The Surprising Hybrid Pedigree of Measures of Diversity and Economic Concentration
Bibliographic record
Abstract
Measures of economic concentration, such as the k-firm concentration index and the Hirschman-Herfindahl Index (HHI) are commonly used to ascertain the competitiveness of a product market.Within a Cournot model industry equilibrium, it is known a relationship exists between the HHI and the gap between industry price and marginal cost, but the economic theory foundations and intuition underlying the HHI formula are seemingly arbitrary.Here we document that there are indeed powerful and intuitive theoretical foundations to the HHI, but those foundations emanate from outside economics, namely, ecology, where the HHI is known as Simpson's Diversity Index.We discuss the origins of the HHI and Simpson's Diversity Index, summarize other measures of concentration, and link them to common measures of inequality.Based on a priori reasoning, we conclude there is little on which to base a choice between the HHI and non-HHI measures of market concentration.We empirically illustrate the implementation of the HHI and other concentration indexes as the statin drug LipitorTM lost patent protection and faced generic competition in 2012; we find very similar empirical trends and high correlations among them.Our research provides support for the continued use of HHI as a measure of concentration, provided one recognizes its link to market power is equivocal.
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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 | 0.008 | 0.043 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.005 | 0.005 |
| Science and technology studies | 0.002 | 0.016 |
| Scholarly communication | 0.005 | 0.014 |
| Open science | 0.001 | 0.004 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.003 | 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".