Polarization and the Middle Class in Uruguay

Abstract

There is an increasing literature that discusses how to measure the middle class. Some approaches are based on an arbitrary deÖnition such as income quartiles or the poverty line. Recently, Foster and Wolfson developed a methodology which lacks of arbitrariness that enables us to compare the middle class of two di§erent income distributions. We apply this new tool jointly with a complementary method ñrelative distribution approach- to household income data in 1994-2004 and 2004-2010, to analyze the evolution of the middle class and polarization in Uruguay. During the Örst period, which is characterized by an increasing income inequality, we Önd that the middle class declined and income polarization increased. In the second one, where the Uruguayan economy experienced a recovery from the downturn su§ered in 2002, we Önd that the middle class rose and polarization decreased. However, this last result is attenuated when we do not consider the household income imputation because of the new health system implemented in 2008.

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Documentos de Trabajo
Polarization and the Middle Class
Fernando Borraz, Nicolas González Pampillón y Máximo Rossi
Documento No. 20/11
Agosto 2011
ISSN 0797-7484

Polarization and the Middle Class 
Fernando BorrazyNicolas González PampillónzMáximo Rossix
August 2011
The views expressed here are those of the authors and do not re‡ect necessarily the views of the Banco
Central del Uruguay. We are grateful to Marisa Bucheli, Andrea Vigorito and Marcel Vaillant for useful
comments. All errors are our responsibility.
yBanco Central del Uruguay and Deparmento de Economía FCS-UDELAR. Email: fborraz@bcu.gub.uy.
zUniversidad de Montevideo. Email: ngonzalez@correo.um.edu.uy.
xDepartamento de Economía, Facultad de Ciencias Sociales, Universidad de la República. E-mail:
mito@decon.edu.uy.

Abstract
There is an increasing literature that discusses how to measure the middle class. Some
approaches are based on an arbitrary de…nition such as income quartiles or the poverty
line. Recently, Foster and Wolfson developed a methodology which lacks of arbitrariness
that enables us to compare the middle class of two di¤erent income distributions. We apply
this new tool jointly with a complementary method –relative distribution approach- to
household income data in 1994-2004 and 2004-2010, to analyze the evolution of the middle
class and polarization in Uruguay. During the …rst period, which is characterized by an
increasing income inequality, we …nd that the middle class declined and income polarization
increased. In the second one, where the Uruguayan economy experienced a recovery from
the downturn su¤ered in 2002, we …nd that the middle class rose and polarization decreased.
However, this last result is attenuated when we do not consider the household income
imputation because of the new health system implemented in 2008.
Keywords: income polarization, middle class, inequality, social policies, bipolarization
JEL classi…cations: D3, D6, I3
Resumen
Existe una creciente literatura que discute como medir la clase media. Algunos enfoques
se basan en una de…nición arbitraria como quintiles de ingreso o la línea de pobreza.
Recientemente, Foster and Wolfson desarrollaron un metodología no arbitaria que nos
permite comparar la clase media de dos diferentes distribuciones de ingreso. Aplicamos
dicha nueva herramienta junto al método complementario -enfoque de distribución relativa-
a datos de ingreso de hogares en 1994-2004 y 2004-2009, para analizar la evolución de la
clase media y polarización en Uruguay. En el primer período que se caracteriza por creciente
inequidad encontramos que la clase media cae y la polarización aumenta. En el segundo
período las conclusiones se revierten. Sin embargo, este último resultado se atenua cuando
no consideramos la imputación en el ingreso de los hogares por la nueva reforma de salud
implementada en 2008.
Palabras claves: clase media, polarization, social policies, bipolarization, inequidad
Códigos JEL: D3, D6 ,I3

1Introduction
Previous research observes a tendency toward income inequality during the nineties in
almost all Latin American and Caribbean (LAC) countries (IADB, 1998 or Bourguignon
and Morrison, 2002). Uruguay is not the exception and during the nineties we observe an
increase in income inequality (Amarante and Vigorito, 2006). In addition, there is a common
perception that because of the vigorous economic growth in the last years the middle class
in LAC countries is declining. However, this fact is rarely con…rmed in research documents.
From an economic and social perspective, the middle class could play an important role in
the development of a democratic country since it contributes with a signi…cant share of the
labor force, and therefore is closely related with the country´s output and usually represents
the main source of tax revenue.1Moreover, an increase in the middle class because of the
reduction of the lower and upper class could enhance the positive externalities mentioned
above, that is, to reduce income inequality and the antagonism between classes which is an
important source of social tensions.
However, an opening question is, what is the appropriate de…nition of the middle class?
First of all, the middle class in economics is usually based on the distribution of an indicator of
social welfare such as household income (the most commonly used), household expenditure,
labor status, education attainment, etc. Consequently the de…nition of the middle class
is related to the distribution of one variable. Therefore, the main problem is to arbitrary
identify which range of the income distribution represents the middle class. The literature is
not unanimous in this issue (see Foster and Wolfson, 2009 for a further discussion in developed
countries and Cruces, et al., 2010 for developing countries) and di¤erent de…nitions could
lead to diverse and uncomparable results. In order to analyze the evolution of the middle
class, Foster and Wolfson (2009) developed a methodology which lacks of arbitrariness that
it is based on the concept of “partial orderings” and …rst (and second) degree stochastic
dominance. This method yield two curves (one for each population we would like to compare)
1In Uruguay, considering the 2001 tributary system, Grau and Lagomarsino, 2002 show that the …rst two
income quantiles contribute with 22% of the tax revenue, while the top two income quantiles contribute with
18%. The middle income quantiles (3 to 6) contribution is 60%.
1

that enables us to unambiguously determine which distribution concentrates more population
around its median.
A second concept related to middle class and income inequality is income polarization.
Esteban and Ray (1994) employ two elements to de…ne polarization: 1) the sense of
“identi…cation” with a group who shares common features within it; 2) the level of
“alienation” between the identi…ed groups. Thus, a polarized society is one which could
be divided into few groups who share a similar level of income and there is a considerable
distance (in terms of income) between each group. Income polarization and income inequality
could go in the same direction or in the opposite one depending on the variation of the shape
of the income distribution, which could be a¤ected by several factors (e.g. tax reforms,
social policies). Duclos et al. (2004) derive a polarization index that is related with the Gini
coe¢ cient. Using this methodology for LAC countries in the period 1989-2004, Gasparini
et al. (2008) …nd that, overall, income polarization increased and in the case of Uruguay it
increased sharply. This fact represents a relevant issue from a social point of view since a
high level of polarization is positively correlated with a high level of social con‡ict.
In generally, the society could be split into three classes, lower, middle and upper based
on income levels. Sometimes, a declining middle class could be an indicator of increasing
polarization. For instance, polarization could increase in the case of bipolarization, when
we observe higher mass in the lower and upper tails of the income distribution than in the
middle. On the other hand, the widening of the gap between the lower and upper class
could result in higher polarization (via “alienation”according to the terminology of Esteban
and Ray) which do not necessary imply a reduction in the middle class. Foster and Wolfson
(2009) formalize those ideas using a similar methodology as the one employed to measure the
middle class. In their case, the output are two di¤erent polarization curves that enable us
to capture the two aspect of polarization: 1) the “…rst degree” polarization curve, which is
associated with the concept of “increasing spread”; and 2) the “second degree”polarization
curve, which is related to the “increased bipolarity” concept. In addition, they propose an
index to measure bipolarization which is closely related to the Gini index.
All the prior measures are useful in characterizing some sort of stylized facts of the overall
2

income distribution at one period, which are summarized into an index. By comparing this
index in two di¤erent periods we would be able to analyze how does this indicator evolve.
However, we would like to go one step further and compare the entire income distribution in
two di¤erent points in time to analyze the evolution of the whole distribution. Handcock and
Morris (1998, 1999) provide the theoretical framework for the relative distribution approach
which enable us to compare two di¤erent distributions. Moreover, this non-parametric
methodology gives us the tools to separately estimate the e¤ects attributable to changes
in the shape of the income distribution and those which come from changes in the location
of the income distribution.
In recent years, di¤erent kinds of “re-distributive” policies, which potentially could
have an impact on the income distribution have been introduced. For instance, in 2005
a conditional cash transfer program was launched 2and the real minimum wage grew 63%.
In addition, in 2007 a tax reform was implemented. Rodriguez and Perazzo (2007) conclude
that the changes in sale taxes (VAT) favors household in the …rst and last quantiles of the
income distribution. Regarding the new personal income tax, Barriex and Roca (2007) …nd
that the Gini index decreases 0.022 points. A shortcoming of these studies of the income
distribution implications of the tax reform is the lack of general equilibrium e¤ects. However,
we expect an impact of the "re-distributive" policies on the income distribution.
Additionally, between 2005 and 2010 the Uruguayan economy grew around 30% in real
terms (5% yearly). The relationship in the literature, between inequality and economic
growth remains open (Aghion, Caroli and Gracia-Penalosa, 1999). For instance, growth
could lead to wage inequality by spreading the gap across educational cohorts. Nevertheless,
the new theoretical framework does not imply a trade-o¤ between growth and inequality. In
the last years, we observe that income inequality ‡uctuates without a trend. Therefore, if
growth is positively correlated with inequality then policy e¤orts could slow down inequality
but not reduce it.
The aim of this paper is to de…ne and characterize the middle class, as well as, to
analyze the evolution of income polarization and the middle class in two di¤erent periods:
2See Borraz and González (2009).
3

1)1994-2004, in where inequality raised dramatically; and 2) 2004-2010, in where inequality
remains stable and the Uruguayan economy experienced a recovery from the downturn
su¤ered in 2001. We use the Uruguayan National Household Survey to apply di¤erent and
complementary methodologies. In order to de…ne the middle class, we follow Esteban et al.
(1999) and we estimate multinomial (and ordered) logit model to disentangle some features
of the middle class. To quantify polarization and bipolarization we compute the polarization
index developed by Duclos et al. (2004) and the bipolarization index derived by Foster and
Wolfson (2009). We also use the Foster and Wolfson´s curves to analyze the evolution of
the middle class. Finally, following Handcock and Morris (1998, 1999) we apply the relative
distribution approach.
Several issues motivate us to carry out this research: 1) apply these new tools to analyze
the Uruguayan case and contribute with new evidence for the discussion on this topic; 2)
analyze whether the tendency toward income polarization and inequality observed during
the nineties is reversed in recent years; and 3) analyze how sensitive are the results to some
component of the household income, speci…cally, if we do not consider the imputed income
because of the new medical system (NMS) implemented in Uruguay in 2008. We conclude
that the middle class declined and income polarization increased between 1994 and 2004
and decreased between 2010 and 2004. However, this last result is attenuated when we do
not consider the household income imputation because of the new health system.
2 Measuring the Middle Class
One important issue about the concept of the middle class is its lack of consensus, principally
because di¤erent de…nitions lead to dissimilar results. Using the income distribution function,
our main concern is to de…ne at which speci…c income range the middle class belongs to.
For instance, let mbe the middle of the income distribution measured by the median. We
could consider that those households with an income between m-"and m+"belong to the
4

middle class and therefore, the proportion of households between the latter range represent
a measure of the middle class size. However, this prior de…nition depends on the value of
":In this context, the methodology proposed by Foster and Wolfson (2009) is not subject to
a speci…c income interval and hence it does not su¤er from arbitrariness. This approach is
derived from the idea of partial ordering and stochastic dominance.
Let Frepresent an income distribution function in one period. Since di¤erent distribution
functions might have di¤erent medians, we consider a median-normalized Fdenoted as ~
Fto
make a robust comparison between two di¤erent distributions functions. The middle class
index for ~
Fgiven an income range R= ["; "]is de…ned as:
M~
F(R) = M~
F(") + M~
F(") = h~
F(1) ~
F(")i+h~
F(")~
F(1)iwith 0"1"(1)
where ~
F(1) = 0:5and M~
F(")and M~
F(")are the “lower middle class”and the “upper middle
class”, respectively. For example, for the income range R1= [0:5;1:5] we obtain the following
middle class index: M~
F(R1) = M~
F(0:5) + M~
F(1:5). By considering di¤erent income ranges,
we are able to construct a curve that is not restricted to one particular de…nition of the
middle class: M~
F(Ri)with i = 1; :::n, in where the index idenote the income range and
thus, giving the idea that the latter measure support any de…nition of the middle class.
Thus, considering two distribution functions Fand Gand using the notion of partial
ordering, the following binary relation Mcan be stated:
F M G () M~
F(Ri)M~
G(Ri)8i= 1; :::; n and M ~
F(Ri)> M ~
G(Ri)for some i
(Proposition 1)
In other words, if Proposition (1) holds “F has an unambiguously larger middle class than
G”, for any de…nition of the middle class. This proposition can also be formalized using the
notion of stochastic dominance,
If 1) ~
F(")~
G(")8"1and 2) ~
F(")~
G(")8"1 =)F M G (Proposition 2)
5

The …rst condition implies that ~
Fstochastically dominates ~
Gfor all "1, while the second
one implies the opposite for "1. That is, the distribution Facummulate more mass
around its median than distribution G, which acummulate more mass in the upper and
lower tail. In our case, we estimate three curves, one for the 1994 income distribution, other
for the 2004 income distribution and …nally one for the 2009 income distribution. After that,
we compare 1994 with 2004 and this latter year with 2010. If the estimated curves do not
cross at any part in each period, we are able to draw an unambiguous conclusion about the
evolution of the middle class during both periods. Otherwise, we only have the information
of the di¤erent income ranges that support prior de…nitions.
2.1 Polarization Measures
A declining middle class could be related with a more bipolarized income distribution
whenever the middle class reduction occurs jointly with an increase of the lower and upper
class. The Foster and Wolfson bipolarization index and polarization curves are based on
the idea that movements away from the middle via increased spread or increased extreme’s
in the income distribution lead to a rise in polarization. Thus, they divide the income
distribution in two, forming two income groups one above and one below the median.The
approach to derive the …rst "degree" polarization curve is similar to the one used to measure
the middle class, but here the aim is to …nd out the income interval that includes all the
households belonging to a given population range. For example, for a given population range
Q= [!; !], the distribution Fhas a certain income range. The greater the income range
required to quantify any de…ned population range the greater the income spread (growth
in polarization). Hence, we are interested in measuring income spread as the width of the
income range in the distribution Fgiven a population range. Formally,
SF(!i) = ~
F1(!i)~
F1(0:5)with 0!i18i= 1; :::; n (2)
6

Note that in this case irefers to population range. Again, using the notion of partial
ordering, the following proposition is derived:
F SG () SF(!i)SG(!i)8i= 1; :::; n and SF(!i)> SG(!i)f or some i
(Proposition 3)
This proposition states that for a given population range ithe income distribution F
reveals a greater income spread than the income distribution G, that is, Fhas a greater
income polarization than G. This results holds for any population range. Furthermore,
since a greater income spread implies less proportion of population around the middle,
Proposition (3) implies that the income distribution Ghas a greater middle class than
the income distribution F, and therefore Gdominates F(GM F ):Additionally, Foster and
Wolfson construct a second curve called "second-degree" polarization which considers at the
same time both sources of polarization: "increased spread" and "increased bipolarity".It is
de…ned as the area under the …rst degree polarization curve between 0:5and a population
share !i:
BF(!i) = Z0:5
!i
SF(p)dpwith 0!i18i= 1; :::; n (3)
The second-degree polarization curve is similar to the Lorenz curve which acumulate the
population share from the lowest to the highest incomes. This new curve acumulate income
spreads from the middle to the top and the bottom, respectively, and it places more weight
on changes around the middle of the income distribution.The following proposition applies
when the income distribution Fpresents a greater level of polarization than the income
distribution G,
F BG () BF(!i)BG(!i)8i= 1; :::; n and BF(!i)> BG(!i)f or some i
(Proposition 4)
Finally, Foster & Wolfson construct a polarization index consistent with the …rst and
second polarization curves and similar to Gini index. It is de…ned as twice the area under
7

the second degree polarization curve: P=R1
02BF(!)d!:As mentioned before, this analysis
is based on an income distribution which is divided in two group, those with incomes below
the median and those with income above the median. For this reason, this index can be
de…ned as a bipolarization index. A greater value could be indicative of greater income
spread between these two groups and/or that the group become more sharply de…ned. The
distance between these two groups as proportion of the overall mean is de…ned as the relative
median deviation:T=UL= . Then, it can be proved that: 1) T= 2GB, in where
GBis the between groups Gini index; 2) G=GB+GW, that is, the Gini index is equal to
the sum of the between Gini index GBand the within groups Gini index GW; and 3) the
polarization index is equal to P= (TG)
m, in where is the overall mean and mis the
median. Based in these three result we can de…ne the polarization index as:
P=GBGW
m(4)
Equation (4) re‡ects the fact that an increment in inequality between the two de…ned
groups raises polarization, in other words it increases alienation. However, an increment
in inequality in each group decrease polarization, that is, each group is less homogeneous.
Equation (4) also tell us that polarization increases depending on the source of inequality and
thus, polarization and inequality could or could not go in the same direction. For example,
a rise in the spread of the income distribution as a result of a regressive transfer tends to
enhance both polarization and inequality. On the other hand, an increment in bipolarization
as result of a progressive transfer leads to a growth in polarization but not in inequality.
The polarization measure presented above is focus on the idea of only two income groups.
In order to relax this assumption and based on the concepts of alienation and identi…cation,
Esteban and Ray (1994) developed a polarization index in which the number of income group
are determined by the analyst or by using common rules. Formally,
P(F) = ZZ T(I(y ; F ); r ((yi; yj)) dF (x)dF (y)(5)
8

where Tis the "e¤ective antagonism" between individual yand individual x(under F)
which is compouned by the identi…cation function Ithat measures the degree of association
of an individual with a group in terms of income; and the alienation function, which measures
the distance (usually the euclidean metric) between the identi…ed income groups. The main
drawback of this index is that it assumes that individuals have been "regrouped" in each
of the relevant groups. Thus, now the problem is how to set the optimal "partition" for
a given number nof groups. Esteban, et al. (1999) introduce some re…nements to the
previous polarization index in order to …nd out the optimal way to construct the optimal
boundaries that de…ne the ngroups. Relying on the assumption that the income distribution
can be represented by a density function fin a bounded interval, the function fcould has an
"n-spike" representation denoted by : The "n-spike" representation di¤ers from the actual
representation of f, in an error term "(f; )which can be called the "grouping error". This
error term need to be introduced in order to correct the previous polarization measure.
Moreover, the error term "(f; )can be de…ned as G(f)G(p)which is the di¤erence
between the gini index using the actual density function and the one that arise from optimally
separating the population in de…nied nnumber of groups. Thus, this polarization measure
is obtained by minimizing the within-group dispersion using a iterative procedure. The new
polarization measure is:
P(f; ;  ) = ER(; )"(f; )(6)
where is the "n-spike" representation of the density function f,is a parameter related
to the importance of the identi…cation factor and is de…ned by the user, and …nally is the
weight placed on the grouping error term and it is also a user de…ned parameter. As a result
of the application of this method with n= 3, we can de…ne the lower, middle and upper
class because we can calculate the values of income that de…ne each category. After that, we
characterize the middle class and estimate a multinomial ordered logit to …nd out the main
features of the middle class.
Duclos et al. (2004) extend the prior analysis by letting the number of groups be
9

determined endogenously. The identi…cation process is based on the estimation of a
non-parametric Kernel density for the income variable (yi). The density for a given income
range can be viewed as the proportion of population in this range. The degree of identi…cation
arise when this proportion or density is powered by the parameter (with  [0;1]), which
is an ethical parameter that express the level of feeling of identi…cation within a population
group given by a level of income. In other words, for each density point "window of
identi…cation" is de…ned. Individuals beloning to a particual window are weighted by their
distance with respect to each density point. In this context, the alienation factor is a measure
of the income distance between each group previously determinated. Then, the polarization
index for the distribution Fcan be de…ned as,
P(F) = Zy
f(y)a(y)dF (y)(7)
where yrepresent the income variable and Fits distribution funtion. The identi…cation
e¤ect, which is sensitive to the parameter ;is denoted as f(y)and …nally, a(y)denotes the
alienation e¤ect. One drawback of this index is that is subject to the choice of the parameter
, which as we mentioned above is related to the identi…cation process. A higher value of
emphasizes the role of identi…cation in the construction of this polarization indicator. In
contrast, when is zero, there is no weight placed on the identi…cation e¤ect and therefore,
the polarization index equals the alienation e¤ect (the Gini index). In order to circumvent
such disadvantage, we estimate Duclos et al. polarization index for a set of values of . In
addition, f(y)is estimated using a Kernel procedure. We use a Gaussian Kernel function
and the "optimal" bandwidth is derived by minimizing the mean square error (see Duclos et
al. for more details).
Finally, the polarization index can be descomposed as it follows,
P(f) = a i[1 + ](8)
where ais the average alienation e¤ect, iis the average identi…cation e¤ect and is the
10

normalized covariance between iand a. This equation provide us interesting information
since we can observe the contribution of each component to polarization.
3 Relative Distribution Approach
Although this approach is di¤erent to those previously described, it can be viewed as a
complement of them. Based on the "relative distribution" method, this tool is helpful to
…nd changes in patterns across the entire income distribution for a given period and it is
also capable of distinguishing between changes in the location and the shape of the income
distribution. The theoretical framework is introduced by Handcock and Morris (1998,1999)
and assumes that we have two di¤erent populations,the "reference" population and the
"comparison" population. The initial step is to de…ne a relative rank. First, we introduce
some notation: let Ytand Yt+1be the income variable with cumulative distribution functions
Ftand Ft+1respectively. Then, a relative rank Rbetween 0 and 1 is de…ned as R=Ft(yt+1).
This relative rank is considered as a random variable and it quanti…es the accumulated mass
of population in taccording to the income variable in t+1. For one realization of Rwe have,
r=Ft(yt+1;r)with 0r1and the associated quantile function F1
t(r) = yt+1;r. Then,
the relative distribution function is de…ned as G(r) = Ft+1(F1
t(r)) with 0r1and the
relative density function of interest is de…ned as,
g(r) = ft+1(F1
t(r))
ft(F1
t(r)) with 0r1(9)
where frepresent the density function in t+ 1 and t, respectively; g(r)is the relative
density function evaluated at the income level of the reference group tat the quantile r:This
function is de…ned as the ratio of the density of the reference group to the density of the
comparison group evaluated in the income level of the reference group at quantile r. It has
the properties of a density function (for example, it integrates to 1). When the relative
density function shows values near to one, it means that the two density function have a
similar density at the quantile rof the reference group and thus, Rhas a uniform distribution
11

in the interval [0;1]. A relative density greater than one means that the comparison density
has more density than the reference density evaluated at the quantile rof the reference
group. Finally, a relative density function less than one indicates the opposite.
The density functions are estimated using a non-parametric Kernel method. Once we
obtain the estimated relative density functions for di¤erent realizations of R, we …t a local
polynimial for each estimated point in order to have an accurate description of the relative
density. One of the major advantage of this method is the possibility to descompose the
relative distribution into location e¤ect, usually associated with changes in the mean of the
income distribution, and shape e¤ect, which could be linked with several factors like social
policies or polarization for instance. Formally,
g(r) = ft+1(F1
t(r))
ft(F1
t(r))
| {z }
Overall eff ect
=ft;L(yt+1;r )
ft(yt+1;r)
| {z }
Location effect
ft+1(yt+1;r )
ft;L(yt+1;r )
| {z }
Shape ef f ect
with 0r1(10)
where ft+1;L(yt+1;r) = ft+1 (yt+1;r +)is a density function adjusted by an additive shift
=median(Yt+1)median(Yt). An increasing location e¤ect means that the comparison
income distribution is greater than the reference income distribution and vice versa. The
second term which is the shape e¤ect function is useful to identify movements in the entire
distribution function. For instance, as a consequence of the redistributive policies launched in
2005 we could expect a reduction in the upper tail in 2010, which could lead to an increment
in the middle class, observing a shape e¤ect function with some sort of U form. We could
expect the opposite (an inverse U shape) if we compare the 1994 income distribution with
the 2004 income distribution.
This approach also include a "median relative polarization index" that is based on changes
in the shape of the income distribution to account for polarization. This index measures the
average of the absolute value from the median of the shape e¤ect function normalized to
vary between -1 and 1. Negative values indicates that income polarization decreases, while
positive values indicates the opposite. When the index takes the value of zero it means that
there is no changes in polarization patterns. The index is formally de…ned for the reference
population (period t+ 1) and the comparison population (period t)as follows,
12

MRP index = 4 Z1
0r1
2
ft+1(yt+1;r )
ft;L(yt+1;r )
| {z }
gs(yt+1;r)
dr 1(11)
where gs(yt+1;r)is the shape e¤ect function. The index can be estimated using
non-parametric techniques. Finally, the MRP index can be descomposed into a lower and
upper relative polarization index, which are also normalized to vary between -1 and 1. These
two new indexes can shed light on income bipolarization and therefore on declining middle
class issues. They are formally de…ned as,
LRP index = 8 Z1=2
0r1
2gs(yt+1;r)dr 1(12)
URP index = 8 Z1
1=2r1
2gs(yt+1;r)dr 1(13)
4 Data and Results
We use the annual National Household Survey (ECH) conducted yearly by the National
Statistical O¢ ce of Uruguay (INE). We employ cross sectional data for 1994, 2004 and 2010 to
analyze two di¤erent periods, 1994-2004 and 2004-2010. The …rst period is characterized by
increasing inequality and it comprises the 2002 economic downturn3, while in the second one
redistributive policies were introduced and the real GDP growth was 6% the yearly average
.The ECH is the main source of socio-economic information about Uruguayan households
and their members at the national level. Due to the fact that the 1994 and 2004 surveys
only include households in urban areas with more than 5,000 inhabitants, we restrict the
analysis to such population.4We are interested in the total household income variable of
the the survey. This variable includes all the di¤erent sources of income (members ´salaries,
pensions, bene…ts from cash transfer programs, etc) and it also considers the imputed rents
(for example in the case of home owners, the imputed rent is the hypothetical value the
3The real GDP decreased 11% in 2002 and the unemployment reach 17% in this year.
4Note that only around the 5% of the Uruguay population is located in rural areas.
13

members would have to pay for it). It is necessary to point out that the household income
reported in the survey is net of social security and income taxes. Speci…cally, our outcome
variable is the per capita household income in 1997 Uruguayan pesos since we adjusted it by
the consumer index price with base in 1997.
4.1 Characterizing the Middle Class
In this section, we de…ne and characterize the middle class following Esteban, et al. (1999)
and then we compare it with the other social classes (lower and upper). In Figure 1, we
observe the density of the (log) real household income jointly with the middle class boundaries
in 1994, 2004 and 2010. In 1994 and 2010 the de…nition seems to be quite similar, while in
2004 the middle class interval has a left shift probably explained by the 2002 economic crisis.
Based on these middle class intervals, Table 1 shows summary statistics of the middle
classes. First of all, we observe that in Uruguay around 37% of the households belong to the
middle class. The low class income is the greatest with 45% approximately and the high class
represents the smallest (around 12%). Therefore, Uruguay is basically compounded by low
and middle income households. Other interesting feature is that we observe a great income
dispersion in the high class, while the low class appear to be more homogeneous. Also, the
income share of the middle and high class seems to be similar between 1994 and 2010, despite
their size di¤erences. As it is expected, the income share of the low class decreases in 2004,
while that of the high class increases.
We present a second group of indicators that are related to education. Overall, we
observe that educational attainment increases from the low to the high class. For instance,
if we consider the average years of education of adult household members, the high class has
the greatest average while the low class has the lowest5. The level of the attendance rate is
similar across classes for the age cohort [6,12]6. However, when we take into account higher
cohorts the attendance rate decreases, mainly in the low class case. In addition, the low class
show a high level of education gap in children between 7 and 15 years old in comparison with
5The same conclusion arises when we consider the average years of education of the head of household.
6This is not surpring since primary school attendance is almost universal.
14

the middle and high class. Both of them (middle and upper) have a similar education gap.
Regarding living conditions, around the 70% of the middle class household are
homeownership. Nevertheless, it is interesting to point out that this proportion decline
in recent years and around 64% are homeownership in 2010. This fact also applies for the
other social classes. In addition, there is a considerably di¤erence in terms of overcrowded
households between the lower and the middle and the upper class. Sanitation is another
variable that rises as we move to a higher income classes. We construct an asset index
as a weighted average of a series of indicator variables for the availability of the following
assets at home: refrigerator, dishwasher, laundry machine, regular TV, internet connection,
computer, car and household help. The weights are the relative distance between 1 and
the proportion of households having this item and therefore the index places more weight
on items possesed only by few households. The index varies between 0 and 1. The asset
index shows a di¤erence between the low and middle of around 0.10 points and this gap
remains constant for the three years. The asset gap between the middle and high class is
wider (approximately 0.14). We construct another wealth index with the same variables but
considering a normal standarized transformation of them. In this case, we observe higher
gaps and this index varies on a higher set of values than before.
In what concerns to population composition, the low class is compounded by younger
people in relation with the other classes. The middle and upper have more adults with more
than 60 years old.
The labor status indicators show that the unemployment rate is the highest for the
lower income class. The majority of the middle class workers are wage earners. In second
place we have self-employed and entrepreneur is third. This pattern is quite similar in
the other class categories. The major di¤erence is that the high income class has a greater
proportion of workers in the entrepreneur category. We use the de…nition of informal workers
adopted by the International Labour Organization in the 15th International Conference
of Labor Statisticians (1993), which consider informal workers as those who work in the
housekeeping sector, unpaid household members, private wage earners working in …rms with
less than …ve employees and self-empolyed workers (excluding administrative, professionals
15

and technicians). Using this de…nition, the highest proportion of informal workers is in the
low income class. The proportion of informal workers in the middle class in 1994 is just over
0.17 and it decreases in 2004 and in 2010. Finally, the middle and high class show a similar
share of inactive people.
Table 2 presents multinomial logit estimates for the three years. As dependent variable
we use the category variable which takes the value of 1 if the household belongs to the low
income class, 2 if it belongs to the middle and 3 if belongs to the high income class. We
consider the middle class as the base category and we report the marginal e¤ects. It is
interesting to point out that the signs of the coe¢ cients do not change when we consider
di¤erents years and that almost all the coe¢ cient are statistically di¤erent from zero at the
1% level. For instance, the probability of being a low class household (with respect of being a
middle class household) decrease whether the household is in the capital city (Montevideo).
The opposite happend if we analyze the probability of being a high income household. This
fact could be associated with di¤erent living cost between the capital and the rest of the
country. As mentioned earlier, households with young children have higher probabilities
of being low income class than middle class. The same fact holds for the household size
variable. A more educated head of household rises the probabilities of being high income
class and decline the probability of being low income class (with respect to the middle). In
what concerns to labor market variables, unemployed or informal head of household increase
the probabilities of being low class income, while decrease the probability of being high. In
addition, whether the head of household is an enterpreneur grows the probability of being
high. The housing variables have the expected signs.
Because in this case the dependent variable seems to have a natural order, an ordered
logit model appears as the most appropriate. However, if this assumption does not hold
we will have a bias estimator. Otherwise, the ordered logit model produces more e¢ cient
estimates than the multinomial logit. However, the results of both models are quite similar
and then we do not report the ordered logit estimation.7
7The results are available from the authors upon request.
16

4.2 Evolution of the Middle Class and Polarization
In this section, we apply the methodology related to the evolution of the middle class and
the polarization measures. Table 3 presents summary statistics that helps us to describe
the income distribution for the di¤erent years. As we can see, the mean and the median
of the income distribution fell between 1994 and 2004 and both of them increased in 2010.
The mean is greater than the median indicating that the income distribution is left skewed.
With respect to income concentration, the …rst quantile has approximately 5% of the total
income, while the …fth quantile represent the 50%, approximately. Interestingly, during the
…rst period the proportion of the …rst quantile declines whereas that of the …fth rises. In the
second period we observed the opposite pattern. This also can be viewed in the income share
measures. The bottom …ve percentile has an income share of just under 1% and decrease
in the …rst period and after that it increases. The top …ve percentile has an income share
of 20% in 1994, which rise one percent point and then declines to just over 20%. The next
group of indicators measure the population share given a speci…c income range. For instance,
we observe that there is a 10% of households with income less than 40% of the median in
1994, and so on. Considering low and high income values as percentage of the median, we
observe that the population share growth in the …rst period and in the subsequent period
it drops. However, if we consider income intervals near or around the median this trend
reverses. This fact give us the preception of a deterioration in the middle class during the
period 1994-2004, which then increase in the next period.
Using the M curve, this perception is con…rmed. The middle class decreased around
3% throughout the period 1994-2004 (a movement away from the middle to both upwards
and downwards), and then rise two percent points in the following period. When analyzing
di¤erent population ranges around the middle, we also observe that a greater income spread
is required to capture those ranges in 2004, re‡ecting a greater income spread in the income
distribution in this latter year. For example, given a population rage between 20% and 80%,
we require an income spread of 141% of the median income in 2004. This percentage is
reduced 8% in 2010.
17

All these observed features are illustrated in Figure 2. In the top panels we plot the
M - curve, which is aimed to measure the concentration of mass around the median of
the income distribution. We observe that the M curve of the income distribution of 1994 is
above the M curve of the income distribution of 2004 (and they do not cross each other), and
thus Proposition (1) holds: “the income distribution function in 1994 has an unambiguously
larger middle class than the income distribution function in 2004”. In other words, the 1994
income distribution has more mass around the median than the 2004 income distribution.
Moreover, the …rst and second degree polarization curves (middle and lower panels) lead
to the same conclusions than before. From the observation of those latter curves, we …nd
out that polarization in the income distribution in 2004 is higher than polarization in the
income distribution in 1994, revealing that the latter has a greater income spread. Since a
greater income spread implies less proportion of population around the middle, Proposition
(3) means that the1994 income distribution has a greater middle class than the 2004 income
distribution and therefore, the former dominates the latter. Additionaly, the second degree
polarization curve in 1994 is below the second degree polarization curve in 2004, which
implies that the income distribution in 2004 has a greater spread, as well as, a greater
bipolarity than the income distribution in 1994. The second period, 2004-2010, shows the
opposite picture. The middle class increases while polarization tends to decline.
Table 4 shows inequality and polarization indices.The inequality indicators show a sharp
increase between 1994 and 2004. For instance, the Gini index rises from 0.409 to 0.439. The
Generalized entropy index, the Atkinson index and the Coe¢ cient of variation index increase
0.054, 0.021 and 0.143 points, respectively. As mentioned above, this period is characterized
by a tendency toward increasing inequality which is enhaced by the economic downturn
initiated in the late nineties. This period of growing inequality is also accompanied by a
relevant rising in income polarization. Duclos, et. al. index grows around 0.015 for di¤erents
level of identi…cation represented by the parameter . That is, for di¤erent values of the
change in the Duclos et al. index between 1994 and 2004 is statistically di¤erent from zero at
the 1% level. A greater value of means that more emphasis is placed on the identi…cation
process. In order to analyze the contribution of each of the sources of polarization, the index
18

can be descomposed into three (multiplicative) components: identi…cation, alienation (which
is equal to the gini index) and correlation (between the latter measures). It is interesting
to point out that while the alienation and correlation components evolve positively, the
identi…cation component declines. This results holds for di¤erent values of the parameter.
In other words, polarization basically increases because the gap between the identi…ed group
rises. For the second period, 2004-2010, the …rst main result is a decline in inequality. With
the exception of the coe¢ cient of variation index, the reduction is statistically di¤erent from
zero. The second interesting result is that, as we have already noticed, is that polarization
falls. If we focus on the Duclos, et al. (2004) index the magnitude of the reduction decreases
with the value of the parameter. This can be explained by the fact that we weight the most
the identi…cation e¤ect which in this case goes in the opposite direction. Despite polarization
decline slightly, the identi…cation component rises but not enough to outset the reduction of
the alienation e¤ect.
The Foster and Wolfson polarization measures deserve a quite similar lecture. In the …rst
period, we observe an increase in the bipolarization index which is statistically signi…cant. In
this case, we observe a increase in inequality within and between the two groups. 8Therefore,
both groups spread out and the distance between them increases ("increased spread" and
"increased bipolarity"). In the second period, the reduction in the within and the between
Gini indices indicates a decreases in polarization.
We apply the relative distribution approach in order to …nd changes in the whole income
distribution. Figure 3 shows the actual income distribution in 1994 and 2004 in the left plot
and the relative distribution in the right plot in the top panel. At …rst glance, we observe a
shift from the right to the left which implies a reduction of the mean income in this period.
On the contrary, we observe a shift from the left to the right in the income distribution
during the period 2004-2010 (see lower panel of Figure 3).
In Figure 4, we observe the location and the shape e¤ect. The left plots con…rm our
prior observation since we …nd a decreasing and increasing location e¤ect for the …rst and
second period, respectively. The right (top) plot shows how the lower and upper tail of the
8As previously mentioned Foster and Wolfson identify only two groups, those above and those below the
median of the income distribution.
19

income distribution increase during the 1994-2004 period. This fact supports prior …ndings
cocerning a decline arround the middle of the income distribution. In the other period, the
shape e¤ect shows that the lower and upper tail decline and the middle increase slightly.
To formalize this result, and based on the relative density, we calculate relative polarization
measures where positive values means that polarization increase. In fact, we observe positive
values and statistically di¤erent fro zero for the three measures in the …rst period. In the
second period, the three indices are negative. This means that polarization decreases which
is in line with our previous …ndings. However, the change is smaller than in the …rst period.
To summarize, throughout the nineties and until 2004 the income distribution become
more unequal distributed and more polarized and then middle class decrease considerably,
while during the period 2004-2010, we observe some improvements.
4.3 Robustness Analysis
In order to analyze the robustness of are our results, we do not impute as household income
the health services derived from the new health system (NHS) implemented in 2008.9In
the new scheme, children under 18 years old of formal employees automatically acquired the
right of medical services and therefore, they do not have to pay the monthly payment.10 The
reform implies an important increase in the number of a¢ liations in the private hospitals.11
The National Statistical O¢ ce of Uruguay (INE) decided to account for this change
imputing a monthly payment in the household income for health services12 . From a
theoretical point of view it is not clear if we have to include this as income. If we do
not impute this income the results could change because the income distribution is sensitive
to this imputation (mainly for low income households). As we can see in Table 3 (fourth
9For a complete discussion of the 2008 health reform see Bérgolo and Cruces (2010).
10 This change was …nanced with an increase in worker’s contribution.
11 The Ministry of Public Health states that the number of customers of a Collective Health Care
Institution, which is the main private health supplier, increased in 314,976 between December of 2007 and
December of 2008.
12 In 2004, INE also includes in the household income the amount which account for the health service of
each member which was a wage earner.
20

and …fth column) the proportion of income in the …rst and in the second quantiles decreases.
What is more, the percentage of households around the median drops while the proportion
in the extreme’s tend to increases. This fact is con…rmed in the summary statistics related to
the M curve. We concluded that the middle class increases in the previous section. However,
if we do not included as household income the imputation for the health reform (as well as
the imputed income for health service to wage earners in 2004), the change in the middle
is ambiguous. This fact can be viewed graphically in Figure 5 in where the M curve of the
income distribution of 2004 is still below the M curve of the income distribution of 2010,
but around the middle both curves are quite similar. This result implies that the middle
class increases. Nevertheless, around the middle its increment is not so pronounced as we
observed in the previous section. The same is also observed when we look to the shape e¤ect
panel, in where the extreme’spoles seems to have decline and the middle increase, but in a
lower level than the previous section.
With respect to to polarization and inequality measures in Table 4, the di¤erent indicators
decreases as before, but to a lesser extent. For instance, the Gini index decreases from 0.447
in 2004 to 0.432 in 2010 (it decreases 0.015 points), while if we do not impute income for
health services the decline is 0.021. The same pictures holds for the other indices where the
changes are statistically di¤erent from zero, but with a lower change than in the original case.
Furthermore, polarization grows for di¤erent values of the parameter. In this case, the
most important component of polarization is alienation since identi…cation remains steady.
Therefore, the higher value of , the lower e¤ect that we are going to …nd. The cocnlusions
are the same with respect to the Foster and Wolfson.
5 Concluding Remarks
In the last years there is a increasing concern about inequality and polarization. The
expansion of the middle class is one of the key issues towards lower inequality and lower
polarizaton. From an economic and social perspective, the middle class could play an
important role in the development of a democratic country since it contributes with a
21

sign…cant share of the labor force, and therefore is closely related with the country´s output
and usually represents the main source of tax revenue for the country. Furthermore, an
increase in the middle class because of the reduction of the lower and upper class could
enhance the positive externalities mentioned above, reduce income inequality, and the
antagonism between classes which is an important source of social tensions.
We analyze the middle class and polarization in Uruguay in the last two decades. We
conclude that the middle class declined and income polarization increased between 1994 and
2004, while the situation is the opposite between 2004 and 2010. However, when we do not
include the income imputation because of the health reform implemented in 2008 results
tend to be attenuated. In other words, the increases in the middle class between 2004 and
2010 is lower than before and the magnitude of the declines is sensible to the health income
imputation. This fact highlights the importance of the analysis of income imputation when
using household surveys.
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23

Ta b le 1. C ha r a ct e r is t ic s of so c ia l cla s s e s. S u m m a ry st a t is t ic s
1994 2004 2010
Va ri a b le s L ow M id d l e H ig h L ow M id d l e H ig h L ow M id d l e H ig h
% of p e r so n s 54 . 1 7 3 2. 5 0 13 . 3 3 58. 2 9 3 0. 1 6 11 .5 6 56 .6 2 3 1 . 37 1 2 .0 1
% of h o u se h o ld s 44 . 5 7 3 7. 2 6 18 . 1 7 46. 4 2 3 6. 9 5 16 .6 2 45 .4 5 3 7 . 15 1 7 .4 0
A ve r a g e ( p e r c a p it a ) h o u s e ho l d inc o m e 1, 9 7 7 4, 5 7 8 1 1, 4 2 7 1 ,3 4 6 3 ,3 9 6 9 ,2 5 2 2 , 1 03 4 , 9 75 1 2 , 8 91
St a n d a rd de v ia t i o n 71 6 . 7 2 1, 0 0 2 6, 1 3 4 5 2 0 79 4 5, 8 59 75 1 1 , 11 5 8 , 7 82
H o us e h o ld in co m e sh a r e 25 . 6 8 3 7. 2 6 37 . 0 6 23. 1 4 3 5. 3 3 41 .5 3 26 .0 1 3 7 . 03 3 6 .9 6
% of la b o r inc o m e 61 . 6 7 6 0. 2 8 60 . 1 60 .0 6 5 8 .1 7 57 . 21 58 . 8 8 6 0. 9 6 59 . 15
% of h h s b e l ow th e p ove r ty lin e 29 . 6 9 0 .0 0 0 .0 0 57 .3 3 0 . 00 0 .0 0 27 . 72 0 . 0 0 0. 0 0
% of h h s b e lo w t h e e xt r em e po ve r ty l in e 1.5 6 0. 0 0 0 . 00 4 .6 6 0. 0 0 0 .0 0 1. 1 1 0. 00 0 .0 0
E d u ca t i o n
A ve r a g e h o u se h o l d e d u c a ti o n 6. 4 7 7 .8 5 1 0 .8 7. 5 6 9 .2 4 12 . 50 7 .5 9 9 . 6 1 1 2 . 80
% hou s e h o ld s in < 7 5 1. 9 8 3 8 .8 0 16 . 8 8 36. 3 6 2 7 .5 9 11 .0 8 34 . 73 2 3 . 1 9 9. 2 5
% hou s e h o ld s in [ 7, 9 ] 32 . 8 5 2 8. 5 8 18 . 2 6 38. 0 2 2 3. 0 8 10 .0 4 40 .3 6 2 3 . 75 9 . 88
% hou s e h o ld s in [ 10 , 1 2 ] 1 2 .0 2 2 1 .3 4 2 8. 7 0 20 .3 6 2 7 .7 7 24 . 5 3 19. 9 7 2 9. 9 9 25 . 6 5
% hou s e h o ld s in > 1 2 2. 9 7 1 1. 2 7 3 6 .1 6 5 . 25 2 1 . 56 54 . 3 6 4 .9 4 2 3 .0 7 5 5 .2 2
H ea d o f h h ld y e a rs o f ed u c a t io n 6. 0 5 7. 4 1 10 . 7 4 7 . 1 7 8. 9 4 12. 6 0 7. 3 0 9. 3 8 1 2 . 8 0
% h e ad o f h h ld w ith c o m p l e te d h i g h sc h o o l 1 0 . 34 2 0 . 4 4 4 7 . 47 9 .5 1 2 8 .1 4 6 2 .9 8. 3 4 2 8 .2 4 61 . 2 3
% h e ad o f h h ld w ith a u n i ve r s it y d eg r e e 0. 5 9 2. 7 9 15 . 59 0 .6 5 5 .2 3 24 . 1 9 0 . 2 8 3. 0 1 1 6 . 0 4
At t e n d an c e r a te b y a g e i nt e rv a l:
[6,12] 98.23 99.78 99.53 98.34 99.23 99.14 98.88 99.12 99.51
[13,17] 68.86 86.56 94.47 82.83 95.84 99.45 80.56 95.09 98.68
[18,23] 20.95 42.46 61.83 33.59 64.99 83.05 28.42 55.85 77.55
% o f ch il d r en i n [ 7 ,1 5 ] w it h e d u ca t i on g a p 43 . 1 6 25 . 6 9 26 . 48 46 . 6 4 27 . 0 0 2 6 . 6 8 4 7 . 2 2 29 . 0 2 2 8 . 6 9
L iv i n g co n d it io n s
H o us e ow n er s h ip 59 . 9 1 7 3. 2 7 81 . 0 5 5 7 . 88 7 1 . 2 4 8 1 . 1 7 5 4 . 38 6 3 . 6 5 7 1 . 6 5
Pe r s on pe r ro om 2. 0 7 1 .4 5 1 .1 8 2. 0 0 1 .3 8 1 .2 0 1. 8 7 1 .2 8 1 .0 3
% of ov e r cr o w d e d h o u s eh o l d s 30 . 6 0 7 .0 5 1 .3 2 27 .0 2 3 . 64 0 .9 3 22 . 66 2 . 7 4 0. 3 7
Wa t e r s u p p ly - g e n e ra l net w o rk 97 . 2 2 9 8. 4 4 99 . 4 3 9 8 . 24 9 9 . 2 2 9 9 . 75 98 . 1 7 9 8. 9 5 99 . 5 7
N et w o rk eva c u a ti o n 44 . 6 2 6 9. 9 0 91 . 0 8 5 2 . 91 7 8 . 0 7 9 2 . 50 48 . 7 4 7 1. 9 0 87 . 1 5
A ss e t i n d e x 0. 1 4 0 .2 2 0 .3 3 0. 1 7 0 .2 9 0 .4 2 0. 2 4 0 .3 3 0 .4 4
We a l th In d ex -0. 8 0 0. 1 0 1. 2 2 - 1 . 14 0 . 3 3 1 . 6 0 - 1 .0 4 0 . 4 0 1. 7 0
H o us e h o ld siz e 3. 9 2 2 .8 1 2 .3 4 3. 8 3 2 .5 2 2 .1 5 3. 5 4 2 .4 0 1 .9 5
Po p u l a t io n co m p os i ti o n
C h il d re n ag e d 0 - 5 1 1 . 3 8 5. 5 3 3. 6 5 10 .9 1 4 . 49 3 .4 6 10 . 43 4 . 7 5 3. 4 0
C h il d re n ag e 1 2 - 17 16 . 3 7 8 .4 7 6 .3 7 16 .6 4 7 . 15 5 .4 9 17 . 09 7 . 2 5 4. 9 1
A d u lt s > 6 0 14 . 6 3 2 6. 6 2 29 . 2 2 1 3 . 16 2 9 . 3 6 3 3 . 73 12 . 8 3 2 6. 1 9 31 . 7 7
L ab or st a tu s
E m p lo y m e n t r a te 86 . 2 7 9 4. 3 7 96 . 6 3 8 1 . 73 9 1 . 6 9 9 5 . 5 3 8 9 . 50 9 5 . 8 5 9 7 . 6 7
Wa g e e a r n e r 6 3 . 5 6 69 . 1 9 63 . 16 54 . 8 9 68 . 6 4 65 .7 0 63 .6 8 7 3 . 27 6 8 .6 9
Se l f- e m p l oy e d 19 . 6 5 1 8. 5 1 18 . 7 7 2 4 . 06 1 7 . 7 8 1 8 . 1 7 2 2 . 77 1 6 . 7 2 1 6 . 7 7
E nt r ep r e n e u r 1. 3 7 4. 7 7 1 2 .8 6 1 .0 8 4 .1 6 10 . 7 0 1. 7 3 5. 0 7 1 1 .6 1
Z er o inc o m e 1. 6 7 1 .8 9 1 .7 9 1. 6 9 1 .1 0 0 .9 6 1. 2 7 0 .7 8 0 .5 8
In f o rm al w o r ke r s 27 . 6 4 1 7. 3 3 10 . 6 5 2 5 . 47 1 4 . 3 3 6 . 9 1 2 5 . 2 4 13 . 0 5 5. 2 2
U n em pl oy m en t r at e 13 . 7 2 5 .6 2 3 .3 7 18 .2 6 8 . 3 0 4 . 4 6 1 0 . 4 9 4. 1 4 2. 3 2
% of in a c t iv e 30 . 4 8 3 6. 0 1 35 . 2 1 2 9 . 05 3 7 . 6 4 3 8 . 1 8 2 7 . 16 3 1 . 3 0 3 2 . 3 3
% of r et i re d 8.0 0 1 3 .5 6 1 1 .6 3 6 . 8 2 19 . 1 9 2 0 . 90 5 . 9 8 1 5. 6 0 1 8 .3 0
So u r ce : O w n c a lc u la t io n b a s ed on the Ur u gu a ya n Na ti o na l H o u s eh o ld Su r ve y ( E C H ) .
N o te : C al c u la t i on b a s e d o n th e r e al p e r c ap i t a h ou s e h o ld i n c om e in 1 99 7 U r u g u ay a n p e s os , n e t of s o c ia l se c u r it y an d
in c om e tax . Da t a w ei g ht ed us in g s am p l e w ei gh ts .
24

Ta b le 2a . M ul t in o m ia l l o g it es t im at io n
1994 2004 2010
Va ri a bl e s L o w H ig h L ow H i g h L ow H ig h
Capital -0.132*** 0.074*** -0.044*** 0.055*** -0.028*** 0.037***
(0.007) (0.006) (0.007) (0.006) (0.005) (0.004)
H o us e h o ld w ith c h il d r en a g e d 0 -5 0 . 0 8 0* * * -0 . 04 8 * * * 0. 0 51 * * * -0 .0 3 1 * * * 0 . 0 7 5* * * -0 .0 3 2 * * *
(0.009) (0.008) (0.008) (0.009) (0.006) (0.006)
H o us e h o ld w ith c h il d r en a g e 1 2 -1 7 0. 0 94 * * * -0 .0 4 2 * * * 0 . 0 7 8* * * -0 . 02 7 * * * 0.0 9 9 * * * - 0 .0 3 4 * **
(0.008) (0.007) (0.008) (0.008) (0.005) (0.005)
H o us e h o ld wi t h a d u l ts >6 0 -0 . 04 7 * * * 0 .0 1 9 * * * -0 . 0 5 5* * * 0 . 03 8 * * * -0. 0 4 1 ** * 0. 0 1 5* * *
(0.008) (0.006) (0.008) (0.006) (0.006) (0.004)
Household size 0.083*** -0.075*** 0.098*** -0.073*** 0.111*** -0.088***
(0.003) (0.003) (0.003) (0.003) (0.002) (0.002)
H ea d o f h h ld a v er a g e ed u c a t io n -0 . 01 7 * * * 0. 0 15 * * * -0 .0 1 8 * * * 0 . 0 1 6* * * -0 .0 2 2 * * * 0 .0 1 6 * * *
(0.001) (0.001) (0.001) (0.001) (0.001) (0.000)
H ea d o f h h ld u n e m p l oy e d 0. 1 9 0 ** * -0 . 0 69 * * * 0. 1 53 * * * -0 .1 1 8 * * * 0 . 1 3 4 ** * -0 .0 8 1 * * *
(0.022) (0.020) (0.015) (0.020) (0.013) (0.014)
H ea d o f h h ld o c c u p a t io n : en t re p r en e u r -0. 1 1 1 * ** 0 .0 7 2 * ** -0 . 0 9 9* * * 0. 0 7 9 ** * -0 .0 8 3 * * * 0 .0 7 2 * * *
(0.016) (0.008) (0.018) (0.009) (0.011) (0.006)
H o us e h o ld s wi th in fo r m a l w o r ke r s 0 .0 3 2 * * * -0 . 0 4 0* * * 0 . 0 25 * * * - 0. 0 3 0 * ** 0. 0 5 2* * * -0 .0 5 2 * * *
(0.007) (0.007) (0.007) (0.008) (0.005) (0.005)
H ou s e o w n er s hi p -0 .0 9 4 * ** 0. 0 59 * * * -0.043*** 0.046*** -0.048*** 0.046***
(0.007) (0.006) (0.007) (0.006) (0.004) (0.004)
O ve r cr ow d e d h o u se h o ld s 0. 0 60 * * * - 0 .0 4 2* * * 0 . 04 7 * ** -0 . 03 2 * 0 . 03 1 * ** -0 .0 5 0 ** *
(0.010) (0.016) (0.012) (0.019) (0.009) (0.019)
Network evacuation -0.060*** 0.051*** -0.032*** 0.005 -0.044*** 0.017***
(0.007) (0.007) (0.008) (0.009) (0.005) (0.005)
Wealth index -0.080*** 0.050*** -0.078*** 0.049*** -0.071*** 0.046***
(0.003) (0.002) (0.002) (0.002) (0.001) (0.001)
P se u d o R 20.374 0.374 0.414 0.414 0.395 0.395
L og Li ke l ih o o d -7 , 6 78 . 0 8 -7 , 67 8 . 0 8 -7 ,0 6 4 . 40 - 7 ,0 6 4 .4 0 - 1 7 ,0 2 3 . 34 -1 7 ,0 2 3 . 34
O bs e rv at io n s 11 . 90 6 11 . 90 6 11 . 74 8 11 . 74 8 27 .9 1 4 2 7 .9 14
M a rg i n a l e¤ ec t s a n d ro u b s t st a n d a rd e r ro r s re p o r t e d.
B as e c a t eg o r y = mi d d le cla s s
* si g n i… ca n t a t 1 0% ; ** s ig n i …c a nt a t 5 % ; * * * s ig n i …c a nt a t 1 % .
25

Ta b le 2b . O rd e re d lo g it es t im at i on
1994 2004 2010
Va ri ab le s M id d le Mi dd le M i dd l e
Capital 0.042*** 0.015*** 0.012***
(0.002) (0.002) (0.001)
H o us e h o ld w ith c h il d r en a g e d 0 -5 - 0. 0 2 6 ** * -0 .0 1 3 * * * - 0 .0 2 1 * * *
(0.003) (0.002) (0.002)
H o us e h o ld w ith c h il d r en a g e 1 2 -1 7 -0. 0 2 8 ** * -0 .0 1 8 * * * - 0 .0 2 6 * * *
(0.002) (0.002) (0.001)
H ou s e ho l d w i th ad u lt s > 6 0 0. 0 13 * * * 0.0 1 5 ** * 0.0 1 0 ** *
(0.002) (0.002) (0.001)
H ou s e ho l d s iz e - 0. 0 30 * * * - 0 .0 2 7* * * - 0 .0 3 5* * *
(0.001) (0.001) (0.001)
H ea d o f h h ld a v er a g e ed u c a t io n 0. 0 0 7 ** * 0. 0 0 6 ** * 0. 0 07 * * *
(0.000) (0.000) (0.000)
H ea d o f h h ld u n e m p l oy e d -0 . 05 6 * * * -0. 0 4 3 * ** -0 .0 4 0 * * *
(0.007) (0.004) (0.004)
H ea d o f h h ld o c c u p a t io n : en t re p r en e u r 0. 03 5 * * * 0. 0 28 * * * 0.0 2 9 * * *
(0.004) (0.003) (0.002)
H ou s e ho l ds wi th in fo r m al wo rk er s -0 . 01 3 * ** -0 .0 0 8 ** * -0. 0 17 * * *
(0.002) (0.002) (0.001)
H ou s e o w n er s hi p 0. 0 31 * * * 0.0 1 4 ** * 0.0 1 7 ** *
(0.002) (0.002) (0.001)
O ve r cr ow d e d h o u se h o ld s -0 .0 1 5 ** * -0 .0 1 2* * * - 0 .0 0 7* * *
(0.003) (0.003) (0.003)
N et w or k e va c u a ti on 0. 0 21 * * * 0.0 0 7 ** * 0.0 1 2 ** *
(0.002) (0.002) (0.001)
Wealth index 0.025*** 0.021*** 0.021***
(0.001) (0.001) (0.000)
P se u d o R 20.368 0.413 0.393
L og Li ke l ih o o d -7 ,7 5 6 . 56 - 7 ,0 7 7 .7 5 -1 7 ,1 4 0 .9 3
O bs e rv at io n s 1 1 .9 0 6 1 1 .7 4 8 2 7. 9 14
M a rg i n a l e¤ ec t s a n d ro u b s t st a n d a rd e r ro r s re p o r t e d.
B as e c a t eg o r y = mi d d le cla s s
* si g n i… ca n t a t 1 0% ; ** s ig n i …c a nt a t 5 % ; * * * s ig n i …c a nt a t 1 % .
26

Ta b l e 3. D e s c ri p t io n of th e in c o m e di s t ri b u t io n an d m i d d l e c l a ss m e a su r e s
1 9 9 4 2 0 0 4 2 0 1 0 20 0 4 a2 0 1 0 bD i¤ 20 0 4 - 1 9 9 4 D i ¤ 2 0 1 0 - 2 0 0 4 D i¤ 20 1 0 b- 2 0 0 4 a
C e n t r a li ty m e a su r e s
M e a n 4 ,6 6 4 3 , 3 7 4 5 , 0 0 3 3 , 2 6 2 4 , 7 9 1 - 1 , 2 9 0 .4 7 1 , 6 2 8 . 9 1 1 ,5 2 9 . 4 0
M e d i a n 3, 4 7 6 2 , 4 1 0 3, 6 6 9 3 ,2 8 6 3 , 4 4 4 - 1 , 0 6 6 . 4 4 1 , 2 5 9 . 5 8 1 1 5 7 ,. 6 1
M e d i a n / m e a n 74 . 5 3 7 1 . 4 3 7 3 .3 5 7 0 . 0 9 7 1 . 8 8 - 3 .1 0 1. 9 2 1 .7 9
Q u an t i l e s (% )
1 s t Q u a n t i l e 5 . 6 1 4 .2 2 5 .1 7 4 .1 4 4 . 8 8 6 -0 . 6 6 0 .9 5 0 . 7 4
2 s d Q u a nt i l e 1 0 .3 2 8 . 2 7 9 . 6 3 8 .0 4 9 .1 8 - 0 .8 5 1 . 36 1 .1 4
3 rd Q u a n t il e 1 4 . 9 9 13 . 0 3 1 4 .3 4 1 2 . 8 6 1 4 .0 4 - 0 . 6 1 1. 3 1 1 . 1 8
4 t h Q u a nt i l e 2 1 .9 6 2 0 . 6 9 2 1 . 5 0 2 0 .4 3 2 1 . 4 0 -0 . 2 2 0 .8 1 0 . 9 5
5 t h Q u a nt i l e 4 7 .1 2 5 3 . 8 0 4 9 . 3 7 5 4 .5 4 5 0 . 4 9 2 . 3 4 -4 . 4 3 -4 . 0 5
In c o m e sh a r e (% )
B o t t o m 5% 0 .7 8 0 .7 1 0 .8 1 0 . 7 1 0. 7 7 - 0 . 0 7 0. 1 0 0 . 0 6
B o t t o m 10 % 2 . 0 7 1 .8 3 2 .0 7 1 .8 2 1 . 9 4 - 0 . 2 4 0. 2 4 0 . 1 2
B o t t o m 20 % 5 . 6 0 4 .9 4 5 .5 0 4 .8 5 5 . 1 6 - 0 . 6 6 0. 5 6 0 . 3 1
To p 20 % 4 7 . 1 3 4 9 . 4 7 4 7 .8 3 5 0 . 1 9 4 8 .9 5 2 . 3 4 -1 . 6 4 - 1 .2 4
To p 10 % 3 0 . 8 4 3 3 . 1 5 3 1 .6 1 3 3 . 7 9 3 2 .5 2 2 . 3 1 -1 . 5 4 - 1 .2 7
To p 5% 19 . 6 9 2 1 . 6 5 2 0 .4 6 2 2 . 1 4 2 2 . 1 3 1 . 9 6 -1 . 1 9 - 0 .0 1
% of Po p u la t i o n wi t h in c o m e s :
< 40 % o f m e d i a n 10 . 3 8 1 2 . 6 8 1 0 .7 1 1 2 . 8 1 11 . 9 2 . 3 0 -1 . 9 7 - 0 . 9 1
< 50 % o f m e d i a n 16 . 6 1 1 9 . 3 9 1 7 .1 0 1 9 . 5 6 1 8 .2 2 2 . 7 8 -2 . 2 9 - 1 . 3 4
< 60 % o f m e d i a n 23 . 4 1 2 6 . 2 0 2 4 .1 4 2 6 . 3 8 2 5 .3 5 2 . 7 9 -2 . 0 6 - 1 . 0 3
6 0 % to 75 % 1 0 . 7 6 9 . 2 6 10 . 5 8 9 . 2 7 1 0 . 2 8 8. 9 2 -1 .5 0 1 . 3 2 1 .0 1
7 5 % to 10 0 % 1 5 .8 2 1 4 .5 4 1 5 . 2 8 1 4 . 3 4 1 4 . 3 8 - 1 . 2 8 0. 7 4 0 . 0 4
1 0 0 % to 12 5 % 1 2 . 7 1 1 1 .2 4 1 1 . 9 3 1 0 . 8 8 1 1 . 3 8 - 1 . 4 7 0. 6 9 0 . 5 0
1 2 5 % to 15 0 % 8 .8 0 8 .7 9 8 .9 9 8 .5 1 8 . 8 3 - 0 . 0 1 0. 2 0 0 . 3 2
> 20 0 % 1 7 .5 7 1 8 . 6 0 1 7 . 7 8 19 . 2 8 1 8 . 7 5 1 . 0 3 -0 . 8 2 -0 . 5 3
% in M cu r v e gi ve n in c o m e ra n g e
7 5 % to 15 0 % of m e d ia n 3 7 . 3 3 3 4 .5 7 3 6 .1 9 3 3 . 7 3 3 4 .5 9 - 2 . 7 6 1. 6 2 0 . 8 6
7 5 % to 12 5 % 2 8 .5 3 2 5 .7 8 2 7 . 2 0 2 5 . 2 2 2 5 . 7 6 - 2 . 7 5 1. 4 2 0 . 5 4
5 0 % to 15 0 % 5 4 .9 0 5 0 .6 4 5 3 . 8 2 4 9 . 8 2 5 1 . 9 9 - 4 . 2 6 3. 1 8 2 . 1 7
S gi v en p o p ra n g e :
4 0 % to 60 % 3 5 . 5 8 39 . 9 2 3 7 .2 3 4 0 . 8 7 3 9 .2 6 4 . 3 4 -2 . 6 9 - 1 . 6 1
3 5 % to 65 % 5 4 . 3 4 60 . 3 8 5 7 .2 2 6 2 . 2 4 6 0 .2 0 6 . 0 4 -3 . 1 6 - 2 . 0 4
3 0 % to 70 % 7 5 . 3 0 83 . 8 0 7 9 .0 8 8 6 . 0 8 8 2 .5 7 8 . 5 0 -4 . 7 2 - 3 . 5 1
2 5 % to 75 % 10 0 . 4 7 10 9 . 9 1 1 0 3 .6 7 1 1 3 .4 7 1 0 9 .1 2 9 . 4 4 -6 . 2 4 - 4 . 3 5
2 0 % to 80 % 13 1 . 2 5 14 1 . 3 0 1 3 3 .2 3 1 4 4 .7 8 1 4 0 . 3 1 0 . 0 5 -8 . 0 7 - 4 . 4 8
A v g di s t a n c e g i v e n po p r a n g e :
4 0 % to 60 % 1 , 0 0 6 1, 0 0 9 1 ,0 0 7 1 , 0 0 9 1 . 0 0 5 0 . 0 0 3 - 0 .0 0 2 -0 . 0 0 4
3 5 % to 65 % 1 , 0 1 1 1, 0 1 9 1 ,0 1 4 1 , 0 2 0 1 . 0 1 3 0 . 0 0 8 - 0 .0 0 5 -0 . 0 0 7
3 0 % to 70 % 1 , 0 2 1 1, 0 3 3 1 ,0 2 5 1 . 0 3 6 1 , 0 2 5 0 . 0 1 2 - 0 .0 0 8 -0 . 0 1 1
2 5 % to 75 % 1 , 0 3 6 1, 0 5 1 1 ,0 4 2 1 , 0 5 5 1 . 0 4 4 0 . 0 1 5 - 0 .0 0 9 -0 . 0 1 1
2 0 % to 80 % 1 , 0 5 7 1, 0 7 8 1 ,0 6 4 1 , 0 8 3 1 . 0 6 9 0 . 0 2 1 - 0 .0 1 4 -0 . 0 1 5
O b s e r va t i o n s 18 , 3 8 6 18 , 3 9 2 4 0 ,5 3 9 1 8 ,3 9 2 4 0 ,5 3 9
S o u rc e : O w n ca l c u la t i on b a se d on th e Ur u g u a y an N a t io n a l H o u s e h o l d S u r v e y ( E C H ) .
N o t e : C a l c u l a t io n b a s e d o n th e re a l pe r ca p i t a h ou se h o l d in c o m e i n 1 99 7 U r u g u a y a n pe s o s , n et of so c i a l s e c u r i t y a n d in c o m e t a x .
In co m e d a t a we i g h t e d us i n g sa m p le we i g h t s .
ah o u se h o l d i n c o m e wi t h o u t c o n s id e r i n g t h e o l d he a l th sy s t e m (O H S ) in c o m e
bh o u se h o l d i n c o m e wi t h o u t c o n s id e r i n g t h e n e w h e al t h s y s t e m (N M S ) i n co m e
27

Ta b l e 4. P o l a r iz a t i o n an d in e q u a l i ty m e a s u r e s
1 9 9 4 2 0 0 4 2 0 1 0 2 0 0 4 a2 0 1 0 bD i¤ 20 0 4 - 1 9 9 4 D i¤ 20 1 0 - 2 0 0 4 D i ¤ 2 0 1 0 b- 2 0 0 4 a
In e q u a l it y
G i n i i n d e x 0 . 4 0 9 ( 0 . 0 0 3 ) 0. 4 3 9 ( 0 . 0 0 3 ) 0. 4 1 8 (0 .0 0 2 ) 0 .4 4 7 (0 . 0 0 3 ) 0. 4 3 2 (0 . 0 0 2 ) 0 . 0 3 0 * * * - 0 .0 2 1 * * * -0 . 0 1 5 * * *
G e n e r a l iz e d en t r o p y i n d e x 0 .2 9 8 (0 . 0 0 5 ) 0. 3 5 3 (0 . 0 0 8 ) 0 . 3 2 1 (0 .0 1 1 ) 0 .3 6 6 (0 . 0 0 8 ) 0. 3 4 3 (0 . 0 0 7 ) 0 . 0 5 4 * * * - 0 .0 3 2 * * * 0 . 0 2 3 * *
A t k in s o n in d e x 0. 1 3 6 ( 0 . 0 0 2 ) 0. 1 5 8 (0 . 0 0 2 ) 0 . 1 4 3 (0 .0 0 2 ) 0 .1 6 3 (0 . 0 0 3 ) 0. 1 5 2 (0 . 0 0 2 ) 0 . 0 2 1 * * * - 0 .0 1 5 * * * -0 . 0 1 1 * * *
C o e ¢ c ie n t of v a r ia t i o n in d e x 0. 9 3 4 (0 . 0 1 6 ) 1 . 0 7 7 (0 . 0 3 8 ) 1 . 0 4 9 (0 . 0 3 9 ) 1 . 1 0 6 (0 . 0 4 0 ) 1 . 0 9 2 (0 . 0 4 0 ) 0 . 1 4 3 * * * - 0 . 0 2 8 -0 . 0 1 3
P o la r i z a t io n
D u c lo s , E st e b a n an d Ra y (p o l a ri z a t io n ) In d e x
= 0 . 2 5 0 .2 9 9 (0 . 0 0 1 ) 0. 3 1 7 ( 0 . 0 0 2 ) 0. 3 0 5 (0 . 0 0 1 ) 0 . 3 2 2 (0 . 0 0 2 ) 0 . 3 1 4 (0 . 0 0 1 ) 0 . 0 1 8 * * * - 0 .0 1 3 * * * 0 .0 0 8 * * *
Id e n t i … ca t i o n 0 . 8 3 4 0. 8 1 7 0 .8 3 1 0 .8 1 8 0 . 8 2 9
C o r r e la t i o n 0 . 8 7 7 0 .8 8 4 0 .8 7 8 0 . 8 8 1 0 . 8 7 7
= 0. 5 0 0. 2 4 3 ( 0 . 0 0 1 ) 0. 2 5 8 (0 .0 0 1 ) 0 .2 4 9 (0 . 0 0 1 ) 0. 2 6 2 (0 . 0 0 1 ) 0 . 2 5 6 (0 . 0 0 1 ) 0 . 0 1 5 * * * - 0 .0 0 9 * * * -0 . 0 0 6 * * *
Id e n t i … ca t i o n 0 . 7 2 5 0. 7 0 2 0 .7 2 3 0 .7 0 4 0 . 7 2 0
C o r r e la t i o n 0 . 8 1 9 0 .8 3 7 0 .8 2 4 0 . 8 3 3 0 . 8 2 3
= 0. 7 5 0. 2 0 9 ( 0 . 0 0 1 ) 0. 2 2 2 (0 .0 0 1 ) 0 .2 1 5 (0 . 0 0 1 ) 0. 2 2 6 (0 . 0 0 2 ) 0 . 2 2 1 (0 . 0 0 1 ) 0 . 0 1 3 * * * - 0 .0 0 7 * * * - 0 . 0 0 5 * *
Id e n t i … ca t i o n 0 . 6 4 6 0. 6 2 1 0 .6 4 5 0 .6 2 5 0 . 6 4 2
C o r r e la t i o n 0 . 7 9 1 0 .8 1 4 0 .7 9 7 0 . 8 0 9 0 . 7 9 7
Fo s t e r a n d W o lf s o n
R e l a ti v e m e d i a n d e v i a t io n 0 . 5 4 5 0. 5 8 2 0 .5 5 5 0 . 5 9 1 0 . 5 7 4 0. 0 3 7 * * * - 0 . 0 1 4 * * * - 0 . 0 1 7 * * *
B i p o l a ri z a t i o n I n d e x 0 . 1 8 2 0. 2 0 0 0 .1 8 8 0 .2 0 6 0 . 1 9 7 0 . 0 1 8 * * * - 0 . 0 1 2 * * * - 0 . 0 0 9 * * *
W i t h i n g i n i i n d e x 0 . 1 3 7 0. 1 4 8 0 .1 4 0 0 .1 5 1 0 . 1 4 5 0. 0 1 1 * * * - 0 .0 0 8 * * * - 0 .0 0 6 * * *
B e t w e en g in i in d e x 0. 2 7 2 0 . 2 9 1 0 .2 7 8 0 . 2 9 6 0 . 2 8 7 0. 0 1 9 * * * - 0 . 0 1 4 * * * - 0 . 0 0 9 * * *
O b s e r va t i o n s 1 8 . 3 8 6 1 8. 3 9 2 4 0 . 5 3 9 18 , 3 9 2 4 0 , 5 3 9
S o u rc e : O w n ca l c u la t i on b a se d on th e Ur u g u a y an N a t io n a l H o u s e h o l d S u r v e y ( E C H ) .
N o t e : C a l c u l a t io n b a s e d o n th e re a l pe r ca p i t a h ou se h o l d in c o m e i n 1 99 7 U r u g u a y a n pe s o s ne t of s o ci a l s e c u r i t y a nd in c o m e t a x e s .
In co m e d a t a we i g h t e d us i n g sa m p le we i g h t s .
ah o u se h o l d i n c o m e wi t h o u t c o n s id e r i n g t h e o l d he a l t s y s te m (O H S ) i n c o m e
bh o u se h o l d i n c o m e wi t h o u t c o n s id e r i n g t h e n e w h e al t h s y s t e m (N M S ) i n co m e
* s ig n i … c a n t a t 1 0 % ; * * si g n i… c a n t a t 5% ; * * * s i g n i …c a n t at 1 % .
28

Ta b le 5 . R e l a t iv e p o l a ri z a ti o n m e a s u r e s
1994-2004 2004-2010 2004a-2010b
M e d ia n r e la t iv e p o l ar i z at i o n in d e x 0.0 6 9 * * * (0 . 0 0 6) -0 .0 5 2 * * * ( 0. 0 0 5 ) 0 . 03 5 * * * ( 0. 0 0 5 )
L ow e r re l a ti v e p o la r iz a t io n i n d ex 0. 0 76 * * * ( 0 .0 1 0 ) - 0 .0 5 8 * * * (0 . 0 0 9 ) - 0 .0 4 1 * * * (0 . 0 09 )
U pp e r r e la ti v e p o la ri z at io n ind e x 0. 0 62 * ** (0 .0 1 0) -0 .0 4 5* * * ( 0 .0 0 9) -0 .0 2 9* * * ( 0. 0 09 )
So u r ce : O w n c a lc u la t io n b a s ed on the Ur u gu a ya n Na ti o na l H o u s eh o ld Su r ve y ( E C H ) .
N o te : C al c u la t i on b a s e d o n th e r e al p e r c a pi t a h ou s e h o ld i n c o m e in 1 9 9 7 U r u gu a y an p es o s,
ne t o f s o c ia l se c u r it y a n d in c o m e t a x .I n c o m e d a ta w e i g ht e d u s in g s a m p l e we i g ht s .
aho u s e h o ld i n co m e wi th o u t c o n si d e ri n g t he o l d h ea l t h sy s t e m ( O H S ) in c o m e
bho u se h ol d i n co m e w it h ou t c o ns id e ri ng th e n ew he a lt h s ys t em (N M S ) in c om e
* si g n i… ca n t a t 1 0% ; ** s ig n i …c a nt a t 5 % ; * * * s ig n i …c a nt a t 1 % .
29

Figure 1
Middle class de…nition
30

Figure 2
Middle class and polarization curves
31

Figure 3
Actual and relative density
32

Figure 4
Location and shape e¤ects
33

Figure 5
Robustness analysis
34