A defense of an entropy based index of multigroup segregation

This paper defends the use of the entropy based Mutual Information index of multigroup segregation for the following five reasons. (1) It satisfies 14 basic axioms discussed in the literature when segregation takes place along a single dimension. (2) It is additively decomposable into between- and within-group terms for any partition of the set of occupations (or schools) and the set of demographic groups in the multigroup case. (3) The underlying segregation ordering has been recently characterized in terms of 8 properties. (4) It is a monotonic transformation of log-likelihood tests for the existence of segregation in a general model. (5) It can be decomposed so that a term independent of changes in either of the two marginal distributions can be isolated in pair wise segregation comparisons. Other existing measures of segregation have not been characterized, fail to satisfy one or more of the basic axioms, do not admit a between- within-group decomposition, have not been motivated from a statistical approach, or are based on more restricted econometric models

The axiomatic properties of an entropy based index of segregation

This paper reviews the properties suggested in the methodological literature on the measurement of occupational gender segregation. It is found that an index of (relative) segregation based on the entropy concept, IE, satisfies thirteen basic axioms previously proposed in the single-dimensional case, and can be expressed as the sum of a between-group and a within-group term both for any partition of the set of occupations and in the two-dimensional case

Additively decomposable segregation indexes. The case of gender segregation by occupations and human capital levels in Spain

Building upon the ideas first exposed by Theil and Finizza (1971) and Fuchs (1975), this paper presents an additively decomposable segregation index based on the entropy concept used in information theory. For any pair of classification variables in a given year, the index is decomposed into a between-group and a within-group term. To analyze intertemporal changes in gender segregation for a given partition, the index is decomposed into two terms that capture, respectively, gender composition effects, and changes in the groups' demographic importance. These decompositions are illustrated with Spanish data on occupations and human capital levels for 1977 and 1992. It is found that, in both years, the higher the educational level, the smaller is gender segregation for all age groups. Moreover, gender segregation decreases with age in all educational categories. However, most gender segregation takes place within, rather than between, age/education categories. Lastly, changes in gender composition across occupations, nearly offset by occupational mix changes, account for a decline of 2% in total gender segregation over this period

ADDITIVELY DECOMPOSABLE SEGREGATION INDEXES. THE CASE OF GENDER SEGREGATION BY OCCUPATIONS AND HUMAN CAPITAL LEVELS IN SPAIN

Building upon the ideas first exposed by Theil and Finizza (1971) and Fuchs (1975), this paper presents an additively decomposable segregation index based on the entropy concept used in information theory. For any pair of classification variables in a given year, the index is decomposed into a between-group and a withingroup term. To analyze intertemporal changes in gender segregation for a given partition, the index is decomposed into two terms that capture, respectively, gender composition effects, and changes in the groups’ demographic importance. These decompositions are illustrated with Spanish data on occupations and human capital levels for 1977 and 1992. It is found that, in both years, the higher the educational level, the smaller is gender segregation for all age groups. Moreover, gender segregation decreases with age in all educational categories. However, most gender segregation takes place within, rather than between, age/education categories. Lastly, changes in gender composition across occupations, nearly offset by occupational mix changes, account for a decline of 2% in total gender segregation over this period.

GENDER SEGREGATION BY OCCUPATION IN THE PUBLIC AND THE PRIVATE SECTOR. THE CASE OF SPAIN

In many countries, recruiting and promotion procedures in the public sector would appear to leave less room for gender discrimination than in the private sector. Using data for Spain in 1977 and 1992, this paper explores the consequences of these practices for gender segregation in those occupations where there is a private and a public sector of a minimum size. In particular, an additive index based on the entropy concept is used to compare occupational gender segregation in the private versus the public sector. It is found that gender segregation in the private sector is 14% larger than in the public sector in 1977 and 32% larger in 1992. During the 1977-1992 period, gender segregation in the public sector remains basically constant but increases by 15% in the private sector. The additive decomposability property of the index is used to highlight the role of public hiring procedures and other socio-economic factors in differences of gender segregation across occupations.

THE AXIOMATIC PROPERTIES OF AN ENTROPY BASED INDEX OF SEGREGATION

This paper reviews the properties suggested in the methodological literature on the measurement of occupational gender segregation. It is found that an index of (relative) segregation based on the entropy concept, IE, satisfies thirteen basic axioms previously proposed in the single-dimensional case, and can be expressed as the sum of a between-group and a within-group term both for any partition of the set of occupations and in the two-dimensional case.

GENDER SEGREGATION: FROM BIRTH TO OCCUPATION

This paper offers a framework to study the gender segregation induced, not only by occupational choices among the employed population, but also by human capital characteristics and labor market participation decisions in the population consisting of non-students of working age. For that purpose, an additively decomposable gender segregation index related to the entropy notion in information theory is used. The approach is illustrated with Labor Force Survey data for Spain in 1977 and 1992. It is found that gender differences in labor market participation behavior is the most important source generating gender segregation in a given moment in time and the reduction in overall gender segregation during this period.

AN EVALUATION OF AN ENTROPY BASED INDEX OF SEGREGATION

This paper reviews the properties suggested in the methodological literature on the measurement of gender segregation by occupation. It is found that an index of segregation based on the entropy concept satisfies twelve basic axioms previously proposed in the single-dimensional case. This index can be expressed as the sum of a between-group and a within-group term in the two-dimensional case. In pair-wise comparisons, it can be meaningfully decomposed into three terms, one of which is independent of both the gender composition of the population and the population’s distribution across occupations. Finally, it can be motivated as two different loglikelihood tests in nonparametric econometric models. Other existing measures of segregation either fail to satisfy one or more of the basic axioms, do not admit a between/within decomposition, have not been motivated from a statistical approach, or are based on more restricted econometric models.