Identification-robust methods for comparing inequality with an application to regional disparities
Bibliographic record
Abstract
Abstract We propose Fieller-type methods for inference on generalized entropy inequality indices in the context of the two-sample problem which covers testing the statistical significance of the difference in indices, and the construction of a confidence set for this difference. In addition to irregularities arising from thick distributional tails, standard inference procedures are prone to identification problems because of the ratio transformation that defines the considered indices. Simulation results show that our proposed method outperforms existing counterparts including simulation-based permutation methods and results are robust to different assumptions about the shape of the null distributions. Improvements are most notable for indices that put more weight on the right tail of the distribution and for sample sizes that match macroeconomic type inequality analysis. While irregularities arising from the right tail have long been documented, we find that left tail irregularities are equally important in explaining the failure of standard inference methods. We apply our proposed method to analyze income per-capita inequality across U.S. states and non-OECD countries. Empirical results illustrate how Fieller-based confidence sets can: (i) differ consequentially from available ones leading to conflicts in test decisions, and (ii) reveal prohibitive estimation uncertainty in the form of unbounded outcomes which serve as proper warning against flawed interpretations of statistical tests.
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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 | 0.022 | 0.112 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.004 | 0.003 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 0.000 |
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".