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     Carlos Gradín and Máximo Rossi (*)

    Published in El Trimestre Economico, Vol. 67, No. 267, July-September 2000, Mexico


    The aim of this paper is to study the evolution of wage polarization in Uruguay during the last twelve years. The results show that wage distribution in Uruguay has gradually become more unequal and, in particular, more bipolarized. At the root of this process there lie the

    increasing premiums for qualification and experience, as well as the increasing wage differential among the different industries.

    JEL: D300, D630, I320

    (*) Respectively Departamento de Economía Aplicada, Universidade de Vigo (Spain) (cgradí and Departamento de Economía, Facultad de Ciencias Sociales, Universidad de la República (Uruguay) ( The authors thank the

    financial support given by Sida/SAREC of Sweden and the Committee for Scientific Research (CSIC) of the University of the Republic, Uruguay. We also thank the favourable comments made at the seminar of Network of Social Economics Centers in Lima, Peru, at the II Latin American Seminar of Social Economics, as well as the suggestions made by an anonymous speaker.


1- Introduction

     The aim of this paper is to study the evolution of wage polarization in Uruguay between 1986 and 1997. The analysis of polarization and, in particular, of the changes in the size of the middle-class are of particular interest if we consider that this country has always been characterized by stable indicators of inequality, despite all its structural changes (Bucheli and Rossi, 1994; Vigorito, 1998).

    Recent studies on the evolution of inequality for certain items of households’ total income reveal some important changes that had usually remained hidden in the global analysis. Bucheli and Rossi (1994) describe significant changes in pension distribution

    while Miles and Rossi (1999) show the growing trend of inequality in wage income distribution since the early nineties. These changes are closely related to changes in the labor market. As regards the supply, there has been an increase in women?s participation rate and in the educational levels of the new generations; and as regards the demand, there seems to be an increasing preference for educated labor force. All these changes have taken place within the framework of a more open economy since the advent of MERCOSUR, and of some crucial changes in the mechanisms of wage negotiation, which have become more decentralized as of 1990.

    This paper is divided into six sections. In the next section we shall be discussing inequality and polarization measures. In section three we have included the sources of data for Uruguay; in section four we outline the results; in section five we analyze the causes of the growing polarization process and, in section six, we present the most relevant conclusions.

2- Inequality and polarization.

     2.1.- Measuring inequality.

     Wage inequality is given by the degree of wage dispersion with respect to a reference value, the mean wage, which describes the situation of perfect equality as being the same wage for every worker. To measure it we shall be employing three indices that are 1consistent with Lorenz criterion: the Gini coefficient, the Theil coefficient and the

    coefficient of variation. Therefore, if we transfer a monetary unit from any individual to another one with a lower wage, the three indices will register a fall in inequality levels. The

    main difference among them is that if we consider two transfers at the same time, one that

    reduces inequality and another one that increases it, the final result will depend on the weight that each index gives to both of them. Such weight will depend, in turn, on the position of each of the affected individuals within distribution, as each index has different sensitivities to transfers that occur at different points in income distribution.

    Let us consider a set of wages xi, I=1,…,n that have F as the distribution function.

     1 That means they satisfy the principles of anonymity, scale independence and population, as well as the Pigou-Dalton transfer principle.


The mean is indicated by . The Gini coefficent G is defined as twice the area between the

    Lorenz curve and the perfect equality line, and can be expressed as:

    nn1xx. (1) G(F)=??ij22nij!!11

     This index is more sensitive to the transfers that occur in the center of the distribution, while the coefficient of variation and Theil coefficient are more sensitive to the upper and lower tails respectively. For ln, the natural log, Theil is defined by:

    n?xx1ii T(F)= (2) ??1n???n1i?

And the coefficient of variation by:

    n112 CV(F)= (3) ;;x.?in1i

     2 We should bear in mind that the Gini coefficient is bounded between 0 and 1, while 3the other two indices take values equal to or larger than 0 but do not have an upper bound.

     2.2- Measuring polarization.

     The notion of inequality refers to the existence of only one pole and the measurement of dispersion with respect to that pole. However, if we wish to study to what extent different poles are beginning to form in the distribution, then the notion of polarization is more appropriate. Thus, the situation of extreme polarization is reached when distribution is divided into two large groups internally homogeneous, situated at the extremes of the distribution, each of them holding half the population.

    Esteban and Ray (1994) describe polarization as having three basic characteristics: it increases with the degree of heterogeneity between the groups of the distribution, and with their internal homogeneity; and, as far as it concerns polarization, small groups are not very relevant. The last two characteristics, point out the differences between polarization

    and inequality since more internal homogeneity brings about a fall in inequality levels and

    2 This is true for the case of non-negative incomes and it applies in our case since we are taking into account hourly wages.

    3n1 The upper limits increase with n: in Theil, ln(n) and in CV, . See Cowell (1995) for more details.


    an increase in polarization, and the highest level of inequality is reached when the entire income is gathered in only one individual.

    To measure polarization we shall use the measure described in Esteban, Gardín and Ray (1999) which is just an extension of Esteban and Ray’s initial proposal.

     We are interested in learning to what extent the distribution F is comprised by k

    groups, and the degree of intensity of the polarization associated to those k groups. A

    ~=(z,z,z,…,z; y,y,…y; p,p,…,p) simplified representation of F is given by a partition 012k12k12k

    which generates k groups, where the i-th group is defined by a share p of the workers i

    ,(z,zwhose wages fall within the interval and whose mean wage is y. When we use ~ ii1i

    to represent F we make an approximation error (F;~) that we define in terms of the degree

    of wage dispersion within the groups, measured by the Gini coefficient:

     :;F;~; G(F)-G;~;, (4)

    That is to say, the difference between the inequality -measured by Gini- of the 4population and the inequality we would have if the groups were internally homogeneous.

    The error represents the lack of internal identification of the k groups of distribution, and we will choose the optimal partition ~ which, given k, generates more internally identified

    and cohesive groups, that is, it minimizes the error given by (4).

     Since, according to Esteban and Ray, polarization increases with heterogeneity among groups (polarization in ~) and with their internal homogeneity (or identification), EGR express total polarization of the distribution F as the polarization of said partition,

    minus the lack of internal identification:

     P(F; , , ~; ER;;, ~; -,:;F, ~;, (5)

     5where ER represents the polarization measure in Esteban and Ray (1994) applied to ~:

    kk1;;ER,~ (6) ppyy??ijiji1i1

     4 In other words, the within group component after decomposing the Gini coefficient into a within group term and a between group one. 5 Basically, the polarization adds the antagonistic feelings existing in the distribution, as a result of the identification among the members of the same group and of the alienation towards the members of different groups. The subtraction of the error term in (5) takes into account that no group is completely homogeneous. Thus, the greater the internal dispersion among these groups, the lower the identification of their members will be and, therefore, so will polarization. The median is the only family consistent both with a model of individual attitudes and a set of axioms that describe situations in which polarization should increase.


    6. And is the weight given to the for in [1;1.6] indicating the sensitivity to polarization7lack of internal identification.

     If we replace ~ with ~ in (5), we shall obtain the measure of polarization that we employed for this study, although we shall only focus on the creation of two poles, or bipolarization. In this way, we will be able to investigate to what extent the distribution 8tends to emphasize the two extremes in detriment of its center.

     In this particular case where k=2 the measure will divide the population into two

    groups as homogeneous as possible, and then it shall calculate the bipolarization between them subtracting the lack of internal identification. The optimal partition shall divide the population into those who are below the mean, a proportion p=F(;;, and those who are

    above the mean. In the case that ;!,!1 is given by:

     P(F; 1,,! 1,z!;; 2p L;p;( 2D(F) G(F), (7)


     D=pL(p) (8)

     9is the Mean Relative Deviation.

     We have also employed the measure W proposed by Wolfson (1994, 1997), a

    transformation of (5) when we establish that the two underlying groups have the same size, 10thus the median m shall indicate the cutting point. This index that takes values between 0

    and 1 is given by:

     6 The interval is obtained as a consequence of establishing a set of axioms. The higher the sensitivity to polarization, the further we get from the notion of inequality as we give more weight to the concentration in groups. 7 The ER index takes values between 0 and 2 when it is expressed in incomes relative to the mean, but does not have an upper bound when it is expressed in incomes in log as it happens in Esteban and Rray 1994). As

    a result, the index expressed in (5) has 2 as a maximum, but the minimum will depend on and on the way of

    obtaining ~. In any case, it will never be less than -. 8 See Wolfson’s (1994) example to understand why in the case of an increasing bipolarization, the indices consistent with Lorenz reveal a decrease in inequality levels. 9 The index expressed in (7) shall take values between 0 and 2, although this is not the case when using incomes in log, such as in Esteban and Ray (1994), for ER. 10 Consequently, in the case ;!,!1, the differences between the two indices shall be given by the treatment given to the progressive transfers crossing the mean but not the median (and viceversa). In that case, said transfers will produce an increase in bipolarization with W and an decrease with EGR (and viceversa). If the transference crosses both the mean and the median, then both indices will register a lower bipolarization level; if it crosses none of them, both will register a higher bipolarization level. See Gradín (1999c).


    ((11? (9) ;;;;W2PF;1,1,zm22LGF??)?)?mm22?????

     In this approach we assume that the element which determines the group a worker belongs to, is his/her wage. But there may be other characteristics that determine said belonging, such as the sector (private or public), the industry, his/her educational level, sex, etc. In this case we shall choose the partition determined by each of the observed

    characteristics. Therefore, the total polarization shall be the polarization observed in the representation or polarization between groups, subtracting their lack of internal identification. In this case, said lack of identification depends not only on wage dispersion within the group but also on its overlapping degree with respect to the rest of the groups. 11We shall employ the transformation P=P+ so that the index takes non-negative values.

     2.3.- Bipolarization determinants.

     In the case of bipolarization, and assuming that the groups are as heterogeneous as possible in terms of wage internal differences, we are interested in learning about the causes of said bipolarization. Thus, the two large groups could be actually based on the individuals’ qualification, so that the group with lower wages corresponds to the poorly qualified workers and the group with higher wages corresponds to the better-qualified workers, according to their educational level. In the same way, other factors, such as occupation, private or public sector, sex, etc., could also explain the division.

     Gradín (1999b) set out to compare the bipolarization observed when the determining factor for the creation of the two groups was wage proximity, as shown in the previous section, to the bipolarization resulting from grouping individuals according to a certain characteristic. From said comparison there arose what we call bipolarization proportion, which is explained by each one of the observable characteristics. This simple descriptive analysis allows us to identify the elements associated to a certain level of wage bipolarization, as well as its evolution in time.

     For a given characteristic, if q is the share of workers belonging to categories of that

    characteristic such that the mean wage is situated below the global mean, and y being its 1

    mean wage, with y being the mean wage of the remaining 1-q individuals. Thus, we 2

    define DB as:

    yy21;;DBq1q (10)

     11 The minimum value of P is -. Let us take into account that, unlike (5), in this case the groups are not income intervals.


     D being the Relative Deviation with respect to the Mean as defined in (8), the index which gathers the explanatory degree, is defined as:

     EP(F)=DB/D (11)

     Said index takes values between 0, when the characteristic does not explain 12anything, and 1, when the characteristic explains everything. The latter shall occur when,

    given the characteristic of any one individual, we are able to deduce which group –“rich” or

    “poor”- s/he belongs to. This would be the case if, for example, all the members of the poor group shared certain educational levels while all the members of the rich group shared other educational levels. But should crossings occur and should we find individuals with a similar educational level in different groups, then said variable will prove less explanatory. Due to the correlation between the different characteristics, the sum of the different indices may exceed 1.

3 - The data.

     This paper is based on the Continue Household Survey conducted by the Statistics National Office in Uruguay. This survey provides information on urban population in two large regions: Montevideo, the capital city, where over half the total population lives, and the Rest of the Urban Country (RUC).

     This survey has been conducted, with the present layout, monthly since 1981 and contains individual data on monthly wage income, non-wage income, age, sex, educational

    levels, working hours and other significant variables.

     For this study we have taken into account the data of currently employed individuals who have received a positive wage in their main occupation.

     The variable under study is hourly compensation for the main occupation, which has been deflated by the Consumer Price Index for December 1996.

    4 - Inequality and bipolarization in wage distribution in Uruguay.

     The characteristic feature of wage distribution in Uruguay, within the South American framework, has always been low inequality levels. Several studies on the matter by Bucheli and Rossi (1994) and Vigorito (1998) reveal that income distribution in the last fifteen years has not presented any significant changes, unlike the situation in the rest of the Latin American countries where there has been an increase in inequality levels.

     12 Although we talk about an explanatory degree, the index does not establish causal relations, due to the fact that polarization may be explained by another variable, highly correlated to the one we are actually observing.


     Studies such as the ones carried out by Bucheli and Rossi, Miles and Rossi or Vigorito, shed light on the fact that such stable equality levels are accompanied by other changes between the different income sources and within those sources themselves. More detailed analyses refer to pension distribution and the distribution of wage compensations.

     If we observe the behavior of the Uruguayan economy from 1986 to 1994, it is noticeable that the GNP grown substantially in comparison to previous years; in 1995 the economy suffered from a recession but recovered in 1996.

     The economic policy during such period was mainly characterized by: i) a gradual trade opening and the creation of a free trade zone (MERCOSUR) and ii) the implementation of a stabilization plan which resulted in a considerable fall in inflation.

     As regards the labor market, there was a rise in employment and in real wage up to 1994, due to the increase in women’s participation and to higher levels of human capital of

    the working force. Trade openness brought along a fall in employment both in the industrial sector and, as a consequence of the policies implemented for the State reform, in the public sector.

     An important institutional reform was introduced in the labor market in connection with the degree of decentralization of wage negotiation: since 1990 negotiations have become decentralized and union affiliation levels have fell.

     In graphs 1 to 17 we present the results obtained.


    In graphs 1 and 2 we can see that after a period of certain stability in wage income distribution, there followed a clear increment in inequality levels, both in the capital and in the rest of the country, especially as of 1990. This increment is registered by the three indices and it becomes more noticeable if sensitivity to transfers increases in the lower tail of the distribution. The Theil index rose by 36% between 1990 and 1996 in the capital,

    compared to 17% for Gini and CV, and something similar happened in the rest of the country between 1986-97 where there was an increase of 30% compared to a 12% and a 21% respectively. Starting from similar levels of inequality, the increase was more significant in the capital than in the rest of the country, except for the case of the coefficient of variation, since CV is more sensitive to the transfers that occur in the upper tail of the distribution.


    If we calculate bipolarization indices, as shown in graphs 3 and 4, we will find that said tendencies have become more pronounced. There was a sharp increment in bipolarization, especially in the capital and, to a lesser extent, in the rest of the country. This increase has been steady in both cases since 1987, except for the term 1992-93 in the capital, but it proved sharper in the rest of the country in the late eighties and in the capital as of the mid-nineties. From 1987 to 1997, bipolarization increased between a 20% and a 33% in the rest of the country, and between a 25% and a 38% in the capital (mostly concentrated as of 1990). In both cases polarization increased with sensitivity to polarization. This, together with the fact that distributive changes have been more appreciable and continuous than those in inequality, leads us to believe that the former are better registered when using these types of indices.


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