DO VOTERS LEARN FROM DYNAMIC TAX COMPETITION?
Ilaria Petrarca1
06 May 2011
PRELIMINARY DRAFT
Please do not quote
1. Introduction
The political economics literature stresses the advantages from yardstick competition as
a mechanism to constrain the incumbents’ rent during the electoral year (Besley and
Case, 1995; Bordignon et al., 2003). This paper analyzes strategic interaction among local
governments from a different perspective and investigates how persistent is the
reduction of selection powers that yardstick competition it is supposed to solve.
When yardstick competition is at work, in fact, voters learn the true type of the
incumbent running for re-election only if a separating equilibrium in tax rates is
observed. Although yardstick competition reduces the asymmetric information problem
of the voters, the empirical literature on yardstick competition suggests a pattern of
mimicking both in US (Besley and Case, 1995) and in many European countries (Solè
Ollè in Spain, Bordignon et al. in Italy, Revelli in England, and so on). When mimicking
occurs a pooling equilibrium is observed and voters receive a signal of high competence
regardless the true competence level of the incumbent. This illusion is generated by the
strategic behavior of the less competent incumbent who mimics the fiscal decision of the
more competent incumbent in the neighborhood when re-election concerns are binding,
by setting a tax rate lower than his rent maximizing level. Before elections voters update
their electoral preferences with a misleading information, the incumbent’s competence is
overestimated and his probability of being re-elected is distorted upwards. As a
consequence, tax mimicking arising from yardstick competition advantages the bad
incumbent to the detriment of voters’ selection powers. The re-elected less competent
incumbent, moreover, will set higher tax rates than a good incumbent during the next
term of office to finance his rent seeking activity and the rent reduction experienced
during the electoral year is offset by the decrease of voters’ future utility.
Since the existing models of yardstick competition are static, the present work
investigates if yardstick competition, once repeated in time, removes the possibility that
a pooling equilibrium arises. The key assumption of the model is that the informational
capital does not perish every time the game is repeated, but it accumulates up to the
point that voters are able to infer if the incumbent is mimicking or not.
The learning process of the voters is generated by the information on the tax rate set in
both the domestic and in the neighboring jurisdictions as in the static yardstick
competition model, but the longitudinal dimension of the information available in the
1
PhD Candidate at IMT Alti Studi Lucca. E-mail: i.petrarca@imtlucca.it
2
dynamic setting makes it possible that voters learn the strategy of the past incumbent
and infer the probability that the current incumbent is mimicking. The amount of
learning is determined by three factors: an exogenous possibility to learn, the probability
that voters gather enough information to learn and the weight attached to past
experience. The dynamic model proves that when the learning process is maximized
voters’ beliefs are correctly updated, selection powers are restored and mimicking
incumbents would not be re-elected.
The consequences of the dynamic learning on selection powers are thus crucial for the
electoral accountability mechanism to work properly. The improvement with respect to
the static learning by tax rates is huge, and to make a strong point the graphical solution
of the model by Besley and Case (1995) has been replicated in Graph 1. The cost shock
level is measured on the horizontal axis while the tax rate level is measured on the
vertical axis.
The authors predict that when the cost shock assumes values too low or too high, a
separating equilibrium arises because the bad incumbent can either signal good
competence while maximizing his ego rent (low cost), or he finds it too costly to seek for
votes and he sets the highest tax rate no matter the electoral consequences (high cost).
The tax function in this situation is a positive sloping line depending on the cost shock
level and the amount of rent diverted R. When the cost shock takes intermediate values,
the bad incumbent faces a trade off between vote seeking and rent seeking. The
horizontal dotted segment of the tax function represents the mimicking tax level set to
signal good competence to voters.
When an incremental learning process occurs, on the contrary, successful mimicking
becomes much more difficult to implement because voters learn about the cost function
and they infer the incumbents’ strategy. The bad incumbent running for re-election
would not find it optimal to behave strategically because he would renounce to a share
of rent without increasing the probability of re-election. As a consequence a separating
equilibrium will be observed also for intermediate values of the cost shock. In the Graph
below, this result is represented by the bold continuous segment of the tax function. The
same segment indicates the interval of values for which selection powers are enhanced
and yardstick competition is effective in improving accountability at the local level.
Graph 1. Dynamic learning and bad incumbent’s tax rate decision
3
The topic of this work is the main contribution to the literature because the effect of
yardstick competition on voter’s selection powers is a topic that has not been addressed
yet by the scholars. Previous works focused on testing tax mimicking (for a survey see
Allers and Elhorts, 2004) or attempted at shaping the incumbents’ incentives to mimic
(Bordignon et al., 2003; Solè Ollè, 2008; Shaltegger and Kuttel, 2002). Beside this aspect
this paper introduces several innovations with respect to the baseline theoretical
framework. First, the model of yardstick competition is here developed by the voter’s
point of view and the utility maximization problem of the citizens is solved with respect
to the electoral decision (re-elect the incumbent or not). This choice is motivated by the
research question, which focuses on the behavior of the voters. Second, the model is
applied to a dynamic setting, expanding the two-period time horizon of the existing
models of yardstick competition. The dynamic setting assumes that information does
not perish every time period but it incrementally accumulates in time, modeling the
evolution of voters’ behavior depending on the extent to which the learning process
occurs. The existing literature, on the contrary, has so far assumed the mere replication
of the game every two periods. Finally, this paper offers an empirical test of the
predictions of the dynamic model. Dynamic Bayesian updating of the beliefs and probit
estimation have been applied on a dataset of Italian Municipalities in which static
yardstick competition has been previously verified.
The rest of the paper is organized as follows. Section Two reviews the contributions in
the literature that refer to yardstick competition and learning. Section Three describes
the timing, the object and the exogenous conditions for learning to occur. The dynamic
model of yardstick competition is presented in Section Four, providing formal results of
the effect of the dynamic learning process on selection powers. Section Five describes the
dataset on Italian Municipalities and shows the results of the empirical analyses. Finally,
Section Six concludes.
2. Related literature
Learning from tax rates has been mainly studied by the local public finance literature.
The baseline model of yardstick competition developed by Besley and Case (1995) shares
the common view in economics that decentralized jurisdiction are ‘local laboratories’ in
which policies are experimented and the observed outcomes determine the citizens’
judgment of the policy makers (Salmon, 1987). Yardstick competition is a mechanism of
informational spillover exploited by voters to overcome the agency problem between
citizens and politicians regarding the cost of public provision. Since the cost is correlated
among neighbors, the relative performance of the incumbent in the region reveals
information about the size of his rent seeking activity. The baseline model of yardstick
competition predicts a pooling equilibrium in tax rates when a bad incumbent observes
lower tax rates in nearby jurisdictions. In such a situation he mimics the neighbors by
setting their same tax rate, renouncing to a share of his ego rent to seek for re-election.
The learning by tax game is comparable with the learning by prices models developed
by the industrial organization scholars. Benabou and Gertner (1992) studied strategic
4
competition in a market with two sellers of different types selling a homogeneous good
to a customer, assuming the price as a performance indicator revealing the true type of
the seller. The authors obtained the same theoretical results as Besley and Case (1993) as
the bad seller mimics the good seller by reducing the markup.
The model´s assumption, however, are quite stringent. The prerequisite for static
learning from yardstick competition to work is that voters gather and exploit
information on the fiscal performance only during the current electoral year. Bordignon
et al. (2003) derive the conditions for a successful mimicking of the bad incumbent in the
static setting, taking as given that voters gather information about domestic and
neighbor´s tax rates. This assumption is not trivial and should not be underestimated
since voters’ incentives to be informed are small. The change of regime, in fact, is a pure
public good and the probability of being pivotal is reasonably close to zero, generating
free riding concerns that discourage voters from acquiring information (Schnellenbach,
2005). In the dynamic setting this assumption becomes crucial because if the flow of
information is stopped, learning does not occur. Bar-Isaac (2003) investigated the
dynamic learning from prices and he proved that when learning occurs in time only the
good seller survives in the market. By similarity, in time in the yardstick competition
setting only good incumbents find it optimal to choose to run for re-election. The
analytical policy literature reached a similar result by studying the diffusion of policy
decisions. If several policy makers face a decision and they are exposed to the same
stock of information, their beliefs on the performance of the policy converge and they
will select the best performing policy among the feasible set of alternatives. The
contribution of this strand of literature to this paper, beside the focus on policy decisions
that are easily comparable with the voting decision, is the introduction of empirical
methodologies to test for the presence of a learning process. The most recent
contribution comes from the work of Meseguer (2009), who developed a model in which
a government must decide between two alternative policies. In this model the
government learns in light of experience and then makes rational choices. Beliefs are
updated with the information about own and neighboring past experiences according to
the Bayes’ rule. Since every agent in the model is exposed to the same information, the
performance of each policy decision is common knowledge and the learning process is
spurred. The author tests the model to a sample of south-American countries during the
90s, finding that the implementation of institutional and economic reforms has been
driven by a learning process consistent with the theory.
The main critique to Bayesian estimation claims that learning is conditional on prior
beliefs and new information is taken into account differently from different policy
makers, leading to different paths of learning among the agents. As an example, Gilardi
(2010) suggest that agents learn from agents sharing their same ideological preferences.
Recent papers found support for the political trends hypotheses in yardstick
competition, showing that incumbents mimic neighboring jurisdictions ruled by the
same political party (Santolini, 2009; Delgado et al., 2011). Although this critique is
appealing, it does not apply to voters’ behavior. First, at the sub-national level ideology
may not play an important role as in the national elections because preferences may be
5
strictly determined by the local policy platform (e.g. building a bridge, opening new
nursery schools, improving the public transportation and so on). Moreover, the smaller
the tier of government analyzed the more relevant is the phenomenon of the local lists,
which are not formally linked to any political party and are characterized by a platform
focusing on territorial issues and not on ideology. Finally, although voters have a
preference towards higher public expenditure, if they find it out that the incumbent is
mimicking and the share of additional expenditure is wasted in rents, the incumbents’
reputation worsens and voters do not trust him anymore. Hence, he would hardly be re-
elected.
3. The incremental learning process: a step-by-step description
This Section introduces dynamic learning from tax rates by expanding the model of
yardstick competition developed by Bordignon et al. (2003). First, the environment is
described then the timing and the object of the learning process is described. Finally, the
results are proved to be robust also when the assumptions of a term limited incumbent
and constant cost shocks are relaxed. This preliminary argumentation explains what is
meant for learning – the object, the timing and the necessary conditions. In particular,
the requirements for learning discussed in the final part of this Section will be used in
Section 4.2 to define the feasibility of a learning process to occur.
3.1 The environment
Consider a world made of two jurisdictions. Jurisdiction i is assumed to be a neighbor of
–i and vice versa. When the number of jurisdictions increases, the set of i’s neighbors
does not necessarily include all of them. The game lasts for two periods, (t=1, 2). Each
period is an electoral term consisting of N years. The last year of each period an election
is held between the incumbent and a challenger.
The utility of the voters in each jurisdiction during the period t depends on the
consumption of both private (C) and public goods (g):
v
it it itu C g= + [1]
where private consumption is the amount of income (y) net of taxes (T):
it it itC y T= − [2]
The tax rate proxies the cost of the public provision of goods and services, T:
it t it iT p θ ε= + − [3]
where i refers to the jurisdiction and t refers to time. Tit is determined by the observed
national price of the public provision (pt), and by two factors that are observed by the
incumbent but not by the voters: a random cost shock (θit) and the competence level of
the incumbent (εi). The competence of the incumbent is an individual specific
characteristic, constant in time, representing a measure of efficiency in providing public
goods. The mayor of each jurisdiction may be competent (good type) or not (bad type)
where competence is inversely related with the undertaken rent-seeking activity:
6
' '
' '
H
i
L
if good
if bad
ε
ε
ε

= 
 [4]
such that εH >εL > 0 and Prob (εi =εH)= ϕ.
The utility level of the voters can be summarized as:
it
V
it it t it iu g y p θ ε= + − − + [5]
From equation 5 the link between the electoral decision of the voters and the voters’
utility is clear.
Voters are rational agents who choose between re-electing or not the incumbent in
period 1 with the purpose to maximize their expected utility (equation 5). The static
setting assumes that information is costly and voters gather information about the
performance of the incumbent only the year nearest to elections. Furthermore,
information fully depreciates every period and voters must begin the process from
scratch. The performance indicator considered is the domestic local tax rate, which is
benchmarked with the neighbors’ tax rate. However, sometimes it is impossible to
distinguish a good incumbent from a bad incumbent during the electoral period. To
explain why, let us describe the process of tax setting.
When choosing the level of the domestic tax rate, the good incumbent only takes into
account the cost shock realization in the first period. When a negative shock occurs
(θit>0), an additional amount of resources (Δ>0) is needed to finance the public
provision. The good incumbent thus sets Tit = T+Δ when the shock is negative and Tit = T
otherwise.
The bad incumbent, on the contrary, sets the tax rate to finance both the public provision
of goods and services and his private rent seeking activity. As a consequence, he will
always – ceteris paribus - set a higher tax rate than the good incumbent. Let us define the
bad incumbents’ tax rate as Tit = T+kΔ, where k is the share of additional resources
diverted to rents. When the shock is negative 1≤k≤R, assuming some finite upper bound
to the rent extraction, R2 which is determined by technology constraints or the fact that
the size of the rent is so high that the incumbent is unmasked.
The timing of the game is set as follows:
1. At the beginning of period 1 Nature selects a competence level of the
incumbent and a cost shock;
2. The incumbent in i observes his competence level, his cost shock realization,
then he sets T1i;
3. Voters in i observe (T1i) and (T1-i) and update their beliefs on the relative
competence level of the incumbent in the neighborhood;
4. At the end of period 1 an election is held between the incumbent and a
challenger with a majoritarian electoral rule;
5. At the beginning of period 2 Nature selects a cost shock and the game restarts;
if the challenger has been elected his competence level is randomly selected by Nature.
2
Assuming a Laffer curve for the rent extraction of the type L=kΔ+ kΔ2
, the value R that maximizes L is
R=1/2Δ. For k>R as the share of the revenue diverted to rents increases the effective rent received by the
incumbent decreases.
7
Now suppose that in period 1 a bad incumbent runs for re-election and observes a
domestic positive cost shock. In the same period in the neighboring jurisdiction a good
mayor is experiencing a negative shock. The good incumbent sets T+Δ, while the bad
incumbent can choose between setting T+kΔ, his rent maximizing tax rate, or the pooling
tax rate T+Δ. In the last case the bad incumbent renounces to the rent, voters observe a
signal of high competence, mistake him for a good mayor and he gains re-election. The
yardstick competition literature claims that, as long as some conditions are met3, a
pooling equilibrium arises during the electoral year. The tax rates set during the
electoral year are the same in the two jurisdictions: Ti1 = T-i 1 = T+Δ. In such a situation
voters observe a signal of good competence, also when the incumbent is in fact bad.
Table 1 summarizes the tax decisions in period 1 conditional on the type of incumbent
and the cost shock realization. The cell marked with an asterisk indicates the yardstick
competition outcome.
Table 1. The incumbent’s tax rate strategies in period 1
Bad i; Good -i Bad i; Bad i Good i; Good -i
Ni; N-i T+kΔ, T+Δ T+kΔ, T+kΔ T+Δ, T+Δ
Ni; P-i T+kΔ, T T+kΔ, T+Δ T+Δ, T
Pi; P-i T+Δ, T T+Δ, T+Δ T, T
Pi; N-i T+Δ, T+Δ * T+Δ, T+kΔ T, T+Δ
N=negative cost shock, P=positive cost shock; i refers to the domestic jurisdiction, -i to the neighbor(s). The asterisk
indicates the yardstick competition outcome.
During the second period of the model no election is held and the assumption of a limit
of at most two terms in office removes any reputational concerns of the local incumbent.
This is a classical assumption in the literature and it is kept here for simplicity.
In the second period the bad incumbent sets his rent-maximizing tax rate because he
cannot run for re-election anymore and he is not incentivized to care about his electoral
popularity. Consequently, in period 2 the bad incumbent does not find it optimal to
renounce to a share of his ego rent and he would always set Ti2 =T+kΔ. The tax rate
decisions in period 2 are shown in Table 2.
Table 2. The incumbent’s tax rate strategies in the period 2
Bad i; Good j Bad i; Bad j Good i; Good j
Ni; Nj T+kΔ, T+Δ T+kΔ, T+kΔ T+Δ, T+Δ
Ni; Pj T+kΔ, T T+kΔ, T+kΔ T+Δ, T
Pi; Pj T+kΔ, T T+kΔ, T+kΔ T, T
Pi; Nj T+kΔ, T+Δ T+kΔ, T+kΔ T, T+Δ
N=negative cost shock, P=positive cost shock; i refers to the domestic jurisdiction, -i to the neighbor(s).
3
See Bordignon et al. (2003) for a detailed description.
8
3.2 The object and the timing of learning
This Section extends the timing of the existing two-period yardstick competition models,
by describing the process through which voters learn the electoral strategy of the
incumbent.
Let us consider the third electoral year of the game. A pooling equilibrium arises again,
and assuming that the conditions for a successful mimicking hold, the bad incumbent in
jurisdiction i sets Ti3 =Ti1 =T+Δ. However, the information on the tax rates set in both i
and -i during both the first and the second period are now available to the voters. This
information triggers the incremental learning process.
As a first step, by comparing the tax rates set in the second period with the tax rate set in
the first period voters learn about their incumbent’s true type and the neighbor’s true
type.
Tax rates in the second period are not strategic4, therefore the bad incumbent will set
Ti2=T+kΔ regardless of the cost shock realization while the good incumbent will set
Ti2=T+Δ if the shock is negative and Ti2=T if the shock is positive.
The additional amount of resources needed to face a negative cost shock is assumed to
be the same in all the periods and for both the incumbents: Δt =Δ. This assumption may
seem unreasonable because the technological shock may change its magnitude every
period and in every jurisdiction. However, even fixing the magnitude of the shock to a
constant parameter, the sign of the shock still plays the leading role in determining the
strategy of the incumbent. To stress this point at this stage of the discussion |Δt| is
assumed to be a constant.
If voters in i observe Ti2>Ti1 during the second period, they know for sure that the
incumbent is bad and that he mimicked in the first period. Otherwise, if they observe a
tax rate not higher than the tax rate set in the first period (Ti2≤ Ti1) they infer that the
incumbent’s true type is good.
By observing the tax rates set in the second period voters gather information also about
the cost shock realization in the jurisdiction where the incumbent is good. A good
incumbent who sets T1 = T+Δ in the first period would set the same tax rate T1 =T2 = T+Δ
in the second period when facing again a negative cost shock. On the contrary, he would
set T2 < T1 = T when facing a positive cost shock. To sum up:
2 1
2
2 1
| H
T T TN if
T T TP if
θ ε
= = + ∆
= 
< = [6]
The incumbent and his neighbor’s true type are valuable information about the first
period’s tax setting equation, although they are not directly useful in updating beliefs in
the third period because the incumbents have changed.
The cost shock is assumed to be spatially correlated among neighbors, reflecting the
socio-economic interdependence of the jurisdictions. As an example, the cost of streets
maintenance work depends on weather conditions which are similar among neighbors,
but they are unknown to laymen because the extent of the damage is difficult to gauge
4
This assumption is relaxed in Section 3.2.1.
9
without expertise. Moreover, while the local government controls the whole territory of
the jurisdiction, voters have reasonably not information on every street condition.
The degree of correlation among jurisdictions is the same in both periods (σi2=σ-i2)
because the technological interdependence between neighboring economies is based on
the geographical nearness, common natural resources, possible joint public provision
and other factors which are unlikely to unexpectedly change in the short period.
The cost shock is specified as:
it it itθ σ −=∆ + ∆ [7]
where Δit is the increase in the tax rate due to a cost shock specific to i (Δit = 0 if a positive
shock occurs), σΔ-it is the portion of cost shock specific to -i which is reflected in i
according to the correlation parameter 0<σ<1, and Δit and Δ-it are assumed to be the
same in both the jurisdiction.
Given this setting, during the first period voters ignore both θi1 and εi. In the second
period the true type of the incumbent εi is revealed and the information on θi1 and θ-i1 is
easily inferred according to:
1 1 1i i ip Tθ ε= − − [8]
and
1 1 1i i ip Tθ ε− − −= − − [9]
The information on θi1 is not directly useful in updating beliefs in the third period, but it
may be used to infer the value of Δ and the correlation coefficient σ.
The correlation of the cost shock is:
,1
,0
i H
i L
if
if
ε ε
σ
ε ε
=
= 
=
[10]
Equation 10 exploits the fact that during the first period the good incumbent in the
neighborhood experiences a negative cost shock (Δ1 =Δ) and pooling equilibrium is
feasible. If the incumbent in the domestic jurisdiction is the good type, the cost shock
increases the unit cost of public provision of goods and services according to reflection
of the cost shock from the neighbors (σ∆ ), while if the incumbent is the bad type and
faces a positive cost shock, no additional resources need to be spent.
When the parameter Δ is known, the information on σ is easily inferred and the learning
process is complete. The exogenous conditions for the disclosure of the information
about Δ are stated in Proposition 1.
Proposition 1. Dynamic learning by tax rates is feasible if the value of the parameter Δ is
known or inferred by voters. Voters infer the value of Δ when both the following
requirements are met:
• One of the incumbents is good;
• The good incumbent experienced a negative shock in the first period and a
positive shock in the second period.
The presence of at least a good incumbent is a condition for having a non strategic
benchmark behavior to refer to. The good incumbent’s tax rate depends on the cost
10
shocks realization. Sequential shocks of opposite magnitude in the two periods are a
necessary requirement to compute the differential (T+Δ)-(T) = Δ. Moreover, since a
pooling equilibrium has been observed during the first period, the negative shock must
occur before the positive shock.
As shown in Table 3, assuming a pooling equilibrium (implying a negative shock) has
been observed in the first period, the required conditions to learn Δ hold only when the
incumbent in the second period is good and experiences a positive cost shock. As the
Table indicates, Proposition 1 holds in five cases over twelve.
Table 3. The tax rates in period 2 and Proposition 1.
Bad-Good Bad-Bad Good-Good
NN Does not hold Does not hold Does not hold
NP Holds Does not hold Holds
PP Holds Does not hold Holds
PN Does not hold Does not hold Holds
N=negative cost shock, P=positive cost shock; the first letter (or word) refers to i, the second to -i
The tax setting equation in the third period is:
3 3 3 3i i i iT p σ ε−= + ∆ + ∆ − [11]
When Proposition 1 holds, voters observe the tax rate Ti3, the national price of the public
provision p3, the additional resources needed to face a negative shock Δ3 and the spatial
correlation parameter σ.
Voters can now infer the competence level εi from Equation 11. In such a situation the
bad incumbent would not find it optimal to mimic the good incumbent behavior
because the strategic behavior would not increase his probability of being re-elected and
a separating equilibrium would arise. Eventually, the bad incumbent would not run for
re-election and renounce to the second term rent. On the contrary, if the bad incumbent
is not aware of the voters’ learning process he would mimic the good neighbor, but this
time he will be unmasked and turned down. In both cases, the electoral competition
would select only competent politicians and entail an improvement in the quality of the
political class.
3.2.1 Bad incumbent with career concerns
This paragraph relaxes the assumption of a non strategic behavior of the incumbent
during the electoral period when there is a binding term limit. The motivation for this
excurse is the consideration that incentive to mimic the good neighbor may arise even if
the incumbent cannot run for re-election. This situation for example occurs whenever
the incumbent aspires to continue his public career and be elected or appointed to other
offices, or because he is subject to party control and a signal of bad competence would
disadvantage the party at the next election.
The findings suggest that conditions stated in Proposition 1 are robust to the
introduction of career concerns of the bad incumbent.
11
The utility function of the incumbent is determined by the exogenous office rent from
being in office (mt), the extra rent diverted from public resources for rent seeking
purposes (0≤rit≤R), and the discounted value of the future rent (ωt+1):
1
inc
it t it itu m r βω += + + [12]
Career concerns are relevant when the bad incumbent prefers to give up to the rent to
increase his possibility to be appointed to another office after the second period. The
discounted value of the future rent ( 1itβω + ) is larger than the maximum rent he can
expropriate in the second period:
1( 1) itk βω ++ ∆ < [13]
When a pooling equilibrium is observed again during the third period, under the
assumption of a constant cost shock the strategic tax rate T+Δ equals the tax rate set in
period 1. If the pooling equilibrium is driven by mimicking, one of the incumbents is
surely bad (the one who mimics) and another is good (the mimicked), and the good
incumbent’s decision is not affected by the bad incumbents’ reputational concerns.
Hence, the parameter Δ can be inferred when the tax differential T+Δ-T=Δ can be
computed, that is when the conditions in Proposition 1 hold. As a conclusion, the results
of the previous paragraph are robust to the introduction of career concerns of the bad
incumbent.
3.2.2 Non-constant cost shocks
So far Δ has been taken as a time constant parameter. This Section relaxes this
assumption allowing Δ to change every period.
Let us consider the two cases in which Δ2= Δ’ where Δ’> Δ or Δ2= Δ’’ where Δ’’< Δ.
If Δ2 = Δ’, during the second period voters cannot distinguish if the incumbent sets the
highest tax rate T+kΔ’ or the pooling tax rate T+Δ’ because both the levels are higher
than the pooling tax rate T+Δ observed in the first period. Voters, in fact, extract a signal
revealing a bad incumbent in the jurisdiction where the tax rate is the highest and a
good incumbent in the jurisdiction where the tax rate is the lowest. Suppose that the
good neighbor experienced a negative cost shock also during the second period. In this
situation voters in i observe the domestic tax rate T+Δ’ > T+Δ and erroneously guess that
the incumbent is a bad type. Moreover, voters cannot learn about the public cost
function because they infer the cost shock is 1 1iθ σ= ∆ , they compute (T+Δ’) - (T+Δ) = Δ’Δ
but they cannot learn σ using equation 10.
On the contrary, when the tax rate decreases in the second period (T1=T+Δ, T2=T) voters
gather information about Δ, they learn the correlation coefficient σ and they infer the
competence level of the past incumbent. However, they don’t know the level of Δ’ and
they cannot learn the true type of the current incumbent. If voters assume Δ= Δ’, they
end up underestimating the competence level of the incumbent.
As shown in Table 4, Proposition 1 holds in the same cases as for a constant Δ, signaled
by a an asterisk.
12
Table 4. Tax rates in period 2 and the respect of Proposition 1 when Δ2= Δ’> Δ.
Bad-Good Bad-Bad Good-Good
NN T+kΔ’, T+Δ’ T+kΔ’, T+kΔ’ T+Δ’, T+Δ’
NP T+kΔ’, T * T+kΔ’, T+kΔ’ T+Δ’, T *
PP T+kΔ’, T * T+kΔ’, T+kΔ’ T, T *
PN T+kΔ’, T+Δ’ T+kΔ’, T+kΔ’ T, T+Δ’ *
N=negative cost shock, P=positive cost shock; the first letter (or word) refers to i, the second to -i
Now let us turn to the second case, that is Δ2= Δ’’ where Δ’’< Δ. Since k>1 two situations
may arise:
1. If kΔ’’≤Δ and the rent maximizing tax rate of the bad incumbent T+kΔ’’≤T+Δ,
voters always observe a lower or the same tax rates as the first period and they
cannot learn σ;
2. If kΔ’’>Δ and the rent maximizing tax rate of the bad incumbent T+kΔ’’>T+Δ,
although voters cannot distinguish T from T+Δ’’ they understand when the
incumbent is bad because he sets the highest tax rate. However, learning σ is
feasible only when a pooling equilibrium was observed in the first period and
the good neighbor incumbent experienced a positive shock in the second period,
as in the three cases marked with an asterisk in Table 5.
As in the previous case, however, the learning process is limited to the true type of the
past incumbent.
Table 5. Tax rates in period 2 and the respect of Proposition 3 when Δ2= Δ’’< Δ.
Bad-Good Bad-Bad Good-Good
NN T+kΔ’’, T+Δ’’ T+kΔ’’, T+kΔ’’ T+Δ’’, T+Δ’’
NP T+kΔ’’, T * T+kΔ’’, T+kΔ’’ T+Δ’’, T *
PP T+kΔ’’, T * T+kΔ’’, T+kΔ’’ T, T
PN T+kΔ’’, T+Δ’’ T+kΔ’’, T+kΔ’’ T, T+Δ’’
N=negative cost shock, P=positive cost shock; the first letter (or word) refers to i, the second to -i
4. Learning from tax rates: the voters’ point of view
This Section models the citizens’ voting behavior as a rational response to the observed
signal of competence. First, the static model is described, then the assumption on the
information depreciation is relaxed and the learning process is formalized. Finally, the
solution to the utility maximization is derived for both the static and the dynamic
games.
4.1 The static model
The voters’ problem is:
( )1 1 1 2 1 1 2( ) max ( ) ( ); ( ) ( )V VI V VC
i i i i i i i i
j
V u T V u T Vε β β= + + [14]
where j is the electoral rule implemented by voters. Since the voter’s maximization is the
same in each jurisdiction, in what follows the index i is suppressed.
The solution of Equation 14 depends on the level of competence of the incumbent. The
right hand side of the equation lists the present value of the two-year electoral term
13
utility when the incumbent is re-elected ( 1 1 2( ) ( )V VI
u T Vβ+ ) and when he is defeated at
election and a challenger takes his place( 1 1 2( ) ( )V VC
u T Vβ+ ). Since the pooling tax rate is
observed, the utility during the first period is the same.
On the contrary, the utility level during the second period differs depending on the
decision of the voters. Re-electing a good incumbent increases the voters’ utility because
the tax rate set by a good incumbent is by definition lower than the tax rate set by a bad
incumbent ( H L
T Tε ε< ). Utility from defeating the bad incumbent will be higher than
utility from re-electing him:
2 2( ) ( )H L
VI VI
V T V Tε ε> [15]
The value of the tax rate set by the good incumbent 1, |i i HT ε ε= is approximated by the
tax rate set by the neighbors, 1, iT − ~ 1, |i i HT ε ε− = , because it is the assumed benchmark
for the voters. The information exploited refers to the tax rates set only in period 1.
However, voters’ expectations about the expected tax rate set during the second period
( 2( )E T ) are computed as:
2 1 1( ) ( ) (1 )( )H L
E T T Tε εµ µ= + − [16]
where H
Tε and L
Tε are the tax rates conditional on the probability that the incumbent is
good or bad and 1µ is the updated belief on the competence level before voting. Voters’
beliefs are updated with the information on the tax rate set in both the domestic
jurisdiction i and the neighbors -i according to the Bayes’ rule.
The belief 1µ depends on the relative performance of 1,iT with respect to 1, iT − and on the
ex-ante beliefs that the incumbent is good type ϕ. The parameter ϕ behaves as a random
variable, ϕ ~ (1/ 2,1)N and it is bounded between zero and one.
1 1 , 1 1 ,
1 1 1
1 1 , 1 1 , 1 1 ,
Pr( , ) | Pr( , ) |
( , , )
Pr( , ) | Pr( , ) | Pr( , ) |
i i i i H i i i L i H
i i
i i i i H i i i L i H i i i i L
T T T T
T T
T T T T T T
ε ε
µ ϕ
ε ε ε
− − = − = − =
−
− −= −= −= − −=
+
=
+ +
[17]
Equation 17 expresses the conditional probability of a good incumbent in i in terms of
the prior probability of a good incumbent in both the jurisdictions ( 1 1 ,Pr( , ) |i i i i HT T ε− − = ),
the prior probability of a bad incumbent in both the jurisdictions ( 1 1 ,Pr( , ) |i i i i LT T ε− − = ),
and the conditional probability of a bad incumbent in i given a good incumbent in -i
( 1 1 ,Pr( , ) |i i i L i HT T ε− = − = ).
Voters judge the incumbent as competent if the utility level he provides them is at least
as large as the utility provided by the incumbents in the neighborhood, , ,i t i t
V V
u u−
≥
. Simple
calculations show that the necessary condition for this inequality to hold is a null tax
distance it itT T−− :
it it it it it ity T G y T G− − −− + ≥ − + [18]
Keeping the assumptions y=1 and G homogenous among jurisdictions as in the baseline
models:
14
1 1it itT T−− ≥ − [19]
Rearranging:
0it itT T−− ≤ [20]
When the tax distance is non positive and the pooling equilibrium is observed, the
incumbent is considered as a good type and his probability of re-election increases.
In the static setting each electoral year the game repeats itself and the expected tax rate
during the following term is obtained through Equation 16. That is, anytime a pooling
equilibrium is observed the incumbent is considered as a good type. In such a situation
the incentive for a bad incumbent to mimic increases.
The voting rule states that an incumbent is re-elected if his performance is no worse than
the performance of a challenger whose ex ante probability of being good is measured by
the parameter ϕ:
1 1
1
1 1
( ) (1 )( ) ( ) (1 )( )0
1 ( ) (1 )( ) ( ) (1 )( )
H L H
H L H
L
L
T T T Tif
j
if T T T T
ε ε ε ε
ε ε ε ε
µ µ ϕ ϕ
µ µ ϕ ϕ
+ − > + −
= 
+ − ≤ + −
[21]
which reduces to:
1
1
1
( _ )0
( )1
non re electif
j
re electif
µ ϕ
µ ϕ
< −
= 
≥ −
[22]
Equation 22 claims that voters re-elect the candidate incumbent when the updated belief
about his competence is at least as large as the ex-ante probability that the mayor is good
type. When the updated belief on the expected tax rate during the second period is
higher than the non-updated expected tax rate, the incumbent is considered bad type
and he is not re-elected5.
4.2 The dynamic model
In the dynamics setting, when voters face an incumbent who runs for re-election and
sets a pooling tax rate, they update their beliefs considering not only the actual tax rate
but also the information on the past performances in both jurisdictions governed by reelected
pooling incumbents and jurisdictions governed by challengers who defeated
local incumbents.
If the two-period model is repeated the timing of the baseline model extends to the
following stages:
6. During period 2 the incumbent in i is term limited and he sets his rentmaximizing
tax rate (Ti2); an election is held between two challengers with a majoritarian
electoral rule;
7. At the beginning of period 3 Nature selects a competence level of the new
incumbent and a cost shock;
8. The incumbent in i observes his competence level and his cost shock
realization and sets a tax rate (Ti3);
5
The formal conditions for the inequality μ1≥ϕ to hold are derived by Bordignon et al. (2003). Since the
solution of the static model is not the main goal of this work, this Section does not go through the details of
the two periods signaling game.
15
9. Voters in i observe the tax rates (Ti3) and (T-i3), the realized tax rates (Ti2) and (Ti2)
conditional on the past electoral decisions, then they update their beliefs on the
relative competence level of the incumbent in the neighborhood;
10. At the end of period 3 an election is held between the incumbent and a
challenger with a majoritarian electoral rule;
11. At the beginning of period 4 Nature selects a cost shock and the game
restarts; if the challenger has been elected his competence level is randomly selected by
Nature.
The crucial factor determining the outcome of the election is now the probability that a
learning process takes place during the third period. Learning is represented by a
function L assumed to be bounded between zero and a maximum value L , and it
depends on three factors: the feasibility of learning (1-q2), the probability of gathering
enough information (π) and the weight attached to past experience (ρ). These three
factors are independent from each other, e.g. a variation in the propensity to learn does
not affect the realization of the cost shock or the weight attached to new information.
Hence, L can be expressed as a product function:
2
3 2( )(1 )L qπ αρ βρ= − − [23]
The feasibility of learning refers to the conditions stated in Proposition 1: if they do not
hold, any information is useful in learning the incumbent’s strategy6. Since the model
assumes that a pooling equilibrium is observed during the first period, the respect of
Proposition 1 relies on the realization of a positive shock in the jurisdiction governed by
the good incumbent during the second period. Defining 0 ≤ q2 ≤1 as the probability of the
realization of a negative cost shock during the second period in the jurisdiction
governed by the good incumbent, learning is a decreasing function of q2. The feasibility
of learning is a factor exogenous to the model because voters’ decisions do not affect it.
However, as pointed out, it is a necessary condition for the process to work.
The probability that voters gather enough information to learn π is indeed an
endogenous factor shaping L. The probability π depends on the propensity to learn.
Learning requires a stock of information P* including the tax rates set in the
neighborhood during the second and the third period. Voters are rational agents and
they acquire new information when costs are no larger than benefits. The costs of
obtaining information are represented by the marginal cost of obtaining both the
domestic and the neighbors’ tax rate information. The marginal cost of obtaining the
information about the domestic tax rate is assumed to be small and constant, since a tax
rate is information that the government must periodically release to claim its payment.
The marginal cost of obtaining the neighbors’ tax rate, on the contrary, is supposed to
change depending on the size of the neighborhood. When the number of neighbors is
large many pieces of information must be gathered and the total cost of being informed
6
Assuming a constant cost shock learning leads to perfect selection. Relaxing this assumption allows
learning the true type of only the past incumbent, which is still a relevant information because it unmasks a
possible past mimicking behavior. If the current voting decision depends on past experience, it is a type of
learning as well.
16
about the neighbors’ performance increases. However, the information spillover
generated by the inter-jurisdictional comparison of citizens may generate social
networks giving rise to economies of scale in the diffusion of the information. The
marginal cost of the information decreases as the number of neighbors increase. Being
the size of the neighborhood constant in time, it affects the slope of the marginal cost
function but not its shape. Finally, there is a cost attached to the action of retaining
information, implying the effort of storing information in memory and being able to
recall it when an election is approaching. The marginal information needs a larger
memory capacity, therefore its cost increases with the size of the information stock
retained.
The marginal benefit of being informed, on the contrary, is determined by the difference
between the realized fiscal performance of the past incumbent during his second period
of office, 2T , and the updated belief of the fiscal performance before his re-election,
E( 2T ). To understand the reason for this specification, assume that the realization of the
tax rate set by the past incumbent is higher than its expectation. Voters infer if the
incumbent was strategic (bad) during the first period and they attach a larger marginal
benefit to new information if compared with a situation in which the incumbent was
non strategic (good). In other words, voters find it more convenient to improve their
monitoring powers when they realize that their past beliefs have been mistaken and
they become more prone to obtaining new information. The slope of the marginal
benefit curve is assumed to be negative because voters may come out with a clear idea
about the incumbent after having acquired the first pieces of information. In such a
situation, their marginal utility from the marginal information decreases.
The following Graph depicts information (quantitatively measured) as a function of the
marginal cost and the marginal benefit of gathering information. When the cost is larger
than the benefit, voters do not to search for new information. When the benefit is larger
than the cost voters find it profitable to gather new information up to the critical level P1
pinned down by the intersection of the two curves. The quantity P1 represents the
maximum amount of information that voters would gather given the shape of the cost
and benefit curves. The probability that voters obtain enough information to learn is the
probability that P1 is at least as large as a critical value P*, π = Pr (P1 ≥ P*).
Graph 1. Costs and benefit of gathering information
17
The last factor determining the learning function is the weight attached to the past
experience ρ, computed through a Bayesian updating of voters’ beliefs taking into
account both present and past information. The process to come up with ρ follows
Meseguer (2009) and relies on a larger set of assumption than the static updating
explained in the previous section.
Assume that the tax distance T to be a random variable normally distributed with an
unknown mean M and an unknown variance V. M and V are random variables, and
voters learn about them by observing the performance of other incumbents under
alternative past voting decisions j. The conditional distribution of the mean is Normal
while the conditional distribution of the variance is scaled-Inverse Х2. The decision of
these distributions is a classical assumption in Bayesian updating and allows the mean
and the variance to be interdependent. Thus,
2
2 2
( , )
( , / )
( , )
j j j
j j j j
j j j
T N M V
M N m
V ScaledInv v
σ τ
χ σ
=
=
= −
[24]
Where m is the location of the mean,
2
/j jσ τ
is the variation of the mean, v are the
degrees of freedom and
2
jσ
is the scale of the variance, τ is the factor that relates the
prior variance of the mean to the sampling variance.
During the third period the information available to voters about the performance of the
incumbent is the tax distance under alternative voting decisions for all the jurisdiction
that re-elected (j=1) or did not re-elect (j=0) the incumbent during the first period, 3 |j
T j .
The information is assumed to be a random variable independent and identically
distributed. Hence, the sample mean and the sample sum of squares are sufficient
statistics to summarize the information in the sample of countries under each of the
alternative voting decisions. When prior beliefs are combined with new information, by
applying the Bayes’ rule the posterior belief about the mean and the variance of the tax
distance is7:
3 2 3(1 )xω ρω ρ= + − [25]
2 3
3
3
S
s
v
= [26]
where 0 < ρ < 1, ω2 is the updated belief on the performance of the past incumbent at the
end of the second period and 3x is the current observed performance of the incumbent;
S3 is the posterior for the sum of squares, v is the posterior for the degrees of freedom.
As Equation 25 shows, although extreme values of ρ are ruled out, when the parameter
is close to zero the past experience has a little influence on the updating process and
voters hardly learn the determinants of the public cost function; vice versa, when ρ tends
to one the belief hardly takes into account new information. Learning is here assumed to
7
For a detailed description of how to obtain this result, see Meseguer (2009), Appendix to Chapter 2.
18
be a quadratic function of ρ, and its maximum value is associated to a level ρ*
determined by the shape of the curve8.
Graph 2. Learning as a function of rho
The function L is maximized when the conditions π=1, ρ =ρ* and q2=0 jointly hold. On
the contrary, no learning occurs if π=0 or q2=1, that is if voters do not want or they
cannot learn.
It is noteworthy to stress that the location of ρ* indicates the optimal weight to attach to
past experience. This parameter is fundamental when the electoral rule prescribes a term
limitation, because the past incumbent is a different person than the current incumbent
and the information gathering process may be stopped. Competence is in fact an
individual specific characteristic, and if voters believe that the electoral strategy of the
past incumbent does not affect the electoral strategy of the current incumbent in any
possible way, ρ is close to one. The probability that the current incumbent is strategic,
however, is not independent from the probability that past incumbents have been
strategic. If a bad incumbent knows that his predecessor mimicked and he was reelected
(incumbents know the performance of the past incumbents), it is likely that he
would play the same strategy. As a consequence, voters always gain positive utility
from the marginal information since that is the only way to come out with a distribution
of the type of the past pooling incumbents. The maximum value of the learning function
is such that 1-ρ* equals the probability that a bad incumbent in period 3 behaves as a
bad incumbent in period 1 (equals to one) times the distribution of the type of the
incumbents9. This condition is taken as an assumption here.
During the third period the problem of the voters is:
( )( )3 3 3 4 3 4 3 3 3 4( ) max ( ) * ( ) (1 )* ( ) ; ( ) ( )V VI VI V VC
i L L
j
V u T I V I V u T Vε β ω µ β= + + − + [27]
This maximization is similar to the maximization during the first period, but the
function now depends on the belief updated using Equation 25 (instead of using
Equation 16). Specifically, voters’ expectations about the tax distance set during the
fourth period 4( )E T are:
4 3 2( ) (1 )E T T Tρ ρ= + − [28]
8
Formally, L=αρ-βρ2
. The function is maximixed when α/2β=ρ.
9
This condition suggests an alternative interpretation of ρ as the share of good incumbents in the
population of incumbents during period 3. Of course voters lack this information.
19
Another innovation introduced in Equation 27 with respect to its counterpart in the
static model is the presence of the probability function L in the second term of the intertemporal
utility function. The indicator function IL indicates if the learning function has
been maximizes. When voters optimally learn about the incumbent’s true type in the
dynamic setting, in fact, the updated beliefs on competence do not depend exclusively
on the tax distance observed during the current electoral year (T3). For IL = 0, learning
does nor occur, the static setting is restored and given a pooling equilibrium during
period 3, he will be re-elected as long as the condition for successful pooling hold.
If learning occurs IL = 1, two situations may arise. In the first one the past incumbent
played a pooling equilibrium during the second period, 4( )E T =0 and the current
pooling incumbent will be re-elected in period 3. In other words, perpetual pooling does
not provide voters with any useful new information. Of course, this situation is driven
by a factor q2=1, indicating that a positive shock to the good incumbent occurred during
the second period. Optimal learning IL = 1 implies q2>0, and 4( )E T =0 is ruled out by
definition.
In the second situation the past incumbent did not play a pooling strategy during period
2 and T2 conveys with useful information. Specifically, the past incumbent is recognized
as bad type and his behavior has consequences on his successor. The updated tax
distance 4( )E T becomes positive and voters do re-elect the incumbent in period 3 only
if 4 4* VI VC
LI V V≥ . The equality is included in the condition because we assume that
voters have a strong preference for dismissing an incumbent who cheated them10.
Given that the updating process provided voters with posterior beliefs on both the mean
and the variance of the tax distance set by the incumbent during the fourth period, the
expected utility 4
V
V reasonably takes into account both these information.
4 3 3 1 3 2 3 3( , ) |j j j j
V EU s j sω β ω β ε= = + + [29]
Where ε is an error term included to account for the inaccuracy of the voters in updating
their beliefs and j is the re-election probability. Voters re-elect the incumbent if:
3 3 3 3( , ) | ( 1) ( , ) | ( 0)EU s j EU s jω ω=≥ = [30]
In case of a defeat of the incumbent, a challenger is elected. The right hand side of the
equation can thus be interpreted as the expected utility from electing a challenger.
Substituting Equation 29 in Equation 30 and rearranging terms we obtain:
( ) ( )1 3 3 2 3 3 3 3
I C I C C I
s sβ ω ω β ε ε− + − ≥ − [31]
where I stands for the incumbent and C for the challenger. Denoting the differences with
a d,
1 0
3 3 3
d j j
µ µ µ= =
= − ,
1 0
3 3 3
d j j
s s s= =
= − and
1 0
3 3 3
d j j
ε ε ε= =
= − , we obtain:
1 3 2 3 3( )d d d
sβ µ β ε+ ≥ [32]
The probability that a voter re-elects the pooling incumbent during the third period is:
10
The incumbent in this case has a probability of being good equal to zero, while the probability that a
challenger is good is above zero.
20
( ) ( )
( ) ( )
3 3 3 1 3 2 3
1 3 2 3 1 3 2 3
( 1) ( )
1
I C d d d
d d d d
P j P EU EU P s
F s F s
ε β µ β
β µ β β µ β
== ≥ = ≥ + =
 =− − + = + 
[33]
Equation 33 allows us to summarize the theoretical predictions of the dynamic model.
If the incremental learning by tax rates presented in this paper occurs, β1 and β2 are
significant and negative coefficients. A large mean of the tax distance is associated with
an incumbent extracting rent, while a large volatility of the tax distance is associated
with an ambiguous outcome. Assuming that voters are risk averse and prefer certainty
of policy outcomes rather than uncertainty, also β2 is expected to be negative.
If the learning process does not take place, due to the failure of Proposition1, a stock of
information insufficient for learning, or almost extreme weight attached to past
experience, updated beliefs on the tax distance do not have any influence on the decision
to re-elect the incumbent. As a consequence, the coefficients in Equation 33 will be not
statistically significant.
5. An empirical test of the dynamic learning from tax rates
5.1 Italian Municipalities: institutional setting, accountability system and yardstick competition
Municipalities are the lowest tier of government in Italy, and they are a suitable
framework for this paper’s empirical test. In the early 1990s, in fact, an institutional
reform aimed at strengthening local accountability introducing tax decentralization and
reforming the electoral rule, setting the framework for yardstick competition to arise.
The local property tax rate (ICI, Imposta comunale sugli Immobili), introduced in 1993,
increased the tax autonomy of local governments and in the period 1993-2007 accounted
for more than 55% of total Municipality revenue and more than 25% of local
expenditure11. ICI is a highly autonomous tax rate, specifically a level b in the OECD
tax autonomy scale ranging from ´a´ to ´e´ (OECD, 1999). The previous setting was
characterized by the lowest degree of tax autonomy, level e, being the tax rate and the
tax base both set by the central government. In 1995 the tax rate has been differentiated
between the house tax rate applied to the main living property and the business tax rate
applied to holiday houses, offices, shops, and so on. Local house property taxation
accounts only for 6% of local tax revenues, but it is a cost that voters directly link to the
house and makes it clear to the citizens the relationship between the costs and the
benefits of local public services in a certain jurisdiction. In addition to this, more than
80% of the residents in Italy are home-owner12, making the local house tax rate the main
indicator of jurisdictional performance. Since the tax base is fixed and property value
reassessments are nationally implemented, local autonomy is restricted to only one
dimension, the tax rate level. The tax rate can be set in a range between 4‰ and 7‰.
Although the tax interval is small, a marginal variation of the tax rate determines a
consistent variation in the per capita tax paid by the citizen and in the overall tax
11
Source: ANCI, National Association of Italian Municipalities.
12
Source: ISTAT, L’abitazione delle famiglie residenti in Italia - Anno 2008, published in Spring 2010.
21
revenue13. Moreover, the single dimension of the decision makes it easier for the voters
to exploit this information when forming their voting preferences.
Regarding election, the Italian local electoral rule has been reformed in 1993 from
proportional to majoritarian, introducing the direct election of the mayor according to
the plurality rule in Municipalities with less than 15000 inhabitants (9% of the total
number of Municipalities) and according to the majority rule with runoff elections in the
others. The local legislature lasted four years before 1999 and it has now been extended
to five years, and a term limit is fixed to two terms. In case of motion of no confidence
both the mayor and the council must resign and new elections are held. Because of the
early fall of many executives in the past Italian Municipalities hold elections in different
years. There is, however, a concentration of local elections in 1995, 1999 and 2004, when
more than 60% of the jurisdictions are called to the ballot. These three years are
considered as ‘first order electoral years’.
There is evidence of strategic tax setting among Italian Municipalities, as studied by
Bordignon et al. (2003), Santolini (2007), Bartolini and Santolini (2009)14. Given these
facts it is natural to guess that selection powers have been constrained and a certain
number of mimicking incumbents have been re-elected to the detriment of their citizens.
However, the results of the model in Section 4 predict that election after election, voters
may learn the incumbents’ strategy and since the third electoral period they can
correctly judge the fiscal performance. The next paragraph tests this hypothesis.
5.2 Methodology and data
The methodology applied in this analysis stems from the model of learning from
economic policies by Meseguer (2009). This section adapts the original cross-countries
economic policy decision setting to the sub-national electoral learning environment.
During the third electoral year of the model of dynamic learning from tax rates voters
choose among two different electoral policies, which are not re-elect the incumbent who
pools (j3=0) or re-elect the incumbent who pools (j3=1). Pooling is defined as setting a tax
rate which is no higher than the tax rate in the neighborhood. Equation 33 makes the
empirical link between re-election and the updated beliefs.
The method suggested by Meseguer (2009) includes three-steps:
13
The average value of the house properties in Italy was 182000 euro in 2008 (source: Dipartimento delle
Finanze and Agenzia del Territorio, Gli Immobili in Italia, published in 2010). Using this value as a proxy
for the tax base of ICI, a marginal variation in the tax rate leads to a variation of 182 euro of the individual
tax burden. In turn, this amount accounts for a 7‰ of the he average yearly income of an employee in 2009
(ISTAT).
14
The findings of Chapter 1 of the author’s Ph.D. Dissertation confirm the previous results in the literature,
since neighboring jurisdictions set similar tax rates during the electoral year. The dataset implemented,
however, is significantly wider and longer, including all the Municipalities belonging to the 15 Italian
Ordinary Regions from 1995 to 2004. The same work estimated both a local vote popularity equation and a
local tax distance equation – tax distance is computed as the difference between the domestic tax rate and
the neighbors’ tax rate - accounting for the simultaneity between the local tax distance and the local win
margin. The results are consistent with the static model of yardstick competition, since a decrease in the
electoral tax distance is associated with an increase in the electoral popularity of the incumbent, and an
increase in the incumbents’ expectation of popularity is associated with a decrease of the tax distance
during the electoral year.
22
1. the posterior beliefs 3 3
d d
and sµ are calculated using Bayesian
updating;
2. posterior beliefs conditional on the voting decision are compared. The prediction
is a worse performance (higher expected average and a higher expected
volatility) associated to the non re-elected incumbents;
3. a regression is estimated, using as dependent variable the voting decision j .
The function estimated in the original model is:
3 1 3 2 3 3 3 3
d d d
j s Xβ µ β β ξ= + + + [34]
The main independent variables are the differences in posterior beliefs about average
results and variability of results under each status,
1 0
3 3 3
d j j
µ µ µ= =
= − and
1 0
3 3 3
d j j
s s s= =
= − ,
and X is a vector of explanatory variables.
Meseguer updates the agent’s beliefs conditional on policy decision using data on GDP
growth, a variable which is yearly observable.
The electoral scenario of Italian Municipalities, however, is much more complicated. The
dataset is a cohort of 228 obbservations. The mean and the variation of the tax rate is
observed during every electoral period, but the neighbors do not hold necessarily
belong to the cohort, therefore they do not hold elections in the same years. As a
consequence, the descriptive statistics for the realization of the tax rate conditional on
the past voting decision is not feasible if not picking different electoral years for the
neighbors. This option is not followed at this stage of the analyses for two main reasons.
The first one is theoretical, because this approach would catch different years of the
political electoral cycle, making the values not comparable. The second one is technical,
because such a computation complicates the calculus of the beliefs and would not be
possible for data before 1995.
Hence, the empirical test of this paper estimates Equation 29 separately for each policy
decision, focusing on the domestic past experience. Since the dependent variable takes
values zero or one, and since the available data refer to only one year, the chosen model
is a static probit. The null hypothesis states that voters did not switch from re-electing
the pooling incumbent to not re-electing him as a result of dynamic learning from tax
rates. The empirical predictions are that β1 and β2 should be significantly negative
because both a high average and a high volatility of the tax rate reduce the voters’
utility.
The data used for the estimation come from a comprehensive dataset of Italian
Municipalities (Padovano, 2007). The considered observations are 227 Municipalities
meeting the following requirements:
• are members of the cohort of Municipalities that held local elections in 1995, 1999
and 2004;
• a local house tax rate set in 1995 at most equal than the average tax rate set by its
neighbors (defined as a ‘pooling’ tax rate);
• a local house tax rate set in 1999 higher than the average tax rate set by its
neighbors (defined as ‘non pooling’ tax rate);
• an incumbent running for re-election in 2004;
23
• a local house tax rate set in 2004 at most equal than the average tax rate set by its
neighbors (‘pooling’ tax rate).
As the following graph shows, the selected observations are in their third electoral
year since the local fiscal and electoral system has been reformed, and they belong to
a cohort of jurisdictions experiencing two full local legislatures (1995-1999, 1999-
2004). Among them, in 2004 the incumbent was defeated in 33 Municipalities (about
the 15% of the sub-sample) while in the remaining 194 Municipalities he was re-
elected.
Graph 4. Electoral dynamics of the 227 Municipalities in the dataset
5.3 Estimation and results
The first empirical step implies computing the posterior beliefs in 2004 using Bayesian
updating.
Several set of priors have been used to calculate different updated beliefs.
The first update considers as priors the average and the variability of the tax distance in
the dataset (measured as the standard deviation from the possible interval of values of
the tax distance). The tax distance is measured as the difference between the domestic
tax rate and the average tax rate in the neighborhood. This set of priors (uptd) is closer to
the specification of the model presented in this paper, but since the existing literature on
yardstick competition focused separately on the domestic and the neighbors’ tax rate,
alternative sets of priors have been investigated.
The alternative sets of priors calculate updated beliefs with respect to the average and
the variation of the domestic tax rate, taking as priors the average and the variation from
the possible interval (up1) or from the average and the variation from the observed
values in the neighborhood (up2).
Summary statistics for the posterior point estimates for the location and the scale are
reported in Table 7.
24
Table 7. Posterior beliefs using different sets of priors
own xp priors Obs Mean Std. Dev. Min Max
Updated average, μ3
UP1
227 4.776 0.477 4.000 5.880
Updated variance, s3 227 0.894 0.953 0.000 2.638
Ρ 227 0.364 0.026 0.333 0.4
1-ρ 227 0.636 0.026 0.595 0.67
Updated average, μ3
UP2
222 4.769 0.485 4.000 5.878
Updated variance, s3 222 0.331 0.273 0.020 2.024
Ρ 223 0.351 0.012 0.334 0.41
1-ρ 223 0.649 0.012 0.594 0.67
Updated average, μ3
UPTD
227 -0.504 0.372 -1.696 0.159
Updated variance, s3 227 0.497 0.741 0.000 5.768
Ρ 227 0.353 0.022 0.333 0.43
1-ρ 227 0.647 0.022 0.573 0.67
The mean updated domestic tax rate using both the sets of priors is about 4.77 (note that
the tax rates are scaled between 4 and 7), but the variation is smaller when using the set
of priors exploiting the neighbors’ information. These figures suggest that benchmarking
the domestic performance with the neighboring performance allows voters to have a
more precise expectation of the future performance.
When a direct indicator of performance comparison is used and voters’ belief are
updated with the priors on the tax distance, μ3 ranges from -1.696 to 0.159, with a
negative tax distance mean of -0.504. In other words, in some Municipalities voters
expect a bad performance (positive tax distance) and in other Municipalities they expect
a good performance (non positive tax distance)
From these results we can also see that the contribution of past information to the
updating process is stable at about 35% regardless the specification of the priors15. These
results for ρ suggest that voters form their electoral beliefs taking into account both the
current incumbents’ performance and the past performance. Meseguer (2009) argues
that a low value of ρ indicates that the learning process has already occurred, while a
high value tells that new information is still relevant for voters and in time they will
complete the learning. We can comment that a learning process had started in the
analyzed sample, but we cannot say if this is the level of ρ that maximizes the learning
function. Consequently, this information does not answer the question if a learning
process took place or not.
A closer look at the posterior beliefs is helpful in asking this question. Table 8 reports the
posterior beliefs conditional on the voting decision.
15
In the updating with the neighbors priors the number of observations has been set to one and does not
equal the number of neighbors. The reason for this choice is that the information included in the formula is
the average tax rate in the neighborhood and not the single tax rates in the contiguous jurisdictions.
Specifying the number of neighbors leads to an underestimation of rho and to updated average neighbors
tax rates falling outside the feasible set.
25
Table 8. Posterior beliefs conditional on voting decision
re-elected incumbent not re-elected incumbent
Variable priors Obs Mean Variable priors Obs Mean
Updated average, μ3 UP1 194 4.79 Updated average, μ3 UP1 33 4.71
Updated variance, s3 194 0.89 Updated variance, s3 33 0.89
Updated average, μ3 UP2 189 4.78 Updated average, μ3 UP2 33 4.71
Updated variance, s3 189 0.33 Updated variance, s3 33 0.35
Updated average, μ3 UPTD 194 -0.50 Updated average, μ3 UPTD 33 -0.53
Updated variance, s3 194 0.49 Updated variance, s3 33 0.55
This comparison of the updated beliefs on the tax levels does not support the learning
hypotheses since the level of the posterior belief about the average tax rate for the
incumbent re-elected in 2004 is always higher than the level of the posterior for the
incumbent non re-elected in 2004 (4.79>4.71 using UP1, and 4.78>4.71 using UP2). The
tax distance, however, is expected to be larger for non re-elected incumbents. An
explanation for this results is that voters consider the fiscal comparison and not the
domestic tax level as a performance indicator.
The results regarding the variation of the updated beliefs disaggregated by the
incumbent status indicate as expected that the re-elected incumbent is always associated
with a smaller or equal variation than the non re-elected incumbent. Voters, thus, should
behave as risky adverse agents.
At this stage of the analyses it is interesting to perform a comparison based on the
history of voting decision. If a learning process occurred we expect that the average
updated beliefs in the jurisdictions switching from re-election in 1995 to not re-election
in 2004 (coded as ´RNR´) should be higher than the updated beliefs in the jurisdictions
that re-elected the incumbent in 2004 (coded as ´NRR´). The summary statistics in Table
9 support this hypothesis only when the updating process exploits the set of priors UP2,
(column 8). This figure suggests that a learning process may have occurred if voters
updated their beliefs based on the performance in the neighborhood.
Table 9. Comparison of posterior beliefs with respect to the history of voting decisions
RNR>NRR
Variable priors RR NRR NRNR RNR Column 8
Updated average, μ3 UP1 4.792 4.775 4.507 4.769 FALSE
Updated variance, s3 0.895 0.893 1.324 0.748 FALSE
Updated average, μ3 UP2 4.785 4.763 4.506 4.769 TRUE
Updated variance, s3 0.326 0.337 0.634 0.253 FALSE
Updated average, μ3 UPTD -0.493 -0.521 -0.560 -0.525 FALSE
Updated variance, s3 0.467 0.559 0.796 0.473 FALSE
Observations 150 44 8 25
Notes: Rr=re-elected in both 1995 and in 2004; Nrr=not re-elected in 1995 and re-elected in 2004; Rnr=reelected
in 1995 and not re-elected in 2004; Nrnr = not re-elected in both 1995 and in 2004. 227 total
observations.
These results still give ambiguous indication about the presence of a learning process in
the sample, therefore equation 34 must be estimated to measure the extent to which the
26
updated beliefs determine the voting decision of the citizens. Specifically, the vote
decision is regressed upon the posteriors for the tax distance and both own and regional
experience. The time period available, however, poses some problems in the
specification. A time period of three subsequent elections tightly fits the model but the
experience observed inside each Municipality is either re-election in 1995 or not reelection
in 1995. This characteristic of the data does not allow us to compute the
differential between the updated beliefs conditional on the policy decision, but we still
can analyze it separately.
Table 10 presents the results from probit estimations obtained without covariates (Model
1-4) and with covariates16 (Model 5-12).
16
The covariates included are considered relevant determinants of the voting decision in the literature (see
Petterson-Libdom, 2006).
Table 10. Dynamic learning from tax rates, probit regression, marginal effects
Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Model 7 Model 8 Model 9 Model 10 Model 11 Model 12 Model 13
dy/dx dy/dx dy/dx dy/dx dy/dx dy/dx dy/dx dy/dx dy/dx dy/dx dy/dx dy/dx dy/dx
tax(i, 04) 0.006 -0.002
tax(-i, 04) 0.040 0.029
tax distance(i,04) -0.001 -0.006
μ3UP1*reel95 0.001 -0.003
s3UP1*reel95 0.020 0.027
μ3UP2*reel95 -0.009 -0.014 -0.019 -0.013
s3UP2*reel95 0.211 0.229 . 0.240* 0.206
μ3UPTD*reel95 0.073 0.097 0.110
s3UPTD*reel95 0.50 0.057 0.070
right party -0.957 -0.062 -0.064 -0.061 -0.063 -0.064 -0.060 -0.063
unemployment rate 03 -0.195 -0.191 -0.246 -0.323 -0.204 -0.248 -0.267 0.419
popularity 99 0.073 0.071 0.073 0.100 0.083 0.067 0.074 0.065
past performance
tax level 0.097*
past performance
tax distance 0.003 0.010
performance
tax distance -0.089 -0.091
Indep. Vars. No No No No No Yes Yes Yes Yes Yes Yes Yes Yes
Updating Static static dynamic dynamic Dynamic static Static dynamic dynamic dynamic dynamic dynamic Dynamic
level or distance Level distance level level distance level Distance level level distance level level Distance
Note: dependent variable: binary variable equal to one if incumbent re-elected in 2004 and zero otherwise.
The fit of the model is very limited, and the coefficients do not show a high degree of
significance. However, there are some expected results.
Model 1-2 and Model 6-7 test the static yardstick competition model. The domestic tax
rate shows the expected negative sign only when the covariates are include (Model 6).
The neighbors’ tax rate shows an unexpected positive sign, while the coefficient for the
tax distance is negative as the theory predicts.
Models 3-4 and Models 8-9 tests the dynamic learning from tax rates including the
updated beliefs UP1 and UP2 interacted with the dummy indicating re-election in 1995.
the interaction term has been chosen to control the effect of the updated belief
conditional on past re-election or not. The results using UP2, which seems to use
specification of the priors more appropriate in this frameowrk, confirm that an increase
in the expected average tax rate in the Municipalities re-electing a pooling incumbent in
1995 reduces the probability of being re-elected in 2004 with respect to the
Municipalities not experiencing a past pooling incumbent re-elected, while an increase
in the variation of the tax rate in the same Municipalities is associated with an increase
in the probability of being re-elected with respect to the control group. In Model 9,
moreover, the updated belief on the variation is statistically significant at the 10% level.
Model 5 and Model 10 control for the updated beliefs on the tax distance, but the results
are both not significant and unexpectedly positive.
Model 11 introduces as covariate the past performance (tax rate 1999 – tax rate 1995).
The results are significant but at odds with the theory because voters do not seem to
punish a term limited incumbent performing badly. The last two Models, 12 and 13,
replicate the results of Model 9 and 10, but including the past performance on the tax
distance (td99-td95) and the current performance on the tax distance (td04-td99). The
results indicate that the probability of being re-elected increases with the increase of the
past performance and decrease with an increase of the current performance. In other
words, voters seem to punish the first term incumbent performing worst than the past
term limited incumbent, but not the present pooling incumbent if his predecessor was
unmasked as a mimicking bad incumbent.
To sum up, the coefficients of the regressions are rarely significant and they show a
pattern of learning when using updated beliefs on the average tax rates based on the
priors UP2 (Model 4, 9, 11, 12), but this result is not backed by a negative coefficient of
the updated belief on the variation using the priors UP2.
6. Concluding remarks
The political economics literature recognized that re-election mechanism is an imperfect
device to select good politicians when the candidate incumbent behaves strategically.
This paper analyzes how persistent is the reduction of selection powers caused by
yardstick competition. The theoretical results of the model show that a learning process
restores selection powers by granting the correct update of voters’ beliefs also when a
pooling equilibrium in tax rates arises during the electoral year. When learning occurs
voters overcome the asymmetric information on the cost of the public production of
goods and services and they infer the competence level of the current incumbent. The
29
learning process, however, relies on a set of exogenous and endogenous factors that
hardly take place together, as the feasibility of learning, the willingness to learn, the
weight attached to past experience. Furthermore, the assumption of a Δ constant in time
is required to learn the true type of the current incumbent. If this assumption does not
hold, voters realize the extent to which mimicking occurred in the past and if they have
been deceived by the past incumbent, but the way in which this consciousness affects
their voting behavior cannot be univocally derived.
In order to test the model of dynamic learning from tax rates an empirical test has been
conducted on a sample of Italian Municipalities characterized by a pattern of yardstick
competition. The results reject the presence of a voters’ learning process in the data
because when voters face a pooling equilibrium the re-election of the incumbent is not
influenced by the updated beliefs on his fiscal performance, as suggested by the non
significant marginal effects. The results confirm that the advantages coming from
yardstick competition, that is the reduction of the incumbent’s rent during the electoral
year, has to be weighed against a reduction of voters’ selection powers that the
informational spillover is not able to remove, even in the long run.
This paper is the first attempt at analyzing the consequence of yardstick competition on
selection powers, therefore it calls for future research. A natural extension of the
dynamic model is investigating voters’ learning from different stock of information than
the ones considered so far. The relevant information, as an example, could be the whole
term performance of the candidate incumbent measured as the intra-term mean and
variation of the tax rate. The literature on strategic interaction in expenditure levels
should also suggest to exploit expenditure measures as performance indicators. These
perspectives could shed light also on the interaction between the political business cycle
in taxation with the cycle in expenditure.
30
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