Inference in second-order identified models
Bibliographic record
Abstract
We explore the local power properties of different test statistics for conducting inference in moment condition models that only identify the parameters locally to second order. We consider the conventional Wald and LM statistics, and also the Generalized Anderson–Rubin (GAR) statistic (Anderson and Rubin, 1949; Dufour, 1997; Staiger and Stock, 1997; Stock and Wright, 2000), KLM statistic (Kleibergen, 2002; Kleibergen, 2005) and the GMM extension of Moreira (2003) (GMM-M) conditional likelihood ratio statistic. The GAR, KLM and GMM-M statistics are so-called “identification robust” since their (conditional) limiting distribution is the same under first-order, weak and therefore also second order identification. For inference about the model specification, we consider the identification-robust J statistic (Kleibergen, 2005), and the GAR statistic. Interestingly, we find that the limiting distribution of the Wald statistic under local alternatives not only depends on the distance to the null hypothesis but also on the convergence rate of the Jacobian. We specifically analyse two empirically relevant models with second order identification. In the panel autoregressive model of order one, our analysis indicates that the Wald test of a unit root value of the autoregressive parameter has better power compared to the corresponding GAR test which, in turn, dominates the KLM, GMM-M and LM tests. For the conditionally heteroskedastic factor model, we compare Kleibergen (2005) J and the GAR statistics to Hansen (1982) overidentifying restrictions test (previously analysed in this context by Dovonon and Renault, 2013) and find the power ranking depends on the sample size. Collectively, our results suggest that tests with meaningful power can be conducted in second-order identified models.
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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 | 0.037 | 0.199 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.004 | 0.003 |
| Bibliometrics | 0.004 | 0.003 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.004 | 0.007 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.003 | 0.004 |
| Insufficient payload (model declined to judge) | 0.006 | 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".