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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 yardstick comparison can contribute both to disciplining and to selecting politicians.
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 kI0;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 h10;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 vgðBðhÞTÞor vgðTÞ;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 vbðBðhÞT;RþTÞor vbðT;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;RÞmaxTvbðBðh1ÞT;RþTÞwith optimal cash transfer T¼T1
and similarly, v
bð0;0ÞmaxTvbðT;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 d0;1representing the incumbents’
discount factor).
Assumption 2. vbðBðh0Þ;RÞ>vbð0;0Þ.
Assumption 3. (i) v
bðBðh1Þ;RÞvbðBðh1Þ;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;h1based 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 HðP;0;BHÞ,LðP;0;BLÞ, and
NðN;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;NgfH;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 ¼1;
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 q
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 q0;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;gÞ1vgðBðh1ÞÞ  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;gÞ1vbðBðh0Þ;RÞvbð0;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;gÞv
bðBðh1Þ;RÞvbðBðh1Þ;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;gÞ1vbðBðh0Þ;RÞvbð0;0Þ
dv
bð0;0Þ
pbðh1;h0;gÞmax 1 vgðBðh1ÞÞvgð0Þ
dvgð0Þ;v
bðBðh1Þ;RÞvbðBðh1Þ;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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Yardstick competition 169
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