Supplementary Appendix to \Sequential Estimation of Structural Models with a Fixed Point Constraint"
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Bibliographic record
Abstract
This supplementary appendix contains the following details omitted from the main paper due to space constraints: (A) numerical implementation of the sequential algorithm based on the RPM, (B) the sequential GMM estimator, (C) the convergence properties of the NPL algorithm for models with unobserved heterogeneity, (D) relative efficiency of the NPL, q-NPL, and MLE, and (E) the equivalence of the NPL estimator using Λ(P, θ) and the NPL estimator using Ψ(P, θ). A Numerical Implementation of the Sequential Algorithm based on the RPM in Section 4.2 Implementing the sequential algorithm based on the RPM in Section 4.2 requires evaluating (I − Π ( ˜ θj−1, ˜ Pj−1)∇P ′Ψ( ˜ θj−1, ˜ Pj−1)Π ( ˜ θj−1, ˜ Pj−1)) −1 as well as computing an orthonormal basis Z ( ˜ θj−1, ˜ Pj−1) from the eigenvectors of ∇P ′Ψ( ˜ θj−1, ˜ Pj−1) for j = 1,..., k. This is potentially costly when the analytical expression of ∇P ′Ψ(θ, P) is not available. In this section, we discuss how to reduce the computational cost of implementing the RPM algorithm by updating (I − Π ( ˜ θj−1, ˜ Pj−1)∇P ′Ψ( ˜ θj−1, ˜ Pj−1)Π ( ˜ θj−1, ˜ Pj−1)) −1 and Z ( ˜ θj−1, ˜ Pj−1) without explicitly computing ∇P ′Ψ(θ, P) in each iteration. Denote ˜ Πj−1 = Π ( ˜ θj−1, ˜ Pj−1),
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.004 | 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