compute inequality metrics

This paper addresses the challenge of measuring subgroup inequality under continuous covariates. Methodologically, it proposes conditional inequality curves—specifically, conditional Zenga and D indices—and develops a unified estimation framework based on quantile regression. To ensure monotonicity of the conditional quantile function and prevent quantile crossing, the framework incorporates isotonic regression—a novel adaptation in this context. Furthermore, the paper introduces the concept of the “conditional quantile inequality curve,” enabling fine-grained characterization of how inequality evolves continuously with covariates. Simulation studies demonstrate that the proposed estimators achieve superior accuracy compared to alternatives. Empirical application to wage data reveals that each additional year of employee age is associated with a statistically significant increase in wage inequality, underscoring the method’s validity, robustness, and substantive interpretability. This work constitutes the first systematic extension of conditional inequality measurement to settings with continuous covariates, thereby filling a critical methodological gap in inequality econometrics.

This study addresses the lack of cross-national comparability in global Gini coefficient estimates, which arises from discrepancies in data sources, welfare metrics, and methodological choices. By harmonizing 12 international databases, the authors construct a unified dataset encompassing 222 countries and over 122,000 observations. They provide the first systematic quantification of pairwise inconsistencies among alternative Gini estimates for the same country-year and rigorously assess the influence of key factors—including welfare indicators, reference units, equivalence scales, and survey design. The analysis reveals that Gini coefficients for identical country-years can differ by as much as 50 percentage points, with the choice of welfare metric identified as the primary driver of cross-country incomparability. The paper proposes a methodological framework to enhance temporal and spatial comparability, establishing a standardized foundation for measuring economic inequality.

This study investigates whether classical inequality measures satisfy the decomposability axiom in the context of three-person income distributions and reveals the geometric manifestations of their violations. By modeling such distributions on a two-dimensional income-share simplex, the decomposition of overall inequality into within- and between-group components is recast as a geometric constraint. The paper provides the first visual characterization—within the simplest nontrivial setting—of the decomposition behavior of prominent indices, including the mean log deviation, Gini coefficient, coefficient of variation, and Theil index. It clearly identifies the distinct geometric patterns through which each measure deviates from strict decomposability, thereby deepening the understanding of their structural properties and offering an intuitive basis for selecting and comparing inequality measures.

This study constructs a continuous family of inequality measures that unifies the Hoover index and the Gini coefficient. By normalizing a convex combination of mean deviation and the expected absolute pairwise difference, the authors propose a new class of indices satisfying scale invariance and the Pigou–Dalton transfer principle. Under the assumption of a gamma distribution, closed-form expressions are derived using the incomplete gamma function, and an explicit formula for the bias of the plug-in estimator is provided. Monte Carlo simulations demonstrate that both bias and mean squared error of the estimator decline substantially with increasing sample size. Empirical analysis using per capita GDP data confirms the practical utility and flexibility of the proposed framework.

This paper addresses the low estimation accuracy of the Gini coefficient in small samples by proposing a new class of income inequality measures that are analytically tractable and asymptotically equivalent to the Gini coefficient. Methodologically, it establishes a generalized inequality measurement framework that balances theoretical rigor with computational feasibility. Theoretically, the strong consistency and asymptotic normality of the proposed estimator are rigorously established. Through Monte Carlo simulations and empirical analyses using micro-level income data from multiple countries, the estimator demonstrates superior finite-sample performance compared to conventional interpolation or kernel density–based approaches—exhibiting lower bias and mean squared error, and greater robustness in capturing tail behavior and structural shifts in income distributions. The work contributes both a novel theoretical tool and a practical solution for measuring economic inequality.

Traditional inequality measures struggle to capture the joint inequality structure of multidimensional socioeconomic variables. This study addresses this limitation by extending the Zenga inequality measure to the bivariate setting for the first time, constructing a Zenga surface and a vector-valued Zenga curve based on the bivariate quantile function, along with corresponding nonparametric estimation methods. The proposed framework enables a nuanced characterization of the distributional features of multidimensional inequality. Empirical analysis focusing on digital inequality reveals complex patterns of disparity between national broadband penetration rates and digital literacy levels across countries, thereby demonstrating the effectiveness and practical utility of the method.

This study addresses significant discrepancies in global Gini coefficient estimates across data sources, which undermine the accuracy of policy formulation. By systematically integrating over 120,000 Gini observations spanning 158 years and covering 222 countries and territories, the authors construct the first unified and comparable database. Through a comprehensive literature review and statistical modeling, they quantify how measurement dimensions—such as income versus consumption and pre-tax versus post-tax—systematically affect Gini estimates. The analysis reveals that income-based Gini coefficients are on average 4.7 points higher than consumption-based ones, with this gap widening over time. To correct for welfare concept–induced biases, the study proposes adjustment factors and underscores data transparency as essential for achieving cross-source comparability.

This study addresses a critical flaw in the existing Beta Lorenz curve, whose parameter space fails to satisfy the theoretical constraints inherent to Lorenz curves, leading to systematic bias in estimating poverty and inequality from grouped income data. The authors explicitly identify this deficiency for the first time and propose a novel four-parameter family of Lorenz curves that rigorously adheres to all formal properties of genuine Lorenz curves while retaining practical usability. Through parametric modeling, derivation of necessary constraints, and extensive empirical validation across more than 2,000 datasets, the new model demonstrates superior performance in estimating poverty and inequality metrics. Specifically, it significantly reduces the systematic underestimation of poverty levels observed in over 80% of cases compared to the widely used General Quadratic (GQ) Lorenz curve.

This study investigates the finite-sample bias of inequality index estimators based on order statistics, with a focus on unbiasedness under non-negative distributions such as the gamma family. By developing a unified framework encompassing several classical inequality measures, the work proposes a U-statistic-based estimator that averages weighted order statistics over fixed-size subsamples and normalizes by the sample mean. The paper establishes, for the first time, that this estimator is exactly unbiased for gamma populations at any sample size. It further introduces a general bias decomposition technique that isolates the effect of random normalization across different rank levels. Asymptotic unbiasedness is proven under mild moment conditions, and Monte Carlo simulations corroborate the theoretical findings.