Specification testing for conditional moment restrictions under local identification failure
Bibliographic record
Abstract
In this paper, we study the asymptotic behavior of specification tests in conditional moment restriction models under first‐order local identification failure with dependent data. More specifically, we obtain conditions under which the conventional specification test for conditional moment restrictions retains its standard normal limit when first‐order local identification fails but global identification is still attainable. In the process, we derive some novel intermediate results that include extending the first‐ and second‐order local identification framework to models defined by conditional moment restrictions, establishing the rate of convergence of the GMM estimator and characterizing the asymptotic representation for degenerateU‐statistics under strong mixing dependence. Importantly, the specification test is robust to first‐order local identification failure regardless of the number of directions in which the Jacobian of the conditional moment restrictions is degenerate and remains valid even if the model is first‐order identified.
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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 | 0.039 | 0.245 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.006 |
| Scholarly communication | 0.002 | 0.007 |
| Open science | 0.003 | 0.005 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.004 | 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".