Simulation-Based Finite-Sample Inference in Simultaneous Equations
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Bibliographic record
Abstract
In simultaneous equation (SE) contexts, nuisance parameter, weak instruments and identification problems severely complicate exact and asymptotic tests (except for very specific hypotheses). In this paper, we propose exact likelihood based tests for possibly nonlinear hypotheses on the coefficients of SE systems. We discuss a number of bounds tests and Monte Carlo simulation based tests. The latter involves maximizing a randomized p-value function over the relevant nuisance parameter space which is done numerically by using a simulated annealing algorithm. We consider limited and full information models. We extend, to non-Gaussian contexts, the bound given in Dufour (Econometrica, 1997) on the null distribution of the LR criterion, associated with possibly non-linear- hypotheses on the coefficients of one Gaussian structural equation. We also propose a tighter bound which will hold: (i) for the limited information (LI) Gaussian hypothesis considered in Dufour (1997) and for more general, possibly cross-equation restrictions in a non-Gaussian multi-equation SE system. For the specific hypothesis which sets the value of the full vector of endogenous variables coefficients in a limited information framework, we extend the Anderson-Rubin test to the non-Gaussian framework. We also show that Wang and Zivot's (Econometrica, 1998) asymptotic bounds-test may be seen as an asymptotic version of the bound we propose here. In addition, we introduce a multi-equation Anderson-Rubin-type test. Illustrative Monte Carlo experiments show that: (i) bootstrapping standard instrumental variable (IV) based criteria fails to achieve size control, especially (but not exclusively) under near non-identification conditions, and (ii) the tests based on IV estimates do not appear to be boundedly pivotal and so no size-correction may be feasible. By contrast, likelihood ratio based tests work well in the experiments performed
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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 | 0.002 | 0.519 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.000 | 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