Higher order properties of GMM and generalised empirical likelihood estimators
Bibliographic record
Abstract
In an effort to improve the small sample properties of generalized method of moments (GMM) estimators, a number of alternative estimators have been suggested. These include empirical likelihood (EL), continuous updating, and exponential tilting estimators. We show that these estimators share a common structure, being members of a class of generalized empirical likelihood (GEL) estimators. We use this structure to compare their higher order asymptotic properties. We find that GEL has no asymptotic bias due to correlation of the moment functions with their Jacobian, eliminating an important source of bias for GMM in models with endogeneity. We also find that EL has no asymptotic bias from estimating the optimal weight matrix, eliminating a further important source of bias for GMM in panel data models. We give bias corrected GMM and GEL estimators. We also show that bias corrected EL inherits the higher order property of maximum likelihood, that it is higher order asymptotically effcient relative to the other bias corrected estimators.
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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 | 0.013 | 0.083 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.007 | 0.002 |
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".