Identification-robust inference for endogeneity parameters in linear structural models
Bibliographic record
Abstract
We provide a generalization of the AndersonRubin (AR) procedure for inferenceon parameters that represent the dependence between possibly endogenous explanatoryvariables and disturbances in a linear structural equation (endogeneity parameters). We stressthe distinction between regression and covariance endogeneity parameters. Such parametershave intrinsic interest (because they measure the effect of latent variables, which inducesimultaneity) and play a central role in selecting an estimation method (such as ordinary leastsquaresor instrumental variable methods). We observe that endogeneity parameters mightnot be identifiable and we give the relevant identification conditions. These conditions entaila simple identification correspondence between regression endogeneity parameters and theusual structural parameters, while the identification of covariance endogeneity parameterstypically fails as soon as global identification fails. We develop identification-robust finitesampletests for joint hypotheses involving structural and regression endogeneity parameters,as well as marginal hypotheses on regression endogeneity parameters. For Gaussian errors,we provide tests and confidence sets based on standard Fisher critical values. For a wideclass of parametric non-Gaussian errors (possibly heavy-tailed), we show that exact MonteCarlo procedures can be applied using the statistics considered. As a special case, this resultalso holds for usual AR-type tests on structural coefficients. For covariance endogeneityparameters, we supply an asymptotic (identification-robust) distributional theory. Tests forpartial exogeneity hypotheses (for individual potentially endogenous explanatory variables)are covered as special cases. The proposed tests are applied to two empirical examples: therelation between trade and economic growth, and the widely studied problem of returns toeducation.
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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 | 0.024 | 0.142 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.003 | 0.005 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.012 | 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".