk sharing.

1. INTRODUCTION

In most federations, a primary responsibility of the federal government is to implement a system of interregional transfers. Interregional transfers can serve both to redistribute income from rich to poor regions and to stabilize regional income in response to transitory asymmetric shocks. (1) The literature has recognized that interregional transfers can give rise to moral hazard problems if transfers are dependent on variables that can be manipulated by regional governments. Person and Tabellini (1996b), for example, show how an interregional transfer scheme can reduce regional governments' incentives for investment in risk-reducing activities. In order to mitigate this type of moral hazard problem, von Hagen and Hammond (1998) argue that a stabilization scheme should provide transfers only in response to shocks with zero conditional expectation. If this is not done, then transfers are tied to predictable shocks and recipient governments may invest little resources in efforts to avoid them.

There is also a growing theoretical and empirical literature that examines the incentive effects of transfers on regional governments' spending and borrowing behavior. (2) In particular, incentive problems arise when regional governments expect that part or all of their spending and/or borrowing costs will be covered by the federal government in the form of additional transfers, and this expectation affects their behavior. This type of incentive problem thus constitutes a negative externality in that regional governments do not take into account the welfare of national taxpayers when making their spending and/or borrowing decisions. As a result, too much spending or borrowing is undertaken relative to the efficient level. If this occurs, regional governments are said to have soft budget constraints. The term "soft budget constraint" was first coined by Kornai (1979, 1980) in relation to loss-making state-owned enterprises in transition economies. According to Kornai, a soft budget constraint arises when a state-owned enterprise expects an additional subsidy if it experiences financial difficulty. The expectation of additional resources in turn results in opportunistic behavior that may precipitate a financial crisis in the firm.

The primary cause of the soft budget constraint problem is fiscal decentralization in combination with the federal government's inability to commit to a transfer scheme that is chosen prior to the spending decisions of regional governments. A transfer scheme chosen ex ante is dynamically inconsistent, and the federal government faces an incentive ex post to renege on its announced transfer scheme. Regional governments are aware of this incentive and they take it into account when making their spending decisions. In this paper, the soft budget constraint problem is compounded when regional government spending decisions are made prior to the realization of shocks to regional incomes, which is realistic for many public expenditure projects that take time to implement. In this setting, the federal government has an incentive to equalize consumption levels across regions after the realization of the shock to regional incomes, but this necessitates the basing of transfers on the levels of spending and taxation chosen by the regional governments. Commitment to a transfer scheme can therefore eliminate inefficiencies arising from soft budget constraints. However, commitment necessarily entails forgoing the flexibility to respond to shocks to regional incomes. The federal government may therefore face a trade-off between the benefits of risk-sharing and the benefits of hard budget constraints, as examined in Sanguinetti and Tomassi (2004). The purpose of the paper is to explore this trade-off in a repeated game setting.

Akai and Silva (2009) also examine the soft budget constraint problem when the higher-level government implements an interregional redistribution scheme. As in our model, the government has an incentive to equalize consumption levels across regions. In their model, however, the higher-level government faces an informational constraint in that it cannot observe the cost of providing the regional public good prior to the production stage, and must therefore base ex ante transfers on costs reported by the regional governments. It does, though, learn the true cost ex post. Akai and Silva show that soft budget constraints can arise if the transfer scheme is implemented only ex ante, but hard budget constraints arise if additional transfers are allowed ex post because ex post transfers induce regional governments to truthfully report costs.

The analysis in this paper extends the literature on soft budget constraints in two directions. First, it provides an analysis of plausible scenarios wherein commitment and hard budget constraints can yield lower levels of welfare than non-commitment and soft budget constraints. The literature on time-inconsistency in general and soft budget constraints in particular describes the discretionary outcome as necessarily being inferior to one with commitment. However, as Kornai et al (2003) points out, if this were always true, the problem of soft budget constraints would likely not be so widespread. In our model, because regional governments choose their spending levels prior to the realization of shocks to regional incomes, the federal government's commitment to an interregional transfer scheme necessarily provides less than full insurance against shocks to regional incomes. When citizens are risk-averse, it is easy to imagine scenarios for which commitment could be inferior to discretion.

The second way in which the paper extends the theoretical literature on soft budget constraints is to examine the problem in a repeated game setting. In reality, the federal and regional governments interact repeatedly. Modeling this repeated interaction allows for reputational forces to drive the federal government's behavior. In particular, the federal government in each period weighs the short-run benefits of reneging on its announced transfer scheme against the long-run costs of such an action. The model explores the federal government's dilemma in a finite horizon model where the time horizon corresponds to the federal government's mandate. In this setting, a federal government with constrained commitment ability may find it optimal to masquerade as a dependable government if doing so eases the soft budget constraint problem in future periods. An essential assumption of the finite horizon model is that regional governments face uncertainty with respect to the federal government's ability to commit to its announced transfer scheme. Without this assumption, the discretionary outcome occurs in every period. The analysis allows for the derivation of the time-path of regional government spending and its dependence on factors such as the magnitude of regional shocks, the length of the federal mandate, the discount rate, and the regional government's initial uncertainty regarding the federal government's commitment ability. Such an analysis was first proposed but not formally modeled by Inman (2003). Inman argues that regional governments are not likely to be fully aware of all the costs borne by the central government in avoiding the discretionary outcome. He describes these costs as stemming from two sources. The first is the financial cost of denying additional transfers, which arises if regional governments' financial crises create spillovers to the rest of the economy. The second is the distributional cost of denying additional resources, which arises when regional taxpayers and creditors are favored over national taxpayers. When one or both of these costs is sufficiently large, the central government faces a commitment problem and soft budget constraints are likely to result. It is questionable whether regional governments are fully aware of the values of these costs, especially the latter one. The analysis introduces risk-sharing as an opportunity cost borne by a central government if it avoids the discretionary outcome, and, if large enough, can result in soft budget constraints.

Wildasin (1997, 2004) also explores scenarios where softening budget constraints only sometimes occurs due to trade-offs both at the higher and lower levels of government. In these models, lower-level governments provide a local public good or service that generates positive externalities to citizens outside the local jurisdiction. If the lower-level government reduces provision of the good to zero, for example, the higher-level government has an incentive to finance a minimum level that respects the preferences of all citizens, but at a cost to all citizens. In such a case, the lower-level government faces a trade-off of having a lower level of the public good, but having the cost of providing the good borne partly by non-residents. The result of this trade-off can be hard or soft budget constraints.

The multi-period model examined is a very simple one. In order to focus on the risk-sharing incentive for discretionary transfers, the model abstracts from distortionary taxation, externalities in public good provision, mobility of citizens across regions, and regional government borrowing. Distortionary taxation could easily be incorporated into the model. However, distortionary regional taxes would add an additional motive for interregional transfers that have already been examined in Bordignon et al (2001) in connection with soft budget constraints. Furthermore, the implications of overlapping distortionary regional and federal taxes have been examined by Boadway and Tremblay (2004), and externalities in public good provision have been examined by Wildasin (1997). Relaxing the assumption of no citizen mobility could in principle serve to eliminate the need for interregional transfers in stabilizing regional income. Risk-sharing schemes could also result in inefficiencies if they interfere with the efficient migration of individuals from low- to high-income regions (see Wildasin (1995)) or if mobile citizens respond to differences in regional fiscal capacity (see Boadway and Flatters (1982)). However, given that the analysis focuses primarily on transitory shocks to regional incomes, the assumption of immobile citizens is a reasonable one. Empirical evidence supports this assumption. Barro and Sala-i-Martin (1991), Blanchard and Katz (1992), and Adrubali, Soresen, and Yosha (1996), for example, provide evidence that even in the United States where there are few language or cultural barriers, mobility is at best only important in the long run. The costs of uprooting the family and finding new employment can be quite high, and individuals are unlikely to incur these costs in response to transitory shocks. (3)

Individual or regional government borrowing in response to transitory shocks could also serve to eliminate the need for interregional transfers as risk-sharing devices. For this to be true, individuals and/or regional governments must have unconstrained access to private capital markets. Private capital markets are assumed to not provide this service to regional governments either because of constitutional balanced budget requirements or because of imperfections in private capital markets. Empirical evidence provides support for the latter assertion. For example, in a study of the United States and Europe, Atkeson and Bayoumi (1993) find that national private capital markets provide only a limited degree of insurance against regional fluctuations. Shiller(1995) confirms Atkeson and Bayoumi's results in a study for the United States. His investigation shows that financial markets smooth shocks to corporate dividends, but these represent less than three percent of national income. The remainder of the paper is organized as follows. Section 2 sets up the basic model in a static setting in order to highlight the incentives facing the federal and regional governments. Section 3 extends the model to a multi-period setting. Section 4 summarizes the predictions of the model, and concluding comments are provided in section 5.

2. THE BASIC MODEL

The setup of the model is similar to that in Bordignon, Manasse, and Tabellini (2001) and Boadway and Tremblay (2004). There is a federation consisting of two regions, indexed by A and B, and two levels of government, a regional level and a federal level. The government of region k is responsible for providing a regional public good [g.sub.k] financed by a lump-sum tax, [t.sub.k], and a federal lump-sum transfer, [S.sub.k]. The role of the federal government is to implement a lump-sum regional transfer scheme. To keep the model as simple as possible, it is assumed that each region is comprised of identical and immobile individuals who are endowed with one type of good that can be used for private consumption or for the public good. The population of each region is normalized to one.

Regional endowments are subject to random shocks that are negatively correlated. Thus, with probability p, the endowments in regions A and B are [y.sup.1.sub.A] = [z.sub.A] + [theta] and [y.sup.1.sub.B] = [z.sub.B] - [pi][theta], respectively, where [theta] is the random shock and the superscript 1 denotes state 1 for the distribution of the shock across the two regions. The parameter [pi][member of] (0,1) serves to differentiate the magnitude of the shock [theta] across the two regions. Similarly, with probability 1-p, the regional endowments in state 2 in regions A and B are [y.sup.2.sub.A] = [z.sub.A] - [theta] and [y.sup.2.sub.B] = [z.sub.B] + [pi][theta], respectively. Region A is assumed to have a higher deterministic endowment than region B, and thus [z.sub.A] > [z.sub.B], but with [pi][member of] (0,1), region A experiences shocks of larger magnitude than does region B. The shock [theta] is assumed to be a continuous random variable with mean zero and density in the range [-[??],[??]]. It is further assumed that [??] > 0 and [z.sub.B] > [??].

The resident of region k is risk averse and has the following preferences over consumption and the regional public good:

U([c.sup.i.sub.k], [g.sub.k]) = V([c.sup.i.sub.k]) + H ([g.sub.k]), (1)

for i = 1,2 and k = A, B. The functions V(c) and H(g) are well-behaved concave functions. The individual's budget constraint is given by

[c.sup.i.sub.k] = [y.sup.i.sub.k] - [t.sup.i.sub.k]. (2)

The regional government selects a tax rate and the level of spending on the public good to maximize the utility of the representative individual within its region, subject to the budget constraint:

[g.sub.k] = [t.sup.i.sub.k] + [S.sub.k] (3)

The federal government seeks to maximize the welfare of all citizens within the federation, and faces the budget constraint

[S.sub.A] + [S.sub.B] = 0. (4)

The decision sequence in the model depends on the federal government's ability to commit to an announced regional transfer scheme. In all cases, it is assumes that the regional governments select the levels of spending on the public good prior to the realization of the shock [theta] and its distribution across regions. Regional tax rates are then adjusted ex post to balance the regional governments' budget constraints. This assumption reflects the observation that regional governments' spending decisions are often chosen well in advance, and hence prior to the realization of shocks to regional economies. The implication of this assumption for the analysis is extremely important. In particular, if the federal government is able to commit to an announced regional transfer scheme, it must be the case that the optimal transfer scheme is chosen prior to the realization of the shock [theta] and the state i = 1,2. As we shall see, this provides an obvious motivation for the federal government to renege on its announcement once the shock [theta] and the state i are observed.

With the above discussion in mind, the timing of events is the following:

Timing of Events with Commitment

Stage 1: Federal government selects the regional transfers [S.sub.A] and [S.sub.B]

Stage 2: Regional governments select [g.sub.A] and [g.sub.B]

Stage 3: Realization of shock [theta] and state i = 1,2

Stage 4: Regional tax rates adjust to balance regional government budgets.

Timing of Events without Commitment

Stage 1: Regional governments select [g.sub.A] and [g.sub.B]

Stage 2: Realization of shock [theta] and state i = 1,2

Stage 3: Realization of shock [theta] and state i = 1,2

Stage 4: Federal government selects the regional transfers, [S.sub.A] and [S.sub.B], and regional tax rates adjust to balance regional government budgets.

2.1. THE EQUILIBRIUM WITH COMMITMENT

The timing of events for the case when the federal government is able to commit to its regional transfer scheme is described above. The analysis begins with the problem for the regional governments. Consider the problem for the government of region k. Its problem is to select the level of the public good [g.sub.k] so as to maximize the utility of the representative resident of region k given the announced federal transfer [S.sub.k] and subject to the budget constraints (2) and (3):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (5)

Note that since the level of the public good is chosen prior to the realization of the shock [theta] and the state i, the level of g is independent of the shock. Substituting the constraints into the regional government's objective function and maximizing yields the first order condition for the choice of [g.sub.k]:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (6)

First order condition (6) is quite intuitive. The regional government selects the level of the public good, when constrained by budget balance ex post, so as to equate the expected marginal utility of consumption of the representative individual to the marginal utility of the public good. Condition (6) defines the reaction function for the regional government; that is, it defines [g.sub.k] as a function of [S.sub.k].

Working backwards, the problem for the federal government is considered next. The federal government selects the regional transfers to maximize welfare for the federation as a whole, i.e.:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (7)

subject to the reaction functions [g.sub.k]([S.sub.k]), k = A, B and the federal budget constraint (4). Using the envelope theorem, the first order condition to this problem is given by:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (8)

First order condition (8) is also quite intuitive. When the federal government commits to a transfer scheme prior to the selection of the regional public good and prior to the realization of the shock, welfare is maximized by equating the expected utility of consumption across regions. This is a familiar risk-sharing result. It is a simple matter to show that conditions (6) and (8) constitute the unitary optimum when [g.sub.k] and [S.sub.k] are chosen prior to the realization of the shock. For the unitary optimum, the unitary state government selects [g.sub.k] and [t.sub.k] to maximize (7) subject to constraints (2), (3), and (4) and allowing [t.sub.k] to adjust ex post to balance the regional budgets. (4)

2.2. THE FEDERAL GOVERNMENT'S INCENTIVE TO RENEGE ON ITS ANNOUNCED TRANSFER SCHEME

As has been examined in many varied circumstances, the commitment outcome presents a temptation for policymakers to renege on their announcements. In past analyses, however, this temptation is due to distortions in the economy arising from, for example, distortionary taxation, price rigidities, and externalities (see, for example, Kydland and Prescott (1977), Fischer (1980), Barro and Gordon (1983a, 1983b), Barro (1986) and Boadway and Tremblay (2004)). In this model, there are no such distortions because taxation is lumpsum. Rather, it is the informational structure that presents the federal government with a temptation to renege on its announced transfer policy. As will be shown below, the federal government recognizes that welfare can be increased if it has the flexibility to change its policy after the realization of the shock [theta] and its distribution across regions. Without this ability to adjust its transfer policy, there is no incentive for the federal government to deviate from the policy chosen with commitment.

Suppose now that the federal government announces a transfer policy prior to the realization of the shock and its distribution across regions A and B . Suppose also that the regional governments believe the announced transfer policy will be implemented. The regional governments subsequently select the levels of the regional public goods based on the federal government's announced transfer scheme. The announced transfer policy satisfies condition (8) above. Thus, the selection of [g.sub.k] is governed by condition (6) above. Now, after the shock is observed, the federal government is tempted to select a transfer policy to maximize welfare, given the shock [theta] and given [g.sub.k], k = A, B. That is, the federal government seeks to

Max [v([c.sub.A]|[theta]) + V([c.sub.B]|[theta]) + H([g.sub.A]) + H([g.sub.B])] subject [c.sub.k] = [y.sub.k] -[t.sub.k] [g.sub.k] given (9) [t.sub.k] = [g.sub.k] - [S.sub.k] [S.sub.A] + [S.sub.B] = 0.

If we combine the regional and federal governments' budget constraints, we can then write [t.sub.A] as a function of [t.sub.B], with [dt.sub.A]/[dt.sub.B] = -1. The federal government's problem then simplifies to one of selecting [t.sub.B] to

Max [V([y.sub.A] - [t.sub.A] ([t.sub.B])) + V{[y.sub.B] -[t.sub.B]) + H([g.sub.A]) + H([g.sub.B])]. (10)

The first order condition to this problem yields the result that V'([c.sub.A]) = V'([c.sub.B]), or, given the concavity of the utility function, [c.sub.A] = [c.sub.B]. Thus, the federal government can fully equalize consumption ex post across regions. The representative resident of each region is fully insured against an adverse distribution of the shock [theta] but is not insured against the aggregate shock [theta] itself. Note that in this "cheating outcome", the levels of the regional public good are not distorted, and thus welfare is higher for this outcome than when the federal government commits to its announced transfer policy. (5)

2.3. THE NON-COOPERATIVE OUTCOME WITHOUT COMMITMENT

The temptation for the federal government to renege on an announced transfer policy is evident to all players in this game. If the federal government is unable to commit to its transfer policy, then the regional governments will rationally take this into account when selecting the levels of the regional public good. The resulting equilibrium in this setting is the subgame perfect one. To determine this equilibrium, the federal government's problem is examined first. The solution to the federal government's problem is the same as was determined for the "cheating" outcome examined in section 2.2. That is, for whatever realization of the shock [theta] and given the levels of the public good previously chosen by the regional governments, the federal government will maximize welfare by equalizing consumption across regions. The regional governments take this into account when selecting [g.sub.k]. Consider then the problem for the government of region A. Its problem is to select [g.sub.A] to

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (11)

If we substitute the first three constraints into the objective function, the problem for the regional government simplifies to one of selecting [t.sup.1.sub.A] and [t.sup.2.sub.A] to:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (12)

The first order conditions of this problem are:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (13)

Combining the two first order conditions of the above problem yields the following condition to be satisfied for the selection of [g.sub.A]:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (14)

Note that an identical analysis can be performed for region B . The difference between this condition and condition (6) obtained under commitment is the presence of the Lagrange multipliers in condition (14). The presence of the term ([[lambda].sup.1] + [[lambda].sup.2]) implies that the level of the public good is higher when the federal government is unable to commit to a transfer policy. This is a familiar result in the soft budget constraint literature. The reasoning is that an increase in [g.sub.A] necessitates an increase in [t.sub.A], which reduces consumption. The federal government responds ex post to the reduction in consumption by increasing the transfer to region A at the expense of region B. Thus, part of the burden of financing the increased spending is borne by residents of region B . Region A takes this into account when selecting its level of [g.sub.A].

It is important to note that although the level of spending on the regional public good is distorted in the outcome without commitment, this does not necessarily imply that welfare is higher when the federal government is able to commit to its announced transfer policy. Recall that the sequence of decisions is such that under commitment the federal government selects its transfer policy prior to the realization of the shock and its distribution across regions, whereas without commitment the federal government has the flexibility to adjust the transfer to eliminate idiosynchratic risk to residents. Whether welfare is higher with or without commitment depends on the size of the shock, the residents' degree of risk aversion, and on the severity of the soft budget constraint problem. It may well be that for very large shocks the level of welfare without commitment may be higher than with commitment. Efforts to mitigate the soft budget constraint problem would then be welfare decreasing in the presence of large shocks.

3. THE MULTI-PERIOD MODEL

The one-period model is now extended to one with a known finite horizon. Later, the implications of extending the model to an infinite horizon are examined. In the multi-period model, the federal government is elected into office for T periods. The model therefore comprises a repeated game wherein the one-period sequential-move game examined in section 2 is repeated every period. Note that the term of office for the regional governments has no bearing on the analysis because it is only the federal government that may have a commitment problem, and hence it is only the federal government whose behavior has implications for credibility in future periods. As in section 2, the regional governments select their spending levels in each period, prior to the realization of the shock to their endowments, so as to maximize the expected utility of the representative individual in their region.

If the regional governments know that the federal government is unable to commit to its announced transfer policy, then in a finite horizon model there is a unique sequential equilibrium that resembles the "chain-store paradox" first explored by Selten (1978). That is, the equilibrium in each period is the same as the one-period outcome without commitment analyzed in section 2.3. Interest in a finite horizon model therefore rests with the notion that a federal government with constrained ability to commit to a transfer policy may have an incentive to masquerade as a "dependable" government if doing so reduces the distortion in future regional governments' spending levels--that is, if it eases the soft budget constraint problem in future periods. Obviously, in the final period T, an unconstrained federal government will renege on its announced transfer scheme and the non-commitment outcome will result. But for periods t < T, the benefit from masquerading as a "dependable" government may exceed the cost. The cost of masquerading as a "dependable" government is the lack of flexibility in responding to shocks ex post to equalize consumption across regions. Thus, it is the regional governments' uncertainty as to the type of federal government--dependable or not--that prevents the one-period subgame perfect outcome from occurring every period.

The analysis of the multi-period model most resembles Barro's (1986) analysis of central bank reputation in the conduct of monetary policy. (6) As in Barro (1986), let [alpha] denote the probability that the federal government commits to its announced transfer scheme. This type of government is referred to as type 1. A federal government who is unable to commit to its announced transfer scheme is referred to as type 2. Consider now the period [tau] such that for t < [tau], a federal government of type 2 has had no incentive to reveal its type. The absence of this incentive will be developed more formally below. Therefore, the regional governments have learned nothing about the federal government's type up to period [tau], and hence their subjective probability that the federal government is type 1 is [alpha], the same as it was in period 0.

The problem for the federal government of any type is to select its transfer policy in each period to maximize the expected present value of welfare:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (15)

where r is the known exogenous discount rate. A federal government of type 2, however, must weigh the benefit of masquerading as a type 1 government against the cost. If the federal government reneges on its announced policy, then welfare for the current period may be increased, but the regional governments learn the federal government is type 2 (i.e. [[alpha].sub.j] = 0 for j = t + 1 ... T), and therefore future welfare in each period reverts to the level without commitment. Let [W.sup.R] denote one-period welfare if the federal government reneges on its announced transfer policy with 0 < [alpha] < 1. Similarly, let [W.sup.C] refer to one-period welfare under commitment with 0 < [alpha] < 1 and let [W.sup.NC] refer to one-period welfare under no commitment with [alpha] = 0. With this notation, if the federal government reneges on its announced transfer policy, then the expected present value of welfare is given by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (16)

where

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (17)

If the federal government does not renege on its announced transfer policy, then the expected present value of welfare is given by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (18)

From (17) and (18), we can view the federal government's problem as weighing the temptation to renege on its transfer policy against the cost, given the realization of the shock [[theta].sub.t] and given the levels of the regional public good selected in the preceding stage of period t. The temptation to renege in period t < T and the cost of reneging are given by:

Temptation to renege: [[GAMMA].sub.t] = [W.sub.t.sup.R] ([[theta].sub.t]) - [W.sub.t.sup.C] ([[theta].sub.t]);

Cost of reneging: [[DELTA].sub.t] = [E.sub.t] {[[OMEGA].sub.t+1]/1+r} -[E.sub.t]{[[OMEGA].sup.NC.sub.t+1]/1+r} (19)

From the analysis in section 2, the temptation to renege is obviously positive for all realizations of the shock [theta]. The cost of reneging is also positive. To see why, note that [[OMEGA].sub.t+1] contains the option to masquerade as a dependable federal government or to renege on its announced policy, whereas for [[OMEGA].sup.NC.sub.t+1], [alpha] = 0, and thus [[OMEGA].sup.NC.sub.t+1] does not contain this option. Reneging in period t+1 generates a "temptation payoff" in period t+1, but also generates the same present value of welfare from period t+2 onward that reneging in period t does. For some values of [[theta].sub.t+1] reneging in period t+1 may thus be optimal when 0 < [alpha] < 1. For other values of [[theta].sub.t+1], however, the option to masquerade as being dependable may be optimal. The option to renege or not that is imbedded in [[OMEGA].sub.t+1] thus provides a higher present value of welfare than does the present value of the non-commitment outcome for the remainder of the federal government's term in office.

It is easy to show that the cost of reneging increases the greater the number of periods remaining in the federal government's mandate. Thus, if T is large and we are early on in the federal government's mandate, then the cost of reneging may exceed the temptation for any realization of the shock [theta]. Conversely, as t approaches T, the cost of reneging may be quite small, and thus the incentive to renege may arise for a wide range of values for [theta]. Suppose then that the time horizon is long enough so that (i) there exists a period [tau] < T such that for t < [tau] the temptation to renege is less than the cost of reneging (i.e. [[GAMMA].sub.t] < [[DELTA].sub.t]) for all [theta] [member of](-[??],[??]) and (ii) for t [greater than or equal to] [tau], the temptation to renege equals the cost of reneging (i.e. [[GAMMA].sub.t] = [[DELTA].sub.t]) for some [theta] [member of] (-[??],[??]). For (i), the outcome with commitment is observed in each period up to [tau]. For an analysis of (ii), first consider the value of [theta] such that [[GAMMA].sub.t] = [[DELTA].sub.t] and state 1 has occurred, so that it is region A that has experienced a favorable shock to its endowment. Let [[??].sub.t] be this value of [theta]. Now, it must also be the case that [[GAMMA].sub.t] = [[DELTA].sub.t] for [theta] = [[??].sub.t] if state 2 has occurred, since such a shock yields the same regional endowments. Next suppose that state 2 has occurred in period t, so that region A experiences an adverse shock to its endowment and let [[??].sub.t] be the value of [theta] such that [[GAMMA].sub.t] = [[DELTA].sub.t] if state 2 has occurred. It must therefore also be the case that [[GAMMA].sub.t] = [[DELTA].sub.t] for [theta] = [[??].sub.t] if state 1 has occurred. Thus, if state 1 has occurred and [[theta].sub.t] < -[[??].sub.t] or [[theta].sub.t] > [[??].sub.t], then the federal government will renege on its announced transfer policy and will set the transfer ex post such that [c.sup.1.sub.A] = [c.sup.1.sub.B]. Similarly, if state 2 has occurred and [[theta].sub.t] < [[??].sub.t] or [theta] > [[??].sub.t], then the federal government will renege on its announced transfer policy and will set the transfer ex post such that [c.sup.2.sub.A] = [c.sup.2.sub.B]. In a subgame perfect equilibrium, the regional governments take this into account in determining their levels of spending on the public good. Recall, however, that the regional governments face an asymmetry of information in that they do not know the federal government's type.

Consider now the problem for the government of region A in period t. A similar analysis can be conducted for region B . Its objective is to select the level of the public good to maximize the expected welfare of its representative resident, taking into account its budget constraint, that of the federal government, and the incentive facing a type 2 federal government in the subsequent stage of the one-period game. As in section 2, the problem for regional government A in selecting [g.sub.A] is, with appropriate substitutions, equivalent to one of selecting [t.sup.1.sub.A] and [t.sup.2.sub.A] to

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (20)

subject to budget constraints (2), (3), and (4) and the constraint that [c.sup.i.sub.A] = [c.sup.i.sub.B], i = 1,2 for the values of [theta] such that a type 2 federal government reneges on its announced transfer policy. After simplifying the objective function in (19), the first order conditions of this problem are:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (21)

Combining the first order conditions to the regional government's problem yields the following simplified condition for the solution to the regional government's problem:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (22)

First order condition (22) defines [g.sub.At] as a function of [S.sub.At], [[??].sub.t], [[??].sub.t], and [alpha]. Substituting this function into [[GAMMA].sub.t] and [[DELTA].sub.t] for t = 0 ... T determines the time-paths for [??], [??], and [g.sub.A] as functions of [alpha], T, and r. The following section examines the implications of a multi-period horizon for the soft budget constraint problem.

3.1. THE SOFT BUDGET CONSTRAINT PROBLEM IN THE MULTI-PERIOD MODEL

First order condition (22) in addition to the relationship between the benefit of reneging on the transfer policy, [GAMMA], and its cost, [DELTA], determine the degree of "softness" in the regional governments' budgets and how it evolves over the federal government's mandate. To begin the analysis, we learn from (22) that if [[??].sub.t] = [[??].sub.t] = [??], the two last terms equal zero and the first order condition reduces to the same one as under commitment. Such a scenario arises in period t if there is no shock large enough to induce a type 2 government to renege on its announced transfer policy. Thus, if [[??].sub.t] = [[??].sub.t] = [??], regional governments face hard budget constraints regardless of the federal government's type. Also from (22), we see that the larger are [[??].sub.t] and [[??].sub.t], the closer is [g.sub.k] to the level chosen in the commitment outcome. Similarly, the smaller are [[??].sub.t] and [[??].sub.t], the closer is [g.sub.k] to the level chosen in the non-commitment outcome analyzed in section 2.3.

3.2. THE EFFECT OF TIME ON THE SOFT BUDGET CONSTRAINT PROBLEM

The analysis of section 3 showed that the cost of reneging on the transfer policy decreases over time. Consequently, as t approaches T, the incentive to renege may occur for a wide range of values of [theta], and hence [??] and [??] decrease over time. The degree of softness in regional government budgets thus increases with time. The analysis in section 3 also focused on period t > [tau], where [tau] is the period such that for t < [tau], the cost of reneging exceeds the temptation to renege, and hence a type 2 federal government has had no incentive to reveal its type; i.e. [[GAMMA].sub.t] < [[DELTA].sub.t] for t < [tau]. The value of [tau] depends on [alpha], T, and r. In particular, for long but finite federal government mandates, [tau] > 0. Thus, for periods t < [tau], [[??].sub.t] = [[??].sub.t] = [??], and thus [g.sub.k] is constant at the level under a hard budget constraint.

From the regional government's problem in (19) and a comparison of the benefit of reneging on the transfer policy, [GAMMA], and the cost, [DELTA], we learn that from period [tAU] onward, [??] and [??] decrease and approach zero as t [right arrow] T, so long as [theta] < [??] and [theta] < [??]; that is, so long as the shock to the regional endowments is not too large. Consequently, with relatively mild shocks and for t = [tau] + 1 ... T, [g.sub.k] increases from its level under commitment to its level under non-commitment. This result is summarized in the following proposition:

Proposition 1. When regional governments face uncertainty regarding the federal government's ability to commit to its announced transfer scheme, then under a long and finite federal government mandate and for small shocks to regional endowments, the model predicts a period of constant and efficient level of regional government spending early on in the federal government's mandate, followed by inefficient increases in spending until the end of the mandate.

In proposition 1, the period in which regional governments face hard budget constraints depends on the values of [alpha] and r. Clearly, the higher the discount rate, the less costly it is for the federal government to renege on its announced policy. Thus, [tau] decreases with r. For high enough values of r, it is conceivable for [tau] to equal zero, and thus regional government spending levels are inefficiently high from period 0 onward. Furthermore, from (22), we also observe that the higher the probability that the federal government is type 1 (i.e. the closer is [alpha] to 1), the closer is [g.sub.k] to the level chosen in the commitment outcome. As a result, [tau] increases with [alpha] because a higher probability that the federal government is of type 1 reduces the levels of spending on the regional public good closer to the levels under commitment. Factors then that can increase [alpha] have the effect of increasing the period in which hard budget constraints prevail. Such factors might include the appointment of "dependable" ministers to oversee the intergovernmental transfer program and institutional constraints on federal government behavior. This discussion is summarized in the following corollary to proposition 1:

Corollary 1.1 The length of time under which spending levels are efficient decreases with the discount rate and increases with the probability that the federal government is able to commit to its announced transfer policy.

Proposition 1 and Corollary 1.1 capture the observation that soft budget constraint problems occur more frequently under unstable federal governments with short mandates. Instability in such a case is reflected in a high discount rate.

The implications of an infinite time horizon are considered next. An infinite time horizon might arise under a succession of federal governments of similar type. From an examination of the cost of reneging, [DELTA], it is clear that allowing the time horizon to become infinite allows the commitment outcome to occur forever. As T [right arrow] [infinity], the cost of reneging on an announced policy becomes infinite, and so [??] = [??] = [??] for all t. An infinite time horizon thus results in efficient regional government spending levels for all periods. This result is summarized in the following proposition:

Proposition 2. An infinite time horizon results in efficient levels of regional spending in all periods.

4. FEDERAL GOVERNMENT BEHAVIOR IN THE PRESENCE OF LARGE SHOCKS TO REGIONAL ENDOWMENTS

The discussion above focused on shocks to regional endowments that are relatively small, and hence a federal government of type 2 has an incentive to masquerade as a dependable government until the final period T. A large shock, however, can result in a federal government of type 2 reneging on its announced transfer policy prior to period T. When the regional governments observe such a large shock, the federal government's transfer policy reveals its type; that is, [alpha] can jump up to 1 or down to 0 depending on the type of federal government. Following from the analysis in section 3 and the discussion above, the likelihood that the shock to the regional endowment is of sufficient magnitude to induce a type 2 federal government to renege on its transfer policy increases with t for t = [tau] + 1 ... T. This result is summarized in the following proposition:

Proposition 3. If the regional governments face uncertainty about the federal government's ability to commit to its announced transfer scheme, then under a finite federal government mandate, a large shock to regional endowments results in a discrete decrease in regional government spending if the federal government is type 1 or a discrete increase in regional government spending if the federal government is type 2.

An interesting implication of proposition 3 is that welfare may actually increase if the federal government is type 1 and a large shock is realized early on because this induces the commitment outcome for all future periods of the federal government's mandate. A large shock, therefore, allows a federal government of type 1 the opportunity to "prove itself" dependable.

5. CONCLUDING COMMENTS

The objective of the paper is to examine the incentive effects of interregional transfers on regional government spending levels in a multi-period model. Interregional transfers redistribute income among regions in a federation and provide insurance against shocks to regional endowments. The paper models the repeated strategic interaction between the regional and federal governments and explores the factors influencing the time-path of regional government spending when regional governments face uncertainty in regard to the federal government's ability to commit to its announced transfer scheme. The paper shows that in the presence of small shocks to regional endowments, the softness of regional government budget constraints increases over time if the federal government has a known finite mandate. Large shocks, however, can result in discrete changes in regional government spending that persist for the remainder of the federal government's mandate. In particular, if the federal government is able to commit to its announced transfer scheme, then a large shock allows the federal government to prove itself dependable, and regional government spending levels decrease as a result. If instead, the federal government is unable to commit to its announced transfer scheme, then a large shock results in an increase in regional government spending that reflects the full incentive effect of a soft budget constraint. The paper also shows that the speed in which regional government spending levels increase over time depends positively on the discount rate and negatively on the prior probability that the federal government is able to commit to its announced transfer scheme.

The model analyzed is a very simple one and is a first step at extending the theoretical literature on soft budget constraints to a repeated-game setting. The model can be extended in several directions. For example, a multi-period model could also be used to examine the time-path of regional government borrowing in the presence of soft budget constraints. In particular, the federal government's incentive to increase transfers in response to excessive borrowing can be examined in a repeated-game framework similar to the one adopted in this paper. A further extension would be to incorporate other sources of the central government's commitment problem besides the incentive for risk-sharing that has been adopted here. Allowing for distortionary taxation, externalities in public good provision, and political benefits, for example, would provide additional sources of time inconsistency in the federal government's transfer policy that would impact the softness of regional budget constraints.

REFERENCES

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(1) The goal of redistributive transfers is to address long-run income differentials across regions, whereas the goal of stabilizing transfers is to provide insurance in response to short-run income differentials. In general, interregional transfer schemes address both of these goals, and the simple transfer scheme employed in this paper reflects this reality. Note that the set of instruments available to the federal government may prevent the government from achieving the separate goals of risk-sharing and redistribution. Persson and Tabellini (1996a) examine the trade-offs between risk-sharing and redistribution in this case. Furthermore, the federal government may also be constrained by institutional factors that prevent it from treating citizens differently across regions.

(2) See, for example, Aizenman (1998), Boadway and Tremblay (2004), Garcia-Mila, Goodspeed, and McGuire (2002), Goodspeed (2002), Inman (2003), Pisauro (2001), Rodden (2001), Sanguinetti and Tomassi (2004), von Hagen et al. (2000), von Hagen and Dahlberg (2002), and Wildasin (1997)). See Vigneault (2007) for a survey.

(3) Note, however, that the qualitative results of the model would be unaffected by allowing for costly mobility.

(4) Note that if [pi] = 1 in the specification of the magnitude of the shock to the endowment in region B , then the regional shocks are perfectly negatively correlated, and there is therefore no aggregate risk. The optimal transfer scheme would then have the federal government allocating half of the aggregate endowment to the representative resident in each region.

(5) This is true as long as the shocks to regional endowments are not perfectly negatively correlated. Otherwise, as was explained in footnote 4, there is no aggregate uncertainty, and the outcome here is the same as with commitment.

(6) One important difference between Barro's analysis and ours is that, in Barro's model, a policymaker with constrained ability to commit to its announced policy may find it optimal to randomize its choice of being "dependable" or not prior to the final period. The incentive to randomize does not arise in the model due to the presence of the random shock to the regional endowments. That is, depending on the realization of the shock to the regional endowments, a federal government with constrained ability to commit to its announced policy has an incentive to adopt a pure strategy of either masquerading as a dependable government or reneging on its announced policy, as will be seen below.

Marianne Vigneault

Department of Economics

Bishop's University

2600 College Street

Sherbrooke, Quebec, Canada

J1M 1Z7
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