Measuring income inequality via percentile relativities
Bibliographic record
Abstract
The adage "the rich are getting richer" refers to increasingly skewed and heavily-tailed income distributions. For such distributions, the mean is not the best measure of the center, but the classical indices of income inequality, including the celebrated Gini index, are mean based. In view of this, it has been proposed in the literature to incorporate the median into the definition of the Gini index. In the present paper we make a further step in this direction and, to acknowledge the possibility of differing viewpoints, investigate three median-based indices of inequality. These indices overcome past limitations, such as: (1) they do not rely on the mean as the center of, or a reference point for, income distributions, which are skewed, and are getting even more heavily skewed; (2) they are suitable for populations of any degree of tail heaviness, and income distributions are becoming increasingly such; and (3) they are unchanged by, and even discourage, transfers among the rich persons, but they encourage transfers from the rich to the poor, as well as among the poor to alleviate their hardship. We study these indices analytically and numerically using various income distribution models. Real-world applications are showcased using capital incomes from 2001 and 2018 surveys from fifteen European countries.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.004 | 0.026 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.006 | 0.007 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.001 | 0.004 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".