Debts and deficits with fragmented fiscal policymaking

Journal of Public Economics 76 (2000) 105–125www.elsevier.nl / locate /econbase

Debts and deficits with fragmented fiscal policymakinga,b ,*Ándres Velasco

aDepartment of Economics, New York University, 269 Mercer Street, 7th Floor, New York,NY 10003-6687, USA

bNBER, 1050 Massachussetts Ave., Cambridge, MA 02138, USA

Received 1 July 1998; received in revised form 1 February 1999; accepted 1 April 1999

Abstract

This paper develops a political-economic model of fiscal policy — one in whichgovernment resources are a ‘common property’ out of which interest groups can financeexpenditures on their preferred items. This setup has striking macroeconomic implications.Transfers are higher than a benevolent planner would choose them to be; fiscal deficitsemerge even when there are no reasons for intertemporal smoothing, and in the long rungovernment debt tends to be excessively high; peculiar time profiles for transfers canemerge, with high net transfers early on giving rise to high taxes later on. 2000Elsevier Science S.A. All rights reserved.

Keywords: Fiscal deficits; Debt; Tragedy of the commons; Dynamic games

JEL classification: E6; H6

1. Introduction

Many countries of the world — both OECD economies and developing1countries such as those in Latin America — have systematically run budget

deficits since 1973, and this has often led to unsustainable debt accumulation. In

*Tel.: 11-212-998-8900; fax: 11-212-995-4186.E-mail address: [email protected] (A. Velasco)1On the OECD, see Alesina and Perotti (1994). The fiscal experience of a number of Latin American

countries is also reported and analyzed in Tornell and Velasco (1991) and references therein. See alsothe essays in Larrain and Selowsky (1991).

0047-2727/00/$ – see front matter 2000 Elsevier Science S.A. All rights reserved.PI I : S0047-2727( 99 )00054-7

106 A. Velasco / Journal of Public Economics 76 (2000) 105 –125

some extreme cases, such as those of Mexico, Argentina and Bolivia in the 1980s,drastic changes in spending and taxes were eventually required to restore solvency.In other serious but less dramatic cases — such as those of Belgium and Italy,where the public debt is above 100% of GNP — lasting fiscal stabilization is yet tooccur.

This phenomenon is not easy to reconcile with the neoclassical model (Barro,1979) that views debt accumulation as a way to spread over time the costs ofdistortionary taxation. While the neoclassical model fits the US data reasonablywell (Barro, 1986), cyclical and intertemporal smoothing factors cannot fullyaccount for the recent increase in peacetime deficits in OECD countries (Roubini

2and Sachs, 1989). Furthermore, the tax-smoothing model does not seem to fit thebudget data from developing countries (Edwards and Tabellini, 1991; Roubini,1991).

Hence, the recent fiscal policy of many countries implies a ‘deficit puzzle’. Thispaper presents a model of ‘fragmented fiscal policymaking’ that offers anexplanation for the apparently puzzling behavior of debts and deficits. Rather thanfocusing on a representative individual and a benevolent policymaker bent onmaximizing the individual’s welfare, I instead consider a society divided intoseveral influential interest groups, each of which benefits from a particular kind ofgovernment spending. The government is assumed to be weak, in that each of theinterest groups can influence fiscal authorities to set net transfers on the group’starget item at some desired level. Finally, a key assumption is that all interestgroups share the same budget constraint, enjoying ‘common access’ to governmentresources.

This policymaking regime can be interpreted in one of several ways, all ofwhich have counterparts in countries’ recent experience. First, spending pressuresmay arise from sectoral ministers or parliamentary committees with specialinterests that overwhelm a weak Finance Minister. In a detailed set of studies ofthe European Community in the 1970s and 1980s, von Hagen (1992) and vonHagen and Harden (1994) conclude that budgeting procedures that lend the financeminister ‘strategic dominance over spending ministers’ and ‘limit the amendmentpowers of parliament’ are strongly conducive to fiscal discipline. The opposite

3arrangement often leads to sizeable deficits and debts. The three countries withweakest budgetary procedures (those with the weakest finance minister, mostparliamentary amendments, etc.) had deficits that averaged 11% of GDP in the

2Bizer and Durlauf (1990) argue that US tax rates do not seem to be a random walk, as implied bythe theory. Rather, they find an eight-year cycle for tax changes, a feature suggestive of a politicalequilibrium.

3More specifically, von Hagen (1992) constructs an index characterizing EU national budgetprocesses on four grounds: (a) strength of the Prime Minister or Finance Minister in budgetnegotiations; (b) existence of overall budget targets fixed early on and limits on parliamentary powersof amendment; (c) transparency of the budget document; and (d) limited discretion in the implementa-tion of the budget.

A. Velasco / Journal of Public Economics 76 (2000) 105 –125 107

1980s, while the three countries with the strongest procedures had deficit ratios of2%. The accumulated public debt stocks were also very different between these

4two sets of countries. Similar results are reported by Alesina et al. (1996) in theirstudy of 20 Latin American and Caribbean countries. Using a methodology quitesimilar to that of von Hagen, they find that the six countries with the strongestfiscal processes had, between 1980 and 1993, fiscal surpluses that averaged 1.8%of GDP; the seven countries with the weakest processes had deficit ratios of 2.2%over the same period.

Second, spending may be set by decentralized fiscal authorities representing5particular geographical areas. The cases of Argentina and Brazil are instructive.

They are both federal countries in which over the last two decades many spendingresponsibilities have been transferred to the sub-federal level. Lacking sufficientrevenues of their own and facing unclear rules, sub-federal governments havesystematically run deficits which de facto have become the responsibility of thefederal authorities. There have generally been three mechanisms through whichstate and provincial entities could ‘pass on’ their deficits: (a) borrowing from statedevelopment banks which in turn could rediscount their loans at the Central Bank— in effect monetizing the sub-federal deficits; (b) obtaining discretionary lumpsum transfers from the federal government, generally requested around electiontime and after large debts had been accumulated; and (c) accumulating arrears withsuppliers and creditors, which (for either legal or political reasons) were eventuallycleared up by the federal authorities. Understanding that at least part of the costwould be borne by others, sub-federal governments have been tempted tooverspend and overborrow. Similar troubles affected the former Yugoslavia. Theyare also becoming increasingly severe in Russia, as Wallich (1992) and Sachs(1994) argue.

Third, transfers may be determined by money-losing state enterprises facing softbudget constraints — for instance in Mexico and Brazil in the 1970s or in Russiaand some countries of Eastern Europe more recently. As Kornai (1979) empha-sized, state firms have an incentive to pay excessive wages (thus simply reducingthe profit stream that would go to the Treasury) and engage in large and riskyinvestments (managers benefit from running larger firms but bear none of theinvestment risk). Bankruptcy is not a real threat, as government subsidies andbailouts from state banks often extend the life of distressed firms. Lipton andSachs (1990), among others, have pointed out this problem became increasinglyacute with the decline of communism and the beginning of transition. Holzmann

4More generally, Roubini and Sachs (1989) and Grilli et al. (1991) have shown that among OECDcountries, those with proportional representation and fractionalized party systems tend to display highdeficits and debt.

5The case of Argentina is studied in Jones et al. (1997) and World Bank (1990a,b,c), and that ofBrazil in Shah (1990) and Bomfin and Shah (1991). Stein et al. (1997) discuss fiscal arrangements atthe subnational level for all of Latin America and the Caribbean.


(1991) estimates that in Eastern Europe during the 1980s budgetary subsidies tostate enterprises averaged almost 10% of GDP. In Cuba in 1994, such subsidiesreached 21% of GDP.

The inefficiencies that arise when several groups or officials with redistributiveaims have control over fiscal policy have been recognized in the literature.Weingast et al. (1981) and, more recently, Chari and Cole (1993) and Chari et al.(1994) have shown that having the supply of local public goods financed withnational or federal revenues creates incentives for pork barrel spending. Aizenman(1992) and Zarazaga (1993) have argued that if fiscal and/or monetary policy aredecided upon in a decentralized manner, a ‘competitive externality’ arises whichgives the economy an inflationary bias. What all these models have in common isthat, because the benefits from spending accrue fully to each group, while the costsare spread over all groups, incentives are distorted and a ‘spending bias’ emerges.

As Alesina and Perotti (1994) stress, however, the models in the literature so farare essentially static, focusing on the level of expenditures rather than on the

6behavior of debt and deficits. This paper, by contrast, focuses on the dynamicaspects of fragmented fiscal policymaking in the context of an infinite horizonmodel. Fiscal authorities are confronted with an explicit intertemporal trade-off:high deficits today mean lower spending or higher taxes tomorrow. Does a dividedgovernment structure lead rational fiscal authorities to run debts and deficits thatare ‘too high’ in some well defined sense? The model below provides anaffirmative answer to this question. If government net assets (the present value offuture income streams minus outstanding debts) is the common property of allfiscal authorities, then a problem arises that is logically quite similar to the‘tragedy of the commons’ that occurs in marine fisheries or public grazing lands(Levhari and Mirman, 1980; Benhabib and Radner, 1992).

Two distortions are present if n agents share the stock of the resource. First,each uses the whole stock and not one nth of it as the basis for consumption orspending decisions. Second, the return on savings as perceived by one agent is thetechnological rate of return (the rate of interest or the rate of growth of naturalresource stocks) minus what the other n 2 1 agents take out. Hence, to the extentthat savings depends positively on the rate of return, each agent undersaves(overspends in the case of fiscal policy, overexploits in the case of naturalresources). This means that deficits are incurred and debts accumulated even incontexts where there is no incentive for intertemporal smoothing, so that a centralplanner guiding fiscal policy would run a balanced budget. In short, and in contrast

7to earlier work, the model exhibits a ‘deficit bias’.

6A partial exception is Chari and Cole (1993), who consider a two-period model.7Of course, this is not the only type of political economy story that can yield a deficit bias. An

important alternative explanation is provided by Persson and Svensson (1989) and Tabellini andAlesina (1990). In their models, society is divided into groups with different preferences (over thecomposition of government spending, for instance). Because current majorities know that in the future adifferent majority with different preferences may be in control of fiscal policy, those currently in powerattempt to ‘bind’ the actions of their successors by leaving them a large public debt.


A related implication of the model is that long-run levels of public debt arehigher than those that would be chosen by a benevolent planner. In fact, deficitsand debt accumulation continue until the government reaches its debt ceiling.

The time path of spending and deficits is interesting. Along the equilibrium pathtransfers are positive and high for large stocks of government wealth, but shrinkand eventually become negative (groups begin to pay taxes) as government wealthbecomes smaller. Since the trajectory involves hitting the credit ceiling, debtaccumulation stops when the ceiling is reached, and interest groups are stuckservicing the debt via high taxes forever thereafter.

Comparative dynamics are also non-standard. A temporary windfall gain togovernment income can be associated with ongoing budget deficits — in contrastto standard theory, which predicts that a surplus should materialize whilegovernment income is abnormally high.

In a companion paper (Velasco, 1999) I have analyzed whether these dynamicbudget inefficiencies can be overcome by allowing the groups within thegovernment to develop ‘reputations’ for low spending. I show in that paper thatreputation may indeed cause groups to moderate spending and stabilize the growthof government debt, but only after a period of time during which debt is built upand government wealth falls. Hence, fiscal stabilization is typically ‘delayed’ in

8the sense of Alesina and Drazen (1991).The paper is structured as follows. Section 2 sets up the basic model, while

Section 3 characterizes the benevolent planner’s solution to the relevant fiscalpolicy problem. Sections 4 rules out the possibility of extreme equilibria in whichgroups transfer at the maximum feasible rate. Sections 5, 6 and 7 constitute thecore of the paper: there I characterize an equilibrium in which fragmented fiscalpolicy-making leads to a ‘deficit bias’ relative to the planner’s solution. Section 8shows budget surpluses cannot occur in equilibrium, and Section 9 concludes.

2. The basic model

There are n . 1 symmetric groups, indexed by i, i 5 1, 2, . . . , n. Each can bethought of as a particular constituency or recipient of government largesse. Nettransfers to group i — denoted by g — can be interpreted as subsidies to itsi

members minus the taxes that group pays, or net spending on a public good thatonly benefits those in group i. Hence, g can be positive or negative. In additioni

¯there is a maximum transfer (denoted by g .0) and a minimum transfer (denoted¯by 2g ) that can be made to any group. Notice that since that minimum transfer is

negative, it is in fact the maximum tax that can be levied. This maximum tax could

8There are also number of technical differences between the papers. The other paper employs adiscrete time model, and the equilibrium concept is not Markovian. Rather, it is a ‘switchingequilibrium’ of the kind developed by Benhabib and Radner (1992).


exist because of political constraints not modeled here, or simply because eachgroup’s own resources are finite.

Any excess of expenditure over revenues can be financed by borrowing in theworld capital market at a constant real rate r, which is exogenous given theassumption that the economy is small and open. Accumulated debts are a jointliability of all n groups, as would be the case with the national debt in any country.The government budget constraint therefore is

n

~b 5 rb 1 y 2O g (1)t t iti51

where y denotes exogenous non-tax government revenue (e.g., income from stateenterprises or transfers from abroad) and b is the stock of the internationallyt

traded bond held by the government at time t, which can be interpreted as thegross international reserves minus outstanding public debt — both earning or

9paying the interest rate r.As is usual in this kind of setting, I impose on the government the solvency

condition

2rtlim b e $ 0 (2)tt→`

10which prevents unbounded debt growth.If we define non-tax government wealth (hereafter government wealth for

simplicity) as w ; b 1 y /t, constraint (1) can be written ast t

n

~w 5 rw 2O g (3)t t iti51

which is the expression I shall use from now on.How do groups interact in order to determine fiscal policy? The key assumption

is that the central fiscal authority is weak, and that group i itself can determine the`sequence hg j . While each group has many members, they act in a coordinatedit t50

fashion (through a congressional leader or member of the cabinet, for example) insetting the level of net transfers g .it

The leader of group i maximizes the objective function

9As usual with continuous time formulations, care must be exercised to ensure that law of motionEq. (1) is well defined for all relevant levels of w . For a discussion of this issue in the context oft

related differential games, see Benhabib and Radner (1992) and Friedman (1971).10Throughout I abstract from the issue of default on outstanding government obligations, which is

clearly beyond the scope of this paper. The standard literature on optimal debt management — forinstance Barro (1979) also neglects the issue of default. For important papers that study defaultexplicitly in related contexts, see Bulow and Rogoff (1989), Atkeson (1991) and Chari and Kehoe(1993a,b).


`

1 2 2r(s2t )] ¯S DU 5 2 E (g 2 g ) e ds (4)it is2t

with respect to g starting at each time t.0, subject to (1) [or, equivalently, (3)]it

and (2). I assume a quadratic formulation in order to get closed-form solutions tothe dynamic games that follow. Notice also that the subjective rate of timediscounting has been set equal to the world interest rate in order to abstract fromthe conventional reasons for borrowing and debt accumulation.

Groups’ utility is a decreasing function of the gap between the actual net¯transfer they receive and a bliss level g (for simplicity, this bliss level and the

maximum transfer are assumed to be the same). Notice that this formulation¯implies that U is concave in g as long as g # g; satisfaction of this condition isi it it

¯ensured by the fact that g is also the maximum transfer level. Notice also that thisformulation implies that groups derive utility from the transfer (presumably byconsuming it) as soon as they receive it. This is the way real-world budgetingoccurs. You use it or lose it: expenditures are authorized for a given budget cycle,and if the money is not spent within that cycle the authorization expires.Allocations are also linked to particular expenditure items — a provincialgovernment or state enterprise is typically not allowed to obtain resources from the

11central government and just stash them away for unspecified future use.Finally, some remarks about government wealth are in order. We must ensure

that at the start the government is rich enough to be solvent, but poor enough tomake the story interesting. The assumption that

¯ ¯ng ng] ]2 , w ,0r r

guarantees exactly that. Notice also that, given the assumption of a maximum tax¯ ¯per group equal to 2g, the level 2 (ng ) /r constitutes minimum allowable

government wealth. Beyond that no lender would advance additional resources tothe government, for clearly the value of its debts would exceed the present value

¯of its maximum tax revenue. Therefore, the debt level b 5 2 (ng 1 y) /r consti-tutes the maximum debt level or, equivalently, the country’s credit ceiling. At thatpoint credit rationing sets in, forcing the groups to reduce the transfers they exactand causing a stabilization in the growth of government debt.

¯Notice that once government wealth reaches 2 (ng ) /r (or, equivalently, debt¯reaches 2 (ng 1 y) /r) it is stuck there: building wealth back up would require

¯ ¯transfers smaller (more negative) than 2 g; transfers larger than 2 g would cause

11The alternative and unrealistic case in which groups can hold resources and consume thenwhenever they please would surely yield different results than the ones derived below. Groups wouldhave an incentive to grab as much as possible from the common pool at the start of the game, and couldthen choose their preferred time profiles for consumption independently of the actions of others.


debt to accumulate further; clearly, neither situation is feasible. In other words,12¯wealth level 2 (ng ) /r is an absorbing state.

¯If starting at some time T, government wealth reaches 2 (ng ) /r (and remains¯there forever, implying that each group pays taxes equal to 2 g forever), group

utility as of that time is

2r 2] ¯S DU 5 2 g (5)iT r

where the superscript ‘r’ stands for ‘rationing’.Eqs. (2)–(4), plus the assumed initial condition on wealth and the bounds on

feasible transfers, provide the setting for a dynamic game among the leaders of then groups.

3. The benevolent planner’s policy

Before constructing equilibria for that game, however, it is useful to ask aboutthe level of transfers that would be chosen by a benevolent planner whomaximized the joint welfare of all groups (with equal weights for each). In thissituation in which all the groups become symmetric, such a planner wouldmaximize (4) subject to (2), to

~w 5 rw 2 ng (6)t t it

and to w . 0 given. The solution to that standard optimal control problem is0

rwt]g 5 ;t $ 0 (7)it n

so that at each point in time each group consumes ‘its share’ of governmentpermanent income. Plugging this transfer rule into the budget constraint (6) yields~w 5 0. Hence, the budget is always balanced and government wealth is constantt

throughout. This is simply an expression of the principles of public debtmanagement developed by Barro (1979): since the rate of interest equals the rateof subjective discounting and government non-interest income is flat over time,there are no transfer-smoothing reasons for debt accumulation.

The reaction of transfers and debt accumulation to temporary changes ingovernment income y is also guided by smoothing reasons. Suppose, for instance,

H L H Lthat such income can take two levels, y and y , y ,y . Suppose, in addition,that at some time t*.0, the planner unexpectedly learns that income will be at its

12Again, this whole discussion makes sense only if default is assumed away.


H Lhigher level y until some time t**.t*, and it will settle at the lower level yforever thereafter. Then, using standard methods one can show

**H L 2r(t 2t )~b 5 ( y 2 y ) e . 0, t* # t # t** (8)t

That is to say, the government will run a surplus and accumulate assets (repaydebt) during the time of the temporary windfall.

4. On the non-existence of corner equilibria

A strategy profile that would seem to be a natural candidate for equilibrium isone in which n groups receive the maximum (and ‘bliss’) transfer rate until thecredit ceiling is reached. If groups are fragmented and act myopically, this is whatone might expect them to do. This section shows that this conjecture is incorrect,and there is no subgame perfect equilibrium in which transfers are at a ‘corner’ aslong as it is feasible.

More formally, the proposed strategy profile is:

¯ ¯ng ng¯ ] ]g if . w . 2tr rg 5 (9)it ¯ng5 ¯ ]2 g if w 5 2t r

When is this strategy profile a subgame perfect equilibrium? As argued in the¯previous section, it clearly is after wealth reaches 2 (gn) /r; it only remains to

check whether such strategies are best responses to one another for larger levels ofwealth.

Suppose one group i expects all other (n21) groups to extract transfersfollowing (9). For time 0 # t # T it then faces the budget constraint

¯~w 5 rw 2 (n 2 1)g 2 g (10)t t it

To compute its best response group i must then maximize

T

1 2 2r(s2t ) 2r(T2t ) r] ¯S D2 E (g 2 g ) e dt 1 e U (11)is iT2t

for all 0 # t # T, where T is the first time the credit ceiling is reached (for-¯mally, T5sup hw . 2 (ng ) /rj), subject to Eq. (10), w . 0 given, and w 5t$0 t 0 T

r¯2 (ng ) /r. Recall that U is given by (5).iT

Let m be the costate variable associated with state variable w . Necessary andt t

sufficient conditions for a maximum arise from the solution to the system given by¯law-of-motion (10), w given, w 5 2 (ng ) /r, and0 T


¯2 g 2 g $ m , 0 # t # T (12)it t

~m 5 0, 0 # t # T (13)t

13plus the transversality condition at T :

1 2 r] ¯ ¯S D2 (g 2 g ) 1 m (rw 2 (n 2 1)g 2 g ) 2 rU 5 0 (14)iT T T iT iT2¯From these conditions we can infer a condition for transfers equal to g 5 g,it

0 # t # T, to be a best response on the part of group i. If it is, then we have anequilibrium with maximum (corner) transfers.

Suppose that such a transfer profile does indeed take place. Using w 5Tr¯ ¯2 (ng ) /r, g 5 g, and the expression for U from (5), expression (14) can beiT it

rearranged to yield a terminal condition for the costate variable:

g]m 5 . 0 (15)T n

Since (13) implies that the costate is constant always in the interval between times¯0 and T, it must be the case that m takes on the value g /n at time 0 and stayst

there. Hence, all m , 0 # t , T, are positive.t

¯This means that g 5 g cannot be a best response to itself in the time intervalit

¯between 0 and T : setting g 5 g implies driving the marginal utility of spending toit

zero; since the costate at all such points is positive, that would violate first-ordercondition (12).

The intuition is the same as in any consumption-savings problem: in calculatingtheir best response groups trade current against future transfers; the valuation ofgovernment wealth as a source of future transfers is summarized by the costate; aslong as such shadow value of wealth is positive, it cannot be optimal to transfermaximally today, thereby driving marginal utility to zero.

5. Constructing interior Markov equilibria

In this section and the next I construct decentralized fiscal policy equilibria, inwhich groups use simple Markovian strategies in which net transfers are a function

13For a derivation of this transversality condition, see Kamien and Schwartz (1981), Part I, Section11 and Part II, Section 7. For an application in a similar problem, see Rustichini (1992). The problem

¯here is one of optimal control with a fixed terminal state w 5 (ng ) /r, a free terminal time T, and aTrsalvage value U . The interpretation of the transversality condition is that the terminal time should beiT

chosen so that the Hamiltonian (which summarizes current and future utility prospects, in Dorfman’sclassic interpretation), plus the time derivative of the present value of the salvage term, must equal zeroat T.


of a state variable — in this case government wealth. And, in contrast to theprevious section, such strategies are interior, since groups do not operate atmaximum transfer levels. In the next section we will see that such equilibria implyendogenous budget deficits and debt accumulation.

Since the setting is linear-quadratic, I study policy rules such that actions arelinear functions of the relevant state variable:

¯ ¯ng ng] ]f 1 brw if # w , 2t t tr rg 5 (16)it ¯ng5 ¯ ]2 g if w 5 2t r

14where f and b are two policy coefficients to be determined. Notice that while ft t15is allowed to vary, b is assumed to be constant.

As we did earlier, let T be the first time, if any, that the government hits its¯credit ceiling: T5sup hw . 2 (ng ) /rj. Focus on the time interval 0 # t # T. Ift$0 t

all other (n21) groups are expected to use rule (16), the remaining ith group facesthe budget constraint

~w 5 rw [1 2 (n 2 1)b] 2 (n 2 1)f 2 g , 0 # t # T (17)t t t it

To compute its best response group i must then maximize

T

1 2 2r(s2t ) 2r(T2t ) r] ¯S D2 E (g 2 g ) e dt 1 e U (18)is iT2t

for all t # T, subject to (2) and (17), and w . 0 given. Characterizing this best0

response, and using the fact that all groups are symmetric, one can endogenouslydetermine the optimal values of policy coefficients f and b.t

Let l be the costate variable associated with state variable w . Necessary andt t

sufficient conditions for an interior maximum are budget constraint (17) plus

g 2 g 5 l ; 0 # t # T (19)it t

l 5 rb(n 2 1)l , 0 # t # T (20)t t

plus one of two transversality conditions. If T tends to infinity we have

14 ¯By free disposal, cases in which w . (ng ) /r need not be considered.t15This assumption is not restrictive in that I am simply constructing equilibria in which strategies

have this form. Whether other equilibria exist in which strategies are different is an open question.


2rTlim l w e 5 0 (21)T TT →`

16while if T is finite we have

1 2 r] ¯S D0 5 2 (g 2 g ) 1 l (rw [1 2 (n 2 1)b] 2 (n 2 1)f 2 g ) 2 rUiT T T T iT iT2(22)

~~ ~The policy rule g 5 f 1 brw implies g 5 f 1 brw . Combining this withit t t it t t

Eqs. (17), (19) and (20) yields

~ft¯ ]~w 5 rw (n 2 1)b 1 (n 2 1)(f 2 g ) 2 (23)t t t rb

Application once again of the policy rule to (17) yields

~w 5 rw (1 2 nb ) 2 nf (24)t t t

Equating coefficients on the term rw in Eqs. (23) and (24) yieldst

1]]b 5 (25)2n 2 1

Next, equating coefficients on the term involving f yields the differentialt

equation

n 2 1~ ¯ ¯ ]]F S DGf 5 r[f 2 g(1 2 nb )] 5 r f 2 g (26)t t t 2n 2 1

whose only steady state is

n 2 1¯ ]]S Df 5 g .2n 2 1

Notice this differential equation is unstable around that steady state.Differential equations (24) and (26) can also be expressed in terms of g and w .it t

For the first one only needs to undo the application of the policy rule:

~w 5 rw 2 ng , 0 # t # T (27)t t it

For the second, again differentiate the policy rule with respect to time, and use(24) and (26). This yields

n 2 1]] ¯~ S Dg 5 r ( g 2 g ) (28)it it2n 2 1

16Once again, for a derivation of this transversality condition, see Kamien and Schwartz (1981), PartI, Section 11 and Part II, Section 7. For an interpretation and intuition, see the previous section, inwhich the same condition is used.


where we have used Eq. (25) to eliminate b. Eqs. (27) and (28) constitute asystem of two differential equations in two unknowns. The initial condition w is0

given.ss ¯The unique interior steady state of the system (27) and (28) is given by g 5 gi

ss ¯and w 5 (ng ) /r. Notice also that the system given by Eqs. (27) and (28) caneasily be shown to have two positive (and real) roots; hence, the system is unstable

ss ¯around its unique steady state. There is also a ‘corner’ steady state at g 5 2 giss ¯and w 5 2 (ng ) /r. It is easy to see this steady state is a ‘sink’.

Notice, finally, that the Markov strategies postulated in (16), whose policycoefficients we have just determined, and whose associated dynamics are given bythe system of equations (27) and (28) (plus appropriate endpoint conditions),clearly give rise to a subgame perfect equilibrium: the strategies are, byconstruction, best responses to themselves, and these best responses have beenconstructed by allowing each group to reoptimize at each point in time.(Alternatively, subgame perfection obtains because the strategies are specified as afunction of the state, not of time, so that they constitute best responses in thesubgame beginning at any arbitrary level of the state.)

6. Prodigal transfers and endogenous budget deficits

In this section I show that the Markovian equilibrium strategies just computedcause sustained fiscal deficits and, as a consequence, the government reaches itscredit limit in finite time.

It is convenient to construct the equilibrium backwards, starting with theterminal conditions. We know that if the credit ceiling is reached we have

¯w 5 (ng ) /r. What about g ? Take first-order condition (19) evaluated at T,T iTr¯w 5 2 (ng ) /r and U from (5) and substitute them into transversality conditionT iT

(22). That yields the quadratic equation

1 2 2] ¯ ¯ ¯ ¯S D2 (g 2 g ) 2 (g 2 g )(g 1 g ) 1 2g 5 0iT iT iT2

5 ¯ ¯]whose roots are g 5 h 2 g, ( )g j. Only the root 2g satisfies the requirementiT 3

¯ ¯ ¯g # g # g and is therefore admissible. Notice also that at time T, w 5 2 (ng ) /riT T17¯ ~and g 5 2 g yield the necessary property that w 50.iT T

Fig. 1 depicts equilibrium dynamics. Only the area within the box is admissible:because the initial condition w is below the steady-state level by assumption, g0 i0

must also be below the steady-state level in order to be feasible; in addition, both

17 ~ ~Clearly, w , 0 would violate the credit ceiling. But w . 0 is not possible either, for it wouldT T

¯require taxes larger than 2 g, and this is ruled out by assumption.


Fig. 1. Dynamics of spending and wealth.

w and g must be above their allowable minima. We know the terminal conditiont itss ss¯ ¯is at the ‘corner’ steady state at g 5 2 g and w 5 2 (ng ) /r. The initial positioni

of the system must be at a point such as A, where w is given and g follows from0 i0

the need to reach the terminal condition at time T. Clearly, w declinest

~monotonically throughout, for it starts and ends above the w 5 0 line. Transferst

are such that there is a budget deficit over the whole time interval between 0 andT, and the government reaches its credit limit precisely at this latter time.

The trajectory of spending on transfers is interesting. Notice first that there isover-spending relative to the planner’s solution, for the planner would choose, for

¯ ¯any arbitrary initial wealth 2 (ng ) /r , w , (ng ) /r, a path for transfers such that0

¯wealth either increases or remains constant. Notice also that since g 5 2 giT

transfers are obviously negative at the terminal time; by continuity of theequilibrium trajectories, g must be negative in the neighborhood of the terminalit

time as well. In other words, transfers start out large and positive, they shrink overtime, and become negative (groups begin paying taxes) before the credit ceiling isreached.

We can summarize the results of this section in the following way. Anequilibrium exist in which each group demands prodigal transfers, large enough tocause fiscal deficits and a sustained decline in government wealth (equivalently, asustained increase in government debt). Eventually, the government hits its credit


ceiling, and is locked forever in a position of paying sufficient taxes to service theassociated maximal debt level.

The intuition for this result is simple. Property rights are not defined over eachgroup’s share of overall revenue or assets. A portion of any government wealth notspent by one group will be spent by the other group. Hence, there are incentives toraise net transfers above the collectively efficient rate. As in the ‘tragedy of thecommons’ literature, this leads to overspending (here, excessively large transfers)and overborrowing relative to the planner’s solution.

7. Comparative dynamics with prodigal transfers

Two features of the equilibrium we have just characterized are noteworthy.First, the transfer-smoothing principles of Barro (1979) no longer hold, in thesense that deficits occur even if government income y is flat and the rate ofdiscount equals the rate of interest. And, in addition, transfer behavior by groupsdoes not react to temporary changes in government income y in the way predictedby received theory.

To see that, let us revisit next the experiment considered under the planner’sLsolution. Suppose that until some time t* . 0 groups had expected y forever. At

Hthat point groups learn income will be at its higher level y until some time t**,LT . t** . t*, and it will settle at the lower level y forever thereafter. The

resulting behavior of the budget can be analyzed quite simply using graphicalmethods.

Fig. 2 contains the phase diagram drawn with b instead of w on the horizontalaxis, in order to see the effects of changes in y. Suppose that just before time t* the

~system was at a point such as B. When the shock hits the b 5 0 locus shifts up inparallel fashion. The precise outcome depends of the size of the windfall. Consider

H ~first a not-too-large y , associated with the b 9 5 0 locus. At time t* transfers mustjump up (the government is now wealthier in present value terms) to a point such

~ ~as C. Since C is necessarily above the b 9 5 0 locus and below the g 5 0 locus, thei

system must continue to move to the South-West. Not only do transfers continue tofall, but so do government assets: the groups jointly run a budget deficit, even

18though the government as a whole is experiencing a temporary windfall. Contrastthis with the case of the planner, in which a budget surplus takes place regardlessof the size of the windfall.

But that is not the only case. Consider what happens if the windfall is veryVH ~large: y , associated with the b 0 5 0 locus. In that case, no matter how high gi

jumps (within the feasible range) at time t*, the system will always find itself~below the b 0 5 0 locus. Hence, starting from a point such as D, the system will

18 ¯Of course, dynamics must still be such that the system will eventually hit the point w 5 2 (ng ) /rT

¯and g 5 2 g, at some time that in general will not be the original T.iT


Fig. 2. Reaction to a temporary shock.

move to the South-East between times t* and t**: transfers will fall but19government assets will be accumulated as a result of a budget surplus.

The other noteworthy feature of the equilibrium is the reaction of debts anddeficits to changes in the number of interest groups. Perform the following experi-ment. Increase the number n of groups, holding the initial wealth-per-group ratio

w b 1 y /r0 0] ]]]5n n

constant. This separates the incentive effect of changing n from its possible wealtheffect. A quick look to a phase diagram such at that in Fig. 2 reveals that this

~ ~moves neither the b 5 0 nor the g 5 0 locus. Hence, the qualitative dynamics ofi

the system are invariant to the change: sustained deficits lead to sustained debtaccumulation and eventual bumping against the credit ceiling.

Only qualitative features of the trajectory change. Appendix A shows that as thenumber n of groups rises, the time T it takes to reach the credit ceiling decreases.

19Once again, dynamics must still be such that the system will eventually hit the point w 5T

~¯ ¯2 (ng ) /r and g 5 2 g. In this case this means that the system must be above the b50 locus at timeiT

t**. This requirement pins down the size of the jump at t*.


Notice also from (28) that the higher is n, the more quickly g falls over time.it

These two facts together imply that the initial level of transfers is higher the largeris n. The intuition is that, the larger the number of groups, the smaller eachbecomes relative to the total, and the more each can neglect the effect of its actionson the aggregate behavior of the budget. Hence, a larger n leads to initially highertransfers and a shortening of the period during which the government can keepborrowing.

8. On the non-existence of frugal transfers and endogenous budgetsurpluses

Does decentralized fiscal policymaking always lead to budget deficits? Yes. Inthis section I show that there can be no equilibria with sustained surpluses, so that

¯debt decreases over time and government wealth converges to the level (ng ) /r,¯which can sustain ‘bliss’ transfers g.

As before, I construct the equilibrium starting from the terminal condition andproceed backwards. The Markovian policy rule (16) still holds. Let t be the timewhen wealth reaches its bliss level. Then, the policy rule g 5 f 1 brw mustit t t

yield

¯ng¯ S]Dg 5 f 1 br .t r

This clearly means that, at that point, the term f must be constant. But inspectiont

of differential equation (26), which is unstable around its steady state, reveals thatf can only be constant at some point in time if it is constant throughout — that is,t

if it starts at its steady state. Hence, our first result is that, in this equilibrium, sucha path would require

n 2 1¯ ]]S Df 5 f 5 g , ; 0 # t # t (29)t 2n 2 1

Combining this with the fact that the optimal value of the policy coefficient b isstill given by (25), we have that each group’s policy rule would be

¯r ng¯ ]] S ]Dg 2 g 5S D w 2 , 0, 0 # t # t (30)it t2n 2 1 r

¯where the inequality comes from the initial assumption that w , (ng ) /r, so that0

¯w , (ng ) /r for all 0 # t # t. Hence, we have a contradiction. The spending patternt

by groups required by the first-order conditions would imply that debt actuallygoes down, not up. We conclude that there can be no equilibria with sustainedfiscal surpluses.


9. Conclusions

Economists have spent much time and energy modelling the allocation ofresources in those regions of the modern economy where the market system indeeddoes allocate resources. But there is a very large portion of such economies — thegovernment sector — within which there are no private property rights, and wherethe allocation of resources does not follow market forces. If we move beyond theview of government as a monolithic entity that behaves like a single individual,economics must provide an account of how economic decisions are made amonggovernment groups, and how politics both frames and determines those decisions.

This paper suggests one of the simplest possible models of a government withmany controllers — one in which government net income is a ‘commons’ fromwhich interest groups can extract resources. This setup has striking macro-economic implications. Transfers are higher than a benevolent planner wouldchoose them to be; fiscal deficits emerge even when there are no reasons forintertemporal smoothing, and in the long run government debt tends to beexcessively high; peculiar time profiles for transfers can emerge, with highpositive net transfers early on giving way to high taxes later on. All these resultsemerge exclusively from the strategic interaction among competing groups, in acontext in which fiscal policymaking is decentralized and interest groups haveopen access to government resources.

Acknowledgements

An earlier version of this paper was presented at Columbia, Harvard, theInstitute for International Economic Studies (Stockholm), the MassachusettsInstitute of Technology, New York University, and the Federal Reserve Bank of

´Minneapolis. I am grateful to Alberto Alesina, Jess Benhabib, Raul Laban, TorstenPersson, Dani Rodrik, Gilles St. Paul, Federico Sturzenegger, Mariano Tommasi,and Aaron Tornell, to two anonymous referees and to seminar participants forhelpful comments. The C.V. Starr Center for Applied Economics at New YorkUniversity and the Harvard /MIT Research and Teaching Group on PositivePolitical Economy provided generous support.

Appendix A

From the overall solvency constraint of the government it must be the case that

T

w02rt ]E g e dt 5 (A.1)it n0


while Eq. (28) in the text implies2rh(T2t ) 2rh(T2t )¯g 5 g e 1 g(1 2 g e ) (A.2)it T T

where we have defined h ; (n 2 1) /(2n 2 1). Note that h is increasing in n.¯Recalling from the text that at terminal time T the transfer level must be g 5 2 g,T

using (A.2) and rearranging, we can write (A.1) as

2rhT rwe 0rT(h21)]] ]2 [(1 1h) e 2 2] 5 1 2 (A.3)S D ¯h 2 1 ng

which uniquely pins down the terminal time T as a function of h and of the otherparameters and initial conditions of the problem. Notice that the R.H.S. of (A.3) is

rT(h21)positive by assumption. Hence, it must be the case that (1 1h) e . 2.Expression (A.3) can be rewritten as

2rhT rwe 0rT(h21)]] ]f(T,h) 5 2 [(1 1h)e 2 2] 1 2 1 5 0 (A.4)S D ¯h 2 1 ng

Now change the number n of groups, holding the initial wealth-per-group ratiow 5 n constant. To see how the change in n affects T, compute,0

fdT n] ]5 2 , 0dh fT

where2rT 2rhT2e 2rT er(12h)T]]] ]]]f 5 [e 2 1] 2 . 0h 2 h 2 1(h 2 1)

and2rhTr e rT(h21)]]f 5 2 [(1 1h) e 2 2h] . 0S DT h 2 1

where this last inequality comes from the fact, established earlier, that it must berT(h21)the case that (1 1h) e .2, and h , 1 always. We conclude that, since h is

increasing in n, T must be decreasing in n.

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Debts and deficits with fragmented fiscal policymaking

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