Shared government and electoral cycles

Jorge M. Streb Gustavo Torrens

June 2007

Abstract

This paper examines how aggregate political budget cycles (ag-gregate PBC) are affected by checks and balances when the politicalparties are office motivated. When the legislature has to authorizenew debt, there are no PBC if there is divided government and perfectcompliance with the budget law. PBC are only possible when there isunified government or low compliance with the budgetary law. Whatdrives these results are effective checks and balances, that providea commitment device to solve the credibility problem behind PBC.An extension of the basic model is to analyze the tradeoff voters facewhen divided government comes at the cost of government efficiency.JEL Classification: D72, D78.

Keywords : Rational political budget cycles; time consistency;separation of powers; checks and balances; budgetary process.

1 Introduction

The standard results on rational PBC not only require asymmetric informa-tion, but also a fiscal authority with discretion over fiscal policy. Once onedrops the assumption of a single fiscal authority, the possibility of PBC willdepend on the leeway that the legislature allows the executive in pursuingelectoral destabilization (Streb 2005).

Saporiti and Streb (2004) formally analyze the implications for PBC ofconsidering that in constitutional democracies the process of drafting, re-vising, approving and implementing the budget requires the concourse ofthe legislature. Their approach relies on the Romer and Rosenthal (1978)and (1979) agenda setter model; Persson, Roland and Tabellini (1997) use asimilar framework to analyze how to control the rents of politicians throughseparation of powers. The executive wants to win elections, and the legis-lature represents the interests of the people. In a setup with asymmetricinformation on the budgetary process similar to the Lohmann (1998a) tim-ing, separation of powers is needed to make the budget rule credible, i.e., tocommit the executive to not distort the composition of government spending

1

towards visible items in electoral periods. Though they show the legislaturehas a moderating role on electoral cycles, compliance of the executive withthe budget law is required. Otherwise, the process is moot.

The approach developed in this paper emphasizes electoral competitionbetween political parties. Separation of powers has a bite in the fiscal processwhen the executive and legislative branches are not perfectly aligned. Thisdraws on the insight of Alesina and Rosenthal (1995) on the moderatinginfluence of an opposition legislature. Through the metric of veto players(Tsebelis 2002), this insight applies not only to divided government in pres-idential systems, but more generally to coalition governments. Coalitionmembers start to compete among themselves for votes, so it is particularlyhard for different political parties to collude close to elections.

We now sketch the relationship between separation of powers and PBCthat we model here. Suppose, as in Shi and Svensson (2006) and Alt andLassen (2005), that deficit financing is distortionary. However, there is asym-metric information and the competency of the executive just before electionsmatters for performance after elections. In electoral periods, the executivewill be tempted to increase expenditure and reduce taxes in electoral periodsto increase its electoral chances. Hence, the ex-ante optimal policy is notcredible ex-post.

Let the legislature have the veto power to reject new indebtedness, as isstandard in all budget rules. In a non-electoral period, the executive has noincentive to distort the optimal budget, because whatever it does that periodwill not affect its future electoral chances. Hence, optimal policy will beimplemented in non-electoral periods. In an electoral period, the executiveincumbent will still be tempted to distort the budget. If the legislatureis aligned with the executive, it will not curb cycles because it shares itssame electoral objectives. However, if the legislature is not aligned with theexecutive, it will not be interested in increasing the chances of success ofthe executive, so it will veto electoral changes in the budget. For this vetopower to be effective in avoiding PBC, the legislature needs the oversightand enforcement capacity to insure that the executive complies with theapproved budget law.

Following this interpretation, one can derive a sharp empirical implica-tion for aggregate PBC: if there is perfect compliance with the budget law,the budget rule is credible if the party of the executive’s leader does notcontrol the legislature. On the other hand, if there is imperfect compliance,the budget rule is never credible. Consequently, PBC should be larger eitherin countries with low legislative checks and balances, or with low observanceof the rule of law.

2

2 Checks and balances

Consider an infinite-horizon society composed by a large but finite numberof identical individuals, labeled i = 1, 2, . . . , n. Let t denote time, whereodd positive integers are electoral periods and even positive integers arenon-electoral periods.

2.1 Preferences

In every period t, individual i plays roles both as a consumer and as acitizen. The representative consumer derives utility from a public good gt

and a private good ct. The representative consumer’s per-period payoff isgiven by a quasi-linear utility function,

u(ct, gt) = ct + α ln(gt), (1)

where 0 < α < 1. The intertemporal utility function U is given by

U =∞∑

t=0

βtu(ct, gt), 0 < β < 1. (2)

Output yt is exogenous, with yt = y. By the consumer’s per-periodbudget constraint, consumption ct equals disposable income, namely, y netof government impositions pt:

ct = y − pt. (3)

2.2 Government budget

Each period t, the government is subject to the budget constraint

γt = πt + dt − (1 + r)dt−1, (4)

where γt denotes actual budget expenditures on public goods, πt are taxrevenues, dt is public debt and r is the interest rate on debt, that is constant1.

Public resources γt are transformed into the public good gt according tothe competence θt of the government:

gt = θtγt. (5)

Similarly, the competence of the government affects how impositions pt

become actual government tax receipts πt, reflecting, among other things,the use of more or less distortionary taxes:

pt =πt

θt. (6)

1We consider that government could be a net lender, i.e. dt < 0, in which case weassume that the relevant interest rate, not necessarily equal to r, is r′.

3

By (5), to provide a given level of public goods expenditure must behigher with less competent governments. Similarly by (6), with a givenlevel of impositions less competent governments generate less tax receipts.

The representative individual cares about the competence of the incum-bent in providing public goods.2 Since the incumbent does not know itscompetence when it takes budget decisions, from its viewpoint the electoraloutcome is uncertain.3

Since voters are inclined to reelect more competent incumbents, thiscreates an electoral incentive for governments to lower taxes in electoralyears. It also creates an incentive to increase expenditure using debt finance.In contrast, in Shi and Svensson (2002), and Alt and Lassen (2006), electoralcycles in the budget balance are exclusively through expenditure cycles, nottax and expenditure cycles. Here, taxes and expenditures fluctuate with thecompetence of the government.

2.3 Government competence

We assume that the competence of the government depends on the compe-tence of the party that controls the executive branch E. For each partyi = A,B, the competence shock εi is a random i.i.d. variable which

is uniformly distributed over the interval[

− 12ξ

, 12ξ

]

, with expected value

E(ε) = 0 and density function ξ > 0. A higher value of εi correspondsto a more competent politician. The probability distribution of compe-tence θi

t conditional on εit−1, F (θi

t

∣

∣εit−1 ), is also uniform, with support

[

θ + εit−1 −

12ξ

, θ + εit−1 + 1

2ξ

]

, and E(θit

∣

∣εit−1 ) = θ + εi

t−1.

Actual competence of the government is partially lasting, following afirst-order moving average process as in Rogoff and Sibert (1988) and others:

θt = θ + εt−1 + εt. (7)

Henceforth, θ > 1/ξ, so θt > 0 and (5) and (6) are well-defined.

2.4 Discount factor and interest rates

Following the insight in Shi and Svensson (2006), the quasilinear preferencesin (1), jointly with an assumption about the value of the discount factor β

2Alternatively, there could be heterogenity among voters. In that case, these prefer-ences would represent the median voter who is indifferent between the incumbent and theopposition in terms of ideology, so its vote is in equilibrium determined by the expectedcompetence of each. If the median voter were more inclined towards one of the parties,this could be represented by an additional term that pulled preferences towards right orleft, to capture the ideas in Alt and Lassen (2005).

3Given our timing, to have uncertain electoral outcomes it is not necessary to introduceprobabilistic voting through a looks shock as in Rogoff (1990), or uncertainty about relativepreferences for candidates as in Shi and Svensson (2006).

4

and the interest rates, can drastically simplify the optimal policy problem.Whereas Shi and Svensson (2006) assume the interest rate is increasing inthe level of debt, we assume that the rate r > 0 at which the governmentcan borrow is constant, but this borrowing rate is larger than the rate r′ > 0at which it can lend.

Furthermore, we assume the following condition is satisfied:

1

(1 + r)

Et

(

1θt

)

Et

(

1θt+1

) < β <1

(1 + r′)

Et

(

1θt

)

Et

(

1θt+1

) . (8)

This condition will assure that neither debt nor holding financial assetswill be optimal in equilibrium.

Also, let

(1 + r) > (1 + r′)

(

θ + 1ξ

θ − 1ξ

)2

. (9)

Given this, sinceθ− 1

ξ

θ+ 1

ξ

<Et

�1

θt

�Et

�1

θt+1

� <θ+ 1

ξ

θ− 1

ξ

, a sufficient condition for (8) to

hold is

1

(1 + r)

θ + 1ξ

θ − 1ξ

< β <1

(1 + r′)

θ − 1ξ

θ + 1ξ

. (10)

Given the parameter values of the interest rates in (9) and the discountfactor in (10), condition (8) will be met.

2.5 Asymmetric Information

The timing, as in Lohmann (1998b), is that in each period t, incumbents donot observe the value of εt before making budget decisions. The interpreta-tion of this timing is that policy is decided under uncertainty, so it leads toa lottery of outcomes. If decisions were taken instead under certainty, thechoice of the policy instrument would be the choice of the outcome.

The representative (median) voter does not observe either the executiveleader’s most recent competence shock, εt, or the budget decisions (γt, πt,dt) before voting. The only information it receives is the amount of publicgood gt that is provided, and of tax payments pt it makes. Thus, incumbentshave a temporary information advantage over the actual budget allocationimplemented. All past competence shocks are common knowledge. Weassume voters know the incentives political parties face and the objectivesthey try to achieve.4

4It is assumed that the median voter knows the parameters of the budget process.

5

2.6 Veto players

The agenda setter model of Romer and Rosenthal (1978, 1979) allows toreduce the policy-making process carried out to set the budget to the inter-action of the current leaders of the two branches of government, the executiveand the legislature.

The terms in office in the executive and legislative branches last two pe-riods (we are abstracting from midterm legislative elections). Every otherperiod, the electorate removes or confirms the executive and legislative lead-ers in an explicit electoral contest. If the incumbent is confirmed, it controlsthis branch for another term. Otherwise, the opposition takes office.

We assume there are two parties, A and B. A party’s payoffs are asfollows. Besides caring about the utility from the consumption of private andpublic goods, when a party wins executive elections and its leader becomesthe E incumbent, it receives an exogenous rent χE > 0 at the beginning ofeach term in office. The party that wins legislative elections and controls Lreceives a rent χL ≥ 0, where χL < χE. These rents reflect the strength ofthe electoral goal, to use Lohmann’s (1998b) words, and will be the sourceof conflict between political parties and the electorate.

Through the idea of veto players, the agenda setter model can be used toreflect not only presidential systems, but also the working of parliamentarysystems (Tsebelis 2002). While in a presidential system, E is the leader ofthe executive and L is the leader of the legislature, in a parliamentary systemE can be taken to represent the leader of the majority coalition party, andL the leader of the minority coalition party.

If E and L are controlled by the same party, there is no veto player: ina presidential system, this is referred to as unified government, when theexecutive has an aligned legislature; in a parliamentary system, as single-party rule where one party has a majority of seats in the legislature. Thereare veto players in a presidential system when there is divided government,and the legislature is controlled by opposition party whose electoral motivesare strictly opposed to those of the executive; in a parliamentary system,something similar happens when the party that leads government is forcedto form a coalition to reach a majority of seats in parliament.

2.7 Budget process

The process for setting the budget involves a specific system of checks andbalances. At the stage of budget formulation and approval, E makes abudget allocation proposal, which must be accepted by L to become law.We first assume no amendment rights exist, so L faces a take-it-or-leave-itproposal where the reversion outcome (the status quo) in case of rejectionis specified below. The proposals are in terms of budget expenditure and

6

debt, because the budget restriction determines the required tax revenues(only two of these three variables can be chosen freely).

• The timing of the budget process in period t is as follows:

1. E proposes γEt , dE

t to L.

2. Since L has no amendment rights, L chooses whether to accept pro-posal or not. If the proposal is not accepted, the budget is given bystatus quo γt, dt. This will determine the approved budget γt, dt.

3. E implements γt, dt, which equals the approved budget under perfectcompliance (below we will consider the case of imperfect compliance).

4. εt is realized and gt and pt are determined according to (5) and (6);

5. Voters observes gt and pt, but not εt nor (γt, πt, dt), forming a beliefθt about the incumbent’s competency.

6. Without loss of generality, we assume party A controls E. If t is anodd positive integer, i.e., an electoral period, voters decide whetherto reelect party A in E, and whether to vote incumbent party A oropposition party B for L.

7. Individuals observe εt and (γt, πt, dt) and period t ends.

2.8 Budget rule

As is standard in the agenda setting model, if the executive’s budget proposalis rejected, the status quo for expenditure is given by an exogenous reversionoutcome:

γt = γ. (11)

As to the status quo for debt, we assume that there is an endogenousdebt ceiling:

dt ≤ dt−1. (12)

This endogenous debt ceiling merely reflects the restriction that, unlessauthorized by L, there can be no new debt. This budget rule is typical ofall budget processes.

Though taxes, just like new debt, must be authorized by the legislature,for simplicity the budget rules in the model do not restrain the executive inrelation to the amount of tax receipts. Since in equilibrium the executivewill have no incentive to tax beyond expenditure (or, if there is outstandingdebt, beyond expenditure plus the amount needed to rescue outstandingdebt), it is not necessary to explicitly introduce this restriction.

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3 Equilibrium

We first study the case when there are no elections, as a benchmark.

3.1 No elections

A candidate is randomly selected in period t = 0, and he remains in officeforever. By quasilinear preferences, the marginal utility of consumption isequal to one. If, in expected value, the marginal utility of the governmentconsumption good is equal to the marginal utility of consumption, any extraresources the government may have will be optimally used to reduce taxes.

Suppose the government resorts to an extra dollar of debt in period t toreduce taxes. From expressions (1), (2), (3) and (6), it follows that expected

utility increases Et

(

1θt

)

in period t. If the extra dollar of debt is repaid next

period, utility falls by (1 + r)Et

(

1θt+1

)

in period t + 1. Since the future is

discounted at the rate β, by (8) it will never be optimal to borrow an extradollar and repay it in the next period because:

β(1 + r)Et

(

1

θt+1

)

> Et

(

1

θt

)

Here Et

(

1θt+1

)

equals unconditional expectation, since there is no informa-

tion on current shock when decision is taken, so expectation for t + 1 equalsexpectation for all future time periods. This condition also rules out thatrepaying the debt farther out in the future is optimal, because (1 + r) > 1,so the compounding effect makes the condition more binding for t > t + 2.Following an analogous argument, condition (8) also rules out the possibil-ity that the government may become a net lender. This leads to a cornersolution with no debt nor financial assets.

Since our assumptions about β, r and r′ in (8) assure that dt = 0 (i.e.,γt = πt) for t = 0, 1, ..., the intertemporal problem can be broken in asequence of simpler optimization problems.

Max{γt,πt}

Et[ct + α ln(gt)]

s.t. (3), (4), (5) and (6).

The solution, using the properties of the uniform distribution, and thenintegrating, is:

Proposition 1 Without elections, the executive will choose optimal expen-diture and tax collection each period:

γ∗t = π∗

t =α

Et[1

θ+εt+εt−1]

=α

ξ ln(θ+εt−1+

1

2ξ

θ+εt−1−1

2ξ

)

, t = 0, 1, . . . (13)

8

Fiscal policy γ∗t and π∗

t depend on expected competence, and are in-creasing in the past shock. Since the budget is decided ex-ante, it cannotbe conditioned on actual competency. However, ex-post, a more competentincumbent generates a greater provision of the public good g with a given γand imposes a lower burden on the tax payers, lowering the relative cost ofpublic vs. private goods.

3.2 Unchecked executive

Consider next the model with regular elections every two periods. Thereis only one policy-maker, the executive. In period t = 0 a candidate israndomly selected for the executive. Subsequently, odd integers are electoralperiods and even integers are non-electoral years.

The players are the incumbent party, the opposition party, the repre-sentative voter V , and Nature. Because the two parties only differ in com-petence, and these competence shocks are transitory, the solution of theinfinite-horizon model described can be broken down into a sequence ofsteps. The solution can be found by backward induction, in four steps.

Step 1: The incumbent’s decision in a nonelectoral period

In period t+1, a nonelectoral period, the incumbent (either A or B) hasno incentive to manipulate the voters’ perception of its competence, sincethe outcome of future elections will depend on the expected competence int + 3, which is uncorrelated with competence in t + 1. Since the optimalstrategies of all incumbents in the post-electoral period are the same, thedistinction between the original and the potential incumbents is omitted tosimplify the notation. Hence:

γuet+1 = γ∗

t+1 =α

Et+1[1

θt+1]=

α

ξ ln( θ+εt+

1

2ξ

θ+εt−1

2ξ

)

, (14)

πuet+1 = γ∗

t+1 + (1 + r)dt, (15)

where the superscript ue refers to unchecked executive.Notice that in a nonelectoral period the expenditure is the same as in a

setup without elections, but there may be more taxes if the incumbent hasto pay off the debt incurred in the last election period.

Step 2: The government’s plausibility restriction and the

voter’s perception of government competence

At election time, voters observe gt, pt, but not dt, γt and πt. They knowthat consumers and the government are subject to restrictions (3), (4), (5),(6).

There is an additional restriction, that we label a “plausibility” restric-tion. If the incumbent relies on debt, it must preserve the ratio betweenexpenditures on public goods and tax collection that would obtain without

9

electoral manipulation of the budget, to avoid making that action transpar-ent to voters. This restricts the way the incumbent can use debt, forcing itto split it in specific proportions between more expenditure and less taxes.

Let π∗t = γ∗

t denote the budget that is not affected by opportunisticconcerns, the optimal budget choice when there is no previous debt. Toderive the observed levels of gt and pt that satisfy our plausibility restriction,let the budget choices γt and πt be given by a scale factor ωt that determinesvalues of gt and pt possible under technological restrictions (5) and (6):

γt = ωtγ∗t , πt =

π∗t

ωt. (16)

This plausibility restriction implies that

γt

πt= ω2

t .

This pattern of budget choices allows to replicate the original distributionof shocks, with the expected value of the distribution shifted to the rightgiven ωt > 1 (the government is tempted to mimic positive competenceshocks, not negative ones). That is to say, the budget items have to satisfya certain ratio to replicate the distribution without electoral manipulation.This restriction implies that, beyond identity (4), debt must also satisfy:

dt = γt − πt =(

ω2t − 1

)

πt =

(

ωt −1

ωt

)

π∗t .

This restriction makes it clear that debt must be used in predefined propor-tions to reduce taxes and increase expenditures, to preserve the character-istics of the original distribution of competency shocks.

Voters know this restriction on government actions and they include itin their estimation of the incumbent’s competence. If voters could observeωt, they could easy calculate θt, since gt

pt= γt

πtθ2t = ω2

t θ2t , which implies that:

θt =

√

gt

pt

ωt.

However, voters do not really observe ωt. They must estimate it, in orderto estimate θt. Therefore, if we call ωt voters’ estimate of ωt, the estimateθt of θt is:

θt =

√

gt

pt

ωt.

Using this expression, voters can estimate the incumbent’s current com-petence shock (εt−1 is known in period t):

εt = θt − θ − εt−1 =

√

gt

pt

ωt− θ − εt−1. (17)

10

Step 3: The citizen’s vote

Voters compare the expected utility next period if they vote either theincumbent or the challenger. Voters can estimate the competence shock ofthe incumbent, but nothing can be concluded about the opposition fromthe observed policy actions of the government. In regard to the opposition,voters only know the distribution of εt and hence that Et[εt] = 0.

Expected utility from a vote for the incumbent is:

Et[ct+1 + α ln(gt+1) | εt] = Et[y −πue

t+1

θt+1+ α ln(θt+1γ

uet+1) | εt] (18)

Expected utility from a vote for the opposition is:

Et[ct+1 + α ln(gt+1)] = Et[y −πue

t+1

θt+1+ α ln(θt+1γ

uet+1)] (19)

In order to determine voters’ decision we must compare these two ex-pressions. We formally do this comparison in the following proposition.

Proposition 2 Et[ct+1 + α ln(gt+1) | εt] ≥ Et[ct+1 + α ln(gt+1)] if and onlyif εt ≥ 0.

Corollary 1 Voters vote for the incumbent if and only if εt ≥ 0.

Proof 1 For a proof of the proposition please see appendix A. The proof ofthe corollary is immediate from (18) and (19).

We now employ this proposition to compute the probability that theincumbent wins the election. Let’s call this probability µt = Pr(εt >

0) = Pr

(qgtpt

ωt− θ − εt−1 > 0

)

. Considering that the actual value of εt

equals

qgtpt

ωt− θ − εt−1, adding this to both sides and simplifying, we get

µt = Pr[

εt >√

gt

pt

(

1ωt

− 1ωt

)]

. Finally, considering that εt follows a uni-

form distribution with density ξ, we obtain:

µt = 1 − Pr

[

εt <

√

gt

pt

(

1

ωt−

1

ωt

)]

=1

2+ ξ

√

gt

pt

(

1

ωt−

1

ωt

)

. (20)

Notice that if voters are surprised (ωt > ωt) the incumbent increases itsprobability of wining over 1

2 . Furthermore, note that:

∂µt

∂ωt= ξ

√

gt

pt

1

ω2t

> 0. (21)

Step 4: The incumbent’s decision in an electoral period

Taking into account µt, the endogenous probability that the incumbentis reelected, the incumbent’s objective function is:

11

Max{γt,πt,dt}

Et[ct + α ln(gt) + β(ct+1 + α ln(gt+1)) + βµt χE]

s.t.(3), (4), (5), (6), (16) and (20).

Incorporating these restrictions, the government’s problem in the elec-toral period can be reframed in terms of the choice of ωt, that will determineall the fiscal variables:

Max{ωt≥1}

Et

{

y −π∗

t

ωt

1

θt+ α ln(θt + ln π∗

t + ln ωt)+

+β

y −γ∗

t+1 + (1 + r)π∗t

(

ωt −1ωt

)

θt+1+ α ln(θt+1 + ln γ∗

t+1)

+

+β

[

1

2+ ξθt

(

ωt

ωt− 1

)]

χE

}

The first order condition is given by:

dEt [·]

dωt= Et[

π∗t

θt

1

ω2t

+α

ωt−

β(1 + r)π∗t

θt+1

(

1 +1

ω2t

)

+ βξθt

ωtχE ] ≤ 0,

with strict equality if ωt > 1,

which can be simplified, using the definition of π∗t :

dEt [·]

dωt=

α

ω2t

+α

ωt− β(1 + r)

α Et

(

1θt+1

)

Et

(

1θt

)

(

1 +1

ω2t

)

+ βξθ + εt−1

ωtχE ≤ 0,

with strict equality if ωt > 1. (22)

Note that d2Et[.]dω2

t

= −2αω3

t

− αω2

t

+ 2αβ(1 + r)Et

�1

θt+1

�Et

�1

θt

� 1ω3

t

, which it is strictly

negative for ωt ≥ 1 if the following condition holds:

β(1 + r)Et

(

1θt+1

)

Et

(

1θt

) <3

2. (23)

Assuming (23) the first order condition (22) becomes sufficient for an opti-mum.

12

People have rational expectations; so in equilibrium ωt must be equal toωt. Therefore, if we call ωue

t the equilibrium value of ωt, we obtain:

dEt[·].

dωt=

α

(ωuet )2

+α

ωuet

− β(1 + r)αEt

(

1θt+1

)

Et

(

1θt

)

(

1 +1

(ωuet )2

)

+

+βξθ + εt−1

ωuet

χE ≤ 0, with strict equality if ωuet > 1.

It is clear that if there is no opportunistic motive (χE = 0), then thisexpression evaluated at ωue

t = 1 is negative (recall condition (8)) and theincumbent will not distort fiscal outcomes. On the other hand, with positiveexogenous rents from power (χE > 0) the above expression can becamepositive at ωue

t = 1, which implies that the incumbent prefers a strictlypositive ωt. We summarize these results in the following proposition.

Proposition 3 With an unchecked executive, assume that conditions

(8) and (23) hold, i.e., 1 < β(1 + r)Et

�1

θt+1

�Et

�1

θt

� < 32 . Let χt =

2α

24β(1+r)Et

�1

θt+1

�Et

�1θt

� −1

35βξ(θ+εt−1)

. Then in an electoral period (t odd):

1. If χE ≤ χt an unchecked executive does not distort fiscal outcomes(ωue

t = 1)

2. If χE > χt an unchecked executive distorts fiscal outcomes (ωuet > 1).

Corollary 2 Employing the expression (16) we obtain in an electoral period(t odd):

1. If χE ≤ χt then γuet = γ∗

t and πuet = π∗

t

2. If χE > χt then γuet = ωue

t γ∗t and πue

t =π∗

t

ωuet

Suppose that the ramdomly selected and unconstrained executive E mustformulate optimal plans in the initial non-electoral period t = 0. Viewedat t = 0, when the government sets policy in advance, the probabilities ofreelection µt are exogenous and equal to 1/2 in expected value. Therefore,the government’s best policy is to plan to pick γ∗

t and π∗t , that is socially

optimal every period, which maximizes social welfare.The problem with this optimal plan, of course, is that it is not time-

consistent: when an electoral period arrives, the government has an incentiveto increase expenditure and reduce taxes. This credibility problem underliesProposition 3 under an unchecked executive.

13

What happens if the status quo is set according to rule (11)-(12)? Well,if the rule were binding, this would effectively curb the credibility problem:in an electoral period the executive would prefer to use debt to increaseexpenditures and reduce taxes in order to look more competent, but thestatus quo rules out public indebtedness. However, it does not make senseto assume that the executive is constrained to follow any rule, unless it hasto share the power to change rules with another body. Otherwise, if theexecutive is also vested with legislative power, it can do and undo any ruleit likes, being effectively unconstrained. The natural environment where theexecutive shares rule-making power is when there is divided government,and an agreement has to be reached with the veto player L on changes inthe budget.

3.3 Separation of powers

We know turn to fiscal policy under separation of powers. We distinguishbetween divided and unified government. For both presidential and parlia-mentary systems, we describe divided government in terms of E being inthe hands of one party and L in the hands of the other.5

Suppose that in period t = 0 the randomly selected government is aunified one. Without loss of generality, assume that party A control boththe executive and the legislature. Let debt d−1 ≥ 0. Since we have an alignedlegislature or a single party government, nobody will veto proposals by E.This implies, by Proposition 3, that with sufficiently large opportunism therewill be an electoral cycle in fiscal policy in t = 1, the first electoral period. Inperiod t = 0 party A does not have any incentive to distort fiscal variables.Hence, it just selects optimal expenditures and repays past debt, if any.

As regards voters, at election in t = 1 they will want the party with thehighest expected competency holding the executive, just as in the case ofan unchecked executive. At the same time, we conjecture they will wantto have divided government. This is so, because in terms of govermentcompetence it is indifferent for voters whether a single party controls boththe executive and the legislature, or if two parties share control. But in termsof the distortion of fiscal variables, divided government is strictly preferredif an opposition legislature can block the executive’s attempts to distort thebudget in period t = 3 to look more competent. Putting all this together,we deduce that voters will prefer to vote for divided government in periodt = 1.

Does what actually happens in periods t = 2 and t = 3 under dividedgovernment conform to these conjectures? Let us assume that A controls

5Saporiti and Streb (2004)consider separation of powers with a randomly elected leg-islature that represents the interests of the people, so the legislature is never aligned withthe executive. Here, the issue of unified or divided government is endogenous and dependson voters.

14

the executive and B the legislature. In the electoral period t = 3, theexecutive would like to increase its electoral chance by using debt to selectπue

3 and γue3 . However, party B can veto this and any attempt of A to employ

debt to increase expenditures and reduce taxes, since the status quo debtrestriction given by (12), i.e., d3 ≤ d2, introduces an effective restriction inthe executive’s opportunities. Party B has the motivation and the power toveto any attempt of party A to use debt to increase its electoral chances.Therefore, party A is forced to set expenditures equal to taxes. Given thatit cannot affect its perceived competency, the best party A can do is toselect an optimal level of taxes and expenditures. Notice also that, shouldthe legislature veto these optimal level of taxes and expenditures, this wouldnot affect the voters’ perception of party A’s competence, since what votersuse in their inference problem is the no new debt restriction, which impliesthat γ3 = π3, so the ratio gt/pt can be used to infer competency whateverthe level of expenditure. Given this, the legislature has no incentive to blockoptimal expenditure in election periods.

As to the non-electoral period t = 2, the executive, controlled by partyA, chooses an optimal expenditure and repays past debt, if any, becausewhatever it does then does not affect its electoral chances in the next elec-toral period, only current welfare. The legislature, controlled by party B,does not want to veto this proposal, because if does not affect future reelec-tion prospects of either party, and lead to optimal outcome in non-electoralperiod. This confirms the voters’s conjectures we assumed at the outset.

Putting together the arguments of the last three paragraphs, and ex-tending the logic to all future time periods, we get the following conclusion:

Proposition 4 Suppose there is separation of powers and the legislaturemust authorize new debt. Under perfect compliance with the budget law,there is no electoral cycles, except in the first electoral period if we beginwith a unified government.

3.4 Imperfect compliance

At the implementation stage, E supplies the public goods, but it is moni-tored by L. We now introduce a measure of the effective compliance withthe balanced budget rule. Either there is perfect compliance, or imperfectcompliance: λ ∈ {0, 1} . The measure λ can be interpreted as the degree ofcompliance with the authorized budget, and describes the effective limits Limposes on the executive office. If there is no compliance with the budgetlaw, divided government is useless: the legislature cannot check the electoralmanipulation of the budget. Hence, there is no incentive to have dividedgovernment.

This proposition implies a sharp (and falsifiable) prediction: PBC shouldbe present in countries with imperfect compliance with the law. These

15

countries should also have less incidence of divided goverment. This canbe empirically related to the evidence on the existence of stronger cycles indeveloping countries, where there is typically less compliance with the ruleof law than in developed countries (Streb, Lema, and Torrens 2007 studythese empirical implications).

4 Shared government

An extension of the model is to combine the agenda setter model of Romerand Rosenthal (1978, 1979), where the policy-making process carried out toset the budget can be reduced to the interaction of the current leaders ofthe two branches of government, the executive and the legislature, with astylized model of government performance when parties share power.

4.1 Government competence

We assume that under separation of powers the competence of the gov-ernment depends on the competence of both the executive and legislativebranches, E and L:

θt = ρθEt + (1 − ρ)θL

t , for ρ ∈ (1/2, 1], (24)

where ρ > 1/2 to capture the characteristic that the executive has themain responsibility for government performance, though unlike the earlierliterature on PBC, government competence need not be identical with thatof the executive.

The competence of the two branches of government depend in turn onthe competence of the two political parties A and B in charge,

θEt =

{

θAt if party (leader) A control the executive

θBt if party (leader) B control the executive

, (25)

θLt =

{

θAt if party (leader) A control the legislative

θBt if party (leader) B control the legislative

, (26)

and

θAt = θ + εA

t−1 + εAt , (27)

θBt = θ + εB

t−1 + εBt . (28)

For each party i = A,B, the variable εi is a random i.i.d. vari-

able which is uniformly distributed over the interval[

− 12ξ

, 12ξ

]

, with ex-

pected value E(ε) = 0 and density function ξ > 0. A higher value of

16

εi corresponds to a more competent politician. The probability distrib-ution of θi

t conditional on εit−1, F (θi

t|εit−1), is also uniform, with support

[

θ + εit−1 −

12ξ

, θ + εit−1 + 1

2ξ

]

, and E(θit

∣

∣

∣εit−1) = θ + εi

t−1.

Replacing the competence of parties in charge of E and L in (7) leads to

θt = θ +(

ρεit−1 + (1 − ρ)εj

t−1

)

+(

ρεit + (1 − ρ)εj

t

)

. (29)

Replacing ε = ρεi + (1− ρ)εj , with i, j ∈ {A,B}, leads to equation (29),where actual competence of the government is partially lasting, following afirst-order moving average process as in Rogoff and Sibert (1988) and others:

θt = θ + εt−1 + εt.

Henceforth, θ > 1/ξ, so θt > 0 and (5) and (6) are well-defined.

4.2 Signal extraction problem

Since there are two parties, A and B, whose leaders can control E and L,government can be as follows:

Table 1. Government formationParties in government Leader of E Leader of L(i) A,A A A(ii) A,B A B(iii) B,A B A(iv) B,B B B

In cases (i) A,A and (iv) B,B, government competence reflects the com-petence of the sole party in charge of government. Given a uniform distrib-ution, equal competence has zero probability, and voters will strictly prefereither the incumbent or the opposition party.

In cases (ii) A,B and (iii) B,A, to determine the competence of theparties in charge of running government, the voters face a signal extractionproblem. Without loss of generality, let A be in E and B in L (the conversecase is analogous). Hence, εA represents the shock to party that runs E,and εB the shock to the party that runs L. Given ρ > 1/2, if there isa positive shock the conditional probability that incumbent of E has highcompetence will be larger than the conditional probability that incumbentof L has high competence, so based solely on competence citizens will wantto vote for party in charge of E for both roles (we liken political party toparty leader: if E and L are in hands of same party, competence of partyleader rules performance in both branches). In case of negative shocks, thevote will favor the leader of L, that is opposition.

With a uniform distribution, the signal extraction problem has a simpleanalytic solution. As to the conditional probability E is competent, since

17

the distributions of εA and εB are symmetric and independent, the sumof both shocks is positive half the times. This forms the denominator ofthe conditional probability. As to the numerator, one fourth of the time,both shocks are positive, so the sum is positive. One fourth of the time,the shocks εA are positive, while the shocks to εB are negative: the sumis positive if ρεA + (1 − ρ)εB > 0, which is the case whenever

∣

∣

εA

εB

∣

∣ > (1 −ρ)/ρ, with probability (1− (1− ρ)/ρ) because of uniform distribution; whenthis condition is not met, this is true only half the time, (1/2)(1 − ρ)/ρ,again because of uniform distribution. Hence, with a positive shock, theconditional probability A is competent is

P (εA > 0|ε > 0) =1/4(1 + (1 − (1 − ρ)/ρ) + (1 − ρ)/2ρ))

1/2, (30)

so if ρ = 1/2, P (εA > 0|ε > 0) = 3/4, while if ρ = 1, P (εA > 0|ε > 0) = 1,with dP/dρ = 1/2(1/ρ2) > 0.

As to the conditional probability B is competent, both shocks are pos-itive one fourth of the time, so sum is positive; one fourth of the time, theshocks to εA are negative and the shocks to εB are positive, and the sum isonly positive half the time that

∣

∣

εA

εB

∣

∣ < (1 − ρ)/ρ:

P (εB > 0|ε > 0) =1/4(1 + (1 − ρ)/2ρ)

1/2. (31)

Thus, if ρ = 1/2, P (εB > 0|ε > 0) = 3/4, so government performanceleads to the same expected competence for both parties, while if ρ = 1,P (εB > 0|ε > 0) = 1/2, so we learn nothing about the competence of theopposition party in charge of the legislature from government actions as inthe standard PBC models. Here, dP/dρ = −1/2(1/ρ2) < 0.

Our presentation has been done in terms of the leaders of the twobranches of government, E and L. However, equation (29) carries overfrom a presidential system to a parliamentary system, where the players arethe major and minor members of the government coalition. Cases (i) and(iv) in Table 1 now refer to a single party governments, while cases (ii) and(iii) refer to a coalition government were there is a major partner and aminor partner. Since coalition governments divide cabinet posts accordingto the importance of the members of ruling coalition, it is immediate to putthe largest share of responsibility for government performance on the majorpartner.

4.3 Voting decision

What does not translate so easily from a presidential system to a parliamen-tary system is the voting decision that leads to governments in Table 1. In apresidential system, the representative voter has two separate votes, and candecide whether to support the same party in the executive branch and the

18

legislature. In a parliamentary system, an individual voter cannot literallysplit its vote among the two political parties, since there is no separate votefor the legislature. However, the representative voter has a preference forwhether it wants only one party to run the government, or whether it wantstwo parties to share power. If we allow for fictitious vote splitting, allowingthe representative voter to split its vote in a given proportion between par-ties A and B, this can artificially recreate what the electorate at large cando, with a certain proportion voting one party and another proportion vot-ing the other. With our representative (median) voter who can split votes,we are skipping over the need to coordinate votes among the electorate atlarge, and the specific process by which certain vote totals lead either to asingle party or to a coalition government. Our purpose at hand is whetheronly one or more than one party run the government.

5 Conclusions

The fact that the executive incumbent is unable to credible compromise tothe optimal allocation policy is at the heart of these electoral distortions.Furthermore, it turns out that this problem is in fact generated by concen-tration of powers, which allows the executive to choose any policy it desires.Instead, when there exists separation of powers, appropriate checks and bal-ances work as a commitment device that reduces the size of electoral fiscalcycles, making all players better off (including the executive incumbent).With an exogenous status quo, this moderating force depends on the detailsof the bargaining game, namely the exact status quo location, the actualagenda-setting authority and the degree of compliance with the budget law.With an endogenous status quo given by the previous period’s budget, thepredictions are a lot simpler: separation of powers eliminates PBC, unlessthere is a low degree of compliance with the approved budget.

More generally, in relation to the debate on rules versus discretion, ourdiscussion of PBC shows that a way to solve the credibility problem, mak-ing the budget rule a credible commitment, is to introduce an institutionalarrangement of separation of powers that limits the discretion to changerules. Even though we do not consider signaling models of PBC a la Rogoff,it should be expected that separation of powers affect electoral fiscal cyclesin a similar way. The legislature basically tries to avoid distortions in the al-location of budget resources. This should reduce the electoral distortions offiscal policy, preserving the signaling role of the provision of public goods.6

6Notice that in models of PBC a la Rogoff, the timing of events is reversed in relationto Lohmann. That is, the incumbent observes its competence before choosing the per-period policy, not afterwards. However, the informativeness of the signal is not larger inequilibrium, since there is a separating equilibrium with both types of models. Besides,the Rogoff timing brings in an extra complication. The signal depends on the incum-bent’s type, something that is not required to explain the policy bias in electoral periods.

19

Our results are derived in a stationary environment where the optimalallocation of the budget is constant over time. In a stochastic environment,one can conjecture that the budget rule we analyze may still be optimalif shocks to the desired budget allocation follow a random walk. Whatmay change the results more fundamentally is lifting the assumption thatthe legislature has no electoral stakes. In this regard, our case is the bestscenario where the legislature controls the executive to try to assure thesocially optimal policy is followed.

Our model might be extended to study the role of divided governmentin presidential systems, as well as coalition governments in parliamentarysystems. For instance, Alesina and Rosenthal (1995) show how dividedgovernment is a tool to moderate the executive in a presidential system. Asimilar logic may apply in an opportunistic framework, where an oppositionlegislature may play a special role in moderating cycles. Finally, our modelof PBC under separation of powers could also be employed to understandhow the incumbent chooses among different fiscal instruments or why it usessome of them more frequently in some countries than in others. Even thoughfiscal policy includes several items, like taxes, expenditure and debt, thereis no general model of rational PBC that explains how politicians choosebetween these instruments. Following the logic of our model, it should beexpected that institutional details play an important role in the selection.This is because the executive should manipulate those fiscal instrumentswhere it has greater agenda-setting authority. It is left for a future researchto formally explore this conjecture, as well as its empirical validity.

This may be empirically relevant, since Alesina, Roubini, and Cohen(1997, chaps. 4 and 6) trace the lack of recent evidence on opportunisticcycles in the United States back to the fact that after 1980 many federaltransfer programs have become mandatory by acts of Congress, so theycannot be easily manipulated for short run purposes.

6 Appendix A: Proof of Proposition 2

We will prove this proposition in two steps. First, we will prove that theexpected value of a function of two stochastic independent variables is equalor greater than the expected value of the same function, conditional on therealization of a third variable that generates an estimation of one of thevariables, if and only if the function is increasing and concave. Secondly,we will prove that u(c, g), considered as a function of the two independentstochastic variables εt and εt−1 is increasing and concave.

Moreover, it has the unappealing implication that competent incumbents distort the most,while the utterly incompetent incumbents do not (Streb 2003 shows how heterogeneity inopportunism can overcome this feature).

20

Lemma 1 Let Z = h(X,Y ) be a function of two independent stochasticvariables X and Y , with marginal densities fx(x) and fy(y). Let us callg(x) = E [Z | x] the expected value of Z conditional on x. Consider a knownvector of information variables W that allows to estimate X and call x(w)the calculated value of X when W adopts the value w. Suppose that g(x) isan increasing and concave function of x. Then

E [Z | x(w)] ≥ E [Z] if and only if x(w) ≥ E [X] .

Proof 2 First notice that since X and Y are independent stochastic vari-ables g(x) = E [Z | x] =

∫

h(x, y) fy(y) dy. Since g(x) is concave, byJensen’s inequality it follows that g[E(X)] ≥ E[g(x)]. Employing the def-inition of g the first term of the inequality is just E [Z | E [X]], while thesecond term is equal to EX [E [Z | X]]. Therefore, we get E [Z | E [X]] ≥EX [E [Z | X]]. By the law of iterated expectations E [Z] = EX [E [Z | X]].Hence,

E [Z | E [X]] ≥ E [Z] . (32)

Now, consider the vector of information variables W , whose realization wis known. It is clear from inspection of (32) that if g(x) = E [Z | x] is anincreasing function of x, then E [Z | x(w)] ≥ E [Z | E [X]] if and only ifx(w) ≥ E [X]. Therefore, E [Z | x(w)] ≥ E [Z] if and only if x(w) ≥ E [X].

In our case the two stochastic independent variables are εt and εt+1,the vector of information variables is integrated by gt, pt, and ωt, andh(εt, εt+1) = ct+1 +α ln(gt+1). It remains to prove that Et[ct+1 +α ln(gt+1) |εt] is an increasing and concave function. We begin using expressions ((3),(4), (5), (6)) to replace ct+1 and gt+1 (line 1). Next we replace γue

t+1 andπue

t+1 for their respective values (lines 2 and 3). Finally in lines 4 and 5 weapply the conditional expected value operator.

21

Et[ct+1 + α ln(gt+1) | εt] = Et[y −πue

t+1

θt+1+ α ln(θt+1γ

uet+1) | εt] =

= Et[y −

α

ξ ln (θ+εt+

12ξ

θ+εt−12ξ

)+ (1 + r)dt

θ + εt + εt+1+

+α ln(θ + εt + εt+1) + α ln

α

ξ ln( θ+εt+

1

2ξ

θ+εt−1

2ξ

)

| εt] =

= y − α − (1 + r)d∗t ξ ln

(

θ + εt + 12ξ

θ + εt −12ξ

)

+

+α Et[ln(θ + εt+1 + εt) | εt] + α ln

α

ξ ln( θ+εt+

1

2ξ

θ+εt−1

2ξ

)

The last expression is increasing in εt; a fact that can be confirmedderiving it with respect to εt:

∂Et[ct+1 + α ln(gt+1) | εt]

∂εt=

(1 + r)dt

(θ + εt)2 −1

4ξ2

+

+αξ ln

(

θ + εt + 12ξ

θ + εt −12ξ

)

+α

ξ[

(θ + εt)2 −1

4ξ2

]

ln( θ+εt+

1

2ξ

θ+εt−1

2ξ

)

> 0.

Et[ct+1 + α ln(gt+1) | εt] is also concave in εt, which is true for α suffi-ciently low.

∂2Et[ct+1 + α ln(gt+1) | εt]

∂ε2t

= (−1)(1 + r)dt2(θ + εt)[

(θ + εt)2 −1

4ξ2

]2 +

−α

[

(θ + εt)2 −1

4ξ2

] −

α

{

2(θ + εt) ln( θ+εt+

1

2ξ

θ+εt−1

2ξ

)

− 1ξ

}

ξ

{

[

(θ + εt)2 −1

4ξ2

]

ln( θ+εt+

1

2ξ

θ+εt−1

2ξ

)

}2 < 0

References

[1] Alesina, A. and H. Rosenthal. (1995). Partisan Politics, Divided Gov-ernment and the Economy. Cambridge: Cambridge University Press.

22

[2] Alt, J. E., and D. D. Lassen (2005). ”Fiscal Transparency, PoliticalParties and Fiscal Policy Outcomes in OECD Countries.” EuropeanEconomic Review, forthcoming.

[3] Alt, J. E., and D. D. Lassen (2006). Transparency, Political Polariza-tion, and Political Budget Cycles in OECD Countries. American Jour-nal of Political Science 50: 530-550.

[4] Brender, Adi and Allan Drazen. 2005. Political Budget Cycles inNew Versus Established Democracies. Journal of Monetary Economics,forthcoming.

[5] Kydland, F. and E. Prescott. (1977). Rules rather than Discretion.Journal of Political Economy, 83: 1009-21.

[6] Lohmann, S. (1998a). Institutional checks and balances and the politicalcontrol of the money supply. Oxford Economic Papers 30: 360-377.

[7] Lohmann, S. (1998b). Rationalizing the political business cycle: Aworkhorse model. Economics and Politics 10: 1-17.

[8] Persson, T., Roland, G. and G. Tabellini. (1997). Separation of powersand political accountability. Quarterly Journal of Economics 112: 1163-1202.

[9] Romer, T. and H. Rosenthal. (1978). Political resource allocation, con-trolled agendas, and the status quo. Public Choice 33: 27-44.

[10] Romer, T. and H. Rosenthal. (1979). Bureaucrats vs. voters: On thepolitical economy of resource allocation by direct democracy. QuarterlyJournal of Economics 93: 563-588.

[11] Rogoff, K. and A. Sibert. (1988). Elections and macroeconomic policycycles. Review of Economic Studies 55: 1-16.

[12] Rogoff, K. (1990). Equilibrium political budget cycles. American Eco-nomic Review 80: 21-36.

[13] Saporiti, A. D. and J. M. Streb. 2004. Separation of Powers and PoliticalBudget Cycles. Manuscript, Universidad del CEMA.

[14] Schuknecht, L. (1996). Political business cycles in developing countries.Kyklos 49, 155-70.

[15] Shi, M., and J. Svensson. 2006, Political Budget Cycles: Do They Differacross Countries and Why? Journal of Public Economics 90: 1367-89.

[16] Streb, J. M. (2005). Signaling in political budget cycles. How far areyou willing to go? Journal of Public Economic Theory.

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