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Abstract. We examine how yardstick competition between jurisdictions

aﬀects the agency problem resulting from uncertainty about politicians

(adverse selection) and their policies (moral hazard). We ﬁnd that yard-

stick comparison can contribute both to disciplining and to selecting pol-

iticians.

1 Introduction

Elections may be seen as a way for sorting ‘good’ from ‘bad’ incumbents (by

‘good’ incumbent, we mean someone who is honest, competent and not

easily bought oﬀ by special interests). However elections do not work well in

controlling and sorting politicians. There are severe problems in monitoring

and evaluating the incumbent’s behavior in order to make informed deci-

sions about whether to reelect or not. Voters face a formidable agency

problem because they are inevitably poorly informed about politicians’

behavior and type. Moreover, the electoral sanction (pass or fail) is such a

crude incentive scheme that it can hardly induce the politicians to do what

the public wants. A theoretical model that captures this political agency

Soc Choice Welfare (2005) 24: 155–169

DOI: 10.1007/s00355-003-0297-8

Earlier versions of this paper have circulated as Queen Mary Working Paper No. 444

and CORE Discussion Paper 2002/29. We would like to thank our editor, Maurice

Salles, two anonymous referees, Mark Armstrong and Enrico Minelli for helpful

comments and suggestions. We would also like to thank seminar participants at

CORE, Queen Mary, Marseilles, and the 2002 Public Economic Theory conference,

Universite

´Paris 1.

Yardstick competition and political agency problems

Paul Belleﬂamme1, Jean Hindriks1;2

1CORE and IAG, Universite

´catholique de Louvain, Voie du Roman Pays 34, 1348

Louvain-la-Neuve, Belgium (e-mails: {belleﬂamme; hindriks}@core.ucl.ac.be)

2

CORE and Economic Department, Universite

´Catholique de Louvain

Received: 30 January 2003 / Accepted: 15 September 2003

problem simply but usefully must combine the elements of adverse selection

and moral hazard.1

Given the diﬃculty of the agency problem voters face, it might be rea-

sonable to try and organize yardstick competition among politicians for

controlling problems of moral hazard and adverse selection. In this respect,

the Brennan and Buchanan (1980) view is that competition among diﬀerent

decentralized governments can exercise a disciplinary force and break the

monopoly power of a large central government. Comparing performances in

oﬃce among diﬀerent incumbents would help in sorting good types from bad

types as well as controlling moral hazard.

We analyze the nature and eﬀectiveness of yardstick competition on one

particular aspect of the political agency problem: the possibility that

incumbent politicians might use ineﬃcient mechanisms to transfer resources

to special interests.2To this end, we consider a multi-jurisdiction version of a

political agency model due to Coate and Morris (1995). In this model, the

incumbent in each jurisdiction chooses a policy. Then, the respective elec-

torate, uninformed about the quality of both the incumbents and their policy,

but informed about their relative performance, choose whether to retain their

representative. In the second (and last) period, if reelected, and depending on

his type, the incumbent chooses a transfer and the electorate receive utility.

With a single agency, Coate and Morris (1995) show that an incumbent

seeking reelection may behave ineﬃciently in equilibrium either by under-

taking non-valuable policies or by not undertaking valuable ones. The aim of

this paper is to examine how yardstick competition inﬂuences the incentives

to behave eﬃciently in a multi-agency framework. Our main result is that for

any correlation short of perfect correlation between agencies, it is less likely

that bad politicians behave ineﬃciently under yardstick competition (Prop-

osition 1).

This paper is related to the emerging literature on yardstick competition in

political agency.3The common feature of this literature as well as most of the

literature on electoral accountability is that the desire for reelection can

motivate politicians to behave in the interest of citizens (see Wittman 1995).

1Banks and Sundaram (1993) present an inﬁnite horizon model that incorporates both

elements. Politicians are constrained to serve at most two terms and, as in Ferejohn

(1986), politicians’ choice variable is eﬀort not policy. In Barro (1973), the political

agency problem is overprovision of public good. See Laﬀont (2000) for a nice review of

political agency theory whereas Shleifer and Vishny (1998) provide more focus on

transition economics. See also Przeworsky et al. (1999) for a broader historical

perspective of political agency problems.

2For instance, public employment is often argued to be used as an indirect and

possibly ineﬃcient method of redistribution (see, Alesina et al. 2000).

3A very nice survey of this literature can be found in Persson and Tabellini (2000,

Chapts. 4 and 9). See more speciﬁcally the papers by Besley and Case (1995) and

Besley and Smart (2001). See also some recent papers like Wrede (2001) and

Bodenstein and Ursprung (2001).

156 P. Belleﬂamme, J. Hindriks

Besley and Case (1995) provide empirical support to the idea that voters use

relative performance criterion in deciding whether to retain or not their

incumbent. Besley and Smart (2001) is more theoretical and shows that the

eﬀect of yardstick competition can go either way depending on the initial

reputation of the incumbent. The ambiguity arises essentially from the fact

that yardstick comparison facilitates the detection of bad incumbent but has

the adverse eﬀect of inducing more rent diversion by bad incumbents who are

less likely to be re-elected (last period eﬀect). The distinctive feature of our

analysis is that the electoral incentive and the desire for reelection are

themselves the source of ineﬃciency and we assess the role of yardstick

comparison in this context.4One consequence of this diﬀerent approach is

that yardstick competition cannot go the wrong way because in facilitating

the detection of bad incumbents (sorting eﬀect) it also makes it less likely that

they will distort ineﬃciently their policy choice (discipline eﬀect) in order to

preserve their chance of reelection. Therefore the extra information that

yardstick comparisons bring about cannot hurt the principal in our model:

discipline and sorting eﬀects work in the same direction.5

The model used to assess the eﬀect of yardstick competition is set out in

the next section. Our main result on the disciplining eﬀect of yardstick

comparison is presented in Sect. 3. Some concluding remarks are presented in

Sect. 4.

2 A multi-jurisdiction political agency model

We use a two-period political agency model due to Coate and Morris (1995)

(hereafter CM) that we extend to two agencies (jurisdictions) so that in a

correlated environment, voters can use a relative performance criterion (i.e.,

yardstick competition) to decide whether or not to reelect their incumbent. In

the ﬁrst period, both incumbents choose independently and simultaneously

4For evidence that politicians are strongly motivated by the desire for reelection, see

Cain et al. (1987).

5This ﬁnding that more information can not hurt the principal should be contrasted

with career concerns literature. For instance, Dewatripont et al. (1999) provide two

examples in which a more precise signal about the agent’s performance reduces

discipline. Morris (2001) shows that observing more informative signals can worsen

discipline because the good type may be induced to take more extreme action to

separate from the bad type (‘‘political correctness’’ eﬀect). There is also a literature on

the trade-oﬀ between transparency and eﬃciency. Bordignon and Minelli (2001)

present a political agency model where it is optimal to have low powered incentives but

more transparent rules (with negative discipline eﬀect) to facilitate detection of bad

politician (positive sorting eﬀect). Prat (2001) presents a model in which better

information on the agent’s action (more transparency over actions) can unambigu-

ously hurt the principal by producing conformism. Conformism is detrimental because

the agent is taking less appropriate action and his performance is less informative of

his type.

Yardstick competition 157

whether or not to implement a public policy, and whether or not to make cash

transfers to some ‘special interest’.6Each incumbent may be of two types: the

‘‘good’’ type always behaves in the interest of his electorate, and the ‘‘bad’’

type may do rent-seeking at the expense of his electorate. The problem for

voters is to distinguish a good from a bad incumbent on the basis of their

performance relative to the other incumbent. In the second period, the

incumbent, if reelected, simply selects a cash transfer to the special interest.

At the beginning of the game, nature selects an incumbent type in each

jurisdiction. Incumbent is good with probability kI2ð0;1Þand bad with

probability 1 kIin the domestic jurisdiction (the corresponding probabili-

ties in the other jurisdiction are ~

kIand 1 ~

kI, respectively). Then nature

selects a policy quality in each jurisdiction according to some joint distribu-

tion p. There is uncertainty about the beneﬁt of any policy. The valuable

policy produces a high net beneﬁt BHwith probability h12ð0;1Þand a low

net beneﬁt BLwith probability 1 h1(with BL<0<BH). The non-valuable

policy produces the same high net beneﬁt BHbut with a lower probability h0

(with 0 <h0<h1<1). To simplify the analysis (and without any loss of

generality), we assume that the joint probability distribution of policy types,

pðh;hÞ, is symmetric: pðh0;h0Þ¼pðh1;h1Þ¼q=2 and pðh0;h1Þ¼

pðh1;h0Þ¼ 1qðÞ=2. We focus here on the case where 1=2q1, so that

there is positive (or no) correlation between the two jurisdictions.

There is asymmetric information between the incumbents and voters

insofar as incumbents know more about their type and the desirability of a

public policy: incumbents, but not voters, observe h2fh0;h1gbefore decid-

ing whether to implement the policy or not. For simplicity we shall also

assume that there is symmetric information between politicians. In each

jurisdiction the expected beneﬁt from a policy his BðhÞ¼hBHþð1hÞBL.

Moreover, both types of policy produce a rent R>0 for a special interest

group. We make the same assumption as CM.

Assumption 1. (i)

Bðh1Þ>0, (ii)

Bðh0Þ<R<0:

Part (i) says that a valuable policy (h¼h1) produces positive expected

beneﬁt to the voters. Part (ii) says that a non-valuable policy (h¼h0) yields

expected cost to the voters in excess of the rent to the interest group; as a

result, the voters would prefer to pay directly cash transfer of Rto the special

interest instead of having the policy implemented (if they could credibly

commit doing so).

In addition to the implementation of a policy, each incumbent can make a

cash transfer T0 from the voters to the interest group. A good politician

(i¼g) cares only about the expected welfare of the voters and about being in

oﬃce. Thus, his ﬁrst-period utility is vgðBðhÞTÞor vgðTÞ;depending on

6The policy choice may refer to some government procurement of goods and services

or regulatory activities; and the cash transfers refer to subsidies programs.

158 P. Belleﬂamme, J. Hindriks

his decision to implement or not a policy of type h2fh0;h1gand to make a

cash transfer T0. Preference for being in oﬃce is reﬂected by vgð0Þ>0. A

bad politician (i¼b), on the other hand, also cares about the interest group

and his utility is vbðBðhÞT;RþTÞor vbðT;þTÞ;depending on his decision

to implement or not the policy h2fh0;h1gand to make a cash transfer T0.

We assume that vbð:; :Þis smooth and increasing in both arguments and that

vbð0;0Þ>0 is the value of holding oﬃce for the bad incumbent. Let

v

bðBðh1Þ;RÞmaxTvbðBðh1ÞT;RþTÞwith optimal cash transfer T¼T1

and similarly, v

bð0;0ÞmaxTvbðT;þTÞwith optimal cash transfer T¼T0.

As in CM we make the following assumptions on the preference of a bad

politician in the two jurisdictions (with d2½0;1representing the incumbents’

discount factor).

Assumption 2. vbðBðh0Þ;RÞ>vbð0;0Þ.

Assumption 3. (i) v

bðBðh1Þ;RÞvbðBðh1Þ;RÞ<dv

bð0;0Þ;(ii) v

bð0;0Þ vbð0;0Þ

<dv

bð0;0Þ.

Assumption 2 says that ignoring the reelection constraint, a bad incum-

bent wants to implement a non-valuable policy, at the expense of the voters, if

it gives a rent Rto the interest group. Assumption 3 says that the bad in-

cumbent has a suﬃciently strong desire for reelection that he would prefer to

give up the optimal cash transfer if he could be reelected for sure.

Upon observing the policy type h, an incumbent of type i2fg;bgmakes a

policy and cash transfer decision. A ﬁrst-period strategy for the incumbent in

any jurisdiction speciﬁes a policy and transfer decision for each type of

incumbent (i2fg;bg) and each realization of policy type in that jurisdiction

(h2fh0;h1gÞ based on his (perfect) information Habout the politician and

policy type in the other jurisdiction: siðh;HÞ2DRþ, where D¼P(D¼N)

denotes (no) policy implementation. Voters observe their incumbent’s record

R¼ðD;T;BÞ, as well as the other incumbent’s record ~

R¼ð~

D;~

T;~

BÞ(with

B2fBL;BHgfor D¼Pand B¼/for D¼N). On the basis of these obser-

vations, voters update their initial belief (kI) that their incumbent is good as

aðR;~

RÞ2½0;1, which also denotes the probability that they will reelect their

incumbent.7If reelected, and depending on his type, the incumbent makes a

cash transfer decision and the game ends. There is no policy decision to be

made in the second period.

We solve the game for its perfect Bayesian equilibria. Like CM, we reﬁne

the equilibrium concept by requiring out-of-equilibrium beliefs to be consis-

tent with a monotonicity criterion (monotone beliefs). The logic of this

7This simplifying assumption can be justiﬁed as follows. An incumbent is reelected

when his posterior reputation exceeds the reputation of some challenger, whose

reputation is drawn from a uniform distribution on ½0;1.

Yardstick competition 159

criterion is that posterior belief should reﬂect the fact that a bad type is more

likely to deviate from the equilibrium play to make higher cash transfers.8

We now examine how yardstick competition aﬀects the possibility that

incumbent politicians use non-valuable policies as disguised transfers to the

special interest. Due to the complexity of the model, we make no attempt at

fully characterizing the set of PBE, but we focus instead on the equilibria

studied in CM.

3 Disciplining eﬀect of yardstick competition

The main insight of CM is that a bad politician may prefer to implement a

non-valuable policy rather than to make a direct cash transfer. Implementing

the policy indeed allows the politician to make a disguised transfer to the

interest group without compromising his chance of reelection. In this section,

we investigate how, in an imperfectly correlated environment, yardstick

competition could aﬀect the occurrence of this form of ineﬃciency. We

consider the following strategy:

Deﬁnition 1. Strategy S is such that in each jurisdiction, for any conﬁgurations

of politician and policy in the other jurisdiction, (i) both types of incumbent

make no cash transfers, (ii) a good incumbent implements valuable policies

only, (iii) a bad incumbent implements both valuable and non-valuable policies.

We now demonstrate that strategy S constitutes an equilibrium behavior if

the incumbent’s initial reputation is suﬃciently high, but that yardstick com-

petition makes this kind of equilibrium less likely to arise (and in fact impos-

sible in a perfectly correlated environment). We proceed in three steps. First,

we compute the posterior beliefs induced by strategy S. Second, we derive the

reelection probabilities. Third, we prove that given the induced probability of

reelection, it is optimal for both types of incumbent to play strategy S when

the incumbent in the other jurisdiction does the same.

3.1 Posterior beliefs

From strategy S, incumbents do not make cash transfers and the possible

records in each jurisdiction are HðP;0;BHÞ,LðP;0;BLÞ, and

NðN;0;0Þ, yielding 3 3 diﬀerent record proﬁles. The posterior belief that

8This monotonicity requirement implies that a good politician will never make cash

transfers since this would only hurt his reputation without bringing any beneﬁt. It

follows that by making cash transfers the bad politician will reveal himself and thus he

would rather choose optimal cash transfers if any (i.e., T0when the policy is non-

valuable and T1when the policy is valuable).

160 P. Belleﬂamme, J. Hindriks

the domestic incumbent is good for any record proﬁle ðR;~

RÞ2

fH;L;NgfH;L;Ngis

aij ¼kI

kIþð1kIÞ1þ/ij

8i;j2fH;L;Ng

where /ij is a measure of the reputational cost (i.e., aij kI() /ij 0).

Straightforward but tedious calculations establish the following (with ~

kI

denoting the incumbent’s initial reputation in the other jurisdiction):

0</HH ¼h0

h1

ð1qÞh1þqh0ð1~

kIÞ

qh1þð1qÞh0ð1~

kIÞ

!

</LH ¼h1

h0

1h0

1h1

/HH ;

0</HL ¼h0

h1

ð1qÞð1h1Þþqð1h0Þð1~

kIÞ

qð1h1Þþð1qÞð1h0Þð1~

kIÞ

!

</LL ¼h1

h0

1h0

1h1

/HL;

0</HN ¼h0

h1

q

ð1qÞ</LN ¼h1

h0

1h0

1h1

/HN :

Thus, there is always a reputational cost to implement any policy because,

with strategy S, bad politicians are more likely to implement than good

politicians. Since a bad politician always implements, a good politician can

reveal himself by not undertaking the policy, and thus

/NH ¼/NL ¼/NN ¼1;

so that aNH ¼aNL ¼aNN ¼1 (the non-implementation decision guarantees

reelection). When there is no correlation (i.e., q¼1=2) the model is similar to

CM and the reputation costs from undertaking the policy does not depend on

the outcome of the policy in the other jurisdiction:

0</HH ¼/HL ¼/HN ¼h0

h1

<1</LH ¼/LL ¼/LN ¼1h0

1h1

:

Straightforward comparisons of posterior beliefs highlight a number of

instructive results. First, there is a direct reputational eﬀect: regardless of the

outcome in the other jurisdiction, (i) a good performance BHimproves rep-

utation relative to bad performance BL(because bad politicians undertake

non-valuable policies, which are more likely to fail) and (ii) undertaking the

policy reduces reputation relative to no implementation (because bad politi-

cians are more likely to implement); that is,

aLK <aHK <kI<aNK ¼18K¼H;L;N:

This direct reputational eﬀect is already present in CM’s analysis. However,

in a correlated environment, voters observe a relative performance that is not

directly controlled by their incumbent. As a result, a second, indirect, repu-

tational eﬀect (or informational externality) appears in our model. It says that

for any given domestic record, the reputation of the politician also depends

Yardstick competition 161

on the record of the politician in the other jurisdiction. More precisely, we

have the following rankings (8K¼H;L):

aKN <aKL <aKH if q>1=2;

aKN ¼aKL ¼aKH aKif q¼1=2;

ð1Þ

(where aHand aLdenote the posterior beliefs in an uncorrelated environment

when respectively high and low beneﬁts are observed). In words, when there is

positive correlation, the reputation of the domestic incumbent undertaking

the policy is the lowest when the policy is not undertaken in the other

jurisdiction and the highest when the policy is undertaken and is a success in

the other jurisdiction. This is because not undertaking the policy in the other

jurisdiction reveals that it was a non-valuable policy which, by positive cor-

relation, makes it more likely that the domestic policy is also non-valuable.

Since only a bad incumbent implements non-valuable policies, undertaking

the policy leads voters to believe that their incumbent is bad. On the other

hand, observing a successful policy in the other jurisdiction increases the

chance that it was a valuable policy (since it is more likely to succeed) which,

by positive correlation, increases the chance that the domestic policy is also

valuable and therefore, that it could have been implemented by a good or bad

politician alike. In this case the reputation cost for undertaking the policy is

less than when the policy is not undertaken in the other jurisdiction.

Lastly, for K¼H;L, positive correlation improves the incumbent’s rep-

utation when the policy is successful in the other region, but hurts it in the

case of no implementation:9

aKN <aK<aKH if q>1=2:ð2Þ

3.2 Reelection probability

We can now derive the (ex ante) probability of reelection of each type of

incumbent as a function of the type of the other incumbent and the policy

proﬁle. First, when ðh;~

hÞ¼ðh1;h0Þ, the domestic policy is valuable and from

strategy S, both types of incumbent act in the same way while in the other

jurisdiction, the policy is non-valuable leading both types of incumbents to

act diﬀerently. Therefore, the probability of reelection of the domestic

incumbent is independent of his type due to pooling but depends on the type

of the other politician: 8i2fg;bg;

9How posterior beliefs respond to a low beneﬁt in the other jurisdiction is ambiguous.

Indeed, upon observing a low beneﬁt in the other jurisdiction, posterior beliefs when

undertaking the policy (regardless of its outcome) are higher in a positively correlated

environment (i.e., aHL >aHand aLL >aL) if and only if 1 h1>ð1h0Þð1kIÞ:This

condition means that a low beneﬁt is more likely to arise from the failure of a valuable

policy (always undertaken) rather than from the failure of a non-valuable policy (only

undertaken if the incumbent is bad).

162 P. Belleﬂamme, J. Hindriks

piðh1;h0;gÞ¼h1aHN þð1h1ÞaLN

piðh1;h0;bÞ¼h1h0aHH þð1h0ÞaHL

½

þð1h1Þh0aLH þð1h0ÞaLL

½.

Second, when ðh;~

hÞ¼ðh1;h1Þ, the policy is valuable in both jurisdictions and

from strategy S, both types of incumbents pool on the same action in both

jurisdictions. Therefore, the probability of reelection of the domestic incumbent

is independent of his own type and of the other politician’s type: 8ij 2fg;bg;

piðh1;h1;jÞ¼h1h1aHH þð1h1ÞaHL

½

þð1h1Þh1aLH þð1h1ÞaLL

½.

Third, when ðh;~

hÞ¼ðh0;h0Þ, the policy is non-valuable in both jurisdictions

and by strategy S, both types of incumbent in each jurisdiction separate on

diﬀerent actions. Therefore, the probability of reelection of the domestic

politician depends both on his own type and on the other politician’s type:

pbðh0;h0;gÞ¼h0aHN þð1h0ÞaLN;

pbðh0;h0;bÞ¼h0h0aHH þð1h0ÞaHL

½

þð1h0Þh0aLH þð1h0ÞaLL

½;

pgðh0;h0;gÞ¼pgðh0;h0;bÞ¼1:

Fourth, when ðh;~

hÞ¼ðh0;h1Þ, both types of incumbents act the same in the

other jurisdiction and the domestic reelection probability is independent of the

other politician’s type (with the good incumbent revealing himself): 8j2fg;bg

pbðh0;h1;jÞ¼h0h1aHH þð1h1ÞaHL

½

þð1h0Þh1aLH þð1h1ÞaLL

½;

pgðh0;h1;jÞ¼1.

Lastly, in the absence of correlation, there is no informational externality and

the reelection probabilities are

pbðh0Þ¼h0aHþð1h0ÞaL;

pgðh0Þ¼1;

pbðh1Þ¼pgðh1Þ¼h1aHþð1h1ÞaL:

We can now rank the probabilities of reelection for the two types of

incumbents.

Lemma 1. With positive correlation (q>1=2), a bad incumbent playing

strategy S in each jurisdiction faces probabilities of reelection that depend on the

situation in the other jurisdiction as follows: 8h2fh0;h1g,

(i) pbðh;h0;gÞ<pbðh;h0;bÞ<pbðh;h1;gÞ¼pbðh;h1;bÞ;

(ii) pbðh;h0;gÞ<pbðhÞ:

Yardstick competition 163

From part (i), a bad incumbent has the lowest chance of re-election when

the other policy is non-valuable and the other politician is good. From part

(ii) the bad incumbent is hurt by performance comparison.

3.3 Eﬀect of yardstick competition

We are now in a position to check whether yardstick competition in a cor-

related environment can eﬀectively reinforce the ability of voters to restrain

bad incumbents from undertaking non-valuable policies. We proceed in two

steps. First, we derive the minimum initial reputation beyond which it is

optimal for both types of politicians to play strategy S. Second, we show that

yardstick competition increases the minimum initial reputation required for

the incumbent to play strategy S. Thus, yardstick competition eﬀectively re-

duces the incentive for undertaking non-valuable policies.

To ensure that both types of incumbent behave as prescribed by strategy S,

their reelection probability when playing strategy S must be high enough; since

reelection probabilities increase, ceteris paribus, with the initial reputation, this

amounts to say that the initial reputation must be high enough. Since strategy S

prescribes actions for both types of incumbent that are independent of the

situation in the other jurisdiction, both types of incumbent must ﬁnd it optimal

to play these actions for all possible conﬁgurations of policies and politician

types in the other jurisdiction, and in particular for the least favorable situation.

From part (i) of Lemma 1, we know that the prospect of reelection is worst when

the incumbent faces a good politician with non-valuable policy. We further

know, from part (ii) of that lemma, that greater correlation makes this worst

reelection prospect even worse by increasing the ability of voters to detect bad

incumbents. This reasoning establishes our main result about the desirable

eﬀect of yardstick comparisons to restrain (bad) incumbents undertaking non-

valuable policies, which is stated formally in the following proposition.

Proposition 1. Under Assumptions 1-3, there exists kðqÞ<1for all q2½

1

2;1Þ

such that a symmetric PBE involving incumbent strategy S in both jurisdictions

exists if kI>kðqÞ.Furthermore, kðqÞ<kðq0Þ81

2q<q0<1. However, at

the limit for q¼1, there is no kð1Þ<1and a PBE involving incumbent

strategy S in both jurisdictions cannot exist.

Proof. See the appendix

The interpretation of this proposition is that yardstick competition can

reduce (and even eliminate in case of perfect correlation) the risk of

undertaking non-valuable policies by improving the ability of voters to

detect those policy choices that are not in their interest, along with the bad

incumbents who make such choices. This result ﬁts nicely with what seems

to be the most popular argument for yardstick competition and performance

comparisons.

164 P. Belleﬂamme, J. Hindriks

To see this more clearly, suppose ﬁrst that there is no correlation between

jurisdictions so that no information is revealed about the type of the incumbent

from the policy outcome in the other jurisdiction. In this context, a bad

incumbent seeking reelection with a good initial reputation may rely on wasteful

(ineﬃcient) policies to redistribute in favor of some special interest, instead of

foregoing reelection by making explicit cash transfers. This follows from the

stochastic relationships between policy types and outcomes (i.e., non-valuable

policies have some chance of success while valuable policies might fail). How-

ever, in a correlated environment, voters have the additional possibility of

drawing inference about the quality of their incumbent from observing the

policy outcome in the other jurisdiction. Not undertaking the policy in the other

jurisdiction reveals that it is a non-valuable policy and given positive correla-

tion, voters would infer that the domestic policy is likely to be non-valuable,

reducing the chance of reelection of the incumbent undertaking it. Hence,

incumbents will have lower incentive to implement non-valuable policies that

are more easily detected through performance comparison.

A natural question is whether the bad incumbent could, to some extent,

neutralize the eﬀect of yardstick competition by conditioning his decision to

the type of politician and policy in the other jurisdiction. The idea is that a

bad incumbent might choose to behave eﬃciently when facing a good poli-

tician or a non-valuable policy in the other jurisdiction. However, this con-

jecture is false for reasons that we now brieﬂy explain.10

Consider ﬁrst a modiﬁed version of strategy S in which the bad incumbent

refrains from implementing a non-valuable policy if the policy in the other

jurisdiction is non-valuable. This strategy cannot be an equilibrium. Suppose

indeed that the policy is not undertaken in the other jurisdiction. Voters infer

that it has to be a non-valuable policy and expect pooling from their own

incumbent. But then, there is no reputation cost from implementing at home

and the bad incumbent would deviate.

Consider next a strategy in which the bad incumbent refrains from

implementing a non-valuable policy if the other incumbent is good. Again,

such strategy cannot be an equilibrium. Suppose indeed that politicians in

both jurisdictions adopt such strategy. If the policy is valuable in the other

jurisdiction, then it will be implemented whatever the type of the politician.

But since good and bad politicians pool on the same action in the other

jurisdiction, the chance of reelection of the domestic incumbent cannot de-

pend on the other politician’s type, and therefore the bad politician cannot

ﬁnd it proﬁtable to condition his decision on the type of the other politician.

4 Concluding remarks

CM prove the non-existence of an equilibrium in which both types of

incumbent behave eﬃciently. The idea is the following. On eﬃciency grounds,

10 See Belleﬂamme and Hindriks (2002) for a formal treatment of this issue.

Yardstick competition 165

the incumbent should only implement the high quality policy. When reelec-

tion is likely ex ante, bad incumbents refrain from using direct transfers to

avoid revealing their type. However, both types are equally likely to produce

any record when playing the same no-transfer strategy. Thus if voters expect

both types to behave eﬃciently, bad incumbents deviate to implement both

policies since they are no less likely to be re-elected. It is straightforward to

show that this non-existence result goes through under yardstick competition.

This is because just as observing any particular record within a jurisdiction

carries no information when both types are expected to behave eﬃciently, so

observing an extra record in another jurisdiction is uninformative. Conse-

quently, the incentive for bad incumbents to deviate from eﬃciency to dis-

honesty persists irrespective of performance comparison.11 The same could be

said for the under-implementation result of CM in which both types refrain

from implementing both policies. This result is driven by two assumptions: (i)

both incumbents have an overwhelming desire for re-election and (ii) voters

believe that a deviation to policy implementation is certain to come from a

bad incumbent. Again since voters expect both types to act the same,

observing the record in another jurisdiction is uninformative and so this

existence result also goes through under yardstick competition. It is also

possible to show that there is no other underprovision equilibrium involving

both types of incumbents choosing diﬀerent actions. For instance, there is no

equilibrium in which the good incumbent refrains from undertaking any

policy (either valuable or not) and the bad incumbent chooses to implement

at least one type of policy.12

Obviously these results rest on the assumption that politicians are equally

competent and so they are equally likely to produce the same record when

playing the same strategy. One interesting extension would be to explore the

impact of politicians that diﬀer not only in their honesty but also in their

competency. While this would be a new research, it might improve the

model’s realism and deepen the contribution to the literature.

We now summarize our main result about the eﬀect of yardstick com-

petition. The usual presumption is that decentralized decision makers are

more accountable. One possible reason is that decentralization allows per-

11 However there is a discontinuity at perfect correlation (q¼1). To see this, consider

that voters observe that no cash transfers are made and no policy is undertaken in the

other jurisdiction. Expecting politicians to behave eﬃciently, voters infer that the

policy is wasteful in that jurisdiction and thus (by perfect correlation), that the policy

is also wasteful in their own jurisdiction. Therefore, a bad incumbent deviating from

the eﬃcient equilibrium play by undertaking a wasteful policy would reveal himself,

and forego any chance of reelection.

12 The reason is that if the good incumbent never implements, the bad incumbent

would reveal himself by implementing. Facing no chance of reelection, the bad

incumbent makes cash transfers. But then, since voters do not expect good incumbents

making cash transfers, there is no reputational penalty for a good incumbent from

deviating by implementing but without cash transfers.

166 P. Belleﬂamme, J. Hindriks

formance comparison. In this paper we examine the role of yardstick com-

petition for improving political decisions. Can yardstick competition make

politicians more accountable? It is well known that in a general principal-

agent relationships within a correlated environment, incentive schemes based

on relative performance can enhance (Holmstrom 1982) and even restore

(Shleifer 1985) eﬃciency. However, in political agency, voters are restricted to

a very crude incentive scheme which is to re-elect or to vote their politicians

out. In this context, Besley and Smart (2001) have shown that the eﬀect of

yardstick competition can go either way, depending on the residual degree of

conﬁdence about politicians.

In this paper, we use a diﬀerent political agency framework and show that

yardstick competition cannot go the wrong way, although in several cases it

has no eﬀect at all. Our political agency model is similar to Coate and Morris

(1995). In this model, ineﬃciency arises from the fact that politicians may use

non-valuable public policies as an indirect and disguised method of chan-

neling resources to some special interest, when more transparent transfer

would not ﬁnd political support. Assuming symmetric information between

politicians across jurisdictions, we ﬁnd that yardstick competition can help

discipline politicians, which is in contrast with some earlier work. In future

work, it would be interesting to relax the assumption that incumbents have

complete information and to give the opportunity for the good incumbent to

separate from the bad one (e.g. by taxing the special interest).

Appendix: Proof of Proposition 1

We ﬁrst prove that, for all q2ð0;1Þ, there is a kðqÞ<1 such that there exists

a PBE involving strategy S when kIkðqÞ. We start by deriving the con-

ditions under which strategy S is an equilibrium play for both types of

incumbent. The good incumbent never makes cash transfers and thus always

chooses ðN;0Þwhen h¼h0.Whenh¼h1, he prefers ðP;0Þover ðN;0Þfor all

policy and politician types in the other jurisdiction if and only if:

pgðh1;h0;gÞ1vgðBðh1ÞÞ vgð0Þ

dvgð0Þ:ð3Þ

Consider now a bad incumbent. When h¼h0, our assumptions guarantee that

he prefers ðN;0Þover ðN;T0Þ. He also prefers ðP;0Þover ðN;0Þfor all policy

and politician types in the other jurisdiction if and only if:

pbðh0;h0;gÞ1vbðBðh0Þ;RÞvbð0;0Þ

dv

bð0;0Þ:ð4Þ

As the payoﬀ from choosing ðP;0Þis always larger when h¼h1than when

h¼h0, condition (4) guarantees that the bad incumbent does not prefer ðN;0Þ

when h¼h1. The condition for the bad incumbent to prefer ðP;0Þover ðP;T1Þ

for all policy and politician types in the other jurisdiction is given by:

Yardstick competition 167

pbðh1;h0;gÞv

bðBðh1Þ;RÞvbðBðh1Þ;RÞ

dv

bð0;0Þ:ð5Þ

Combining conditions (3), (4), and (5) and using the facts that (i) the prob-

abilities of reelection increase in kI, and (ii) pgðh1;h;gÞ¼pbðh1;h;gÞ, we can

derive the threshold kðqÞsuch that all three conditions are satisﬁed when

kI>kðqÞ. In particular, kðqÞmust be the smallest value of kIsuch that

pbðh0;h0;gÞ1vbðBðh0Þ;RÞvbð0;0Þ

dv

bð0;0Þ

pbðh1;h0;gÞmax 1 vgðBðh1ÞÞvgð0Þ

dvgð0Þ;v

bðBðh1Þ;RÞvbðBðh1Þ;RÞ

dv

bð0;0Þ

no

:

8

<

:

Assumptions 1–3 guarantee that the two RHS are below one. We have

that, for all q<1;the left-hand side reelection probabilities are increasing in

kIand converging to one as kI!1. Therefore there exists such a kðqÞ<1.

As the above probabilities of reelection are decreasing with q, it follows

that kðqÞ<kðq0Þfor all 1

2q<q0<1. Lastly for q¼1;the two proba-

bilities are equal to zero for all kI<1. It is therefore clear that condition (6)

cannot be met and that there is no kðqÞ<1 for q¼1. QED

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