On the size distortion of tests after an overidentifying restrictions pretest
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Bibliographic record
Abstract
SUMMARY In the linear instrumental variables model, we provide theoretical and Monte Carlo evidence for the size distortion of a two‐stage hypothesis test that uses a test of overidentifying restrictions (OR) in the first stage. We derive a lower bound for the asymptotic size of the two‐stage test. The lower bound is given by the asymptotic size of a test that rejects the null hypothesis when two conditions are met: the test of OR used in the first stage does not reject and the test in the second stage rejects. This lower bound can be as large as 1 − ε P , where ε P is the pretest nominal size, for a parameter space that allows for local non‐exogeneity of the instruments but rules out weak instruments. Copyright © 2011 John Wiley & Sons, Ltd.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 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 it