Imposing equilibrium restrictions in the estimation of dynamic discrete games
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Bibliographic record
Abstract
Imposing equilibrium restrictions provides substantial gains in the estimation of dynamic discrete games. Estimation algorithms imposing these restrictions have different merits and limitations. Algorithms that guarantee local convergence typically require the approximation of high‐dimensional Jacobians. Alternatively, the Nested Pseudo‐Likelihood (NPL) algorithm is a fixed‐point iterative procedure, which avoids the computation of these matrices, but—in games—may fail to converge to the consistent NPL estimator. In order to better capture the effect of iterating the NPL algorithm in finite samples, we study the asymptotic properties of this algorithm for data generating processes that are in a neighborhood of the NPL fixed‐point stability threshold. We find that there are always samples for which the algorithm fails to converge, and this introduces a selection bias. We also propose a spectral algorithm to compute the NPL estimator. This algorithm satisfies local convergence and avoids the approximation of Jacobian matrices. We present simulation evidence and an empirical application illustrating our theoretical results and the good properties of the spectral algorithm.
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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 | 0.003 | 0.002 |
| 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 | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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