Asymptotic local power of pooled t-ratio tests for unit roots in panels with fixed effects
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Bibliographic record
Abstract
We derive analytically the local asymptotic power of two pooled t‐ratio tests for the presence of a unit root in a panel with fixed effects. We consider two statistics which differ according to the method used to remove the bias of the pooled OLS estimator. We show that when we bias‐correct the numerator only, the resulting test has significant local power in n−1/4T−1 neighbourhoods of the null of a panel unit root, while when the entire estimator is corrected for bias, the resulting statistic has local asymptotic power in neighbourhoods shrinking at the faster rate of n−1/2T−1. This latter test is equivalent to the well‐known pooled t test proposed by Levin et al. (2002, Journal of Econometrics 108, 1–24), and its power depends only on the mean of the local‐to‐unity parameters. This implies that it has the same power against homogeneous and heterogeneous alternatives with the same mean autoregressive parameter. We then compare these tests to a panel version of the Sargan‐Bhargava (1983, Econometrica 51, 153–74) statistic for a unit root and the common point‐optimal test of Moon et al. (2007, Journal of Econometrics 141, 416–51). Monte Carlo simulations confirm the usefulness of our local‐to‐unity framework.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.002 | 0.002 |
| 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) | 0.000 | 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