polarization, fractionalization and conflict(*)

POLARIZATION, FRACTIONALIZATION
AND CONFLICT(*)
Autores: Joan Esteban. IAE (CSIC)
Debraj Ray. NYU and IAE (CSIC)(**)
P. T. N.o 7/07
(*) We are thankful to Marta Reynal-Querol and Gerald Schneider for useful comments.
Esteban gratefully acknowledges support from the Instituto de Estudios Fiscales, the
Polarization and Conflict project CIT-2-CT-2004-506084 funded by the European
Commission-DG Research Sixth Framework Programme, Barcelona Economics (XREA) and
the CICYT grant no. SEJ2006-00369. Ray gratefully acknowledges funding under National
Science Foundation grant no. 0241070.
(*) [email protected] and [email protected]
N.B.: Las opiniones expresadas en este trabajo son de la exclusiva responsabilidad de los
autores, pudiendo no coincidir con las del Instituto de Estudios Fiscales.
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Edita: Instituto de Estudios Fiscales N.I.P.O.: 602-07-012-X I.S.S.N.: 1578-0252 Depósito Legal: M-23772-2001 INDEX
1. INTRODUCTION
2. POLARIZATION AND FRACTIONALIZATION
3. A MODEL OF WAR AND PEACE
3. 3.1. Conflict
3. 3.2. Peace
4. POLARIZATION, FRACTIONALIZATION, CONFLICT AND THE
4. POLITICAL SYSTEM (G=2)
5. POLARIZATION, CONFLICT AND THE POLITICAL RULES WITH
4. SEVERAL GROUPS
6. CONCLUSIONS
REFERENCES
SÍNTESIS. Principales implicaciones de política económica
— 3 —
RESUMEN
Este trabajo proporciona una marco teórico para analizar los determinantes
del conflicto y de su intensidad. Específicamente estudiamos el papel de la
polarización y la fraccionalización social, condicionadas al sistema político vigente.
Los resultados alcanzados son los siguientes: (i) los índices de fraccionalización
y de polarización tienden a moverse en direcciones opuestas, (ii) el que estalle un
conflicto depende críticamente del sistema político vigente, (iii) las causas del
estallido de un conflicto y las de su intensidad también se mueven en direcciones
opuestas. (iv) la relación entre polarización (o fracionalización) y conflicto es no­
monotónica y (v) la intensidad de un conflicto depende positivamente del grado
de polarización.
La relación entre política fiscal, distribución de la renta, polarización y cohesión
social es bien conocida. Nuestros resultados implican que situaciones con un
moderado grado de desigualdad pueden conducir al conflicto social, mientras que
situaciones extremadamente polarizadas puede ser compatibles con la paz.
JEL: D 31, D72 y D74.
Palabras clave: Distribución de la Renta, Polarización, Conflicto, Cohesión
Social.
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Instituto de Estudios Fiscales
1. INTRODUCTION
A recent upsurge of empirical studies on the causes of conflict attempts to
connect various features of the distribution of the relevant characteristic (typically
ethnicity or religion) to conflict. The distributional indices differ(polarization,
fractionalization or Lorenz-domination) and so do the various specifications of
“conflict” (onset, incidence or intensity). Overall, the results are far from clear,
and combined with the mixture of alternative indices and notions of “conflict” it is
not surprising that the reader may come away thoroughly perplexed.
The aim of this paper is to provide a theoretical framework that permits us
to distinguish between the occurrence of conflict and its severity and that
clarifies the role of polarization and fractionalization in each of these cases. Our
analysis brings together strands from three of our previous contributions: on
polarization (Esteban and Ray, 1994, and Duclos, Esteban and Ray, 2004), on
conflict and distribution (Esteban and Ray, 1999) and on the viability of political
systems (Esteban and Ray, 2001).
Interest in the connections between inequality and conflict is not new, of
course. Political scientists have been much concerned with these issues; see, for
instance, the prominent contributions by Brockett (1992), Midlarski (1988),
Muller and Seligson (1987), and Muller, Seligson and Fu (1989). Midlarski (1988)
and Muller, Seligson and Fu (1989) had already voiced their reservations with
respect to the standard notions of inequality as an appropriate tool for conflict
analysis. To go even further back, Nagel (1974) had argued that the relationship
between inequality and conflict should be non-linear. Indeed, as Lichbach’s
(1989) survey concludes, the empirical studies on the relationship between
inequality and conflict-and these typically posit a linear relationship-have only
come up with ambiguous results.
In the area of economics, the analysis of the link between distribution and
conflict was largely inspired by a desire to study pathways between inequality
and growth1. Certainly the possibility that inequality is a determinant of social
conflict and –via this route– impedes growth is a contender for one of the more
important pathways. The most recent round of interest in this connection was
triggered by the contribution of Easterly and Levine (1997) who shifted the
emphasis to ethnic fractionalization rather than economic inequality, but
continued to emphasize the “reduced-form” connections with growth. Among
the more relevant contributions to this literature are the papers by Alesina et al.
(2003), Collier (1998, 2001), Collier and Hoeffler (2004), Fearon and Laitin
(2003), Hegre et al. (2001), La Porta et al. (1999), Montalvo and Reynal-Querol
(2005), Reynal-Querol (2002a) and Schneider and Wiesehomeier (2006a).
1
See Bénabou (1996) for a deep and comprehensive survey.
— 7 —
But the empirical results are ambiguous, if not controversial. If the pathway
between fractionalization and growth runs through conflict, it is empirically hard
to spot. By and large, it is fair to say that most of the literature fails to find any
significant evidence of ethnic fractionalization as a determinant of conflict. This
negative finding is underlined by Montalvo and Reynal-Querol (2005) who
obtain, instead, a significant relationship between ethnic polarization and the
incidence of conflict. (As we shall see below, the two variables are often at odds
with each other.) While formally not using a measure of polarization, Collier and
Hoeffler (2004) also argue that the contested dominance of one large group
rather than fractionalization increases the probability of civil conflict. The
Montalvo-Reynal-Querol result has recently been reassessed by Schneider and
Wiesehomeier (2006a) using a different data set and focusing on onset, rather
than incidence, of conflict. They argue that fractionalization is a better predictor
of conflict than polarization.
Without necessarily taking sides on the empirical merits of these papers, our
purpose is to provide a simple theoretical framework that might help in
ordering the various definitions, and in providing some explanations for the
seemingly confusing evidence. To do this, we follow Esteban and Ray (2001)2.
We first model the behaviour of players in case of conflict as a game and
compute the equilibrium payoffs to all players. The status quo against which
groups might rebel is characterized by a set of political institutions that channel
the different opposing societal interests and turn them into a collective decision.
Examples of such institutions are majoritarian or proportional democracies,
dictatorships, oligarchies… We abstractly represent these institutions as
alternative functions mapping the share of the population supporting each
interest group into collective decisions. We take political institutions as given
and hence disregard any potential endogeneity3. Groups will rebel against the
ruling political institutions whenever the outcome is worse than what they can
obtain through conflict.
It is imperative to note that we distinguish between the intensity of conflict,
conditional on conflict breaking out, and the likelihood that conflict actually
occurs. The point that we make is very simple. When society is highly polarized,
there may actually be a wider range of status-quo allocations that groups are
willing to accept. This is because the potential cost of rebellion is extremely
2
This line is also adopted in Reynal-Querol (2002b).
The point was already made by Lipset and Rokkan (1967) that political systems might be
endogenous, influenced by the particular social structure of the country. Why then societies fail
to adapt their institutions to the change of the environment so as to always prevent domestic
conflict? A number of arguments have been put forward by Powell (2004) –incomplete
information–, Fearon (1995), Powell (2006) and Leventoglu and Slantchev (2006) –inability to
credibly commit–, and Esteban and Ray (2006c) –empty core– to explain the break out of
conflict. We shall not pursue this line of enquire here and will take the political system as given.
3
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Instituto de Estudios Fiscales
high, and this cost of conflict serves as the guarantor of peace. Put another way,
if conflict is very costly as it will be in highly polarized societies, it is easier to find
an agreement that is Pareto superior to the conflict regime. At the same time, if
conflict were to occur for some reason, its intensity would be higher in
polarized societies. It follows that the intensity of conflict (conditional on its
occurrence) and the likelihood of conflict may move in opposite directions with
respect to changing polarization.
In particular, when the cost of conflict is low, the parties will more easily
reject proposals that slightly depart from what they can get through conflict. In
the spirit of the fractionalization vs polarization controversy this argument can
be summarized as follows. Highly fractionalized societies might be more prone
to the onset of conflict, but its intensity will be moderate. In highly polarized
societies, the occurrence of open conflict should be rare but its intensity very
severe. In this paper we develop this argument and show that: (i) measures of
fractionalization and polarization tend to run in opposite directions, (ii) the
onset of conflict critically depends on the political system in place, (iii) the
occurrence of conflict and the intensity of conflict also tend to move in opposite
directions, (iv) the relationship between polarization or fractionalization and
conflict is non-monotonic and (v) the intensity of conflict depends positively on
the degree of polarization4.
Our paper is organized as follows. We start by comparing the indices of
fractionalization and polarization. Section 3 develops a simple model of conflict
based on the general class studied in Esteban and Ray (1999). In order to
present the ideas in the sharpest form, in Section 4 we start our study of the
occurrence and intensity of conflict focusing on the case of two opposing groups
only. This case permits a very neat understanding of the causes of intensity of
conflict and the causes of its occurrence. However, as we shall see, in the case
of two groups the notions of fractionalization and polarization are
undistinguishable from each other. In section 5 we generalize the results to the
case of an arbitrary number of groups and examine the different performance of
the indices of polarization and fractionalization. Section 6 concludes.
2. POLARIZATION AND FRACTIONALIZATION
We begin by defining the indices of fractionalization and polarization.
The index of fractionalization F is intended to capture the degree to which a
society is split into distinct groups. The measure has been widely used in studies
4
This discussion can also shed some light on the controversy on the stabilizing or
destabilizing effects of “polarity”; a classic the international relations literature. See Waltz
(1964) and Deutsch and Singer (1964), for instance.
— 9 —
that attempt to link ethnolinguistic diversity to conflict, public goods provision,
or growth (see, e.g., Collier and Hoeffler (1998), Fearon and Laitin (2003),
Easterly and Levine (1997) and Alesina, Baqir and Easterly (1999).
Let ni be the share of the population belonging to group i, i 1, ,G . The
fractionalization index is defined as the probability that two randomly chosen
individuals belong to different groups. The probability that an individual of group
i is chosen is ni . Hence that probability that if chosen she is matched with
someone from another group is ni 1 ni . It follows that the probability that
any two individuals belong to different groups is
F
¦ ni (1 ni )
1
¦ ni2
(1)
F is a strictly concave function of each population share. From this strict
concavity we can derive the following properties of F.
a) Any transfer of population from a group to a smaller one increases F.
b) For a given number of groups, G, F is maximized at the uniform
population distribution over these groups.
c) Over the set of uniform distributions F increases with the number of
groups; and
d) The split of any group with population n into two new groups with n’ and
n”, n’ + n” = n, increases F.
Polarization is conceptualized in Esteban and Ray (1994) as the sum of inter­
personal “antagonisms”. Antagonism results from the interplay of the sense of
group identification (group size) and the sense of alienation with respect to
members of other groups (inter-group distance, bij ).5 Esteban and Ray’s
polarization measure6 P can be written as
i
P(V,b)
i
¦¦ ni1Vn jbij
i
jzi
,
(2)
where b is the matrix of inter-group distances and V is a positive parameter
that captures the extent of group identification. Esteban and Ray (see also
5
Alternative notions of polarization not based on the identity/alienation framework have
been proposed by Wang and Tsui (2000), Reynal-Querol (2002c), and Zhang and Kanbur
(2001). Another alternative and –considerably cruder– specification of polarization which also
does not include a proxy for intra-group homogeneity in the absence of information is the
concept of dominance that Collier (2001) introduced. It qualifies societies as “dominated” if
the largest group contains between 45 and 90% of the overall population.
6
Esteban and Ray (1994) examine the main properties of this measure. The interested
reader can also see Duclos, Esteban and Ray (2004) for a measure of polarization for
continuous distributions.
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Instituto de Estudios Fiscales
Duclos et al. (2004) derive restrictions on V that bound it both above and
below. The exact form of these restrictions is not particularly important here,
though we record for use below that V must be less than 2.
A situation of particular relevance is the special case in which individuals in
each group feel equally alien towards all groups other than their own. That is,
bij bi for all j z i . In this case P reduces to
P(V,b)
¦ ni1V 1 ni bi .
(3)
i
Observe that if we set V 1 and bi 1 for all i we obtain the measure of
polarization introduced by Reynal-Querol (2002c); a special case of (2). This
specific measure of polarization was later used in Montalvo and Reynal-Querol
(2005) to test the relationship between polarization and conflict.
It is also true that we can formally set V 0 in (3), as well as bi 1 for all i, to
arrive at the measure of fractionalization (1). We emphasize that this is a formal
and not a conceptual connection: for (3) to be a measure of polarization it is
necessary that V be strictly positive, and –depending on the exact character­
rization– perhaps more than that7. Nevertheless, it is useful to record that
P (1,1) RQ and P (0,1) F ,
(4)
where the entry 1 stands for the matrix of all 1’s.
In order to simplify the computations, in this paper we shall work with the
special class of polarization indices, P 1,1 , that is
P { P (1,1)
¦ ni2 (1 ni ) .
(5)
i
In order to examine the properties of P we start by observing that P is the
2
sum of the function p n n 1 n evaluated at the different ni . But now
p . is convex or concave as n ! 1 3 . Therefore, we have the following
properties for P.
Properties of P
a’) A transfer of population from a group to a smaller one increases P if
both groups are larger than 1/3. If the two groups are smaller than 1/3
the equalization of populations will bring P down.
b’) For any given number of groups, P is maximized when the population is
concentrated on two equally sized groups only.
c’) Over the set of uniform distributions P decreases with the number of
groups, provided that there are at least two groups to begin with; and
7
For instance, Duclos, Esteban and Ray (2004) argue that s is at least 0.25.
— 11 —
d’) The split of a group with population n into two groups with n’ and n”, n’ +
n” = n, increases P if and only if n • 2/3.
The contrast between the two sets of properties clearly shows that the two
measures behave quite differently from each other, except when there are just
two groups. The difference is clear: fractionalization is maximal when each
individual is different from the rest while polarization is maximal when there are
only two types of individuals.
The reader is referred to Montalvo and Reynal-Querol (2005) for further
discussion on the difference between these two measures.
This completes our discussion of the indices. We now turn to a model of
conflict and peace.
3. A MODEL OF WAR AND PEACE
3.1. Conflict
We start with conflict as our first building block. In modeling conflict we
follow Esteban and Ray (1999). We concentrate on a special case studied in that
paper: the class of conflict games called contests. Assume that there are G
alternatives, i 1, ,G . Individuals differ in the alternative they like the most and
are indifferent over the other available alternatives. Individuals in a specific
group i are all alike, in that they like alternative i the best, and the difference in
valuation between their most preferred alternative and any other is the
common value bi . Let ni denote the relative size of group i. Note that the
alternatives here are public goods because their valuation by the individuals is
independent of the number of beneficiaries. Therefore, we can think of
alternatives as different kinds of public goods to be financed by the public budget.
By a political system we shall refer to a particular way of choosing among the
different alternatives. By conflict we mean a challenge to such a system, which is
costly. Specifically, we take the following view. Conflict entails resource
contributions ri (to be determined presently) from every member of group i, so
that the overall contribution of group i is niri In the absence of a political rule,
the particular alternative that will eventually come about is seen by the players
as probabilistic. The probability that alternative i will be established is assumed
to be equal to the resources niri expended by group relative to the total
resources R expended. In short, the probability of success pi is just.
pi
niri
nr
{ ii,
R
n jr j
¦
j
— 12 —
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Instituto de Estudios Fiscales
where R is the sum of all the group contributions. In the sequel, we shall take
this very R to be a measure of the overall intensity of conflict (or wastage) in the
society.
To understand how contributions are determined, suppose that there is a
utility cost of spending ri ; call it c ri . Take this function to be of the constant­
elasticity form
ri1D
c(ri )
, with D ! 0 .
(7)
1 D
Given the resources expended by the others, ri , the expected utility of an
individual of group i when spending ri is
E(ui (ri ))
pibi c(ri )
niri
ri1 D
bi .
1 D
n jr j
¦
(8)
j
Expected utility is clearly concave in ri and hence the utility maximizing level
of expenditure can be characterized by the first order condition:
§
·
¨
¸
ni ¨
ni
niri ¸
1 pi bi riD .
1
bi
(9)
R
n jrj ¨
n jrj ¸
¨
¸
j
j
©
¹
An equilibrium of the conflict game is a vector r such that (9) is satisfied for all
i 1, ,G .
¦
¦
There is always an equilibrium of the conflict game. Esteban and Ray (1999)
demonstrate, furthermore, that if D t 1 then such an equilibrium must be unique.
In order to simplify the computations we shall focus on the case of
symmetric valuations, with bi 1 for all i, and D 1.
Multiplying both sides of (9) by
ni
we obtain
R
2
§ ni ·
¨ ¸ 1 pi pi ,
©R¹
And transposing terms, we conclude that
pi
ni 2
ni 2 R 2
.
(10)
(11)
The equilibrium value of R has to be such that the sum of the probabilities
given by (11) adds up to unity, that is
— 13 —
ni 2
¦ pi ¦ n 2 R 2
i
i
1.
(12)
i
The LHS of (12) is strictly decreasing in R. Using (10), it is immediate that
when R goes to zero the LHS tends to G ! 1 and that when R tends to infinity
the LHS tends to zero. Therefore a solution to (12) always exists and it is unique.
Substituting the equilibrium R into (11) yields the equilibrium probabilities.
In order to obtain a useful expression for equilibrium payoffs we multiply
both sides of (9) by
ri
to see that
2
1
pi 1 pi 2
1 2
ri { c(ri ) .
2
(13)
Using (13) in (8) yields
pi (pi 1)
.
2
For the case of two groups, G 2 , setting n1
equilibrium values are easy to compute:
E(ui (ri ))
p
R
E(u1(r1 ))
(14)
n and p1 p , the
n,
(15)
n(1 n) , and
n(n 1)
and E(u2 (r2 ))
2
(16)
(1 n)2 n
.
2
(17)
The equilibrium payoffs to conflict for player i will be simply denoted ui .
3.2. Peace
In the previous subsection we have examined the equilibrium outcome of a
conflict game under the assumption that conflict actually takes place. Now we are
in a position to compare a conflictual situation with that of peace. Under peace,
individuals must accept the payoff that the ruling political system allocates to
them. As mentioned before, the political allocation can be interpreted as the
share of the public budget allocated to the production of the type of public good
most preferred by each group. We define a policy to be a vector J of shares,
with J L denoting the share of group i. Hence, we can interpret J as a
“compromise policy” composed of a convex linear combination over the
available alternative types of public goods.
Formally, we shall have peace whenever
ui d J L for all i 1, ,G .
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Instituto de Estudios Fiscales
It is trivial but nevertheless useful to observe that whether we have conflict
or peace critically depends on what the ruling political system delivers to the
different contending groups.
A political system is a particular way of mapping the population shares
supporting each alternative into policies.
We shall examine here various political systems and check for their ability to
guarantee peace. Specifically, we shall study dictatorship, fixed shares,
majoritarian rule and proportional rule.
Our first example of a political system is a dictatorship. This will be the case
when the alternative preferred by some group i is brought into effect,
irrespective of the number of individuals for whom this is the best choice. If
group i is the dictator, then J i 1 and J j 0 for all j z i .
The second case is fixed shares, which generalizes a dictatorship. The policy
consists of a vector J assigning a share to each group independent of its
population size. There are many instances of such a political system. Various
political bodies have fixed proportional representations of the different opposing
interests (often rural vs urban). There are also cases where the chairs of the two
chambers have to alternate between the different ethnic or religious groups in
the country8.
The majoritarian rule generates the policies that earn the support of a
majority of citizens. For the case of G 2 this is very easy to define: J L 1 if
and only if ni ! 1/29. For G ! 2 the characterization of the policies resulting
from a majoritarian rule is more intricate as it involves the formation of a
majoritarian coalition. In some special environments there is a well-defined
pivotal group (the median voter) who can impose its preferred policy to the rest
of the majoritarian coalition. This is not the case here and hence most of what
we can say will be restricted to the two-group case.
Finally, the proportional rule produces the policy that assigns to each group a
share equal to its population size: J i ni . Parliamentary representations satisfy
8
This was the first constitutional arrangement for the Lebanon after independence. The
constitution established that the president had to be a Christian. The faster population
growth rate among the Muslim population made this provision untenable and possibly
contributed to the outbreak of the civil war. Another example is the EU “rotating presidency”
across the member countries with a frequency that is independent of their population.
9
This is a extremely stylized representation of the majoritarian rule. Real world majoritarian
democracies do not work like this. A number of written and/or unwritten rules protect
minorities from the tyranny of the majority. This observation has led Lijphart (1977) to launch
the concept of “consociational” policies that end up producing an outcome that approaches
the proportionality rule. Lijphart has been a steady supporter of “consociational”
constitutions for countries with deep ethnic cleavages.
— 15 —
this rule for most countries (not in the UK where each seat corresponds to one
constituency). Although most decisions simply require a majority vote in the
chamber, the resulting policies tend to give some weight to the minoritarian
opposition. Multi-level government also contributes to give to the different
groups an overall weight that brings them closer to their population share.
In the next section we study the relationship between polarization,
fractionalization and conflict under the different political systems for the case of
two groups. In section 5 we generalize to G groups.
4. POLARIZATION, FRACTIONALIZATION, CONFLICT AND
4. THE POLITICAL SYSTEM G 2
We are interested here in two quite different aspects of conflict. In the first
place, we want to characterize the relationship between the intensity conflict
and polarization when conflict actually takes place. This relationship is
independent of the political system. Secondly, we wish to identify the
relationship between polarization and the occurrence of conflict (or peace!).
Intensity of conflict
We start by noting that for G 2 the measures F and P (and hence RQ) are
proportional to each other. Furthermore, they all attain their maximum at n =
1/2. It follows that any comparative test of the performance of P (or RQ) relative
to F as a predictor of conflict should focus on cases with G t 3 . We discuss this
case in the next section.
In view of (16), the level of conflict R is the square root of P and hence
conflict intensity is an increasing function of polarization and of
fractionalization10.
10
If we drop now the restriction that a = 1 but retain that b = 1, P(a,1) ceases to be
proportional to F, but continues to behave like it. Indeed, P(a,1) is concave and attains its
maximum at n = 1/2. Therefore, we will still have that increases in P(a,1) go with increases in
the level of conflict R. Things are different when we allow for asymmetric inter-group
distances. It can be readily verified that if b < 1 (>) both polarization and conflict are
maximized at (two different) values nP,nR > 1/2 (<). Therefore, except for values of n within
this interval, the level of conflict will be strictly increasing with polarization. The non­
monotonicity with respect to F and RQ will be for n in the interval (1/2,nR).
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Instituto de Estudios Fiscales
Figure 1
R
R
0
1/2
1
0
n
1/4
P
In figure 1 we plot the intensity of conflict as a function of the population
shares n (left figure) and of the corresponding level of polarization P (right
figure). Intensity is maximal for n = ½, that is when polarization is also maximal
with P = 1/4.
Figure 2
u2
1
1 n''
1 n'
0
n''
n'
1
u1
It will also be useful to record the equilibrium utility payoffs as given by (17)
and which we represent in figure 2. These payoffs depend on the population
distribution parameter n. The equilibrium utility for each player is the win
probability p n minus the cost of the resources expended in conflict, equal for
both types of players for G 2 . The win probabilities are points on the straight
line between (0,1) and (1,0), the utility possibility frontier. Given n, from the
corresponding point on the frontier we move inwards along a 45º line for a
length equivalent to the utility loss caused by the spent resources. This gives us
— 17 —
a utility equilibrium pair. As we vary n we generate all the points of the
equilibrium payoff curve. The maximum distance between the payoff curve and
the frontier is at n = ½ where the conflict loss is maximal.
So much for intensity. Let us now turn to the occurrence of conflict. This
depends on the payoffs obtained in peace and these in turn depend on the
political system.
Dictatorship
The first political system we examine is dictatorship. Will there ever be
peace? The answer is no. The reason is simple. In equilibrium conflict, all players
receive a strictly positive payoff because they could have opted for contributing
nothing to conflict, thus guaranteeing for themselves a payoff of zero. Hence,
for a non-dictator obtaining a peace payoff of zero is always dominated by the
conflict payoff.
Fixed shares
We next examine the case of fixed shares J .
The necessary and sufficient condition for conflict is that either
n(1 n)
(1 n)(2 n)
! J or
! 1 J .
2
2
(19)
Figure 3
u2
1
1 n' '
1 J
1 n'
0
n' '
n'
1
u1
The situation is captured in figure 3. Consider the peace share J and the
corresponding utility payoff. For a population parameter like n’ the payoffs to
conflict are dominated by the peace payoff for the two players. However, if we
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Instituto de Estudios Fiscales
decrease sufficiently the population share of the first group–all the way down to
n”, the second group would have a strong advantage over the first in conflict and
thus prefers conflict to the peace payoff.
To be more specific, let us rewrite the inequalities in (19) as
n(1 n)
n(1 n)
! J or n J.
(20)
2
2
The LHS of the two inequalities is strictly increasing in n (one convex and the
other concave). Therefore, there exist n’ and n” such that if n  [n',n" ] there is
peace and conflict otherwise.
In figure 4 we depict the values of n for which, given J , we shall have peace.
These are the values of n corresponding to the points on the equilibrium utility curve
at which one of the two players is indifferent with respect to the peace payoff.
Figure 4
n
u2
1
1 n'
1 J
1 n' '
0
n'
J
n''
1
u1
Clearly, the interval of values of n for which there will be peace depends on
the bias exhibited by the fixed-shares policy J . Let us take as a benchmark the
case of equal treatment of the two groups of players with J = ½. From our
previous analysis it follows that for very low polarization (i.e. for very low or
very large n) there will be conflict, but its level will be low. As polarization
increases the level of conflict will increase too. But, further increases in
polarization will produce peace and bring the level of conflict down to zero. The
overall relationship between polarization or fractionalization and conflict is therefore
non-monotonic.
We can address the complementary question of the range of policies J that
would guarantee peace for given n. This range is given by the gap between the
— 19 —
two bounds: n(1-n). Hence the widest range for peaceful policies corresponds
to n = 1/2. High polarization allows for a wider choice of peaceful fixed-share
policies. The intuition for this result is straightforward. If there is conflict, higher
polarization produces larger losses. Hence, it is only when the policy is very
biased against one group that that group will decide to incur the heavy cost of
conflict. With low polarization the costs are smaller and hence a lower bias in J
might be enough to trigger conflict.
Majority rule
The case of majority rule is equivalent to letting the largest group become a
dictator. By the same argument as before, we shall never have peace as the
minoritarian group will always obtain a higher payoff under conflict than under
peace. Hence, with majority rule we shall always have conflict11 and the level of
conflict will positively depend on the degree of polarization.
Proportional rule
We start by noting that in the previous case of fix shares, in view of (20),
when J is sufficiently close to the win probability of that group peace will not
be challenged. Under our assumptions, p n and hence making J n would
guarantee peace. This precisely is the proportional rule that gives each group a
share equal to its population size, that is, J i ni .
Therefore, for symmetric valuations we should never observe conflict under the
proportionality rule12.
The intuition for this result is that the proportionality rule gives to each
group a weight that is close to their win probability under conflict. Hence, it
never pays to challenge the peace allocation13. As we will see, this result is
specific to the two-group case and does not extend to the case of a larger
number of groups.
Diagrammatically, we can see in figure 2 that the point (n,1-n) always
dominates the conflict equilibrium payoffs.
11
Let us insist in that this statement is not meant to be empirically relevant as none of the
existing majoritarian democracies permits the tyranny of the majority. From an empirical
point of view the practical distinction between majoritarian and proportional democracies is
far from clear. The use of the notion of “inclusiveness” of a political system as in ReynalQuerol (2005) might be more relevant.
12
This is no longer true for asymmetric valuations. The equilibrium p can be made arbitrarily
close to unity by choosing b for one group sufficiently close to zero.
13
This result seems to substantiate Lijphart’s view that “consociational” systems, because
they are essentially proportional, permit peaceful arrangement in ethnically divided societies.
[see more in footnote 13].
— 20 —
Instituto de Estudios Fiscales
Summing up
In this section we have obtained two main results. The first one is that it does
matter for conflict which political system is in place. Dictatorships and
majoritarian systems never yield peace. Fixed shares may give peaceful
outcomes for some parameter values. The proportional system always yields
peace, at least whenever there are just two groups.
The second result is that while the intensity of conflict is positively related to
the degree of polarization, the incidence of conflict is not. Only in the fixed
shares system does the incidence of conflict depend on the distribution of the
population across the two groups. For the other three political systems the
incidence of conflict is independent of the distribution (and hence of the degree
of polarization). For the fixed shares system conflict is more likely at low levels
of polarization and peace more likely at high levels. Therefore, if there is any
relation between conflict and polarization this is non-monotonic.
Our analysis also suggests that if one wishes to test for the occurrence of
conflict, the political system appears to be a key variable, along with the degree
of social polarization (or fractionalization).
5. POLARIZATION, CONFLICT AND POLITICAL RULES WITH
5. SEVERAL GROUPS
We shall examine now whether our previous conclusions can be extended to
the general case of several groups.
Intensity of conflict
We start with the relationship between polarization and the intensity of
conflict, R. The relationship between the intensity of conflict and polarization
has been extensively studied in Esteban and Ray (1999, section 6). Using
Esteban and Ray (1999, expression 16) we can write
R
¦
i
ni 2
ni (1 ni )bi .
pi
(21)
Comparing (21) with the measure of polarization P in (4) we can observe
that, if pi ni , the level of conflict R would be equal to the index of polarization
P 1,b .
The n/p ratio is determined in equilibrium and will generally be different from
unity. Therefore, how closely related P is to R critically depends on how much
n/p varies across the different groups in equilibrium. It can be shown that the
— 21 —
case in which ni pi 1 for all i is specific to the symmetric case for G 2 or for
uniform distributions over G ! 2 groups. Therefore, on these grounds alone,
we should a priori expect a positive but incomplete association between
polarization P 1,b [and hence P 1,1 RQ ] and the level of conflict R.
However, the discussion that now follows suggests that there are pretty tight
connections between the two.
Drawing on the results in Esteban and Ray (1999) we can restate the
following properties of R, implicitly determined in (12), to be contrasted with
the properties of F and P presented in section 2.
(i) A transfer of population from a group to a smaller one increases R if both
groups are larger than 1/3. If the two groups are small enough the
equalization of populations will bring R down.
(ii) For any given G, R is maximized when the population is concentrated on
two equally sized groups only.
(iii) Over the set of uniform distributions R decreases with the number of
groups G; and
(iv) The split of a group with population n into two groups with n’ and n”, n’
+ n” = n, increases R if and only if the group size is sufficiently large. If n
is small, the split will decrease R.
Do the properties of our theoretical model align with our intuition on the
intensity of conflict? Consider conflict among three groups of varying size.
Property (i) says that equalizing the size of the two largest groups will increase
conflict while reducing the size of the second largest group at the benefit of the
smallest will reduce conflict. Property (ii) appears to conform to the common
intuition that conflict is worst when society is split into two equally sized groups.
In the case considered by Property (iii) each group becomes progressively
smaller, while its collective opponent (the rest of the groups) becomes larger. In
this case the smaller groups will commit less resources into conflict. As for
Property (iv), consider first the case of a monolithic society that gets split into
two distinct groups. This must increase the intensity of conflict. The same has to
be true even if the initial society was not monolithic, but had a small “dissident”
group. But suppose now that after the first split the second sized group splits
into two smaller groups. Then we would expect that conflict would come down
because now the untouched group has become relatively larger than the others.
The smaller groups may not be willing to contribute a lot of resources to
conflict.
In sum, the properties displayed by our conflict model do not seem to
contradict our intuitions about conflict intensity.
Let us now compare the properties of R and P. It is immediate that the two sets
of properties describe movements in the same direction for the type of population
— 22 —
Instituto de Estudios Fiscales
changes considered. Hence, we should expect a strong positive relation between
polarization and conflict intensity. [See a parametric illustration below].
How does the index of fractionalization F behave relative to R? Property (i)
of R is not satisfied by F. Property (a) of F says that any equalization of sizes will
increase F. In contrast, R may go either up or down depending on the size of
the groups involved. Properties (ii) and (b) are aligned as long as there are two
groups in conflict to start with. With more groups F is maximized at the uniform
distribution while R continues to be maximal when the population is
concentrated on two equally sized groups. Properties (iii) and (c) are exactly the
opposite of each other. Finally, when we compare Properties (iv) and (d) we
observe that any split always increases F, while R may either decrease or
increase depending on the size of the broken group.
We can thus conclude that we can expect a strong positive relationship
between polarization and conflict, and a weak and (if anything) negative
relationship between fractionalization and conflict, at least insofar as intensity is
concerned.
We now turn to an analysis of the incidence of conflict when there are more
than two groups.
Dictatorship and majoritarian rule
Notice our arguments on the impossibility of peace under dictatorship or the
majoritarian rule did not depend on the number of groups. In both cases, the
excluded groups will obtain a lower payoff than what they can obtain under
conflict.
Fixed shares
From (14) we have that there will be conflict whenever
pi (1 pi )
! J i for some i 1, ,G .
2
Using (11) in (22) we obtain that the condition for conflict is
ui
1 ni2 §¨
ni2 ·¸
1
! Ji .
2 ni2 R 2 ¨© ni2 R 2 ¸¹
(22)
(23)
Consider any given vector of shares J and a particular group of size ni .
Observe that the payoff ui can take values in (0,1) depending on R. Therefore,
the condition for conflict is most likely to be satisfied when R is small and hence
polarization is small too. To be precise, suppose that all the remaining groups have
the same size, n j
1 ni
, j z i . It can be readily verified from (12) that R is strictly
G 1
— 23 —
decreasing in G. It follows that there is a G sufficiently large so that a uniform
distribution over the G-1 remaining groups would induce group i to prefer conflict.
Note that as G becomes large polarization comes down and fractionalization goes
up. Therefore we shall see conflict with low levels of polarization and high levels
of fractionalization, but the intensity of conflict will be low.
In the discussion above, observe that it is the untouched group, the group
which has become larger relative to the others, is the one who prefers conflict to
peace. Hence, even in this case, one might argue that it is not high
fractionalization as such that precipitates conflict but the coexistence of one large
group with numerous small groups. In fact, if we now equalize the size of all the
groups, thus increasing F and decreasing P, no group would have an incentive to
challenge the peace share and we would have peace with higher fractionalization.
To sum up, for the egalitarian fixed shares policy, conflict will not occur in
economies with high polarization/low fractionalization. For distributions displaying
low polarization/high fractionalization, the relation between conflict and F or P
will be non-linear. Conflict will be most likely for distributions with one large group
and many small ones (and hence with relatively high fractionalization and low
polarization).
As the rule of fixed shares departs from egalitarianism, the occurrence of
conflict will critically depend upon the bias introduced by the rule.
Proportional rule
Once again, from (14) we have that under the proportional rule there will be
conflict whenever
p i 1 ni
!
for some i 1, ,G .
2
pi
(24)
In the previous section we have seen that for G 2 the proportional rule
always guarantees peace. Does this property extend to G ! 2 ?
A first observation is that for the distributions under which the equilibrium
win probabilities are very close to the population shares condition (24) will not
be satisfied and we shall observe peace. We shall only have conflict when pi is
sufficiently larger than ni for some group i.
Using (10) in (14), we can rewrite condition (24) as
2
·
§
ni
1
¨1 ni
¸ ! 1.
2
2
2
2
¨
2 ni R ©
ni R ¸¹
The LHS of (25) can take values in (0,
(25)
1
), depending on R. Provided 2ni 1,
2ni
we have already seen that there is a distribution of the population (for
— 24 —
G
Instituto de Estudios Fiscales
sufficiently large) so that group i will prefer conflict over peace. Esteban and Ray
(2001) demonstrate that under these assumptions there always are distributions
for which (25) is satisfied for one group. Here are two numerical examples:
G 5 with one group being 1/3 of the population and the other four of size 1/6;
and G 4 with one group of size 1/2 and the other three of size 1/614.
As in the case of fixed coefficients conflict occurs in very skewed
distributions by size. One large group together with a number of small sized
groups is the type of distribution that would be more likely to generate open
conflict. Because of the returns to scale in conflict, the win probability of the large
group may amply exceed its population share. Furthermore, precisely because of
the returns to scale the small groups will be deterred from expending much
resources in such an uneven conflict and hence we shall observe a low conflict
loss R. High win probabilities together with small aggregate losses make conflict
preferable to peace as far as the large group is concerned.
Therefore, we may conclude that with G ! 2 under the proportional rule we may
have conflict. This will be associated with distributions with low polarization and
high fractionalization. However, the relationship will be non-monotonic: additional
increases in fractionalization may bring peace rather than further conflict.
In order to illustrate this relationship consider the following parametric
example. There are three groups with n1 = ½, n2 = O ½, and n3 = (1- O ½, 0 ” O
” ½. When O = 0 we have two groups with the same population and thus
maximal polarization. When O = ½ we shall have the same first group facing two
groups of half the size. F and P can be computed to be
F(O)
1 O O2
, and
2
(26)
3 O O2 1 F
P(O)
.
(27)
8
2 4
From (27) it is plain that when O changes fractionalization and polarization
move in opposite directions: as we move away from the perfect bipolar
distribution P comes down but F goes up.
Using this parametrization for the distribution of the population in expression
(12) we implicitly obtain the equilibrium intensity of conflict R as a function of O .
Totally differentiating, we obtain that R decreases as O increases, i.e. as P
14
The case of India has been taken as a critical test for Lijphart’s claim that “consociational”
systems –hence proportional– are guarantors of ethnic peace. Most of the debate, Lijphart
(1996) and Wilkinson (2000), has focused on whether India was more “consociational” under
Nerhu or more recently. Our analysis suggests that the change in population sizes of Hindus,
Muslims and others that has actually taken place in India in 1961-2001 might also have a role
in explaining the evolution of ethnic conflict.
— 25 —
decreases and as F increases. Conflict intensity goes from R(0) = 0.5 to R(1/2) =
0.211. This is depicted in figure 5.
Whether there will be conflict or peace under the proportional rule depends
on whether the untouched group –always with population ½– obtains a conflict
equilibrium utility higher or lower than ½. In figure 5 we also depict u1 as a
function of O . Not surprisingly, as O increases group 1 is facing smaller and
smaller enemies. Hence, u1 increases with O . The large group obtains a higher
utility from conflict the less polarized the distribution is. The equilibrium utility
goes from u1 (0) = 0.375 to u1 (1/2) = 0.837. It follows that for low O the
equilibrium utility of group 1 will be below the peace payoff and there will be
peace. This corresponds to the highest levels of polarization and lowest of
fractionalization. For O ! O0 [see figure 5] there will be conflict. Therefore, open
conflict will be associated with low polarization and high fractionalization.
Figure 5
~
5
6
u1
1
2
3
8
O
0
1
2
O
We finally combine the intensity with the occurrence of conflict and derive
the relationship between observable intensity of conflict and both
fractionalization and polarization. This is depicted in figure 6. As we can see, in
both cases the relation is nonmonotonic. For the case of fractionalization, there
is peace until the threshold level F0 is reached. At this point, there is conflict
and it attains its maximum intensity. For higher values of F we continue to have
conflict but its intensity monotonically comes down. The relationship between P
and observable intensity of conflict is the other side of the coin. Open conflict
occurs at low levels of polarization. As polarization goes up the intensity of
conflict raises until the threshold P0 is attained. For higher levels of polarization
— 26 —
Instituto de Estudios Fiscales
the costs of conflict are so high that we will observe peace. The two functions
are depicted in figure 6.
Figure 6
R
R
F0
F
P0
P
Summing up
When we consider distributions with more than two groups it is still true that
the occurrence of conflict critically depends on the particular political system in
place. Dictatorship and the majoritarian rule can never bring peace, as we
already observed for G 2 . But in general, both fixed shares and proportional
rule fail to universally guarantee peaceful outcomes. We shall not see conflict
neither for very low nor for very high levels of fractionalization15 and a similar
(but inverse) pattern would be followed by polarization.
Concerning the general relationship between polarization, fractionalization and
conflict our results suggest that they will be significantly nonlinear. Under some
political systems the occurrence of conflict is independent of the shape of the
distribution while in other systems it does depend on the shape. Under the first
class of political systems the intensity of conflict will be closely (positively) related
to the degree of polarization (and negatively to fractionalization). Under the second
class (fixed and proportional shares) we shall observe zero intensity at high and
very low levels of polarization (and fractionalization). For the range of levels of
15
This seems to contradict the result obtained by our parametric example above. This is due
to the very special change in the distribution that our parametrization allows for. Consider for
instance our limit case with l = ½ (n1 = ½, n2 = ¼, n3 = ¼). Fractionalization is maximal and
we still have conflict. However, if we now move to n1 = n2 = n3 = 1/3 –not allowed by our
parametrization– fractionalization would be even higher but there would be no conflict.
— 27 —
polarization for which we shall have conflict, higher polarization will be positively
related to higher intensity of conflict. As far as fractionalization is concerned there
seems to be no regular relationship between its level and the intensity of conflict.
All these results suggest that there may be more to be learned from
empirical exercises that put all the evidence together and also attempt to
control for the political system of each country16.
6. CONCLUSIONS
We provide an analytical framework that permits an interpretation of recent
empirical exercises attempting to identify a meaningful relationship between
population distributions over opposing groups and emergence or intensity of
conflict. Conflict breaks out when the payoffs delivered by the political system fall
short of what one group can obtain by precipitating conflict. While the intensity of
conflict clearly depends on the shape of the distribution, the occurrence of conflict
also depends on the responsiveness of each political system to the popular
support for each of the competing alternatives. When we combine occurrence
with intensity, the relationship between conflict and polarization/fractionalization
becomes significantly non-linear and contingent on the ruling political system.
The rationale behind our result is quite straightforward. Conflict is costly.
That is overall payoffs are less than what are achievable under peace. The
costlier conflict is (if it actually takes place) the easier it becomes to assign
payoffs to groups that Pareto dominate what they can obtain under conflict.
Therefore, only the political systems with very unfair outcomes (such as
dictatorship or majoritarian rule) will be always be challenged even when the
cost of doing so is high. However, under “fairer” systems no group would be
willing to pay too high a cost to obtain a different payoff. Therefore, it is only
when conflict is nearly costless to one group (such as the case of one large
group and a number of small opponents) that the outcome of the political
system will be challenged, by that precisely that large group17.
16
Political scientists have been aware for long of the critical role played by the political
institutions in preventing domestic conflict. The work of Lijphart (1977) is fundamental here.
See also the recent controversy between Horowitz (2006) and Fraenkel and Grofman (2006)
on the effectiveness of constitutional engineering. Our point is that in spite of this important
line of literature, empirical tests on the determinants of conflict have very seldom controlled
for the political system. An exception is the work by Reynal-Querol (2002b, 2005) and by
Schneider and Wiesehomeier (2006b) who do study the relationship between political
systems and domestic conflict.
17
Note the similarity of this point with the findings of Collier (2001) on the dominant
ethnicity provoking civil war. One should qualify these points, however, by observing that
small groups can provoke conflict when private goods are at stake. For more on this issue,
see Esteban and Ray (2006b).
— 28 —
Instituto de Estudios Fiscales
Highly polarized situations may well be fairly peaceful. This is what happened
during the Cold War period, for instance. The cost of challenging the
international status quo was so immense that even if one of the two sides
considered the division of international power disproportionate it could not-or
would not-trigger a world conflict. At the same time, when polarization is
extremely low, there is little to fight about. Consequently, we would expect the
overall degree of conflict to be maximal in societies with intermediate levels of
polarization.
What, then, are the hopes for the empirical exercises that try to identify a
relationship between polarization/fractionalization and conflict? Two
recommendations appear to emerge. First, there should be a serious attempt to
account for the nonlinearity. For instance, in a parametric context, some
progress may be possible by entering both polarization and its square on the
right-hand-side of a regression18. But the prescription is simply this: the
empirical specification needs to be more firmly grounded in theory, even if that
theory is extremely simple.
Second, we have seen that the incidence of conflict depends not only on the
shape of the distribution but also critically on the ruling political system.
Alternative political systems perform quite differently in guaranteeing peace. For
the countries with political systems that always yield conflict we shall observe
that the intensity of conflict is (roughly) positively related to polarization (and
negatively) to fractionalization. However, in countries with political systems that
may yield peace, the occurrence and intensity of conflict will typically have a
highly non-linear relationship with polarization and/or fractionalization. It follows
that the exercise critically demands that political systems be controlled for19.
18
On a similar issue arising in the empirical debate on inequality and growth (though for very
different reasons), see Banerjee and Duflo (2003).
19
Reynal-Querol (2002b) has tested the relationship between type of political system (their
degree of inclusiveness) and conflict. However, in Montalvo and Reynal-Querol (2005) the
empirical test of whether polarization or fractionalization are the best predictors for conflict
does not use the political systems as controls. Schneider and Wieserhomeier (2006b) also
emphasize the critical role played by the political institutions in the occurrence of conflict.
— 29 —
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— 32 —
SÍNTESIS
PRINCIPALES IMPLICACIONES DE POLÍTICA ECONÓMICA
Explícita o implícitamente se justifica la necesidad de la redistribución de la renta
con el argumento de que una excesiva desigualdad amenaza la cohesión social y puede
provocar situaciones de conflicto abierto. Este es el argumento central del reciente
trabajo de Acemoglu y Robinson (2000) –véase también su reciente libro– sobre la
extensión del derecho de voto en muchos países industrializados a finales del siglo
XIX. Dar derecho de voto a los trabajadores industriales era la forma de garantizar la
irreversibilidad de un nivel de redistribución de renta que desalentase las tentaciones
revolucionarias. Otro ejemplo del mismo razonamiento [quizás más cercano a temas
relevantes para España] es el trabajo de Lebreton y Weber (2003) y Haimanko,
Lebreton y Weber (2005) en el que estudian el diseño de transferencias
interregionales que eviten secesiones en un estado. De hecho, este tema no es más
que otra forma de plantear el clásico dilema en Economía Pública entre los objetivos
de eficiencia y equidad. Los incentivos que demanda la mera eficiencia pueden ser
incompatibles con la mínima equidad necesaria para garantizar la paz social.
Esta cuestión está también en el centro del actual debate sobre las causas de los
frecuentes conflictos étnicos, religiosos y nacionalistas que parecen caracterizar el
mundo contemporáneo tras el colapso de la URSS. Si los conflictos ocurren y tienen
altos costes económicos ha de ser cierto que los mecanismos políticos no han
permitido establecer el grado de redistribución que hubiese impedido el conflicto. El
tema del presente trabajo es precisamente el estudio de la relación entre la
distribución de la población, el sistema político vigente y la existencia de conflicto.
Tal como se argumenta en Esteban y Ray (1994 y 1999), es la polarización, más que
la desigualdad, la que conduce al conflicto. En Esteban y Ray (1999) se presenta un
modelo de conflicto en el que se demuestra que el nivel de conflicto de equilibrio
crece con el grado de polarización. Sin embargo, ello es cierto en el caso de que
efectivamente haya conflicto. Situémonos en el momento en el que hay que decidir si
se acepta el status quo o se desencadena una situación de conflicto. El hecho de saber
que el conflicto va a ser muy intenso y costoso hace que para todos los grupos
participantes el conflicto sea poco atractivo y que, por tanto, la decisión óptima sea la
paz. Al contrario, cuando las ganancias esperadas de un conflicto son pequeñas, el
coste del conflicto será también pequeño, por lo que puede resultar que el balance
neto de un conflicto sea positivo. De este argumento se sigue que la relación entre
desigualdad/conflicto será no-lineal.
Los politólogos siempre han estado interesados en la relación entre desigualdad y
conflicto: Brockett (1992), Midlarski (1988), Muller y Seligson (1987), y Muller,
Seligson y Fu (1989). Midlarski (1988) y Muller, Seligson y Fu (1989) ya han
manifestado sus reservas respecto a las nociones estándar de desigualdad como
— 33 —
instrumento útil para el análisis del conflicto. Mucho antes, Nagel (1974) ya argumentó
que la relación entre desigualdad y conflicto tenía que ser no-lineal. Con todo, tal
como concluye el survey de Lichbach (1989), el resultado de todas estas
contribuciones es completamente ambiguo.
En el área de la Economía, el interés es mucho más reciente, pero los resultados no
son mejores. La relación entre desigualdad y conflicto ha sido estudiada desde la
perspectiva del desarrollo económico [ver Bénabou (1996) para un detallado survey].
Tras la contribución de Easterly y Levine (1997) –quien puso énfasis en la
“fraccionalización” (en vez de la desigualdad)– han habido contribuciones relevantes
por parte de Alesina et al. (2003), Collier (1998, 2001), Collier y Hoeffler (2004),
Fearon y Laitin (2003), Hegre et al. (2001), La Porta et al. (1999), Montalvo and
Reynal-Querol (2005), Reynal-Querol (2002) y Schneider y Wiesehomeier (2006).
Donde los resultados empíricos son más esperanzadores es en el papel de la
polarización en el conflicto, tal como se desprende del trabajo de Montalvo y ReynalQuerol (2005). Pero aún en esta cuestión existen dudas y ambigüedades. ¿Cuándo
puede decirse que una sociedad está en conflicto? ¿Hemos de medir la eclosión de un
conflicto o la frecuencia con la que un país se encuentra en conflicto?.
El objetivo de esta investigación es proporcionar un marco analítico que permite
desarrollar un estudio ordenado del efecto de la desigualdad y/o polarización sobre el
conflicto. Para ello, construimos un modelo de conflicto y computamos los pagos de
equilibrio que reciben los jugadores. El status quo contra el que los grupos sociales
pueden rebelarse está caracterizado por un conjunto de instituciones políticas que
canalizan los distintos intereses contrapuestos hacia una decisión colectiva. La
democracia proporcional o mayoritaria, la oligarquía o la dictadura son ejemplos de
instituciones políticas. Habrá paz social siempre que las instituciones políticas
proporcionen a todos los grupos sociales un pago no inferior al que pueden obtener
provocando una situación de conflicto.
Con este marco analítico demostramos los siguientes puntos: (i) las medidas de
fraccionalización y de polarización tienden a ir en direcciones opuestas; (ii) el que pueda
o no estallar un conflicto depende críticamente del sistema político vigente; (iii) el que
haya conflicto y su intensidad tienden a moverse en direcciones opuestas; (iv) la relación
del conflicto tanto con polarización como con fraccionalización es no-monotónica; y (v)
la intensidad del conflicto depende positivamente del nivel de polarización.
Las implicaciones de este trabajo son relevantes respecto a la reciente literatura
que intenta establecer empíricamente un nexo entre desigualdad o polarización y
conflicto social. La relación entre política fiscal, distribución de la renta, polarización y
cohesión social es bien conocida. Las distorsiones creadas por los impuestos
redistributivos son el coste necesario para moderar la conflictividad social potencial.
Esta visión está basada en la visión de que la única fuente relevante de conflictos
sociales deriva de las desigualdades económicas entre “clases”. Cuanto mayor es la
desigualdad más probable es que se registre conflictividad social. Por lo tanto, según
esta visión, un grado suficiente de igualdad garantiza la paz y cohesión social.
Este argumento presentas dos problemas. En primer lugar, hay motivos para
sospechar que la relación entre conflicto y tanto desigualdad como polarización es no­
— 34 —
lineal. Ello implica que situaciones con un moderado grado de desigualdad pueden
conducir al conflicto social, mientras que situaciones extremadamente polarizadas
puede ser compatibles con la paz social. En segundo lugar, y siguiendo con el punto de
vista de la política presupuestaria y fiscal, este trabajo sugiere que en la distribución de
los recursos públicos es preciso tener presente otras dimensiones, aparte de las clases
sociales definidas por nivel de renta. Los recientes argumentos sobre “balanzas
fiscales” territoriales indican un incremento de la sensibilidad en esta dimensión. Pero
tampoco hay que descartar otras dimensiones, como la religiosa o la étnica que
pueden estar actualmente latentes.
En síntesis, la visión subyacente a la Economía Pública de la segunda mitad del siglo
XX ha estado dominada por la necesidad de moderar las desigualdades generadas por
el mercado con el fin de evitar un conflicto entre clases sociales. El actual estado del
bienestar ha sido la respuesta europea a este reto y ha alejado completamente el
riesgo de una revolución social. Sin embargo, observamos que en la actualidad las
fracturas sociales se fundamentan en motivos nacionalistas, religiosos o étnicos, frente
a los cuales aún aplicamos de forma inercial los razonamientos del siglo pasado. La
política redistributiva no debería perder de vista la distribución de recursos sociales –
especialmente los de la administración– teniendo también en cuenta las nuevas
características relevantes. Tal como se razona –y se demuestra– en este trabajo, el
que en estas nuevas dimensiones las desigualdades no sean muy grandes no es
indicativo de que no puedan ser pronto una fuente de conflicto abierto.
REFERENCIAS
ACEMOGLU, D. and ROBINSON, J.A. (2000): "Why Did The West Extend The Franchise?
Democracy, Inequality, And Growth In Historical Perspective," The Quarterly
Journal of Economics 115, 1167-1199.
ALESINA, A.; DEVLEESCHAUWER, A.; EASTERLY, W.; KURLAT, S. and WACZIARG, R. (2003):
“Fractionalization.” Journal of Economic Growth 8, 155-194.
BÉNABOU, R. (1996): “Inequality and Growth,” NBER Macroeconomics Annual, B.
Bernanke and J. Rotemberg eds. MIT Press, 11-74.
COLLIER, P. (1998): “The Political Economy of Ethnicity.” Paper prepared for the
Annual World Bank Conference on Development Economics, Washington D.C.,
april 20-21, 1998.
– (2001): “Implications of Ethnic Diversity.” Economic Policy 129-66.
COLLIER, P. and HOEFFLER, A. (1998): “On economic causes of civil war.” Oxford
Economic Papers 50, 563–573.
– (2004): “Greed and Grievance in Civil War”. Oxford Economic Papers 56, 563-95.
EASTERLY, W. and LEVINE, R. (1997): “Africa’s Growth Tragedy: Policies and Ethnic
Divisions.” Quarterly Journal of Economics 112, 1203-50.
— 35 —
ESTEBAN, J. and RAY, D. (1994): “On the Measurement of Polarization.” Econometrica
62, 819-51.
– (1999): “Conflict and Distribution.” Journal of Economic Theory 87, 379-415
FEARON, J.D. and LAITIN, D.D. (2003): “Ethnicity, Insurgency, and Civil War.” American
Political Science Review 97, 75-90.
FRAENKEL, J. and GROFMAN, B. (2006): “Does the alternative vote foster moderation in
ethnically divided societies? The case of Fiji.” Comparative Political Studies 39, 623-651.
HAIMANKO O.; LEBRETON, M. and WEBER, S. (2005): "Transfers in a Polarized Country
Bridging the Gap between Efficiency and Stability", Journal of Public Economics 89,
1277-1303
HEGRE, H.; ELLINGSON, T.; GATES, S. and GLEDITSCH, N.P. (2001): "Towards a
Democratic Civil Peace? Democracy, Political Change, and Civil War, 1816-1992."
American Political Science Review 95, 33-48.
LA PORTA, R.; LOPEZ DE SILANES, F.; SHLEIFER, A. and VISHINY, R. (1999): “The Quality
of Government.” Journal of Law Economics and Organization 15, 222-79.
LEBRETON M. and S. WEBER, S. (2003): "The Art of Making Everybody Happy: How to
Prevent a Secession", IMF Staff Papers 50, 403-435.
MONTALVO, J.G. and REYNAL-QUEROL, M. (2005): “Ethnic Polarization, Potential
Conflict, and Civil Wars.” American Economic Review 95, 796-815.
REYNAL-QUEROL, M. (2000): “Ethnicity, Political Systems, and Civil Wars.” Journal of
Conflict Resolution 46, 29-54.
– (2005): “Does Democracy Preempt Civil Wars?.” European Journal of Political
Economy 21, 445-465.
SCHNEIDER, G. and WIESEHOMEIER, N. (2006): “Ethnic Polarization, Potential Conflict,
and Civil Wars, Comment.” Unpublished Manuscript.
— 36 —
NORMAS DE PUBLICACIÓN DE PAPELES DE TRABAJO DEL
INSTITUTO DE ESTUDIOS FISCALES
Esta colección de Papeles de Trabajo tiene como objetivo ofrecer un vehículo de
expresión a todas aquellas personas interasadas en los temas de Economía Pública. Las
normas para la presentación y selección de originales son las siguientes:
1. Todos los originales que se presenten estarán sometidos a evaluación y podrán
ser directamente aceptados para su publicación, aceptados sujetos a revisión, o
rechazados.
2. Los trabajos deberán enviarse por duplicado a la Subdirección de Estudios
Tributarios. Instituto de Estudios Fiscales. Avda. Cardenal Herrera Oria, 378. 28035
Madrid.
3. La extensión máxima de texto escrito, incluidos apéndices y referencias
bibliográfícas será de 7000 palabras.
4. Los originales deberán presentarse mecanografiados a doble espacio. En la primera
página deberá aparecer el título del trabajo, el nombre del autor(es) y la institución a la
que pertenece, así como su dirección postal y electrónica. Además, en la primera
página aparecerá también un abstract de no más de 125 palabras, los códigos JEL y las
palabras clave.
5. Los epígrafes irán numerados secuencialmente siguiendo la numeración arábiga.
Las notas al texto irán numeradas correlativamente y aparecerán al pie de la
correspondiente página. Las fórmulas matemáticas se numerarán secuencialmente
ajustadas al margen derecho de las mismas. La bibliografía aparecerá al final del
trabajo, bajo la inscripción “Referencias” por orden alfabético de autores y, en cada
una, ajustándose al siguiente orden: autor(es), año de publicación (distinguiendo a, b, c
si hay varias correspondientes al mismo autor(es) y año), título del artículo o libro,
título de la revista en cursiva, número de la revista y páginas.
6. En caso de que aparezcan tablas y gráficos, éstos podrán incorporarse
directamente al texto o, alternativamente, presentarse todos juntos y debidamente
numerados al final del trabajo, antes de la bibliografía.
7. En cualquier caso, se deberá adjuntar un disquete con el trabajo en formato word.
Siempre que el documento presente tablas y/o gráficos, éstos deberán aparecer en
ficheros independientes. Asimismo, en caso de que los gráficos procedan de tablas
creadas en excel, estas deberán incorporarse en el disquete debidamente identificadas.
Junto al original del Papel de Trabajo se entregará también un resumen
de un máximo de dos folios que contenga las principales implicaciones de
política económica que se deriven de la investigación realizada.
— 37 —
PUBLISHING GUIDELINES OF WORKING PAPERS AT THE
INSTITUTE FOR FISCAL STUDIES
This serie of Papeles de Trabajo (working papers) aims to provide those having an
interest in Public Economics with a vehicle to publicize their ideas. The rules gover­
ning submission and selection of papers are the following:
1. The manuscripts submitted will all be assessed and may be directly accepted for
publication, accepted with subjections for revision or rejected.
2. The papers shall be sent in duplicate to Subdirección General de Estudios
Tributarios (The Deputy Direction of Tax Studies), Instituto de Estudios Fiscales
(Institute for Fiscal Studies), Avenida del Cardenal Herrera Oria, nº 378, Madrid
28035.
3. The maximum length of the text including appendices and bibliography will be no
more than 7000 words.
4. The originals should be double spaced. The first page of the manuscript should
contain the following information: (1) the title; (2) the name and the institutional affi­
liation of the author(s); (3) an abstract of no more than 125 words; (4) JEL codes and
keywords; (5) the postal and e-mail address of the corresponding author.
5. Sections will be numbered in sequence with arabic numerals. Footnotes will be
numbered correlatively and will appear at the foot of the corresponding page.
Mathematical formulae will be numbered on the right margin of the page in sequence.
Bibliographical references will appear at the end of the paper under the heading
“References” in alphabetical order of authors. Each reference will have to include in this
order the following terms of references: author(s), publishing date (with an a, b or c in
case there are several references to the same author(s) and year), title of the article or
book, name of the journal in italics, number of the issue and pages.
6. If tables and graphs are necessary, they may be included directly in the text or
alternatively presented altogether and duly numbered at the end of the paper, before
the bibliography.
7. In any case, a floppy disk will be enclosed in Word format. Whenever the
document provides tables and/or graphs, they must be contained in separate files.
Furthermore, if graphs are drawn from tables within the Excell package, these must
be included in the floppy disk and duly identified.
Together with the original copy of the working paper a brief two-page
summary highlighting the main policy implications derived from the
research is also requested.
— 38 —
ÚLTIMOS PAPELES DE TRABAJO EDITADOS POR EL INSTITUTO DE ESTUDIOS FISCALES 2004
01/04 Una propuesta para la regulación de precios en el sector del agua: el caso español. Autores: M.a Ángeles García Valiñas y Manuel Antonio Muñiz Pérez. 02/04 Eficiencia en educación secundaria e inputs no controlables: sensibilidad de los
resultados ante modelos alternativos.
Autores: José Manuel Cordero Ferrera, Francisco Pedraja Chaparro y Javier Salinas Jiménez.
03/04 Los efectos de la política fiscal sobre el ahorro privado: evidencia para la OCDE.
Autores: Montserrat Ferre Carracedo, Agustín García García y Julián Ramajo Hernández.
04/04 ¿Qué ha sucedido con la estabilidad del empleo en España? Un análisis desagregado
con datos de la EPA: 1987-2003.
Autores: José María Arranz y Carlos García-Serrano.
05/04 La seguridad del empleo en España: evidencia con datos de la EPA (1987-2003).
Autores: José María Arranz y Carlos García-Serrano.
06/04 La ley de Wagner: un análisis sintético.
Autor: Manuel Jaén García.
07/04 La vivienda y la reforma fiscal de 1998: un ejercicio de simulación.
Autor: Miguel Ángel López García.
08/04 Modelo dual de IRPF y equidad: un nuevo enfoque teórico y su aplicación al caso español.
Autor: Fidel Picos Sánchez.
09/04 Public expenditure dynamics in Spain: a simplified model of its determinants.
Autores: Manuel Jaén García y Luis Palma Martos.
10/04 Simulación sobre los hogares españoles de la reforma del IRPF de 2003. Efectos sobre
la oferta laboral, recaudación, distribución y bienestar.
Autores: Juan Manuel Castañer Carrasco, Desiderio Romero Jordán y José Félix Sanz Sanz.
11/04 Financiación de las Haciendas regionales españolas y experiencia comparada.
Autor: David Cantarero Prieto.
12/04 Multidimensional indices of housing deprivation with application to Spain.
Autores: Luis Ayala y Carolina Navarro.
13/04 Multiple ocurrence of welfare recipiency: determinants and policy implications.
Autores: Luis Ayala y Magdalena Rodríguez.
14/04 Imposición efectiva sobre las rentas laborales en la reforma del impuesto sobre la renta
personal (IRPF) de 2003 en España.
Autoras: María Pazos Morán y Teresa Pérez Barrasa.
15/04 Factores determinantes de la distribución personal de la renta: un estudio empírico a
partir del PHOGUE.
Autores: Marta Pascual y José María Sarabia.
16/04 Política familiar, imposición efectiva e incentivos al trabajo en la reforma de la
imposición sobre la renta personal (IRPF) de 2003 en España.
Autoras: María Pazos Morán y Teresa Pérez Barrasa.
17/04 Efectos del déficit público: evidencia empírica mediante un modelo de panel dinámico
para los países de la Unión Europea.
Autor: César Pérez López.
— 39 —
18/04 Inequality, poverty and mobility: Choosing income or consumption as welfare
indicators.
Autores: Carlos Gradín, Olga Cantó y Coral del Río.
19/04 Tendencias internacionales en la financiación del gasto sanitario.
Autora: Rosa María Urbanos Garrido.
20/04 El ejercicio de la capacidad normativa de las CCAA en los tributos cedidos: una
primera evaluación a través de los tipos impositivos efectivos en el IRPF.
Autores: José María Durán y Alejandro Esteller.
21/04 Explaining. budgetary indiscipline: evidence from spanish municipalities.
Autores: Ignacio Lago-Peñas y Santiago Lago-Peñas.
22/04 Local governmets' asymmetric reactions to grants: looking for the reasons.
Autor: Santiago Lago-Peñas.
23/04 Un pacto de estabilidad para el control del endeudamiento autonómico.
Autor: Roberto Fernández Llera
24/04 Una medida de la calidad del producto de la atención primaria aplicable a los análisis
DEA de eficiencia.
Autora: Mariola Pinillos García.
25/04 Distribución de la renta, crecimiento y política fiscal.
Autor: Miguel Ángel Galindo Martín.
26/04 Políticas de inspección óptimas y cumplimiento fiscal.
Autores: Inés Macho Stadler y David Pérez Castrillo.
27/04 ¿Por qué ahorra la gente en planes de pensiones individuales?
Autores: Félix Domínguez Barrero y Julio López-Laborda.
28/04 La reforma del Impuesto sobre Actividades Económicas: una valoración con
microdatos de la ciudad de Zaragoza.
Autores: Julio López-Laborda, M.ª Carmen Trueba Cortés y Anabel Zárate Marco.
29/04 Is an inequality-neutral flat tax reform really neutral?
Autores: Juan Prieto-Rodríguez, Juan Gabriel Rodríguez y Rafael Salas.
30/04 El equilibrio presupuestario: las restricciones sobre el déficit.
Autora: Belén Fernández Castro.
2005
01/05 Efectividad de la política de cooperación en innovación: evidencia empírica española.
Autores:Joost Heijs, Liliana Herrera, Mikel Buesa, Javier Sáiz Briones y Patricia Valadez.
02/05 A probabilistic nonparametric estimator.
Autores: Juan Gabriel Rodríguez y Rafael Salas.
03/05 Efectos redistributivos del sistema de pensiones de la seguridad social y factores
determinantes de la elección de la edad de jubilación. Un análisis por comunidades
autónomas.
Autores: Alfonso Utrilla de la Hoz y Yolanda Ubago Martínez.
14/05 La relación entre los niveles de precios y los niveles de renta y productividad en los países
de la zona euro: implicaciones de la convergencia real sobre los diferenciales de inflación.
Autora: Ana R. Martínez Cañete.
05/05 La Reforma de la Regulación en el contexto autonómico. Autor: Jaime Vallés Giménez. — 40 — 06/05 Desigualdad y bienestar en la distribución intraterritorial de la renta, 1973-2000.
Autores: Luis Ayala Cañón, Antonio Jurado Málaga y Francisco Pedraja Chaparro.
07/05 Precios inmobiliarios, renta y tipos de interés en España.
Autor: Miguel Ángel López García.
08/05 Un análisis con microdatos de la normativa de control del endeudamiento local.
Autores: Jaime Vallés Giménez, Pedro Pascual Arzoz y Fermín Cabasés Hita.
09/05 Macroeconomics effects of an indirect taxation reform under imperfect competition.
Autor: Ramón J. Torregrosa.
10/05 Análisis de incidencia del gasto público en educación superior: nuevas aproximaciones.
Autora: María Gil Izquierdo.
11/05 Feminización de la pobreza: un análisis dinámico.
Autora: María Martínez Izquierdo.
12/05 Efectos del impuesto sobre las ventas minoristas de determinados hidrocarburos en la
economía extremeña: un análisis mediante modelos de equilibrio general aplicado.
Autores: Francisco Javier de Miguel Vélez, Manuel Alejandro Cardenete Flores y Jesús
Pérez Mayo.
13/05 La tarifa lineal de Pareto en el contexto de la reforma del IRPF.
Autores: Luis José Imedio Olmedo, Encarnación Macarena Parrado Gallardo y María
Dolores Sarrión Gavilán.
14/05 Modelling tax decentralisation and regional growth.
Autores: Ramiro Gil-Serrate y Julio López-Laborda.
15/05 Interactions inequality-polarization: characterization results.
Autores: Juan Prieto-Rodríguez, Juan Gabriel Rodríguez y Rafael Salas.
16/05 Políticas de competencia impositiva y crecimiento: el caso irlandés.
Autores: Santiago Díaz de Sarralde, Carlos Garcimartín y Luis Rivas.
17/05 Optimal provision of public inputs in a second-best scenario.
Autores: Diego Martínez López y A. Jesús Sánchez Fuentes.
18/05 Nuevas estimaciones del pleno empleo de las regiones españolas.
Autores: Javier Capó Parrilla y Francisco Gómez García.
19/05 US deficit sustainability revisited: a multiple structural change approach.
Autores: Óscar Bajo-Rubio. Carmen Díaz-Roldán y Vicente Esteve.
20/05 Aproximación a los pesos de calidad de vida de los “Años de Vida Ajustados por
Calidad” mediante el estado de salud autopercibido.
Autores: Anna García-Altés, Jaime Pinilla y Salvador Peiró.
21/05 Redistribución y progresividad en el Impuesto sobre Sucesiones y Donaciones: una
aplicación al caso de Aragón.
Autor: Miguel Ángel Barberán Lahuerta.
22/05 Estimación de los rendimientos y la depreciación del capital humano para las regiones
del sur de España.
Autora: Inés P. Murillo.
23/05 El doble dividendo de la imposición ambiental. Una puesta al día.
Autor: Miguel Enrique Rodríguez Méndez.
24/05 Testing for long-run purchasing power parity in the post bretton woods era: evidence
from old and new tests.
Autor: Julián Ramajo Hernández y Montserrat Ferré Cariacedo.
— 41 —
25/05 Análisis de los factores determinantes de las desigualdades internacionales en las
emisiones de CO2 per cápita aplicando el enfoque distributivo: una metodología de
descomposición por factores de Kaya.
Autores: Juan Antonio Duro Moreno y Emilio Padilla Rosa.
26/05 Planificación fiscal con el impuesto dual sobre la renta.
Autores: Félix Domínguez Barrero y Julio López Laborda.
27/05 El coste recaudatorio de las reducciones por aportaciones a planes de pensiones y las
deducciones por inversión en vivienda en el IRPF 2002.
Autores: Carmen Marcos García, Alfredo Moreno Sáez, Teresa Pérez Barrasa y César
Pérez López.
28/05 La muestra de declarantes IEF-AEAT 2002 y la simulación de reformas fiscales:
descripción y aplicación práctica.
Autores: Alfredo Moreno, Fidel Picos, Santiago Díaz de Sarralde, María Antiqueira y
Lucía Torrejón.
2006
01/06 Capital gains taxation and progressivity.
Autor: Julio López Laborda.
02/06 Pigou’s dividend versus Ramsey’s dividend in the double dividend literature.
Autores: Eduardo L. Giménez y Miguel Rodríguez.
03/06 Assessing tax reforms. Critical comments and proposal: the level and distance effects.
Autores: Santiago Díaz de Sarralde Míguez y Jesús Ruiz-Huerta Carbonell.
04/06 Incidencia y tipos efectivos del impuesto sobre el patrimonio e impuesto sobre
sucesiones y donaciones.
Autora: Laura de Pablos Escobar.
05/06 Descentralización fiscal y crecimiento económico en las regiones españolas. Autores: Patricio Pérez González y David Cantarero Prieto. 16/06 Efectos de la corrupción sobre la productividad: un estudio empírico para los países
de la OCDE.
Autores: Javier Salinas Jiménez y M.ª del Mar Salinas Jiménez.
07/06 Simulación de las implicaciones del equilibrio presupuestario sobre la política de
inversión de las comunidades autónomas.
Autores: Jaime Vallés Giménez y Anabel Zárate Marco.
18/06 The composition of public spending and the nationalization of party sistems in western
Europe.
Autores: Ignacio Lago-Peñas y Santiago Lago.Peñas.
09/06 Factores explicativos de la actividad reguladora de las Comunidades Autónomas
(1989-2001).
Autores: Julio López Laborda y Jaime Vallés Giménez.
10/06 Disciplina credititicia de las Comunidades Autónomas.
Autor: Roberto Fernández Llera.
11/06 Are the tax mix and the fiscal pressure converging in the European Union?.
Autor: Francisco J. Delgado Rivero.
12/06 Redistribución, inequidad vertical y horizontal en el impuesto sobre la renta de las
personas físicas (1982-1998).
Autora: Irene Perrote.
— 42 — 13/06 Análisis económico del rendimiento en la prueba de conocimientos y destrezas
imprescindibles de la Comunidad de Madrid.
Autores: David Trillo del Pozo, Marta Pérez Garrido y José Marcos Crespo.
14/06 Análisis de los procesos privatizadores de empresas públicas en el ámbito internacional.
Motivaciones: moda política versus necesidad económica.
Autores: Almudena Guarnido Rueda, Manuel Jaén García e Ignacio Amate Fortes.
15/06 Privatización y liberalización del sector telefónico español.
Autores: Almudena Guarnido Rueda, Manuel Jaén García e Ignacio Amate Fortes.
16/06 Un análisis taxonómico de las políticas para PYME en Europa: objetivos, instrumentos
y empresas beneficiarias.
Autor: Antonio Fonfría Mesa.
17/06 Modelo de red de cooperación en los parques tecnológicos: un estudio comparado.
Autora: Beatriz González Vázquez.
18/06 Explorando la demanda de carburantes de los hogares españoles: un análisis de
sensibilidad.
Autores: Santiago Álvarez García, Marta Jorge García-Inés y Desiderio Romero Jordán.
19/06 Cross-country income mobility comparisons under panel attrition: the relevance of
weighting schemes.
Autores: Luis Ayala, Carolina Navarro y Mercedes Sastre.
20/06 Financiación Autonómica: algunos escenarios de reforma de los espacios fiscales.
Autores: Ana Herrero Alcalde, Santiago Díaz de Sarralde, Javier Loscos Fernández,
María Antiqueira y José Manuel Tránchez.
21/06 Child nutrition and multiple equilibria in the human capital transition function.
Autores: Berta Rivera, Luis Currais y Paolo Rungo.
22/06 Actitudes de los españoles hacia la hacienda pública.
Autor: José Luis Sáez Lozano.
23/06 Progresividad y redistribución a través del IRPF español: un análisis de bienestar social
para el periodo 1982-1998.
Autores: Jorge Onrubia Fernández, María del Carmen Rodado Ruiz, Santiago Díaz de
Sarralde y César Pérez López.
24/06 Análisis descriptivo del gasto sanitario español: evolución, desglose, comparativa
internacional y relación con la renta.
Autor: Manuel García Goñi.
25/06 El tratamiento de las fuentes de renta en el IRPF y su influencia en la desigualdad y la
redistribución.
Autores: Luis Ayala Cañón, Jorge Onrubia Fernández y María del Carmen Rodado Ruiz.
26/06 La reforma del IRPF de 2007: una evaluación de sus efectos.
Autores: Santiago Díaz de Sarralde Míguez, Fidel Picos Sánchez, Alfredo Moreno Sáez,
Lucía Torrejón Sanz y María Antiqueira Pérez.
27/06 Proyección del cuadro macroeconómico y de las cuentas de los sectores
institucionales mediante un modelo de equilibrio.
Autores: Ana María Abad, Ángel Cuevas y Enrique M. Quilis.
28/06 Análisis de la propuesta del tesoro Británico “Fiscal Stabilisation and EMU” y de sus
implicaciones para la política económica en la Unión Europea.
Autor: Juan E. Castañeda Fernández.
— 43 —
29/06 Choosing to be different (or not): personal income taxes at the subnational level in
Canada and Spain.
Autores: Violeta Ruiz Almendral y François Vaillancourt.
30/06 A projection model of the contributory pension expenditure of the Spanish social
security system: 2004-2050.
Autores: Joan Gil, Miguel Ángel Lopez-García, Jorge Onrubia, Concepció Patxot y
Guadalupe Souto.
2007
11/07 Efectos macroeconómicos de las políticas fiscales en la UE. Autores: Oriol Roca Sagalés y Alfredo M. Pereira. 12/07 Deficit sustainability and inflation in EMU: an analysis from the fiscal theory of the
price level.
Autores: Oscar Bajo Rubio, Carmen Díaz Roldán y Vicente Esteve.
13/07 Contraste empírico del modelo monetario de tipos de cambio: cointegración y ajuste
no lineal.
Autor: Julián Ramajo Hernández.
14/07 An empirical analysis of capital taxation: equity vs. tax compiance. Autores: José M.ª Durán Cabré y Alejandro Esteller Moré. 15/07 Education and health in the OECD: a macroeconomic approach. Autoras: Cecilia Albert y María A. Davia. 16/07 Understanding the effect of education on health across European countries. Autoras: Cecilia Albert y María A. Davia. 17/07 Polarization, fractionalization and conflict. Autores: Joan Esteban y Debraj Ray. — 44 —