Transparency and Economic Policy∗

Alessandro Gavazza§ and Alessandro Lizzerik

September 2004.

Abstract

This paper analyses the effect of voters’ information on politicians’ incentive to tax andtransfer resources. In particular we investigate why fiscal churning arises. We provide a multi-period model of political competition in which voters imperfectly observe the electoral promisesmade to other voters. Voters are homogeneous and taxation is distortionary, but candidateshave an incentive to offer inefficient levels of transfers and in equilibrium fiscal churning arises.Voters whose transfers are more visible receive lower transfers. Increasing the transparency ofthe electoral campaign does not unambigously raise voters’ welfare: transparency on transfersis good but transparency on taxes is bad.

Incomplete Draft

∗We would like to thank Guido Tabellini for helpful comments. Alessandro Lizzeri gratefully acknoweldges financial

support from the NSF.§Department of Economics, New York University. Email: alessandro.gavazza@nyu.edukDepartment of Economics, New York University. Email: alessandro.lizzeri@nyu.edu

1

1 Introduction

Most voters have imperfect information about government policy. Even avid viewers of C-SPAN

have no way to fully compute the real resource costs of the thousands of government programs.

In a recent article in the New York Times1 we read: “Mr. Hollings [U.S. Senator], who contends

that the government hides its debt no less egregiously than Enron did, asked Mitchell E. Daniels

Jr., the White House budget director, to swear personally to the accuracy of the government’s

financial reports....By any standard, Washington does not do a good job of keeping its own books.

Mr. Daniels issued a report card this year on government performance that gave poor grades for

financial management to every major cabinet department, and his own agency to boot. ‘This is

a serious subject,’ Mr. Daniels said. ‘No one could attest to the accuracy of the government’s

books.”’

The idea that voters’ imperfect information may have an effect on policy goes back at least to

Downs (1957), and has received a lot of recent attention.2 This paper focuses on a basic form of

imperfect information that has been largely ignored. In the model, the lack of information is about

what other voters are offered. Why should a voter care about this? Because the amounts offered

to other voters determine the size of the government debt, and hence future taxes and policies. It

turns out that this simple channel potentially generates a rich set of implications about government

policy. These predictions about government policy emerge despite the absence of any of the more

standard channels that have been explored in the literature. We assume no direct conflict between

voters and politicians: we assume that politicians are only interested in getting elected, they do

not extract rents from voters as in much of the prior literature. The model also does not require

any asymmetry of information between the voters and the politician with respect to the ‘type’ of

the politician: we assume that all politicians are identical.

To see how imperfect information of this type may have an impact, suppose that all voters

are identical, that taxation creates distortions, and that there are two identical periods. In such

a world, there is no scope for government and, if voters are perfectly informed, candidates would

promise to do nothing. Suppose now that voters cannot see what others are being offered. It is easy

to see that promising nothing is no longer an equilibrium. Suppose it were. Then candidates have

an incentive to privately promise some voters that, if elected, they will give them some transfers.1August 15, 2002.2See Persson and Tabellini (2000) for a survey and Grossmand and Helpman (2001) for a discussion of the literature.

Several recent papers are concerned with the effects of inferior information on the ability of politician to shirk or

to extract rents (e.g., Besley and Burgess (2002)). Other papers consider models with an agent of uncertain ability

and discuss the effect of imperfect information on the incentives of the agents, and on screening (e.g. Prat, 2002).

Stromberg (2002) discusses the role of mass media in informing voters, and shows that more informed voters obtain

higher transfers. Particularly related is Alt and Lassen (2002). See below.

2

Country/Year ChurningGDP

Gov0t ExpenditureGDP

ChurningGov0t Expenditure

Government DebtGDP

Australia (1993-4) 6.5 % 36.8 % 17.66% 17.78%

US (1995) 9.0 % 32.9 % 27.36% 49.14%

Japan (1994) 11.6 % 34.4 % 33.72% 46.51%

Canada (1994) 11.7 % 47.5 % 24.63% 78.50%

Finland (1995) 15.5 % 57.9 % 26.77% 64.15%

Germany (1994) 15.7 % 48.9 % 32.11% 29.58%

Netherlands (1994) 21.1 % 52.8 % 39.96% 59.05%

Italy (1993) 22.7 % 57.4 % 39.55% 124.90%

Belgium (1995) 23.7 % 53.8 % 44.05% 124.34%

Denmark (1994) 28.0 % 59.3 % 47.22% 77.41%

Sweden (1994) 34.2 % 68.3 % 50.07% 68.79%

Average 18.2 % 50.0 % 36.40% 67.28%

Source: OECD Economic Outlook 1998.

Table 1: Level of Fiscal Churning in Selected Countries.

Since other voters cannot observe such promises, they keep voting as in the purported equilibrium.

However, the groups that are being offered transfers are now more likely to vote for the candidate

who is offering them. In equilibrium voters are all offered transfers and they understand that these

will result in deficits.

The goal of this paper is to fully explore the scope of this type of phenomenon. It seems that

this simple idea can have far reaching implications.

The model can address the following puzzle. A large fraction of individuals are at the same time

taxpayers and recipients of government transfers (in various forms). These two way transactions

between individuals and the public sector are very inefficient since both taxes and transfers generate

distortions: everybody would be better off if all these taxes and transfers were netted-out so that

those who are net recipients of resources would pay no taxes, and those who are net payers of

resources would receive no transfers. In other words, a puzzling feature of modern public finances

is that a large fraction of what citizens pay to the government through taxes is returned to them

through transfers. As Peggy and Richard A. Musgrave (1988) note, “fiscal systems have been

criticized for generating an excessive amount of “churning” or “cross-hauling”, that is, useless tax

and expenditure flows which increase the size of the budget but which are mutually offsetting and

thus impose an unnecessary burden.”

3

Table 1 documents the importance of this phenomenon for selected OECD countries. Fiscal

churning varies from 6.5% of GDP in Australia to 34.2% for Sweden. On average, one third of

all Government expenditure is returned back to the same citizens who pay for it. These numbers

suggest that there would be a simple way to obtain a major improvement in the efficiency of fiscal

systems that would have no redistributive impact: simply net-out everyone’s fiscal obligations.

The argument does not apply with full force to spending programs such as education that can in

part be justified on the grounds of the externalities provided by such spending. Other, programs,

such as welfare programs, can be justified on the basis of social altruism. But a large part of

transfers in western democracies seem to be conflicting with any public or social criterion and to

be inspired by horizontal redistribution among different socioeconomic groups. The 2002 Farm

Bill distributes 30 billion dollars of direct transfers to farmers for 2003-2008. In 2002 US airlines

received 15 billion dollars in cash and loans. Federal subsidies to oil are provided to producers,

transporters, and consumers in varied ways and they amount to around 20 billion dollars per year.

It is somewhat surprising that the electorate tolerates such inefficient redistribution of resources

towards special interest groups. A growing literature has addressed the question of how such

inefficient transfers can be part of a political equilibrium.3 However, it is probably more surprising

that many groups are at the same time taxpayers and recipients of transfers, since taxes and

transfers generate distortions. It seems that electoral competition should guarantee that such

blatant inefficiencies ought to disappear. Any candidate could increase his electoral prospects by

reducing taxes and transfers simultaneously for any voter who is suffering ‘churning’ so as to make

each voter a net payer or a net receiver.

This paper analyses the forces behind fiscal churning. These issues are not typically studied

in standard political economy models of redistribution that rely on median voter tools (Roberts

1977, Meltzer and Richard 1981) because such netting-out is not feasible by construction: most

models allow very limited tax instruments for the government. The standard framework in those

models involves a proportional tax on income and a general transfer which is independent of income.

In such a model, anyone with an income is a tax payer and everyone is a recipient of transfers.

However, these assumptions are made for reasons of tractability, and it is not clear that the fiscal

tools available to governments are so highly constrained to generate the very high levels of churning

that we observe in table 1. It seems that some partial netting-out should be possible. In any event,

it is useful to understand whether churning could emerge in a model that does not impose it

via constraints on the feasible set of policies available to the government. Furthermore, it seems

implausible to argue that the large degree of variation in churning across countries that we see

in table 1 could be explained exclusively by different constraints on the fiscal instruments. By3See for instance Coate and Morris (1995).

4

investigating whether churning can emerge absent such constraints, we can begin to understand

the role of the political process in generating such different outcomes.

We show how fiscal churning emerges as an equilibrium outcome when voters are imperfectly

informed of the transfers that are received by other groups. Thus, the model can explain why

netting-out does not take place. The basic idea behind this phenomenon is the following. Given

that information about transfers is imperfect, as discussed above, candidates will have an incentive

to offer transfers to voters that will result in deficits. If in addition to signals about transfers, voters

have a separate signal about revenues, then, for any positive deficit, smoothing the burden of the

taxes across periods is desirable and therefore in equilibrium all voters receive transfers and pay

taxes. Thus, politicians are led to simultaneously request a tax and offer a transfer to each group.

Roughly, this arises because churning reduces suspicions among other voters that any group is being

offered excessively high net transfers. Note that this outcome would not arise if the political system

were perfectly transparent.

A surprising feature of our analysis is that voters can be worse off when they have perfect

information about others groups’ taxes. When taxes are perfectly observed, candidates have the

incentive to simultaneously offer high transfer and high taxes and this results in more inefficient

outcomes. Thus, our model calls for enhancing transparency on the expenditure side more than on

the taxation side.

A second set of results in our model concerns politicians incentives to choose from several alter-

native means of offering transfers. Different means may come with varying degrees of transparency,

as well as varying degrees of inefficiency. Direct lump sum transfers are probably most efficient,

but it is relatively easy for voters to understand the aggregate value of such transfers and their

consequences for deficits and future distortions. In contrast, distorting the construction of public

projects in a way that leads to rents for some groups is a less efficient way to transfer resources to

such groups but it is probably harder for voters to figure out the true cost of these transfers. In

some cases politicians will favor transfers that are less transparent even if they are more inefficient.

Analogously, taxes that are less easily observable are probably going to be lower in equilibrium.

Thus, transparency introduces an additional dimension to optimal taxation in the eyes of the politi-

cian. This extension of the model is related to Coate and Morris (1995) who focus on the form

of transfers to special interests. They consider the important question of why such transfers are

often implemented through inefficient means. They show that inefficient transfers can be chosen if

voters have imperfect information on the value of such transfers (they might be efficient) and on

the type of politician (they might be corrupt), but the choice of inefficient means of redistribution

happens through a different channel. Interestingly, in our model, the incentives of politicians go

in opposite directions regarding the transparency of taxation and transfers. Politicians favor the

5

most transparent means of raising revenues and the least transparent means of offering transfers.

The reason is that both are ways to try to convince other voters that the deficit - and hence future

taxes - is going to be small.

Finally, it is also possible to study the consequences of differential transparency across groups.

If transfers to some groups are more easily detectable, such groups will, in equilibrium, receive

lower transfers. An interesting feature of this analysis should be that political systems with the

same average transparency may have markedly different outcomes.

This paper contributes to a growing literature that identifies the inefficiencies in the dynamics

of electoral competition. A large part of this literature has focused on the incentives to run budget

deficits. Persson and Tabellini (1997) survey this literature. Coate and Morris (1995) analyze the

form of transfers when voters have imperfect information about both the effects of policies and the

type of politicians. Recently, a small strand of the literature has connected economic policy with

the transparency of the political process. Milesi-Ferretti (2003), Shi and Svensson (2002) and Alt

and Lassen (2002) obtain that higher transparency reduces incentives to accumulate debt. A very

small literature has analyzed fiscal churning. Lindbeck (1985) and Musgrave and Musgrave (1988)

noted that a characteristic of modern fiscal systems is that gross transfers are much larger than net

transfers, while Palda (1997) provides estimates of churning for Canada. However, we are aware of

no model that attempts to explain this phenomenon.

2 Model

We build on the model of redistributive politics provided by Lindbeck and Weibull (1987) and Dixit

and Londregan (1996). We depart from these authors in three ways: we introduce endogenous labor

supply, we look at a dynamic environment with an intertemporal linkage provided by debt, and we

allow for imperfect voter information.

We first describe the structure of the model in a static environment, and then we describe the

intertemporal links between periods.

2.1 Economy

There is a unit measure of voters living in an economy where there is a single consumption good.

Each voter has the same utility function u (c− γ (l)) over consumption c and labor l, where u is,strictly increasing and concave, γ is strictly increasing and convex. Both u and γ are assumed to

be differentiable three times. This specific form of separability between consumption and labor is

assumed mainly because it simplifies the derivation of some properties of the equilibrium. A more

6

general utility function would complicate the analysis but should not change the substance of the

results.

Initially we assume that all workers receive the same wage which is normalized to 1. Extending

the model to heterogenous wages is straightforward. Voters are divided into groups indexed by

i ∈ {1, 2, ..., N}. We assume for simplicity that each group has the same mass of individuals 1/N .A voter in group i receives a lump-sum transfer yi and pays taxes on labor income according to

a proportional rate ti. Note that taxes are distortionary, as they are levied on the labor income.4

The budget constraint of the individual is then

ci = yi + (1− ti) li (1)

So each individual chooses ci and li to maximize u (ci − γ (li)) to (1). Denote by l (ti) voter i’soptimal labor supply given tax rate ti. Thus, labor supply l (ti) in period i is given by

γ0 (li (ti)) = 1− ti (2)

Let U (yi, ti) = maxli u (ci − γ (li)) voter i’s indirect utility function over taxes and transfers.

2.2 Politics

There are two candidates, R and L. We assume that candidate are office motivated, so they have

no interest in policy per se. Candidates compete to maximize their vote share5 by making binding

promises of taxes ti and transfers yi to each group of voters i, subject to an aggregate balanced

budget constraint.

In addition to those ‘material’ preferences, voters also have ideological preferences. Each voter

in group i is endowed with a personal ideological parameter x, which captures the additional utility

that the citizen enjoys if party R is elected. For each individual, x is the realization of an inde-

pendent draw of a random variable Xi. This ideological parameter is meant to capture additional

elements of the political platforms of the two parties which is not related to economic policy. An

example would be the parties’ attitudes towards issues such as foreign policy or religious values.

Candidates do not observe the ideological parameter of voters, they only know the distribution4Assuming that taxes are proportional to income simplifies the analysis. We could write down a model where

voters privately observe their abilities and politicians are allowed to choose taxes optimally from any nonlinear, group

specific, tax schedule.

All that is needed for the substance of our results is that distortions from taxation are convex in the amount that

is raised from a group.5For the purpose of the analysis, it does not matter whether candidates only care about winning or they care

about the share of the vote.

7

Fi and the density fi of the ideology in group i. Thus, candidate promises cannot depend on x,

although they can depend on i.

Suppose a voter in group i with ideological preference x is promised tax rate tLi and transfer

yLi by candidate L and tax rate t

Ri and transfer y

Ri by candidate R. Then this voters will vote for

candidate L if and only if

U³yL

i , tLi

´− U

³yR

i , tRi

´> x

Thus, the probability that voter i votes for candidate L given the candidates promise³yL

i , tLi

´and³

yRi , t

Ri

´is

Fi

³U³yL

i , tLi

´− U

³yR

i , tRi

´´.

Given that there are infinitely many voters in each group, Fi

³U³yL

i , tLi

´− U

³yR

i , tRi

´´is also the

fraction of group i voters who vote for candidate L. Adding up across groups, we obtain candidate

L’s total vote share

SL =1

N

NXi=1

Fi

³U³yL

i , tLi

´− U

³yR

i , tRi

´´(3)

Party R’s vote share is 1− SL.

Given candidate R’s platform³yR

i , tRi

´N

i=1, candidate L chooses

³yL

i , tLi

´N

i=1that maximizes SL

subject to the non-negativity constraints

yLi , t

Li ≥ 0 for all i

and the aggregate budget constraint

NXi=1

tLi l³tLi

´≥

NXi=1

yLi . (4)

As in Lindbeck andWeibull (1987), in order to guarantee existence of a pure strategy equilibrium

we assume that the objective function of both candidates is strictly concave. A sufficient condition

is that, for all i, Fi

³U³yL

i , tLi

´−U

³yR

i , tRi

´´is concave in yL

i , tLi , and convex in y

Ri , t

Ri . We refer

the reader to Lindbeck and Weibull (1987) to details.

2.3 Equilibrium

We will first consider the special case in which all groups are identical, namely, fi = f for all i.

This is a useful benchmark. When we look at the dynamic model, we will make this assumption

because it clarifies the effects of imperfect information: as will become clear, this is a model where,

in the absence of imperfect information, candidates are completely inactive. Thus, all of the action

will come from informational considerations.

8

In the static setting, when there is no heterogeneity between groups, equilibrium takes a very

simple form: taxes and transfers are zero. Given that groups are identical, candidates offer the

same transfers to all groups. Because taxation is distortionary it is better for a candidate to set

this common level of transfers to zero, i.e. to promise to do nothing. Furthermore, this outcome

does not depend on the information available to each group of voters because the voting decision

is not affected by the offers made to other voters. Each voter only cares about the offer he has

received. The following result formalizes this discussion.

Proposition 1 In a one period model, regardless of voters’ information,

(i) Any equilibrium is symmetric-symmetric³yL

i , tLi

´i=N

i=1=³yR

i , tRi

´i=N

i=1= (y, t): both candi-

dates make the same offers to all groups;

(ii) each candidate offers (y, t) = (0, 0)

Proof. See Appendix.This result says that, when groups are homogeneous and there is a single period, this model

generates no government activity. The intuition is that, because voters are identical, and because

candidates objective functions are concave in transfers, there is no gain to offering different transfers

to different voters. Because taxation distorts labor supply decisions, candidates will choose zero

taxes and hence zero transfers.

When groups have different characteristics, namely, they have different Fi’s, the equilibrium

platforms are more interesting. Let us order the indeces i = 1, ...,N so that fi (0) > fj (0) if and

only if i < j, i.e., lower indexed groups are more responsive.

Proposition 2 There exists an H > 1 such that, all groups with i < H receive positive transfers

and pay no taxes, while all groups with i ≥ H receive no transfers and pay positive taxes.

Proof. See Appendix.The intuition for this result is the following. As in Lindbeck and Weibull (1987), candidates

have the incentive to appeal to voters who are more responsive (as measured by fi (0)). Given the

balanced budget constraint, the only way to offer something to these voters is to tax other voters,

and candidate will tax voters who are less responsive. Note however that for any given group, in

this single period model, candidates either offer a transfer to a group of voters, or they tax this

group; candidates never engage in fiscal churning. The reason is that if a group pays positive taxes

and receives positive transfers, it is possible to increase this groups’s welfare and therefore the vote

share gained by the candidate from this group without affecting any other group. This can be done

by reducing transfers and tax revenue from this group by the same amount, i.e., by netting-out the

fiscal position of the group. Because taxes are distortionary, the group benefits by this netting out.

9

3 Two periods

We now move to a two period environment. Intertemporal considerations, in particular the possi-

bility of deficit financing are essential for a discussion of the role of transparency.

In a static setting, Proposition 1 showed that the equilibrium was invariant to the information

available to voters regarding the offers made to other groups of voters. This was because each voter

cared only about his own offer. However, in a dynamic setting, information becomes relevant, since

aggregate promises have implications for the size of government debt, and debt has to be repaid

out of future taxes. Thus, the voter prefers small promises to other groups as these imply lower

debt.

There are two periods, each period is the same as the one described in Section 2: preferences

are the same in both periods, the set of voters and the set of candidates are the same at both

dates and elections are held in both periods. We assume that the government finances the debt by

borrowing from abroad and we rule out the possibility of default on the debt. We assume that the

interest rate is zero and there is no discounting in order to save on notation.

We now assume that all groups are identical.

The second period game is like the game described in Section 2, except that budget balance

requires that the debt D accumulated in the first period is repaid

NXi=1

tji2l³tji2

´= D +

NXi=1

yji1 for j = L,R

In the second period the extent of information available to voters has no effect, since they will simply

vote for the party that promise them the higher utility. A simple modification of the argument in

Proposition 1 implies that candidates will not promise any positive transfers in the second period

(yji2 = 0) and the burden of the debt will be divided equally among the N homogenous groups:

tji2l³tji2

´=D

Nfor j = L,R and for all i (5)

In the first period, voters take into account the equilibrium that will arise in the second period

subgame. In particular, the voting decision will be based not only on the first period offer, but

also on the total debt resulting from all offers. For any first period offer³yj

i1, tji1

´he receives, the

voter forms a conjecture about period 2 taxes tji2, where, as will become clearer in the next section,

this conjecture is based on the amount of information he receives. Of course, this conjecture is

consistent with candidates’ equilibrium offers.

Moreover, for any³yj

i1, tji1, t

ji2

´, each voter chooses savings to smooth consumption across peri-

ods. In our framework, this implies that a voter equalizes utility perfectly across periods. Hence,

10

for any³yj

i1, tji1, t

ji2

´, he chooses labor supply in the two periods to maximize

maxli1,li2

2u

µ1

2

³yj

i1 +³1− tji1

´lji1 − γ

³lji1

´+³1− tji2

´lji2 − γ

³lji2

´´¶

Thus, labor supply l³tjk

´in period k is given by

γ0 ³l ³tjk´´ = 1− tjk (6)

The value to a voter over two periods can be written as

U³yj

i1, tji1, t

ji2

´= 2u

µ1

2

³yj

i1 +³1− tji1

´l³tji1

´− γ

³l³tji1

´´+³1− tji2

´l³tji2

´− γ

³l³tji2

´´´¶(7)

Let T jik = t

jikl³tjik

´. Then, the intertemporal budget constraint is given by:

NXi=1

T ji1 +

NXi=1

T ji2 =

NXi=1

tji1l³tji1

´+

NXi=1

tji2l³tji2

´=

NXi=1

yji1 for j = L,R

or, using the fact that, in equilibrium, second period taxes are the same for all groups,

NXi=1

T ji1 +NT

j2 =

NXi=1

tji1l³tji1

´+Ntj2l

³tj2

´=

NXi=1

yji1

Thus, given promises³yL

i1, tLi1

´and

³yR

i1, tRi1

´a voter in group i votes for candidate L iff

U³yL

i1, tLi1, t

Li2

´− U

³yR

i1, tRi1, t

Ri2

´> x (8)

tji2 is the tax rate that will ensue at time 2 if candidate j wins the elections at time 1. So it may be

the case that a voter chooses a candidate that does not offer him the highest period 1 utility. For

example, a voter with ideology x = 0 might prefer candidate L even though candidate R offers him

a higher transfer yLi1 < y

Ri1and a lower tax rate t

Li1 > t

Ri1. This would be the case because the voter

anticipates that if candidate R is elected, the period 2 taxes will be so high that on aggregate he

will be better off under candidate L’s policy.

Thus, the vote share maximized by candidate L is

SL1 =1

N

NXi=1

F³U³yL

i1, tLi1, t

Li2

´−U

³yR

i1, tRi1, t

Ri2

´´(9)

where tLi2, tRi2 are the tax rates that voters expect are necessary given the promises made by the two

candidates in the first period.

11

3.1 Benchmark: Perfect Information

When voters perfectly observe all promises made by the two candidates, the best thing that a

candidate can promise is again nothing. Voters will detect for sure any transfer offered to some

groups and therefore candidates do not offer any transfer.

Proposition 3 Under perfect information, in equilibrium³yL

i1, tLi1

´=³yR

i1, tRi1

´= (0, 0) for all i

Proof. See AppendixNotice the contrast between this result and the previous literature on government deficits.

Again, this is a useful benchmark because it will show that all the action in our model is coming

from information imperfections.

3.2 Imperfect information

We assume now that each group of voters perfectly observe the taxes and transfers that each

candidate promise to them. However they only see a signal of the promises to other groups. More

formally, with probability p they observe perfectly taxes and transfers to other groups,6 and with

the complementary probability 1− p they receive no information whatsoever.In the event that voters do not observe all the offers, their voting decision in this game depends

on their beliefs about offers that the two candidates made to other voters. Arbitrary beliefs can

be assigned following out-of-equilibrium offers. We follow the Vertical Contracting literature by

assuming individual holds “passive beliefs” (McAfee and Schwartz, 1996; Segal, 1999): even after

observing an out-of-equilibium promise from a candidate, the voter believes that the other voters

face their equilibrium promise. We have investigated the robustness of our results to this assump-

tion. In particular, we have considered a model where candidates control promises only with noise

and have obtained very similar results. See below, and Appendix B.

Consider candidate’s L incentive to deviate from an equilibrium outcome³yL

i1, tLi1

´i=N

i=1offering

an arbitrary profile of promises,³yL

i1, tLi1

´i=N

i=1while candidate R is promising the equilibrium profile³

yRi1, t

Ri1

´i=N

i=1. When taxes and transfers are not observed, a voter in Group 1 will vote for candidate

L iff

U

ÃyL

11, tL11, t

L12

à eDL

N

!!− U

ÃyR

11, tR11, t

R12

ÃDR

N

!!> x

6 the only thing that matters for a voter is the aggregate debt resulting form offers to other groups and not the

precise composition of those offers. So for voters in group i it doesn’t matter if group j has been offered yj,1L = y > 0

and group k yk,1L = 0 or viceversa.

12

since he holds passive beliefs. tL12

µ eDLN

¶is the tax rate that will ensue in the period two subgame

for a level of the budget deficit of eDL = yL11 +

PNi=2 y

Li1 − tL11l

³tL11

´−PN

i=2 tLi1l³tLi1

´= DL + y

L11 −

yL11 − tL11l

³tL11

´+ tL11l

³tL11

´, while Dj =

PNi=1 y

ji1 −

PNi=1 t

ji1l³tji1

´is the equilibrium budget deficit

for candidate j. Note that when the voter is calculating next period level of taxes, she is only

considering the deviation she has observed, while other voters offers are held at their equilibrium

level.

When all promises are observed, this voter in Group 1 will vote for candidate L iff

U

µyL

11, tL11, t

L12

µDL

N

¶¶− U

ÃyR

11, tR11, t

R12

ÃDR

N

!!> x

where now DL =PN

i=1 yLi1 −

PNi=1 t

Li1l³tLi1

´. Potentially, candidate’s L deviation can take very

different forms. Candidate’s L can consider a change in the transfer to one group only, two groups

or changing taxes and transfers simultaneously. The following lemma helps us in narrowing down

the kind of deviations that the equilibrium must be immune to.

Lemma 4 Consider a putative equilibrium³yj

i1, tji1

´i=N

i=1profile of promises by candidate j. Suppose

there exists a profitable deviation by candidate k that involves changing the transfer or the taxes to

two or more groups. Then there exists a profitable deviation by candidate k that involves changing

the transfer to one group only.

Proof. See AppendixThe power of the lemma is that without loss of generality we can restrict our attention to

deviations to one group only. Note that in this case for the group that receives an out-of-equilibrium

offer, the events of observing the offers made to other groups or not observing them yield the same

indirect utility

U

yL11, t

L11, t

L12

yL11 +

PNi=2 y

Li1 − tL11l

³tL11

´−PN

i=2 tLi1l³tLi1

´N

.Groups receiving the equilibrium offer

³yi1, ti1

´with probability 1−p will not observe the deviation

and therefore their indirect utility is

U

ÃyL

i1, tLi1, t

Li2

ÃDL

N

!!.

With probability p they will observe the deviation and in which case, their expected time 2 utility

is

U

yLi1, t

Li1, t

Li2

yL11 +

PNi=2 y

Li1 − tL11l

³tL11

´−PN

i=2 tLi1l³tLi1

´N

.13

The vote share of the candidate following the deviation is

F

ÃU

ÃyL

11, tL11, t

L12

à eDL

N

!!− U

ÃyR

11, tR11, t

R12

ÃDR

N

!!!+ (10)

(N − 1) pFÃU

ÃyL

i1, tLi1, t

Li2

à eDL

N

!!− U

ÃyR

i1, tRi1, t

Ri2

ÃDR

N

!!!+

(N − 1) (1− p)FÃU

ÃyL

i1, tLi1, t

Li2

ÃDL

N

!!− U

ÃyR

i1, tRi1, t

Ri2

ÃDR

N

!!!The first term is the vote share obtained from the group that receives the deviation. The second

term is the vote share from the remaining N − 1 groups in the event they observe the deviation(probability p) and the last term is the vote share when they instead do not observe the deviation

(probability 1− p).A candidate’s strategy

³yL

i1, tLi1

´i=N

i=1must solves the above maximization. As in the static model,

an equilibrium can only be symmetric-symmetric, so that both candidates make the same offers to

all groups of the population. This is intuitive, since voters are homogeneous and have no a priori

preference for one candidate.

The following Lemma shows that in the first information scenario, first period taxes must be

zero. Hence, there is no churning.

Lemma 5 If the only aggregate measure voters observe is government debt, then first period taxes

will be set at zero.

Proof. To prove this, note first that the statement is obviously true if transfers are zero (it isclear that there is no gain from budget surpluses). Assume now transfers and first period taxes are

strictly positive. But then a candidate can obtain more votes by reducing transfers and taxes to

keep debt unchanged. Contradiction

From the expression 10, it seems intuitive that, when p < 1, y1 = 0 cannot be part of an

equilibrium. If yi1 = 0 for all i, each candidate would have the incentive to give a small positive

transfer to one group, gaining an increase in vote share of ∆1 from this group. This deviation is

only detected with probability p < 1 by the other groups, with a decrease in vote share of ∆2. Note

that ∆1and ∆2 are of the same order of magnitude for a small deviation if y1 = 0. However the

vote loss ∆2 ensues with a probability p < 1 while the vote gain ∆1 happens with certainty, which

destroys the purported equilibrium. This corroborates our intuition that y1 = 0 cannot be part of

any equilibrium:

Proposition 6 When p < 1, equilibrium debt is positive: D (p) > 0. All voters are treated identi-

cally. In the first period, transfers are positive and taxes are zero y1 > 0 and t1 = 0. In the second

14

period, transfers are zero and taxes are positive y2 = 0 and t2 > 0. Furthermore, if γ000 ≥ 0 and

p < 1, then debt is positive and decreasing in p.

Proof. See Appendix.The construction of the equilibrium heavily relies on the assumption of passive beliefs. However,

the assumption is not essential for the main effects highlighted in this paper. What is important

is that when voters receive an out-of-equilibrium offer, they do not believe that other groups have

received an even better offer. In Appendix B we modify the model by allowing for the possibility

that offers are observed with noise and we show that in such a model the unique equilibrium has

features that are essentially identical to those of the model described above.

The result that debt is higher in less transparent political systems has recently emerged in the

literature. Milesi-Ferretti (2003), Shi and Svensson (2002) and Alt and Lassen (2002) theoretically

demonstrate too that higher transparency reduces incentives to accumulate debt. These last two

papers and Alesina et al. (1999) empirically show in a cross-section of countries that indices of

transparency help predict fiscal performances.

3.3 Fiscal Churning

We now enrich the previous information structure. We still assume that voters have imperfect

information regarding the electoral promises of the candidates. However they see separate signals

about aggregate transfers and aggregate taxes. Specifically, voters in each group observe two signals.

The first signal reveals aggregate transfers perfectly with probability p and reveals nothing with

probability 1− p. The second signal reveals aggregate tax revenues with probability q and nothingwith probability 1− q.

This richer, more disaggregated information structure can give candidates an incentive to

smooth taxes across periods. This then implies fiscal churning.

Proposition 7 If γ000 ≥ 0, and 1 > q > p, then t2 > t1 > 0. Debt (and t2) are independent of qbut t1 is increasing in q. Thus, transfers increase with q and welfare decreases with q. If q < p,

t1 = 0. If q = 1, then t1 = t2.

Proof. See AppendixNote that we now have fiscal churning. In the first period, voters receive transfers and pay taxes

at the same time, while they would clearly be better off if the taxes would be reduced to zero and

the transfer reduced accordingly. However, this cannot happen in equilibrium. Transfers will be

positive in this environment for the same reason as they were before. What is more, if a candidate

promises zero taxes and positive transfers in the first period to all voters, he will lose for sure, as

15

the other candidate can win just by promising the same transfer, but smoothing taxes perfectly

across periods. In the previous environment, this wasn’t profitable because with probability 1− pvoters would have no information on aggregate debt, while now they observe tax revenues. So an

out-of-equilibrium offer of increasing taxes and transfers at the same times becomes very attractive,

as with probability 1− p voters believe that their taxes tomorrow will be lower.This opportunity for candidates has very unfavorable consequences for voters. The transfer

they receive is higher now, but this comes at the price of higher taxes and hence higher distortions.

As a result, the welfare of the voters is now lower. Higher transparency on taxes may be harmful.

3.4 Heterogenous Information

Assume now that groups are heterogenous in the information they have. Some offers are observed

with a higher probability than others. More specifically, transfers to N1 groups are observed with

probability p1, while transfers to the remaining N2 groups are observed with probability p2 > p1.

Taxes are observed perfectly, i.e. q = 1. The incentive is now to offer higher transfers to groups

that are observed with a lower probability pi.

Proposition 8 In equilibrium voters are not treated identically. For N1 large enough, in the first

period yi1 (p1) > yi1 (p2) . In the second period ti2 = t2 and y2 = 0 for all groups.

Proof. See AppendixThe Appendix also shows that a similar result holds when groups are heterogeneous with respect

to the probability of observing taxes qi. Candidates tax more heavily groups that are observed with

a higher probability qi.

This result provides an interesting interpretation of a puzzling phenomenon discussed in Palda

(1997). Palda finds that in Canada fiscal churning rises with income deciles: higher income indi-

viduals face more churning. Palda argues that this phenomenon is puzzling because it is reasonable

to expect that higher income individuals are more informed about fiscal policy and the political

process, and that therefore they should be faced with less distortionary policies. A consequence

of Proposition 8 is that there is more churning for groups whose transfers are observed with lower

probability. Assume then that higher income individuals indeed possess better information. This

can be interpreted as lower income individuals having worse information about transfers offered to

high income people. Therefore, Proposition 1 suggests that an explanation of higher churning for

higher income individuals is that, precisely because these individuals have better information, trans-

fers offered to them are relatively hard to observe by the rest of the population, leading candidates

to favor offering higher transfers to these voters.

16

Another interesting implication of Proposition 8 involves a comparison of two societies with the

same level of average aggregate transparency that differ in the extent of heterogeneity of trans-

parency across groups. For instance, assume that one society has the same level of transparency p

for all groups, whereas in the second society transfers to N1 groups are observed with probability

p1, and transfers to N2 groups are observed with probability p2, withp1N1+p2N2

N = p. a corollary of

Proposition 8 is that the size of government, taxes, transfers, and deficits are larger in the second,

more heterogeneous society. The intuition is that what determines the size of government is the

marginal incentive to offer transfers to a group. In the heterogenous society this incentive is de-

termined by the least transparent group. Thus total future distortions have to be sufficiently high

to deter sneaky transfers to such a group. This emerges very starkly if u is linear: in this case,

all that matters for determining the size of the deficit is the transparency of the least trasparent

group: all other groups receive nothing.

4 Public Goods

To be added

5 Appendix A

Proof of Proposition 1. (i) The Lagrangian for Candidate L isPN

i=1F¡U¡yLi , t

Li

¢− U ¡yRi , tRi ¢¢N

− λ"

NXi=1

tLi l¡tLi¢− NX

i=1

yLi

#The first order condtions are

yLi :f¡U¡yLi , t

Li

¢− U ¡yRi , tRi ¢¢N

∂U¡yLi , t

Li

¢∂yLi

+ λ = 0 (11)

tLi :f¡U¡yLi , t

Li

¢− U ¡yRi , tRi ¢¢N

∂U¡yLi , t

Li

¢∂tLi

− λ"l¡tLi¢+ tLi

∂n¡tLi¢

∂tLi

#= 0 (12)

and similarly for candidate R. Taking ratios

∂U(yLi ,tLi )

∂yLi

∂U(yRi ,tRi )

∂yRi

=λ

µfor all i

Suppose∂U(yLi ,t

Li )

∂yLi

>∂U(yRi ,t

Ri )

∂yRi

. Then either yLi < yRi or tLi > tRi or both for all i. The “both” case is impossible

because it implies that one candidate doesn’t satisfy the budget constraint with equality. If yLi < yRi and tLi < tRi

then either U¡yLi , t

Li

¢− U ¡yRi , tRi ¢ = 0 for all i or there exists at least one i such that U ¡yLi , tLi ¢− U ¡yRi , tRi ¢ > 0.If U

¡yLi , t

Li

¢ − U ¡yRi , tRi ¢ > 0 for some i, then candidate R can increase his vote share simply decreasing taxes

17

and and transfers to group i without affecting the budget balance condition. If U¡yLi , t

Li

¢ − U ¡yRi , tRi ¢ = 0 for

all i, again candidate R can increase his vote share simply decreasing taxes and and transfers to group i without

affecting the budget balance condition. The other cases are similar, and the only possibility is∂U(yLi ,t

Li )

∂yLi

=∂U(yRi ,t

Ri )

∂yRi

, U¡yLi , t

Li

¢− U ¡yRi , tRi ¢ = 0 and ¡yLi , tLi ¢i=Ni=1=¡yRi , t

Ri

¢i=Ni=1

= (y, t) .

(ii) Combining (11) and (12), we have

f¡U¡yLi , t

Li

¢− U

¡yRi , t

Ri

¢¢N

Ã∂U¡yLi , t

Li

¢∂tLi

+∂U¡yLi , t

Li

¢∂yLi

Ãl¡tLi¢+ tLi

∂l¡tLi¢

∂tLi

!!= 0

∂U¡yLi , t

Li

¢∂tLi

+∂U¡yLi , t

Li

¢∂yLi

Ãl¡tLi¢+ tLi

∂l¡tLi¢

∂tLi

!= 0 (13)

Now

∂U (y, t)

∂y=

∂u (c, l)

∂c

∂U (y, t)

∂t=

∂u (c, l)

∂c

µ(1− t) ∂l (t)

∂t− l(t)− γ0 (l) ∂l (t)

∂t

¶At the optimum

γ0 (l (t)) = 1− tThus,

∂U

∂y=

∂u (c, l)

∂c

∂U

∂t= −∂u (c, l)

∂cl(t)

Substituting into (13) and using¡yLi , t

Li

¢= (y, t)

−∂u (c, l)∂c

l(t) +∂u (c, l)

∂c

µl (t) + t

∂l (t)

∂t

¶=∂u (c, l)

∂ct∂l (t)

∂t= 0

which can hold iff t∂l(t)∂t

= 0, i.e. if t = 0. From the budget balance condition (4) we then have y = 0

Proof of Proposition 2. The equilibrium conditions are:

fi (0)∂U

∂yi= fj (0)

∂U

∂yjif i, j < H

fi (0)∂U

∂yi= −fj (0) ∂U

∂tjif i < H ≤ j

fi (0)∂U

∂ti= fj (0)

∂U

∂tjif i, j ≥ H

Proof of Proposition 3. Forming the LagrangianPN

i=1F¡U¡yLi1, t

Li1, t

Li2

¢− U ¡yRi1, tRi1, tRi2¢¢N

− λ"

NXi=1

tLi1l¡tLi1¢+NtL2l (tL2)−

NXi=1

yLi1

#

18

FOC

yLi1 :f¡U¡yLi1, t

Li1, t

Li2

¢− U ¡yRi1, tRi1, tRi2¢¢N

∂U¡yLi1, t

Li1, t

Li2

¢∂yLi1

+ λ = 0

tLi1 :f¡U¡yLi1, t

Li1, t

Li2

¢− U ¡yRi1, tRi1, tRi2¢¢N

∂U¡yLi1, t

Li1, t

Li2

¢∂tLi1

− λÃl¡tLi1¢+ tLi1

∂l¡tLi1¢

∂tLi1

!= 0

tLi2 :f¡U¡yLi1, t

Li1, t

Li2

¢− U

¡yRi1, t

Ri1, t

Ri2

¢¢N

∂U¡yLi1, t

Li1, t

Li2

¢∂tLi2

− λÃNl¡tLi2¢+NtLi2

∂l¡tL2¢

∂tL2

!= 0

and similarly for candidate R.

Combining

∂U¡yLi1, t

Li1, t

Li2

¢∂tLi1

+∂U¡yLi1, t

Li1, t

Li2

¢∂yLi1

Ãl¡tLi1¢+ tLi1

∂l¡tLi1¢

∂tLi1

!= 0

∂U¡yLi1, t

Li1, t

Li2

¢∂tLi2

+∂U¡yLi1, t

Li1, t

Li2

¢∂yLi1

ÃNl¡tLi2¢+NtLi2

∂l¡tL2¢

∂tL2

!= 0

which by the same argument of the Proof of Proposition 1 can hold only if¡yLi1, t

Li1, t

Li2

¢= (0, 0, 0) .

Proof of Lemma 4. Consider candidate R offering an equilibrium profile of promises¡yRi1, t

Ri1

¢i=Ni=1

. A

deviation involving a change of z to the transfer to 1 < M < N groups by candidates L yields

M (1− p)hU³yLi1 + z, t

Li1, t

Li2

³yLi1 +

z

N

´´− U ¡yRi1, tRi1, tRi2 ¡yRi1¢¢i+

MphU³yLi1 + z, t

Li1, t

Li2

³yLi1 +

zM

N

´´− U ¡yRi1, tRi1, tRi2 ¡yRi1¢¢i+ (14)

(N −M) phU³yLi1, t

Li1, t

Li2

³yLi1 +

zM

N

´´− U

¡yRi1, t

Ri1, t

Ri2

¡yRi1¢¢i

+

(N −M) (1− p) £U ¡yLi1, tLi1tLi2 ¡yLi1¢¢− U ¡yRi1, tRi1, tRi2 ¡yRi1¢¢¤where the two terms represent the gain in vote share from the M groups that receive an additional transfer and

the last two terms represent the loss in vote share from the remaining N −M groups. The second and third terms

represent the change in vote share when taxes and transfers are observed perfectly, which happen with probability p.

In particular, all groups realize that tomorrow’s tax rate will be such that a per capita revenue of yLi1+zMNhas to be

raised. Furthermore, M groups will receive a transfer of yLi1+ z. The first and the forth term represent the change in

vote share when taxes and transfers are not observed perfectly , which happens with the complementary probability

of 1−p. Voters hold passive beliefs, so those receiving a transfer of yLi1+z think that tomorrow’s tax rate will be suchthat a per capita revenue of yLi1 +

zNhas to be raised (first term), while those that don’t receive a different transfer

from the putative equilibrium still think that the tax rate will not change from the equilibrium tax rate.

Maximizing (14) with respect to z we obtain

M (1− p)"∂U¡yLi1 + z, t

Li1, t

Li2

¡yLi1 +

zN

¢¢∂y

+1

N

∂U¡yLi1 + z, t

Li1, t

Li2

¡yLi1 +

zN

¢¢∂t

∂t

∂T

#+

Mp

"∂U¡yLi1 + z, t

Li1, t

Li2

¡yLi1 +

zMN

¢¢∂y

+M

N

∂U¡yLi1 + z, t

Li1, t

Li2

¡yLi1 +

zMN

¢¢∂t

∂t

∂T

#+ (15)

19

(N −M) p"M

N

∂U¡yLi1, t

Li1, t

Li2

¡yLi1 +

zMN

¢¢∂t

∂t

∂T

#= 0

or

∂U¡yLi1 + z, t

Li1, t

Li2

¡yLi1 +

zN

¢¢∂y

+1− pN

∂U¡yLi1 + z, t

Li1, t

Li2

¡yLi1 +

zMN

¢¢∂t

∂t

∂T+p∂U¡yLi1 + z, t

Li1, t

Li2

¡yLi1 +

zMN

¢¢∂t

∂t

∂T= 0

(16)

Consider now a deviation z to a single group. (14) reads as

(1− p)hU³yLi1 + z, t

Li1, t

Li2

³yLi1 +

z

N

´´− U ¡yRi1, tRi1, tRi2 ¡yRi1¢¢i+ (17)

phU³yLi1 + z, t

Li1, t

Li2

³yLi1 +

z

N

´´− U ¡yRi1, tRi1, tRi2 ¡yRi1¢¢i+

(N − 1) phU³yLi1, t

Li1, t

Li2

³yLi1 +

z

N

´´− U ¡yRi1, tRi1, tRi2 ¡yRi1¢¢i+

(N − 1) (1− p)£U¡yLi1, t

Li1t

Li2

¡yLi1¢¢− U

¡yRi1, t

Ri1, t

Ri2

¡yRi1¢¢¤

Maximizing with respect to z

∂U¡yLi1 + z, t

Li1, t

Li2

¡yLi1 +

zN

¢¢∂y

+1− pN

∂U¡yLi1 + z, t

Li1, t

Li2

¡yLi1 +

zN

¢¢∂t

∂t

∂T+ p

∂U¡yLi1 + z, t

Li1, t

Li2

¡yLi1 +

zN

¢¢∂t

∂t

∂T= 0

(18)

Comparing (16) and (18) we see that they can both hold only if z = 0 Note that z = 0 is what is required for¡yRi1, t

Ri1

¢i=Ni=1

to be an equilibrium profile. If z > 0¡yRi1, t

Ri1

¢i=Ni=1

cannot be an equilibrium profile. Furthermore, both

equations cannot hold since the last term in (16) is negative and smaller than the last term in (18), while the first

two terms are the same. This means that for z > 0, the yLi1 that satisfies (16) is smaller than yLi1 that satisfies (18).

But then evaluating (18) at the yLi1 that satisfies (16) we would have

∂U¡yLi1 + z, t

Li1, t

Li2

¡yLi1 +

zN

¢¢∂y1

+1− pN

∂U¡yLi1 + z, t

Li1, t

Li2

¡yLi1 +

zN

¢¢∂t2

∂t2∂T2

+p∂U¡yLi1 + z, t

Li1, t

Li2

¡yLi1 +

zN

¢¢∂t2

∂t2∂T2

> 0

which implies that for any deviation that involves Mz resources distributed to M groups, there exists a (more)

profitable deviation that involves z resources only distributed to a single group.

Proof of Proposition 6. In order to characterize the equilibrium, we need to understand government

incentives to distribute taxes across periods. Recall that the value to the voter over two periods can be written is

U (y, t1, t2) = 2u³1

2(y + (1− t1) l1 − γ (l1) + (1− t2) l2 (t2)− γ (l2 (t2)))

´and Ti = tili (ti) . When only the aggregate debt is observable, we know that t1 = T1 = 0.

When debt is D, voters’ value function over the two periods is defined by

U(y, 0, t2 (y)) = 2u³1

2

³y + l1 (0) + (1− t2) l2

³t2

³D

N

´´− γ (l1 (0))− γ

³l2

³t2

³D

N

´´´´´(19)

where y = t2l2 (t2 (y)) .

20

Consider a debt D = Ny and a deviation of additional transfer z to group 1. The vote share gain for a deviating

candidate is proportional to

U³y + z, 0, t2

³y +

z

N

´´− U (y, 0, t2 (y)) + p(N − 1)

³U³y, 0, t2

³y +

z

N

´´− U (y, 0, t2 (y))

´.

Differentiating with respect to z, we obtain

∂U¡y + z, 0, t2

¡y + z

N

¢¢∂z

+1

N

∂U¡y + z, 0, t2

¡y + z

N

¢¢∂t2

∂t2∂T2

+p(N − 1)

N

∂U¡y, 0, t2

¡y + z

N

¢¢∂t2

∂t2∂T2

which must be zero at z = 0.

∂U (y, 0, t2 (y))

∂z+1

N

∂U (y, 0, t2 (y))

∂t2

∂t2∂T2

+p(N − 1)

N

∂U (y, 0, t2 (y))

∂t2

∂t2∂T2

= 0

rearranging we obtain the equilibrium condition:

∂U (y, 0, t2 (y))

∂z= −p(N − 1) + 1

N

∂U (y, 0, t2 (y))

∂t2

∂t2∂T2

(20)

For p = 1 equation 20 becomes∂U (y, 0, t2 (y))

∂z= −∂U (y, 0, t2 (y))

∂t2

∂t2∂T2

which can only hold for y = 0.

Note that, as N →∞ equation 20 becomes

∂U (y, 0, t2 (y))

∂z= −p∂U (y, 0, t2 (y))

∂t2

∂t2∂T2

At equilibrium, candidates should not have incentive to offer “sneaky” transfers. Distortions must be sufficiently high

that, when deviation is observed, voters are sufficiently badly-off that vote share loss deters candidate from offering

increased transfers.

Now observe that from equation (19),

∂U (y, 0, t2 (y))

∂y= u0

∂U (y, 0, t2 (y))

∂t2

∂t2∂T2

=³−l2 + ∂l2

∂t2

¡1− t2 − γ0

¢´u0∂t2∂T2

= −l2u0 ∂t2∂T2

where the second equality holds because of optimality of labor supply. In addition, we have that

∂t2∂T2

=l2 (t2 (T2))

(l2 (t2 (T2)))2 + ∂l2

∂t2T2

=l2

l22 +∂l2∂t2l2t2

=1

l2 +∂l2∂t2t2

Thus,∂U (y, 0, t2 (y))

∂t2

∂t2∂T2

= − l2u0

l2 +∂l2∂t2t2.

Substituting into equation (??) and simplifying we obtain

l2 (t2 (y (p))) =1

γ00 (l2 (t2 (y (p))))t2 (y (p))¡

1− p(N−1)+1N

¢ (21)

where we have substituted ∂l2∂t2

= − 1γ00(l2(t2))

which can be verified by differentiating implicitly in equation (6).

21

To obtain the relation between debt and transparency, differentiate equation (??) implicitly with respect to p toobtain:

y0 (p) =N−1Nl2

∂t2∂T2

µ∂l2∂t2

¡1− p(N−1)+1

N

¢− γ00−t2γ000∂l2∂t2

(γ00)2

¶ =N−1Nl2

∂t2∂T2

µ−1γ00¡1− p(N−1)+1

N

¢− γ00+t2γ000γ00

(γ00)2

¶ .Since ∂t2

∂T2≥ 0 (in equilibrium we must be on the increasing portion of the Laffer curve), debt is decreasing in p if

and only if the term in parenthesis in the denominator of the right hand side is negative, i.e.,

−γ00 ¡1− p(N−1)+1N

¢− ³γ00 + t2 γ000γ00

´(γ00)2

< 0

which holds iff

γ00µ2− p(N − 1) + 1

N

¶+ t2

γ000

γ00> 0 (22)

Since γ00 > 0, inequality (22) holds if γ000 ≥ 0.Proof of Proposition 7. Fix first period tax revenues at T1, consider a debt D (implying second period

revenues of D), and a deviation of an additional transfer z to group 1. The vote share gain for a deviating candidate

is proportional to

U³y + z, t1 (T1) , t2

³y − T1 +

z

N

´´− U (y, t1 (T1) , t2 (y − T1))

+p(N − 1)³U³y, t1 (T1) , t2

³y − T1 +

z

N

´´− U (y, t1 (T1) , t2 (y − T1))

´Differentiating with respect to z, we obtain

∂U¡y + z, t1 (T1) , t2

¡y − T1 +

zN

¢¢∂y

+1

N

∂U¡y + z, t1 (T1) , t2

¡y − T1 +

zN

¢¢∂T2

+p(N − 1)

N

∂U¡y, t1 (T1) , t2

¡y − T1 +

zN

¢¢∂T2

which must be zero at z = 0.

∂U (y, t1 (T1) , t2 (y − T1))

∂y+1

N

∂U (y, t1 (T1) , t2 (y − T1))

∂T2+p(N − 1)

N

∂U (y, t1 (T1) , t2 (y − T1))

∂T2= 0

rearranging we obtain the equilibrium condition

∂U (y, t1 (T1) , t2 (y − T1))

∂y= −p(N − 1) + 1

N

∂U (y, t1 (T1) , t2 (y − T1))

∂T2

Since

∂U (y, t1 (T1) , t2 (y − T1))

∂y= u0

∂U (y, t1 (T1) , t2 (y − T1))

∂T2= −l2u0 ∂t2

∂T2

∂t2∂T2

=1

l2 +∂l2∂t2t2

we can rewrite the equilibrium condition as

1 =p(N − 1) + 1

N

l2

l2 +∂l2∂t2t2

or

l2 =1

γ00t2¡

1− p(N−1)+1N

¢22

which is the same as equation (??). Thus, t2 is independent of q.Let us now obtain the optimal relation between t1 and t2. Consider a candidate equilibrium y∗, t∗1, t

∗2 in which

debt is D∗ = y∗− t∗1l1 (t∗1) and suppose a candidate deviates and increases t1 on group 1 to t1+ z. Then, incrementalrevenue in period 1 (reduction in debt) following the deviation is

∆D = ((t1 + z) l1 (t1 + z)− t∗1l1 (t∗1))implying that needed (and equilibrium) revenue in period 2 falls by ∆D, leading to a new tax rate for everybody in

period 2 of

t2 = t2

µD∗ −∆D

N

¶.

Thus, the change in vote share for the candidate is:

U

µy∗, t1 (T1 +∆D) , t2

µD∗ −∆D

N

¶¶− U

µy∗, t1 (T1) , t2

µD∗

N

¶¶+q (N − 1)

µU

µy∗, t1 (T1) , t2

µD∗ −∆D

N

¶¶− U

µy∗, t1 (T1) , t2

µD∗

N

¶¶¶= U

µy∗, t1 ((t1 + z) l1 (t1 + z)) , t2

µD∗ − ((t1 + z) l1 (t1 + z)− t∗1l1 (t∗1))

N

¶¶− U

µy∗, t1 (T1) , t2

µD∗

N

¶¶+q (N − 1)

µU

µy∗, t1 (T1) , t2

µD∗ − ((t1 + z) l1 (t1 + z)− t∗1l1 (t∗1))

N

¶¶− U

µy∗, t1 (T1) , t2

µD∗

N

¶¶¶differentiate this expression with respect to z to obtain:¡

l1 + (t1 + z) l01

¢ ∂U∂T1

− q (N − 1) + 1N

∂U

∂T2

¡l1 + (t1 + z) l

01

¢which, in equilibrium, should be zero at z = 0. Thus, the expression simplifies to¡

l1 + t1l01

¢ ∂U∂T1

− q (N − 1) + 1N

∂U

∂T2

¡l1 + t1l

01

¢= 0

or∂U

∂T1=q (N − 1) + 1

N

∂U

∂T2. (23)

Since

U (y, t1, t2) = 2u³1

2(y + (1− t1) l1 (t1)− γ (l1 (t1)) + (1− t2) l2 (t2)− γ (l2 (t2)))

´we have

∂U

∂T1= − ∂t1

∂T1l1u

0 = − l1u0

l1 +∂l1∂t1t1

∂U

∂T2= − ∂t2

∂T2l2u

0 = − l2u0

l2 +∂l2∂t2t2

Substituting in equation (23) we obtain

l1 (t1 (q))

l1 (t1 (q)) +∂l1∂t1

(t1 (q)) t1 (q)=q (N − 1) + 1

N

l2 (t2 (q))

l2 (t2 (q)) +∂l2∂t2

(t2 (q)) t2 (q)(24)

The result that t1 < t2 for q < 1 follows if we show thatli(ti)

li(ti)+∂li∂ti

(ti)tiis decreasing in t.

∂ l(t(q))

l(t)+ ∂l∂t

(t)t

∂t=

¡l + ∂l

∂tt¢∂l∂t− l³∂l∂t+ ∂l

∂t+ ∂2l

∂t2 t´

¡l + ∂l

∂tt¢2 =

t¡∂l∂t

¢2 − l³∂l∂t+ ∂2l

∂t2t´

¡l + ∂l

∂tt¢2

23

by substitute into this equation the following expressions

∂l2 (t2)

∂t2= − 1

(γ00 (l2 (t2)))and

∂2l2 (t2)

∂t22=γ000 (l2 (t2))

∂l2(t2)∂t2

(γ00 (l2 (t2)))2 = − γ000 (l2 (t2))

(γ00 (l2 (t2)))3

we obtain∂ l(t(q))

l(t)+ ∂l∂t (t)t

∂t=t¡

1γ00¢2 − l

³− 1γ00 − γ000

(γ00)3 t´

¡l + ∂l

∂tt¢2 .

The right-hand side of this expression is positive if and only if tγ00+ l (γ00)2+ lγ000t > 0 which holds because γ000 ≥ 0.

We now show that t1 (q) is increasing in q1. Differentiate equation (24) with respect to q to obtain

N − 1N

l2

l2 +∂l2∂t2t2+q (N − 1) + 1

N

(l02)2t2 − l2

³l02 +

∂2l2∂t2

2

t2

´¡l2 +

∂l2∂t2t2¢2 t02 =

(l01)2t1 − l1

³l01 +

∂2l1∂t2

1

t1

´¡l1 +

∂l1∂t1t1¢2 t01.

But, t02 = 0 in equilibrium. Thus,

t01 (q) =

N−1N

l2

l2+∂l2∂t2

t2

(l01)2t1−l1

³l01

+∂2l1∂t2

1

t1

´¡l1+

∂l1∂t1

t1

¢2

Thus,

sign¡t01¢= sign

¡ 1γ00¢2t1 − l1

³− 1γ00 − γ000

(γ00)3 t1

´¡l1 − 1

γ00 t1¢2

µ1

γ00

¶2

t1 − l1µ− 1

γ00− γ000

(γ00)3t1

¶> 0

t1γ00 + l1 (γ00)

2+ l1t1γ

000

(γ00)3> 0

iff t1γ00 + l1

¡γ00¢2+ l1t1γ

000 > 0

which holds because γ000 ≥ 0.Proof of Proposition 8.

1. Assume q = 1 and assume without loss of generality that p1 < p2 and define D = D1 +D2. Assume y1 and y2

are the equilibrium transfers and T are the equilibrium tax revenues, equal for all groups. Since q = 1 we know

y = 2T in equilibrium. The deviation is financed with higher taxes in period 2 only. Hence, any candidate

offering an extra transfer of x to one of the groups in N1 would gain

U³y1 + x, t1 (T ) , t2

³T +

x

N

´´− U (y1, t1 (T ) , t2 (T ))

+p1(N1 − 1)³U³y1, t1 (T ) , t2

³T +

x

N

´´− U (y1, t1 (T ) , t2 (T ))

´+p1N2

³U³y2, t1 (T ) , t2

³T +

x

N

´´− U (y2, t1 (T ) , t2 (T ))

´

24

while offering the same extra transfer to one of the groups in N2 would give him

U³y2 + x, t1 (T ) , t2

³T +

x

N

´´− U (y2, t1 (T ) , t2 (T ))

+p2(N2 − 1)³U³y2, t1 (T ) , t2

³T +

x

N

´´− U (y2, t1 (T ) , t2 (T ))

´+p2N1

³U³y1, t1 (T ) , t2

³T +

x

N

´´− U (y1, t1 (T ) , t2 (T ))

´The first order conditions for an interior solution are

∂

∂xU³y1 + x, t1 (T ) , t2

³T +

x

N

´´+1

N

∂

∂T2U³y1 + x, t1 (T ) , t2

³T +

x

N

´´(25)

+p1N1 − 1N

∂

∂T2U³y1, t1 (T ) , t2

³T +

x

N

´´+ p1

N2

N

∂

∂T2U³y2, t1 (T ) , t2

³T +

x

N

´´= 0

∂

∂xU³y2 + x, t1 (T ) , t2

³T +

x

N

´´+1

N

∂

∂T2U³y2 + x, t1 (T ) , t2

³T +

x

N

´´+p2

N2 − 1N

∂

∂T2U³y2, t1 (T ) , t2

³T +

x

N

´´+p2N1

N

∂

∂T2U³y1, t1 (T ) , t2

³T +

x

N

´´= 0

In equilibrium x = 0. Hence this system of equations can be rewritten as

∂

∂xU (y1, t1 (T ) , t2 (T )) +

1

N

∂

∂T2U (y1, t1 (T ) , t2 (T ))

+p1N1 − 1N

∂

∂T2U (y1, t1 (T ) , t2 (T )) + p1

N2

N

∂

∂T2U (y2, t1 (T ) , t2 (T )) = 0

∂

∂xU (y2, t1 (T ) , t2 (T )) +

1

N

∂

∂T2U (y2, t1 (T ) , t2 (T ))

+p2N2 − 1N

∂

∂T2U (y2, t1 (T ) , t2 (T )) +

p2N1

N

∂

∂T2U (y1, t1 (T ) , t2 (T )) = 0

or Ã∂∂xU (y2, t1 (T ) , t2 (T )) +

1N

∂∂T2

U (y2, t1 (T ) , t2 (T )) + p2N2−1N

∂∂T2

U (y2, t1 (T ) , t2 (T ))

−p2N1N

!=

∂

∂T2U (y1, t1 (T ) , t2 (T ))

=

∂∂xU (y1, t1 (T ) , t2 (T )) + p1

N2N

∂∂T2

U (y2, t1 (T ) , t2 (T ))+

−p1N1−1N

− 1N

Combining

∂∂xU (y2, t1 (T ) , t2 (T )) +

1N

∂∂T2

U (y2, t1 (T ) , t2 (T )) + p2N2−1N

∂∂T2

U (y2, t1 (T ) , t2 (T ))

−p2N1

=

∂∂xU (y1, t1 (T ) , t2 (T )) + p1

N2N

∂∂T2

U (y2, t1 (T ) , t2 (T ))

−p1 (N1 − 1)− 1or

∂∂xU (y2, t1 (T ) , t2 (T ))

p2N1−

∂∂xU (y1, t1 (T ) , t2 (T ))

p1 (N1 − 1) + 1

= −µ

p1N2N

−p1 (N1 − 1)− 1 −1N+ p2

N2−1N

−p2N1

¶∂

∂T2U (y2, t1 (T ) , t2 (T ))

25

where

−µ

p1N2N

−p1 (N1 − 1)− 1 −1N+ p2

N2−1N

−p2N1

¶=

(− (1− p1) (1− p2)−N1p1 (1− p2)−N2p2 (1− p1))

N (N1p1 − p1 + 1)N1p2< 0

Hence∂∂xU (y2, t1 (T ) , t2 (T ))

p2N1−

∂∂xU (y1, t1 (T ) , t2 (T ))

p1 (N1 − 1) + 1 > 0

Note that p2N1 > p1 (N1 − 1) + 1 for N1 large enough. Hence

∂

∂xU (y2, t1 (T ) , t2 (T ))− ∂

∂xU (y1, t1 (T ) , t2 (T )) > 0

u0 (y2, T, T ) > u0 (y1, T, T )

y1 > y2

2. Assume that q1 < q2 and that for each pi = p. Let us now obtain the optimal relation between t1 and t2.

Consider a candidate equilibrium y∗, t∗1, t∗2 in which debt is D

∗ and suppose a candidate deviates and increases

t1 to a group to t1 + z. Then, incremental revenue in period 1 (reduction in debt) following the deviation is

∆D = (ti1 + z) li1 (ti1 + z)−D∗

implying that needed (and equilibrium) revenue in period 2 falls by ∆D, leading to a new tax rate for everybody

in period 2 of

t2 = t2

µD∗ −∆D

N

¶.

Thus, when deviation is offered to one of the Ni groups, the change in vote share for the candidate is

U

µy∗i , ti1 (Ti1 +∆D) , ti2

µD∗ −∆D

N

¶¶− U

µy∗i , ti1 (Ti1) , ti2

µD∗

N

¶¶+qi (Ni − 1)

µU

µy∗i , ti1 (Ti1) , ti2

µD∗ −∆D

N

¶¶− U

µy∗i , ti1 (Ti1) , ti2

µD∗

N

¶¶¶+qiNj

µU

µy∗j , tj1 (Tj1) , tj2

µD∗ −∆D

N

¶¶− U

µy∗j , tj1 (Tj1) , tj2

µD∗

N

¶¶¶which is equal to

U

µy∗i , ti1 ((ti1 + z) l1 (ti1 + z)) , ti2

µD∗ − ((ti1 + z) l1 (ti1 + z)− t∗i1l1 (t∗i1))

N

¶¶− U

µy∗i , ti1 (Ti1) , ti2

µD∗

N

¶¶+qi (Ni − 1)

µU

µy∗i , ti1 (Ti1) , ti2

µD∗ − ((ti1 + z) l1 (ti1 + z)− t∗i1l1 (t∗i1))

N

¶¶− U

µy∗i , ti1 (Ti1) , ti2

µD∗

N

¶¶¶+qiNj

ÃU

Ãy∗j , tj1 (Tj1) , tj2

ÃD∗ − ¡(tj1 + z) l1 (tj1 + z)− t∗j1l1

¡t∗j1

¢¢N

!!− U

µy∗j , tj1 (Tj1) , tj2

µD∗

N

¶¶!

26

differentiate this expression with respect to z and imposing the equilibrium condition z = 0 we obtain:¡li1 + ti1l

0i1

¢ ∂U ¡y∗i , ti1 (Ti1) , ti2 ¡D∗N

¢¢∂t1

− qi (Ni − 1) + 1N

∂U¡y∗i , ti1 (Ti1) , ti2

¡D∗N

¢¢∂t2

¡li1 + ti1l

0i1

¢− qiNj

N

∂U¡y∗j , tj1 (Tj1) , tj2

¡D∗N

¢¢∂t2

¡lj1 + tj1l

0j1

¢= 0

or ¡l11 + t11l

011

¢ ∂U ¡y∗1 , t11 (T11) , t12

¡D∗N

¢¢∂t1

− q1 (N1 − 1) + 1N

∂U¡y∗1 , t11 (T11) , t12

¡D∗N

¢¢∂t2

¡l11 + t11l

011

¢− q1N2

N

∂U¡y∗2 , t21 (T21) , t22

¡D∗N

¢¢∂t2

¡l21 + t21l

021

¢= 0

¡l21 + t21l

021

¢ ∂U ¡y∗2 , t21 (T11) , t22

¡D∗N

¢¢∂t1

− q2 (N2 − 1) + 1N

∂U¡y∗2 , t21 (T21) , t22

¡D∗N

¢¢∂t2

¡l21 + t21l

021

¢− q2N1

N

∂U¡y∗1 , t11 (T11) , t12

¡D∗N

¢¢∂t2

¡l11 + t11l

011

¢= 0

Rearranging

(l11 + t11l011)

∂U¡y∗1 ,t11(T11),t12

¡D∗N

¢¢∂t1

− q1(N1−1)+1N

∂U¡y∗1 ,t11(T11),t12

¡D∗N

¢¢∂t2

(l11 + t11l011)

q1N2N

=∂U¡y∗2 , t21 (T21) , t22

¡D∗N

¢¢∂t2

¡l21 + t21l

021

¢=

(l21 + t21l021)

∂U¡y∗2 ,t21(T11),t22

¡D∗N

¢¢∂t1

− q2N1N

∂U¡y∗1 ,t11(T11),t12

¡D∗N

¢¢∂t2

(l11 + t11l011)

q2(N2−1)+1N

Combining

(l11 + t11l011)

∂U¡y∗1 ,t11(T11),t12

¡D∗N

¢¢∂t1

− q1(N1−1)+1N

∂U¡y∗1 ,t11(T11),t12

¡D∗N

¢¢∂t2

(l11 + t11l011)

q1N2N

=(l21 + t21l

021)

∂U¡y∗2 ,t21(T11),t22

¡D∗N

¢¢∂t1

− q2N1N

∂U¡y∗1 ,t11(T11),t12

¡D∗N

¢¢∂t2

(l11 + t11l011)

q2(N2−1)+1N

Rearranging

∂U¡y∗1 ,t11(T11),t12

¡D∗N

¢¢∂t1q1N2N

− (l21 + t21l021)

∂U¡y∗2 ,t21(T11),t22

¡D∗N

¢¢∂t1

(l11 + t11l011)q2(N2−1)+1

N

=

µ− q2N1

q2 (N2 − 1) + 1 +q1 (N1 − 1) + 1

q1N2

¶∂U¡y∗1 , t11 (T11) , t12

¡D∗N

¢¢∂t2

Note thatµ− q2N1

q2 (N2 − 1) + 1 +q1 (N1 − 1) + 1

q1N2

¶=

N1q1 (1− q2) +N2q2 (1− q1) + (1− q1) (1− q2)

(N2q2 − q2 + 1)N2q1> 0

∂U¡y∗1 , T11,

D∗N

¢∂t2

< 0

27

Hence∂U¡y∗1 ,t11(T11),t12

¡D∗N

¢¢∂t1

q1N2N

−(l21 + t21l

021)

∂U¡y∗2 ,t21(T11),t22

¡D∗N

¢¢∂t1

(l11 + t11l011)q2(N2−1)+1

N

< 0

Or

(l11 + t11l011)

q2N2+(1−q2)N

∂U¡y∗1 ,t11(T11),t12

¡D∗N

¢¢∂t1

− (l21 + t21l021)

q1N2N

∂U¡y∗2 ,t21(T11),t22

¡D∗N

¢¢∂t1

(l11 + t11l011)q2N2+(1−q2)

Nq1N2N

< 0

Using∂U

∂ti= −liu0

Hence− (l11 + t11l

011)

q2N2+(1−q2)N

l11u011 + (l21 + t21l

021)

q1N2Nl21u

021

(l11 + t11l011)q2N2+(1−q2)

Nq1N2N

< 0

We know (l11 + t11l011)

q2N2+(1−q2)N

q1N2N

> 0 since ∂t1∂T1

= 1

l1+∂l1∂t1

t1

> 0. Then

− ¡l11 + t11l011

¢ q2N2 + (1− q2)

Nl11u

011 +

¡l21 + t21l

021

¢ q1N2

Nl21u

021 < 0

Using∂li (ti)

∂ti= − 1

(γ00 (li (ti)))

we obtain

−µl11 − t11

γ00 (l11 (t11))

¶q2N2 + (1− q2)

Nl11u

011 +

µl21 − t21

γ00 (l21 (t21))

¶q1N2

Nl21u

021 < 0

which is satisfied if

−µl11 − t11

γ00 (l11 (t11))

¶l11u

011 +

µl21 − t21

γ00 (l21 (t21))

¶l21u

021 < 0 (26)

sinceq2N2+(1−q2)

Nq1N2N

> 1

for N2 large enough. Note that the above expression (26) is equivalent to

∂U

∂T11<

∂U

∂T21

which can hold if and only if t21 > t11.

6 Appendix B

In this appendix we provide an example of a simple modification of the model in which it is not necessary to assume

passive beliefs: in this version of the model there is a unique equilibrium with properties that are very similar to

28

those of the model described in the text. In order to save on notation and space, we assume that u is linear and that

the disutility of labor is quadratic: γ (l) = γ2l2.

We assume that there is a noise eL1 on transfers offered by L and eR1 for transfers offered by R. There is no noise

on individual level taxes but there is no signal of aggregate revenues. Just as in the previous analysis, this implies

that in equilibrium first period taxes are zero.

Given a choice of yL, yRi of transfers by L and R, the probability that a voter votes for R is:

Pr[yL + eL1 +

1

2γ+

¡1− tL2

¢2

2γ< yR + eR1 +

1

2γ+

¡1− tR2

¢2

2γ]

Because tL2 =12− 1

2

p(1− 4γyL) tR2 = 1

2− 1

2

p(1− 4γyR) we obtain that the probability that voter votes for R is

Pr[yL + eL1 +

1

2γ+

³12+ 1

2

p(1− 4γyL)

´2

2γ< yR + eR1 +

1

2γ+

³12+ 1

2

p(1− 4γyR)

´2

2γ]

which is also R’s expected vote share. This can then be rewritten as:

Pr[eL1 < eR1 + y

R − yL +

³1 +

p(1− 4γyR)

´2

8γ−

³1 +

p(1− 4γyL)

´2

8γ]

If eL1 and eR1 are distributed according to G (with density g), candidate R’s vote share following a deviation is:

SR(y) =

ZG(eR1 + y +

³1 +

q¡1− 4γD+y

N

¢´2

8γ−

³1 +

q¡1− 4γ D

N

¢´2

8γ)dG(eR1 ) +

p(N − 1)ZG(eR1 +

³1 +

q¡1− 4γD+y

N

¢´2

8γ−

³1 +

q¡1− 4γ D

N

¢´2

8γ)dG(eR1 )

Differentiating this with respect to y we obtain:

∂SR(y)

∂y=

1 + 2³1 +

q¡1− 4γD+y

N

¢´8γ

1

2

−4γ 1Nq¡

1− 4γD+yN

¢×

×Zg

eR1 + y +³1 +

q¡1− 4γD+y

N

¢´2

−³1 +

q¡1− 4γ D

N

¢´2

8γ

dG(eR1 ) ++−4γ 1

N

³1 +

q¡1− 4γD+y

N

¢´p(N − 1)

8γ

q¡1− 4γD+y

N

¢ ×

×Zg

eR1 +³1 +

q¡1− 4γD+y

N

¢´2 ³1 +

q¡1− 4γ D

N

¢´2

8γ

dG(eR1 )29

This simplifies to

1−³1 +

q¡1− 4γD+y

N

¢´2N

q¡1− 4γD+y

N

¢×

×Zg

eR1 + y +³1 +

q¡1− 4γD+y

N

¢´2

−³1 +

q¡1− 4γ D

N

¢´2

8γ

dG(eR1 )+p(N − 1)

−³1 +

q¡1− 4γD+y

N

¢´2N

q¡1− 4γD+y

N

¢×

×Zg

eR1 +³1 +

q¡1− 4γD+y

N

¢´2

−³1 +

q¡1− 4γ D

N

¢´2

8γ

dG(eR1 )In equilibrium, this expression should equal 0 for y = 0

Thus,

1−³1 +

q¡1− 4γ D

N

¢´2N

q¡1− 4γ D

N

¢Z g(eR1 )dG(e

R1 )+

+p(N − 1)

−³1 +

q¡1− 4γ D

N

¢´2N

q¡1− 4γ D

N

¢Z g(eR1 )dG(e

R1 ) = 0

or

2N

r³1− 4γD

N

´−Ã1 +

r³1− 4γD

N

´!= p(N − 1)

Ã1 +

r³1− 4γD

N

´!which, as can be easily verified, is the same condition as in in the model with passive beliefs and no noise.

30

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