Impact of Instrument Endogeneity on some Test-Statistics
Bibliographic record
Abstract
When in a regression model some of the explanatory variables are correlated with the disturbance term, one needs further variables to use as instruments in order to make reliable inferences. The test-statistics often used for making these inferences are based on so-called orthogonality conditions, i.e. the instrumental variables are not correlated with the disturbances. However, it is hard to assess whether an instrumental variable is valid in practice because instrument validity is based on the questionable identifying assumption that some of them are exogenous. In this paper, we examine the impact of instrument endogeneity on the standard t-test, Anderson and Rubin (AR)test, Kleibergen K-test and Moreira conditional likelihood ratio (CLR)-test statistics in the context of linear structural model. Our findings are : (i) an AR-type procedure is globally more robust to endogenous instruments than the others procedures and is also robust to missing (endogenous) instrument. This last result Generalizes the finding of Dufour and Taamouti (2005) to the case of endogenous instrument; (ii) a K-test is globally more robust to endogenous instruments than CLR-test but CLR-test is more robust to missing (endogenous) instrument than K-test; (iii) a t-test is less robust to invalid instruments than the others. However, it is more robust to instrument omission than K-test when the excluded instrument is endogenous; (iv) instrument invalidity is much more detrimental than instrument weakness on the inference procedures based on AR, K and CLR statistics, i.e. tests based on strong but invalid instruments have higher size distortions than those based on valid but weak instruments; (v) AR and K statistics are not pivotal even asymptotically when some of the instruments are endogenous.
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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 | 0.167 | 0.644 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.003 |
| Bibliometrics | 0.004 | 0.006 |
| Science and technology studies | 0.002 | 0.009 |
| Scholarly communication | 0.005 | 0.006 |
| Open science | 0.004 | 0.004 |
| Research integrity | 0.003 | 0.007 |
| Insufficient payload (model declined to judge) | 0.005 | 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".