### Abstract

This article analyzes the mathematical connections between two kinds of inequality: inequality between persons (e.g., income inequality) and inequality between subgroups (e.g., racial inequality). The authors define a general inequality parameter in two-parameter continuous distributions. This parameter governs all measures of personal inequality (e.g., the Gini coefficient) and governs as well the gap (difference or ratio) between the means of subdistributions. It is thus established that in the distributions analyzed here, as personal inequality increases, so does inequality between subgroups. This general inequality parameter also governs Lorenz dominance and all quantities in the decomposition of Theil's mean logarithmic deviation into between-subgroup and within-subgroup components in the Pareto case. Thus, the general inequality parameter captures the ''deep structure'' of inequality. Finally, a whole-distribution graphical tool is introduced for assessing personal and subgroup inequality. Substantively, this work suggests that in societies characterized by special income distributions, whenever inequality disrupts social cohesion, it attacks on two fronts, via subgroup inequality as well as personal inequality.

Original language | English (US) |
---|---|

Pages (from-to) | 31-74 |

Number of pages | 44 |

Journal | Sociological Methods and Research |

Volume | 37 |

Issue number | 1 |

DOIs | |

State | Published - Aug 2008 |

### Fingerprint

### Keywords

- Atkinson measure
- Coefficient of variation
- Continuous univariate distributions
- Gini coefficient
- Lognormal distribution
- Lorenz curve
- Pareto distribution
- Power-function distribution
- Theil's MLD
- Two-parameter distributions

### ASJC Scopus subject areas

- Social Sciences (miscellaneous)
- Sociology and Political Science

### Cite this

*Sociological Methods and Research*,

*37*(1), 31-74. https://doi.org/10.1177/0049124108318971

**Two types of inequality : Inequality between persons and inequality between subgroups.** / Jasso, Guillermina; Kotz, Samuel.

Research output: Contribution to journal › Article

*Sociological Methods and Research*, vol. 37, no. 1, pp. 31-74. https://doi.org/10.1177/0049124108318971

}

TY - JOUR

T1 - Two types of inequality

T2 - Inequality between persons and inequality between subgroups

AU - Jasso, Guillermina

AU - Kotz, Samuel

PY - 2008/8

Y1 - 2008/8

N2 - This article analyzes the mathematical connections between two kinds of inequality: inequality between persons (e.g., income inequality) and inequality between subgroups (e.g., racial inequality). The authors define a general inequality parameter in two-parameter continuous distributions. This parameter governs all measures of personal inequality (e.g., the Gini coefficient) and governs as well the gap (difference or ratio) between the means of subdistributions. It is thus established that in the distributions analyzed here, as personal inequality increases, so does inequality between subgroups. This general inequality parameter also governs Lorenz dominance and all quantities in the decomposition of Theil's mean logarithmic deviation into between-subgroup and within-subgroup components in the Pareto case. Thus, the general inequality parameter captures the ''deep structure'' of inequality. Finally, a whole-distribution graphical tool is introduced for assessing personal and subgroup inequality. Substantively, this work suggests that in societies characterized by special income distributions, whenever inequality disrupts social cohesion, it attacks on two fronts, via subgroup inequality as well as personal inequality.

AB - This article analyzes the mathematical connections between two kinds of inequality: inequality between persons (e.g., income inequality) and inequality between subgroups (e.g., racial inequality). The authors define a general inequality parameter in two-parameter continuous distributions. This parameter governs all measures of personal inequality (e.g., the Gini coefficient) and governs as well the gap (difference or ratio) between the means of subdistributions. It is thus established that in the distributions analyzed here, as personal inequality increases, so does inequality between subgroups. This general inequality parameter also governs Lorenz dominance and all quantities in the decomposition of Theil's mean logarithmic deviation into between-subgroup and within-subgroup components in the Pareto case. Thus, the general inequality parameter captures the ''deep structure'' of inequality. Finally, a whole-distribution graphical tool is introduced for assessing personal and subgroup inequality. Substantively, this work suggests that in societies characterized by special income distributions, whenever inequality disrupts social cohesion, it attacks on two fronts, via subgroup inequality as well as personal inequality.

KW - Atkinson measure

KW - Coefficient of variation

KW - Continuous univariate distributions

KW - Gini coefficient

KW - Lognormal distribution

KW - Lorenz curve

KW - Pareto distribution

KW - Power-function distribution

KW - Theil's MLD

KW - Two-parameter distributions

UR - http://www.scopus.com/inward/record.url?scp=47149104082&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=47149104082&partnerID=8YFLogxK

U2 - 10.1177/0049124108318971

DO - 10.1177/0049124108318971

M3 - Article

VL - 37

SP - 31

EP - 74

JO - Sociological Methods and Research

JF - Sociological Methods and Research

SN - 0049-1241

IS - 1

ER -